Finite Group Databasebeta

← #25967320

Subgroups — #25967320

Order 11008.

2166 conjugacy classes of subgroups.

The subgroup lattice has 1284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147924C211yesmaximal, characteristic, complemented
2#19145501C212yesmaximal, complemented
3#19145492C212yesmaximal, complemented
4#19145486C211yesmaximal, characteristic, complemented
5#19145477C212yesmaximal, complemented
6#19145471C212yesmaximal, complemented
7#19145467C211yesmaximal, characteristic, complemented
8#19145462C211yesmaximal, characteristic, complemented
9#19145456C211yesmaximal, characteristic, complemented
10#19145447C212yesmaximal, complemented
11#19145441C212yesmaximal, complemented
12#19144508C212yesmaximal, complemented
13#19144504C212yesmaximal, complemented
14#19144201C212yesmaximal, complemented
15#19144173C212yesmaximal, complemented
16#19143813C212yesmaximal, complemented
17#19143811C212yesmaximal, complemented
18C2×#14582866C211yesmaximal, characteristic, complemented
19C43×#3449C211yesmaximal, characteristic, complemented
20C22×#10621898C2211yescharacteristic, complemented
21C2×#13063345C2212yes—
22C2×#13063345C2212yes—
23C22×#10621877C2211yescharacteristic, complemented
24C23×C43⋊C8C2211yescharacteristic, complemented
25#14583477C2212yes—
26#14583477C2212yescomplemented
27#14583473—21no—
28#14583470C2211yescharacteristic
29#14583470C2211yescharacteristic, complemented
30#14583466—21no—
31#14583463C2211yescharacteristic
32#14583463C2211yescharacteristic, complemented
33#14583458—21no—
34#14583458—21no—
35#14583445—21no—
36#14583445—21no—
37#14583410C2212yes—
38#14583410C2212yescomplemented
39#14583406—21no—
40#14583406—21no—
41C2×#13063284C2211yescharacteristic, complemented
42#14583240C2212yescomplemented
43#14583240C2212yescomplemented
44#14583237C2212yescomplemented
45#14583237C2212yescomplemented
46#14583234C2212yescomplemented
47#14583232C2212yescomplemented
48#14583229C2212yescomplemented
49#14583227C2212yescomplemented
50#14583223C2212yescomplemented
51#14583223C2212yescomplemented
52#14583220C2212yescomplemented
53#14583220C2212yescomplemented
54#14583217C2212yescomplemented
55#14583215C2212yescomplemented
56#14583212C2212yescomplemented
57#14583210C2212yescomplemented
58#14583155C2212yescomplemented
59#14583155C2212yescomplemented
60#14583150C2212yescomplemented
61#14583150C2212yescomplemented
62#14583147C2212yescomplemented
63#14583147C2212yescomplemented
64#14583143C2212yescomplemented
65#14583143C2212yescomplemented
66#14583138C2212yescomplemented
67#14583138C2212yescomplemented
68#14583133C2212yescomplemented
69#14583133C2212yescomplemented
70#14583130C2212yescomplemented
71#14583130C2212yescomplemented
72#14583126C2212yescomplemented
73#14583126C2212yescomplemented
74#14583061C2212yescomplemented
75#14583061C2212yescomplemented
76#14583059C2212yescomplemented
77#14583059C2212yescomplemented
78#14583055C2212yescomplemented
79#14583054C2212yescomplemented
80#14583050C2212yescomplemented
81#14583049C2212yescomplemented
82#14583044C2212yescomplemented
83#14583044C2212yescomplemented
84#14583042C2212yescomplemented
85#14583042C2212yescomplemented
86#14583038C2212yescomplemented
87#14583037C2212yescomplemented
88#14583033C2212yescomplemented
89#14583032C2212yescomplemented
90#14582935C2212yescomplemented
91#14582935C2212yescomplemented
92#14582895C2212yescomplemented
93#14582895C2212yescomplemented
94#14582893C2212yescomplemented
95#14582893C2212yescomplemented
96#14582866C2211yescharacteristic
97#14582866C2211yescharacteristic
98#14582866C2212yescomplemented
99#14582866C2211yescharacteristic, complemented
100#14582866C2211yescharacteristic, complemented
101#14582866C2212yescomplemented
102C2×C22⋊(C43⋊C8)C2212yescomplemented
103C2×C22⋊(C43⋊C8)C2212yescomplemented
104C22×#41×C43C2211yescharacteristic
