Finite Group Databasebeta

← #25968272

Subgroups — #25968272

Order 11008.

2048 conjugacy classes of subgroups.

The subgroup lattice has 1292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148347C211yesmaximal, characteristic, complemented
2#19147928C211yesmaximal, characteristic, complemented
3#19145706C212yesmaximal, complemented
4#19145691C212yesmaximal, complemented
5#19145680C212yesmaximal, complemented
6#19145669C212yesmaximal, complemented
7#19145634C212yesmaximal, complemented
8#19145608C212yesmaximal, complemented
9#19145573C212yesmaximal, complemented
10#19145553C212yesmaximal, complemented
11#19145089C211yesmaximal, characteristic, complemented
12#19145071C211yesmaximal, characteristic, complemented
13#19144962C211yesmaximal, characteristic, complemented
14#19144951C211yesmaximal, characteristic, complemented
15#19144147C211yesmaximal, characteristic, complemented
16#19144136C211yesmaximal, characteristic, complemented
17#19144126C211yesmaximal, characteristic, complemented
18#19144117C211yesmaximal, characteristic, complemented
19#19143857C211yesmaximal, characteristic, complemented
20#19143840C211yesmaximal, characteristic, complemented
21#19143817C211yesmaximal, characteristic, complemented
22C2×#14583063C211yesmaximal, characteristic, complemented
23C43×#2924C211yesmaximal, characteristic, complemented
24C22×#10621898C2211yescharacteristic
25C22×#10621898C2211yescharacteristic
26C2×#13063358C2211yescharacteristic
27C2×#13063358C2211yescharacteristic
28C2×#13063358C2211yescharacteristic, complemented
29C2×#13063353C2211yescharacteristic, complemented
30C2×#13063347C2211yescharacteristic
31C2×#13063347C2211yescharacteristic
32C22×Dic172C2211yescharacteristic, complemented
33C22×#10621873C2211yescharacteristic, complemented
34#14583617—21no—
35#14583604—21no—
36#14583588—21no—
37#14583584—21no—
38#14583582—22no—
39#14583575—22no—
40#14583527C2211yescharacteristic, complemented
41#14583520C2212yescomplemented
42#14583511C2212yescomplemented
43#14583480—21no—
44#14583480—21no—
45#14583475C2211yescharacteristic
46#14583475C2211yescharacteristic
47#14583475C2212yes—
48#14583475C2211yescharacteristic, complemented
49#14583468C2211yescharacteristic
50#14583468C2211yescharacteristic
51#14583468C2212yes—
52#14583461—22no—
53#14583456C2212yescomplemented
54#14583449C2212yes—
55#14583449C2212yes—
56#14583433C2212yescomplemented
57#14583411—22no—
58#14583411—21no—
59#14583411—21no—
60#14583410C2211yescharacteristic
61C2×#13063304C2211yescharacteristic
62#14583379C2211yescharacteristic, complemented
63#14583376C2211yescharacteristic, complemented
64#14583293C2212yescomplemented
65#14583293C2212yescomplemented
66#14583293C2212yescomplemented
67#14583288C2212yescomplemented
68#14583283C2212yescomplemented
69#14583283C2212yescomplemented
70#14583279C2212yescomplemented
71#14583272C2212yescomplemented
72#14583268C2212yescomplemented
73#14583264C2212yescomplemented
74#14583259C2212yescomplemented
75#14583259C2212yescomplemented
76#14583254C2212yescomplemented
77#14583254C2212yescomplemented
78#14583250C2212yescomplemented
79#14583246C2212yescomplemented
80#14583122C2212yescomplemented
81#14583122C2212yescomplemented
82#14583122C2212yescomplemented
83#14583122C2212yescomplemented
84#14583122C2212yescomplemented
85#14583122C2212yescomplemented
86#14583115C2212yescomplemented
87#14583115C2212yescomplemented
88#14583110C2212yescomplemented
89#14583110C2212yescomplemented
90#14583110C2212yescomplemented
91#14583105C2212yescomplemented
92#14583100C2212yescomplemented
93#14583100C2212yescomplemented
94#14583100C2212yescomplemented
95#14583095C2212yescomplemented
96#14583063C2212yes—
