Finite Group Databasebeta

← #26005418

Subgroups — #26005418

Order 11008.

6636 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19149271C218yesmaximal, complemented
2#19149223C214yesmaximal, complemented
3#19149151C214yesmaximal, complemented
4#19149101C212yesmaximal, complemented
5#19149022C212yesmaximal, complemented
6#19148844C211yesmaximal, characteristic, complemented
7#19148834C211yesmaximal, characteristic, complemented
8#19148822C212yesmaximal, complemented
9#19148584C214yesmaximal, complemented
10#19148573C214yesmaximal, complemented
11#19148556C214yesmaximal, complemented
12#19148539C214yesmaximal, complemented
13#19148521C218yesmaximal, complemented
14#19148517C212yesmaximal, complemented
15#19148491C212yesmaximal, complemented
16#19148307C214yesmaximal, complemented
17#19148287C214yesmaximal, complemented
18C2×#14583433C212yesmaximal, complemented
19C43×#3444C211yesmaximal, characteristic, complemented
20#14583652C2214yescomplemented
21#14583648C2218yescomplemented
22#14583648C2214yescomplemented
23#14583646C2218yescomplemented
24#14583639C2214yes—
25#14583636C2214yescomplemented
26#14583634C2214yescomplemented
27#14583632C2218yescomplemented
28#14583627C2214yescomplemented
29#14583622C2214yescomplemented
30#14583621C2218yescomplemented
31#14583616C2218yescomplemented
32#14583612C2218yescomplemented
33#14583611C2214yescomplemented
34#14583609C2214yescomplemented
35#14583606C2214yescomplemented
36#14583603C2218yescomplemented
37#14583600C2218yescomplemented
38#14583599C2218yescomplemented
39#14583598C2218yescomplemented
40#14583598C2218yescomplemented
41#14583595C2214yes—
42#14583595C2214yescomplemented
43#14583592C2218yescomplemented
44#14583590C2218yescomplemented
45#14583589C2214yescomplemented
46#14583589C2214yescomplemented
47#14583588C2218yescomplemented
48#14583585C2218yescomplemented
49#14583582C2218yescomplemented
50#14583582C2218yescomplemented
51#14583581C2218yescomplemented
52#14583580C2214yescomplemented
53#14583579C2214yescomplemented
54#14583578C2218yescomplemented
55#14583578C2218yescomplemented
56#14583576C2218yescomplemented
57#14583574C2218yescomplemented
58#14583573C2218yescomplemented
59#14583573C2218yescomplemented
60D4×Dic86C2214yescomplemented
61#14583558C2214yescomplemented
62#14583558C2214yescomplemented
63#14583553C2214yescomplemented
64#14583548C2218yescomplemented
65#14583545C2214yescomplemented
66#14583545C2214yescomplemented
67#14583538C2218yescomplemented
68#14583537C2218yescomplemented
69#14583536C2218yescomplemented
70D4×D172C2214yes—
71#14583531C2214yes—
72#14583528C2214yescomplemented
73#14583524C2214yescomplemented
74#14583521C2218yescomplemented
75#14583520C2214yescomplemented
76#14583520C2214yescomplemented
77#14583519C2218yescomplemented
78#14583513C2218yescomplemented
79#14583511C2212yescomplemented
80#14583511C2212yescomplemented
81#14583508C2218yescomplemented
82#14583507C2218yescomplemented
83#14583504C2212yes—
84#14583504C2212yescomplemented
85#14583499C2218yescomplemented
86#14583498C2214yescomplemented
87#14583497C2218yescomplemented
88#14583495C2218yescomplemented
89#14583494C2214yescomplemented
90#14583491C2218yescomplemented
91#14583491C2218yescomplemented
92#14583489C2214yes—
93#14583486C2214yescomplemented
94#14583483C2218yescomplemented
95#14583482C2218yescomplemented
96#14583482C2218yescomplemented
97#14583481C2218yescomplemented
98#14583477C2214yescomplemented
99#14583476C2214yescomplemented
100#14583470C2212yescomplemented
101#14583463C2212yes—
102#14583457C2214yes—
103#14583456C2212yescomplemented
104#14583449C2212yescomplemented
105#14583433C2214yescomplemented
106#14583433C2214yescomplemented
107#14583433C2214yescomplemented
108#14583433C2214yescomplemented
109#14583433C2214yescomplemented
110#14583433C2214yescomplemented
111#14583433C2214yescomplemented
112#14583433C2214yescomplemented
113#14583433C2214yescomplemented
114#14583433C2214yescomplemented
115#14583426C2218yescomplemented
116#14583426C2218yescomplemented
117C2×#13063319C2214yescomplemented
118C2×#13063317C2212yescomplemented
119C2×#13063317C2212yescomplemented
120C2×#13063313C2212yescomplemented
121C2×#13063313C2212yescomplemented
