Finite Group Databasebeta

← #25967525

Subgroups — #25967525

Order 11008.

2140 conjugacy classes of subgroups.

The subgroup lattice has 1290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148267C211yesmaximal, characteristic, complemented
2#19147928C211yesmaximal, characteristic, complemented
3#19145508C212yesmaximal, complemented
4#19145495C212yesmaximal, complemented
5#19145484C212yesmaximal, complemented
6#19145482C212yesmaximal, complemented
7#19145435C212yesmaximal, complemented
8#19145429C212yesmaximal, complemented
9#19145386C212yesmaximal, complemented
10#19145380C212yesmaximal, complemented
11#19144567C211yesmaximal, characteristic, complemented
12#19144556C211yesmaximal, characteristic, complemented
13#19144543C211yesmaximal, characteristic, complemented
14#19144289C211yesmaximal, characteristic, complemented
15#19144278C211yesmaximal, characteristic, complemented
16#19144251C211yesmaximal, characteristic, complemented
17#19144235C211yesmaximal, characteristic, complemented
18#19143893C211yesmaximal, characteristic, complemented
19#19143884C211yesmaximal, characteristic, complemented
20#19143835C211yesmaximal, characteristic, complemented
21C2×#14583063C211yesmaximal, characteristic, complemented
22#19143041C211yesmaximal, characteristic, complemented
23C43×#3091C211yesmaximal, characteristic, complemented
24C2×#13063372C2211yescharacteristic
25C22×#10621898C2211yescharacteristic
26C22×#10621898C2211yescharacteristic
27C2×#13063355C2211yescharacteristic, complemented
28C2×#13063350C2211yescharacteristic, complemented
29C22×Dic172C2211yescharacteristic, complemented
30C22×#10621873C2211yescharacteristic, complemented
31C2×#13063331C2211yescharacteristic
32C2×#13063331C2211yescharacteristic
33D4×Dic86—21no—
34#14583558—21no—
35#14583554—21no—
36#14583547—22no—
37#14583545—21no—
38#14583536—22no—
39#14583480C2212yes—
40#14583480C2212yes—
41#14583478C2212yescomplemented
42#14583477C2211yescharacteristic
43#14583475—21no—
44#14583475C2211yescharacteristic
45#14583475C2211yescharacteristic
46#14583475C2211yescharacteristic
47#14583472C2212yescomplemented
48#14583468—21no—
49#14583468C2211yescharacteristic
50#14583468C2211yescharacteristic
51#14583461—22no—
52#14583449—21no—
53#14583449—21no—
54#14583411—22no—
55#14583411C2212yes—
56#14583411C2212yes—
57#14583409C2212yescomplemented
58C2×#13063304C2211yescharacteristic
59C22⋊Q8×D43C2212yescomplemented
60#14583379C2211yescharacteristic
61#14583243C2212yescomplemented
62#14583242C2212yescomplemented
63#14583240C2212yescomplemented
64#14583240C2212yescomplemented
65#14583236C2212yescomplemented
66#14583234C2212yescomplemented
67#14583231C2212yescomplemented
68#14583229C2212yescomplemented
69#14583226C2212yescomplemented
70#14583225C2212yescomplemented
71#14583219C2212yescomplemented
72#14583214C2212yescomplemented
73#14583158C2212yescomplemented
74#14583158C2212yescomplemented
75#14583156C2212yescomplemented
76#14583151C2212yescomplemented
77#14583148C2212yescomplemented
78#14583146C2212yescomplemented
79#14583146C2212yescomplemented
80#14583144C2212yescomplemented
81#14583141C2212yescomplemented
82#14583141C2212yescomplemented
83#14583139C2212yescomplemented
84#14583134C2212yescomplemented
85#14583131C2212yescomplemented
86#14583129C2212yescomplemented
87#14583129C2212yescomplemented
88#14583127C2212yescomplemented
89#14583063C2212yes—
90#14583063C2212yes—
91#14583063C2212yescomplemented
92#14583063C2212yescomplemented
93#14583062C2212yescomplemented
94#14583062C2212yescomplemented
95#14583059C2212yes—
96#14583059C2212yescomplemented
97#14583056C2212yescomplemented
98#14583056C2212yescomplemented
99#14583045C2212yescomplemented
100#14583045C2212yescomplemented
101#14583042C2212yes—
102#14583042C2212yescomplemented
103#14583039C2212yescomplemented
104#14583039C2212yescomplemented
105#14582942C2211yescharacteristic, complemented
106#14582942C2211yescharacteristic, complemented
