Finite Group Databasebeta

← #26005323

Subgroups — #26005323

Order 11008.

6530 conjugacy classes of subgroups.

The subgroup lattice has 1396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19149199C214yesmaximal, complemented
2#19149196C214yesmaximal, complemented
3#19149127C214yesmaximal, complemented
4#19149124C214yesmaximal, complemented
5#19149045C218yesmaximal, complemented
6#19148574C214yesmaximal, complemented
7#19148570C214yesmaximal, complemented
8#19148566C214yesmaximal, complemented
9#19148564C214yesmaximal, complemented
10#19148516C212yesmaximal, complemented
11#19148512C212yesmaximal, complemented
12#19148418C212yesmaximal, complemented
13#19148417C212yesmaximal, complemented
14#19148304C211yesmaximal, characteristic, complemented
15#19148301C214yesmaximal, complemented
16#19148301C212yesmaximal, complemented
17#19148296C214yesmaximal, complemented
18#19147887C212yesmaximal, complemented
19C22×#13063316C211yesmaximal, characteristic, complemented
20C43×#3492C211yesmaximal, characteristic, complemented
21C43⋊#564C2218yescomplemented
22#14583651C2218yescomplemented
23#14583650C2218yescomplemented
24#14583646C2218yescomplemented
25#14583628C2214yescomplemented
26#14583626C2214yescomplemented
27#14583625C2214yescomplemented
28#14583624C2214yescomplemented
29#14583610C2214yescomplemented
30#14583608C2218yes—
31#14583608C2214yescomplemented
32#14583607C2214yes—
33#14583607C2218yes—
34#14583606C2214yes—
35#14583606C2218yes—
36#14583606C2214yescomplemented
37#14583605C2214yescomplemented
38#14583604C2214yes—
39#14583603C2218yes—
40#14583601C2214yes—
41#14583601C2218yes—
42#14583601C2214yescomplemented
43#14583598C2218yes—
44#14583597C2214yes—
45#14583597C2214yescomplemented
46#14583596C2214yescomplemented
47#14583595C2214yes—
48#14583595C2218yes—
49#14583593C2214yescomplemented
50#14583592C2218yes—
51#14583591C2214yes—
52#14583591C2218yes—
53#14583591C2218yescomplemented
54#14583591C2214yescomplemented
55#14583589C2214yes—
56#14583589C2218yes—
57#14583588C2214yescomplemented
58#14583587C2218yescomplemented
59#14583586C2218yes—
60#14583586C2218yescomplemented
61#14583585C2218yescomplemented
62#14583584C2214yes—
63#14583584C2214yescomplemented
64#14583583C2214yescomplemented
65#14583582C2218yes—
66#14583553C2214yes—
67#14583553C2218yes—
68#14583550C2214yes—
69#14583549C2214yes—
70#14583549C2218yes—
71#14583548C2218yes—
72#14583547C2218yes—
73#14583530C2211yescharacteristic
74#14583530C2214yescomplemented
75#14583529C2214yescomplemented
76#14583528C2214yes—
77#14583527C2212yes—
78#14583527C2214yes—
79#14583527C2214yescomplemented
80#14583526C2214yescomplemented
81#14583512C2218yescomplemented
82#14583509C2218yescomplemented
83#14583509C2214yescomplemented
84#14583508C2218yescomplemented
85#14583507C2214yescomplemented
86#14583506C2218yescomplemented
87#14583502C2214yescomplemented
88#14583500C2214yescomplemented
89#14583498C2214yes—
90#14583498C2218yescomplemented
91#14583496C2214yes—
92#14583494C2214yes—
93#14583493C2218yes—
94#14583493C2218yes—
95#14583493C2218yes—
96#14583493C2218yescomplemented
97#14583492C2218yescomplemented
98#14583491C2218yes—
99#14583490C2218yescomplemented
100#14583480C2211yescharacteristic
101#14583477C2214yes—
102#14583477C2212yes—
103#14583476C2214yes—
104#14583454C2214yescomplemented
105#14583452C2212yes—
106#14583452C2214yescomplemented
107#14583451C2212yes—
108#14583451C2212yes—
109#14583445C2212yes—
110#14583444C2212yes—
111#14583444C2212yes—
112#14583436C2214yescomplemented
113#14583435C2212yes—
114#14583435C2212yes—
115#14583435C2214yescomplemented
116#14583431C2214yescomplemented
117#14583430C2212yes—
118#14583430C2212yes—
119#14583430C2214yescomplemented
120#14583429C2214yes—
121#14583429C2214yes—
122#14583426C2214yes—
123#14583426C2214yes—
124C2×#13063316C2214yes—
125C2×#13063316C2214yes—
126C2×#13063316C2214yes—
127C2×#13063316C2214yes—
128C2×#13063316C2212yes—