105C22×#41×C43C2211yescharacteristic, complemented
106C43×#537C2212yes—
107C43×#537C2212yescomplemented
108C43×#536—21no—
109C43×#536C2211yescharacteristic
110C43×#536C2211yescharacteristic, complemented
111C43×#535—21no—
112C43×#535C2211yescharacteristic
113C43×#535C2211yescharacteristic, complemented
114C43×#534—21no—
115C43×#534—21no—
116C43×#532—21no—
117C43×#532—21no—
118C43×#525—21no—
119C43×#525—21no—
120C43×#525C2212yes—
121C43×#525C2212yescomplemented
122C2×#117×C43C2211yescharacteristic, complemented
123C2×#10621898—21no—
124C2×#10621898—21no—
125C2×#10621898—42no—
126C2×#10621898—42no—
127C2×#10621898C2312yes—
128C2×#10621898C2312yes—
129C22×Dic86C2311yescharacteristic
130C22×D172C2311yescharacteristic
131C22×C22⋊D43—21no—
132C22×C4×D43—21no—
133#13063345—44no—
134#13063345—44no—
135C2×#10621885C2312yes—
136C2×#10621885C2312yes—
137C2×#10621883C2312yes—
138C2×#10621883C2312yes—
139C2×#10621884C2312yes—
140C2×#10621884C2312yes—
141C2×#10621882C2312yes—
142C2×#10621882C2312yes—
143C2×#10621877—42no—
144C2×#10621877C2311yescharacteristic
145C2×#10621877C2311yescharacteristic
146C2×#10621877C2312yes—
147C22×C43⋊C8—42no—
148C22×C43⋊C8C2312yes—
149C22×C43⋊C8C2312yes—
150C22×C43⋊C8C2311yescharacteristic
151C22×C43⋊C8C2311yescharacteristic
152C22×C43⋊C8C2312yes—
153#13063323—21no—
154#13063323—21no—
155#13063321—21no—
156#13063321—21no—
157#13063314—21no—
158#13063314—21no—
159#13063312—21no—
160#13063312—21no—
161#13063308—22no—
162#13063308—22no—
163#13063306—21no—
164#13063306—21no—
165#13063306—21no—
166#13063306—21no—
167#13063304C2312yes—
168#13063304C2312yes—
169#13063304C2312yes—
170#13063304C2312yes—
171#13063301—22no—
172#13063301—22no—
173#13063299C2312yes—
174#13063299C2312yes—
175#13063299C2312yes—
176#13063299C2312yes—
177#13063297—22no—
178#13063297—22no—
179#13063297—22no—
180#13063297—22no—
181#13063296—22no—
182#13063296—22no—
183#13063294—22no—
184#13063294—22no—
185#13063293—21no—
186#13063293—21no—
187#13063293—21no—
188#13063293—21no—
189C4×C22⋊D43—22no—
190C4×C22⋊D43—22no—
191C4×C22⋊D43—22no—
192C4×C22⋊D43—22no—
193#13063284—21no—
194#13063284—21no—
195#13063284C2312yes—
196#13063284C2311yescharacteristic
197#13063284C2311yescharacteristic
198C2×C4⋊Dic43C2312yes—
199C2×C22⋊Dic43—21no—
200C2×C4×Dic43—21no—
201#13063258C2312yes—
202#13063258C2312yes—
203#13063258C2312yes—
204#13063258C2312yes—
205#13063256C2312yes—
206#13063256C2312yes—
207#13063256C2312yes—
208#13063256C2312yes—
209#13063249C2312yes—
210#13063249C2312yes—
211#13063249C2312yes—
212#13063249C2312yes—
213#13063248C2312yes—
214#13063248C2312yes—
215#13063248C2312yes—
216#13063248C2312yes—
217#13063246C2312yes—
218#13063246C2312yes—
219#13063246C2312yes—
220#13063246C2312yes—
221#13063245C2312yes—
222#13063245C2312yes—
223#13063245C2312yes—
224#13063245C2312yes—
225C22⋊(C43⋊C8)C2312yes—
226C22⋊(C43⋊C8)C2312yes—
227C22⋊(C43⋊C8)C2312yes—
228C22⋊(C43⋊C8)C2312yes—
229C22⋊(C43⋊C8)C2312yes—
230C22⋊(C43⋊C8)C2312yes—
231C22⋊(C43⋊C8)C2312yes—
232C22⋊(C43⋊C8)C2312yes—
233C2×#41×C43—21no—
234C2×#41×C43—21no—
235C2×#41×C43—42no—
236C2×#41×C43—42no—
237C2×#41×C43—42no—
238C2×#41×C43—42no—
239C2×#41×C43D411yescharacteristic
240C2×#41×C43D411yescharacteristic
241C2×#41×C43D411yescharacteristic
242C2×#41×C43D411yescharacteristic
243C2×#41×C43C2312yes—
244C2×#41×C43C2312yes—
245C2×#41×C43C2311yescharacteristic
246C2×#41×C43C2311yescharacteristic
247C2×#41×C43C2311yescharacteristic
248C2×#41×C43C2311yescharacteristic
249C22×Q8×C43D411yescharacteristic
250C22×Q8×C43C2311yescharacteristic
251C22×D4×C43—21no—
252C22×D4×C43D411yescharacteristic
253C22×D4×C43D411yescharacteristic
254C22×D4×C43D411yescharacteristic
255C22×D4×C43C2311yescharacteristic
256C23×C4×C43—21no—
257C23×C4×C43C2311yescharacteristic
258C23×C4×C43C2311yescharacteristic
259C23×C4×C43C2311yescharacteristic
260C4⋊Q8×C43—21no—