122#14583407C2218yescomplemented
123C2×#13063308C2214yescomplemented
124#123×D43C2218yescomplemented
125C2×#13063304C2212yescomplemented
126C2×#13063299C2212yes—
127#14583379C2214yescomplemented
128#14583378C2218yescomplemented
129#14583376C2212yescomplemented
130#14583373C2212yescomplemented
131#14583371C2218yescomplemented
132C2×C4×Dic86C2212yescomplemented
133C2×C4×D172C2212yescomplemented
134C2×C4×C22⋊D43C2214yescomplemented
135C2×#13063282C2214yescomplemented
136C43×#533C2211yescharacteristic, complemented
137C43×#533C2212yescomplemented
138C43×#532C2212yescomplemented
139C43×#532C2211yescharacteristic, complemented
140C43×#529C2212yescomplemented
141C43×#529C2214yescomplemented
142C43×#529C2214yescomplemented
143C43×#529C2212yescomplemented
144C43×#525C2211yescharacteristic
145C43×#525C2211yescharacteristic, complemented
146C43×#525C2214yescomplemented
147C4×#41×C43C2214yescomplemented
148C4×#41×C43C2211yescharacteristic, complemented
149C4×#41×C43C2211yescharacteristic, complemented
150C22×C42×C43C2211yescharacteristic, complemented
151C2×#10621898C2314yes—
152C2×#10621900C2318yes—
153C22×Dic86C2312yes—
154C22×Dic86C2312yes—
155C22×D172C2312yes—
156C22×D172C2312yes—
157C22×C22⋊D43C2314yes—
158C2×D4×D43C2318yes—
159C22×C4×D43C2314yes—
160#13063325C2314yes—
161#13063325C2312yes—
162#13063324C2318yes—
163#13063323C2318yes—
164#13063323C2314yes—
165#13063322C2312yes—
166#13063321C2314yes—
167#13063320C2318yes—
168#13063320C2318yes—
169#13063320C2318yes—
170#13063320C2318yes—
171#13063320C2318yes—
172#13063320C2318yes—
173#13063319C2318yes—
174#13063319C2318yes—
175#13063319C2318yes—
176#13063319C2318yes—
177#13063319C2318yes—
178#13063319C2318yes—
179#13063318C2318yes—
180#13063318C2318yes—
181#13063318C2318yes—
182#13063318C2318yes—
183#13063317C2314yes—
184#13063317C2318yes—
185#13063317C2312yes—
186#13063317C2314yes—
187#13063317C2312yes—
188#13063317C2314yes—
189#13063317C2314yes—
190#13063316C2318yes—
191#13063315C2318yes—
192#13063315C2318yes—
193#13063315C2318yes—
194#13063315C2318yes—
195#13063315C2318yes—
196#13063315C2318yes—
197#13063314C2318yes—
198#13063314C2314yes—
199#13063313C2314yes—
200#13063313C2314yes—
201#13063313C2314yes—
202#13063313C2318yes—
203#13063313C2314yes—
204#13063313C2314yes—
205#13063312C2314yes—
206#13063311C2318yes—
207#13063311C2318yes—
208#13063311C2318yes—
209#13063311C2318yes—
210#13063310C2318yes—
211#13063310C2318yes—
212#13063310C2318yes—
213#13063310C2318yes—
214#13063310C2318yes—
215#13063310C2318yes—
216#13063309C2318yes—
217#13063309C2318yes—
218#13063308C2318yes—
219#13063308C2318yes—
220#13063308C2318yes—
221#13063308C2318yes—
222#13063308C2318yes—
223#13063308C2318yes—
224#13063307C2318yes—
225#13063307C2318yes—
226#13063307C2318yes—
227#13063307C2318yes—
228#13063306C2314yes—
229#13063306C2314yes—
230#13063306C2318yes—
231#13063306C2318yes—
232#13063305C2318yes—
233#13063304C2314yes—
234#13063304C2314yes—
235#13063304C2314yes—
236#13063304C2318yes—
237#13063304C2314yes—
238#13063304C2314yes—
239#13063304C2314yes—
240#13063303C2318yes—
241#13063303C2318yes—
242#13063303C2318yes—
243#13063303C2318yes—
244#13063303C2318yes—
245#13063303C2318yes—
246#13063302C2318yes—
247#13063302C2318yes—
248#13063302C2318yes—
249#13063302C2318yes—
250#13063301C2318yes—
251#13063301C2318yes—
252#13063301C2318yes—
253#13063300C2318yes—
254#13063299C2314yes—
255#13063299C2314yes—
256#13063299C2314yes—
257#13063299C2318yes—
258#13063299C2314yes—
259#13063299C2314yes—
260#13063299C2314yes—
261#13063298C2318yes—
262#13063298C2318yes—
263#13063298C2318yes—
264#13063298C2318yes—
265#13063297C2318yes—
266#13063297C2318yes—
267#13063297C2318yes—
268#13063297C2318yes—
269#13063297C2318yes—
270#13063297C2318yes—
271#13063296C2318yes—
272#13063295C2318yes—
273#13063295C2318yes—
274#13063293C2314yes—
275#13063293C2314yes—
276#13063293C2318yes—
277#13063293C2318yes—
278C4×Dic86C2314yes—
279C4×Dic86C2314yes—
280C4×Dic86C2314yes—
281C4×Dic86C2318yes—
282C4×Dic86C2314yes—
283C4×Dic86C2314yes—
284C4×Dic86C2314yes—
285#13063290C2318yes—
286#13063290C2318yes—
287C4×D172C2314yes—
288C4×D172C2318yes—
289C4×D172C2314yes—
290C4×D172C2314yes—