107#14582907C2211yescharacteristic, complemented
108#14582907C2211yescharacteristic, complemented
109#14582907C2211yescharacteristic, complemented
110#14582903C2211yescharacteristic, complemented
111C2×#13063250C2211yescharacteristic, complemented
112C2×#13063247C2211yescharacteristic, complemented
113#14582865C2211yescharacteristic
114#14582865C2211yescharacteristic
115#14582864C2212yescomplemented
116#14582864C2212yescomplemented
117#14582863C2211yescharacteristic
118#14582861C2212yescomplemented
119C22⋊C8×D43C2212yescomplemented
120C43×#525C2211yescharacteristic
121C2×#117×C43C2211yescharacteristic
122C43×#485C2211yescharacteristic, complemented
123C43×#485C2211yescharacteristic, complemented
124C43×#484C2211yescharacteristic, complemented
125C43×#483C2211yescharacteristic, complemented
126C43×#482C2211yescharacteristic, complemented
127C43×#482C2211yescharacteristic, complemented
128C43×#481C2211yescharacteristic, complemented
129C43×#480C2211yescharacteristic, complemented
130C43×#427C2211yescharacteristic, complemented
131C43×#427C2211yescharacteristic, complemented
132C43×#416C2211yescharacteristic, complemented
133C43×#416C2211yescharacteristic, complemented
134C2×C22⋊C8×C43C2211yescharacteristic
135#13063372—42no—
136#13063372—42no—
137C2×#10621898—21no—
138C2×#10621898—21no—
139C2×#10621898—21no—
140C2×#10621898—42no—
141C2×#10621898—42no—
142C2×#10621898—42no—
143C2×#10621898—42no—
144C2×#10621898D411yescharacteristic
145C2×#10621898D411yescharacteristic
146C2×#10621898D412yes—
147C2×#10621898C2311yescharacteristic
148C2×#10621898C2311yescharacteristic
149C2×#10621898C2312yes—
150C2×#10621898C2312yes—
151C2×#10621898C2312yes—
152C2×#10621900—22no—
153C2×#10621900C2312yes—
154C22×Dic86—21no—
155C22×Dic86D411yescharacteristic
156C22×Dic86C2311yescharacteristic
157C22×Dic86C2311yescharacteristic
158C2×Q8×D43C2312yes—
159C22×D172D411yescharacteristic
160C22×D172C2311yescharacteristic
161C22×C22⋊D43—21no—
162C22×C22⋊D43D412yes—
163C22×C4×D43—21no—
164C22×C4×D43C2312yes—
165#13063355—42no—
166#13063350—42no—
167C2×Dic172—42no—
168C2×Dic172C2312yes—
169C2×Dic172C2312yes—
170C2×#10621885C2312yes—
171C2×#10621873—42no—
172C2×#10621873C2312yes—
173C2×#10621873C2312yes—
174C2×#10621883C2312yes—
175C2×#10621884C2312yes—
176C2×#10621882C2312yes—
177#13063331—42no—
178#13063331—42no—
179C2×#10621877C2311yescharacteristic
180C2×#10621877C2311yescharacteristic
181C2×#10621872C2312yes—
182C2×#10621872C2312yes—
183C2×C8×D43C2312yes—
184C2×C8×D43C2312yes—
185#13063325—21no—
186#13063325—21no—
187#13063325—21no—
188#13063324—22no—
189#13063322—21no—
190#13063322—21no—
191#13063313—21no—
192#13063313—21no—
193#13063313—21no—
194#13063313—21no—
195#13063313—21no—
196#13063311—22no—
197#13063310—22no—
198#13063309—22no—
199#13063309—22no—
200#13063309—22no—
201#13063309—22no—
202#13063309—22no—
203#13063307—22no—
204#13063307—22no—
205#13063305—22no—
206#13063305—22no—
207#13063305C2312yes—
208#13063305C2312yes—
209#13063305C2312yes—
210#13063305C2312yes—
211#13063305C2312yes—
212#13063305C2312yes—
213#13063304—21no—
214#13063304—21no—
215#13063304—21no—
216#13063304C2312yes—
217#13063304C2312yes—
218#13063303—22no—
219#13063302—22no—
220#13063302—22no—
221#13063301C2312yes—
222#13063300—22no—
223#13063300—22no—
224#13063300C2312yes—
225#13063300C2312yes—
226#13063300C2312yes—
227#13063300C2312yes—
228#13063299—22no—
229#13063299—22no—
230#13063299—22no—
231#13063299—22no—
232#13063299—21no—
233#13063298—22no—
234#13063297—22no—
235#13063297—22no—
236#13063296—22no—
237#13063296C2312yes—
238#13063295—22no—
239#13063295—22no—
240#13063295—22no—
241#13063295—22no—
242#13063293—22no—
243C4×Dic86—21no—
244C4×D172—21no—
245C4×D172—22no—
246C4×D172—22no—
247C4×D172—22no—
248C4×D172—22no—
249D4×Dic43—22no—
250(C22⋊D43)⋊C4—22no—
251(C22⋊D43)⋊C4—22no—
252#13063283C2312yes—
253C2×C4⋊Dic43C2311yescharacteristic
254C2×Dic43⋊C4—21no—
255C4⋊C4×D43—22no—
256C4⋊C4×D43C2312yes—
257C2×C22⋊Dic43—21no—
