Finite Group Databasebeta

← #25967519

Subgroups — #25967519

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#19148275C211yesmaximal, characteristic, complemented
2#19145501C212yesmaximal, complemented
3#19145492C212yesmaximal, complemented
4#19145471C212yesmaximal, complemented
5#19145471C212yesmaximal, complemented
6#19145432C212yesmaximal, complemented
7#19145421C212yesmaximal, complemented
8#19145383C212yesmaximal, complemented
9#19145372C212yesmaximal, complemented
10#19144558C211yesmaximal, characteristic, complemented
11#19144547C211yesmaximal, characteristic, complemented
12#19144543C211yesmaximal, characteristic, complemented
13#19144508C211yesmaximal, characteristic, complemented
14#19144282C211yesmaximal, characteristic, complemented
15#19144271C211yesmaximal, characteristic, complemented
16#19144247C211yesmaximal, characteristic, complemented
17#19144231C211yesmaximal, characteristic, complemented
18#19143888C211yesmaximal, characteristic, complemented
19#19143879C211yesmaximal, characteristic, complemented
20#19143837C211yesmaximal, characteristic, complemented
21C2×#14583061C211yesmaximal, characteristic, complemented
22#19143044C211yesmaximal, characteristic, complemented
23C43×#3449C211yesmaximal, characteristic, complemented
24C2×#13063372C2211yescharacteristic
25C2×#13063356C2211yescharacteristic, complemented
26C2×#13063351C2211yescharacteristic, complemented
27C22×#10621885C2211yescharacteristic, complemented
28C22×#10621883C2211yescharacteristic, complemented
29C2×#13063332C2211yescharacteristic
30C2×#13063332C2211yescharacteristic
31Q8×C22⋊D43—21no—
32#14583556—21no—
33#14583548—22no—
34#14583548—21no—
35#14583543—22no—
36#14583543—21no—
37#14583477C2211yescharacteristic
38#14583477C2212yescomplemented
39#14583470C2211yescharacteristic
40#14583470C2212yescomplemented
41#14583410C2211yescharacteristic
42#14583410C2212yescomplemented
43C2×#13063304C2211yescharacteristic
44C2×#13063304C2212yescomplemented
45#14583382C2211yescharacteristic
46#14583240C2211yescharacteristic, complemented
47#14583240C2211yescharacteristic, complemented
48#14583240C2212yescomplemented
49#14583240C2212yescomplemented
50#14583237C2212yescomplemented
51#14583237C2212yescomplemented
52#14583234C2212yescomplemented
53#14583234C2211yescharacteristic, complemented
54#14583232C2212yescomplemented
55#14583229C2212yescomplemented
56#14583229C2211yescharacteristic, complemented
57#14583227C2212yescomplemented
58#14583223C2211yescharacteristic, complemented
59#14583223C2211yescharacteristic, complemented
60#14583220C2212yescomplemented
61#14583220C2212yescomplemented
62#14583217C2211yescharacteristic, complemented
63#14583215C2212yescomplemented
64#14583212C2211yescharacteristic, complemented
