Finite Group Databasebeta

← #25968249

Subgroups — #25968249

Order 11008.

2108 conjugacy classes of subgroups.

The subgroup lattice has 1320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148330C211yesmaximal, characteristic, complemented
2#19147928C211yesmaximal, characteristic, complemented
3#19145706C212yesmaximal, complemented
4#19145691C212yesmaximal, complemented
5#19145658C212yesmaximal, complemented
6#19145647C212yesmaximal, complemented
7#19145634C212yesmaximal, complemented
8#19145592C212yesmaximal, complemented
9#19145573C212yesmaximal, complemented
10#19145530C212yesmaximal, complemented
11#19145081C211yesmaximal, characteristic, complemented
12#19145071C211yesmaximal, characteristic, complemented
13#19144962C211yesmaximal, characteristic, complemented
14#19144951C211yesmaximal, characteristic, complemented
15#19144147C211yesmaximal, characteristic, complemented
16#19144136C211yesmaximal, characteristic, complemented
17#19144108C211yesmaximal, characteristic, complemented
18#19144099C211yesmaximal, characteristic, complemented
19#19143849C211yesmaximal, characteristic, complemented
20#19143840C211yesmaximal, characteristic, complemented
21#19143817C211yesmaximal, characteristic, complemented
22C2×#14583046C211yesmaximal, characteristic, complemented
23C43×#2924C211yesmaximal, characteristic, complemented
24C22×#10621898C2211yescharacteristic
25C22×#10621898C2211yescharacteristic
26C2×#13063358C2211yescharacteristic, complemented
27C2×#13063353C2211yescharacteristic
28C2×#13063353C2211yescharacteristic
29C2×#13063353C2211yescharacteristic, complemented
30C2×#13063347C2211yescharacteristic
31C2×#13063347C2211yescharacteristic
32C22×#10621873C2211yescharacteristic, complemented
33C22×D344C2211yescharacteristic, complemented
34#14583612—21no—
35#14583597—21no—
36#14583593—21no—
37#14583573—22no—
38#14583550—21no—
39#14583539—22no—
40#14583527C2211yescharacteristic, complemented
41#14583520C2212yescomplemented
42#14583504C2212yescomplemented
43#14583480—21no—
44#14583480—21no—
45#14583475C2211yescharacteristic
46#14583475C2211yescharacteristic
47#14583475C2212yescomplemented
48#14583468C2211yescharacteristic
49#14583468C2211yescharacteristic
50#14583468C2211yescharacteristic, complemented
51#14583468C2212yescomplemented
52#14583461—22no—
53#14583449C2212yescomplemented
54#14583449C2212yescomplemented
55#14583449C2212yescomplemented
56#14583433C2212yescomplemented
57#14583411—22no—
58#14583411—21no—
59#14583411—21no—
60#14583410C2211yescharacteristic
61C2×#13063299C2211yescharacteristic
62#14583379C2211yescharacteristic, complemented
63#14583373C2211yescharacteristic, complemented
64#14583293C2212yescomplemented
65#14583288C2212yescomplemented
66#14583288C2212yescomplemented
67#14583288C2212yescomplemented
68#14583283C2212yescomplemented
69#14583283C2212yescomplemented
70#14583276C2212yescomplemented
71#14583272C2212yescomplemented
72#14583268C2212yescomplemented
73#14583264C2212yescomplemented
74#14583259C2212yescomplemented
75#14583259C2212yescomplemented
76#14583254C2212yescomplemented
77#14583254C2212yescomplemented
78#14583250C2212yescomplemented
79#14583246C2212yescomplemented
80#14583122C2212yescomplemented
81#14583122C2212yescomplemented
82#14583115C2212yescomplemented
83#14583115C2212yescomplemented
84#14583115C2212yescomplemented
85#14583115C2212yescomplemented
86#14583115C2212yescomplemented
87#14583115C2212yescomplemented
88#14583110C2212yescomplemented
89#14583105C2212yescomplemented
90#14583105C2212yescomplemented
91#14583105C2212yescomplemented
92#14583100C2212yescomplemented
93#14583095C2212yescomplemented
94#14583095C2212yescomplemented
95#14583095C2212yescomplemented
96#14583063C2211yescharacteristic, complemented
97#14583063C2212yescomplemented
98#14583063C2211yescharacteristic, complemented
99#14583063C2212yescomplemented
100#14583057C2211yescharacteristic, complemented
101#14583052C2211yescharacteristic, complemented
102#14583046C2212yes—
103#14583046C2212yes—