291C4×D172C2314yes—
292C4×D172C2314yes—
293C4×D172C2314yes—
294D4×Dic43C2318yes—
295D4×Dic43C2318yes—
296#13063287C2318yes—
297#13063287C2318yes—
298C4×C22⋊D43C2318yes—
299C4×C22⋊D43C2318yes—
300C4×C22⋊D43C2318yes—
301C4×C22⋊D43C2318yes—
302C4×C22⋊D43C2318yes—
303C4×C22⋊D43C2318yes—
304(C22⋊D43)⋊C4C2318yes—
305(C22⋊D43)⋊C4C2318yes—
306(C22⋊D43)⋊C4C2318yes—
307(C22⋊D43)⋊C4C2318yes—
308(C22⋊D43)⋊C4C2318yes—
309(C22⋊D43)⋊C4C2318yes—
310#13063284C2312yes—
311#13063284C2312yes—
312#13063283C2318yes—
313#13063283C2318yes—
314#13063282C2318yes—
315#13063282C2318yes—
316#13063282C2318yes—
317#13063282C2318yes—
318#13063282C2318yes—
319#13063282C2318yes—
320#13063281C2318yes—
321#13063281C2318yes—
322#13063281C2318yes—
323C2×C4⋊Dic43C2312yes—
324C2×C4⋊Dic43C2314yes—
325C2×C4⋊Dic43C2312yes—
326C2×Dic43⋊C4C2314yes—
327C2×Dic43⋊C4C2318yes—
328C2×Dic43⋊C4C2314yes—
329C2×Dic43⋊C4C2314yes—
330C2×Dic43⋊C4C2314yes—
331C4⋊C4×D43C2318yes—
332C4⋊C4×D43C2318yes—
333C2×C22⋊Dic43C2314yes—
334C2×(C2×D43)⋊C4C2314yes—
335C2×(C2×D43)⋊C4C2318yes—
336C2×(C2×D43)⋊C4C2314yes—
337C2×(C2×D43)⋊C4C2314yes—
338C2×(C2×D43)⋊C4C2314yes—
339C22⋊C4×D43C2318yes—
340C22⋊C4×D43C2318yes—
341C22⋊C4×D43C2318yes—
342C2×C4×Dic43C2314yes—
343C2×#41×C43C2311yescharacteristic
344C2×#41×C43C2311yescharacteristic
345C2×#41×C43C2314yes—
346C23×C4×C43C2311yescharacteristic
347C23×C4×C43C2312yes—
348C4⋊Q8×C43C2312yes—
349C4⋊Q8×C43C2311yescharacteristic
350#127×C43C2311yescharacteristic
351#126×C43C2314yes—
352#126×C43C2314yes—
353#125×C43C2312yes—
354#125×C43C2314yes—
355#124×C43C2311yescharacteristic
356#124×C43C2311yescharacteristic
357#124×C43C2314yes—
358#123×C43C2312yes—
359#123×C43C2312yes—
360#123×C43C2314yes—
361#123×C43C2314yes—
362C22⋊Q8×C43C2314yes—
363C22⋊Q8×C43C2312yes—
364C22⋊Q8×C43C2314yes—
365C22⋊Q8×C43C2312yes—
366#121×C43C2312yes—
367#121×C43C2314yes—
368#121×C43C2312yes—
369#121×C43C2314yes—
370#120×C43C2312yes—
371#120×C43C2312yes—
372C4×Q8×C43C2312yes—
373C4×Q8×C43C2314yes—
374C4×Q8×C43C2312yes—
375C4×Q8×C43C2314yes—
376C4×D4×C43C2314yes—
377C4×D4×C43C2314yes—
378C4×D4×C43C2314yes—
379C4×D4×C43C2312yes—
380C4×D4×C43C2314yes—
381C4×D4×C43C2314yes—
382C4×D4×C43C2314yes—
383C4×D4×C43C2314yes—
384C4×D4×C43C2312yes—
385C4×D4×C43C2314yes—
386#117×C43C2314yes—
387#117×C43C2314yes—
388#117×C43C2311yescharacteristic
389#117×C43C2311yescharacteristic
390#117×C43C2314yes—
391#117×C43C2312yes—
392#117×C43C2312yes—
393C2×C42×C43C2312yes—
394C2×C42×C43C2311yescharacteristic
395C2×C42×C43C2312yes—
396C2×C42×C43C2312yes—
397C2×C42×C43C2312yes—
398C2×C42×C43C2312yes—
399C2×C42×C43C2311yescharacteristic
400C2×C42×C43C2312yes—
401C2×C42×C43C2312yes—
402C24×C43C2411yescharacteristic
403C23×D43C2414yes—
404C23×D43C2414yes—
405#41×C43—42no—
406#41×C43—42no—
407#41×C43—48no—
408C2×Q8×C43C2411yescharacteristic
409C2×Q8×C43C2414yes—
410C2×Q8×C43C2411yescharacteristic
411C2×D4×C43C2414yes—
412C2×D4×C43C2414yes—
413C2×D4×C43C2412yes—
414C2×D4×C43C2412yes—
415C2×D4×C43C2411yescharacteristic
416C2×D4×C43C2414yes—
417C2×D4×C43C2411yescharacteristic
418C22×C4×C43—44no—
419C22×C4×C43—42no—
420C22×C4×C43C2412yes—
421C22×C4×C43C2411yescharacteristic
422C22×C4×C43C2412yes—
423C22×C4×C43C2412yes—
424C22×C4×C43C2412yes—
425C22×C4×C43C2412yes—
426C22×C4×C43C2412yes—
427C22×C4×C43C2412yes—
428C22×C4×C43C2412yes—
429C22×C4×C43C2412yes—
430C22×C4×C43C2412yes—
431C22×C4×C43C2411yescharacteristic
432C22×C4×C43C2414yes—
433C22×C4×C43C2414yes—
434C2×C22⋊D43—48no—
435C2×C22⋊D43C2418yes—
436C2×C22⋊D43C2418yes—
437C2×C22⋊D43C2418yes—
438C2×C22⋊D43C2418yes—
439C2×C22⋊D43C2418yes—
440C22×Dic43C2414yes—
441C22×Dic43C2414yes—
442C22×Dic43C2414yes—
443C22×Dic43C2414yes—
444C22×Dic43C2418yes—
445#10621900—416no—
446D4×D43—416no—
447#10621898—48no—
448C2×D172—44no—
449C2×D172—44no—
450C2×D172C2414yes—
451C2×D172C2414yes—
452C2×D172C2418yes—
453C2×D172C2414yes—
454C2×C4×D43—48no—
455C2×C4×D43C2418yes—
456C2×C4×D43C2418yes—
457C2×C4×D43C2418yes—
458C2×C4×D43C2418yes—
459C2×C4×D43C2418yes—
460C2×Dic86—44no—
461C2×Dic86—44no—
462C2×Dic86C2414yes—
463C2×Dic86C2414yes—
464C2×Dic86C2418yes—
465C2×Dic86C2414yes—
466C4⋊C4×C43C2412yes—
467C4⋊C4×C43C2414yes—