97#14583063C2212yes—
98#14583063C2212yes—
99#14583063C2211yescharacteristic, complemented
100#14583063C2212yescomplemented
101#14583063C2212yescomplemented
102#14583063C2212yescomplemented
103#14583063C2212yescomplemented
104#14583063C2212yescomplemented
105#14583063C2211yescharacteristic, complemented
106#14583057C2211yescharacteristic, complemented
107#14583057C2212yescomplemented
108#14583052C2211yescharacteristic, complemented
109#14583052C2212yescomplemented
110#14583046C2212yes—
111#14583046C2211yescharacteristic, complemented
112#14583046C2212yescomplemented
113#14583046C2211yescharacteristic, complemented
114#14583040C2211yescharacteristic, complemented
115#14583035C2211yescharacteristic, complemented
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—42no—
140C2×#10621898—42no—
141C2×#10621898—42no—
142C2×#10621898—42no—
143C2×#10621898C2311yescharacteristic
144C2×#10621898C2311yescharacteristic
145C2×#10621898C2311yescharacteristic
146C2×#10621898C2312yes—
147C2×#10621898C2311yescharacteristic
148C2×#10621898C2312yes—
149C2×#10621898C2311yescharacteristic
150C22×Dic86C2311yescharacteristic
151C22×Dic86C2311yescharacteristic
152C22×Dic86C2311yescharacteristic
153C22×D172C2311yescharacteristic
154C22×D172C2311yescharacteristic
155C22×C22⋊D43—21no—
156C22×C22⋊D43—21no—
157C22×C4×D43—21no—
158C22×C4×D43—21no—
159#13063358—42no—
160#13063358—42no—
161#13063358—42no—
162#13063353—42no—
163#13063347—42no—
164#13063347—42no—
165C2×Dic172—42no—
166C2×Dic172C2311yescharacteristic
167C2×Dic172C2312yes—
168C2×Dic172C2311yescharacteristic
169C2×Dic172C2312yes—
170C2×Dic172C2312yes—
171C2×Dic172C2312yes—
172C2×Dic172C2312yes—
173C2×#10621873—42no—
174C2×#10621873C2311yescharacteristic
175C2×#10621873C2311yescharacteristic
176C2×#10621873C2312yes—
177C2×#10621873C2311yescharacteristic
178C2×#10621873C2312yes—
179C2×#10621873C2311yescharacteristic
180C2×#10621873C2312yes—
181C2×#10621873C2312yes—
182C2×#10621873C2312yes—
183C2×#10621873C2312yes—
184C2×D344C2312yes—
185C2×D344C2311yescharacteristic
186C2×D344C2311yescharacteristic
187#13063325C2312yes—
188#13063325C2312yes—
189#13063325C2312yes—
190#13063325C2312yes—
191#13063324—21no—
192#13063322C2312yes—
193#13063322C2312yes—
194#13063320—22no—
195#13063319—22no—
196#13063318—22no—
197#13063318—22no—
198#13063317—22no—
199#13063317C2312yes—
200#13063316—21no—
201#13063315—22no—
202#13063315—22no—
203#13063313C2312yes—
204#13063313C2312yes—
205#13063313C2312yes—
206#13063313C2312yes—
207#13063313C2312yes—
208#13063311—22no—
209#13063309—22no—
210#13063309—22no—
211#13063309—22no—
212#13063309—22no—
213#13063309—22no—
214#13063308—22no—
215#13063308—21no—
216#13063307—22no—
217#13063305—21no—
218#13063305—21no—
219#13063305—21no—
220#13063305—21no—
221#13063305—22no—
222#13063305—21no—
223#13063305—21no—
224#13063305—22no—
225#13063304—22no—
226#13063304—21no—
227#13063304—21no—
228#13063304C2312yes—
229#13063304C2311yescharacteristic
230#13063304C2312yes—
231#13063304C2311yescharacteristic
232#13063303—22no—
233#13063302—22no—
234#13063300—21no—
235#13063300—21no—
236#13063300—22no—
237#13063300—21no—
238#13063300—21no—
239#13063300—22no—
240#13063299—22no—
241#13063299—22no—
242#13063299—22no—
243#13063299—22no—
244#13063299C2311yescharacteristic
245#13063299C2311yescharacteristic
246#13063295—22no—
247#13063295—22no—
248#13063295—22no—
249#13063295—22no—
250#13063294—21no—
251C4×Dic86—22no—
252C4×Dic86C2312yes—
253C4×Dic86C2312yes—
254C4×Dic86C2312yes—
255#13063290—21no—
256#13063290—21no—
257C4×D172—22no—
258C4×D172—22no—
259C4×D172—22no—
260C4×D172—22no—
261C4×D172C2312yes—
262C4×C22⋊D43—22no—
263C4×C22⋊D43—21no—
