Finite Group Databasebeta

← #26005241

Subgroups — #26005241

Order 11008.

7242 conjugacy classes of subgroups.

The subgroup lattice has 1530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148889C214yesmaximal, complemented
2#19148882C214yesmaximal, complemented
3#19148841C214yesmaximal, complemented
4#19148818C214yesmaximal, complemented
5#19148802C218yesmaximal, complemented
6#19148641C214yesmaximal, complemented
7#19148635C214yesmaximal, complemented
8#19148424C214yesmaximal, complemented
9#19148392C214yesmaximal, complemented
10#19148350C212yesmaximal, complemented
11#19148348C212yesmaximal, complemented
12#19148304C211yesmaximal, characteristic, complemented
13#19148301C214yesmaximal, complemented
14#19148278C214yesmaximal, complemented
15#19148276C212yesmaximal, complemented
16#19148270C212yesmaximal, complemented
17#19148242C212yesmaximal, complemented
18#525×D43C212yesmaximal, complemented
19C22×#13063305C211yesmaximal, characteristic, complemented
20C43×#3492C211yesmaximal, characteristic, complemented
21C2×#13063372C2212yescomplemented
22C2×#41×D43C2212yescomplemented
23C23×Dic86C2211yescharacteristic, complemented
24C23×C4×D43C2211yescharacteristic
25#14583653C2218yescomplemented
26#14583651C2218yescomplemented
27#14583646C2218yescomplemented
28#14583645C2218yescomplemented
29#14583623C2214yescomplemented
30#14583617C2214yescomplemented
31#14583610C2214yescomplemented
32#14583607C2218yescomplemented
33#14583607C2218yescomplemented
34#14583606C2218yescomplemented
35#14583605C2218yescomplemented
36#14583604C2214yescomplemented
37#14583604C2214yescomplemented
38#14583601C2218yescomplemented
39#14583597C2214yescomplemented
40#14583595C2218yescomplemented
41#14583591C2218yescomplemented
42#14583589C2218yescomplemented
43#14583588C2214yescomplemented
44#14583587C2214yescomplemented
45#14583587C2214yescomplemented
46#14583584C2214yescomplemented
47#14583584C2214yescomplemented
48#14583578C2218yescomplemented
49#14583576C2218yescomplemented
50#14583574C2218yescomplemented
51#14583573C2218yescomplemented
52#14583572C2218yescomplemented
53#14583572C2218yescomplemented
54Q8×D172C2214yescomplemented
55D4×Dic86C2214yescomplemented
56D4×Dic86C2214yescomplemented
57#14583562C2214yescomplemented
58#14583562C2214yescomplemented
59#14583562C2214yescomplemented
60#14583561C2214yescomplemented
61#14583558C2214yescomplemented
62#14583558C2214yescomplemented
63#14583555C2214yescomplemented
64#14583555C2214yescomplemented
65#14583555C2214yescomplemented
66#14583553C2218yescomplemented
67#14583553C2214yescomplemented
68#14583551C2214yescomplemented
69#14583550C2214yescomplemented
70#14583549C2218yescomplemented
71#14583546C2214yescomplemented
72#14583544C2218yescomplemented
73#14583544C2214yescomplemented
74#14583541C2218yescomplemented
75#14583538C2218yescomplemented
76#14583537C2218yescomplemented
77#14583530C2211yescharacteristic, complemented
78#14583529C2218yescomplemented
79#14583527C2214yescomplemented
80#14583524C2214yes—
81#14583524C2218yescomplemented
82#14583523C2214yescomplemented
83#14583522C2218yescomplemented
84#14583515C2218yescomplemented
85#14583514C2214yescomplemented
86#14583512C2214yescomplemented
87#14583507C2214yescomplemented
88#14583497C2218yescomplemented
89#14583496C2214yescomplemented
90#14583493C2218yescomplemented
91#14583493C2218yescomplemented
92#14583493C2218yescomplemented
93#14583490C2218yescomplemented
94#14583489C2214yescomplemented
95#14583486C2214yescomplemented
96#14583485C2218yescomplemented
97#14583482C2218yescomplemented
98#14583480C2211yescharacteristic, complemented
99#14583480C2214yescomplemented
100#14583478C2214yescomplemented
101#14583477C2214yescomplemented
102#14583475C2212yescomplemented
103#14583475C2214yescomplemented
104#14583472C2214yescomplemented
105#14583471C2218yescomplemented
106#14583470C2212yescomplemented
107#14583457C2214yes—
108#14583454C2214yescomplemented
109#14583453C2214yescomplemented
110#14583434C2214yescomplemented
111#14583431C2214yescomplemented
112#14583412C2212yes—
113#14583412C2212yescomplemented
114#14583411C2212yes—
115#14583411C2214yescomplemented
116#14583410C2214yescomplemented
117#14583410C2212yescomplemented
118#14583409C2212yes—
119#14583409C2212yescomplemented
120#14583409C2214yescomplemented
121#14583408C2214yes—
122#14583408C2214yescomplemented
123#14583407C2214yes—
124#14583406C2212yes—
125#14583405C2214yescomplemented
126#14583405C2218yescomplemented
127#123×D43C2214yescomplemented
128C2×#13063305C2214yes—
129C2×#13063305C2214yescomplemented
130C2×#13063305C2214yescomplemented
131C2×#13063305C2212yescomplemented
132C2×#13063305C2212yescomplemented
133C2×#13063305C2214yescomplemented
134C2×#13063305C2214yescomplemented
135C2×#13063305C2214yescomplemented
136C22⋊Q8×D43C2212yes—
137C22⋊Q8×D43C2212yescomplemented
138C22⋊Q8×D43C2214yescomplemented
139#121×D43C2212yes—
140#121×D43C2212yescomplemented
141#120×D43C2214yes—
142#14583382C2214yescomplemented
143#14583380C2212yescomplemented
144#14583379C2214yescomplemented
145#14583376C2212yescomplemented
146#14583371C2218yes—
147C4×D4×D43C2214yes—