104#14583046C2211yescharacteristic, complemented
105#14583046C2212yescomplemented
106#14583046C2212yescomplemented
107#14583046C2212yescomplemented
108#14583046C2212yescomplemented
109#14583046C2212yescomplemented
110#14583046C2211yescharacteristic, complemented
111#14583046C2212yescomplemented
112#14583040C2211yescharacteristic, complemented
113#14583040C2212yescomplemented
114#14583035C2211yescharacteristic, complemented
115#14583035C2212yescomplemented
116#14582909C2211yescharacteristic, complemented
117#14582905C2211yescharacteristic, complemented
118#14582901C2211yescharacteristic
119#14582901C2211yescharacteristic
120#14582896C2211yescharacteristic
121#14582896C2211yescharacteristic
122C2×#13063250C2211yescharacteristic, complemented
123C2×#13063247C2211yescharacteristic, complemented
124C2×#117×C43C2211yescharacteristic
125C43×#433C2212yescomplemented
126C43×#433C2212yescomplemented
127C43×#432C2212yescomplemented
128C43×#431C2212yescomplemented
129C43×#424C2211yescharacteristic, complemented
130C43×#424C2211yescharacteristic, complemented
131C43×#407C2211yescharacteristic
132C2×C22⋊C8×C43C2211yescharacteristic
133C43×#405C2211yescharacteristic, complemented
134C43×#405C2211yescharacteristic, complemented
135C2×#10621898—21no—
136C2×#10621898—21no—
137C2×#10621898—21no—
138C2×#10621898—21no—
139C2×#10621898—22no—
140C2×#10621898—42no—
141C2×#10621898—42no—
142C2×#10621898—42no—
143C2×#10621898—42no—
144C2×#10621898C2311yescharacteristic
145C2×#10621898C2311yescharacteristic
146C2×#10621898C2311yescharacteristic
147C2×#10621898C2312yes—
148C2×#10621898C2311yescharacteristic
149C2×#10621898C2312yes—
150C2×#10621898C2311yescharacteristic
151C22×Dic86C2311yescharacteristic
152C22×Dic86C2311yescharacteristic
153C22×D172C2311yescharacteristic
154C22×D172C2311yescharacteristic
155C22×D172C2311yescharacteristic
156C22×C22⋊D43—21no—
157C22×C22⋊D43—21no—
158C22×C22⋊D43—21no—
159C22×C4×D43—21no—
160C22×C4×D43—21no—
161#13063358—42no—
162#13063353—42no—
163#13063353—42no—
164#13063353—42no—
165#13063347—42no—
166#13063347—42no—
167C2×Dic172C2311yescharacteristic
168C2×Dic172C2311yescharacteristic
169C2×Dic172C2312yes—
170C2×#10621873—42no—
171C2×#10621873C2311yescharacteristic
172C2×#10621873C2312yes—
173C2×#10621873C2311yescharacteristic
174C2×#10621873C2312yes—
175C2×#10621873C2312yes—
176C2×#10621873C2312yes—
177C2×#10621873C2312yes—
178C2×#10621873C2311yescharacteristic
179C2×#10621873C2311yescharacteristic
180C2×#10621873C2312yes—
181C2×D344—42no—
182C2×D344C2312yes—
183C2×D344C2312yes—
184C2×D344C2312yes—
185C2×D344C2311yescharacteristic
186C2×D344C2312yes—
187C2×D344C2311yescharacteristic
188C2×D344C2312yes—
189#13063325C2312yes—
190#13063325C2312yes—
191#13063325C2312yes—
192#13063324—21no—
193#13063322C2312yes—
194#13063322C2312yes—
195#13063322C2312yes—
196#13063320—22no—
197#13063319—22no—
198#13063317C2312yes—
199#13063316—21no—
200#13063313—22no—
201#13063313C2312yes—
202#13063313C2312yes—
203#13063313C2312yes—
204#13063313C2312yes—
205#13063313C2312yes—
206#13063311—22no—
207#13063310—22no—
208#13063310—22no—
209#13063309—22no—
210#13063309—22no—
211#13063309—22no—
212#13063309—22no—
213#13063308—21no—
214#13063308—22no—
215#13063307—22no—
216#13063305—21no—
217#13063305—21no—
218#13063305—21no—
219#13063305—21no—
220#13063305—22no—
221#13063305—22no—
222#13063304C2311yescharacteristic
223#13063304C2311yescharacteristic
224#13063303—22no—
225#13063302—22no—
226#13063300—21no—
227#13063300—21no—
228#13063300—21no—
229#13063300—21no—
230#13063300—21no—
231#13063300—21no—
232#13063300—22no—
233#13063300—22no—
234#13063299—21no—
235#13063299—21no—
236#13063299—22no—
237#13063299—22no—
238#13063299—22no—
239#13063299—22no—
240#13063299—22no—
241#13063299C2312yes—
242#13063299C2311yescharacteristic
243#13063299C2312yes—
244#13063299C2311yescharacteristic
245#13063298—22no—
246#13063298—22no—
247#13063295—22no—
248#13063295—22no—
249#13063295—22no—
250#13063295—22no—
251#13063295—22no—
252#13063294—21no—
253C4×Dic86C2312yes—
254C4×D172—22no—