258C22⋊C4×D43—22no—
259#13063258C2312yes—
260#13063258C2312yes—
261#13063256C2312yes—
262#13063256C2312yes—
263#13063250C2312yes—
264#13063250C2312yes—
265#13063248C2312yes—
266#13063248C2312yes—
267#13063248C2312yes—
268#13063248C2312yes—
269#13063248C2312yes—
270#13063248C2312yes—
271#13063247C2312yes—
272#13063247C2312yes—
273#13063245C2312yes—
274#13063245C2312yes—
275C22⋊(C43⋊C8)C2312yes—
276C22⋊(C43⋊C8)C2312yes—
277(C2×D43)⋊C8C2312yes—
278(C2×D43)⋊C8C2312yes—
279(C2×D43)⋊C8C2312yes—
280(C2×D43)⋊C8C2312yes—
281C2×#41×C43C2311yescharacteristic
282C23×C4×C43C2311yescharacteristic
283C22×C8×C43C2311yescharacteristic
284C22×C8×C43C2311yescharacteristic
285#123×C43—21no—
286C22⋊Q8×C43C2311yescharacteristic
287C22⋊Q8×C43C2311yescharacteristic
288#121×C43C2311yescharacteristic
289#121×C43C2311yescharacteristic
290#120×C43—21no—
291C4×D4×C43—21no—
292C4×D4×C43—21no—
293#117×C43—21no—
294#117×C43—21no—
295#117×C43C2311yescharacteristic
296#117×C43C2311yescharacteristic
297#117×C43C2311yescharacteristic
298#117×C43C2311yescharacteristic
299#117×C43C2311yescharacteristic
300C2×C4⋊C4×C43C2311yescharacteristic
301C2×C4⋊C4×C43C2311yescharacteristic
302C2×C22⋊C4×C43—21no—
303C2×C42×C43—21no—
304#107×C43C2311yescharacteristic
305#107×C43C2311yescharacteristic
306#107×C43C2311yescharacteristic
307#107×C43C2311yescharacteristic
308#106×C43C2311yescharacteristic
309#106×C43C2311yescharacteristic
310#106×C43C2311yescharacteristic
311#106×C43C2311yescharacteristic
312#103×C43C2311yescharacteristic
313#103×C43C2311yescharacteristic
314#103×C43C2311yescharacteristic
315#103×C43C2311yescharacteristic
316#102×C43C2311yescharacteristic
317#102×C43C2311yescharacteristic
318#102×C43C2311yescharacteristic
319#102×C43C2311yescharacteristic
320C22⋊C8×C43C2311yescharacteristic
321C22⋊C8×C43C2311yescharacteristic
322C22⋊C8×C43C2311yescharacteristic
323C22⋊C8×C43C2311yescharacteristic
324C24×C43C2×D411yescharacteristic
325C23×D43—21no—
326C23×D43C2×D412yes—
327#41×C43—22no—
328#41×C43—22no—
329C2×Q8×C43C2411yescharacteristic
330C2×D4×C43—21no—
331C2×D4×C43—21no—
332C2×D4×C43—21no—
333C2×D4×C43C2411yescharacteristic
334C22×C4×C43—22no—
335C22×C4×C43—22no—
336C22×C4×C43—21no—
337C22×C4×C43—21no—
338C22×C4×C43—21no—
339C22×C4×C43C2×D411yescharacteristic
340C22×C4×C43C2×D411yescharacteristic
341C22×C4×C43C2×D411yescharacteristic
342C22×C4×C43C2411yescharacteristic
343C22×C4×C43C2411yescharacteristic
344C22×C4×C43C2411yescharacteristic
345C2×C22⋊D43—22no—
346C2×C22⋊D43—22no—
347C2×C22⋊D43—22no—
348C2×C22⋊D43—22no—
349C2×C22⋊D43—44no—
350C2×C22⋊D43—44no—
351C2×C22⋊D43C2×D412yes—
352C2×C22⋊D43C2×D412yes—
353C2×C22⋊D43C2×D412yes—
354C2×C22⋊D43C2×D412yes—
355C22×Dic43—22no—
356C22×Dic43—21no—
357C22×Dic43—21no—
358C22×Dic43—21no—
359C22×Dic43C2×D412yes—
360Q8×D43—42no—
361Q8×D43—42no—
362#10621900—42no—
363#10621900—42no—
364#10621900—48no—
365#10621898—22no—
366#10621898—22no—
367#10621898—22no—
368#10621898—22no—
369#10621898—42no—
370#10621898—42no—
371#10621898—42no—
372#10621898—42no—
373#10621898—42no—
374#10621898—42no—
375#10621898—42no—
376#10621898—42no—
377#10621898—44no—
378#10621898—44no—
379#10621898—44no—
380#10621898—44no—
381C2×D172—21no—
382C2×D172—22no—
383C2×D172—22no—
384C2×D172—22no—
385C2×D172—22no—
386C2×D172—22no—
387C2×D172—22no—
388C2×D172—42no—
389C2×D172C2×D411yescharacteristic
390C2×D172C2×D411yescharacteristic
391C2×D172C2×D412yes—
392C2×D172C2412yes—
393C2×C4×D43—22no—
394C2×C4×D43—22no—
395C2×C4×D43—22no—
396C2×C4×D43—22no—
397C2×C4×D43—42no—
398C2×C4×D43—42no—
399C2×C4×D43—44no—
400C2×C4×D43C2×D412yes—
401C2×C4×D43C2×D412yes—
402C2×C4×D43C2412yes—
403C2×C4×D43C2412yes—
404C2×Dic86—22no—
405C2×Dic86—22no—
406C2×Dic86—22no—
407C2×Dic86—22no—
408C2×Dic86—21no—
409C2×Dic86—21no—
410C2×Dic86—22no—
411C2×Dic86—42no—
412C2×Dic86—44no—
413C2×Dic86C2×D411yescharacteristic
414C2×Dic86C2×D411yescharacteristic
415C2×Dic86C2×D412yes—
416C2×Dic86C2412yes—
417C2×Dic86C2412yes—