261C4⋊Q8×C43—21no—
262#127×C43—21no—
263#127×C43—21no—
264#124×C43—21no—
265#124×C43—21no—
266#124×C43—21no—
267#124×C43—21no—
268#123×C43—21no—
269#123×C43—21no—
270#123×C43—21no—
271#123×C43—21no—
272#123×C43—22no—
273#123×C43—22no—
274C22⋊Q8×C43—22no—
275C22⋊Q8×C43—22no—
276C22⋊Q8×C43C2312yes—
277C22⋊Q8×C43C2312yes—
278C22⋊Q8×C43C2312yes—
279C22⋊Q8×C43C2312yes—
280#121×C43—22no—
281#121×C43—22no—
282#121×C43—22no—
283#121×C43—22no—
284#121×C43—22no—
285#121×C43—22no—
286#121×C43C2312yes—
287#121×C43C2312yes—
288#121×C43C2312yes—
289#121×C43C2312yes—
290#120×C43—22no—
291#120×C43—22no—
292#120×C43—21no—
293#120×C43—21no—
294#120×C43—21no—
295#120×C43—21no—
296C4×D4×C43—22no—
297C4×D4×C43—22no—
298C4×D4×C43—22no—
299C4×D4×C43—22no—
300#117×C43—21no—
301#117×C43—21no—
302#117×C43C2312yes—
303#117×C43C2311yescharacteristic
304#117×C43C2311yescharacteristic
305C2×C4⋊C4×C43C2312yes—
306C2×C22⋊C4×C43—21no—
307C2×C42×C43—21no—
308C24×C43—21no—
309C24×C43C2×D411yescharacteristic
310C24×C43C2×D411yescharacteristic
311C24×C43C2×D411yescharacteristic
312C23×D43—21no—
313#41×C43—24no—
314#41×C43—24no—
315#41×C43—42no—
316#41×C43—42no—
317#41×C43—42no—
318#41×C43—42no—
319#41×C43—41no—
320#41×C43—41no—
321#41×C43—41no—
322#41×C43—41no—
323#41×C43—41no—
324#41×C43—41no—
325#41×C43—41no—
326#41×C43—41no—
327#41×C43—42no—
328#41×C43—42no—
329#41×C43—44no—
330#41×C43—44no—
331C2×Q8×C43—21no—
332C2×Q8×C43—42no—
333C2×Q8×C43—41no—
334C2×Q8×C43—41no—
335C2×Q8×C43C2×D411yescharacteristic
336C2×Q8×C43C2×D411yescharacteristic
337C2×Q8×C43C2×D411yescharacteristic
338C2×Q8×C43C2×D411yescharacteristic
339C2×Q8×C43C2412yes—
340C2×D4×C43—21no—
341C2×D4×C43—22no—
342C2×D4×C43—22no—
343C2×D4×C43—22no—
344C2×D4×C43—22no—
345C2×D4×C43—22no—
346C2×D4×C43—22no—
347C2×D4×C43—42no—
348C2×D4×C43—42no—
349C2×D4×C43—42no—
350C2×D4×C43—44no—
351C2×D4×C43—41no—
352C2×D4×C43—41no—
353C2×D4×C43C2×D411yescharacteristic
354C2×D4×C43C2×D411yescharacteristic
355C2×D4×C43C2×D411yescharacteristic
356C2×D4×C43C2×D411yescharacteristic
357C2×D4×C43C2×D411yescharacteristic
358C2×D4×C43C2×D411yescharacteristic
359C2×D4×C43C2×D411yescharacteristic
360C2×D4×C43C2×D411yescharacteristic
361C2×D4×C43C2×D411yescharacteristic
362C2×D4×C43C2×D411yescharacteristic
363C2×D4×C43C2×D411yescharacteristic
364C2×D4×C43C2×D411yescharacteristic
365C2×D4×C43C2412yes—
366C22×C4×C43—22no—
367C22×C4×C43—22no—
368C22×C4×C43—22no—
369C22×C4×C43—22no—
370C22×C4×C43—22no—
371C22×C4×C43—22no—
372C22×C4×C43—22no—
373C22×C4×C43—22no—
374C22×C4×C43—21no—
375C22×C4×C43—22no—
376C22×C4×C43—44no—
377C22×C4×C43C2×D411yescharacteristic
378C22×C4×C43C2×D411yescharacteristic
379C22×C4×C43C2×D411yescharacteristic
380C22×C4×C43C2×D411yescharacteristic
381C22×C4×C43C2×D411yescharacteristic
382C22×C4×C43C2×D411yescharacteristic
383C22×C4×C43C2×D411yescharacteristic
384C22×C4×C43C2×D411yescharacteristic
385C22×C4×C43C2×D411yescharacteristic
386C22×C4×C43C2411yescharacteristic
387C22×C4×C43C2411yescharacteristic
388C22×C4×C43C2411yescharacteristic
389C22×C4×C43C2411yescharacteristic
390C22×C4×C43C2411yescharacteristic
391C22×C4×C43C2411yescharacteristic
392C22×C4×C43C2411yescharacteristic
393C2×C22⋊D43—22no—
394C2×C22⋊D43—22no—
395C2×C22⋊D43—22no—
396C2×C22⋊D43—22no—
397C2×C22⋊D43—22no—
398C2×C22⋊D43—22no—
399C2×C22⋊D43—44no—
400C22×Dic43—21no—
401C22×Dic43—22no—
402#10621898—24no—
403#10621898—24no—
404#10621898—42no—
405#10621898—42no—
406#10621898—44no—
407#10621898—44no—
408C2×D172—21no—
409C2×D172—41no—
410C2×D172—41no—
411C2×D172C2412yes—
412C2×C4×D43—22no—
413C2×C4×D43—22no—
414C2×C4×D43—44no—
415C2×Dic86—21no—
416C2×Dic86—41no—
417C2×Dic86—41no—
418C2×Dic86C2412yes—
419C4⋊C4×C43—22no—
420C4⋊C4×C43—22no—
421C4⋊C4×C43—22no—
422C4⋊C4×C43—22no—
423C4⋊C4×C43—22no—
424C4⋊C4×C43C2412yes—
425C4⋊C4×C43C2412yes—
426C22⋊C4×C43—22no—
427C22⋊C4×C43—22no—