65#14583210C2212yescomplemented
66#14583155C2212yescomplemented
67#14583155C2212yescomplemented
68#14583155C2212yescomplemented
69#14583150C2212yescomplemented
70#14583147C2212yescomplemented
71#14583143C2212yescomplemented
72#14583143C2212yescomplemented
73#14583143C2212yescomplemented
74#14583138C2212yescomplemented
75#14583138C2212yescomplemented
76#14583138C2212yescomplemented
77#14583133C2212yescomplemented
78#14583130C2212yescomplemented
79#14583126C2212yescomplemented
80#14583126C2212yescomplemented
81#14583126C2212yescomplemented
82#14583061C2212yes—
83#14583061C2212yes—
84#14583061C2212yes—
85#14583061C2212yescomplemented
86#14583061C2212yescomplemented
87#14583061C2212yescomplemented
88#14583059C2212yescomplemented
89#14583059C2212yescomplemented
90#14583054C2212yescomplemented
91#14583054C2212yescomplemented
92#14583044C2212yes—
93#14583044C2212yescomplemented
94#14583042C2212yescomplemented
95#14583042C2212yescomplemented
96#14583037C2212yescomplemented
97#14583037C2212yescomplemented
98#14582942C2211yescharacteristic, complemented
99#14582942C2211yescharacteristic, complemented
100#14582935C2211yescharacteristic, complemented
101#14582935C2211yescharacteristic, complemented
102#14582908C2211yescharacteristic, complemented
103#14582907C2211yescharacteristic, complemented
104#14582907C2211yescharacteristic, complemented
105#14582904C2211yescharacteristic, complemented
106#14582893C2211yescharacteristic, complemented
107#14582893C2211yescharacteristic, complemented
108C2×#13063249C2211yescharacteristic, complemented
109C2×#13063246C2211yescharacteristic, complemented
110#14582866C2211yescharacteristic
111#14582866C2211yescharacteristic
112#14582866C2212yescomplemented
113#14582866C2212yescomplemented
114#14582863C2211yescharacteristic
115#14582863C2212yescomplemented
116C2×C22⋊(C43⋊C8)C2211yescharacteristic
117C2×C22⋊(C43⋊C8)C2212yescomplemented
118C22×#41×C43C2211yescharacteristic
119C22×#41×C43C2211yescharacteristic
120C43×#537C2212yes—
121C43×#537C2212yes—
122C43×#536—21no—
123C43×#536C2211yescharacteristic
124C43×#536C2211yescharacteristic
125C43×#535—21no—
126C43×#535C2211yescharacteristic
127C43×#535C2211yescharacteristic
128C43×#534—22no—
129C43×#532—21no—
130C43×#532—21no—
131C43×#525—22no—
132C43×#525C2212yes—
133C43×#525C2212yes—
134C2×#117×C43C2211yescharacteristic
135#13063372—42no—
136#13063372—42no—
137C2×#10621898C2311yescharacteristic
138C2×#10621898C2312yes—
139C2×#10621900—22no—
140C2×#10621900—21no—
141C22×Dic86C2311yescharacteristic
142C22×Dic86C2312yes—
143C2×Q8×D43—21no—
144#13063356—42no—
145#13063351—42no—
146C2×#10621885—42no—
147C2×#10621885C2312yes—
148C2×#10621885C2312yes—
149C2×#10621885C2312yes—