418C2×C8×C43—22no—
419C2×C8×C43—22no—
420C2×C8×C43C2411yescharacteristic
421C2×C8×C43C2411yescharacteristic
422C2×C8×C43C2411yescharacteristic
423C2×C8×C43C2411yescharacteristic
424C4⋊C4×C43—21no—
425C4⋊C4×C43—21no—
426C4⋊C4×C43—21no—
427C4⋊C4×C43—21no—
428C4⋊C4×C43C2411yescharacteristic
429C4⋊C4×C43C2411yescharacteristic
430C4⋊C4×C43C2411yescharacteristic
431C4⋊C4×C43C2411yescharacteristic
432C4⋊C4×C43C2411yescharacteristic
433C4⋊C4×C43C2411yescharacteristic
434C22⋊C4×C43—21no—
435C22⋊C4×C43—21no—
436C22⋊C4×C43—21no—
437C22⋊C4×C43—21no—
438C22⋊C4×C43—21no—
439C22⋊C4×C43—21no—
440C22⋊C4×C43—21no—
441C22⋊C4×C43—21no—
442C22⋊C4×C43—21no—
443C42×C43—21no—
444C42×C43—21no—
445C42×C43—21no—
446C42×C43—21no—
447C42×C43—21no—
448C22⋊Dic43—22no—
449C22⋊Dic43—22no—
450C22⋊Dic43—22no—
451#10621885—42no—
452#10621884—42no—
453#10621883—42no—
454#10621882—42no—
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—
461(C2×D43)⋊C4—22no—
462(C2×D43)⋊C4—22no—
463(C2×D43)⋊C4—22no—
464(C2×D43)⋊C4—22no—
465(C2×D43)⋊C4—22no—
466(C2×D43)⋊C4—22no—
467C4⋊Dic43—21no—
468C4⋊Dic43—22no—
469C4⋊Dic43—22no—
470C4⋊Dic43—22no—
471C4⋊Dic43—22no—
472C4⋊Dic43—22no—
473C4⋊Dic43—22no—
474C4⋊Dic43C2412yes—
475Dic43⋊C4—22no—
476Dic43⋊C4—22no—
477Dic43⋊C4—22no—
478Dic43⋊C4—22no—
479C4×Dic43—22no—
480#10621877—22no—
481#10621877—22no—
482C2×C43⋊C8C2412yes—
483C2×C43⋊C8C2412yes—
484Dic172—42no—
485Dic172—42no—
486#10621873—42no—
487#10621873—42no—
488#10621872—42no—
489#10621872—42no—
490C8×D43—42no—
491C8×D43—42no—
492C23×C43—22no—
493C23×C43—21no—
494C23×C43—41no—
495C23×C43—41no—
496C23×C43C22×D411yescharacteristic
497C23×C43C22×D411yescharacteristic
498C23×C43C22×D411yescharacteristic
499C22×D43—22no—
500C22×D43—42no—
501C22×D43—42no—
502C22×D43—42no—
503C22×D43—42no—
504C22×D43—81no—
505C22×D43—81no—
506C22×D43C22×D412yes—
507C22×D43C22×D412yes—
508Q8×C43—21no—
509Q8×C43—21no—
510D4×C43—21no—
511D4×C43—21no—
512D4×C43—42no—
513D4×C43—42no—
514D4×C43—81no—
515C2×C4×C43—22no—
516C2×C4×C43—22no—
517C2×C4×C43—22no—
518C2×C4×C43—21no—
519C2×C4×C43—21no—
520C2×C4×C43—21no—
521C2×C4×C43—21no—
522C2×C4×C43—21no—
523C2×C4×C43—21no—
524C2×C4×C43—21no—
525C2×C4×C43—21no—
526C2×C4×C43—21no—
527C2×C4×C43—21no—
528C2×C4×C43—21no—
529C2×C4×C43—42no—
530C2×C4×C43—81no—
531C2×C4×C43—81no—
532C2×C4×C43C22×D411yescharacteristic
533C2×C4×C43C22×D411yescharacteristic
534C2×C4×C43C22×D411yescharacteristic
535C2×C4×C43H(5,𝔽2)12yes—
536C2×C4×C43H(5,𝔽2)12yes—
537C2×C4×C43C2511yescharacteristic
538C22⋊D43—24no—
539C22⋊D43—24no—
540C22⋊D43—42no—
541C22⋊D43—42no—
542C22⋊D43—44no—
543C22⋊D43—44no—
544C22⋊D43—44no—
545C22⋊D43—82no—
546C2×Dic43—22no—
547C2×Dic43—22no—
548C2×Dic43—22no—
549C2×Dic43—42no—
550C2×Dic43—44no—
551C2×Dic43—42no—
552C2×Dic43—42no—
553C2×Dic43—81no—
554C2×Dic43C22×D412yes—
555C2×Dic43C22×D412yes—
556D172—22no—
557D172—22no—
558D172—22no—
559D172—22no—
560D172—42no—
561D172—42no—
562D172—82no—
563D172—82no—
564D172—82no—
565D172—82no—
566C4×D43—22no—
567C4×D43—22no—
568C4×D43—22no—
569C4×D43—22no—
570C4×D43—42no—
571C4×D43—42no—
572C4×D43—44no—
573C4×D43—44no—
574C4×D43—44no—
575C4×D43—82no—
576Dic86—22no—
577Dic86—22no—
578Dic86—22no—
579Dic86—22no—
580Dic86—22no—
581Dic86—22no—
582Dic86—42no—
583Dic86—44no—
584Dic86—42no—
585Dic86—42no—
586C8×C43—21no—
587C8×C43—21no—
588C8×C43—21no—
589C8×C43—21no—
590C43⋊C8—22no—
591C43⋊C8—22no—
592#60761—431nomaximal, Sylow
593C22×C43—21no—
594C22×C43—21no—
595C22×C43—21no—
596C22×C43—21no—
597C22×C43—21no—
598C22×C43—21no—
599C22×C43—21no—
600C22×C43—21no—
601C22×C43—41no—
602C22×C43—41no—
603C22×C43—41no—
604C22×C43—82no—
605C22×C43#53412yes—
606C22×C43C23×D411yescharacteristic
607C2×D43—22no—
608C2×D43—22no—
609C2×D43—22no—
610C2×D43—22no—
611C2×D43—22no—
612C2×D43—22no—
613C2×D43—42no—
614C2×D43—42no—
615C2×D43—42no—
616C2×D43—84no—
617C2×D43—84no—
618C4×C43—21no—
619C4×C43—21no—
620C4×C43—41no—
621C4×C43—41no—
622C4×C43—41no—
623C4×C43—41no—
624C4×C43—41no—