255C4×D172—22no—
256C4×D172—22no—
257C4×D172—22no—
258C4×D172—22no—
259C4×D172C2312yes—
260C4×D172C2312yes—
261C4×D172C2312yes—
262#13063287—21no—
263#13063287—21no—
264C4×C22⋊D43—21no—
265C4×C22⋊D43—21no—
266C4×C22⋊D43—22no—
267(C22⋊D43)⋊C4—22no—
268#13063284C2311yescharacteristic
269#13063283—21no—
270#13063282—22no—
271C2×C4⋊Dic43C2311yescharacteristic
272C4⋊C4×D43—21no—
273C2×(C2×D43)⋊C4—21no—
274C22⋊C4×D43—22no—
275#13063250C2312yes—
276#13063250C2312yes—
277#13063250C2311yescharacteristic
278#13063250C2311yescharacteristic
279#13063250C2312yes—
280#13063250C2312yes—
281#13063250C2311yescharacteristic
282#13063250C2311yescharacteristic
283#13063250C2312yes—
284#13063250C2312yes—
285#13063247C2312yes—
286#13063247C2312yes—
287#13063247C2311yescharacteristic
288#13063247C2311yescharacteristic
289#13063247C2312yes—
290#13063247C2312yes—
291#13063247C2312yes—
292#13063247C2312yes—
293#13063247C2311yescharacteristic
294#13063247C2311yescharacteristic
295C23×C4×C43C2311yescharacteristic
296C2×M16×C43C2311yescharacteristic
297C2×M16×C43C2311yescharacteristic
298C22×C8×C43C2311yescharacteristic
299C22×C8×C43C2311yescharacteristic
300#117×C43D412yes—
301#117×C43D411yescharacteristic
302#117×C43D411yescharacteristic
303#117×C43C2311yescharacteristic
304#117×C43C2311yescharacteristic
305#117×C43C2312yes—
306C2×C4⋊C4×C43D411yescharacteristic
307C2×C4⋊C4×C43D411yescharacteristic
308C2×C22⋊C4×C43D412yes—
309C2×C42×C43C2312yes—
310C4⋊C8×C43C2312yes—
311C4⋊C8×C43C2312yes—
312C4⋊C8×C43C2312yes—
313C4⋊C8×C43C2312yes—
314C22⋊C8×C43C2311yescharacteristic
315C22⋊C8×C43C2312yes—
316C22⋊C8×C43C2311yescharacteristic
317C22⋊C8×C43C2311yescharacteristic
318C22⋊C8×C43C2311yescharacteristic
319C22⋊C8×C43C2312yes—
320#97×C43C2312yes—
321#97×C43C2312yes—
322C4×C8×C43C2312yes—
323C4×C8×C43C2312yes—
324C24×C43C2×D411yescharacteristic
325C23×D43—21no—
326C23×D43—21no—
327C23×D43—21no—
328C22×C4×C43—22no—
329C22×C4×C43—22no—
330C22×C4×C43C2×D411yescharacteristic
331C22×C4×C43C2×D411yescharacteristic
332C22×C4×C43C2×D411yescharacteristic
333C22×C4×C43C2×D412yes—
334C22×C4×C43C2×D412yes—
335C22×C4×C43C2411yescharacteristic
336C22×C4×C43C2411yescharacteristic
337C22×C4×C43C2411yescharacteristic
338C2×C22⋊D43—21no—
339C2×C22⋊D43—21no—
340C2×C22⋊D43—22no—
341C2×C22⋊D43—22no—
342C2×C22⋊D43—21no—
343C2×C22⋊D43—21no—
344C2×C22⋊D43—21no—
345C2×C22⋊D43—22no—
346C2×C22⋊D43—21no—
347C2×C22⋊D43—21no—
348C2×C22⋊D43—22no—
349C2×C22⋊D43—44no—
350C2×C22⋊D43—44no—
351C2×C22⋊D43—82no—
352C22×Dic43—21no—
353C22×Dic43—21no—
354C22×Dic43—21no—
355#10621898—22no—
356#10621898—22no—
357#10621898—22no—
358#10621898—22no—
359#10621898—22no—
360#10621898—22no—
361#10621898—42no—
362#10621898—42no—
363#10621898—41no—
364#10621898—41no—
365#10621898—42no—
366#10621898—42no—
367#10621898—41no—
368#10621898—41no—
369#10621898—44no—
370#10621898—44no—
371#10621898—44no—
372#10621898—44no—
373#10621898—84no—
374C2×D172—21no—
375C2×D172—21no—
376C2×D172—21no—
377C2×D172—22no—
378C2×D172—22no—
379C2×D172—22no—
380C2×D172—22no—
381C2×D172—22no—
382C2×D172—22no—
383C2×D172—22no—
384C2×D172—22no—
385C2×D172—22no—
386C2×D172—22no—
387C2×D172—41no—
388C2×D172—41no—
389C2×D172C2412yes—
390C2×D172C2411yescharacteristic
391C2×D172C2411yescharacteristic
392C2×D172C2412yes—
393C2×D172C2411yescharacteristic
394C2×C4×D43—21no—
395C2×C4×D43—21no—
396C2×C4×D43—22no—
397C2×C4×D43—21no—
398C2×C4×D43—22no—
399C2×C4×D43—21no—
400C2×C4×D43—21no—
401C2×C4×D43—22no—
402C2×C4×D43—22no—
403C2×C4×D43—22no—
404C2×C4×D43—44no—
405C2×C4×D43—44no—
406C2×Dic86—22no—
407C2×Dic86—22no—
408C2×Dic86—21no—
409C2×Dic86—21no—
410C2×Dic86—22no—
411C2×Dic86—41no—
412C2×Dic86—41no—
413C2×Dic86C2412yes—
414C2×Dic86C2411yescharacteristic
415C2×Dic86C2411yescharacteristic
416C2×Dic86C2411yescharacteristic
417M16×C43—22no—
418M16×C43—22no—
419C2×C8×C43—22no—
420C2×C8×C43—22no—
421C2×C8×C43C2411yescharacteristic
422C2×C8×C43C2411yescharacteristic
423C2×C8×C43C2412yes—
424C2×C8×C43C2412yes—
425C2×C8×C43C2411yescharacteristic