150C2×#10621883—42no—
151C2×#10621883C2312yes—
152C2×#10621883C2312yes—
153C2×#10621883C2312yes—
154C2×#10621884C2312yes—
155C2×#10621882C2312yes—
156#13063332—42no—
157#13063332—42no—
158C2×#10621877C2311yescharacteristic
159C2×#10621877C2311yescharacteristic
160C2×#10621877C2312yes—
161C2×#10621877C2312yes—
162C22×C43⋊C8C2311yescharacteristic
163C22×C43⋊C8C2311yescharacteristic
164C22×C43⋊C8C2312yes—
165C22×C43⋊C8C2312yes—
166#13063323—21no—
167#13063323—22no—
168#13063312—21no—
169#13063312—22no—
170#13063308—21no—
171#13063308—22no—
172#13063306—22no—
173#13063306—22no—
174#13063306—22no—
175#13063304—21no—
176#13063304—22no—
177#13063304—21no—
178#13063304—22no—
179#13063304C2312yes—
180#13063304C2311yescharacteristic
181#13063304C2312yes—
182#13063304C2311yescharacteristic
183#13063304C2312yes—
184#13063304C2312yes—
185#13063304C2312yes—
186#13063301—21no—
187#13063301—22no—
188#13063299C2311yescharacteristic
189#13063299C2311yescharacteristic
190#13063299C2312yes—
191#13063297—22no—
192#13063297—22no—
193#13063297—22no—
194#13063296—21no—
195#13063296—22no—
196#13063294—21no—
197#13063294—22no—
198Q8×Dic43—21no—
199D4×Dic43—22no—
200D4×Dic43—21no—
201C4×C22⋊D43—21no—
202C4×C22⋊D43—22no—
203C4×C22⋊D43—21no—
204C4×C22⋊D43—22no—
205#13063284C2311yescharacteristic
206#13063284C2312yes—
207C2×C4⋊Dic43C2311yescharacteristic
208C2×C4⋊Dic43C2312yes—
209C2×Dic43⋊C4—21no—
210C2×Dic43⋊C4—22no—
211C2×C22⋊Dic43—21no—
212C2×C22⋊Dic43—22no—
213#13063258C2312yes—
214#13063258C2311yescharacteristic
215#13063258C2311yescharacteristic
216#13063258C2312yes—
217#13063258C2311yescharacteristic
218#13063258C2311yescharacteristic
219#13063256C2311yescharacteristic
220#13063256C2311yescharacteristic
221#13063256C2312yes—
222#13063256C2312yes—
223#13063256C2311yescharacteristic
224#13063256C2311yescharacteristic
225#13063249C2312yes—
226#13063249C2312yes—
227#13063249C2312yes—
228#13063249C2312yes—
229#13063248C2312yes—
230#13063248C2312yes—
231#13063248C2311yescharacteristic
232#13063248C2311yescharacteristic
233#13063248C2312yes—
234#13063248C2312yes—
235#13063248C2311yescharacteristic
236#13063248C2311yescharacteristic
237#13063246C2312yes—
238#13063246C2312yes—
239#13063246C2312yes—
240#13063246C2312yes—
241#13063245C2311yescharacteristic
242#13063245C2311yescharacteristic
243#13063245C2311yescharacteristic
244#13063245C2311yescharacteristic
245C22⋊(C43⋊C8)C2312yes—
246C22⋊(C43⋊C8)C2312yes—
247C22⋊(C43⋊C8)C2312yes—
248C22⋊(C43⋊C8)C2312yes—
249C22⋊(C43⋊C8)C2312yes—
250C22⋊(C43⋊C8)C2312yes—
251C22⋊(C43⋊C8)C2311yescharacteristic
252C22⋊(C43⋊C8)C2311yescharacteristic
253C22⋊(C43⋊C8)C2311yescharacteristic
254C22⋊(C43⋊C8)C2311yescharacteristic
255C2×#41×C43—21no—
256C2×#41×C43—21no—