625C4×C43—41no—
626C4×C43—41no—
627C4×C43#53412yes—
628C4×C43C2×H(5,𝔽2)11yescharacteristic
629C4×C43C2×H(5,𝔽2)11yescharacteristic
630Dic43—22no—
631Dic43—22no—
632Dic43—42no—
633Dic43—42no—
634Dic43—42no—
635#3489—431no—
636#3449—431no—
637#3204—432no—
638#3203—432no—
639#3201—432no—
640#3201—432no—
641#3197—432no—
642#3196—432no—
643#3191—432no—
644#3190—432no—
645#3097—431no—
646#3096—431no—
647#3095—431no—
648#3091D4311yescharacteristic, complemented
649#3063—431no—
650#3062—431no—
651#3059—431no—
652#3057—431no—
653#3011—431no—
654#3010—431no—
655#3005—431no—
656C2×#452—431no—
657#2880—431no—
658C2×C43—22no—
659C2×C43—41no—
660C2×C43—41no—
661C2×C43—81no—
662C2×C43C2×#53411yescharacteristic
663C2×C43#358411yescharacteristic
664C2×C43#358611yescharacteristic
665D43—42no—
666D43—42no—
667D43—82no—
668C2×2−1+4—431no—
669C22×#41—431no—
670C22×#41—431no—
671C2×#137—431no—
672C2×AGL(1,ℤ/8)—431no—
673C22×Q16—431no—
674C22×SD16—431no—
675C2×#131—431no—
676C2×#131—431no—
677D4×Q8—861no—
678#548—861no—
679#547—861no—
680#547—862no—
681#546—861no—
682#546—862no—
683#537—431no—
684#537—432no—
685#537—432no—
686#537—432no—
687#536—432no—
688#536—431no—
689#536—431no—
690#536—431no—
691#536—861no—
692#535—431no—
693#535—431no—
694#535—861no—
695#534—862no—
696#532—861no—
697#532—861no—
698#525—432no—
699#525—432no—
700#525—432no—
701#525—862no—
702#525C2×D4311yescharacteristic
703C2×C22⋊Q8—431no—
704C2×C22⋊Q8—432no—
705#520—431no—
706C2×#117C2×D4311yescharacteristic
707#485—432no—
708#485—432no—
709#485—432no—
710#485—432no—
711#485C2×D4311yescharacteristic, complemented
712#485C2×D4311yescharacteristic, complemented
713#484—432no—
714#484—432no—
715#484C2×D4311yescharacteristic, complemented
716#483—432no—
717#483—432no—
718#483C2×D4311yescharacteristic, complemented
719#482—432no—
720#482—432no—
721#482C2×D4311yescharacteristic, complemented
722#482C2×D4311yescharacteristic, complemented
723#481—432no—
724#481C2×D4311yescharacteristic, complemented
725#480—432no—
726#480C2×D4311yescharacteristic, complemented
727#470—432no—
728#470—432no—
729#470—432no—
730#469—432no—
731#468—432no—
732#468—432no—
733#468—432no—
734#468—432no—
735#467—432no—
736#467—432no—
737#467—432no—
738#466—432no—
739#465—432no—
740#465—432no—
741#465—432no—
742#465—432no—
743#452—432no—
744#452—432no—
745#452—432no—
746#452—432no—
747#452—432no—
748#452—432no—
749#452—432no—
750#452—432no—
751#451—432no—
752#451—432no—
753#449—432no—
754#449—432no—
755#449—432no—
756#449—432no—
757#448—432no—
758#448—432no—
759#428—431no—
760#428—431no—
761#427C2×D4311yescharacteristic, complemented
762#427C2×D4311yescharacteristic, complemented
763#419—431no—
764#419—431no—
765#419—431no—
766#418—431no—
767#416C2×D4311yescharacteristic, complemented
768#416C2×D4311yescharacteristic, complemented
769C2×#103—431no—
770C2×#102—431no—
771#408—431no—
772#408—431no—
773#408—432no—
774#408—432no—
775#407—431no—
776#407—432no—
777C2×C22⋊C8—432no—
778C2×C22⋊C8C2×D4311yescharacteristic
779C43#6076111yescharacteristic, complemented, Sylow
7802−1+4—1722no—
7812−1+4—1722no—
782C2×#41—432no—
783C2×#41—431no—
784C2×#41—431no—
785C2×#41—431no—
786C2×#41—431no—
787C2×#41—432no—
788C2×#41—432no—
789C2×#41—432no—
790C2×#41—432no—
791C2×#41—861no—
792C2×#41—862no—
793C2×#41—861no—
794C2×#41—861no—
795C2×#41—1722no—
796C2×#41—1722no—
797C2×#41—1722no—
798C2×#41—1722no—
799C2×#41C22×D4311yescharacteristic
800C22×Q8—431no—
801C22×Q8—432no—
802C22×Q8—431no—
803C22×Q8—431no—
804C22×Q8—861no—
805C22×D4—432no—
806C22×D4—431no—
807C22×D4—431no—
808C22×D4—861no—
809C23×C4—432no—
810C23×C4—861no—
811C23×C4C22×D4311yescharacteristic
812#137—1722no—
813AGL(1,ℤ/8)—1722no—
814C2×Q16—432no—
815C2×Q16—432no—
816C2×Q16—432no—
817C2×Q16—1722no—
818C2×SD16—432no—
819C2×SD16—432no—
820C2×SD16—432no—
821C2×SD16—432no—
822C2×SD16—1722no—
823C2×D8—432no—
824#131—1722no—
825#131—1722no—
826C2×M16—431no—
827C2×M16—431no—
828C2×M16—432no—