129C2×#13063316C2212yes—
130C2×#13063316C2214yes—
131C2×#13063316C2214yescomplemented
132#125×D43C2214yescomplemented
133#14583410C2214yes—
134#14583410C2212yes—
135#14583405C2214yes—
136#14583405C2218yes—
137#14583405C2214yes—
138#14583382C2214yes—
139#14583382C2212yes—
140#14583380C2212yes—
141#14583379C2214yes—
142#14583379C2212yes—
143#14583378C2218yes—
144#41×Dic43C2212yes—
145#14583367C2212yes—
146C4×#10621900C2214yes—
147C4×#10621900C2214yes—
148C22×C4⋊Dic43C2211yescharacteristic
149C22×C4⋊Dic43C2212yes—
150C22×Dic43⋊C4C2212yes—
151C22×C4×Dic43C2211yescharacteristic
152C43×#554C2214yes—
153C43×#553C2214yes—
154C43×#552C2214yes—
155C43×#547C2214yes—
156C43×#544C2211yescharacteristic
157C43×#539C2214yes—
158C43×#537C2211yescharacteristic
159C43×#525C2214yes—
160C43×#525C2212yes—
161C43×#520C2212yes—
162C22×C4⋊C4×C43C2211yescharacteristic
163C2×#10621898C2312yes—
164C2×#10621898C2314yes—
165C2×#10621900C2314yes—
166C2×#10621900C2318yes—
167C2×#10621900C2314yes—
168C23×Dic43C2311yescharacteristic
169C23×Dic43C2311yescharacteristic
170C23×Dic43C2312yes—
171#13063325C2314yes—
172#13063325C2318yes—
173#13063324C2314yes—
174#13063324C2314yes—
175#13063324C2318yes—
176#13063324C2318yes—
177#13063324C2312yes—
178#13063324C2312yes—
179#13063323C2318yes—
180#13063323C2312yes—
181#13063321C2312yes—
182#13063320C2318yes—
183#13063320C2318yes—
184#13063320C2318yes—
185#13063320C2318yes—
186#13063320C2318yes—
187#13063320C2314yes—
188#13063320C2314yes—
189#13063319C2318yes—
190#13063318C2318yes—
191#13063318C2318yes—
192#13063318C2318yes—
193#13063318C2318yes—
194#13063318C2318yes—
195#13063318C2314yes—
196#13063318C2314yes—
197#13063317C2318yes—
198#13063317C2318yes—
199#13063317C2314yes—
200#13063316C2314yes—
201#13063316C2314yes—
202#13063316C2314yes—
203#13063316C2318yes—
204#13063316C2318yes—
205#13063316C2318yes—
206#13063316C2314yes—
207#13063316C2318yes—
208#13063316C2318yes—
209#13063316C2314yes—
210#13063316C2318yes—
211#13063316C2314yes—
212#13063316C2318yes—
213#13063316C2312yes—
214#13063316C2314yes—
215#13063316C2314yes—
216#13063316C2318yes—
217#13063316C2318yes—
218#13063316C2314yes—
219#13063316C2314yes—
220#13063316C2312yes—
221#13063315C2318yes—
222#13063315C2318yes—
223#13063315C2318yes—
224#13063315C2318yes—
225#13063315C2318yes—
226#13063315C2318yes—
227#13063315C2318yes—
228#13063315C2318yes—
229#13063315C2314yes—
230#13063315C2314yes—
231#13063314C2312yes—
232#13063312C2312yes—
233#13063311C2314yes—
234#13063311C2314yes—
235#13063310C2318yes—
236#13063310C2318yes—
237#13063309C2314yes—
238#13063309C2318yes—
239#13063309C2318yes—
240#13063309C2318yes—
241#13063309C2318yes—
242#13063309C2314yes—
243#13063308C2318yes—
244#13063308C2318yes—
245#13063308C2314yes—
246#13063307C2318yes—
247#13063307C2318yes—
248#13063307C2318yes—
249#13063307C2318yes—
250#13063306C2314yes—
251#13063306C2318yes—
252#13063306C2314yes—
253#13063306C2318yes—
254#13063305C2318yes—
255#13063305C2318yes—
256#13063305C2318yes—
257#13063305C2314yes—
258#13063304C2312yes—
259#13063304C2314yes—
260#13063304C2312yes—
261#13063304C2314yes—
262#13063304C2318yes—
263#13063304C2314yes—
264#13063304C2318yes—
265#13063303C2318yes—
266#13063303C2318yes—
267#13063303C2318yes—
268#13063302C2318yes—
269#13063302C2318yes—
270#13063302C2318yes—
271#13063302C2318yes—
272#13063302C2318yes—
273#13063302C2314yes—
274#13063302C2318yes—
275#13063302C2314yes—
276#13063302C2318yes—
277#13063302C2314yes—
278#13063302C2314yes—
279#13063301C2314yes—
280#13063301C2318yes—
281#13063301C2318yes—
282#13063300C2314yes—
283#13063299C2312yes—
284#13063299C2314yes—
285#13063299C2314yes—
286#13063299C2318yes—
287#13063299C2314yes—
288#13063299C2312yes—
289#13063298C2318yes—
290#13063297C2314yes—
291#13063297C2318yes—
292#13063297C2318yes—
293#13063297C2314yes—
294#13063297C2318yes—
295#13063297C2314yes—
296#13063297C2314yes—
297#13063296C2314yes—