148C4×D4×D43C2214yescomplemented
149#117×D43C2212yescomplemented
150C22×C4⋊Dic43C2212yescomplemented
151C22×(C2×D43)⋊C4C2212yes—
152C43×#554C2214yescomplemented
153C43×#553C2214yescomplemented
154C43×#552C2214yescomplemented
155C43×#547C2214yescomplemented
156C43×#544C2211yescharacteristic, complemented
157C43×#539C2214yescomplemented
158C43×#537C2211yescharacteristic, complemented
159C43×#525C2214yescomplemented
160C43×#525C2212yescomplemented
161C43×#520C2212yescomplemented
162C22×C4⋊C4×C43C2211yescharacteristic, complemented
163C24×D43C2311yescharacteristic
164#13063372—48no—
165C2×#10621902C2312yes—
166C2×#10621898C2312yes—
167C2×#10621898C2314yes—
168C2×#10621898C2314yes—
169C2×#10621898C2314yescomplemented
170C2×#10621900C2312yes—
171C2×#10621900C2314yes—
172C2×#10621900C2318yes—
173C2×#10621900C2314yescomplemented
174#41×D43—48no—
175C22×Dic86—44no—
176C22×Dic86C2312yes—
177C22×Dic86C2314yes—
178C22×Dic86C2314yes—
179C22×Dic86C2312yes—
180C22×Dic86C2314yescomplemented
181C2×Q8×D43C2312yes—
182C2×Q8×D43C2314yescomplemented
183C2×D4×D43C2314yes—
184C2×D4×D43C2314yes—
185C2×D4×D43C2314yes—
186C2×D4×D43C2312yes—
187C23×Dic43C2312yes—
188C23×Dic43C2311yescharacteristic
189C22×C4×D43—44no—
190C22×C4×D43C2312yes—
191C22×C4×D43C2312yes—
192C22×C4×D43C2314yes—
193C22×C4×D43C2312yes—
194C22×C4×D43C2312yes—
195C22×C4×D43C2312yes—
196C22×C4×D43C2312yes—
197#13063325C2314yescomplemented
198#13063325C2318yescomplemented
199#13063324C2318yescomplemented
200#13063324C2318yescomplemented
201#13063324C2318yescomplemented
202#13063324C2314yescomplemented
203#13063323C2314yescomplemented
204#13063320C2318yes—
205#13063320C2318yes—
206#13063320C2318yes—
207#13063320C2318yescomplemented
208#13063320C2318yescomplemented
209#13063320C2318yescomplemented
210#13063319C2318yes—
211#13063318C2318yescomplemented
212#13063318C2318yescomplemented
213#13063317C2318yescomplemented
214#13063316C2314yescomplemented
215#13063316C2318yescomplemented
216#13063316C2318yescomplemented
217#13063316C2318yescomplemented
218#13063315C2318yescomplemented
219#13063315C2318yescomplemented
220#13063315C2318yescomplemented
221#13063314C2318yes—
222#13063313C2318yes—
223#13063313C2314yescomplemented
224#13063312C2314yescomplemented
225#13063311C2318yes—
226#13063311C2318yes—
227#13063311C2318yescomplemented
228#13063311C2318yescomplemented
229#13063310C2318yes—
230#13063310C2318yes—
231#13063310C2318yes—
232#13063310C2314yes—
233#13063310C2314yes—
234#13063310C2318yescomplemented
235#13063309C2314yes—
236#13063309C2318yes—
237#13063309C2318yes—
238#13063309C2318yescomplemented
239#13063309C2318yescomplemented
240#13063308C2318yes—
241#13063308C2318yes—
242#13063308C2314yes—
243#13063307C2318yes—
244#13063307C2314yes—
245#13063307C2314yes—
246#13063307C2318yescomplemented
247#13063307C2318yescomplemented
248#13063306C2318yes—
249#13063306C2314yes—
250#13063305C2314yes—
251#13063305C2314yes—
252#13063305C2314yes—
253#13063305C2318yes—
254#13063305C2314yes—
255#13063305C2318yes—
256#13063305C2318yes—
257#13063305C2312yes—
258#13063305C2314yes—
259#13063305C2312yes—
260#13063305C2314yes—
261#13063305C2318yes—
262#13063305C2314yes—
263#13063305C2314yes—
264#13063305C2318yes—
265#13063305C2318yescomplemented
266#13063305C2314yescomplemented
267#13063305C2318yescomplemented
268#13063305C2314yescomplemented
269#13063305C2314yescomplemented
270#13063304C2312yes—
271#13063304C2312yes—
272#13063304C2314yes—
273#13063304C2314yes—
274#13063304C2314yescomplemented
275#13063304C2314yescomplemented
276#13063304C2318yescomplemented
277#13063303C2318yes—
278#13063303C2318yes—
279#13063303C2314yes—
280#13063303C2314yes—
281#13063303C2318yescomplemented
282#13063303C2318yescomplemented
283#13063303C2318yescomplemented
284#13063302C2318yes—
285#13063302C2318yes—
286#13063302C2314yes—
287#13063302C2314yes—
288#13063302C2318yescomplemented
289#13063302C2318yescomplemented
290#13063302C2318yescomplemented
291#13063302C2318yescomplemented
292#13063301C2318yes—
293#13063301C2312yes—
294#13063301C2312yes—
295#13063301C2318yescomplemented
296#13063300C2318yes—
297#13063300C2312yes—
298#13063300C2312yes—
299#13063300C2314yescomplemented
300#13063299C2314yes—
301#13063299C2318yes—
302#13063299C2312yes—
303#13063299C2312yes—
304#13063299C2314yes—
305#13063299C2318yescomplemented
306#13063298C2314yes—
307#13063298C2314yes—
308#13063298C2318yes—
309#13063297C2318yes—
310#13063297C2318yes—
311#13063297C2318yes—
312#13063297C2314yes—
313#13063297C2314yes—
314#13063296C2312yes—
315#13063296C2312yes—
316#13063296C2318yescomplemented
317#13063295C2314yes—
318#13063295C2318yes—
319#13063295C2314yes—
320#13063295C2314yes—
321#13063294C2314yes—
322#13063293C2314yes—
323#13063293C2318yes—
324#13063293C2314yes—
325#13063293C2314yes—
326Q8×Dic43C2318yescomplemented
327C4×Dic86C2314yescomplemented
328C4×Dic86C2314yescomplemented
329C4×Dic86C2318yescomplemented
330#13063290C2314yescomplemented
331#13063290C2314yescomplemented
332#13063290C2314yescomplemented
333C4×D172C2314yes—
334C4×D172C2318yes—
335C4×D172C2314yes—
336C4×D172C2318yescomplemented
337D4×Dic43C2318yes—