829C2×M16—432no—
830C22×C8—432no—
831C22×C8—432no—
832C22×C8C22×D4311yescharacteristic
833C22×C8C22×D4311yescharacteristic
834C4⋊Q8—861no—
835C4⋊Q8—861no—
836C4⋊Q8—861no—
837C4⋊Q8—862no—
838#127—861no—
839#127—861no—
840#124—861no—
841#124—861no—
842#124—861no—
843#124—861no—
844#124—861no—
845#124—862no—
846#123—21no—
847#123—862no—
848#123—862no—
849#123—862no—
850#123—862no—
851#123—862no—
852#123—862no—
853#123—862no—
854#123—862no—
855C22⋊Q8—432no—
856C22⋊Q8—432no—
857C22⋊Q8—432no—
858C22⋊Q8—432no—
859C22⋊Q8—432no—
860C22⋊Q8—432no—
861C22⋊Q8—432no—
862C22⋊Q8—432no—
863C22⋊Q8—432no—
864C22⋊Q8—862no—
865C22⋊Q8—862no—
866C22⋊Q8—862no—
867C22⋊Q8—862no—
868C22⋊Q8—862no—
869C22⋊Q8—861no—
870C22⋊Q8—861no—
871C22⋊Q8—861no—
872C22⋊Q8C22×D4311yescharacteristic
873C22⋊Q8C22×D4311yescharacteristic
874#121—432no—
875#121—432no—
876#121—432no—
877#121—432no—
878#121—432no—
879#121—862no—
880#121—862no—
881#121—862no—
882#121—862no—
883#121—862no—
884#121—862no—
885#121—862no—
886#121—861no—
887#121—862no—
888#121—862no—
889#121—862no—
890#121C22×D4311yescharacteristic
891#121C22×D4311yescharacteristic
892#120—21no—
893#120—862no—
894#120—862no—
895#120—862no—
896#120—862no—
897#120—862no—
898C4×Q8—861no—
899C4×D4—21no—
900C4×D4—21no—
901C4×D4—862no—
902C4×D4—862no—
903C4×D4—862no—
904C4×D4—862no—
905C4×D4—861no—
906C4×D4—862no—
907C4×D4—862no—
908C4×D4—862no—
909#117—21no—
910#117—21no—
911#117—432no—
912#117C22×D4311yescharacteristic
913#117C22×D4311yescharacteristic
914#117C22×D4311yescharacteristic
915#117C22×D4311yescharacteristic
916#117C22×D4311yescharacteristic
917C2×C4⋊C4—431no—
918C2×C4⋊C4—432no—
919C2×C4⋊C4—862no—
920C2×C4⋊C4—861no—
921C2×C4⋊C4C22×D4311yescharacteristic
922C2×C4⋊C4C22×D4311yescharacteristic
923C2×C22⋊C4—21no—
924C2×C22⋊C4—862no—
925C2×C22⋊C4—861no—
926C2×C42—21no—
927#107—432no—
928#107—432no—
929#107C22×D4311yescharacteristic
930#107C22×D4311yescharacteristic
931#107C22×D4311yescharacteristic
932#107C22×D4311yescharacteristic
933#106—432no—
934#106—432no—
935#106C22×D4311yescharacteristic
936#106C22×D4311yescharacteristic
937#106C22×D4311yescharacteristic
938#106C22×D4311yescharacteristic
939#103—432no—
940#103—432no—
941#103—432no—
942#103—432no—
943#103—432no—
944#103—432no—
945#103—432no—
946#103—432no—
947#103C22×D4311yescharacteristic
948#103C22×D4311yescharacteristic
949#103C22×D4311yescharacteristic
950#103C22×D4311yescharacteristic
951#102—432no—
952#102—432no—
953#102—432no—
954#102—432no—
955#102C22×D4311yescharacteristic
956#102C22×D4311yescharacteristic
957#102C22×D4311yescharacteristic
958#102C22×D4311yescharacteristic
959C22⋊C8—432no—
960C22⋊C8—432no—
961C22⋊C8—432no—
962C22⋊C8—432no—
963C22⋊C8—432no—
964C22⋊C8—432no—
965C22⋊C8C22×D4311yescharacteristic
966C22⋊C8C22×D4311yescharacteristic
967C22⋊C8C22×D4311yescharacteristic
968C22⋊C8C22×D4311yescharacteristic
969C24—432no—
970C24—861no—
971C24D4×D4311yescharacteristic
972#41—22no—
973#41—22no—
974#41—862no—
975#41—862no—
976#41—862no—
977#41—862no—
978#41—1722no—
979#41—1722no—
980#41—1724no—
981#41—1722no—
982#41—1722no—
983#41—1722no—
984#41—1722no—
985#41—1722no—
986#41—1722no—
987#41—1724no—
988#41—1724no—
989#41—1724no—
990#41—1722no—
991#41—1722no—
992#41—1728no—
993C2×Q8—431no—
994C2×Q8—431no—
995C2×Q8—432no—
996C2×Q8—432no—
997C2×Q8—432no—
998C2×Q8—862no—
999C2×Q8—861no—
1000C2×Q8—861no—
1001C2×Q8—862no—
1002C2×Q8—862no—
1003C2×Q8—862no—
1004C2×Q8—862no—
1005C2×Q8—1722no—
1006C2×Q8—1724no—
1007C2×Q8—1722no—
1008C2×Q8—1722no—
1009C2×Q8C23×D4311yescharacteristic
1010C2×D4—21no—
1011C2×D4—21no—
1012C2×D4—21no—
1013C2×D4—432no—
1014C2×D4—432no—
1015C2×D4—432no—
1016C2×D4—432no—
1017C2×D4—431no—
1018C2×D4—431no—
1019C2×D4—432no—
1020C2×D4—432no—
1021C2×D4—862no—
1022C2×D4—862no—
1023C2×D4—862no—
1024C2×D4—862no—
1025C2×D4—862no—
1026C2×D4—862no—
1027C2×D4—862no—
1028C2×D4—862no—
1029C2×D4—861no—
1030C2×D4—862no—
1031C2×D4—862no—
1032C2×D4—1722no—
1033C2×D4—1724no—
1034C2×D4—1724no—