298#13063296C2318yes—
299#13063294C2314yes—
300Q8×Dic43C2312yes—
301Q8×Dic43C2318yes—
302Q8×Dic43C2314yes—
303Q8×Dic43C2312yes—
304C4×Dic86C2318yes—
305C4×Dic86C2318yes—
306C4×Dic86C2314yes—
307C4×Dic86C2314yes—
308C4×Dic86C2314yes—
309#13063290C2314yes—
310#13063290C2312yes—
311#13063290C2318yes—
312#13063290C2312yes—
313#13063290C2314yes—
314#13063290C2314yes—
315C4×D172C2318yes—
316C4×D172C2314yes—
317D4×Dic43C2318yes—
318D4×Dic43C2318yes—
319D4×Dic43C2314yes—
320D4×Dic43C2318yes—
321D4×Dic43C2312yes—
322D4×Dic43C2314yes—
323D4×Dic43C2314yes—
324D4×Dic43C2312yes—
325D4×Dic43C2314yes—
326D4×Dic43C2314yes—
327#13063287C2312yes—
328#13063287C2314yes—
329#13063287C2312yes—
330C4×C22⋊D43C2314yes—
331C4×C22⋊D43C2314yes—
332C4×C22⋊D43C2314yes—
333C4×C22⋊D43C2314yes—
334C4×C22⋊D43C2318yes—
335C4×C22⋊D43C2318yes—
336C4×C22⋊D43C2318yes—
337(C22⋊D43)⋊C4C2318yes—
338(C22⋊D43)⋊C4C2318yes—
339(C22⋊D43)⋊C4C2314yes—
340(C22⋊D43)⋊C4C2318yes—
341(C22⋊D43)⋊C4C2314yes—
342(C22⋊D43)⋊C4C2314yes—
343(C22⋊D43)⋊C4C2314yes—
344(C22⋊D43)⋊C4C2314yes—
345(C22⋊D43)⋊C4C2314yes—
346#13063284C2314yes—
347#13063284C2314yes—
348#13063284C2318yes—
349#13063284C2312yes—
350#13063284C2314yes—
351#13063283C2318yes—
352#13063283C2314yes—
353#13063283C2314yes—
354#13063283C2314yes—
355#13063283C2314yes—
356#13063282C2318yes—
357#13063282C2314yes—
358#13063281C2314yes—
359#13063281C2314yes—
360#13063281C2318yes—
361#13063281C2314yes—
362#13063281C2314yes—
363#13063281C2318yes—
364C2×C4⋊Dic43C2314yes—
365C2×C4⋊Dic43C2318yes—
366C2×C4⋊Dic43C2314yes—
367C2×C4⋊Dic43C2318yes—
368C2×C4⋊Dic43C2314yes—
369C2×C4⋊Dic43C2314yes—
370C2×C4⋊Dic43C2314yes—
371C2×C4⋊Dic43C2312yes—
372C2×C4⋊Dic43C2314yes—
373C2×C4⋊Dic43C2314yes—
374C2×C4⋊Dic43C2312yes—
375C2×Dic43⋊C4C2318yes—
376C2×Dic43⋊C4C2318yes—
377C2×Dic43⋊C4C2314yes—
378C2×Dic43⋊C4C2314yes—
379C2×Dic43⋊C4C2314yes—
380C2×Dic43⋊C4C2314yes—
381C4⋊C4×D43C2314yes—
382C4⋊C4×D43C2318yes—
383C4⋊C4×D43C2318yes—
384C4⋊C4×D43C2314yes—
385C2×C4×Dic43C2312yes—
386C2×C4×Dic43C2312yes—
387C2×C4×Dic43C2312yes—
388C2×C4×Dic43C2312yes—
389C2×C4×Dic43C2312yes—
390C2×C4×Dic43C2312yes—
391C2×C4×Dic43C2314yes—
392C42×D43C2314yes—
393C2×#41×C43C2312yes—
394C2×#41×C43C2314yes—
395C23×C4×C43C2311yescharacteristic
396C23×C4×C43C2312yes—
397C4⋊Q8×C43C2314yes—
398#126×C43C2318yes—
399#125×C43C2318yes—
400#125×C43C2314yes—
401#123×C43C2318yes—
402#123×C43C2314yes—
403#123×C43C2318yes—
404C22⋊Q8×C43C2312yes—
405C22⋊Q8×C43C2314yes—
406C22⋊Q8×C43C2314yes—
407C22⋊Q8×C43C2312yes—
408C22⋊Q8×C43C2314yes—
409C22⋊Q8×C43C2318yes—
410#121×C43C2314yes—
411#121×C43C2312yes—
412#121×C43C2312yes—
413#121×C43C2314yes—
414#121×C43C2314yes—
415#120×C43C2314yes—
416C4×Q8×C43C2314yes—
417C4×D4×C43C2314yes—
418C4×D4×C43C2318yes—
419C4×D4×C43C2318yes—
420C4×D4×C43C2314yes—
421C4×D4×C43C2314yes—
422#117×C43C2312yes—
423#117×C43C2314yes—
424#117×C43C2314yes—
425C2×C4⋊C4×C43C2311yescharacteristic
426C2×C4⋊C4×C43C2314yes—
427C2×C4⋊C4×C43C2311yescharacteristic
428C2×C4⋊C4×C43C2312yes—
429C2×C4⋊C4×C43C2314yes—
430C2×C4⋊C4×C43C2314yes—
431C24×C43C2411yescharacteristic
432#41×C43—28no—
433#41×C43—48no—
434C2×Q8×C43C2412yes—
435C2×Q8×C43C2414yes—
436C2×D4×C43C2414yes—
437C2×D4×C43C2414yes—
438C2×D4×C43C2412yes—
439C2×D4×C43C2414yes—
440C2×D4×C43C2414yes—
441C22×C4×C43—24no—
442C22×C4×C43—44no—
443C22×C4×C43C2414yes—
444C22×C4×C43C2412yes—
445C22×C4×C43C2412yes—
446C22×C4×C43C2411yescharacteristic
447C22×C4×C43C2414yes—
448C22×C4×C43C2412yes—
449C22×C4×C43C2414yes—
450C22×C4×C43C2412yes—
451C22×C4×C43C2418yes—
452C22×C4×C43C2411yescharacteristic
453C2×C22⋊D43C2414yes—
454C2×C22⋊D43C2414yes—
455C2×C22⋊D43C2414yes—
456C2×C22⋊D43C2418yes—
457C2×C22⋊D43C2414yes—
458C2×C22⋊D43C2414yes—
459C22×Dic43—42no—
460C22×Dic43—44no—
461C22×Dic43—42no—
462C22×Dic43C2412yes—
463C22×Dic43C2412yes—
464C22×Dic43C2414yes—
465C22×Dic43C2411yescharacteristic
466C22×Dic43C2412yes—
467C22×Dic43C2411yescharacteristic