264C4×C22⋊D43—21no—
265(C22⋊D43)⋊C4—22no—
266#13063284—22no—
267#13063284C2311yescharacteristic
268#13063283—21no—
269#13063282—22no—
270#13063281—22no—
271C2×C4⋊Dic43C2311yescharacteristic
272C2×Dic43⋊C4—21no—
273C4⋊C4×D43—21no—
274C2×C22⋊Dic43—21no—
275#13063250C2311yescharacteristic
276#13063250C2311yescharacteristic
277#13063250C2312yes—
278#13063250C2311yescharacteristic
279#13063250C2311yescharacteristic
280#13063250C2312yes—
281#13063250C2312yes—
282#13063250C2312yes—
283#13063250C2312yes—
284#13063250C2312yes—
285#13063247C2312yes—
286#13063247C2311yescharacteristic
287#13063247C2311yescharacteristic
288#13063247C2312yes—
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×C43C2312yes—
319C22⋊C8×C43C2311yescharacteristic
320#97×C43C2312yes—
321#97×C43C2312yes—
322C4×C8×C43C2312yes—
323C4×C8×C43C2312yes—
324C24×C43C2×D411yescharacteristic
325C23×D43—21no—
326C23×D43—21no—
327C22×C4×C43—22no—
328C22×C4×C43—22no—
329C22×C4×C43C2×D411yescharacteristic
330C22×C4×C43C2×D411yescharacteristic
331C22×C4×C43C2×D411yescharacteristic
332C22×C4×C43C2×D412yes—
333C22×C4×C43C2×D412yes—
334C22×C4×C43C2411yescharacteristic
335C22×C4×C43C2411yescharacteristic
336C22×C4×C43C2411yescharacteristic
337C2×C22⋊D43—21no—
338C2×C22⋊D43—21no—
339C2×C22⋊D43—22no—
340C2×C22⋊D43—21no—
341C2×C22⋊D43—21no—
342C2×C22⋊D43—21no—
343C2×C22⋊D43—22no—
344C2×C22⋊D43—21no—
345C2×C22⋊D43—21no—
346C2×C22⋊D43—44no—
347C2×C22⋊D43—44no—
348C22×Dic43—21no—
349C22×Dic43—21no—
350C22×Dic43—21no—
351C22×Dic43—21no—
352#10621898—22no—
353#10621898—22no—
354#10621898—22no—
355#10621898—22no—
356#10621898—22no—
357#10621898—22no—
358#10621898—42no—
359#10621898—42no—
360#10621898—41no—
361#10621898—41no—
362#10621898—42no—
363#10621898—42no—
364#10621898—41no—
365#10621898—41no—
366#10621898—44no—
367#10621898—44no—
368#10621898—44no—
369#10621898—44no—
370C2×D172—21no—
371C2×D172—21no—
372C2×D172—22no—
373C2×D172—22no—
374C2×D172—22no—
375C2×D172—22no—
376C2×D172—22no—
377C2×D172—22no—
378C2×D172—41no—
379C2×D172—41no—
380C2×D172C2412yes—
381C2×D172C2411yescharacteristic
382C2×D172C2411yescharacteristic
383C2×D172C2411yescharacteristic
384C2×C4×D43—21no—
385C2×C4×D43—21no—
386C2×C4×D43—22no—
387C2×C4×D43—21no—
388C2×C4×D43—22no—
389C2×C4×D43—21no—
390C2×C4×D43—21no—
391C2×C4×D43—22no—
392C2×C4×D43—44no—
393C2×C4×D43—44no—
394C2×Dic86—22no—
395C2×Dic86—22no—
396C2×Dic86—22no—
397C2×Dic86—22no—
398C2×Dic86—21no—
399C2×Dic86—21no—
400C2×Dic86—21no—
401C2×Dic86—22no—
402C2×Dic86—41no—
403C2×Dic86—41no—
404C2×Dic86C2412yes—
405C2×Dic86C2411yescharacteristic
406C2×Dic86C2411yescharacteristic
407C2×Dic86C2412yes—
408C2×Dic86C2411yescharacteristic
409M16×C43—22no—
410M16×C43—22no—
411C2×C8×C43—22no—
412C2×C8×C43—22no—
413C2×C8×C43C2411yescharacteristic
414C2×C8×C43C2411yescharacteristic
415C2×C8×C43C2412yes—
416C2×C8×C43C2412yes—
417C2×C8×C43C2411yescharacteristic
418C2×C8×C43C2411yescharacteristic
419C4⋊C4×C43C2×D411yescharacteristic
420C4⋊C4×C43C2×D411yescharacteristic
421C4⋊C4×C43C2×D412yes—
422C4⋊C4×C43C2×D411yescharacteristic
423C4⋊C4×C43C2×D411yescharacteristic
424C4⋊C4×C43C2×D412yes—
425C22⋊C4×C43C2×D412yes—
426C22⋊C4×C43C2×D412yes—
427C22⋊C4×C43C2×D412yes—
428C22⋊C4×C43C2×D412yes—
429C42×C43C2×D412yes—
430C42×C43C2×D412yes—
431C42×C43C2412yes—
432C42×C43C2412yes—
433C22⋊Dic43—22no—
434C22⋊Dic43—22no—
435C22⋊Dic43—21no—
436C22⋊Dic43—21no—
437C22⋊Dic43—21no—
438(C2×D43)⋊C4—21no—
439(C2×D43)⋊C4—22no—
440(C2×D43)⋊C4—22no—
441(C2×D43)⋊C4—21no—
442(C2×D43)⋊C4—22no—
443(C2×D43)⋊C4—22no—
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—22no—
451C4⋊Dic43—21no—
452C4⋊Dic43—22no—
453C4⋊Dic43—22no—
454C4⋊Dic43—22no—