338D4×Dic43C2318yes—
339D4×Dic43C2314yes—
340D4×Dic43C2314yes—
341D4×Dic43C2318yescomplemented
342#13063287C2314yes—
343#13063287C2318yes—
344#13063287C2314yes—
345#13063287C2314yescomplemented
346C4×C22⋊D43C2314yes—
347C4×C22⋊D43C2314yes—
348C4×C22⋊D43C2314yes—
349C4×C22⋊D43C2314yes—
350C4×C22⋊D43C2318yes—
351C4×C22⋊D43C2318yes—
352C4×C22⋊D43C2318yes—
353(C22⋊D43)⋊C4C2318yes—
354(C22⋊D43)⋊C4C2318yes—
355(C22⋊D43)⋊C4C2318yes—
356(C22⋊D43)⋊C4C2314yes—
357(C22⋊D43)⋊C4C2314yes—
358(C22⋊D43)⋊C4C2314yes—
359(C22⋊D43)⋊C4C2314yes—
360#13063284C2314yes—
361#13063284C2312yes—
362#13063284C2318yescomplemented
363#13063283C2318yes—
364#13063283C2312yes—
365#13063283C2312yes—
366#13063283C2318yescomplemented
367#13063283C2314yescomplemented
368#13063282C2318yes—
369#13063282C2314yes—
370#13063281C2318yes—
371#13063281C2314yes—
372C2×C4⋊Dic43C2314yes—
373C2×C4⋊Dic43C2314yes—
374C2×C4⋊Dic43C2318yes—
375C2×C4⋊Dic43C2314yes—
376C2×C4⋊Dic43C2314yes—
377C2×C4⋊Dic43C2318yescomplemented
378C4⋊C4×D43C2312yes—
379C4⋊C4×D43C2312yes—
380C4⋊C4×D43C2314yes—
381C4⋊C4×D43C2314yes—
382C4⋊C4×D43C2314yescomplemented
383C4⋊C4×D43C2318yescomplemented
384C2×(C2×D43)⋊C4C2318yes—
385C2×(C2×D43)⋊C4C2318yes—
386C2×(C2×D43)⋊C4C2314yes—
387C2×(C2×D43)⋊C4C2314yes—
388C2×(C2×D43)⋊C4C2314yes—
389C2×(C2×D43)⋊C4C2314yes—
390C22⋊C4×D43C2314yes—
391C22⋊C4×D43C2314yes—
392C22⋊C4×D43C2318yes—
393C22⋊C4×D43C2314yes—
394C22⋊C4×D43C2314yes—
395C22⋊C4×D43C2314yes—
396C42×D43C2314yes—
397C2×#41×C43C2312yes—
398C2×#41×C43C2314yes—
399C23×C4×C43C2311yescharacteristic
400C23×C4×C43C2312yes—
401C4⋊Q8×C43C2314yescomplemented
402#126×C43C2318yescomplemented
403#125×C43C2314yescomplemented
404#125×C43C2318yescomplemented
405#123×C43C2318yes—
406#123×C43C2314yes—
407#123×C43C2318yescomplemented
408C22⋊Q8×C43C2312yes—
409C22⋊Q8×C43C2312yes—
410C22⋊Q8×C43C2314yes—
411C22⋊Q8×C43C2314yes—
412C22⋊Q8×C43C2314yescomplemented
413C22⋊Q8×C43C2318yescomplemented
414#121×C43C2312yes—
415#121×C43C2312yes—
416#121×C43C2314yes—
417#121×C43C2314yes—
418#121×C43C2314yescomplemented
419#120×C43C2314yes—
420C4×Q8×C43C2314yescomplemented
421C4×D4×C43C2318yes—
422C4×D4×C43C2314yes—
423C4×D4×C43C2314yes—
424C4×D4×C43C2318yes—
425C4×D4×C43C2314yescomplemented
426#117×C43C2314yes—
427#117×C43C2312yes—
428#117×C43C2314yescomplemented
429C2×C4⋊C4×C43C2311yescharacteristic
430C2×C4⋊C4×C43C2314yes—
431C2×C4⋊C4×C43C2311yescharacteristic
432C2×C4⋊C4×C43C2312yes—
433C2×C4⋊C4×C43C2314yes—
434C2×C4⋊C4×C43C2314yescomplemented
435C24×C43C2411yescharacteristic
436C23×D43—24no—
437C23×D43—42no—
438C23×D43—42no—
439C23×D43C2412yes—
440C23×D43C2412yes—
441C23×D43C2414yes—
442C23×D43C2411yescharacteristic
443C23×D43C2411yescharacteristic
444#41×C43—28no—
445#41×C43—48no—
446C2×Q8×C43C2412yes—
447C2×Q8×C43C2414yes—
448C2×D4×C43C2414yes—
449C2×D4×C43C2414yes—
450C2×D4×C43C2414yes—
451C2×D4×C43C2412yes—
452C2×D4×C43C2414yes—
453C22×C4×C43—24no—
454C22×C4×C43—44no—
455C22×C4×C43C2414yes—
456C22×C4×C43C2412yes—
457C22×C4×C43C2412yes—
458C22×C4×C43C2411yescharacteristic
459C22×C4×C43C2414yes—
460C22×C4×C43C2412yes—
461C22×C4×C43C2414yes—
462C22×C4×C43C2412yes—
463C22×C4×C43C2418yes—
464C22×C4×C43C2411yescharacteristic
465C2×C22⋊D43C2414yes—
466C2×C22⋊D43C2414yes—
467C2×C22⋊D43C2414yes—
468C2×C22⋊D43C2414yes—
469C2×C22⋊D43C2414yes—
470C2×C22⋊D43C2414yes—
471C2×C22⋊D43C2418yes—
472C2×C22⋊D43C2414yes—
473C22×Dic43—42no—
474C22×Dic43—44no—
475C22×Dic43C2414yes—
476C22×Dic43C2412yes—
477C22×Dic43C2414yes—
478C22×Dic43C2414yes—
479C22×Dic43C2418yes—
480C22×Dic43C2411yescharacteristic
481C22×Dic43C2412yes—
482C22×Dic43C2411yescharacteristic
483C22×Dic43C2414yes—
484#10621902—44no—
485Q8×D43—44no—
486Q8×D43—48no—
487#10621900—44no—
488#10621900—48no—
489#10621900—48no—
490#10621900—416no—
491D4×D43—216no—
492D4×D43—48no—
493D4×D43—48no—
494D4×D43—44no—
495#10621898—28no—
496#10621898—48no—
497#10621898—48no—
498#10621898—48no—
499C2×D172C2414yes—
500C2×D172C2412yes—
501C2×D172C2414yes—
502C2×D172C2414yes—
503C2×D172C2414yes—
504C2×C4×D43—28no—
505C2×C4×D43—44no—
506C2×C4×D43—44no—
507C2×C4×D43—44no—
508C2×C4×D43—44no—
509C2×C4×D43—44no—
510C2×C4×D43—48no—
511C2×C4×D43C2412yes—
512C2×C4×D43C2414yes—
513C2×C4×D43C2412yes—
514C2×C4×D43C2414yes—
515C2×C4×D43C2412yes—
516C2×C4×D43C2412yes—
517C2×C4×D43C2414yes—
518C2×C4×D43C2412yes—
519C2×C4×D43C2414yes—
520C2×C4×D43C2412yes—
521C2×C4×D43C2418yes—
522C2×C4×D43C2418yes—
523C2×C4×D43C2414yes—
524C2×C4×D43C2412yes—
525C2×C4×D43C2412yes—
526C2×Dic86—28no—
527C2×Dic86—48no—
528C2×Dic86—48no—
529C2×Dic86—48no—
530C2×Dic86—44no—
531C2×Dic86C2412yes—
532C2×Dic86C2414yes—
533C2×Dic86C2414yes—
534C2×Dic86C2414yes—
535C2×Dic86C2414yes—
536C2×Dic86C2418yes—
537C2×Dic86C2418yes—
538C4⋊C4×C43C2414yes—
539C4⋊C4×C43C2414yes—
540C4⋊C4×C43C2418yes—
541C4⋊C4×C43C2412yes—
542C4⋊C4×C43C2418yes—
543C4⋊C4×C43C2412yes—
544C4⋊C4×C43C2414yes—
545C4⋊C4×C43C2414yes—
546C4⋊C4×C43C2414yes—
547C4⋊C4×C43C2418yes—
548C4⋊C4×C43C2414yes—
549C22⋊C4×C43C2414yes—
550C22⋊C4×C43C2414yes—
551C22⋊C4×C43C2418yes—
552C22⋊C4×C43C2414yes—
553C22⋊C4×C43C2418yes—
554C22⋊C4×C43C2414yes—