426C2×C8×C43C2411yescharacteristic
427C4⋊C4×C43C2×D411yescharacteristic
428C4⋊C4×C43C2×D411yescharacteristic
429C4⋊C4×C43C2×D411yescharacteristic
430C4⋊C4×C43C2×D411yescharacteristic
431C4⋊C4×C43C2×D412yes—
432C4⋊C4×C43C2×D412yes—
433C22⋊C4×C43C2×D412yes—
434C22⋊C4×C43C2×D412yes—
435C22⋊C4×C43C2×D412yes—
436C22⋊C4×C43C2×D412yes—
437C42×C43C2×D412yes—
438C42×C43C2×D412yes—
439C42×C43C2412yes—
440C42×C43C2412yes—
441C22⋊Dic43—21no—
442C22⋊Dic43—21no—
443C22⋊Dic43—21no—
444(C2×D43)⋊C4—22no—
445(C2×D43)⋊C4—22no—
446(C2×D43)⋊C4—22no—
447(C2×D43)⋊C4—22no—
448(C2×D43)⋊C4—22no—
449(C2×D43)⋊C4—22no—
450(C2×D43)⋊C4—21no—
451(C2×D43)⋊C4—22no—
452(C2×D43)⋊C4—21no—
453(C2×D43)⋊C4—22no—
454(C2×D43)⋊C4—22no—
455(C2×D43)⋊C4—22no—
456(C2×D43)⋊C4—22no—
457(C2×D43)⋊C4—22no—
458(C2×D43)⋊C4—22no—
459(C2×D43)⋊C4—22no—
460(C2×D43)⋊C4—22no—
461C4⋊Dic43—21no—
462C4⋊Dic43—22no—
463C4⋊Dic43—22no—
464C4⋊Dic43—22no—
465C4⋊Dic43—22no—
466C4⋊Dic43—22no—
467C4⋊Dic43C2412yes—
468C4⋊Dic43C2411yescharacteristic
469C4⋊Dic43C2411yescharacteristic
470Dic43⋊C4—22no—
471Dic43⋊C4—21no—
472Dic43⋊C4—22no—
473Dic43⋊C4—22no—
474Dic43⋊C4—21no—
475C4×Dic43—22no—
476C4×Dic43—21no—
477Dic172—41no—
478Dic172—41no—
479Dic172—42no—
480D344—42no—
481D344—42no—
482D344—41no—
483D344—41no—
484D344—42no—
485D344—42no—
486D344—42no—
487#10621873—42no—
488#10621873—42no—
489#10621873—41no—
490#10621873—41no—
491#10621873—41no—
492#10621873—41no—
493#10621873—42no—
494#10621873—42no—
495#10621873—42no—
496#10621873—42no—
497C23×C43—22no—
498C23×C43—41no—
499C23×C43—41no—
500C23×C43C22×D411yescharacteristic
501C23×C43C22×D411yescharacteristic
502C23×C43C22×D411yescharacteristic
503C22×D43—22no—
504C22×D43—21no—
505C22×D43—21no—
506C22×D43—21no—
507C22×D43—22no—
508C22×D43—42no—
509C22×D43—42no—
510C22×D43—42no—
511C22×D43—81no—
512C22×D43—81no—
513C22×D43—81no—
514C22×D43—81no—
515C22×D43—81no—
516C22×D43—81no—
517C2×C4×C43—22no—
518C2×C4×C43—22no—
519C2×C4×C43—22no—
520C2×C4×C43—21no—
521C2×C4×C43—21no—
522C2×C4×C43—21no—
523C2×C4×C43—21no—
524C2×C4×C43—42no—
525C2×C4×C43—42no—
526C2×C4×C43C22×D412yes—
527C2×C4×C43C22×D412yes—
528C2×C4×C43C22×D412yes—
529C2×C4×C43C22×D412yes—
530C2×C4×C43C22×D411yescharacteristic
531C2×C4×C43C22×D411yescharacteristic
532C2×C4×C43C22×D411yescharacteristic
533C2×C4×C43H(5,𝔽2)12yes—
534C2×C4×C43H(5,𝔽2)12yes—
535C2×C4×C43C2511yescharacteristic
536C22⋊D43—44no—
537C22⋊D43—44no—
538C22⋊D43—42no—
539C22⋊D43—42no—
540C22⋊D43—42no—
541C22⋊D43—44no—
542C22⋊D43—42no—
543C22⋊D43—42no—
544C22⋊D43—42no—
545C22⋊D43—81no—
546C22⋊D43—82no—
547C2×Dic43—21no—
548C2×Dic43—21no—
549C2×Dic43—22no—
550C2×Dic43—21no—
551C2×Dic43—22no—
552C2×Dic43—21no—
553C2×Dic43—21no—
554C2×Dic43—42no—
555C2×Dic43—42no—
556C2×Dic43—81no—
557D172—22no—
558D172—21no—
559D172—22no—
560D172—21no—
561D172—22no—
562D172—21no—
563D172—21no—
564D172—22no—
565D172—21no—
566D172—21no—
567D172—42no—
568D172—42no—
569D172—42no—
570D172—82no—
571D172—82no—
572D172—82no—
573D172—82no—
574D172—82no—
575D172—82no—
576C4×D43—44no—
577C4×D43—44no—
578C4×D43—42no—
579C4×D43—42no—
580C4×D43—42no—
581C4×D43—42no—
582C4×D43—42no—
583C4×D43—82no—
584C4×D43—82no—
585C4×D43—82no—
586Dic86—21no—
587Dic86—22no—
588Dic86—21no—
589Dic86—21no—
590Dic86—21no—
591Dic86—22no—
592Dic86—21no—
593Dic86—21no—
594Dic86—42no—
595Dic86—42no—
596Dic86—82no—
597C8×C43—21no—
598C8×C43—21no—
599C8×C43—22no—
600C8×C43—21no—
601C8×C43—22no—
602C8×C43—21no—
603#60815—431nomaximal, Sylow
604C22×C43—21no—
605C22×C43—21no—
606C22×C43—21no—
607C22×C43—21no—
608C22×C43—21no—
609C22×C43—21no—
610C22×C43—21no—
611C22×C43—21no—
612C22×C43—82no—
613C22×C43#53512yes—
614C22×C43C23×D411yescharacteristic
615C2×D43—42no—
616C2×D43—42no—
617C2×D43—41no—
618C2×D43—41no—
619C2×D43—41no—
620C2×D43—42no—
621C2×D43—42no—
622C2×D43—41no—
623C2×D43—41no—
624C2×D43—41no—
625C2×D43—41no—
626C2×D43—41no—
627C2×D43—42no—
628C2×D43—42no—
629C2×D43—41no—
630C2×D43—84no—
631C2×D43—84no—
632C2×D43—162no—
633C4×C43—22no—
634C4×C43—22no—