468C4⋊C4×C43C2414yes—
469C4⋊C4×C43C2412yes—
470C4⋊C4×C43C2414yes—
471C4⋊C4×C43C2414yes—
472C4⋊C4×C43C2414yes—
473C4⋊C4×C43C2414yes—
474C4⋊C4×C43C2414yes—
475C4⋊C4×C43C2414yes—
476C22⋊C4×C43C2414yes—
477C22⋊C4×C43C2414yes—
478C22⋊C4×C43C2412yes—
479C22⋊C4×C43C2412yes—
480C22⋊C4×C43C2414yes—
481C22⋊C4×C43C2414yes—
482C22⋊C4×C43C2414yes—
483C22⋊C4×C43C2414yes—
484C22⋊C4×C43C2414yes—
485C22⋊C4×C43C2414yes—
486C42×C43C2411yescharacteristic
487C42×C43C2412yes—
488C42×C43C2411yescharacteristic
489C42×C43C2412yes—
490C42×C43C2412yes—
491C42×C43C2412yes—
492C42×C43C2411yescharacteristic
493C42×C43C2412yes—
494C42×C43C2412yes—
495C42×C43C2411yescharacteristic
496C42×C43C2414yes—
497C42×C43C2414yes—
498C42×C43C2412yes—
499C42×C43C2412yes—
500C22⋊Dic43C2414yes—
501C22⋊Dic43C2418yes—
502C22⋊Dic43C2418yes—
503C22⋊Dic43C2418yes—
504C22⋊Dic43C2414yes—
505C22⋊Dic43C2418yes—
506(C2×D43)⋊C4C2418yes—
507(C2×D43)⋊C4C2418yes—
508(C2×D43)⋊C4C2418yes—
509(C2×D43)⋊C4C2418yes—
510(C2×D43)⋊C4C2418yes—
511(C2×D43)⋊C4C2418yes—
512(C2×D43)⋊C4C2418yes—
513(C2×D43)⋊C4C2418yes—
514(C2×D43)⋊C4C2418yes—
515(C2×D43)⋊C4C2418yes—
516(C2×D43)⋊C4C2418yes—
517(C2×D43)⋊C4C2418yes—
518(C2×D43)⋊C4C2418yes—
519(C2×D43)⋊C4C2418yes—
520C4⋊Dic43C2418yes—
521C4⋊Dic43C2418yes—
522C4⋊Dic43C2414yes—
523C4⋊Dic43C2414yes—
524C4⋊Dic43C2414yes—
525C4⋊Dic43C2414yes—
526C4⋊Dic43C2418yes—
527Dic43⋊C4C2418yes—
528Dic43⋊C4C2418yes—
529Dic43⋊C4C2418yes—
530Dic43⋊C4C2418yes—
531Dic43⋊C4C2418yes—
532Dic43⋊C4C2418yes—
533Dic43⋊C4C2418yes—
534Dic43⋊C4C2418yes—
535Dic43⋊C4C2418yes—
536Dic43⋊C4C2418yes—
537Dic43⋊C4C2418yes—
538Dic43⋊C4C2418yes—
539Dic43⋊C4C2418yes—
540Dic43⋊C4C2418yes—
541C4×Dic43C2418yes—
542C4×Dic43C2418yes—
543C4×Dic43C2414yes—
544C4×Dic43C2414yes—
545C4×Dic43C2418yes—
546C4×Dic43C2418yes—
547C23×C43—24no—
548C23×C43—41no—
549C23×C43C2512yes—
550C23×C43C2511yescharacteristic
551C23×C43C2512yes—
552C23×C43C2512yes—
553C22×D43—28no—
554C22×D43—44no—
555C22×D43—44no—
556C22×D43—44no—
557C22×D43—48no—
558C22×D43C2518yes—
559Q8×C43—44no—
560Q8×C43—41no—
561Q8×C43—41no—
562D4×C43—28no—
563D4×C43—28no—
564D4×C43—42no—
565D4×C43—42no—
566D4×C43—41no—
567D4×C43—44no—
568D4×C43—41no—
569C2×C4×C43—24no—
570C2×C4×C43—24no—
571C2×C4×C43—24no—
572C2×C4×C43—24no—
573C2×C4×C43—24no—
574C2×C4×C43—22no—
575C2×C4×C43—41no—
576C2×C4×C43—42no—
577C2×C4×C43—42no—
578C2×C4×C43—42no—
579C2×C4×C43—42no—
580C2×C4×C43—42no—
581C2×C4×C43—44no—
582C2×C4×C43—44no—
583C2×C4×C43C2512yes—
584C2×C4×C43C2512yes—
585C2×C4×C43C2512yes—
586C2×C4×C43C2514yes—
587C2×C4×C43C2514yes—
588C2×C4×C43C2512yes—
589C2×C4×C43C2511yescharacteristic
590C2×C4×C43C2512yes—
591C2×C4×C43C2512yes—
592C2×C4×C43C2512yes—
593C2×C4×C43C2511yescharacteristic
594C22⋊D43—216no—
595C22⋊D43—48no—
596C22⋊D43—48no—
597C22⋊D43—48no—
598C22⋊D43—48no—
599C2×Dic43—28no—
600C2×Dic43—44no—
601C2×Dic43—44no—
602C2×Dic43—48no—
603C2×Dic43—44no—
604C2×Dic43C2518yes—
605C2×Dic43C2518yes—
606C2×Dic43C2518yes—
607D172—28no—
608D172—44no—
609D172—44no—
610D172—48no—
611C4×D43—48no—
612C4×D43—48no—
613C4×D43—48no—
614C4×D43—48no—
615C4×D43—48no—
616Dic86—28no—
617Dic86—44no—
618Dic86—44no—
619Dic86—48no—
620#62829—431nomaximal, Sylow
621C22×C43—22no—
622C22×C43—22no—
623C22×C43—22no—
624C22×C43—24no—
625C22×C43—22no—
626C22×C43—21no—
627C22×C43—24no—
628C22×C43—22no—
629C22×C43—44no—
630C22×C43#58514yes—
631C22×C43C2611yescharacteristic
632C2×D43—28no—
633C2×D43—28no—
634C2×D43—28no—
635C2×D43—88no—
636C2×D43—164no—
637C4×C43—24no—
638C4×C43—22no—
639C4×C43—22no—
640C4×C43—22no—
641C4×C43—22no—
642C4×C43—22no—
643C4×C43—24no—
644C4×C43—22no—
645C4×C43—22no—
646C4×C43—21no—
647C4×C43#58512yes—
648Dic43—28no—
649Dic43—28no—
650Dic43—28no—
651#3566—438no—
652#3564—434no—
653#3560—434no—
654#3557—432no—
655#3551—432no—
656#3538—431no—
657#3537—431no—
658#3536—432no—
659#3516—434no—
660#3515—434no—
661#3514—434no—
662#3513—434no—
663#3513—438no—
664#3512—432no—
665#3510—432no—
666#3493—434no—
667#3491—434no—
668#3444D4311yescharacteristic, complemented
669C2×#529—432no—
670C2×C43—24no—
671C2×C43—42no—
672C2×C43—42no—
673C2×C43—41no—
674C2×C43C2×#58512yes—
675C2×C43C2×#58511yescharacteristic
676D43—48no—