555C22⋊C4×C43C2414yes—
556C42×C43C2418yes—
557C42×C43C2414yes—
558C22⋊Dic43C2414yes—
559C22⋊Dic43C2414yes—
560C22⋊Dic43C2414yes—
561C22⋊Dic43C2414yes—
562C22⋊Dic43C2414yes—
563C22⋊Dic43C2418yes—
564C22⋊Dic43C2418yes—
565(C2×D43)⋊C4C2414yes—
566(C2×D43)⋊C4C2418yes—
567(C2×D43)⋊C4C2414yes—
568(C2×D43)⋊C4C2414yes—
569(C2×D43)⋊C4C2414yes—
570(C2×D43)⋊C4C2414yes—
571(C2×D43)⋊C4C2414yes—
572(C2×D43)⋊C4C2414yes—
573(C2×D43)⋊C4C2414yes—
574(C2×D43)⋊C4C2414yes—
575(C2×D43)⋊C4C2414yes—
576(C2×D43)⋊C4C2418yes—
577(C2×D43)⋊C4C2418yes—
578(C2×D43)⋊C4C2418yes—
579(C2×D43)⋊C4C2418yes—
580(C2×D43)⋊C4C2418yes—
581(C2×D43)⋊C4C2418yes—
582(C2×D43)⋊C4C2418yes—
583C4⋊Dic43C2412yes—
584C4⋊Dic43C2414yes—
585C4⋊Dic43C2412yes—
586C4⋊Dic43C2414yes—
587C4⋊Dic43C2418yes—
588C4⋊Dic43C2418yes—
589C4⋊Dic43C2418yes—
590C4⋊Dic43C2418yes—
591C4⋊Dic43C2414yes—
592C4⋊Dic43C2418yes—
593C4⋊Dic43C2418yes—
594C4⋊Dic43C2414yes—
595Dic43⋊C4C2414yes—
596Dic43⋊C4C2414yes—
597Dic43⋊C4C2414yes—
598Dic43⋊C4C2414yes—
599Dic43⋊C4C2414yes—
600Dic43⋊C4C2414yes—
601Dic43⋊C4C2418yes—
602Dic43⋊C4C2418yes—
603Dic43⋊C4C2418yes—
604Dic43⋊C4C2418yes—
605Dic43⋊C4C2418yes—
606Dic43⋊C4C2418yes—
607C4×Dic43C2414yes—
608C4×Dic43C2414yes—
609C4×Dic43C2414yes—
610C4×Dic43C2418yes—
611C4×Dic43C2418yes—
612C4×Dic43C2418yes—
613C23×C43—22no—
614C23×C43—22no—
615C23×C43—22no—
616C23×C43C2514yes—
617C23×C43C2511yescharacteristic
618C23×C43C2511yescharacteristic
619C23×C43C2511yescharacteristic
620C22×D43—24no—
621C22×D43—22no—
622C22×D43—24no—
623C22×D43—24no—
624C22×D43—24no—
625C22×D43—28no—
626C22×D43—41no—
627C22×D43—42no—
628C22×D43—41no—
629C22×D43—41no—
630C22×D43—42no—
631C22×D43—41no—
632C22×D43—44no—
633C22×D43—44no—
634C22×D43—416no—
635C22×D432−1+414yescomplemented
636C22×D43C2512yes—
637C22×D43C2514yes—
638C22×D43C2512yes—
639Q8×C43—24no—
640Q8×C43—44no—
641D4×C43—28no—
642D4×C43—28no—
643D4×C43—28no—
644D4×C43—24no—
645D4×C43—44no—
646C2×C4×C43—22no—
647C2×C4×C43—28no—
648C2×C4×C43—24no—
649C2×C4×C43—24no—
650C2×C4×C43—28no—
651C2×C4×C43—42no—
652C2×C4×C43—44no—
653C2×C4×C43—42no—
654C2×C4×C43—48no—
655C2×C4×C43H(5,𝔽2)14yes—
656C2×C4×C43C2514yes—
657C2×C4×C43C2514yes—
658C2×C4×C43C2514yes—
659C2×C4×C43C2514yes—
660C2×C4×C43C2512yes—
661C2×C4×C43C2514yes—
662C2×C4×C43C2512yes—
663C22⋊D43—28no—
664C22⋊D43—28no—
665C22⋊D43—28no—
666C22⋊D43—28no—
667C22⋊D43—44no—
668C22⋊D43—44no—
669C22⋊D43—48no—
670C22⋊D43—44no—
671C2×Dic43—28no—
672C2×Dic43—24no—
673C2×Dic43—44no—
674C2×Dic43—44no—
675C2×Dic43—48no—
676C2×Dic43—41no—
677C2×Dic43—42no—
678C2×Dic43—41no—
679C2×Dic43—44no—
680C2×Dic43C2514yes—
681C2×Dic43C2514yes—
682C2×Dic43C2512yes—
683C2×Dic43C2514yes—
684C2×Dic43C2518yes—
685C2×Dic43C2512yes—
686D172—28no—
687D172—24no—
688D172—44no—
689D172—44no—
690D172—44no—
691C4×D43—28no—
692C4×D43—24no—
693C4×D43—24no—
694C4×D43—24no—
695C4×D43—24no—
696C4×D43—28no—
697C4×D43—42no—
698C4×D43—42no—
699C4×D43—42no—
700C4×D43—42no—
701C4×D43—44no—
702C4×D43—44no—
703C4×D43—48no—
704C4×D43—48no—
705C4×D43—44no—
706Dic86—28no—
707Dic86—28no—
708Dic86—24no—
709Dic86—48no—
710Dic86—48no—
711Dic86—44no—
712Dic86—44no—
713#62819—431nomaximal, Sylow
714C22×C43—28no—
715C22×C43—21no—
716C22×C43—21no—
717C22×C43—21no—
718C22×C43—21no—
719C22×C43—21no—
720C22×C43—21no—
721C22×C43—24no—
722C22×C43—24no—
723C22×C43—24no—
724C22×C43C2×H(5,𝔽2)12yes—
725C22×C43C2×2−1+412yes—
726C22×C43#58512yes—
727C22×C43C2611yescharacteristic
728C2×D43—22no—
729C2×D43—22no—
730C2×D43—22no—
731C2×D43—24no—
732C2×D43—22no—
733C2×D43—24no—
734C2×D43—22no—
735C2×D43—24no—
736C2×D43—44no—
737C2×D43—48no—
738C2×D43—48no—
739C2×D43—44no—
740C2×D43—88no—
741C2×D43C2×2−1+414yes—
742C4×C43—22no—
743C4×C43—24no—
744C4×C43—24no—
745C4×C43—24no—
746C4×C43—24no—
747C4×C43—24no—
748C4×C43C2×H(5,𝔽2)14yes—
749Dic43—28no—
750Dic43—24no—
751Dic43—22no—
752Dic43—22no—
753Dic43—24no—
754Dic43—24no—
755#3541—434no—
756#3541—434no—
757#3538—434no—
758#3536—434no—
759#3535—438no—
760#3520—434no—
761#3520—434no—
762#3505—434no—
763#3501—434no—
764#3495—432no—
765#3495—432no—
766#3492—434no—
767#3492—431no—
768#3492D4311yescharacteristic, complemented
769#3490—434no—
770#3489—432no—
771#3489—432no—
772#3486—432no—
773C2×#525—432no—
774C22×C22⋊Q8—431no—
775C2×C43—22no—
776C2×C43—22no—
777C2×C43—22no—
778C2×C43—44no—
779C2×C43C22×H(5,𝔽2)11yescharacteristic
780C2×C43C22×2−1+411yescharacteristic
781C2×C43C2×#58511yescharacteristic
782D43—24no—
783D43—42no—
784D43—44no—
785C2×2−1+4—432no—
786C22×#41—432no—
787C23×Q8—431no—
788C24×C4—431no—
789#563—438no—
790#563—438no—
791#562—438no—
792#562—438no—
793#556—434no—
794#556—434no—
795#554—434no—
796#554—438no—
797#554—438no—
798#554—438no—
799#554—438no—
800#554—434no—
801#554—434no—
802#554C2×D4314yescomplemented
803#553—438no—
804#553—438no—
805#553—434no—
806#553C2×D4314yescomplemented
807#552—434no—
808#552—434no—
809#552—438no—
810#552—438no—
811#552—434no—
812#552—434no—
813#552—434no—
814#552C2×D4314yescomplemented
815#551—438no—
816#551—438no—
817#551—438no—
818#551—438no—
819#551—438no—
820#551—438no—
821D4×Q8—434no—
822D4×Q8—434no—