468C22×Dic43C2411yescharacteristic
469C22×Dic43C2412yes—
470C22×Dic43C2411yescharacteristic
471C22×Dic43C2414yes—
472C22×Dic43C2414yes—
473C22×Dic43C2414yes—
474C22×Dic43C2414yes—
475C22×Dic43C2418yes—
476#10621900—48no—
477#10621900—48no—
478#10621900—416no—
479#10621898—28no—
480#10621898—48no—
481C2×D172C2412yes—
482C2×D172C2414yes—
483C2×C4×D43C2414yes—
484C2×C4×D43C2414yes—
485C2×C4×D43C2414yes—
486C2×C4×D43C2418yes—
487C2×C4×D43C2418yes—
488C2×Dic86C2412yes—
489C2×Dic86C2418yes—
490C2×Dic86C2414yes—
491C2×Dic86C2414yes—
492C2×Dic86C2414yes—
493C4⋊C4×C43C2414yes—
494C4⋊C4×C43C2414yes—
495C4⋊C4×C43C2418yes—
496C4⋊C4×C43C2412yes—
497C4⋊C4×C43C2418yes—
498C4⋊C4×C43C2412yes—
499C4⋊C4×C43C2414yes—
500C4⋊C4×C43C2414yes—
501C4⋊C4×C43C2414yes—
502C4⋊C4×C43C2418yes—
503C4⋊C4×C43C2414yes—
504C22⋊C4×C43C2414yes—
505C22⋊C4×C43C2414yes—
506C22⋊C4×C43C2418yes—
507C22⋊C4×C43C2414yes—
508C22⋊C4×C43C2418yes—
509C22⋊C4×C43C2414yes—
510C22⋊C4×C43C2414yes—
511C42×C43C2418yes—
512C42×C43C2414yes—
513C22⋊Dic43C2414yes—
514C22⋊Dic43C2414yes—
515C22⋊Dic43C2414yes—
516C22⋊Dic43C2414yes—
517C22⋊Dic43C2414yes—
518C22⋊Dic43C2414yes—
519C22⋊Dic43C2418yes—
520C22⋊Dic43C2418yes—
521C22⋊Dic43C2414yes—
522(C2×D43)⋊C4C2414yes—
523(C2×D43)⋊C4C2414yes—
524(C2×D43)⋊C4C2414yes—
525(C2×D43)⋊C4C2418yes—
526(C2×D43)⋊C4C2414yes—
527(C2×D43)⋊C4C2414yes—
528(C2×D43)⋊C4C2414yes—
529(C2×D43)⋊C4C2418yes—
530(C2×D43)⋊C4C2418yes—
531(C2×D43)⋊C4C2418yes—
532C4⋊Dic43C2414yes—
533C4⋊Dic43C2412yes—
534C4⋊Dic43C2414yes—
535C4⋊Dic43C2418yes—
536C4⋊Dic43C2414yes—
537C4⋊Dic43C2418yes—
538C4⋊Dic43C2418yes—
539C4⋊Dic43C2418yes—
540C4⋊Dic43C2418yes—
541C4⋊Dic43C2412yes—
542C4⋊Dic43C2414yes—
543C4⋊Dic43C2414yes—
544C4⋊Dic43C2418yes—
545C4⋊Dic43C2418yes—
546C4⋊Dic43C2414yes—
547C4⋊Dic43C2414yes—
548C4⋊Dic43C2414yes—
549Dic43⋊C4C2414yes—
550Dic43⋊C4C2418yes—
551Dic43⋊C4C2418yes—
552Dic43⋊C4C2418yes—
553Dic43⋊C4C2418yes—
554Dic43⋊C4C2418yes—
555Dic43⋊C4C2418yes—
556Dic43⋊C4C2418yes—
557Dic43⋊C4C2418yes—
558Dic43⋊C4C2414yes—
559Dic43⋊C4C2418yes—
560Dic43⋊C4C2418yes—
561Dic43⋊C4C2414yes—
562Dic43⋊C4C2414yes—
563Dic43⋊C4C2414yes—
564Dic43⋊C4C2414yes—
565Dic43⋊C4C2414yes—
566Dic43⋊C4C2414yes—
567Dic43⋊C4C2414yes—
568Dic43⋊C4C2414yes—
569C4×Dic43C2412yes—
570C4×Dic43C2414yes—
571C4×Dic43C2414yes—
572C4×Dic43C2412yes—
573C4×Dic43C2412yes—
574C4×Dic43C2412yes—
575C4×Dic43C2412yes—
576C4×Dic43C2412yes—
577C4×Dic43C2412yes—
578C4×Dic43C2412yes—
579C4×Dic43C2414yes—
580C4×Dic43C2414yes—
581C4×Dic43C2414yes—
582C4×Dic43C2418yes—
583C4×Dic43C2418yes—
584C4×Dic43C2418yes—
585C23×C43—22no—
586C23×C43—22no—
587C23×C43—22no—
588C23×C43C2514yes—
589C23×C43C2511yescharacteristic
590C23×C43C2511yescharacteristic
591C23×C43C2511yescharacteristic
592C22×D43C2514yes—
593Q8×C43—24no—
594Q8×C43—44no—
595D4×C43—28no—
596D4×C43—28no—
597D4×C43—28no—
598D4×C43—24no—
599D4×C43—44no—
600C2×C4×C43—22no—
601C2×C4×C43—28no—
602C2×C4×C43—24no—
603C2×C4×C43—24no—
604C2×C4×C43—28no—
605C2×C4×C43—42no—
606C2×C4×C43—44no—
607C2×C4×C43—42no—
608C2×C4×C43—48no—
609C2×C4×C432−1+414yes—
610C2×C4×C43C2514yes—
611C2×C4×C43C2512yes—
612C2×C4×C43C2514yes—
613C2×C4×C43C2514yes—
614C2×C4×C43C2514yes—
615C2×C4×C43C2514yes—
616C2×C4×C43C2512yes—
617C22⋊D43—28no—
618C22⋊D43—28no—
619C22⋊D43—28no—
620C22⋊D43—44no—
621C22⋊D43—44no—
622C22⋊D43—48no—
623C2×Dic43—24no—
624C2×Dic43—24no—
625C2×Dic43—28no—
626C2×Dic43—44no—
627C2×Dic43—48no—
628C2×Dic43—44no—
629C2×Dic43—41no—
630C2×Dic43—41no—
631C2×Dic43—42no—
632C2×Dic43—42no—
633C2×Dic43—44no—
634C2×Dic43—44no—
635C2×Dic43—41no—
636C2×Dic43—41no—
637C2×Dic43C2512yes—
638C2×Dic43C2512yes—
639C2×Dic43C2514yes—
640C2×Dic43C2512yes—
641C2×Dic43C2514yes—
642C2×Dic43C2512yes—
643C2×Dic43C2514yes—
644C2×Dic43C2518yes—
645D172—24no—
646D172—44no—
647C4×D43—28no—
648C4×D43—48no—
649C4×D43—48no—
650C4×D43—44no—
651C4×D43—44no—
652Dic86—24no—
653Dic86—44no—