257C2×#41×C43—42no—
258C2×#41×C43—42no—
259C2×#41×C43—42no—
260C2×#41×C43—42no—
261C2×#41×C43D411yescharacteristic
262C2×#41×C43D412yes—
263C2×#41×C43D411yescharacteristic
264C2×#41×C43C2312yes—
265C2×#41×C43C2312yes—
266C2×#41×C43C2311yescharacteristic
267C2×#41×C43C2311yescharacteristic
268C2×#41×C43C2312yes—
269C22×Q8×C43D411yescharacteristic
270C22×Q8×C43C2311yescharacteristic
271C22×D4×C43—21no—
272C22×D4×C43D412yes—
273C22×D4×C43D411yescharacteristic
274C22×D4×C43C2311yescharacteristic
275C23×C4×C43—21no—
276C23×C4×C43C2311yescharacteristic
277C23×C4×C43C2312yes—
278C4⋊Q8×C43—21no—
279C4⋊Q8×C43—21no—
280#127×C43—21no—
281#127×C43—21no—
282#124×C43—21no—
283#124×C43—21no—
284#124×C43—21no—
285#124×C43—21no—
286#123×C43—22no—
287#123×C43—22no—
288#123×C43—22no—
289#123×C43—22no—
290C22⋊Q8×C43—22no—
291C22⋊Q8×C43—22no—
292C22⋊Q8×C43C2312yes—
293C22⋊Q8×C43C2312yes—
294C22⋊Q8×C43C2312yes—
295C22⋊Q8×C43C2312yes—
296#121×C43—22no—
297#121×C43—22no—
298#121×C43—22no—
299#121×C43—22no—
300#121×C43—22no—
301#121×C43—22no—
302#121×C43C2312yes—
303#121×C43C2312yes—
304#121×C43C2312yes—
305#121×C43C2312yes—
306#120×C43—22no—
307#120×C43—22no—
308#120×C43—22no—
309#120×C43—22no—
310C4×D4×C43—22no—
311C4×D4×C43—22no—
312C4×D4×C43—22no—
313C4×D4×C43—22no—
314#117×C43—21no—
315#117×C43—21no—
316#117×C43C2311yescharacteristic
317#117×C43C2311yescharacteristic
318#117×C43C2311yescharacteristic
319#117×C43C2311yescharacteristic
320C2×C4⋊C4×C43C2311yescharacteristic
321C2×C4⋊C4×C43C2311yescharacteristic
322C2×C22⋊C4×C43—21no—
323C2×C42×C43—21no—
324C24×C43—21no—
325C24×C43C2×D411yescharacteristic
326C24×C43C2×D412yes—
327#41×C43—22no—
328#41×C43—22no—
329#41×C43—22no—
330#41×C43—22no—
331#41×C43—42no—
332#41×C43—42no—
333#41×C43—44no—
334#41×C43—42no—
335#41×C43—42no—
336#41×C43—42no—
337#41×C43—42no—
338#41×C43—42no—
339#41×C43—42no—
340#41×C43—44no—
341#41×C43—44no—
342C2×Q8×C43—21no—
343C2×Q8×C43—22no—
344C2×Q8×C43—22no—
345C2×Q8×C43—42no—
346C2×Q8×C43C2×D411yescharacteristic
347C2×Q8×C43C2×D411yescharacteristic
348C2×Q8×C43C2×D412yes—
349C2×Q8×C43C2412yes—
350C2×D4×C43—21no—
351C2×D4×C43—22no—
352C2×D4×C43—22no—
353C2×D4×C43—22no—
354C2×D4×C43—22no—
355C2×D4×C43—22no—
356C2×D4×C43—22no—
357C2×D4×C43—22no—
358C2×D4×C43—22no—
359C2×D4×C43—44no—
360C2×D4×C43—44no—
361C2×D4×C43—42no—
362C2×D4×C43C2×D412yes—
363C2×D4×C43C2×D412yes—
364C2×D4×C43C2×D411yescharacteristic
365C2×D4×C43C2×D411yescharacteristic
366C2×D4×C43C2×D412yes—
367C2×D4×C43C2×D412yes—
368C2×D4×C43C2×D412yes—
369C2×D4×C43C2412yes—
370C22×C4×C43—22no—
371C22×C4×C43—22no—
372C22×C4×C43—22no—
373C22×C4×C43—22no—
374C22×C4×C43—21no—
375C22×C4×C43—21no—
376C22×C4×C43—21no—
377C22×C4×C43—42no—
378C22×C4×C43—42no—
379C22×C4×C43—44no—