823D4×Q8—434no—
824D4×Q8—434no—
825D4×Q8—434no—
826D4×Q8—434no—
827#548—434no—
828#548—434no—
829#548—434no—
830#548—434no—
831#548—434no—
832#548—434no—
833#547—434no—
834#547—438no—
835#547—438no—
836#547—434no—
837#547—434no—
838#547C2×D4314yescomplemented
839#546—438no—
840#546—438no—
841#546—438no—
842#546—434no—
843#546—438no—
844#546—434no—
845#544—438no—
846#544—434no—
847#544—431no—
848#544C2×D4311yescharacteristic, complemented
849#543—434no—
850#543—438no—
851#542—434no—
852#542—438no—
853#542—438no—
854#542—434no—
855#541—434no—
856#541—434no—
857#539—438no—
858#539—438no—
859#539—438no—
860#539—438no—
861#539—438no—
862#539—434no—
863#539C2×D4314yescomplemented
864#538—438no—
865#538—434no—
866#538—434no—
867#538—438no—
868#537—434no—
869#537—434no—
870#537—431no—
871#537—434no—
872#537C2×D4311yescharacteristic, complemented
873#536—432no—
874#536—438no—
875#536—434no—
876#536—432no—
877#536—434no—
878#534—434no—
879#533—434no—
880#533—434no—
881#529—434no—
882#529—434no—
883#525—432no—
884#525—432no—
885#525—434no—
886#525—434no—
887#525—432no—
888#525—432no—
889#525—432no—
890#525—432no—
891#525—434no—
892#525—434no—
893#525—438no—
894#525—434no—
895#525—434no—
896#525—432no—
897#525—434no—
898#525C2×D4312yescomplemented
899#525C2×D4314yescomplemented
900C2×#123—434no—
901C2×C22⋊Q8—432no—
902C2×C22⋊Q8—432no—
903C2×C22⋊Q8—434no—
904C2×C22⋊Q8—434no—
905C2×C22⋊Q8—432no—
906C2×C22⋊Q8—432no—
907C2×C22⋊Q8—434no—
908C2×C22⋊Q8—434no—
909C2×C22⋊Q8—434no—
910C2×C22⋊Q8—434no—
911C2×C22⋊Q8—434no—
912C2×#121—432no—
913C2×#121—432no—
914C2×#120—434no—
915#520—434no—
916#520—434no—
917#520—432no—
918#520C2×D4312yescomplemented
919#519—432no—
920#518—438no—
921C2×C4×D4—434no—
922C2×C4×D4—434no—
923C2×#117—432no—
924C22×C4⋊C4—432no—
925C22×C4⋊C4C2×D4311yescharacteristic, complemented
926C22×C22⋊C4—432no—
927C43#6281911yescharacteristic, complemented, Sylow
928C25—431no—
9292−1+4—1728no—
930C2×#41—432no—
931C2×#41—434no—
932C2×#41—432no—
933C2×#41—438no—
934C2×#41—434no—
935C2×#41—432no—
936C2×#41—434no—
937C2×#41—434no—
938C2×#41—434no—
939C2×#41—1728no—
940C2×#41C22×D4312yes—
941C2×#41C22×D4314yes—
942C22×Q8—432no—
943C22×Q8—434no—
944C22×Q8—432no—
945C22×Q8—432no—
946C22×Q8—434no—
947C22×Q8—434no—
948C22×Q8—434no—
949C22×Q8—1724no—
950C22×D4—434no—
951C22×D4—434no—
952C22×D4—434no—
953C22×D4—432no—
954C23×C4—432no—
955C23×C4—431no—
956C23×C4—432no—
957C23×C4—432no—
958C23×C4—432no—
959C23×C4—434no—
960C23×C4—432no—
961C23×C4—432no—
962C23×C4—432no—
963C23×C4—1724no—
964C23×C4C22×D4311yescharacteristic
965C23×C4C22×D4312yes—
966C4⋊Q8—434no—
967C4⋊Q8—434no—
968C4⋊Q8—438no—
969C4⋊Q8—438no—
970C4⋊Q8—438no—
971C4⋊Q8—434no—
972C4⋊Q8—438no—
973C4⋊Q8C22×D4314yescomplemented
974#126—438no—
975#126—438no—
976#126—438no—
977#126—438no—
978#126—438no—
979#126—438no—
980#126—438no—
981#126—438no—
982#126—438no—
983#126C22×D4318yescomplemented
984#125—434no—
985#125—438no—
986#125—438no—
987#125—438no—
988#125—438no—
989#125—438no—
990#125—438no—
991#125—438no—
992#125C22×D4314yescomplemented
993#125C22×D4318yescomplemented
994#124—438no—
995#124—434no—
996#124—438no—
997#124—438no—
998#124—438no—
999#124—438no—
1000#124—434no—
1001#124—438no—
1002#123—434no—
1003#123—438no—
1004#123—434no—
1005#123—438no—
1006#123—438no—
1007#123—434no—
1008#123—434no—
1009#123—438no—
1010#123—438no—
1011#123—438no—
1012#123—438no—
1013#123—434no—
1014#123—434no—
1015#123—434no—
1016#123—438no—
1017#123—438no—
1018#123—438no—
1019#123—438no—
1020#123—438no—
1021#123—438no—
1022#123—438no—
1023#123C22×D4314yes—
1024#123C22×D4318yes—
1025#123C22×D4318yescomplemented
1026C22⋊Q8—432no—
1027C22⋊Q8—432no—
1028C22⋊Q8—438no—
1029C22⋊Q8—438no—
1030C22⋊Q8—432no—
1031C22⋊Q8—432no—
1032C22⋊Q8—434no—
1033C22⋊Q8—434no—
1034C22⋊Q8—434no—
1035C22⋊Q8—434no—
1036C22⋊Q8—438no—
1037C22⋊Q8—434no—
1038C22⋊Q8—434no—
1039C22⋊Q8—432no—
1040C22⋊Q8—434no—
1041C22⋊Q8—434no—
1042C22⋊Q8—438no—
1043C22⋊Q8—438no—
1044C22⋊Q8—434no—
1045C22⋊Q8—434no—
1046C22⋊Q8—434no—
1047C22⋊Q8—434no—
1048C22⋊Q8—438no—
1049C22⋊Q8—438no—
1050C22⋊Q8—432no—
1051C22⋊Q8—434no—
1052C22⋊Q8—434no—
1053C22⋊Q8—434no—
1054C22⋊Q8—434no—
1055C22⋊Q8—438no—
1056C22⋊Q8—438no—
1057C22⋊Q8—438no—
1058C22⋊Q8—434no—
1059C22⋊Q8—438no—
1060C22⋊Q8—438no—
1061C22⋊Q8—438no—
1062C22⋊Q8—438no—
1063C22⋊Q8—438no—
1064C22⋊Q8—434no—
1065C22⋊Q8—434no—
1066C22⋊Q8—438no—
1067C22⋊Q8—438no—
1068C22⋊Q8—438no—
1069C22⋊Q8—438no—
1070C22⋊Q8—438no—
1071C22⋊Q8—438no—
1072C22⋊Q8C22×D4312yes—
1073C22⋊Q8C22×D4312yes—
1074C22⋊Q8C22×D4314yes—
1075C22⋊Q8C22×D4314yes—
1076C22⋊Q8C22×D4314yescomplemented
1077C22⋊Q8C22×D4318yescomplemented
1078#121—432no—
1079#121—434no—
1080#121—432no—
1081#121—434no—
1082#121—438no—
1083#121—438no—
1084#121—438no—
1085#121—438no—
1086#121—432no—
1087#121—432no—
1088#121—434no—
1089#121—434no—
1090#121—438no—
1091#121—438no—
1092#121—432no—
1093#121—432no—
1094#121—434no—
1095#121—438no—
1096#121—434no—
1097#121—434no—
1098#121—438no—
1099#121C22×D4312yes—
1100#121C22×D4312yes—
1101#121C22×D4314yes—
1102#121C22×D4314yes—
1103#121C22×D4314yescomplemented
1104#120—434no—