455C4⋊Dic43—22no—
456C4⋊Dic43—22no—
457C4⋊Dic43—22no—
458C4⋊Dic43—22no—
459C4⋊Dic43C2412yes—
460C4⋊Dic43C2411yescharacteristic
461C4⋊Dic43C2411yescharacteristic
462Dic43⋊C4—22no—
463Dic43⋊C4—22no—
464Dic43⋊C4—22no—
465Dic43⋊C4—22no—
466Dic43⋊C4—22no—
467Dic43⋊C4—22no—
468Dic43⋊C4—21no—
469Dic43⋊C4—22no—
470Dic43⋊C4—21no—
471C4×Dic43—22no—
472C4×Dic43—22no—
473C4×Dic43—22no—
474C4×Dic43—21no—
475Dic172—42no—
476Dic172—42no—
477Dic172—41no—
478Dic172—41no—
479Dic172—42no—
480Dic172—42no—
481Dic172—42no—
482D344—41no—
483D344—41no—
484D344—42no—
485#10621873—42no—
486#10621873—42no—
487#10621873—41no—
488#10621873—41no—
489#10621873—41no—
490#10621873—41no—
491#10621873—42no—
492#10621873—42no—
493#10621873—42no—
494#10621873—42no—
495C23×C43—22no—
496C23×C43—41no—
497C23×C43—41no—
498C23×C43C22×D411yescharacteristic
499C23×C43C22×D411yescharacteristic
500C23×C43C22×D411yescharacteristic
501C22×D43—21no—
502C22×D43—21no—
503C22×D43—21no—
504C22×D43—22no—
505C22×D43—42no—
506C22×D43—42no—
507C22×D43—81no—
508C22×D43—81no—
509C22×D43—81no—
510C22×D43—81no—
511C2×C4×C43—22no—
512C2×C4×C43—22no—
513C2×C4×C43—22no—
514C2×C4×C43—21no—
515C2×C4×C43—21no—
516C2×C4×C43—21no—
517C2×C4×C43—21no—
518C2×C4×C43—42no—
519C2×C4×C43—42no—
520C2×C4×C43C22×D412yes—
521C2×C4×C43C22×D412yes—
522C2×C4×C43C22×D411yescharacteristic
523C2×C4×C43C22×D411yescharacteristic
524C2×C4×C43C22×D412yes—
525C2×C4×C43C22×D412yes—
526C2×C4×C43C22×D411yescharacteristic
527C2×C4×C43H(5,𝔽2)12yes—
528C2×C4×C43H(5,𝔽2)12yes—
529C2×C4×C43C2511yescharacteristic
530C22⋊D43—44no—
531C22⋊D43—44no—
532C22⋊D43—42no—
533C22⋊D43—42no—
534C22⋊D43—42no—
535C22⋊D43—42no—
536C22⋊D43—42no—
537C22⋊D43—42no—
538C22⋊D43—81no—
539C2×Dic43—21no—
540C2×Dic43—21no—
541C2×Dic43—21no—
542C2×Dic43—22no—
543C2×Dic43—22no—
544C2×Dic43—22no—
545C2×Dic43—21no—
546C2×Dic43—21no—
547C2×Dic43—42no—
548C2×Dic43—42no—
549C2×Dic43—42no—
550C2×Dic43—81no—
551D172—21no—
552D172—22no—
553D172—21no—
554D172—21no—
555D172—21no—
556D172—22no—
557D172—21no—
558D172—21no—
559D172—42no—
560D172—42no—
561D172—82no—
562D172—82no—
563D172—82no—
564D172—82no—
565C4×D43—44no—
566C4×D43—44no—
567C4×D43—42no—
568C4×D43—42no—
569C4×D43—42no—
570C4×D43—42no—
571C4×D43—42no—
572C4×D43—82no—
573Dic86—22no—
574Dic86—21no—
575Dic86—22no—
576Dic86—21no—
577Dic86—22no—
578Dic86—21no—
579Dic86—21no—
580Dic86—22no—
581Dic86—21no—
582Dic86—21no—
583Dic86—42no—
584Dic86—42no—
585Dic86—42no—
586Dic86—82no—
587C8×C43—21no—
588C8×C43—21no—
589C8×C43—22no—
590C8×C43—21no—
591C8×C43—22no—
592C8×C43—21no—
593#60816—431nomaximal, Sylow
594C22×C43—21no—
595C22×C43—21no—
596C22×C43—21no—
597C22×C43—21no—
598C22×C43—21no—
599C22×C43—21no—
600C22×C43—21no—
601C22×C43—21no—
602C22×C43—82no—
603C22×C43#53512yes—
604C22×C43C23×D411yescharacteristic
605C2×D43—42no—
606C2×D43—41no—
607C2×D43—41no—
608C2×D43—41no—
609C2×D43—42no—
610C2×D43—41no—
611C2×D43—41no—
612C2×D43—41no—
613C2×D43—41no—
614C2×D43—41no—
615C2×D43—42no—
616C2×D43—41no—
617C2×D43—84no—
618C2×D43—84no—
619C4×C43—22no—
620C4×C43—22no—
621C4×C43—22no—
622C4×C43—22no—
623C4×C43—21no—
624C4×C43—21no—
625C4×C43#53512yes—
626C4×C43C2×H(5,𝔽2)11yescharacteristic
627C4×C43C2×H(5,𝔽2)11yescharacteristic
628Dic43—41no—
629Dic43—42no—
630Dic43—41no—
631Dic43—42no—
632Dic43—41no—
633Dic43—41no—
634Dic43—42no—
635Dic43—41no—
636#3495—431no—
637#3449—431no—
638#3225—432no—
639#3224—432no—
640#3223—432no—
641#3222—432no—
642#3219—432no—
643#3216—432no—
644#3212—432no—
645#3210—432no—
646#3156—431no—
647#3154—431no—
648#3137—431no—
649#3136—431no—
650#3046—431no—
651#3045—431no—
652#3044—431no—
653#3043—431no—
654#3007—431no—
655#3005—431no—