428C22⋊C4×C43—22no—
429C22⋊C4×C43—22no—
430C22⋊C4×C43—21no—
431C22⋊C4×C43—21no—
432C22⋊C4×C43—22no—
433C22⋊C4×C43—22no—
434C22⋊C4×C43—22no—
435C22⋊C4×C43—22no—
436C22⋊C4×C43—22no—
437C42×C43—22no—
438C42×C43—21no—
439C42×C43—21no—
440C22⋊Dic43—21no—
441C22⋊Dic43—21no—
442C22⋊Dic43—22no—
443C22⋊Dic43—22no—
444C22⋊Dic43—22no—
445C22⋊Dic43—22no—
446C22⋊Dic43—22no—
447#10621885—42no—
448#10621885—42no—
449#10621884—42no—
450#10621884—42no—
451#10621883—42no—
452#10621883—42no—
453#10621882—42no—
454#10621882—42no—
455(C2×D43)⋊C4—22no—
456(C2×D43)⋊C4—22no—
457(C2×D43)⋊C4—22no—
458(C2×D43)⋊C4—22no—
459C4⋊Dic43—22no—
460C4⋊Dic43C2412yes—
461C4⋊Dic43C2412yes—
462Dic43⋊C4—22no—
463Dic43⋊C4—22no—
464Dic43⋊C4—22no—
465Dic43⋊C4—22no—
466C4×Dic43—22no—
467C4×Dic43—21no—
468C4×Dic43—21no—
469#10621877—41no—
470#10621877—42no—
471#10621877—41no—
472C2×C43⋊C8—24no—
473C2×C43⋊C8—24no—
474C2×C43⋊C8—41no—
475C2×C43⋊C8—42no—
476C2×C43⋊C8—41no—
477C2×C43⋊C8C2412yes—
478C2×C43⋊C8C2412yes—
479C2×C43⋊C8C2412yes—
480C2×C43⋊C8C2412yes—
481C23×C43—22no—
482C23×C43—22no—
483C23×C43—22no—
484C23×C43—22no—
485C23×C43—42no—
486C23×C43—42no—
487C23×C43—42no—
488C23×C43—42no—
489C23×C43—82no—
490C23×C43C22×D411yescharacteristic
491C23×C43C22×D411yescharacteristic
492C23×C43C22×D411yescharacteristic
493C23×C43C22×D411yescharacteristic
494C23×C43C22×D411yescharacteristic
495C23×C43C22×D411yescharacteristic
496C23×C43C22×D411yescharacteristic
497C22×D43—22no—
498C22×D43—42no—
499C22×D43—82no—
500Q8×C43—22no—
501Q8×C43—22no—
502Q8×C43—41no—
503Q8×C43—41no—
504Q8×C43—41no—
505Q8×C43—41no—
506Q8×C43—42no—
507D4×C43—22no—
508D4×C43—22no—
509D4×C43—41no—
510D4×C43—41no—
511D4×C43—41no—
512D4×C43—41no—
513D4×C43—41no—
514D4×C43—41no—
515D4×C43—41no—
516D4×C43—41no—
517D4×C43—41no—
518D4×C43—41no—
519D4×C43—41no—
520D4×C43—41no—
521D4×C43—42no—
522D4×C43—44no—
523D4×C43—44no—
524D4×C43—82no—
525D4×C43—82no—
526D4×C43—82no—
527D4×C43—82no—
528C2×C4×C43—22no—
529C2×C4×C43—22no—
530C2×C4×C43—22no—
531C2×C4×C43—22no—
532C2×C4×C43—22no—
533C2×C4×C43—22no—
534C2×C4×C43—22no—
535C2×C4×C43—22no—
536C2×C4×C43—22no—
537C2×C4×C43—21no—
538C2×C4×C43—21no—
539C2×C4×C43—21no—
540C2×C4×C43—21no—
541C2×C4×C43—21no—
542C2×C4×C43—21no—
543C2×C4×C43—21no—
544C2×C4×C43—21no—
545C2×C4×C43—21no—
546C2×C4×C43—21no—
547C2×C4×C43—21no—
548C2×C4×C43—21no—
549C2×C4×C43—22no—
550C2×C4×C43—22no—
551C2×C4×C43—22no—
552C2×C4×C43—44no—
553C2×C4×C43—42no—
554C2×C4×C43—44no—
555C2×C4×C43—82no—
556C2×C4×C43C22×D411yescharacteristic
557C2×C4×C43C22×D411yescharacteristic
558C2×C4×C43C22×D411yescharacteristic
559C2×C4×C43C22×D411yescharacteristic
560C2×C4×C43C22×D411yescharacteristic
561C2×C4×C43C22×D411yescharacteristic
562C2×C4×C43C22×D411yescharacteristic
563C2×C4×C43H(5,𝔽2)12yes—
564C2×C4×C43H(5,𝔽2)12yes—
565C2×C4×C43C2511yescharacteristic
566C22⋊D43—44no—
567C22⋊D43—44no—
568C22⋊D43—82no—
569C22⋊D43—82no—
570C22⋊D43—82no—
571C22⋊D43—82no—
572C2×Dic43—22no—
573C2×Dic43—22no—
574C2×Dic43—22no—
575C2×Dic43—42no—
576C2×Dic43—82no—
577D172—22no—
578D172—22no—
579D172—42no—
580C4×D43—44no—
581C4×D43—44no—
582Dic86—22no—
583Dic86—22no—
584Dic86—42no—
585C43⋊C8—22no—
586C43⋊C8—22no—
587C43⋊C8—22no—
588C43⋊C8—22no—
589#60749—431nomaximal, Sylow
590C22×C43—22no—
591C22×C43—22no—
592C22×C43—22no—
593C22×C43—22no—
594C22×C43—22no—
595C22×C43—22no—
596C22×C43—22no—
597C22×C43—21no—
598C22×C43—21no—
599C22×C43—21no—
600C22×C43—21no—
601C22×C43—21no—
602C22×C43—21no—
603C22×C43—44no—
604C22×C43—42no—
605C22×C43—42no—
606C22×C43—42no—
607C22×C43—82no—
608C22×C43—82no—
609C22×C43—84no—
610C22×C43#53412yes—
611C22×C43C23×D411yescharacteristic
612C2×D43—42no—
613C2×D43—42no—
614C2×D43—42no—
615C2×D43—84no—
616C4×C43—21no—
617C4×C43—21no—
618C4×C43—21no—
619C4×C43—21no—
620C4×C43—21no—
621C4×C43—21no—
622C4×C43—42no—
623C4×C43—42no—