654Dic86—44no—
655Dic86—44no—
656Dic86—48no—
657#62825—431nomaximal, Sylow
658C22×C43—28no—
659C22×C43—21no—
660C22×C43—21no—
661C22×C43—21no—
662C22×C43—21no—
663C22×C43—21no—
664C22×C43—21no—
665C22×C43—24no—
666C22×C43—24no—
667C22×C43—24no—
668C22×C43C2×2−1+412yes—
669C22×C43#58512yes—
670C22×C43#58512yes—
671C22×C43C2611yescharacteristic
672C2×D43—24no—
673C2×D43—24no—
674C2×D43—24no—
675C4×C43—22no—
676C4×C43—24no—
677C4×C43—24no—
678C4×C43—24no—
679C4×C43—24no—
680C4×C43—24no—
681C4×C43C2×2−1+414yes—
682Dic43—24no—
683Dic43—24no—
684Dic43—24no—
685Dic43—22no—
686Dic43—22no—
687Dic43—28no—
688Dic43—22no—
689Dic43—22no—
690#3563—434no—
691#3563—434no—
692#3559—434no—
693#3559—434no—
694#3553—438no—
695#3515—434no—
696#3515—434no—
697#3515—434no—
698#3515—434no—
699#3512—432no—
700#3512—432no—
701#3504—432no—
702#3504—432no—
703#3492—434no—
704#3492—432no—
705#3492—434no—
706#3492—431no—
707#3492D4311yescharacteristic, complemented
708#3444—432no—
709C22×#125—431no—
710C2×C43—22no—
711C2×C43—22no—
712C2×C43—22no—
713C2×C43—44no—
714C2×C43C22×2−1+411yescharacteristic
715C2×C43C2×#58511yescharacteristic
716C2×C43C2×#58511yescharacteristic
717D43—44no—
718#564—438no—
719#563—438no—
720#563—438no—
721#562—438no—
722#557—434no—
723#557—434no—
724#557—434no—
725#557—434no—
726#554—434no—
727#554—434no—
728#554—438no—
729#554—438no—
730#554—434no—
731#554—438no—
732#554—434no—
733#554—434no—
734#554—438no—
735#554—434no—
736#554—434no—
737#554C2×D4314yes—
738#553—438no—
739#553—434no—
740#553—438no—
741#553—434no—
742#553—434no—
743#553—438no—
744#553—434no—
745#553—438no—
746#553—434no—
747#553—434no—
748#553—434no—
749#553C2×D4314yes—
750#552—438no—
751#552—438no—
752#552—438no—
753#552—438no—
754#552—434no—
755#552—438no—
756#552—434no—
757#552—434no—
758#552—438no—
759#552—438no—
760#552—434no—
761#552—438no—
762#552—434no—
763#552—434no—
764#552—434no—
765#552C2×D4314yes—
766#547—438no—
767#547—438no—
768#547—438no—
769#547—434no—
770#547—438no—
771#547—434no—
772#547—434no—
773#547C2×D4314yes—
774#544—434no—
775#544—434no—
776#544—434no—
777#544—432no—
778#544—434no—
779#544—434no—
780#544—431no—
781#544—434no—
782#544C2×D4311yescharacteristic
783#541—438no—
784#541—438no—
785#541—438no—
786#541—434no—
787#541—438no—
788#541—434no—
789#540—434no—
790#540—434no—
791#539—438no—
792#539—438no—
793#539—438no—
794#539—438no—
795#539—438no—
796#539—438no—
797#539—434no—
798#539—438no—
799#539—434no—
800#539—438no—
801#539—434no—
802#539C2×D4314yes—
803#537—432no—
804#537—434no—
805#537—434no—
806#537—431no—
807#537C2×D4311yescharacteristic
808#533—434no—
809#533—432no—
810#533—432no—
811#533—432no—
812#533—434no—
813#532—432no—
814#532—432no—
815#532—432no—
816#529—434no—
817#529—434no—
818#529—432no—
819#529—432no—
820#529—434no—
821#529—432no—
822#529—432no—
823#529—434no—
824#529—434no—
825#529—434no—
826#529—434no—
827#529—434no—
828C2×#125—434no—
829C2×#125—432no—
830C2×#125—432no—
831C2×#125—434no—
832C2×#125—434no—
833C2×#125—434no—
834C2×#125—434no—
835C2×#125—434no—
836C2×#125—434no—
837#525—432no—
838#525—434no—
839#525—434no—
840#525—434no—
841#525—438no—
842#525C2×D4312yes—
843#525C2×D4314yes—
844#520—432no—
845#520—434no—
846#520—438no—
847#520—432no—
848#520—434no—
849#520—432no—
850#520C2×D4312yes—
851C4×#41—432no—
852C4×#41—434no—
853C4×#41—434no—
854C4×#41—432no—
855C22×C4⋊C4—432no—
856C22×C4⋊C4—431no—
857C22×C4⋊C4—432no—
858C22×C4⋊C4C2×D4311yescharacteristic
859C22×C42—431no—
860C43#6282511yescharacteristic, complemented, Sylow
861C2×#41—434no—
862C2×#41—434no—
863C2×#41—438no—
864C2×#41—432no—
865C2×#41—434no—
866C2×#41C22×D4312yes—
867C2×#41C22×D4314yes—
868C23×C4—432no—
869C23×C4—431no—
870C23×C4—431no—
871C23×C4C22×D4311yescharacteristic
872C23×C4C22×D4312yes—
873C4⋊Q8—432no—
874C4⋊Q8—438no—
875C4⋊Q8—432no—
876C4⋊Q8—432no—
877C4⋊Q8—434no—
878C4⋊Q8—434no—
879C4⋊Q8—438no—
880C4⋊Q8—438no—