677#563—434no—
678#563—438no—
679#563—434no—
680#562—438no—
681#560—434no—
682#560—434no—
683#559—434no—
684#559—438no—
685#557—434no—
686#556—438no—
687#556—438no—
688#556—434no—
689#555—434no—
690#555—438no—
691#554—438no—
692#554—434no—
693#554—434no—
694#553—438no—
695#553—438no—
696#553—434no—
697#553—434no—
698#553—438no—
699#553—438no—
700#553—438no—
701#552—438no—
702#552—438no—
703#552—438no—
704#552—434no—
705#552—434no—
706#552—438no—
707#552—438no—
708#552—438no—
709#551—438no—
710#551—434no—
711#551—438no—
712#551—434no—
713#551—438no—
714#551—438no—
715#551—438no—
716#551—438no—
717D4×Q8—434no—
718#548—434no—
719#548—434no—
720#547—438no—
721#547—434no—
722#546—438no—
723#546—438no—
724#546—438no—
725#546—434no—
726#546—434no—
727D42—434no—
728D42—434no—
729#544—434no—
730#543—434no—
731#542—438no—
732#542—438no—
733#542—438no—
734#542—434no—
735#542—434no—
736#541—438no—
737#541—438no—
738#541—432no—
739#541—432no—
740#540—438no—
741#540—432no—
742#540—432no—
743#539—438no—
744#539—434no—
745#539—438no—
746#539—434no—
747#539—438no—
748#539—438no—
749#538—438no—
750#538—434no—
751#538—434no—
752#538—438no—
753#538—438no—
754#538—438no—
755#537—434no—
756#537—434no—
757#536—432no—
758#535—432no—
759#534—434no—
760#533—432no—
761#533C2×D4311yescharacteristic, complemented
762#533C2×D4312yescomplemented
763#532—432no—
764#532C2×D4311yescharacteristic, complemented
765#532C2×D4312yescomplemented
766#529—438no—
767#529—438no—
768#529—434no—
769#529—434no—
770#529—434no—
771#529—434no—
772#529—434no—
773#529—434no—
774#529—434no—
775#529—434no—
776#529—434no—
777#529—434no—
778#529C2×D4312yescomplemented
779#529C2×D4312yescomplemented
780#529C2×D4314yescomplemented
781#529C2×D4314yescomplemented
782C2×#126—434no—
783C2×#125—432no—
784C2×#125—432no—
785C2×#124—432no—
786C2×#124—432no—
787#525—438no—
788#525C2×D4311yescharacteristic
789#525C2×D4314yescomplemented
790#525C2×D4311yescharacteristic, complemented
791C2×#123—434no—
792C2×#123—438no—
793C2×C22⋊Q8—432no—
794C2×#121—432no—
795#520—438no—
796#520—434no—
797#519—432no—
798#518—438no—
799#518—432no—
800C4×#41C2×D4311yescharacteristic, complemented
801C4×#41C2×D4311yescharacteristic, complemented
802C4×#41C2×D4314yescomplemented
803C2×C4×Q8—432no—
804C2×C4×D4—434no—
805C2×C4×D4—432no—
806C2×#117—434no—
807C22×C42C2×D4311yescharacteristic, complemented
808C43#6282911yescharacteristic, complemented, Sylow
809C2×#41—438no—
810C2×#41—434no—
811C2×#41C22×D4311yescharacteristic
812C2×#41C22×D4311yescharacteristic
813C2×#41C22×D4314yes—
814C22×Q8—432no—
815C22×Q8—432no—
816C22×D4—434no—
817C22×D4—438no—
818C22×D4—432no—
819C22×D4—432no—
820C23×C4—434no—
821C23×C4C22×D4312yes—
822C23×C4C22×D4311yescharacteristic
823C4⋊Q8—434no—
824C4⋊Q8—438no—
825C4⋊Q8—438no—
826C4⋊Q8—432no—
827C4⋊Q8—434no—
828C4⋊Q8C22×D4312yes—
829C4⋊Q8C22×D4311yescharacteristic
830#127—434no—
831#127—432no—
832#127C22×D4311yescharacteristic
833#126—438no—
834#126—438no—
835#126—438no—
836#126—438no—
837#126—438no—
838#126—438no—
839#126—438no—
840#126—438no—
841#126—438no—
842#126—438no—
843#126—438no—
844#126—438no—
845#126—438no—
846#126—438no—
847#126—438no—
848#126—438no—
849#126C22×D4314yes—
850#126C22×D4314yes—
851#125—438no—
852#125—438no—
853#125—438no—
854#125—438no—
855#125—438no—
856#125—438no—
857#125—438no—
858#125—434no—
859#125—434no—
860#125—434no—
861#125—434no—
862#125—438no—
863#125—432no—
864#125—432no—
865#125C22×D4314yes—
866#125C22×D4312yes—
867#124—434no—
868#124—438no—
869#124—434no—
870#124—438no—
871#124—438no—
872#124—438no—
873#124—438no—
874#124—434no—
875#124—434no—
876#124—434no—
877#124—434no—
878#124—438no—
879#124—434no—
880#124C22×D4314yes—
881#124C22×D4311yescharacteristic
882#124C22×D4311yescharacteristic
883#123—438no—
884#123—434no—
885#123—434no—
886#123—438no—
887#123—438no—
888#123—438no—
889#123—438no—
890#123—438no—
891#123—438no—
892#123—438no—
893#123—438no—
894#123—438no—
895#123—438no—
896#123—438no—
897#123—438no—
898#123—438no—
899#123—438no—
900#123—438no—
901#123—438no—
902#123—438no—
903#123—438no—
904#123—438no—
905#123C22×D4314yes—
906#123C22×D4314yes—
907#123C22×D4312yes—