656#3002—431no—
657C2×#452—431no—
658#2924D4311yescharacteristic, complemented
659C2×C43—22no—
660C2×C43—41no—
661C2×C43—41no—
662C2×C43C2×#53511yescharacteristic
663C2×C43#358411yescharacteristic
664C2×C43#358611yescharacteristic
665D43—81no—
666D43—82no—
667D43—81no—
668D43—81no—
669C22×#41—431no—
670C22×#41—431no—
671C2×#137—431no—
672C2×#137—431no—
673C2×#137—431no—
674C2×AGL(1,ℤ/8)—431no—
675C2×#135—431no—
676C2×#135—431no—
677C22×Q16—431no—
678C22×SD16—431no—
679#556—861no—
680#554—861no—
681#552—862no—
682#552—861no—
683#552—861no—
684#551—862no—
685#544—431no—
686#542—432no—
687#541—432no—
688#537—861no—
689#537—861no—
690#536—431no—
691#536—431no—
692#536—432no—
693#536—431no—
694#535—431no—
695#535—432no—
696#535—431no—
697#534—862no—
698#533—432no—
699#532—432no—
700#532—432no—
701#529—432no—
702#525—431no—
703#525—861no—
704#525—862no—
705#525—861no—
706C2×C22⋊Q8—431no—
707#520—431no—
708#519—431no—
709C2×#117C2×D4311yescharacteristic
710#497—432no—
711#497—432no—
712#497—432no—
713#496—432no—
714#495—432no—
715#495—432no—
716#494—432no—
717#492—432no—
718#491—432no—
719#490—432no—
720#489—432no—
721#489—432no—
722#488—432no—
723#488—432no—
724#487—432no—
725#486—432no—
726#464—432no—
727#464—432no—
728#464—432no—
729#464—432no—
730#464—432no—
731#464—432no—
732#463—432no—
733#463—432no—
734#462—432no—
735#462—432no—
736#462—432no—
737#461—432no—
738#460—432no—
739#460—432no—
740#460—432no—
741#459—432no—
742#452—432no—
743#452—432no—
744#452—432no—
745#452—431no—
746#452—432no—
747#452—432no—
748#452—432no—
749#452—432no—
750#452—431no—
751#452—432no—
752#451—431no—
753#451—432no—
754#450—431no—
755#450—432no—
756#449—432no—
757#449—431no—
758#449—432no—
759#449—431no—
760#448—431no—
761#447—431no—
762#433C2×D4312yescomplemented
763#433C2×D4312yescomplemented
764#432C2×D4312yescomplemented
765#431C2×D4312yescomplemented
766#424C2×D4311yescharacteristic, complemented
767#424C2×D4311yescharacteristic, complemented
768#419—431no—
769#418—431no—
770#417—431no—
771#417—431no—
772#416—431no—
773#416—431no—
774C2×#103—431no—
775C2×#102—431no—
776#407C2×D4311yescharacteristic
777C2×C22⋊C8C2×D4311yescharacteristic
778#405C2×D4311yescharacteristic, complemented
779#405C2×D4311yescharacteristic, complemented
780C43#6081611yescharacteristic, complemented, Sylow
781C2×#41—431no—
782C2×#41—431no—
783C2×#41—431no—
784C2×#41—431no—
785C2×#41—432no—
786C2×#41—431no—
787C2×#41—432no—
788C2×#41—861no—
789C2×#41—861no—
790C2×#41—861no—
791C2×#41—861no—
792C2×#41—1722no—
793C2×#41—1722no—
794C2×#41—1722no—
795C2×#41—1722no—
796C22×Q8—431no—
797C22×Q8—431no—
798C22×Q8—431no—
799C22×D4—431no—
800C22×D4—431no—
801C22×D4—861no—
802C22×D4—861no—
803C23×C4—861no—
804C23×C4—861no—
805C23×C4C22×D4311yescharacteristic
806#137—1722no—
807#137—1722no—
808#137—1722no—
809AGL(1,ℤ/8)—1722no—
810#135—1722no—
811#135—1722no—
812C2×Q16—432no—
813C2×Q16—432no—
814C2×Q16—431no—
815C2×Q16—431no—
816C2×Q16—432no—
817C2×Q16—432no—
818C2×Q16—432no—
819C2×Q16—1722no—
820C2×SD16—432no—
821C2×SD16—432no—
822C2×SD16—431no—
823C2×SD16—431no—
824C2×SD16—431no—
825C2×SD16—431no—
826C2×SD16—432no—
827C2×SD16—432no—
828C2×SD16—432no—
829C2×SD16—432no—
830C2×SD16—1722no—
831C2×D8—431no—
832C2×D8—431no—
833C2×D8—432no—
834C2×M16C22×D4311yescharacteristic
835C2×M16C22×D4311yescharacteristic
836C22×C8C22×D4311yescharacteristic
837C22×C8C22×D4311yescharacteristic
838C4⋊Q8—432no—
839C4⋊Q8—432no—
840C4⋊Q8—432no—
841C4⋊Q8—432no—
842C4⋊Q8—861no—
843#127—432no—
844#127—432no—
845#126—862no—
846#126—862no—
847#126—862no—
848#126—862no—
849#125—432no—
850#125—862no—
851#125—862no—
852#125—861no—
853#125—862no—