635C4×C43—22no—
636C4×C43—22no—
637C4×C43—21no—
638C4×C43—21no—
639C4×C43#53512yes—
640C4×C43C2×H(5,𝔽2)11yescharacteristic
641C4×C43C2×H(5,𝔽2)11yescharacteristic
642Dic43—41no—
643Dic43—41no—
644Dic43—42no—
645Dic43—42no—
646Dic43—41no—
647Dic43—41no—
648Dic43—41no—
649#3494—431no—
650#3449—431no—
651#3225—432no—
652#3224—432no—
653#3221—432no—
654#3220—432no—
655#3219—432no—
656#3214—432no—
657#3212—432no—
658#3207—432no—
659#3155—431no—
660#3154—431no—
661#3137—431no—
662#3136—431no—
663#3046—431no—
664#3045—431no—
665#3042—431no—
666#3041—431no—
667#3006—431no—
668#3005—431no—
669#3002—431no—
670C2×#449—431no—
671#2924D4311yescharacteristic, complemented
672C2×C43—22no—
673C2×C43—41no—
674C2×C43—41no—
675C2×C43C2×#53511yescharacteristic
676C2×C43#358411yescharacteristic
677C2×C43#358511yescharacteristic
678D43—81no—
679D43—82no—
680D43—81no—
681D43—81no—
682D43—82no—
683C22×#41—431no—
684C22×#41—431no—
685C2×#137—431no—
686C2×AGL(1,ℤ/8)—431no—
687C2×AGL(1,ℤ/8)—431no—
688C2×AGL(1,ℤ/8)—431no—
689C2×#135—431no—
690C2×#135—431no—
691C22×SD16—431no—
692C22×D8—431no—
693#555—861no—
694#553—861no—
695#553—861no—
696#551—862no—
697#547—861no—
698#546—862no—
699#544—431no—
700#542—432no—
701#540—432no—
702#537—861no—
703#537—861no—
704#536—431no—
705#536—432no—
706#536—431no—
707#535—431no—
708#535—431no—
709#535—432no—
710#535—431no—
711#534—862no—
712#532—432no—
713#532—432no—
714#532—432no—
715#529—432no—
716#525—431no—
717#525—862no—
718#525—861no—
719#525—861no—
720C2×#121—431no—
721#520—431no—
722#518—431no—
723C2×#117C2×D4311yescharacteristic
724#497—432no—
725#496—432no—
726#496—432no—
727#496—432no—
728#495—432no—
729#495—432no—
730#493—432no—
731#492—432no—
732#491—432no—
733#490—432no—
734#489—432no—
735#489—432no—
736#488—432no—
737#488—432no—
738#487—432no—
739#486—432no—
740#464—432no—
741#464—432no—
742#463—432no—
743#463—432no—
744#463—432no—
745#463—432no—
746#463—432no—
747#463—432no—
748#462—432no—
749#461—432no—
750#461—432no—
751#461—432no—
752#460—432no—
753#459—432no—
754#459—432no—
755#459—432no—
756#452—431no—
757#452—432no—
758#452—431no—
759#452—432no—
760#451—431no—
761#450—431no—
762#449—432no—
763#449—432no—
764#449—431no—
765#449—432no—
766#449—432no—
767#449—432no—
768#449—432no—
769#449—431no—
770#449—432no—
771#449—432no—
772#448—431no—
773#448—432no—
774#447—431no—
775#447—432no—
776#433C2×D4312yescomplemented
777#433C2×D4312yescomplemented
778#432C2×D4312yescomplemented
779#431C2×D4312yescomplemented
780#424C2×D4311yescharacteristic, complemented
781#424C2×D4311yescharacteristic, complemented
782#419—431no—
783#418—431no—
784#417—431no—
785#417—431no—
786#416—431no—
787#416—431no—
788C2×#103—431no—
789C2×#102—431no—
790#407C2×D4311yescharacteristic
791C2×C22⋊C8C2×D4311yescharacteristic
792#405C2×D4311yescharacteristic, complemented
793#405C2×D4311yescharacteristic, complemented
794C43#6081511yescharacteristic, complemented, Sylow
795C2×#41—431no—
796C2×#41—431no—
797C2×#41—431no—
798C2×#41—431no—
799C2×#41—432no—
800C2×#41—431no—
801C2×#41—432no—
802C2×#41—862no—
803C2×#41—861no—
804C2×#41—861no—
805C2×#41—861no—
806C2×#41—861no—
807C2×#41—1722no—
808C2×#41—1722no—
809C2×#41—1722no—
810C2×#41—1722no—
811C22×Q8—431no—
812C22×Q8—431no—
813C22×D4—431no—
814C22×D4—431no—
815C22×D4—431no—
816C22×D4—861no—
817C22×D4—861no—
818C22×D4—861no—
819C23×C4—861no—
820C23×C4—861no—
821C23×C4C22×D4311yescharacteristic
822#137—1722no—
823AGL(1,ℤ/8)—1722no—
824AGL(1,ℤ/8)—1722no—
825AGL(1,ℤ/8)—1722no—
826#135—1722no—
827#135—1722no—
828C2×Q16—431no—
829C2×Q16—431no—
830C2×Q16—432no—
831C2×SD16—432no—
832C2×SD16—432no—
833C2×SD16—431no—
834C2×SD16—431no—
835C2×SD16—431no—
836C2×SD16—431no—
837C2×SD16—432no—
838C2×SD16—432no—
839C2×SD16—432no—
840C2×SD16—432no—
841C2×SD16—1722no—
842C2×D8—432no—
843C2×D8—432no—
844C2×D8—431no—
845C2×D8—431no—
846C2×D8—432no—
847C2×D8—432no—
848C2×D8—432no—
849C2×D8—1722no—
850C2×M16C22×D4311yescharacteristic
851C2×M16C22×D4311yescharacteristic
852C22×C8C22×D4311yescharacteristic