908#123C22×D4312yes—
909C22⋊Q8—438no—
910C22⋊Q8—438no—
911C22⋊Q8—438no—
912C22⋊Q8—434no—
913C22⋊Q8—434no—
914C22⋊Q8—434no—
915C22⋊Q8—434no—
916C22⋊Q8—434no—
917C22⋊Q8—434no—
918C22⋊Q8—438no—
919C22⋊Q8—438no—
920C22⋊Q8—438no—
921C22⋊Q8—438no—
922C22⋊Q8—438no—
923C22⋊Q8—438no—
924C22⋊Q8—438no—
925C22⋊Q8—438no—
926C22⋊Q8—438no—
927C22⋊Q8—438no—
928C22⋊Q8—438no—
929C22⋊Q8—438no—
930C22⋊Q8C22×D4312yes—
931C22⋊Q8C22×D4314yes—
932C22⋊Q8C22×D4312yes—
933C22⋊Q8C22×D4314yes—
934#121—438no—
935#121—438no—
936#121—438no—
937#121—438no—
938#121—438no—
939#121—438no—
940#121—438no—
941#121—434no—
942#121—434no—
943#121—434no—
944#121—434no—
945#121—434no—
946#121—434no—
947#121—438no—
948#121—438no—
949#121—438no—
950#121—438no—
951#121—438no—
952#121—438no—
953#121C22×D4312yes—
954#121C22×D4312yes—
955#121C22×D4314yes—
956#121C22×D4314yes—
957#120—438no—
958#120—434no—
959#120—434no—
960#120—438no—
961#120—438no—
962#120—438no—
963#120C22×D4312yes—
964#120C22×D4312yes—
965C4×Q8—438no—
966C4×Q8—438no—
967C4×Q8—434no—
968C4×Q8—434no—
969C4×Q8—434no—
970C4×Q8—434no—
971C4×Q8—434no—
972C4×Q8—434no—
973C4×Q8—438no—
974C4×Q8C22×D4314yes—
975C4×Q8C22×D4312yes—
976C4×Q8C22×D4314yes—
977C4×Q8C22×D4312yes—
978C4×D4—438no—
979C4×D4—438no—
980C4×D4—438no—
981C4×D4—438no—
982C4×D4—438no—
983C4×D4—438no—
984C4×D4—438no—
985C4×D4—438no—
986C4×D4—438no—
987C4×D4—438no—
988C4×D4—438no—
989C4×D4—438no—
990C4×D4—438no—
991C4×D4—438no—
992C4×D4—438no—
993C4×D4—438no—
994C4×D4—434no—
995C4×D4—434no—
996C4×D4—434no—
997C4×D4—434no—
998C4×D4—434no—
999C4×D4—438no—
1000C4×D4—434no—
1001C4×D4C22×D4314yes—
1002C4×D4C22×D4314yes—
1003C4×D4C22×D4314yes—
1004C4×D4C22×D4314yes—
1005C4×D4C22×D4314yes—
1006C4×D4C22×D4314yes—
1007C4×D4C22×D4314yes—
1008C4×D4C22×D4314yes—
1009C4×D4C22×D4312yes—
1010C4×D4C22×D4312yes—
1011#117—432no—
1012#117—432no—
1013#117—438no—
1014#117—438no—
1015#117—438no—
1016#117—438no—
1017#117—438no—
1018#117—438no—
1019#117—438no—
1020#117—438no—
1021#117—438no—
1022#117—438no—
1023#117—438no—
1024#117C22×D4312yes—
1025#117C22×D4312yes—
1026#117C22×D4311yescharacteristic
1027#117C22×D4311yescharacteristic
1028#117C22×D4314yes—
1029#117C22×D4314yes—
1030#117C22×D4314yes—
1031C2×C4⋊C4—434no—
1032C2×C4⋊C4—434no—
1033C2×C4⋊C4—432no—
1034C2×C4⋊C4—434no—
1035C2×C4⋊C4—432no—
1036C2×C4⋊C4—434no—
1037C2×C4⋊C4—434no—
1038C2×C4⋊C4—438no—
1039C2×C4⋊C4—438no—
1040C2×C4⋊C4—438no—
1041C2×C22⋊C4—434no—
1042C2×C22⋊C4—434no—
1043C2×C22⋊C4—434no—
1044C2×C22⋊C4—434no—
1045C2×C22⋊C4—434no—
1046C2×C22⋊C4—438no—
1047C2×C22⋊C4—438no—
1048C2×C22⋊C4—438no—
1049C2×C22⋊C4—438no—
1050C2×C42—434no—
1051C2×C42C22×D4312yes—
1052C2×C42C22×D4312yes—
1053C2×C42C22×D4312yes—
1054C2×C42C22×D4312yes—
1055C2×C42C22×D4312yes—
1056C2×C42C22×D4311yescharacteristic
1057C2×C42C22×D4312yes—
1058C2×C42C22×D4312yes—
1059C2×C42C22×D4311yescharacteristic
1060C24—434no—
1061C24—434no—
1062C24C23×D4311yescharacteristic
1063#41—42no—
1064#41—42no—
1065#41—48no—
1066#41—1728no—
1067#41—17216no—
1068C2×Q8—434no—
1069C2×Q8—438no—
1070C2×Q8—434no—
1071C2×Q8—434no—
1072C2×Q8—1724no—
1073C2×Q8—1724no—
1074C2×Q8C23×D4311yescharacteristic
1075C2×Q8C23×D4314yes—
1076C2×Q8C23×D4311yescharacteristic
1077C2×D4—438no—
1078C2×D4—438no—
1079C2×D4—438no—
1080C2×D4—438no—
1081C2×D4—438no—
1082C2×D4—434no—
1083C2×D4—434no—
1084C2×D4—438no—
1085C2×D4—434no—
1086C2×D4—1724no—
1087C2×D4—1724no—
1088C2×D4—17216no—
1089C2×D4—1728no—
1090C2×D4C23×D4314yes—
1091C2×D4C23×D4314yes—
1092C2×D4C23×D4311yescharacteristic
1093C2×D4C23×D4312yes—
1094C2×D4C23×D4314yes—
1095C2×D4C23×D4312yes—
1096C2×D4C23×D4311yescharacteristic
1097C22×C4—42no—
1098C22×C4—44no—
1099C22×C4—434no—
1100C22×C4—434no—
1101C22×C4—434no—
1102C22×C4—434no—
1103C22×C4—438no—
1104C22×C4—438no—
1105C22×C4—438no—
1106C22×C4—438no—
1107C22×C4—438no—
1108C22×C4—438no—
1109C22×C4—1728no—
1110C22×C4C23×D4312yes—
1111C22×C4C23×D4312yes—
1112C22×C4C23×D4312yes—
1113C22×C4C23×D4311yescharacteristic
1114C22×C4C23×D4312yes—
1115C22×C4C23×D4312yes—
1116C22×C4C23×D4312yes—
1117C22×C4C23×D4312yes—
1118C22×C4C23×D4312yes—
1119C22×C4C23×D4312yes—
1120C22×C4C23×D4312yes—
1121C22×C4C23×D4311yescharacteristic