624C4×C43—42no—
625C4×C43#53412yes—
626C4×C43C2×H(5,𝔽2)11yescharacteristic
627C4×C43C2×H(5,𝔽2)11yescharacteristic
628Dic43—42no—
629Dic43—42no—
630Dic43—42no—
631#3449—431no—
632#3449D4311yescharacteristic, complemented
633#3204—432no—
634#3203—432no—
635#3202—431no—
636#3201—432no—
637#3201—432no—
638#3200—431no—
639#3200—431no—
640#3199—431no—
641#3198—432no—
642#3198—432no—
643#3091—432no—
644#3091—432no—
645#3054—432no—
646#3050—432no—
647#3002—432no—
648#3002—432no—
649C2×#408—431no—
650C2×C43—22no—
651C2×C43—41no—
652C2×C43—41no—
653C2×C43—41no—
654C2×C43—41no—
655C2×C43—41no—
656C2×C43—41no—
657C2×C43—82no—
658C2×C43C2×#53411yescharacteristic
659C2×C43#358412yes—
660D43—82no—
661C22×#41—431no—
662C22×#41C2×D4311yescharacteristic
663C22×#41C2×D4311yescharacteristic, complemented
664C2×#135—432no—
665C2×#135—432no—
666C22×M16—431no—
667C23×C8—431no—
668#537—432no—
669#537—432no—
670#537C2×D4312yes—
671#537C2×D4312yescomplemented
672#536—21no—
673#536—431no—
674#536—431no—
675#536—861no—
676#536C2×D4311yescharacteristic
677#536C2×D4311yescharacteristic, complemented
678#535—21no—
679#535—431no—
680#535—431no—
681#535—861no—
682#535C2×D4311yescharacteristic
683#535C2×D4311yescharacteristic, complemented
684#534—21no—
685#534—21no—
686#534—861no—
687#534—861no—
688#532—21no—
689#532—21no—
690#532—861no—
691#532—861no—
692#525—21no—
693#525—21no—
694#525—432no—
695#525—432no—
696#525—861no—
697#525—861no—
698#525C2×D4312yes—
699#525C2×D4312yescomplemented
700C2×#117—431no—
701C2×#117C2×D4311yescharacteristic, complemented
702#485—432no—
703#485—432no—
704#485—432no—
705#485—432no—
706#484—432no—
707#484—432no—
708#483—432no—
709#483—432no—
710#482—432no—
711#482—432no—
712#482—432no—
713#482—432no—
714#481—432no—
715#481—432no—
716#480—432no—
717#480—432no—
718#470—432no—
719#470—432no—
720#469—432no—
721#469—432no—
722#468—432no—
723#468—432no—
724#468—432no—
725#468—432no—
726#467—432no—
727#467—432no—
728#466—432no—
729#466—432no—
730#465—432no—
731#465—432no—
732#465—432no—
733#465—432no—
734#452—432no—
735#452—432no—
736#452—432no—
737#452—432no—
738#451—432no—
739#451—432no—
740#450—432no—
741#450—432no—
742#449—432no—
743#449—432no—
744#449—432no—
745#449—432no—
746#448—432no—
747#448—432no—
748#447—432no—
749#447—432no—
750#427—432no—
751#427—432no—
752#416—432no—
753#416—432no—
754#416—432no—
755#416—432no—
756#408—431no—
757#408—431no—
758#408—432no—
759#408—432no—
760#408—431no—
761#408—431no—
762C2×C22⋊C8—432no—
763C2×C22⋊C8—432no—
764C43#6074911yescharacteristic, complemented, Sylow
765C2×#41—21no—
766C2×#41—21no—
767C2×#41—42no—
768C2×#41—42no—
769C2×#41—42no—
770C2×#41—42no—
771C2×#41—432no—
772C2×#41—432no—
773C2×#41—861no—
774C2×#41—861no—
775C2×#41—1722no—
776C2×#41—1722no—
777C2×#41C22⋊D4311yescharacteristic
778C2×#41C22⋊D4311yescharacteristic
779C2×#41C22⋊D4311yescharacteristic
780C2×#41C22⋊D4311yescharacteristic
781C2×#41C22×D4312yes—
782C2×#41C22×D4312yes—
783C2×#41C22×D4311yescharacteristic
784C2×#41C22×D4311yescharacteristic
785C2×#41C22×D4311yescharacteristic
786C2×#41C22×D4311yescharacteristic
787C22×Q8—431no—
788C22×Q8C22⋊D4311yescharacteristic
789C22×Q8C22×D4311yescharacteristic
790C22×D4—21no—
791C22×D4—431no—
792C22×D4—861no—
793C22×D4C22⋊D4311yescharacteristic
794C22×D4C22⋊D4311yescharacteristic
795C22×D4C22⋊D4311yescharacteristic
796C22×D4C22×D4311yescharacteristic
797C23×C4—21no—
798C23×C4—861no—
799C23×C4C22×D4311yescharacteristic
800C23×C4C22×D4311yescharacteristic
801C23×C4C22×D4311yescharacteristic
802#135—1724no—
803#135—1724no—
804C2×Q16—432no—
805C2×Q16—432no—
806C2×SD16—432no—
807C2×SD16—432no—
808C2×SD16—432no—
809C2×SD16—432no—
810C2×D8—432no—
811C2×D8—432no—
812C2×M16—431no—
813C2×M16—432no—
814C2×M16—431no—
815C2×M16—1722no—
816C22×C8—432no—
817C22×C8—432no—
818C22×C8—431no—
819C22×C8—432no—