853C22×C8C22×D4311yescharacteristic
854C4⋊Q8—432no—
855C4⋊Q8—432no—
856C4⋊Q8—432no—
857C4⋊Q8—861no—
858#127—432no—
859#127—432no—
860#127—432no—
861#126—862no—
862#126—862no—
863#125—432no—
864#125—861no—
865#124—432no—
866#124—432no—
867#124—432no—
868#124—432no—
869#124—432no—
870#124—862no—
871#124—862no—
872#123—861no—
873#123—862no—
874#123—862no—
875#123—862no—
876#123—862no—
877#123—862no—
878#123—862no—
879#123—862no—
880#123—862no—
881C22⋊Q8—431no—
882C22⋊Q8—431no—
883C22⋊Q8—861no—
884C22⋊Q8—861no—
885C22⋊Q8—861no—
886C22⋊Q8—861no—
887C22⋊Q8—862no—
888C22⋊Q8—862no—
889C22⋊Q8—862no—
890C22⋊Q8—862no—
891#121—432no—
892#121—432no—
893#121—431no—
894#121—431no—
895#121—861no—
896#121—861no—
897#121—862no—
898#121—862no—
899#121—862no—
900#121—862no—
901#121—862no—
902#121—861no—
903#121—861no—
904#121—861no—
905#121—861no—
906#121—862no—
907#121—862no—
908#121—861no—
909#121—861no—
910#121—862no—
911#121—862no—
912#120—861no—
913#120—862no—
914#120—862no—
915#120—862no—
916#120—862no—
917#120—862no—
918C4×Q8—432no—
919C4×D4—432no—
920C4×D4—432no—
921C4×D4—432no—
922C4×D4—861no—
923C4×D4—861no—
924C4×D4—862no—
925C4×D4—861no—
926C4×D4—861no—
927C4×D4—862no—
928C4×D4—862no—
929C4×D4—862no—
930C4×D4—862no—
931C4×D4—862no—
932C4×D4—862no—
933#117—431no—
934#117—861no—
935#117—862no—
936#117D17212yes—
937#117D17211yescharacteristic
938#117D17211yescharacteristic
939#117C22×D4311yescharacteristic
940#117C22×D4311yescharacteristic
941#117C22×D4312yes—
942C2×C4⋊C4—431no—
943C2×C4⋊C4—861no—
944C2×C4⋊C4D17211yescharacteristic
945C2×C4⋊C4D17211yescharacteristic
946C2×C22⋊C4—861no—
947C2×C22⋊C4—862no—
948C2×C22⋊C4D17212yes—
949C2×C42C22×D4312yes—
950C4⋊C8C22×D4312yes—
951C4⋊C8C22×D4312yes—
952C4⋊C8C22×D4312yes—
953C4⋊C8C22×D4312yes—
954#103—432no—
955#103—432no—
956#103—431no—
957#103—431no—
958#103—431no—
959#103—431no—
960#103—432no—
961#103—432no—
962#103—432no—
963#103—432no—
964#102—432no—
965#102—432no—
966#102—431no—
967#102—431no—
968#102—431no—
969#102—431no—
970#102—432no—
971#102—432no—
972#102—432no—
973#102—432no—
974C22⋊C8C22×D4311yescharacteristic
975C22⋊C8C22×D4311yescharacteristic
976C22⋊C8C22×D4311yescharacteristic
977C22⋊C8C22×D4311yescharacteristic
978C22⋊C8C22×D4312yes—
979C22⋊C8C22×D4312yes—
980#97C22×D4312yes—
981#97C22×D4312yes—
982C4×C8C22×D4312yes—
983C4×C8C22×D4312yes—
984C24—861no—
985C24—861no—
986C24—861no—
987C24C2×D17211yescharacteristic
988#41—862no—
989#41—862no—
990#41—862no—
991#41—862no—
992#41—862no—
993#41—862no—
994#41—3444no—
995#41—1722no—
996#41—1722no—
997#41—1722no—
998#41—1721no—
999#41—1721no—
1000#41—1722no—
1001#41—1721no—
1002#41—1721no—
1003#41—1724no—
1004#41—1724no—
1005#41—1724no—
1006#41—1724no—
1007C2×Q8—432no—
1008C2×Q8—431no—
1009C2×Q8—431no—
1010C2×Q8—431no—
1011C2×Q8—862no—
1012C2×Q8—861no—
1013C2×Q8—861no—
1014C2×Q8—862no—
1015C2×Q8—862no—
1016C2×Q8—1721no—
1017C2×Q8—1721no—
1018C2×D4—432no—
1019C2×D4—431no—
1020C2×D4—431no—
1021C2×D4—432no—
1022C2×D4—431no—
1023C2×D4—861no—
1024C2×D4—862no—
1025C2×D4—861no—
1026C2×D4—861no—
1027C2×D4—862no—
1028C2×D4—862no—
1029C2×D4—861no—
1030C2×D4—861no—
1031C2×D4—861no—
1032C2×D4—862no—
1033C2×D4—861no—
1034C2×D4—862no—
1035C2×D4—862no—
1036C2×D4—862no—
1037C2×D4—862no—
1038C2×D4—862no—
1039C2×D4—862no—
1040C2×D4—861no—
1041C2×D4—861no—
1042C2×D4—861no—
1043C2×D4—862no—
1044C2×D4—862no—
1045C2×D4—862no—
1046C2×D4—862no—
1047C2×D4—3442no—
1048C2×D4—1721no—
1049C2×D4—1721no—
1050C2×D4—1724no—
1051C2×D4—1724no—
1052C22×C4—22no—
1053C22×C4—22no—
1054C22×C4—861no—
1055C22×C4—861no—
1056C22×C4—861no—
1057C22×C4—862no—
1058C22×C4—862no—
1059C22×C4—862no—
1060C22×C4—861no—
1061C22×C4—861no—
1062C22×C4—862no—
1063C22×C4—861no—
1064C22×C4—862no—
1065C22×C4—861no—
1066C22×C4—861no—
1067C22×C4—1724no—
1068C22×C4—1724no—
1069C22×C4C2×D17211yescharacteristic
1070C22×C4C2×D17211yescharacteristic
1071C22×C4C2×D17211yescharacteristic
1072C22×C4C2×D17212yes—
1073C22×C4C2×D17212yes—
1074C22×C4C23×D4311yescharacteristic
1075C22×C4C23×D4311yescharacteristic