380C22×C4×C43C2×D411yescharacteristic
381C22×C4×C43C2×D411yescharacteristic
382C22×C4×C43C2×D411yescharacteristic
383C22×C4×C43C2×D412yes—
384C22×C4×C43C2×D412yes—
385C22×C4×C43C2×D412yes—
386C22×C4×C43C2411yescharacteristic
387C22×C4×C43C2411yescharacteristic
388C22×C4×C43C2412yes—
389C22×C4×C43C2412yes—
390C22×C4×C43C2411yescharacteristic
391C2×C22⋊D43—21no—
392C2×C22⋊D43—22no—
393C2×C22⋊D43—21no—
394C2×C22⋊D43—22no—
395C2×C22⋊D43—21no—
396C22×Dic43—22no—
397C22×Dic43—21no—
398C22×Dic43—22no—
399C22×Dic43—21no—
400Q8×D43—44no—
401#10621900—48no—
402#10621900—44no—
403#10621898—22no—
404#10621898—22no—
405#10621898—42no—
406#10621898—42no—
407C2×D172C2411yescharacteristic
408C2×C4×D43—22no—
409C2×C4×D43—21no—
410C2×Dic86—22no—
411C2×Dic86—22no—
412C2×Dic86—22no—
413C2×Dic86—21no—
414C2×Dic86—42no—
415C2×Dic86—42no—
416C2×Dic86C2412yes—
417C2×Dic86C2411yescharacteristic
418C4⋊C4×C43—21no—
419C4⋊C4×C43—21no—
420C4⋊C4×C43—22no—
421C4⋊C4×C43—22no—
422C4⋊C4×C43—22no—
423C4⋊C4×C43—22no—
424C4⋊C4×C43C2411yescharacteristic
425C4⋊C4×C43C2411yescharacteristic
426C4⋊C4×C43C2411yescharacteristic
427C4⋊C4×C43C2411yescharacteristic
428C22⋊C4×C43—22no—
429C22⋊C4×C43—22no—
430C22⋊C4×C43—22no—
431C22⋊C4×C43—22no—
432C22⋊C4×C43—21no—
433C22⋊C4×C43—21no—
434C22⋊C4×C43—21no—
435C22⋊C4×C43—21no—
436C22⋊C4×C43—22no—
437C22⋊C4×C43—22no—
438C22⋊C4×C43—22no—
439C22⋊C4×C43—22no—
440C42×C43—21no—
441C42×C43—21no—
442C42×C43—21no—
443C42×C43—21no—
444C22⋊Dic43—22no—
445C22⋊Dic43—21no—
446C22⋊Dic43—22no—
447C22⋊Dic43—22no—
448C22⋊Dic43—22no—
449C22⋊Dic43—22no—
450C22⋊Dic43—21no—
451C22⋊Dic43—22no—
452C22⋊Dic43—21no—
453#10621885—42no—
454#10621885—42no—
455#10621885—42no—
456#10621884—42no—
457#10621883—42no—
458#10621883—42no—
459#10621883—42no—
460#10621882—42no—
461(C2×D43)⋊C4—21no—
462(C2×D43)⋊C4—22no—
463(C2×D43)⋊C4—21no—
464C4⋊Dic43—22no—
465C4⋊Dic43—21no—
466C4⋊Dic43C2411yescharacteristic
467C4⋊Dic43C2412yes—
468C4⋊Dic43C2411yescharacteristic
469Dic43⋊C4—22no—
470Dic43⋊C4—21no—
471Dic43⋊C4—22no—
472Dic43⋊C4—22no—
473Dic43⋊C4—22no—
474Dic43⋊C4—22no—
475Dic43⋊C4—21no—
476C4×Dic43—22no—
477C4×Dic43—21no—
478#10621877—22no—
479#10621877—22no—
480#10621877—42no—
481#10621877—42no—
482C2×C43⋊C8—22no—
483C2×C43⋊C8—22no—
484C2×C43⋊C8—42no—
485C2×C43⋊C8—42no—
486C2×C43⋊C8C2411yescharacteristic
487C2×C43⋊C8C2411yescharacteristic
488C2×C43⋊C8C2411yescharacteristic
489C2×C43⋊C8C2411yescharacteristic
490C2×C43⋊C8C2412yes—
491C2×C43⋊C8C2412yes—
492C23×C43—22no—
493C23×C43—22no—
494C23×C43—42no—
495C23×C43—41no—
496C23×C43—41no—
497C23×C43—42no—
498C23×C43—42no—
499C23×C43—42no—
500C23×C43—81no—
501C23×C43—81no—
502C23×C43C22×D411yescharacteristic
503C23×C43C22×D412yes—
504C23×C43C22×D411yescharacteristic