1122C22×C4C23×D4314yes—
1123C22×C4C23×D4314yes—
1124C4⋊C4—438no—
1125C4⋊C4—438no—
1126C4⋊C4—434no—
1127C4⋊C4—438no—
1128C4⋊C4—434no—
1129C4⋊C4—438no—
1130C4⋊C4—438no—
1131C4⋊C4—438no—
1132C4⋊C4—438no—
1133C4⋊C4—438no—
1134C4⋊C4—438no—
1135C4⋊C4—434no—
1136C4⋊C4—438no—
1137C4⋊C4—438no—
1138C4⋊C4—438no—
1139C4⋊C4—434no—
1140C4⋊C4—438no—
1141C4⋊C4—438no—
1142C4⋊C4—438no—
1143C4⋊C4—438no—
1144C4⋊C4—438no—
1145C4⋊C4C23×D4314yes—
1146C4⋊C4C23×D4314yes—
1147C4⋊C4C23×D4314yes—
1148C4⋊C4C23×D4314yes—
1149C4⋊C4C23×D4314yes—
1150C4⋊C4C23×D4312yes—
1151C4⋊C4C23×D4314yes—
1152C4⋊C4C23×D4314yes—
1153C4⋊C4C23×D4312yes—
1154C4⋊C4C23×D4314yes—
1155C22⋊C4—438no—
1156C22⋊C4—434no—
1157C22⋊C4—438no—
1158C22⋊C4—438no—
1159C22⋊C4—434no—
1160C22⋊C4—438no—
1161C22⋊C4—438no—
1162C22⋊C4—438no—
1163C22⋊C4—438no—
1164C22⋊C4—438no—
1165C22⋊C4—438no—
1166C22⋊C4—438no—
1167C22⋊C4—438no—
1168C22⋊C4—438no—
1169C22⋊C4—438no—
1170C22⋊C4—438no—
1171C22⋊C4—438no—
1172C22⋊C4—438no—
1173C22⋊C4—438no—
1174C22⋊C4—438no—
1175C22⋊C4C23×D4314yes—
1176C22⋊C4C23×D4314yes—
1177C22⋊C4C23×D4314yes—
1178C22⋊C4C23×D4314yes—
1179C22⋊C4C23×D4314yes—
1180C22⋊C4C23×D4314yes—
1181C22⋊C4C23×D4314yes—
1182C22⋊C4C23×D4312yes—
1183C22⋊C4C23×D4312yes—
1184C22⋊C4C23×D4314yes—
1185C42—438no—
1186C42—438no—
1187C42—438no—
1188C42—434no—
1189C42—438no—
1190C42—434no—
1191C42C23×D4311yescharacteristic
1192C42C23×D4311yescharacteristic
1193C42C23×D4312yes—
1194C42C23×D4312yes—
1195C42C23×D4312yes—
1196C42C23×D4311yescharacteristic
1197C42C23×D4312yes—
1198C42C23×D4312yes—
1199C42C23×D4312yes—
1200C42C23×D4311yescharacteristic
1201C42C23×D4314yes—
1202C42C23×D4314yes—
1203C42C23×D4312yes—
1204C42C23×D4312yes—
1205C23—24no—
1206C23—41no—
1207C23—438no—
1208C23—868no—
1209C23—1724no—
1210C23—1724no—
1211C23—1724no—
1212C23—1728no—
1213C23C24×D4312yes—
1214C23C24×D4311yescharacteristic
1215C23C24×D4312yes—
1216C23C24×D4312yes—
1217Q8—41no—
1218Q8—41no—
1219Q8—44no—
1220Q8—868no—
1221Q8—1724no—
1222Q8—1724no—
1223Q8—1728no—
1224D4—28no—
1225D4—28no—
1226D4—41no—
1227D4—41no—
1228D4—44no—
1229D4—42no—
1230D4—42no—
1231D4—8616no—
1232D4—868no—
1233D4—1724no—
1234D4—1724no—
1235D4—1728no—
1236D4—1728no—
1237D4—1728no—
1238D4—1728no—
1239D4—1728no—
1240C2×C4—24no—
1241C2×C4—24no—
1242C2×C4—24no—
1243C2×C4—22no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—42no—
1247C2×C4—42no—
1248C2×C4—42no—
1249C2×C4—42no—
1250C2×C4—42no—
1251C2×C4—41no—
1252C2×C4—44no—
1253C2×C4—44no—
1254C2×C4—438no—
1255C2×C4—438no—
1256C2×C4—438no—
1257C2×C4—868no—
1258C2×C4—1728no—
1259C2×C4—1728no—
1260C2×C4—1728no—
1261C2×C4—1728no—
1262C2×C4—1728no—
1263C2×C4—1724no—
1264C2×C4—1724no—
1265C2×C4—1724no—
1266C2×C4—1728no—
1267C2×C4C24×D4312yes—
1268C2×C4C24×D4312yes—
1269C2×C4C24×D4312yes—
1270C2×C4C24×D4314yes—
1271C2×C4C24×D4314yes—
1272C2×C4C24×D4312yes—
1273C2×C4C24×D4311yescharacteristic
1274C2×C4C24×D4312yes—
1275C2×C4C24×D4312yes—
1276C2×C4C24×D4312yes—
1277C2×C4C24×D4311yescharacteristic
1278C22—22no—
1279C22—22no—
1280C22—21no—
1281C22—22no—
1282C22—22no—
1283C22—22no—
1284C22—24no—
1285C22—24no—
1286C22—44no—
1287C22—868no—
1288C22—868no—
1289C22—868no—
1290C22—3448no—
1291C22—6884no—
1292C22#1458373514yes—
1293C22C25×D4311yescharacteristic
1294C4—22no—
1295C4—22no—
1296C4—22no—
1297C4—22no—
1298C4—21no—
1299C4—22no—
1300C4—22no—
1301C4—22no—
1302C4—24no—
1303C4—24no—
1304C4—868no—
1305C4—868no—
1306C4—868no—
1307C4#1458373512yes—
1308C2—24no—
1309C2—41no—
1310C2—42no—
1311C2—42no—
1312C2—1728no—
1313C2C2×#1458373512yes—
1314C2C2×#1458373511yescharacteristic
subgroupG/H
center, FrattiniC22C25×D43
commutator, socle, cosocleC22×C43C26
FittingC43×#3444C2
hypercenter#3444D43
hypocenterC43#62829
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. #19149271C2semidirect
2. #19149223C2semidirect
3. #19149151C2semidirect
4. #19149101C2semidirect
5. #19149022C2semidirect
6. #19148844C2semidirect
7. #19148834C2semidirect
8. #19148822C2semidirect
9. #19148584C2semidirect
10. #19148573C2semidirect
11. #19148556C2semidirect
12. #19148539C2semidirect
13. #19148521C2semidirect
14. #19148517C2semidirect
15. #19148491C2semidirect
16. #19148307C2semidirect