1076C22×C4C23×D4311yescharacteristic
1077Q16—1721no—
1078Q16—1721no—
1079Q16—1722no—
1080SD16—1722no—
1081SD16—1722no—
1082SD16—1721no—
1083SD16—1721no—
1084SD16—1721no—
1085SD16—1721no—
1086SD16—1722no—
1087SD16—1722no—
1088SD16—1722no—
1089SD16—1722no—
1090D8—1722no—
1091D8—1722no—
1092D8—1721no—
1093D8—1721no—
1094D8—1722no—
1095D8—1722no—
1096D8—1722no—
1097M16—22no—
1098M16—22no—
1099C2×C8—22no—
1100C2×C8—22no—
1101C2×C8C23×D4311yescharacteristic
1102C2×C8C23×D4311yescharacteristic
1103C2×C8C23×D4312yes—
1104C2×C8C23×D4312yes—
1105C2×C8C23×D4311yescharacteristic
1106C2×C8C23×D4311yescharacteristic
1107C4⋊C4—432no—
1108C4⋊C4—431no—
1109C4⋊C4—431no—
1110C4⋊C4—861no—
1111C4⋊C4—862no—
1112C4⋊C4—861no—
1113C4⋊C4—862no—
1114C4⋊C4—862no—
1115C4⋊C4—862no—
1116C4⋊C4—862no—
1117C4⋊C4—862no—
1118C4⋊C4—862no—
1119C4⋊C4—862no—
1120C4⋊C4—861no—
1121C4⋊C4C2×D17211yescharacteristic
1122C4⋊C4C2×D17211yescharacteristic
1123C4⋊C4C2×D17211yescharacteristic
1124C4⋊C4C2×D17211yescharacteristic
1125C4⋊C4C2×D17212yes—
1126C4⋊C4C2×D17212yes—
1127C22⋊C4—861no—
1128C22⋊C4—861no—
1129C22⋊C4—861no—
1130C22⋊C4—862no—
1131C22⋊C4—862no—
1132C22⋊C4—862no—
1133C22⋊C4—862no—
1134C22⋊C4—862no—
1135C22⋊C4—862no—
1136C22⋊C4—861no—
1137C22⋊C4—862no—
1138C22⋊C4—862no—
1139C22⋊C4—862no—
1140C22⋊C4—862no—
1141C22⋊C4—862no—
1142C22⋊C4—862no—
1143C22⋊C4—862no—
1144C22⋊C4—862no—
1145C22⋊C4—862no—
1146C22⋊C4—861no—
1147C22⋊C4C2×D17212yes—
1148C22⋊C4C2×D17212yes—
1149C22⋊C4C2×D17212yes—
1150C22⋊C4C2×D17212yes—
1151C42—861no—
1152C42—862no—
1153C42C2×D17212yes—
1154C42C2×D17212yes—
1155C42C23×D4312yes—
1156C42C23×D4312yes—
1157C23—22no—
1158C23—41no—
1159C23—41no—
1160C23—862no—
1161C23—861no—
1162C23—862no—
1163C23—861no—
1164C23—861no—
1165C23—3441no—
1166C23—3441no—
1167C23—3441no—
1168C23—3441no—
1169C23—3441no—
1170C23—3441no—
1171C23—1722no—
1172C23—1722no—
1173C23—1722no—
1174C23C22×D17211yescharacteristic
1175C23C22×D17211yescharacteristic
1176C23C22×D17211yescharacteristic
1177Q8—861no—
1178Q8—862no—
1179Q8—861no—
1180Q8—861no—
1181Q8—861no—
1182Q8—862no—
1183Q8—861no—
1184Q8—861no—
1185Q8—3442no—
1186Q8—1722no—
1187Q8—1722no—
1188D4—862no—
1189D4—861no—
1190D4—862no—
1191D4—861no—
1192D4—861no—
1193D4—862no—
1194D4—861no—
1195D4—862no—
1196D4—861no—
1197D4—861no—
1198D4—3442no—
1199D4—3442no—
1200D4—3442no—
1201D4—3442no—
1202D4—3442no—
1203D4—3442no—
1204D4—3442no—
1205D4—3441no—
1206D4—1722no—
1207D4—1724no—
1208D4—1724no—
1209D4—1724no—
1210D4—1722no—
1211D4—1722no—
1212D4—1722no—
1213D4—1722no—
1214D4—1722no—
1215D4—1722no—
1216D4—1722no—
1217D4—1722no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—42no—
1226C2×C4—42no—
1227C2×C4—861no—
1228C2×C4—861no—
1229C2×C4—861no—
1230C2×C4—862no—
1231C2×C4—862no—
1232C2×C4—861no—
1233C2×C4—861no—
1234C2×C4—3442no—
1235C2×C4—3442no—
1236C2×C4—3442no—
1237C2×C4—3441no—
1238C2×C4—1724no—
1239C2×C4—1722no—
1240C2×C4—1722no—
1241C2×C4—1724no—
1242C2×C4—1722no—
1243C2×C4—1722no—
1244C2×C4—1722no—
1245C2×C4—1722no—
1246C2×C4—1722no—
1247C2×C4C22×D17212yes—
1248C2×C4C22×D17211yescharacteristic
1249C2×C4C22×D17212yes—
1250C2×C4C22×D17212yes—
1251C2×C4C22×D17212yes—
1252C2×C4C22×D17211yescharacteristic
1253C2×C4C22×D17211yescharacteristic
1254C2×C4#1306337112yes—
1255C2×C4#1306337112yes—
1256C2×C4C24×D4311yescharacteristic
1257C8—21no—
1258C8—21no—
1259C8—21no—
1260C8—21no—
1261C8—22no—
1262C8—22no—
1263C22—21no—
1264C22—21no—
1265C22—21no—
1266C22—21no—
1267C22—21no—
1268C22—21no—
1269C22—21no—
1270C22—21no—
1271C22—82no—
1272C22—3444no—
1273C22—3444no—
1274C22—1722no—
1275C22—1721no—
1276C22—1722no—
1277C22—1721no—
1278C22—1721no—
1279C22—1721no—
1280C22—1722no—
1281C22—1722no—
1282C22—1721no—
1283C22—1721no—
1284C22—1722no—
1285C22—1721no—
1286C22—1721no—
1287C22—1721no—
1288C22—1722no—
1289C22—6882no—
1290C22#1458346812yes—
1291C22C23×D17211yescharacteristic
1292C4—22no—
1293C4—22no—
1294C4—22no—
1295C4—22no—
1296C4—21no—
1297C4—21no—
1298C4—1721no—
1299C4—1722no—
1300C4—1721no—
1301C4—1722no—