1035C2×D4C23×D4311yescharacteristic
1036C22×C4—22no—
1037C22×C4—22no—
1038C22×C4—21no—
1039C22×C4—21no—
1040C22×C4—21no—
1041C22×C4—432no—
1042C22×C4—432no—
1043C22×C4—432no—
1044C22×C4—432no—
1045C22×C4—432no—
1046C22×C4—862no—
1047C22×C4—862no—
1048C22×C4—862no—
1049C22×C4—861no—
1050C22×C4—861no—
1051C22×C4—861no—
1052C22×C4—862no—
1053C22×C4—862no—
1054C22×C4—1722no—
1055C22×C4—1722no—
1056C22×C4—1724no—
1057C22×C4D4×D4311yescharacteristic
1058C22×C4D4×D4311yescharacteristic
1059C22×C4D4×D4311yescharacteristic
1060C22×C4C23×D4311yescharacteristic
1061C22×C4C23×D4311yescharacteristic
1062C22×C4C23×D4311yescharacteristic
1063Q16—1722no—
1064Q16—1722no—
1065Q16—1722no—
1066SD16—1722no—
1067SD16—1722no—
1068SD16—1722no—
1069SD16—1722no—
1070D8—1722no—
1071M16—862no—
1072M16—862no—
1073M16—1722no—
1074M16—1722no—
1075C2×C8—22no—
1076C2×C8—22no—
1077C2×C8—432no—
1078C2×C8—432no—
1079C2×C8—1722no—
1080C2×C8—1722no—
1081C2×C8C23×D4311yescharacteristic
1082C2×C8C23×D4311yescharacteristic
1083C2×C8C23×D4311yescharacteristic
1084C2×C8C23×D4311yescharacteristic
1085C4⋊C4—21no—
1086C4⋊C4—21no—
1087C4⋊C4—21no—
1088C4⋊C4—21no—
1089C4⋊C4—432no—
1090C4⋊C4—862no—
1091C4⋊C4—862no—
1092C4⋊C4—862no—
1093C4⋊C4—862no—
1094C4⋊C4—862no—
1095C4⋊C4—862no—
1096C4⋊C4—862no—
1097C4⋊C4—862no—
1098C4⋊C4—861no—
1099C4⋊C4—862no—
1100C4⋊C4—862no—
1101C4⋊C4C23×D4311yescharacteristic
1102C4⋊C4C23×D4311yescharacteristic
1103C4⋊C4C23×D4311yescharacteristic
1104C4⋊C4C23×D4311yescharacteristic
1105C4⋊C4C23×D4311yescharacteristic
1106C4⋊C4C23×D4311yescharacteristic
1107C22⋊C4—21no—
1108C22⋊C4—21no—
1109C22⋊C4—21no—
1110C22⋊C4—21no—
1111C22⋊C4—21no—
1112C22⋊C4—21no—
1113C22⋊C4—21no—
1114C22⋊C4—21no—
1115C22⋊C4—21no—
1116C22⋊C4—862no—
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—862no—
1128C22⋊C4—862no—
1129C22⋊C4—862no—
1130C22⋊C4—862no—
1131C42—21no—
1132C42—21no—
1133C42—21no—
1134C42—21no—
1135C42—21no—
1136C42—862no—
1137C23—22no—
1138C23—21no—
1139C23—41no—
1140C23—41no—
1141C23—432no—
1142C23—432no—
1143C23—862no—
1144C23—3441no—
1145C23—3441no—
1146C23—1722no—
1147C23—1722no—
1148C23—1722no—
1149C23—1722no—
1150C23C2×D4×D4311yescharacteristic
1151C23C2×D4×D4311yescharacteristic
1152C23C2×D4×D4311yescharacteristic
1153Q8—21no—
1154Q8—21no—
1155Q8—862no—
1156Q8—862no—
1157Q8—862no—
1158Q8—862no—
1159Q8—862no—
1160Q8—862no—
1161Q8—1722no—
1162Q8—1724no—
1163Q8—1722no—
1164Q8—1722no—
1165D4—21no—
1166D4—21no—
1167D4—42no—
1168D4—42no—
1169D4—81no—
1170D4—864no—
1171D4—864no—
1172D4—862no—
1173D4—862no—
1174D4—862no—
1175D4—862no—
1176D4—3442no—
1177D4—3442no—
1178D4—3442no—
1179D4—3442no—
1180D4—3442no—
1181D4—1722no—
1182D4—1722no—
1183D4—1722no—
1184D4—1724no—
1185D4—1724no—
1186D4—1724no—
1187D4—1722no—
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—42no—
1203C2×C4—81no—
1204C2×C4—81no—
1205C2×C4—432no—
1206C2×C4—432no—
1207C2×C4—862no—
1208C2×C4—862no—
1209C2×C4—862no—
1210C2×C4—862no—
1211C2×C4—862no—
1212C2×C4—862no—
1213C2×C4—862no—
1214C2×C4—3442no—
1215C2×C4—3441no—
1216C2×C4—1722no—
1217C2×C4—1722no—
1218C2×C4—1724no—
1219C2×C4—1724no—
1220C2×C4—1724no—
1221C2×C4—1722no—
1222C2×C4—1724no—
1223C2×C4—1722no—
1224C2×C4—1722no—
1225C2×C4C2×D4×D4311yescharacteristic
1226C2×C4C2×D4×D4311yescharacteristic
1227C2×C4C2×D4×D4311yescharacteristic
1228C2×C4#1306337112yes—
1229C2×C4#1306337112yes—
1230C2×C4C24×D4311yescharacteristic
1231C8—21no—
1232C8—21no—
1233C8—21no—
1234C8—21no—
1235C8—862no—
1236C8—862no—
1237C22—21no—
1238C22—21no—
1239C22—21no—
1240C22—21no—
1241C22—21no—
1242C22—21no—
1243C22—21no—
1244C22—21no—
1245C22—41no—
1246C22—41no—
1247C22—41no—
1248C22—82no—
1249C22—862no—
1250C22—862no—
1251C22—862no—
1252C22—862no—
1253C22—862no—
1254C22—862no—
1255C22—3444no—
1256C22—3444no—
1257C22—1722no—
1258C22—1722no—
1259C22—1722no—
1260C22#1458346012yes—
1261C22C22×D4×D4311yescharacteristic
1262C4—21no—
1263C4—21no—
1264C4—41no—