854#124—432no—
855#124—432no—
856#124—432no—
857#124—432no—
858#124—432no—
859#124—862no—
860#123—861no—
861#123—862no—
862#123—862no—
863#123—862no—
864#123—862no—
865#123—862no—
866#123—862no—
867#123—862no—
868C22⋊Q8—432no—
869C22⋊Q8—432no—
870C22⋊Q8—431no—
871C22⋊Q8—431no—
872C22⋊Q8—861no—
873C22⋊Q8—861no—
874C22⋊Q8—862no—
875C22⋊Q8—861no—
876C22⋊Q8—861no—
877C22⋊Q8—861no—
878C22⋊Q8—862no—
879C22⋊Q8—861no—
880C22⋊Q8—862no—
881C22⋊Q8—861no—
882C22⋊Q8—861no—
883C22⋊Q8—862no—
884C22⋊Q8—862no—
885#121—431no—
886#121—431no—
887#121—862no—
888#121—862no—
889#121—862no—
890#121—862no—
891#121—861no—
892#121—861no—
893#121—861no—
894#121—862no—
895#121—861no—
896#121—862no—
897#120—861no—
898#120—862no—
899#120—862no—
900#120—862no—
901#120—862no—
902C4×Q8—432no—
903C4×Q8—432no—
904C4×Q8—432no—
905C4×Q8—861no—
906C4×Q8—861no—
907C4×Q8—862no—
908C4×D4—432no—
909C4×D4—861no—
910C4×D4—861no—
911C4×D4—862no—
912C4×D4—862no—
913C4×D4—862no—
914C4×D4—862no—
915C4×D4—862no—
916C4×D4—862no—
917#117—431no—
918#117—862no—
919#117—861no—
920#117—862no—
921#117—862no—
922#117D17211yescharacteristic
923#117D17212yes—
924#117D17211yescharacteristic
925#117C22×D4311yescharacteristic
926#117C22×D4311yescharacteristic
927#117C22×D4312yes—
928C2×C4⋊C4—431no—
929C2×C4⋊C4—861no—
930C2×C4⋊C4—861no—
931C2×C4⋊C4D17211yescharacteristic
932C2×C4⋊C4D17211yescharacteristic
933C2×C22⋊C4—861no—
934C2×C22⋊C4D17212yes—
935C2×C42C22×D4312yes—
936C4⋊C8C22×D4312yes—
937C4⋊C8C22×D4312yes—
938C4⋊C8C22×D4312yes—
939C4⋊C8C22×D4312yes—
940#103—432no—
941#103—432no—
942#103—431no—
943#103—431no—
944#103—431no—
945#103—431no—
946#103—432no—
947#103—432no—
948#103—432no—
949#103—432no—
950#102—432no—
951#102—432no—
952#102—431no—
953#102—431no—
954#102—431no—
955#102—431no—
956#102—432no—
957#102—432no—
958#102—432no—
959#102—432no—
960C22⋊C8C22×D4311yescharacteristic
961C22⋊C8C22×D4311yescharacteristic
962C22⋊C8C22×D4311yescharacteristic
963C22⋊C8C22×D4311yescharacteristic
964C22⋊C8C22×D4312yes—
965C22⋊C8C22×D4312yes—
966#97C22×D4312yes—
967#97C22×D4312yes—
968C4×C8C22×D4312yes—
969C4×C8C22×D4312yes—
970C24—861no—
971C24—861no—
972C24C2×D17211yescharacteristic
973#41—862no—
974#41—862no—
975#41—862no—
976#41—862no—
977#41—862no—
978#41—862no—
979#41—1722no—
980#41—1722no—
981#41—1722no—
982#41—1721no—
983#41—1721no—
984#41—1722no—
985#41—1721no—
986#41—1721no—
987#41—1724no—
988#41—1724no—
989#41—1724no—
990#41—1724no—
991C2×Q8—432no—
992C2×Q8—431no—
993C2×Q8—431no—
994C2×Q8—432no—
995C2×Q8—431no—
996C2×Q8—862no—
997C2×Q8—861no—
998C2×Q8—861no—
999C2×Q8—861no—
1000C2×Q8—862no—
1001C2×Q8—862no—
1002C2×Q8—862no—
1003C2×Q8—862no—
1004C2×Q8—1721no—
1005C2×Q8—1721no—
1006C2×D4—432no—
1007C2×D4—431no—
1008C2×D4—431no—
1009C2×D4—431no—
1010C2×D4—861no—
1011C2×D4—861no—
1012C2×D4—861no—
1013C2×D4—862no—
1014C2×D4—861no—
1015C2×D4—861no—
1016C2×D4—861no—
1017C2×D4—862no—
1018C2×D4—861no—
1019C2×D4—862no—
1020C2×D4—862no—
1021C2×D4—862no—
1022C2×D4—862no—
1023C2×D4—861no—
1024C2×D4—861no—
1025C2×D4—862no—
1026C2×D4—862no—
1027C2×D4—1721no—
1028C2×D4—1721no—
1029C2×D4—1724no—
1030C2×D4—1724no—
1031C22×C4—22no—
1032C22×C4—22no—
1033C22×C4—861no—
1034C22×C4—861no—
1035C22×C4—861no—
1036C22×C4—861no—
1037C22×C4—862no—
1038C22×C4—861no—
1039C22×C4—861no—
1040C22×C4—862no—
1041C22×C4—861no—
1042C22×C4—862no—
1043C22×C4—861no—
1044C22×C4—861no—
1045C22×C4—1724no—
1046C22×C4—1724no—
1047C22×C4C2×D17211yescharacteristic
1048C22×C4C2×D17211yescharacteristic
1049C22×C4C2×D17211yescharacteristic
1050C22×C4C2×D17212yes—
1051C22×C4C2×D17212yes—
1052C22×C4C23×D4311yescharacteristic
1053C22×C4C23×D4311yescharacteristic
1054C22×C4C23×D4311yescharacteristic