820C22×C8—431no—
821C22×C8—1722no—
822C4⋊Q8—21no—
823C4⋊Q8—21no—
824C4⋊Q8—861no—
825C4⋊Q8—861no—
826#127—21no—
827#127—21no—
828#127—861no—
829#127—861no—
830#124—21no—
831#124—21no—
832#124—21no—
833#124—21no—
834#124—861no—
835#124—861no—
836#124—861no—
837#124—861no—
838#123—21no—
839#123—21no—
840#123—21no—
841#123—21no—
842#123—22no—
843#123—22no—
844#123—861no—
845#123—861no—
846#123—861no—
847#123—861no—
848#123—862no—
849#123—862no—
850C22⋊Q8—22no—
851C22⋊Q8—22no—
852C22⋊Q8—432no—
853C22⋊Q8—432no—
854C22⋊Q8—432no—
855C22⋊Q8—432no—
856C22⋊Q8—862no—
857C22⋊Q8—862no—
858C22⋊Q8C22×D4312yes—
859C22⋊Q8C22×D4312yes—
860C22⋊Q8C22×D4312yes—
861C22⋊Q8C22×D4312yes—
862#121—22no—
863#121—22no—
864#121—22no—
865#121—22no—
866#121—22no—
867#121—22no—
868#121—432no—
869#121—432no—
870#121—432no—
871#121—432no—
872#121—862no—
873#121—862no—
874#121—862no—
875#121—862no—
876#121—862no—
877#121—862no—
878#121C22×D4312yes—
879#121C22×D4312yes—
880#121C22×D4312yes—
881#121C22×D4312yes—
882#120—22no—
883#120—22no—
884#120—21no—
885#120—21no—
886#120—21no—
887#120—21no—
888#120—862no—
889#120—862no—
890#120—861no—
891#120—861no—
892#120—861no—
893#120—861no—
894C4×D4—22no—
895C4×D4—22no—
896C4×D4—22no—
897C4×D4—22no—
898C4×D4—862no—
899C4×D4—862no—
900C4×D4—862no—
901C4×D4—862no—
902#117—21no—
903#117—21no—
904#117—432no—
905#117—431no—
906#117—431no—
907#117—861no—
908#117—861no—
909#117C22×D4312yes—
910#117C22×D4311yescharacteristic
911#117C22×D4311yescharacteristic
912C2×C4⋊C4—432no—
913C2×C4⋊C4C22×D4312yes—
914C2×C22⋊C4—21no—
915C2×C22⋊C4—861no—
916C2×C42—21no—
917C2×C42—861no—
918#107—432no—
919#107—432no—
920#107—432no—
921#107—432no—
922#106—432no—
923#106—432no—
924#106—432no—
925#106—432no—
926#103—432no—
927#103—432no—
928#103—432no—
929#103—432no—
930#103—432no—
931#103—432no—
932#103—432no—
933#103—432no—
934#102—432no—
935#102—432no—
936#102—432no—
937#102—432no—
938#102—432no—
939#102—432no—
940#102—432no—
941#102—432no—
942C22⋊C8—432no—
943C22⋊C8—432no—
944C22⋊C8—432no—
945C22⋊C8—432no—
946C22⋊C8—432no—
947C22⋊C8—432no—
948C22⋊C8—432no—
949C22⋊C8—432no—
950C24—21no—
951C24—861no—
952C24C2×C22⋊D4311yescharacteristic
953C24C2×C22⋊D4311yescharacteristic
954C24C2×C22⋊D4311yescharacteristic
955#41—24no—
956#41—24no—
957#41—41no—
958#41—41no—
959#41—41no—
960#41—41no—
961#41—41no—
962#41—41no—
963#41—41no—
964#41—41no—
965#41—42no—
966#41—42no—
967#41—42no—
968#41—42no—
969#41—42no—
970#41—42no—
971#41—44no—
972#41—44no—
973#41—864no—
974#41—864no—
975#41—1722no—
976#41—1722no—
977#41—1724no—
978#41—1724no—
979C2×Q8—21no—
980C2×Q8—42no—
981C2×Q8—41no—
982C2×Q8—41no—
983C2×Q8—432no—
984C2×Q8—861no—
985C2×Q8—1721no—
986C2×Q8—1721no—
987C2×Q8C2×C22⋊D4311yescharacteristic
988C2×Q8C2×C22⋊D4311yescharacteristic
989C2×Q8C2×C22⋊D4311yescharacteristic
990C2×Q8C2×C22⋊D4311yescharacteristic
991C2×Q8C23×D4312yes—
992C2×D4—22no—
993C2×D4—22no—
994C2×D4—22no—
995C2×D4—22no—
996C2×D4—22no—
997C2×D4—22no—
998C2×D4—21no—
999C2×D4—41no—
1000C2×D4—41no—
1001C2×D4—42no—
1002C2×D4—42no—
1003C2×D4—42no—
1004C2×D4—44no—
1005C2×D4—432no—
1006C2×D4—862no—
1007C2×D4—862no—
1008C2×D4—862no—
1009C2×D4—862no—
1010C2×D4—862no—
1011C2×D4—862no—
1012C2×D4—861no—
1013C2×D4—1721no—
1014C2×D4—1721no—
1015C2×D4—1724no—
1016C2×D4C2×C22⋊D4311yescharacteristic
1017C2×D4C2×C22⋊D4311yescharacteristic
1018C2×D4C2×C22⋊D4311yescharacteristic
1019C2×D4C2×C22⋊D4311yescharacteristic
1020C2×D4C2×C22⋊D4311yescharacteristic
1021C2×D4C2×C22⋊D4311yescharacteristic
1022C2×D4C2×C22⋊D4311yescharacteristic
1023C2×D4C2×C22⋊D4311yescharacteristic
1024C2×D4C2×C22⋊D4311yescharacteristic
1025C2×D4C2×C22⋊D4311yescharacteristic
1026C2×D4C2×C22⋊D4311yescharacteristic
1027C2×D4C2×C22⋊D4311yescharacteristic
1028C2×D4C23×D4312yes—
1029C22×C4—22no—
1030C22×C4—22no—
1031C22×C4—22no—
1032C22×C4—22no—
1033C22×C4—22no—
1034C22×C4—22no—