505C23×C43C22×D412yes—
506C23×C43C22×D411yescharacteristic
507C22×D43—21no—
508Q8×C43—22no—
509Q8×C43—22no—
510Q8×C43—22no—
511Q8×C43—22no—
512Q8×C43—42no—
513Q8×C43—42no—
514D4×C43—24no—
515D4×C43—24no—
516D4×C43—22no—
517D4×C43—22no—
518D4×C43—22no—
519D4×C43—22no—
520D4×C43—42no—
521D4×C43—42no—
522D4×C43—42no—
523D4×C43—44no—
524D4×C43—44no—
525D4×C43—42no—
526D4×C43—82no—
527D4×C43—82no—
528D4×C43—82no—
529D4×C43—82no—
530C2×C4×C43—22no—
531C2×C4×C43—22no—
532C2×C4×C43—22no—
533C2×C4×C43—22no—
534C2×C4×C43—22no—
535C2×C4×C43—22no—
536C2×C4×C43—22no—
537C2×C4×C43—21no—
538C2×C4×C43—21no—
539C2×C4×C43—21no—
540C2×C4×C43—21no—
541C2×C4×C43—21no—
542C2×C4×C43—21no—
543C2×C4×C43—21no—
544C2×C4×C43—21no—
545C2×C4×C43—22no—
546C2×C4×C43—42no—
547C2×C4×C43—42no—
548C2×C4×C43—42no—
549C2×C4×C43—44no—
550C2×C4×C43—44no—
551C2×C4×C43—42no—
552C2×C4×C43—81no—
553C2×C4×C43—81no—
554C2×C4×C43C22×D412yes—
555C2×C4×C43C22×D411yescharacteristic
556C2×C4×C43C22×D412yes—
557C2×C4×C43C22×D411yescharacteristic
558C2×C4×C43C22×D411yescharacteristic
559C2×C4×C43H(5,𝔽2)12yes—
560C2×C4×C43H(5,𝔽2)12yes—
561C2×C4×C43C2511yescharacteristic
562C22⋊D43—44no—
563C22⋊D43—42no—
564C22⋊D43—42no—
565C22⋊D43—81no—
566C22⋊D43—82no—
567C2×Dic43—21no—
568C2×Dic43—22no—
569C2×Dic43—21no—
570C2×Dic43—22no—
571C2×Dic43—21no—
572C2×Dic43—44no—
573C2×Dic43—42no—
574C2×Dic43—81no—
575C2×Dic43—82no—
576D172—21no—
577D172—21no—
578C4×D43—44no—
579C4×D43—42no—
580Dic86—22no—
581Dic86—21no—
582Dic86—22no—
583Dic86—21no—
584Dic86—44no—
585Dic86—42no—
586C43⋊C8—21no—
587C43⋊C8—21no—
588C43⋊C8—21no—
589C43⋊C8—21no—
590C43⋊C8—22no—
591C43⋊C8—22no—
592#60761—431nomaximal, Sylow
593C22×C43—21no—
594C22×C43—21no—
595C22×C43—21no—
596C22×C43—22no—
597C22×C43—21no—
598C22×C43—22no—
599C22×C43—21no—
600C22×C43—21no—
601C22×C43—22no—
602C22×C43—22no—
603C22×C43—21no—
604C22×C43—21no—
605C22×C43—22no—
606C22×C43—22no—
607C22×C43—42no—
608C22×C43—42no—
609C22×C43—42no—
610C22×C43—82no—
611C22×C43—84no—
612C22×C43—84no—
613C22×C43#53412yes—
614C22×C43C23×D411yescharacteristic
615C2×D43—41no—
616C2×D43—41no—
617C2×D43—41no—
618C4×C43—22no—
619C4×C43—21no—
620C4×C43—21no—
621C4×C43—22no—
622C4×C43—41no—
623C4×C43—41no—
624C4×C43—41no—
625C4×C43—41no—
626C4×C43—42no—
627C4×C43#53412yes—
628C4×C43C2×H(5,𝔽2)11yescharacteristic
629C4×C43C2×H(5,𝔽2)11yescharacteristic
630Dic43—42no—
631Dic43—41no—
632Dic43—41no—
633Dic43—42no—
634Dic43—41no—
635#3489—431no—
636#3449D4311yescharacteristic, complemented
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#3091—431no—
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—42no—
660C2×C43—41no—
661C2×C43—42no—
662C2×C43—41no—
663C2×C43—82no—
664C2×C43C2×#53411yescharacteristic