1265C4—41no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—862no—
1272C4—862no—
1273C4—1722no—
1274C4—1722no—
1275C4—1722no—
1276C4#1458346012yes—
1277C4C2×#1306337111yescharacteristic
1278C4C2×#1306337111yescharacteristic
1279C2—22no—
1280C2—41no—
1281C2—41no—
1282C2—81no—
1283C2—3442no—
1284C2—1722no—
1285C2—1722no—
1286C2C2×#1458346011yescharacteristic
1287C2#1914936411yescharacteristic
1288C2#1914937911yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3091C2
socleC22×C43C23×D4
hypercenter#3091D43
hypocenterC43#60761
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3091

Complements

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

NH ≅ G/Ntype
1. #19148267C2semidirect
2. #19147928C2semidirect
3. #19145508C2semidirect
4. #19145495C2semidirect
5. #19145484C2semidirect
6. #19145482C2semidirect
7. #19145435C2semidirect
8. #19145429C2semidirect
9. #19145386C2semidirect
10. #19145380C2semidirect
11. #19144567C2semidirect
12. #19144556C2semidirect
13. #19144543C2semidirect
14. #19144289C2semidirect
15. #19144278C2semidirect
16. #19144251C2semidirect
17. #19144235C2semidirect
18. #19143893C2semidirect
19. #19143884C2semidirect
20. #19143835C2semidirect
21. C2×#14583063C2semidirect
22. #19143041C2semidirect
23. C43×#3091C2semidirect
27. C2×#13063355C22semidirect
28. C2×#13063350C22semidirect
29. C22×Dic172C22semidirect
30. C22×#10621873C22semidirect
41. #14583478C22semidirect
47. #14583472C22semidirect
57. #14583409C22semidirect
59. C22⋊Q8×D43C22semidirect
61. #14583243C22semidirect
62. #14583242C22semidirect
63. #14583240C22semidirect
64. #14583240C22semidirect
65. #14583236C22semidirect
66. #14583234C22semidirect
67. #14583231C22semidirect
68. #14583229C22semidirect
69. #14583226C22semidirect
70. #14583225C22semidirect
71. #14583219C22semidirect
72. #14583214C22semidirect
73. #14583158C22semidirect
74. #14583158C22semidirect
75. #14583156C22semidirect
76. #14583151C22semidirect
77. #14583148C22semidirect
78. #14583146C22semidirect
79. #14583146C22semidirect
80. #14583144C22semidirect
81. #14583141C22semidirect
82. #14583141C22semidirect
83. #14583139C22semidirect
84. #14583134C22semidirect
85. #14583131C22semidirect
86. #14583129C22semidirect
87. #14583129C22semidirect
88. #14583127C22semidirect
91. #14583063C22semidirect
92. #14583063C22semidirect
93. #14583062C22semidirect
94. #14583062C22semidirect
96. #14583059C22semidirect
97. #14583056C22semidirect
98. #14583056C22semidirect
99. #14583045C22semidirect
100. #14583045C22semidirect
102. #14583042C22semidirect
103. #14583039C22semidirect
104. #14583039C22semidirect
105. #14582942C22semidirect
106. #14582942C22semidirect
107. #14582907C22semidirect
108. #14582907C22semidirect
109. #14582907C22semidirect
110. #14582903C22semidirect
111. C2×#13063250C22semidirect
112. C2×#13063247C22semidirect
115. #14582864C22semidirect
116. #14582864C22semidirect
118. #14582861C22semidirect
119. C22⋊C8×D43C22semidirect
122. C43×#485C22semidirect
123. C43×#485C22semidirect
124. C43×#484C22semidirect
125. C43×#483C22semidirect
126. C43×#482C22semidirect
127. C43×#482C22semidirect
128. C43×#481C22semidirect
129. C43×#480C22semidirect
130. C43×#427C22semidirect
131. C43×#427C22semidirect
132. C43×#416C22semidirect
133. C43×#416C22semidirect
648. #3091D43semidirect
711. #485C2×D43semidirect
712. #485C2×D43semidirect
715. #484C2×D43semidirect
718. #483C2×D43semidirect
721. #482C2×D43semidirect
722. #482C2×D43semidirect
724. #481C2×D43semidirect
726. #480C2×D43semidirect
761. #427C2×D43semidirect
762. #427C2×D43semidirect
767. #416C2×D43semidirect
768. #416C2×D43semidirect
779. C43#60761semidirect

Maximal subgroups

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

subgroupindex
#191482672
#191479282
#191455082
#191454952
#191454842
#191454822
#191454352
#191454292
#191453862
#191453802
#191445672
#191445562
#191445432
#191442892
#191442782
#191442512
#191442352
#191438932
#191438842
#191438352
C2×#145830632
#191430412
C43×#30912
#6076143