17. #19148287C2semidirect
18. C2×#14583433C2semidirect
19. C43×#3444C2semidirect
20. #14583652C22semidirect
21. #14583648C22semidirect
22. #14583648C22semidirect
23. #14583646C22semidirect
25. #14583636C22semidirect
26. #14583634C22semidirect
27. #14583632C22semidirect
28. #14583627C22semidirect
29. #14583622C22semidirect
30. #14583621C22semidirect
31. #14583616C22semidirect
32. #14583612C22semidirect
33. #14583611C22semidirect
34. #14583609C22semidirect
35. #14583606C22semidirect
36. #14583603C22semidirect
37. #14583600C22semidirect
38. #14583599C22semidirect
39. #14583598C22semidirect
40. #14583598C22semidirect
42. #14583595C22semidirect
43. #14583592C22semidirect
44. #14583590C22semidirect
45. #14583589C22semidirect
46. #14583589C22semidirect
47. #14583588C22semidirect
48. #14583585C22semidirect
49. #14583582C22semidirect
50. #14583582C22semidirect
51. #14583581C22semidirect
52. #14583580C22semidirect
53. #14583579C22semidirect
54. #14583578C22semidirect
55. #14583578C22semidirect
56. #14583576C22semidirect
57. #14583574C22semidirect
58. #14583573C22semidirect
59. #14583573C22semidirect
60. D4×Dic86C22semidirect
61. #14583558C22semidirect
62. #14583558C22semidirect
63. #14583553C22semidirect
64. #14583548C22semidirect
65. #14583545C22semidirect
66. #14583545C22semidirect
67. #14583538C22semidirect
68. #14583537C22semidirect
69. #14583536C22semidirect
72. #14583528C22semidirect
73. #14583524C22semidirect
74. #14583521C22semidirect
75. #14583520C22semidirect
76. #14583520C22semidirect
77. #14583519C22semidirect
78. #14583513C22semidirect
79. #14583511C22semidirect
80. #14583511C22semidirect
81. #14583508C22semidirect
82. #14583507C22semidirect
84. #14583504C22semidirect
85. #14583499C22semidirect
86. #14583498C22semidirect
87. #14583497C22semidirect
88. #14583495C22semidirect
89. #14583494C22semidirect
90. #14583491C22semidirect
91. #14583491C22semidirect
93. #14583486C22semidirect
94. #14583483C22semidirect
95. #14583482C22semidirect
96. #14583482C22semidirect
97. #14583481C22semidirect
98. #14583477C22semidirect
99. #14583476C22semidirect
100. #14583470C22semidirect
103. #14583456C22semidirect
104. #14583449C22semidirect
105. #14583433C22semidirect
106. #14583433C22semidirect
107. #14583433C22semidirect
108. #14583433C22semidirect
109. #14583433C22semidirect
110. #14583433C22semidirect
111. #14583433C22semidirect
112. #14583433C22semidirect
113. #14583433C22semidirect
114. #14583433C22semidirect
115. #14583426C22semidirect
116. #14583426C22semidirect
117. C2×#13063319C22semidirect
118. C2×#13063317C22semidirect
119. C2×#13063317C22semidirect
120. C2×#13063313C22semidirect
121. C2×#13063313C22semidirect
122. #14583407C22semidirect
123. C2×#13063308C22semidirect
124. #123×D43C22semidirect
125. C2×#13063304C22semidirect
127. #14583379C22semidirect
128. #14583378C22semidirect
129. #14583376C22semidirect
130. #14583373C22semidirect
131. #14583371C22semidirect
132. C2×C4×Dic86C22semidirect
133. C2×C4×D172C22semidirect
134. C2×C4×C22⋊D43C22semidirect
135. C2×#13063282C22semidirect
136. C43×#533C22semidirect
137. C43×#533C22semidirect
138. C43×#532C22semidirect
139. C43×#532C22semidirect
140. C43×#529C22semidirect
141. C43×#529C22semidirect
142. C43×#529C22semidirect
143. C43×#529C22semidirect
145. C43×#525C22semidirect
146. C43×#525C22semidirect
147. C4×#41×C43C22semidirect
148. C4×#41×C43C22semidirect
149. C4×#41×C43C22semidirect
150. C22×C42×C43C22semidirect
668. #3444D43semidirect
761. #533C2×D43semidirect
762. #533C2×D43semidirect
764. #532C2×D43semidirect
765. #532C2×D43semidirect
778. #529C2×D43semidirect
779. #529C2×D43semidirect
780. #529C2×D43semidirect
781. #529C2×D43semidirect
789. #525C2×D43semidirect
790. #525C2×D43semidirect
800. C4×#41C2×D43semidirect
801. C4×#41C2×D43semidirect
802. C4×#41C2×D43semidirect
807. C22×C42C2×D43semidirect
808. C43#62829semidirect

Maximal subgroups

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

subgroupindex
#191492712
#191492232
#191491512
#191491012
#191490222
#191488442
#191488342
#191488222
#191485842
#191485732
#191485562
#191485392
#191485212
#191485172
#191484912
#191483072
#191482872
C2×#145834332
C43×#34442
#6282943