1105#120—434no—
1106#120—434no—
1107#120—434no—
1108#120—438no—
1109#120—434no—
1110#120—434no—
1111#120—434no—
1112#120—438no—
1113#120C22×D4314yes—
1114C4×Q8—438no—
1115C4×Q8—434no—
1116C4×Q8—434no—
1117C4×Q8—434no—
1118C4×Q8—434no—
1119C4×Q8—434no—
1120C4×Q8—438no—
1121C4×Q8C22×D4314yescomplemented
1122C4×D4—434no—
1123C4×D4—434no—
1124C4×D4—438no—
1125C4×D4—438no—
1126C4×D4—438no—
1127C4×D4—434no—
1128C4×D4—434no—
1129C4×D4—434no—
1130C4×D4—434no—
1131C4×D4—438no—
1132C4×D4—438no—
1133C4×D4—438no—
1134C4×D4—434no—
1135C4×D4—434no—
1136C4×D4—438no—
1137C4×D4—434no—
1138C4×D4—434no—
1139C4×D4—434no—
1140C4×D4—434no—
1141C4×D4—434no—
1142C4×D4—438no—
1143C4×D4—438no—
1144C4×D4—438no—
1145C4×D4—434no—
1146C4×D4—434no—
1147C4×D4—438no—
1148C4×D4—438no—
1149C4×D4C22×D4314yes—
1150C4×D4C22×D4314yes—
1151C4×D4C22×D4318yes—
1152C4×D4C22×D4318yes—
1153C4×D4C22×D4314yescomplemented
1154#117—432no—
1155#117—434no—
1156#117—438no—
1157#117—432no—
1158#117—432no—
1159#117—438no—
1160#117—434no—
1161#117—438no—
1162#117—434no—
1163#117—438no—
1164#117—434no—
1165#117—438no—
1166#117C22×D4312yes—
1167#117C22×D4314yes—
1168#117C22×D4314yescomplemented
1169C2×C4⋊C4—434no—
1170C2×C4⋊C4—434no—
1171C2×C4⋊C4—434no—
1172C2×C4⋊C4—434no—
1173C2×C4⋊C4—438no—
1174C2×C4⋊C4—438no—
1175C2×C4⋊C4—432no—
1176C2×C4⋊C4—432no—
1177C2×C4⋊C4—434no—
1178C2×C4⋊C4—434no—
1179C2×C4⋊C4—434no—
1180C2×C4⋊C4—438no—
1181C2×C4⋊C4C22×D4311yescharacteristic
1182C2×C4⋊C4C22×D4311yescharacteristic
1183C2×C4⋊C4C22×D4312yes—
1184C2×C4⋊C4C22×D4314yes—
1185C2×C4⋊C4C22×D4314yes—
1186C2×C4⋊C4C22×D4314yescomplemented
1187C2×C22⋊C4—434no—
1188C2×C22⋊C4—434no—
1189C2×C22⋊C4—434no—
1190C2×C22⋊C4—434no—
1191C2×C22⋊C4—438no—
1192C2×C22⋊C4—438no—
1193C2×C22⋊C4—434no—
1194C2×C22⋊C4—434no—
1195C2×C22⋊C4—434no—
1196C2×C22⋊C4—434no—
1197C2×C22⋊C4—434no—
1198C2×C22⋊C4—438no—
1199C2×C42—434no—
1200C24—431no—
1201C24—432no—
1202C24—432no—
1203C24—434no—
1204C24—431no—
1205C24—864no—
1206C24—1722no—
1207C24—1722no—
1208C24C23×D4311yescharacteristic
1209#41—28no—
1210#41—48no—
1211#41—868no—
1212#41—1728no—
1213#41—1728no—
1214#41—1728no—
1215#41—1728no—
1216#41—17216no—
1217#41—1724no—
1218#41—1728no—
1219#41—1724no—
1220C2×Q8—434no—
1221C2×Q8—434no—
1222C2×Q8—432no—
1223C2×Q8—434no—
1224C2×Q8—438no—
1225C2×Q8—434no—
1226C2×Q8—438no—
1227C2×Q8—868no—
1228C2×Q8—1724no—
1229C2×Q8—1728no—
1230C2×Q8—1728no—
1231C2×Q8—1728no—
1232C2×Q8—1724no—
1233C2×Q8—1728no—
1234C2×Q8C23×D4312yes—
1235C2×Q8C23×D4314yes—
1236C2×D4—434no—
1237C2×D4—434no—
1238C2×D4—434no—
1239C2×D4—434no—
1240C2×D4—434no—
1241C2×D4—438no—
1242C2×D4—434no—
1243C2×D4—434no—
1244C2×D4—434no—
1245C2×D4—432no—
1246C2×D4—434no—
1247C2×D4—434no—
1248C2×D4—434no—
1249C2×D4—8616no—
1250C2×D4—1724no—
1251C2×D4—1728no—
1252C2×D4—1728no—
1253C2×D4C23×D4314yes—
1254C2×D4C23×D4314yes—
1255C2×D4C23×D4314yes—
1256C2×D4C23×D4312yes—
1257C2×D4C23×D4314yes—
1258C22×C4—24no—
1259C22×C4—44no—
1260C22×C4—434no—
1261C22×C4—432no—
1262C22×C4—434no—
1263C22×C4—434no—
1264C22×C4—438no—
1265C22×C4—431no—
1266C22×C4—432no—
1267C22×C4—431no—
1268C22×C4—434no—
1269C22×C4—432no—
1270C22×C4—434no—
1271C22×C4—432no—
1272C22×C4—434no—
1273C22×C4—432no—
1274C22×C4—432no—
1275C22×C4—434no—
1276C22×C4—432no—
1277C22×C4—434no—
1278C22×C4—432no—
1279C22×C4—438no—
1280C22×C4—438no—
1281C22×C4—434no—
1282C22×C4—432no—
1283C22×C4—432no—
1284C22×C4—868no—
1285C22×C4—1724no—
1286C22×C4—1724no—
1287C22×C4—1724no—
1288C22×C4—1724no—
1289C22×C4—1728no—
1290C22×C4—1724no—
1291C22×C4—1722no—
1292C22×C4—1724no—
1293C22×C4C23×D4314yes—
1294C22×C4C23×D4312yes—
1295C22×C4C23×D4312yes—
1296C22×C4C23×D4311yescharacteristic
1297C22×C4C23×D4314yes—
1298C22×C4C23×D4312yes—
1299C22×C4C23×D4314yes—
1300C22×C4C23×D4312yes—
1301C22×C4C23×D4318yes—
1302C22×C4C23×D4311yescharacteristic
1303C4⋊C4—438no—
1304C4⋊C4—438no—
1305C4⋊C4—432no—
1306C4⋊C4—434no—
1307C4⋊C4—434no—
1308C4⋊C4—438no—
1309C4⋊C4—438no—
1310C4⋊C4—434no—
1311C4⋊C4—432no—
1312C4⋊C4—434no—
1313C4⋊C4—434no—
1314C4⋊C4—434no—
1315C4⋊C4—434no—
1316C4⋊C4—434no—
1317C4⋊C4—434no—
1318C4⋊C4—438no—
1319C4⋊C4—438no—
1320C4⋊C4—438no—
1321C4⋊C4—434no—
1322C4⋊C4—438no—
1323C4⋊C4—438no—
1324C4⋊C4—438no—
1325C4⋊C4—438no—
1326C4⋊C4—438no—
1327C4⋊C4C23×D4314yes—
1328C4⋊C4C23×D4314yes—
1329C4⋊C4C23×D4312yes—
1330C4⋊C4C23×D4312yes—
1331C4⋊C4C23×D4314yes—
1332C4⋊C4C23×D4314yes—
1333C4⋊C4C23×D4314yes—
1334C4⋊C4C23×D4318yes—
1335C4⋊C4C23×D4318yes—
1336C4⋊C4C23×D4314yes—
1337C4⋊C4C23×D4318yes—
1338C22⋊C4—434no—
1339C22⋊C4—434no—
1340C22⋊C4—434no—
1341C22⋊C4—434no—
1342C22⋊C4—434no—
1343C22⋊C4—438no—
1344C22⋊C4—438no—
1345C22⋊C4—438no—
1346C22⋊C4—438no—
1347C22⋊C4—434no—
1348C22⋊C4—434no—
1349C22⋊C4—438no—
1350C22⋊C4—438no—
1351C22⋊C4—434no—
1352C22⋊C4—434no—
1353C22⋊C4—434no—
1354C22⋊C4—434no—
1355C22⋊C4—434no—
1356C22⋊C4—434no—
1357C22⋊C4—438no—
1358C22⋊C4—438no—
1359C22⋊C4—434no—
1360C22⋊C4—434no—
1361C22⋊C4—438no—
1362C22⋊C4—438no—
1363C22⋊C4C23×D4314yes—
1364C22⋊C4C23×D4314yes—
1365C22⋊C4C23×D4314yes—
1366C22⋊C4C23×D4318yes—
1367C22⋊C4C23×D4314yes—
1368C22⋊C4C23×D4314yes—
1369C22⋊C4C23×D4318yes—