665C2×C43#358411yescharacteristic
666C2×C43#358611yescharacteristic
667D43—81no—
668C2×2−1+4—431no—
669C22×#41C2×D4311yescharacteristic
670C22×#41C2×D4311yescharacteristic
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—862no—
680#547—861no—
681#546—862no—
682#546—861no—
683#537—432no—
684#537—431no—
685#537C2×D4312yes—
686#537C2×D4312yes—
687#536—21no—
688#536—432no—
689#536—431no—
690#536C2×D4311yescharacteristic
691#536C2×D4311yescharacteristic
692#535—21no—
693#535C2×D4311yescharacteristic
694#535C2×D4311yescharacteristic
695#534—22no—
696#532—21no—
697#532—21no—
698#525—22no—
699#525—431no—
700#525—432no—
701#525C2×D4312yes—
702#525C2×D4312yes—
703C2×C22⋊Q8—431no—
704C2×C22⋊Q8—432no—
705#520—431no—
706C2×#117C2×D4311yescharacteristic
707#485—432no—
708#485—432no—
709#485—431no—
710#485—431no—
711#485—432no—
712#485—432no—
713#484—432no—
714#484—431no—
715#484—432no—
716#483—432no—
717#483—431no—
718#483—432no—
719#482—432no—
720#482—432no—
721#482—431no—
722#482—431no—
723#481—432no—
724#481—431no—
725#480—432no—
726#480—431no—
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#427—431no—
762#427—431no—
763#419—431no—
764#419—431no—
765#419—431no—
766#418—431no—
767#416—431no—
768#416—431no—
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—431no—
778C2×C22⋊C8—432no—
779C43#6076111yescharacteristic, complemented, Sylow
7802−1+4—1722no—
7812−1+4—1722no—
782C2×#41—21no—
783C2×#41—21no—
784C2×#41—42no—
785C2×#41—42no—
786C2×#41—42no—
787C2×#41—42no—
788C2×#41—431no—
789C2×#41—432no—
790C2×#41—862no—
791C2×#41—861no—
792C2×#41C22⋊D4312yes—
793C2×#41C22⋊D4311yescharacteristic
794C2×#41C22⋊D4311yescharacteristic
795C2×#41C22×D4312yes—
796C2×#41C22×D4312yes—
797C2×#41C22×D4311yescharacteristic
798C2×#41C22×D4311yescharacteristic
799C2×#41C22×D4312yes—
800C22×Q8—431no—
801C22×Q8—432no—
802C22×Q8—861no—
803C22×Q8C22⋊D4311yescharacteristic
804C22×Q8C22×D4311yescharacteristic
805C22×D4—21no—
806C22×D4C22⋊D4312yes—
807C22×D4C22⋊D4311yescharacteristic
808C22×D4C22×D4311yescharacteristic
809C23×C4—21no—
810C23×C4C22×D4311yescharacteristic
811C23×C4C22×D4312yes—
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—431no—
831C22×C8—431no—
832C22×C8—432no—
833C22×C8—432no—
834C4⋊Q8—21no—
835C4⋊Q8—21no—
836C4⋊Q8—861no—
837C4⋊Q8—862no—
838#127—21no—
839#127—21no—
840#124—21no—
841#124—21no—
842#124—21no—
843#124—21no—
844#124—861no—
845#124—862no—
846#123—22no—
847#123—22no—
848#123—22no—
849#123—22no—
850#123—862no—
851#123—862no—
852#123—862no—
853#123—861no—
854#123—862no—
855C22⋊Q8—22no—
856C22⋊Q8—22no—
857C22⋊Q8—432no—
858C22⋊Q8—431no—
859C22⋊Q8—432no—
860C22⋊Q8—432no—
861C22⋊Q8—432no—
862C22⋊Q8—431no—
863C22⋊Q8—432no—
864C22⋊Q8—861no—
865C22⋊Q8—862no—