881C4⋊Q8—434no—
882C4⋊Q8—438no—
883C4⋊Q8C22×D4314yes—
884#127—432no—
885#126—434no—
886#126—434no—
887#126—438no—
888#126—438no—
889#126—438no—
890#126—438no—
891#126—438no—
892#126—434no—
893#126—434no—
894#126—438no—
895#126—438no—
896#126—438no—
897#126—438no—
898#126—438no—
899#126—438no—
900#126C22×D4318yes—
901#125—434no—
902#125—434no—
903#125—438no—
904#125—438no—
905#125—434no—
906#125—434no—
907#125—438no—
908#125—434no—
909#125—434no—
910#125—434no—
911#125—434no—
912#125—438no—
913#125—432no—
914#125—432no—
915#125—438no—
916#125—438no—
917#125—438no—
918#125—438no—
919#125—434no—
920#125—434no—
921#125—434no—
922#125—434no—
923#125—438no—
924#125—438no—
925#125—438no—
926#125—438no—
927#125—438no—
928#125—438no—
929#125—438no—
930#125—438no—
931#125—438no—
932#125—434no—
933#125—438no—
934#125—438no—
935#125C22×D4314yes—
936#125C22×D4318yes—
937#124—432no—
938#124—432no—
939#124—434no—
940#124—434no—
941#123—434no—
942#123—434no—
943#123—438no—
944#123—438no—
945#123—434no—
946#123—438no—
947#123—438no—
948#123—438no—
949#123—438no—
950#123—434no—
951#123—434no—
952#123—438no—
953#123—438no—
954#123—438no—
955#123—438no—
956#123—438no—
957#123—438no—
958#123—438no—
959#123—438no—
960#123C22×D4314yes—
961#123C22×D4318yes—
962#123C22×D4318yes—
963C22⋊Q8—434no—
964C22⋊Q8—438no—
965C22⋊Q8—438no—
966C22⋊Q8—432no—
967C22⋊Q8—432no—
968C22⋊Q8—434no—
969C22⋊Q8—434no—
970C22⋊Q8—434no—
971C22⋊Q8—438no—
972C22⋊Q8—438no—
973C22⋊Q8—434no—
974C22⋊Q8—438no—
975C22⋊Q8—438no—
976C22⋊Q8—438no—
977C22⋊Q8—438no—
978C22⋊Q8—438no—
979C22⋊Q8—438no—
980C22⋊Q8—434no—
981C22⋊Q8—434no—
982C22⋊Q8—434no—
983C22⋊Q8—434no—
984C22⋊Q8—438no—
985C22⋊Q8—438no—
986C22⋊Q8—438no—
987C22⋊Q8—438no—
988C22⋊Q8—438no—
989C22⋊Q8—438no—
990C22⋊Q8—438no—
991C22⋊Q8C22×D4312yes—
992C22⋊Q8C22×D4312yes—
993C22⋊Q8C22×D4314yes—
994C22⋊Q8C22×D4314yes—
995C22⋊Q8C22×D4314yes—
996C22⋊Q8C22×D4318yes—
997#121—434no—
998#121—434no—
999#121—434no—
1000#121—434no—
1001#121—438no—
1002#121—438no—
1003#121—434no—
1004#121—438no—
1005#121—438no—
1006#121—432no—
1007#121—432no—
1008#121—434no—
1009#121—434no—
1010#121—434no—
1011#121—438no—
1012#121—434no—
1013#121—438no—
1014#121C22×D4312yes—
1015#121C22×D4312yes—
1016#121C22×D4314yes—
1017#121C22×D4314yes—
1018#121C22×D4314yes—
1019#120—434no—
1020#120C22×D4314yes—
1021C4×Q8—432no—
1022C4×Q8—432no—
1023C4×Q8—434no—
1024C4×Q8—438no—
1025C4×Q8—434no—
1026C4×Q8—434no—
1027C4×Q8—432no—
1028C4×Q8—432no—
1029C4×Q8—434no—
1030C4×Q8—438no—
1031C4×Q8—434no—
1032C4×Q8—434no—
1033C4×Q8—434no—
1034C4×Q8—438no—
1035C4×Q8—438no—
1036C4×Q8C22×D4314yes—
1037C4×D4—434no—
1038C4×D4—434no—
1039C4×D4—434no—
1040C4×D4—434no—
1041C4×D4—432no—
1042C4×D4—432no—
1043C4×D4—438no—
1044C4×D4—438no—
1045C4×D4—438no—
1046C4×D4—434no—
1047C4×D4—434no—
1048C4×D4—434no—
1049C4×D4—434no—
1050C4×D4—434no—
1051C4×D4—438no—
1052C4×D4—438no—
1053C4×D4—438no—
1054C4×D4—432no—
1055C4×D4—432no—
1056C4×D4—434no—
1057C4×D4—434no—
1058C4×D4—434no—
1059C4×D4—434no—
1060C4×D4—434no—
1061C4×D4—434no—
1062C4×D4—434no—
1063C4×D4—438no—
1064C4×D4—438no—
1065C4×D4—438no—
1066C4×D4—438no—
1067C4×D4—434no—
1068C4×D4C22×D4314yes—
1069C4×D4C22×D4314yes—
1070C4×D4C22×D4318yes—
1071C4×D4C22×D4318yes—
1072C4×D4C22×D4314yes—
1073#117—432no—
1074#117—434no—
1075#117—434no—
1076#117—438no—
1077#117—434no—
1078#117—434no—
1079#117—434no—
1080#117—438no—
1081#117—434no—
1082#117—434no—
1083#117—434no—
1084#117—434no—
1085#117—434no—
1086#117—434no—
1087#117—438no—
1088#117—438no—
1089#117—434no—
1090#117—438no—
1091#117C22×D4312yes—
1092#117C22×D4314yes—
1093#117C22×D4314yes—
1094C2×C4⋊C4—432no—
1095C2×C4⋊C4—434no—
1096C2×C4⋊C4—434no—
1097C2×C4⋊C4—434no—
1098C2×C4⋊C4—434no—
1099C2×C4⋊C4—432no—
1100C2×C4⋊C4—438no—
1101C2×C4⋊C4—434no—
1102C2×C4⋊C4—438no—
1103C2×C4⋊C4—434no—
1104C2×C4⋊C4—434no—
1105C2×C4⋊C4—434no—
1106C2×C4⋊C4—434no—
1107C2×C4⋊C4—434no—
1108C2×C4⋊C4—438no—