1370C42—434no—
1371C42—434no—
1372C42—434no—
1373C42—438no—
1374C42—438no—
1375C42—438no—
1376C42C23×D4314yes—
1377C42C23×D4318yes—
1378C23—22no—
1379C23—22no—
1380C23—22no—
1381C23—432no—
1382C23—434no—
1383C23—432no—
1384C23—434no—
1385C23—868no—
1386C23—864no—
1387C23—864no—
1388C23—864no—
1389C23—862no—
1390C23—864no—
1391C23—1724no—
1392C23—1724no—
1393C23—1721no—
1394C23—1722no—
1395C23—1721no—
1396C23—1721no—
1397C23—1722no—
1398C23—1721no—
1399C23—17216no—
1400C23C24×D4314yes—
1401C23C24×D4311yescharacteristic
1402C23C24×D4311yescharacteristic
1403C23C24×D4311yescharacteristic
1404Q8—24no—
1405Q8—44no—
1406Q8—868no—
1407Q8—868no—
1408Q8—864no—
1409Q8—1728no—
1410Q8—1728no—
1411Q8—1724no—
1412Q8—1724no—
1413D4—28no—
1414D4—28no—
1415D4—28no—
1416D4—24no—
1417D4—44no—
1418D4—868no—
1419D4—868no—
1420D4—868no—
1421D4—868no—
1422D4—868no—
1423D4—864no—
1424D4—1724no—
1425D4—1724no—
1426D4—1724no—
1427D4—1724no—
1428D4—1724no—
1429D4—1724no—
1430D4—1728no—
1431C2×C4—22no—
1432C2×C4—28no—
1433C2×C4—24no—
1434C2×C4—24no—
1435C2×C4—28no—
1436C2×C4—42no—
1437C2×C4—44no—
1438C2×C4—42no—
1439C2×C4—48no—
1440C2×C4—434no—
1441C2×C4—434no—
1442C2×C4—432no—
1443C2×C4—438no—
1444C2×C4—434no—
1445C2×C4—432no—
1446C2×C4—868no—
1447C2×C4—864no—
1448C2×C4—868no—
1449C2×C4—864no—
1450C2×C4—864no—
1451C2×C4—864no—
1452C2×C4—864no—
1453C2×C4—868no—
1454C2×C4—1722no—
1455C2×C4—1722no—
1456C2×C4—1722no—
1457C2×C4—1722no—
1458C2×C4—1724no—
1459C2×C4—1724no—
1460C2×C4—1724no—
1461C2×C4—1728no—
1462C2×C4—1728no—
1463C2×C4—1721no—
1464C2×C4—1722no—
1465C2×C4—1721no—
1466C2×C4—1724no—
1467C2×C4—1724no—
1468C2×C4—1724no—
1469C2×C4—1728no—
1470C2×C4#1306337114yes—
1471C2×C4C24×D4314yes—
1472C2×C4C24×D4314yes—
1473C2×C4C24×D4314yes—
1474C2×C4C24×D4314yes—
1475C2×C4C24×D4314yes—
1476C2×C4C24×D4312yes—
1477C2×C4C24×D4312yes—
1478C22—28no—
1479C22—21no—
1480C22—21no—
1481C22—21no—
1482C22—21no—
1483C22—21no—
1484C22—21no—
1485C22—24no—
1486C22—24no—
1487C22—24no—
1488C22—434no—
1489C22—862no—
1490C22—862no—
1491C22—862no—
1492C22—864no—
1493C22—864no—
1494C22—862no—
1495C22—864no—
1496C22—862no—
1497C22—3448no—
1498C22—1724no—
1499C22—1728no—
1500C22—1728no—
1501C22—1724no—
1502C22C2×#1306337112yes—
1503C222−1+4×D4312yes—
1504C22#1458373412yes—
1505C22C25×D4311yescharacteristic
1506C4—22no—
1507C4—24no—
1508C4—24no—
1509C4—24no—
1510C4—24no—
1511C4—24no—
1512C4—862no—
1513C4—862no—
1514C4—864no—
1515C4—868no—
1516C4—864no—
1517C4—864no—
1518C4C2×#1306337114yes—
1519C2—22no—
1520C2—22no—
1521C2—22no—
1522C2—44no—
1523C2—864no—
1524C2—1724no—
1525C2—1722no—
1526C2C22×#1306337111yescharacteristic
1527C2C2×2−1+4×D4311yescharacteristic
1528C2C2×#1458373411yescharacteristic
subgroupG/H
center, FrattiniC22C25×D43
commutator, socle, cosocleC22×C43C26
FittingC43×#3492C2
hypercenter#3492D43
hypocenterC43#62819
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #3492

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #19148889C2semidirect
2. #19148882C2semidirect
3. #19148841C2semidirect
4. #19148818C2semidirect
5. #19148802C2semidirect
6. #19148641C2semidirect
7. #19148635C2semidirect
8. #19148424C2semidirect
9. #19148392C2semidirect
10. #19148350C2semidirect
11. #19148348C2semidirect
12. #19148304C2semidirect
13. #19148301C2semidirect
14. #19148278C2semidirect
15. #19148276C2semidirect
16. #19148270C2semidirect
17. #19148242C2semidirect
18. #525×D43C2semidirect
19. C22×#13063305C2semidirect
20. C43×#3492C2semidirect
21. C2×#13063372C22semidirect
22. C2×#41×D43C22semidirect
23. C23×Dic86C22semidirect
25. #14583653C22semidirect
26. #14583651C22semidirect
27. #14583646C22semidirect
28. #14583645C22semidirect
29. #14583623C22semidirect
30. #14583617C22semidirect
31. #14583610C22semidirect
32. #14583607C22semidirect
33. #14583607C22semidirect
34. #14583606C22semidirect
35. #14583605C22semidirect
36. #14583604C22semidirect
37. #14583604C22semidirect
38. #14583601C22semidirect
39. #14583597C22semidirect
40. #14583595C22semidirect
41. #14583591C22semidirect
42. #14583589C22semidirect
43. #14583588C22semidirect
44. #14583587C22semidirect
45. #14583587C22semidirect
46. #14583584C22semidirect
47. #14583584C22semidirect
48. #14583578C22semidirect
49. #14583576C22semidirect
50. #14583574C22semidirect
51. #14583573C22semidirect
52. #14583572C22semidirect
53. #14583572C22semidirect
54. Q8×D172C22semidirect
55. D4×Dic86C22semidirect
56. D4×Dic86C22semidirect
57. #14583562C22semidirect
58. #14583562C22semidirect
59. #14583562C22semidirect
60. #14583561C22semidirect
61. #14583558C22semidirect
62. #14583558C22semidirect
63. #14583555C22semidirect
64. #14583555C22semidirect
65. #14583555C22semidirect
66. #14583553C22semidirect
67. #14583553C22semidirect
68. #14583551C22semidirect
69. #14583550C22semidirect
70. #14583549C22semidirect
71. #14583546C22semidirect
72. #14583544C22semidirect
73. #14583544C22semidirect
74. #14583541C22semidirect
75. #14583538C22semidirect
76. #14583537C22semidirect
77. #14583530C22semidirect
78. #14583529C22semidirect
79. #14583527C22semidirect
81. #14583524C22semidirect
82. #14583523C22semidirect