1055Q16—1722no—
1056Q16—1722no—
1057Q16—1721no—
1058Q16—1721no—
1059Q16—1722no—
1060Q16—1722no—
1061Q16—1722no—
1062SD16—1722no—
1063SD16—1722no—
1064SD16—1721no—
1065SD16—1721no—
1066SD16—1721no—
1067SD16—1721no—
1068SD16—1722no—
1069SD16—1722no—
1070SD16—1722no—
1071SD16—1722no—
1072D8—1721no—
1073D8—1721no—
1074D8—1722no—
1075M16—22no—
1076M16—22no—
1077C2×C8—22no—
1078C2×C8—22no—
1079C2×C8C23×D4311yescharacteristic
1080C2×C8C23×D4311yescharacteristic
1081C2×C8C23×D4312yes—
1082C2×C8C23×D4312yes—
1083C2×C8C23×D4311yescharacteristic
1084C2×C8C23×D4311yescharacteristic
1085C4⋊C4—432no—
1086C4⋊C4—431no—
1087C4⋊C4—431no—
1088C4⋊C4—861no—
1089C4⋊C4—862no—
1090C4⋊C4—862no—
1091C4⋊C4—862no—
1092C4⋊C4—862no—
1093C4⋊C4—862no—
1094C4⋊C4—862no—
1095C4⋊C4—862no—
1096C4⋊C4—862no—
1097C4⋊C4—861no—
1098C4⋊C4—862no—
1099C4⋊C4—862no—
1100C4⋊C4—862no—
1101C4⋊C4—862no—
1102C4⋊C4—861no—
1103C4⋊C4—862no—
1104C4⋊C4—862no—
1105C4⋊C4C2×D17211yescharacteristic
1106C4⋊C4C2×D17211yescharacteristic
1107C4⋊C4C2×D17212yes—
1108C4⋊C4C2×D17211yescharacteristic
1109C4⋊C4C2×D17211yescharacteristic
1110C4⋊C4C2×D17212yes—
1111C22⋊C4—862no—
1112C22⋊C4—862no—
1113C22⋊C4—861no—
1114C22⋊C4—861no—
1115C22⋊C4—861no—
1116C22⋊C4—861no—
1117C22⋊C4—862no—
1118C22⋊C4—862no—
1119C22⋊C4—862no—
1120C22⋊C4—862no—
1121C22⋊C4—862no—
1122C22⋊C4—862no—
1123C22⋊C4—862no—
1124C22⋊C4—862no—
1125C22⋊C4—862no—
1126C22⋊C4—862no—
1127C22⋊C4—861no—
1128C22⋊C4—862no—
1129C22⋊C4C2×D17212yes—
1130C22⋊C4C2×D17212yes—
1131C22⋊C4C2×D17212yes—
1132C22⋊C4C2×D17212yes—
1133C42—861no—
1134C42—862no—
1135C42—862no—
1136C42—862no—
1137C42C2×D17212yes—
1138C42C2×D17212yes—
1139C42C23×D4312yes—
1140C42C23×D4312yes—
1141C23—22no—
1142C23—41no—
1143C23—41no—
1144C23—861no—
1145C23—862no—
1146C23—861no—
1147C23—861no—
1148C23—3441no—
1149C23—3441no—
1150C23—3441no—
1151C23—3441no—
1152C23—1722no—
1153C23—1722no—
1154C23C22×D17211yescharacteristic
1155C23C22×D17211yescharacteristic
1156C23C22×D17211yescharacteristic
1157Q8—862no—
1158Q8—861no—
1159Q8—862no—
1160Q8—861no—
1161Q8—862no—
1162Q8—861no—
1163Q8—861no—
1164Q8—862no—
1165Q8—861no—
1166Q8—861no—
1167Q8—3442no—
1168Q8—1722no—
1169Q8—1722no—
1170Q8—1722no—
1171D4—861no—
1172D4—861no—
1173D4—862no—
1174D4—861no—
1175D4—861no—
1176D4—862no—
1177D4—861no—
1178D4—861no—
1179D4—3442no—
1180D4—3442no—
1181D4—3442no—
1182D4—3442no—
1183D4—3441no—
1184D4—1722no—
1185D4—1724no—
1186D4—1724no—
1187D4—1722no—
1188D4—1722no—
1189D4—1722no—
1190D4—1722no—
1191D4—1722no—
1192D4—1722no—
1193D4—1722no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—861no—
1204C2×C4—861no—
1205C2×C4—862no—
1206C2×C4—861no—
1207C2×C4—862no—
1208C2×C4—862no—
1209C2×C4—861no—
1210C2×C4—861no—
1211C2×C4—3442no—
1212C2×C4—3441no—
1213C2×C4—1724no—
1214C2×C4—1722no—
1215C2×C4—1722no—
1216C2×C4—1724no—
1217C2×C4—1722no—
1218C2×C4—1722no—
1219C2×C4—1722no—
1220C2×C4—1722no—
1221C2×C4—1722no—
1222C2×C4—1722no—
1223C2×C4C22×D17212yes—
1224C2×C4C22×D17212yes—
1225C2×C4C22×D17211yescharacteristic
1226C2×C4C22×D17212yes—
1227C2×C4C22×D17212yes—
1228C2×C4C22×D17211yescharacteristic
1229C2×C4C22×D17211yescharacteristic
1230C2×C4#1306337112yes—
1231C2×C4#1306337112yes—
1232C2×C4C24×D4311yescharacteristic
1233C8—21no—
1234C8—21no—
1235C8—21no—
1236C8—21no—
1237C8—22no—
1238C8—22no—
1239C22—21no—
1240C22—21no—
1241C22—21no—
1242C22—21no—
1243C22—21no—
1244C22—21no—
1245C22—21no—
1246C22—21no—
1247C22—82no—
1248C22—3444no—
1249C22—3444no—
1250C22—1721no—
1251C22—1722no—
1252C22—1721no—
1253C22—1721no—
1254C22—1722no—
1255C22—1721no—
1256C22—1721no—
1257C22—1721no—
1258C22—1722no—
1259C22—1721no—
1260C22—1721no—
1261C22—1721no—