1035C22×C4—21no—
1036C22×C4—22no—
1037C22×C4—22no—
1038C22×C4—22no—
1039C22×C4—44no—
1040C22×C4—862no—
1041C22×C4—861no—
1042C22×C4—862no—
1043C22×C4—862no—
1044C22×C4—1724no—
1045C22×C4C2×C22⋊D4311yescharacteristic
1046C22×C4C2×C22⋊D4311yescharacteristic
1047C22×C4C2×C22⋊D4311yescharacteristic
1048C22×C4C2×C22⋊D4311yescharacteristic
1049C22×C4C2×C22⋊D4311yescharacteristic
1050C22×C4C2×C22⋊D4311yescharacteristic
1051C22×C4C2×C22⋊D4311yescharacteristic
1052C22×C4C2×C22⋊D4311yescharacteristic
1053C22×C4C2×C22⋊D4311yescharacteristic
1054C22×C4C23×D4311yescharacteristic
1055C22×C4C23×D4311yescharacteristic
1056C22×C4C23×D4311yescharacteristic
1057C22×C4C23×D4311yescharacteristic
1058C22×C4C23×D4311yescharacteristic
1059C22×C4C23×D4311yescharacteristic
1060C22×C4C23×D4311yescharacteristic
1061Q16—1722no—
1062Q16—1722no—
1063SD16—1722no—
1064SD16—1722no—
1065SD16—1722no—
1066SD16—1722no—
1067D8—1722no—
1068D8—1722no—
1069M16—1721no—
1070M16—1722no—
1071M16—1721no—
1072C2×C8—432no—
1073C2×C8—432no—
1074C2×C8—432no—
1075C2×C8—432no—
1076C2×C8—864no—
1077C2×C8—864no—
1078C2×C8—1721no—
1079C2×C8—1722no—
1080C2×C8—1721no—
1081C4⋊C4—22no—
1082C4⋊C4—22no—
1083C4⋊C4—22no—
1084C4⋊C4—22no—
1085C4⋊C4—22no—
1086C4⋊C4—432no—
1087C4⋊C4—432no—
1088C4⋊C4—862no—
1089C4⋊C4—862no—
1090C4⋊C4—862no—
1091C4⋊C4—862no—
1092C4⋊C4—862no—
1093C4⋊C4C23×D4312yes—
1094C4⋊C4C23×D4312yes—
1095C22⋊C4—21no—
1096C22⋊C4—21no—
1097C22⋊C4—22no—
1098C22⋊C4—22no—
1099C22⋊C4—22no—
1100C22⋊C4—22no—
1101C22⋊C4—22no—
1102C22⋊C4—22no—
1103C22⋊C4—22no—
1104C22⋊C4—22no—
1105C22⋊C4—22no—
1106C22⋊C4—861no—
1107C22⋊C4—861no—
1108C22⋊C4—862no—
1109C22⋊C4—862no—
1110C22⋊C4—862no—
1111C22⋊C4—862no—
1112C22⋊C4—862no—
1113C22⋊C4—862no—
1114C22⋊C4—862no—
1115C22⋊C4—862no—
1116C22⋊C4—862no—
1117C42—21no—
1118C42—21no—
1119C42—22no—
1120C42—861no—
1121C42—861no—
1122C42—862no—
1123C23—22no—
1124C23—22no—
1125C23—22no—
1126C23—22no—
1127C23—42no—
1128C23—42no—
1129C23—42no—
1130C23—42no—
1131C23—82no—
1132C23—862no—
1133C23—3442no—
1134C23—1722no—
1135C23C22×C22⋊D4311yescharacteristic
1136C23C22×C22⋊D4311yescharacteristic
1137C23C22×C22⋊D4311yescharacteristic
1138C23C22×C22⋊D4311yescharacteristic
1139C23C22×C22⋊D4311yescharacteristic
1140C23C22×C22⋊D4311yescharacteristic
1141C23C22×C22⋊D4311yescharacteristic
1142Q8—22no—
1143Q8—22no—
1144Q8—41no—
1145Q8—41no—
1146Q8—41no—
1147Q8—41no—
1148Q8—42no—
1149Q8—862no—
1150Q8—862no—
1151Q8—1722no—
1152D4—22no—
1153D4—22no—
1154D4—41no—
1155D4—41no—
1156D4—41no—
1157D4—41no—
1158D4—41no—
1159D4—41no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—41no—
1164D4—41no—
1165D4—41no—
1166D4—42no—
1167D4—44no—
1168D4—44no—
1169D4—82no—
1170D4—82no—
1171D4—82no—
1172D4—82no—
1173D4—862no—
1174D4—862no—
1175D4—3442no—
1176D4—3442no—
1177D4—3442no—
1178D4—3442no—
1179D4—1722no—
1180D4—1724no—
1181D4—1724no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—44no—
1207C2×C4—42no—
1208C2×C4—44no—
1209C2×C4—82no—
1210C2×C4—862no—
1211C2×C4—862no—
1212C2×C4—862no—
1213C2×C4—3442no—
1214C2×C4—1724no—
1215C2×C4—1722no—
1216C2×C4—1724no—
1217C2×C4C22×C22⋊D4311yescharacteristic
1218C2×C4C22×C22⋊D4311yescharacteristic
1219C2×C4C22×C22⋊D4311yescharacteristic
1220C2×C4C22×C22⋊D4311yescharacteristic
1221C2×C4C22×C22⋊D4311yescharacteristic
1222C2×C4C22×C22⋊D4311yescharacteristic
1223C2×C4C22×C22⋊D4311yescharacteristic
1224C2×C4#1306337012yes—
1225C2×C4#1306337012yes—
1226C2×C4C24×D4311yescharacteristic
1227C8—862no—
1228C8—862no—
1229C8—862no—
1230C8—862no—
1231C22—22no—
1232C22—22no—
1233C22—22no—
1234C22—22no—
1235C22—22no—
1236C22—22no—
1237C22—22no—
1238C22—21no—
1239C22—21no—
1240C22—21no—
1241C22—21no—
1242C22—21no—
1243C22—21no—
1244C22—44no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—82no—
1249C22—82no—
1250C22—84no—
1251C22—3444no—
1252C22—1722no—
1253C22—1722no—