1109C2×C4⋊C4—438no—
1110C2×C4⋊C4—434no—
1111C2×C4⋊C4—438no—
1112C2×C4⋊C4—438no—
1113C2×C4⋊C4—434no—
1114C2×C4⋊C4—434no—
1115C2×C4⋊C4C22×D4311yescharacteristic
1116C2×C4⋊C4C22×D4311yescharacteristic
1117C2×C4⋊C4C22×D4312yes—
1118C2×C4⋊C4C22×D4314yes—
1119C2×C4⋊C4C22×D4314yes—
1120C2×C4⋊C4C22×D4314yes—
1121C2×C42—434no—
1122C2×C42—432no—
1123C2×C42—432no—
1124C2×C42—432no—
1125C2×C42—432no—
1126C2×C42—432no—
1127C2×C42—432no—
1128C2×C42—434no—
1129C24C23×D4311yescharacteristic
1130#41—28no—
1131#41—48no—
1132#41—868no—
1133#41—1728no—
1134#41—1728no—
1135#41—1728no—
1136#41—17216no—
1137C2×Q8—432no—
1138C2×Q8—434no—
1139C2×Q8—438no—
1140C2×Q8—434no—
1141C2×Q8—434no—
1142C2×Q8C23×D4312yes—
1143C2×Q8C23×D4314yes—
1144C2×D4—434no—
1145C2×D4—434no—
1146C2×D4—434no—
1147C2×D4—438no—
1148C2×D4—434no—
1149C2×D4—434no—
1150C2×D4—432no—
1151C2×D4—434no—
1152C2×D4C23×D4314yes—
1153C2×D4C23×D4312yes—
1154C2×D4C23×D4314yes—
1155C2×D4C23×D4314yes—
1156C2×D4C23×D4314yes—
1157C22×C4—24no—
1158C22×C4—44no—
1159C22×C4—432no—
1160C22×C4—432no—
1161C22×C4—434no—
1162C22×C4—431no—
1163C22×C4—431no—
1164C22×C4—432no—
1165C22×C4—432no—
1166C22×C4—431no—
1167C22×C4—431no—
1168C22×C4—434no—
1169C22×C4—434no—
1170C22×C4—434no—
1171C22×C4—434no—
1172C22×C4—438no—
1173C22×C4—434no—
1174C22×C4—434no—
1175C22×C4—434no—
1176C22×C4—438no—
1177C22×C4—438no—
1178C22×C4—1722no—
1179C22×C4—1724no—
1180C22×C4—1722no—
1181C22×C4C23×D4312yes—
1182C22×C4C23×D4312yes—
1183C22×C4C23×D4311yescharacteristic
1184C22×C4C23×D4314yes—
1185C22×C4C23×D4314yes—
1186C22×C4C23×D4312yes—
1187C22×C4C23×D4314yes—
1188C22×C4C23×D4312yes—
1189C22×C4C23×D4318yes—
1190C22×C4C23×D4311yescharacteristic
1191C4⋊C4—434no—
1192C4⋊C4—434no—
1193C4⋊C4—438no—
1194C4⋊C4—438no—
1195C4⋊C4—438no—
1196C4⋊C4—438no—
1197C4⋊C4—438no—
1198C4⋊C4—438no—
1199C4⋊C4—438no—
1200C4⋊C4—438no—
1201C4⋊C4—438no—
1202C4⋊C4—432no—
1203C4⋊C4—432no—
1204C4⋊C4—434no—
1205C4⋊C4—434no—
1206C4⋊C4—434no—
1207C4⋊C4—434no—
1208C4⋊C4—438no—
1209C4⋊C4—434no—
1210C4⋊C4—438no—
1211C4⋊C4—438no—
1212C4⋊C4—438no—
1213C4⋊C4—438no—
1214C4⋊C4—438no—
1215C4⋊C4—438no—
1216C4⋊C4—438no—
1217C4⋊C4—434no—
1218C4⋊C4—434no—
1219C4⋊C4—434no—
1220C4⋊C4—434no—
1221C4⋊C4—434no—
1222C4⋊C4—434no—
1223C4⋊C4—434no—
1224C4⋊C4—434no—
1225C4⋊C4—434no—
1226C4⋊C4—434no—
1227C4⋊C4—434no—
1228C4⋊C4C23×D4312yes—
1229C4⋊C4C23×D4314yes—
1230C4⋊C4C23×D4314yes—
1231C4⋊C4C23×D4318yes—
1232C4⋊C4C23×D4314yes—
1233C4⋊C4C23×D4318yes—
1234C4⋊C4C23×D4312yes—
1235C4⋊C4C23×D4318yes—
1236C4⋊C4C23×D4314yes—
1237C4⋊C4C23×D4314yes—
1238C4⋊C4C23×D4314yes—
1239C22⋊C4—434no—
1240C22⋊C4—434no—
1241C22⋊C4—434no—
1242C22⋊C4—434no—
1243C22⋊C4—434no—
1244C22⋊C4—434no—
1245C22⋊C4—434no—
1246C22⋊C4—438no—
1247C22⋊C4—438no—
1248C22⋊C4—434no—
1249C22⋊C4—434no—
1250C22⋊C4—434no—
1251C22⋊C4—434no—
1252C22⋊C4—438no—
1253C22⋊C4—438no—
1254C22⋊C4—438no—
1255C22⋊C4—438no—
1256C22⋊C4—434no—
1257C22⋊C4—434no—
1258C22⋊C4C23×D4314yes—
1259C22⋊C4C23×D4314yes—
1260C22⋊C4C23×D4318yes—
1261C22⋊C4C23×D4314yes—
1262C22⋊C4C23×D4314yes—
1263C22⋊C4C23×D4314yes—
1264C22⋊C4C23×D4318yes—
1265C42—432no—
1266C42—432no—
1267C42—432no—
1268C42—432no—
1269C42—432no—
1270C42—432no—
1271C42—432no—
1272C42—432no—
1273C42—434no—
1274C42—434no—
1275C42—434no—
1276C42—434no—
1277C42—434no—
1278C42—438no—
1279C42—438no—
1280C42—438no—
1281C42C23×D4314yes—
1282C42C23×D4318yes—
1283C23—22no—
1284C23—22no—
1285C23—22no—
1286C23—434no—
1287C23C24×D4314yes—
1288C23C24×D4311yescharacteristic
1289C23C24×D4311yescharacteristic
1290C23C24×D4311yescharacteristic
1291Q8—24no—
1292Q8—44no—
1293Q8—864no—
1294Q8—1724no—
1295Q8—1724no—
1296Q8—1728no—
1297Q8—1724no—
1298D4—28no—
1299D4—28no—
1300D4—28no—
1301D4—24no—
1302D4—44no—
1303D4—868no—
1304D4—868no—
1305D4—868no—
1306D4—864no—
1307D4—1724no—
1308D4—1724no—
1309D4—1728no—
1310D4—1724no—
1311C2×C4—22no—
1312C2×C4—28no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—28no—