1302C4—1721no—
1303C4—1721no—
1304C4—1721no—
1305C4#1458346812yes—
1306C4C2×#1306337111yescharacteristic
1307C4C2×#1306337111yescharacteristic
1308C2—22no—
1309C2—41no—
1310C2—41no—
1311C2—3442no—
1312C2—3441no—
1313C2—3441no—
1314C2—3442no—
1315C2—3441no—
1316C2C2×#1458346811yescharacteristic
1317C2#1914936911yescharacteristic
1318C2#1914937611yescharacteristic
subgroupG/H
centerC22C23×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#2924C2
socleC22×C43C23×D4
hypercenter#2924D43
hypocenterC43#60815
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2924

Complements

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

NH ≅ G/Ntype
1. #19148330C2semidirect
2. #19147928C2semidirect
3. #19145706C2semidirect
4. #19145691C2semidirect
5. #19145658C2semidirect
6. #19145647C2semidirect
7. #19145634C2semidirect
8. #19145592C2semidirect
9. #19145573C2semidirect
10. #19145530C2semidirect
11. #19145081C2semidirect
12. #19145071C2semidirect
13. #19144962C2semidirect
14. #19144951C2semidirect
15. #19144147C2semidirect
16. #19144136C2semidirect
17. #19144108C2semidirect
18. #19144099C2semidirect
19. #19143849C2semidirect
20. #19143840C2semidirect
21. #19143817C2semidirect
22. C2×#14583046C2semidirect
23. C43×#2924C2semidirect
26. C2×#13063358C22semidirect
29. C2×#13063353C22semidirect
32. C22×#10621873C22semidirect
33. C22×D344C22semidirect
40. #14583527C22semidirect
41. #14583520C22semidirect
42. #14583504C22semidirect
47. #14583475C22semidirect
50. #14583468C22semidirect
51. #14583468C22semidirect
53. #14583449C22semidirect
54. #14583449C22semidirect
55. #14583449C22semidirect
56. #14583433C22semidirect
62. #14583379C22semidirect
63. #14583373C22semidirect
64. #14583293C22semidirect
65. #14583288C22semidirect
66. #14583288C22semidirect
67. #14583288C22semidirect
68. #14583283C22semidirect
69. #14583283C22semidirect
70. #14583276C22semidirect
71. #14583272C22semidirect
72. #14583268C22semidirect
73. #14583264C22semidirect
74. #14583259C22semidirect
75. #14583259C22semidirect
76. #14583254C22semidirect
77. #14583254C22semidirect
78. #14583250C22semidirect
79. #14583246C22semidirect
80. #14583122C22semidirect
81. #14583122C22semidirect
82. #14583115C22semidirect
83. #14583115C22semidirect
84. #14583115C22semidirect
85. #14583115C22semidirect
86. #14583115C22semidirect
87. #14583115C22semidirect
88. #14583110C22semidirect
89. #14583105C22semidirect
90. #14583105C22semidirect
91. #14583105C22semidirect
92. #14583100C22semidirect
93. #14583095C22semidirect
94. #14583095C22semidirect
95. #14583095C22semidirect
96. #14583063C22semidirect
97. #14583063C22semidirect
98. #14583063C22semidirect
99. #14583063C22semidirect
100. #14583057C22semidirect
101. #14583052C22semidirect
104. #14583046C22semidirect
105. #14583046C22semidirect
106. #14583046C22semidirect
107. #14583046C22semidirect
108. #14583046C22semidirect
109. #14583046C22semidirect
110. #14583046C22semidirect
111. #14583046C22semidirect
112. #14583040C22semidirect
113. #14583040C22semidirect
114. #14583035C22semidirect
115. #14583035C22semidirect
116. #14582909C22semidirect
117. #14582905C22semidirect
122. C2×#13063250C22semidirect
123. C2×#13063247C22semidirect
125. C43×#433C22semidirect
126. C43×#433C22semidirect
127. C43×#432C22semidirect
128. C43×#431C22semidirect
129. C43×#424C22semidirect
130. C43×#424C22semidirect
133. C43×#405C22semidirect
134. C43×#405C22semidirect
671. #2924D43semidirect
776. #433C2×D43semidirect
777. #433C2×D43semidirect
778. #432C2×D43semidirect
779. #431C2×D43semidirect
780. #424C2×D43semidirect
781. #424C2×D43semidirect
792. #405C2×D43semidirect
793. #405C2×D43semidirect
794. C43#60815semidirect

Maximal subgroups

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

subgroupindex
#191483302
#191479282
#191457062
#191456912
#191456582
#191456472
#191456342
#191455922
#191455732
#191455302
#191450812
#191450712
#191449622
#191449512
#191441472
#191441362
#191441082
#191440992
#191438492
#191438402
#191438172
C2×#145830462
C43×#29242
#6081543