1254C22—1722no—
1255C22#1458345812yes—
1256C22C23×C22⋊D4311yescharacteristic
1257C4—21no—
1258C4—21no—
1259C4—21no—
1260C4—21no—
1261C4—21no—
1262C4—21no—
1263C4—42no—
1264C4—42no—
1265C4—42no—
1266C4—1722no—
1267C4—1722no—
1268C4—1722no—
1269C4#1458345812yes—
1270C4C2×#1306337011yescharacteristic
1271C4C2×#1306337011yescharacteristic
1272C2—22no—
1273C2—41no—
1274C2—41no—
1275C2—41no—
1276C2—41no—
1277C2—41no—
1278C2—41no—
1279C2—82no—
1280C2—3442no—
1281C2C2×#1458345811yescharacteristic
1282C2#1914936612yes—
subgroupG/H
centerC2×C4C22×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3449C2
socleC22×C43C23×D4
hypercenter#3449D43
hypocenterC43#60749
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×#41 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. #19147924C2semidirect
2. #19145501C2semidirect
3. #19145492C2semidirect
4. #19145486C2semidirect
5. #19145477C2semidirect
6. #19145471C2semidirect
7. #19145467C2semidirect
8. #19145462C2semidirect
9. #19145456C2semidirect
10. #19145447C2semidirect
11. #19145441C2semidirect
12. #19144508C2semidirect
13. #19144504C2semidirect
14. #19144201C2semidirect
15. #19144173C2semidirect
16. #19143813C2semidirect
17. #19143811C2semidirect
18. C2×#14582866C2semidirect
19. C43×#3449C2semidirect
20. C22×#10621898C22semidirect
23. C22×#10621877C22semidirect
24. C23×C43⋊C8C22semidirect
26. #14583477C22semidirect
29. #14583470C22semidirect
32. #14583463C22semidirect
38. #14583410C22semidirect
41. C2×#13063284C22semidirect
42. #14583240C22semidirect
43. #14583240C22semidirect
44. #14583237C22semidirect
45. #14583237C22semidirect
46. #14583234C22semidirect
47. #14583232C22semidirect
48. #14583229C22semidirect
49. #14583227C22semidirect
50. #14583223C22semidirect
51. #14583223C22semidirect
52. #14583220C22semidirect
53. #14583220C22semidirect
54. #14583217C22semidirect
55. #14583215C22semidirect
56. #14583212C22semidirect
57. #14583210C22semidirect
58. #14583155C22semidirect
59. #14583155C22semidirect
60. #14583150C22semidirect
61. #14583150C22semidirect
62. #14583147C22semidirect
63. #14583147C22semidirect
64. #14583143C22semidirect
65. #14583143C22semidirect
66. #14583138C22semidirect
67. #14583138C22semidirect
68. #14583133C22semidirect
69. #14583133C22semidirect
70. #14583130C22semidirect
71. #14583130C22semidirect
72. #14583126C22semidirect
73. #14583126C22semidirect
74. #14583061C22semidirect
75. #14583061C22semidirect
76. #14583059C22semidirect
77. #14583059C22semidirect
78. #14583055C22semidirect
79. #14583054C22semidirect
80. #14583050C22semidirect
81. #14583049C22semidirect
82. #14583044C22semidirect
83. #14583044C22semidirect
84. #14583042C22semidirect
85. #14583042C22semidirect
86. #14583038C22semidirect
87. #14583037C22semidirect
88. #14583033C22semidirect
89. #14583032C22semidirect
90. #14582935C22semidirect
91. #14582935C22semidirect
92. #14582895C22semidirect
93. #14582895C22semidirect
94. #14582893C22semidirect
95. #14582893C22semidirect
98. #14582866C22semidirect
99. #14582866C22semidirect
100. #14582866C22semidirect
101. #14582866C22semidirect
102. C2×C22⋊(C43⋊C8)C22semidirect
103. C2×C22⋊(C43⋊C8)C22semidirect
105. C22×#41×C43C22semidirect
107. C43×#537C22semidirect
110. C43×#536C22semidirect
113. C43×#535C22semidirect
121. C43×#525C22semidirect
122. C2×#117×C43C22semidirect
632. #3449D43semidirect
663. C22×#41C2×D43semidirect
671. #537C2×D43semidirect
677. #536C2×D43semidirect
683. #535C2×D43semidirect
699. #525C2×D43semidirect
701. C2×#117C2×D43semidirect
764. C43#60749semidirect

Maximal subgroups

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

subgroupindex
#191479242
#191455012
#191454922
#191454862
#191454772
#191454712
#191454672
#191454622
#191454562
#191454472
#191454412
#191445082
#191445042
#191442012
#191441732
#191438132
#191438112
C2×#145828662
C43×#34492
#6074943