1316C2×C4—42no—
1317C2×C4—44no—
1318C2×C4—42no—
1319C2×C4—48no—
1320C2×C4—432no—
1321C2×C4—432no—
1322C2×C4—434no—
1323C2×C4—434no—
1324C2×C4—434no—
1325C2×C4—432no—
1326C2×C4—432no—
1327C2×C4—438no—
1328C2×C4—864no—
1329C2×C4—864no—
1330C2×C4—868no—
1331C2×C4—868no—
1332C2×C4—1728no—
1333C2×C4—1724no—
1334C2×C4—1724no—
1335C2×C4—1728no—
1336C2×C4—1721no—
1337C2×C4—1722no—
1338C2×C4—1721no—
1339C2×C4—1721no—
1340C2×C4—1722no—
1341C2×C4—1724no—
1342C2×C4—1724no—
1343C2×C4—1721no—
1344C2×C4—1724no—
1345C2×C4—1724no—
1346C2×C4—1728no—
1347C2×C4#1306337214yes—
1348C2×C4C24×D4314yes—
1349C2×C4C24×D4312yes—
1350C2×C4C24×D4314yes—
1351C2×C4C24×D4314yes—
1352C2×C4C24×D4314yes—
1353C2×C4C24×D4314yes—
1354C2×C4C24×D4312yes—
1355C22—28no—
1356C22—21no—
1357C22—21no—
1358C22—21no—
1359C22—21no—
1360C22—21no—
1361C22—21no—
1362C22—24no—
1363C22—24no—
1364C22—24no—
1365C22—864no—
1366C22—864no—
1367C22—864no—
1368C22C2×#1306337212yes—
1369C22#1458373412yes—
1370C22#1458373612yes—
1371C22C25×D4311yescharacteristic
1372C4—22no—
1373C4—24no—
1374C4—24no—
1375C4—24no—
1376C4—24no—
1377C4—24no—
1378C4—864no—
1379C4—862no—
1380C4—862no—
1381C4—864no—
1382C4—862no—
1383C4—868no—
1384C4—862no—
1385C4—864no—
1386C4C2×#1306337214yes—
1387C2—22no—
1388C2—22no—
1389C2—22no—
1390C2—44no—
1391C2—1724no—
1392C2C22×#1306337211yescharacteristic
1393C2C2×#1458373411yescharacteristic
1394C2C2×#1458373611yescharacteristic
subgroupG/H
center, FrattiniC22C25×D43
commutator, socle, cosocleC22×C43C26
FittingC43×#3492C2
hypercenter#3492D43
hypocenterC43#62825
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #3492

Complements

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

NH ≅ G/Ntype
1. #19149199C2semidirect
2. #19149196C2semidirect
3. #19149127C2semidirect
4. #19149124C2semidirect
5. #19149045C2semidirect
6. #19148574C2semidirect
7. #19148570C2semidirect
8. #19148566C2semidirect
9. #19148564C2semidirect
10. #19148516C2semidirect
11. #19148512C2semidirect
12. #19148418C2semidirect
13. #19148417C2semidirect
14. #19148304C2semidirect
15. #19148301C2semidirect
16. #19148301C2semidirect
17. #19148296C2semidirect
18. #19147887C2semidirect
19. C22×#13063316C2semidirect
20. C43×#3492C2semidirect
21. C43⋊#564C22semidirect
22. #14583651C22semidirect
23. #14583650C22semidirect
24. #14583646C22semidirect
25. #14583628C22semidirect
26. #14583626C22semidirect
27. #14583625C22semidirect
28. #14583624C22semidirect
29. #14583610C22semidirect
31. #14583608C22semidirect
36. #14583606C22semidirect
37. #14583605C22semidirect
42. #14583601C22semidirect
45. #14583597C22semidirect
46. #14583596C22semidirect
49. #14583593C22semidirect
53. #14583591C22semidirect
54. #14583591C22semidirect
57. #14583588C22semidirect
58. #14583587C22semidirect
60. #14583586C22semidirect
61. #14583585C22semidirect
63. #14583584C22semidirect
64. #14583583C22semidirect
74. #14583530C22semidirect
75. #14583529C22semidirect
79. #14583527C22semidirect
80. #14583526C22semidirect
81. #14583512C22semidirect
82. #14583509C22semidirect
83. #14583509C22semidirect
84. #14583508C22semidirect
85. #14583507C22semidirect
86. #14583506C22semidirect
87. #14583502C22semidirect
88. #14583500C22semidirect
90. #14583498C22semidirect
96. #14583493C22semidirect
97. #14583492C22semidirect
99. #14583490C22semidirect
104. #14583454C22semidirect
106. #14583452C22semidirect
112. #14583436C22semidirect
115. #14583435C22semidirect
116. #14583431C22semidirect
119. #14583430C22semidirect
131. C2×#13063316C22semidirect
132. #125×D43C22semidirect
707. #3492D43semidirect
860. C43#62825semidirect

Maximal subgroups

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

subgroupindex
#191491992
#191491962
#191491272
#191491242
#191490452
#191485742
#191485702
#191485662
#191485642
#191485162
#191485122
#191484182
#191484172
#191483042
#191483012
#191482962
#191478872
C22×#130633162
C43×#34922
#6282543