83. #14583522C22semidirect
84. #14583515C22semidirect
85. #14583514C22semidirect
86. #14583512C22semidirect
87. #14583507C22semidirect
88. #14583497C22semidirect
89. #14583496C22semidirect
90. #14583493C22semidirect
91. #14583493C22semidirect
92. #14583493C22semidirect
93. #14583490C22semidirect
94. #14583489C22semidirect
95. #14583486C22semidirect
96. #14583485C22semidirect
97. #14583482C22semidirect
98. #14583480C22semidirect
99. #14583480C22semidirect
100. #14583478C22semidirect
101. #14583477C22semidirect
102. #14583475C22semidirect
103. #14583475C22semidirect
104. #14583472C22semidirect
105. #14583471C22semidirect
106. #14583470C22semidirect
108. #14583454C22semidirect
109. #14583453C22semidirect
110. #14583434C22semidirect
111. #14583431C22semidirect
113. #14583412C22semidirect
115. #14583411C22semidirect
116. #14583410C22semidirect
117. #14583410C22semidirect
119. #14583409C22semidirect
120. #14583409C22semidirect
122. #14583408C22semidirect
125. #14583405C22semidirect
126. #14583405C22semidirect
127. #123×D43C22semidirect
129. C2×#13063305C22semidirect
130. C2×#13063305C22semidirect
131. C2×#13063305C22semidirect
132. C2×#13063305C22semidirect
133. C2×#13063305C22semidirect
134. C2×#13063305C22semidirect
135. C2×#13063305C22semidirect
137. C22⋊Q8×D43C22semidirect
138. C22⋊Q8×D43C22semidirect
140. #121×D43C22semidirect
142. #14583382C22semidirect
143. #14583380C22semidirect
144. #14583379C22semidirect
145. #14583376C22semidirect
148. C4×D4×D43C22semidirect
149. #117×D43C22semidirect
150. C22×C4⋊Dic43C22semidirect
152. C43×#554C22semidirect
153. C43×#553C22semidirect
154. C43×#552C22semidirect
155. C43×#547C22semidirect
156. C43×#544C22semidirect
157. C43×#539C22semidirect
158. C43×#537C22semidirect
159. C43×#525C22semidirect
160. C43×#525C22semidirect
161. C43×#520C22semidirect
162. C22×C4⋊C4×C43C22semidirect
169. C2×#10621898C23semidirect
173. C2×#10621900C23semidirect
180. C22×Dic86C23semidirect
182. C2×Q8×D43C23semidirect
197. #13063325C23semidirect
198. #13063325C23semidirect
199. #13063324C23semidirect
200. #13063324C23semidirect
201. #13063324C23semidirect
202. #13063324C23semidirect
203. #13063323C23semidirect
207. #13063320C23semidirect
208. #13063320C23semidirect
209. #13063320C23semidirect
211. #13063318C23semidirect
212. #13063318C23semidirect
213. #13063317C23semidirect
214. #13063316C23semidirect
215. #13063316C23semidirect
216. #13063316C23semidirect
217. #13063316C23semidirect
218. #13063315C23semidirect
219. #13063315C23semidirect
220. #13063315C23semidirect
223. #13063313C23semidirect
224. #13063312C23semidirect
227. #13063311C23semidirect
228. #13063311C23semidirect
234. #13063310C23semidirect
238. #13063309C23semidirect
239. #13063309C23semidirect
246. #13063307C23semidirect
247. #13063307C23semidirect
265. #13063305C23semidirect
266. #13063305C23semidirect
267. #13063305C23semidirect
268. #13063305C23semidirect
269. #13063305C23semidirect
274. #13063304C23semidirect
275. #13063304C23semidirect
276. #13063304C23semidirect
281. #13063303C23semidirect
282. #13063303C23semidirect
283. #13063303C23semidirect
288. #13063302C23semidirect
289. #13063302C23semidirect
290. #13063302C23semidirect
291. #13063302C23semidirect
295. #13063301C23semidirect
299. #13063300C23semidirect
305. #13063299C23semidirect
316. #13063296C23semidirect
326. Q8×Dic43C23semidirect
327. C4×Dic86C23semidirect
328. C4×Dic86C23semidirect
329. C4×Dic86C23semidirect
330. #13063290C23semidirect
331. #13063290C23semidirect
332. #13063290C23semidirect
336. C4×D172C23semidirect
341. D4×Dic43C23semidirect
345. #13063287C23semidirect
362. #13063284C23semidirect
366. #13063283C23semidirect
367. #13063283C23semidirect
377. C2×C4⋊Dic43C23semidirect
382. C4⋊C4×D43C23semidirect
383. C4⋊C4×D43C23semidirect
401. C4⋊Q8×C43C23semidirect
402. #126×C43C23semidirect
403. #125×C43C23semidirect
404. #125×C43C23semidirect
407. #123×C43C23semidirect
412. C22⋊Q8×C43C23semidirect
413. C22⋊Q8×C43C23semidirect
418. #121×C43C23semidirect
420. C4×Q8×C43C23semidirect
425. C4×D4×C43C23semidirect
428. #117×C43C23semidirect
434. C2×C4⋊C4×C43C23semidirect
635. C22×D432−1+4semidirect
768. #3492D43semidirect
802. #554C2×D43semidirect
806. #553C2×D43semidirect
814. #552C2×D43semidirect
838. #547C2×D43semidirect
848. #544C2×D43semidirect
863. #539C2×D43semidirect
872. #537C2×D43semidirect
898. #525C2×D43semidirect
899. #525C2×D43semidirect
918. #520C2×D43semidirect
925. C22×C4⋊C4C2×D43semidirect
927. C43#62819semidirect
973. C4⋊Q8C22×D43semidirect
983. #126C22×D43semidirect
992. #125C22×D43semidirect
993. #125C22×D43semidirect
1025. #123C22×D43semidirect
1076. C22⋊Q8C22×D43semidirect
1077. C22⋊Q8C22×D43semidirect
1103. #121C22×D43semidirect
1121. C4×Q8C22×D43semidirect
1153. C4×D4C22×D43semidirect
1168. #117C22×D43semidirect
1186. C2×C4⋊C4C22×D43semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191488892
#191488822
#191488412
#191488182
#191488022
#191486412
#191486352
#191484242
#191483922
#191483502
#191483482
#191483042
#191483012
#191482782
#191482762
#191482702
#191482422
#525×D432
C22×#130633052
C43×#34922
#6281943