1262C22#1458346812yes—
1263C22C23×D17211yescharacteristic
1264C4—22no—
1265C4—22no—
1266C4—22no—
1267C4—22no—
1268C4—21no—
1269C4—21no—
1270C4—1722no—
1271C4—1721no—
1272C4—1721no—
1273C4—1722no—
1274C4—1721no—
1275C4—1721no—
1276C4—1721no—
1277C4—1722no—
1278C4#1458346812yes—
1279C4C2×#1306337111yescharacteristic
1280C4C2×#1306337111yescharacteristic
1281C2—22no—
1282C2—41no—
1283C2—41no—
1284C2—3442no—
1285C2—3441no—
1286C2—3441no—
1287C2—3441no—
1288C2C2×#1458346811yescharacteristic
1289C2#1914936911yescharacteristic
1290C2#1914938311yescharacteristic
subgroupG/H
centerC22C23×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#2924C2
socleC22×C43C23×D4
hypercenter#2924D43
hypocenterC43#60816
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. #19148347C2semidirect
2. #19147928C2semidirect
3. #19145706C2semidirect
4. #19145691C2semidirect
5. #19145680C2semidirect
6. #19145669C2semidirect
7. #19145634C2semidirect
8. #19145608C2semidirect
9. #19145573C2semidirect
10. #19145553C2semidirect
11. #19145089C2semidirect
12. #19145071C2semidirect
13. #19144962C2semidirect
14. #19144951C2semidirect
15. #19144147C2semidirect
16. #19144136C2semidirect
17. #19144126C2semidirect
18. #19144117C2semidirect
19. #19143857C2semidirect
20. #19143840C2semidirect
21. #19143817C2semidirect
22. C2×#14583063C2semidirect
23. C43×#2924C2semidirect
28. C2×#13063358C22semidirect
29. C2×#13063353C22semidirect
32. C22×Dic172C22semidirect
33. C22×#10621873C22semidirect
40. #14583527C22semidirect
41. #14583520C22semidirect
42. #14583511C22semidirect
48. #14583475C22semidirect
53. #14583456C22semidirect
56. #14583433C22semidirect
62. #14583379C22semidirect
63. #14583376C22semidirect
64. #14583293C22semidirect
65. #14583293C22semidirect
66. #14583293C22semidirect
67. #14583288C22semidirect
68. #14583283C22semidirect
69. #14583283C22semidirect
70. #14583279C22semidirect
71. #14583272C22semidirect
72. #14583268C22semidirect
73. #14583264C22semidirect
74. #14583259C22semidirect
75. #14583259C22semidirect
76. #14583254C22semidirect
77. #14583254C22semidirect
78. #14583250C22semidirect
79. #14583246C22semidirect
80. #14583122C22semidirect
81. #14583122C22semidirect
82. #14583122C22semidirect
83. #14583122C22semidirect
84. #14583122C22semidirect
85. #14583122C22semidirect
86. #14583115C22semidirect
87. #14583115C22semidirect
88. #14583110C22semidirect
89. #14583110C22semidirect
90. #14583110C22semidirect
91. #14583105C22semidirect
92. #14583100C22semidirect
93. #14583100C22semidirect
94. #14583100C22semidirect
95. #14583095C22semidirect
99. #14583063C22semidirect
100. #14583063C22semidirect
101. #14583063C22semidirect
102. #14583063C22semidirect
103. #14583063C22semidirect
104. #14583063C22semidirect
105. #14583063C22semidirect
106. #14583057C22semidirect
107. #14583057C22semidirect
108. #14583052C22semidirect
109. #14583052C22semidirect
111. #14583046C22semidirect
112. #14583046C22semidirect
113. #14583046C22semidirect
114. #14583040C22semidirect
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
658. #2924D43semidirect
762. #433C2×D43semidirect
763. #433C2×D43semidirect
764. #432C2×D43semidirect
765. #431C2×D43semidirect
766. #424C2×D43semidirect
767. #424C2×D43semidirect
778. #405C2×D43semidirect
779. #405C2×D43semidirect
780. C43#60816semidirect

Maximal subgroups

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

subgroupindex
#191483472
#191479282
#191457062
#191456912
#191456802
#191456692
#191456342
#191456082
#191455732
#191455532
#191450892
#191450712
#191449622
#191449512
#191441472
#191441362
#191441262
#191441172
#191438572
#191438402
#191438172
C2×#145830632
C43×#29242
#6081643