866C22⋊Q8—861no—
867C22⋊Q8—862no—
868C22⋊Q8—861no—
869C22⋊Q8—862no—
870C22⋊Q8C22×D4312yes—
871C22⋊Q8C22×D4312yes—
872C22⋊Q8C22×D4312yes—
873C22⋊Q8C22×D4312yes—
874#121—22no—
875#121—22no—
876#121—22no—
877#121—22no—
878#121—22no—
879#121—22no—
880#121—431no—
881#121—431no—
882#121—432no—
883#121—862no—
884#121—862no—
885#121—862no—
886#121—861no—
887#121—862no—
888#121C22×D4312yes—
889#121C22×D4312yes—
890#121C22×D4312yes—
891#121C22×D4312yes—
892#120—22no—
893#120—22no—
894#120—22no—
895#120—22no—
896#120—861no—
897#120—862no—
898C4×Q8—861no—
899C4×D4—22no—
900C4×D4—22no—
901C4×D4—22no—
902C4×D4—22no—
903C4×D4—862no—
904C4×D4—861no—
905C4×D4—861no—
906C4×D4—862no—
907C4×D4—861no—
908C4×D4—862no—
909#117—21no—
910#117—21no—
911#117—431no—
912#117—432no—
913#117C22×D4311yescharacteristic
914#117C22×D4311yescharacteristic
915#117C22×D4311yescharacteristic
916#117C22×D4311yescharacteristic
917C2×C4⋊C4—431no—
918C2×C4⋊C4—432no—
919C2×C4⋊C4—861no—
920C2×C4⋊C4—862no—
921C2×C4⋊C4C22×D4311yescharacteristic
922C2×C4⋊C4C22×D4311yescharacteristic
923C2×C22⋊C4—21no—
924C2×C22⋊C4—861no—
925C2×C22⋊C4—862no—
926C2×C42—21no—
927#107—431no—
928#107—431no—
929#107—431no—
930#107—431no—
931#107—432no—
932#107—432no—
933#106—431no—
934#106—431no—
935#106—431no—
936#106—431no—
937#106—432no—
938#106—432no—
939#103—432no—
940#103—432no—
941#103—432no—
942#103—432no—
943#103—431no—
944#103—431no—
945#103—431no—
946#103—431no—
947#103—432no—
948#103—432no—
949#103—432no—
950#103—432no—
951#102—432no—
952#102—432no—
953#102—432no—
954#102—432no—
955#102—431no—
956#102—431no—
957#102—431no—
958#102—431no—
959C22⋊C8—431no—
960C22⋊C8—432no—
961C22⋊C8—431no—
962C22⋊C8—432no—
963C22⋊C8—432no—
964C22⋊C8—431no—
965C22⋊C8—431no—
966C22⋊C8—432no—
967C22⋊C8—432no—
968C22⋊C8—432no—
969C24—21no—
970C24C2×C22⋊D4311yescharacteristic
971C24C2×C22⋊D4312yes—
972#41—22no—
973#41—22no—
974#41—22no—
975#41—22no—
976#41—42no—
977#41—42no—
978#41—44no—
979#41—42no—
980#41—42no—
981#41—42no—
982#41—42no—
983#41—42no—
984#41—42no—
985#41—44no—
986#41—44no—
987#41—862no—
988#41—862no—
989#41—1722no—
990#41—1722no—
991#41—1728no—
992#41—1724no—
993C2×Q8—21no—
994C2×Q8—22no—
995C2×Q8—22no—
996C2×Q8—42no—
997C2×Q8—432no—
998C2×Q8—431no—
999C2×Q8—862no—
1000C2×Q8—861no—
1001C2×Q8—862no—
1002C2×Q8—862no—
1003C2×Q8—1722no—
1004C2×Q8—1722no—
1005C2×Q8—1724no—
1006C2×Q8C2×C22⋊D4311yescharacteristic
1007C2×Q8C2×C22⋊D4311yescharacteristic
1008C2×Q8C2×C22⋊D4312yes—
1009C2×Q8C23×D4312yes—
1010C2×D4—22no—
1011C2×D4—22no—
1012C2×D4—22no—
1013C2×D4—22no—
1014C2×D4—22no—
1015C2×D4—22no—
1016C2×D4—21no—
1017C2×D4—22no—
1018C2×D4—22no—
1019C2×D4—42no—
1020C2×D4—44no—
1021C2×D4—44no—
1022C2×D4—431no—
1023C2×D4—862no—
1024C2×D4—861no—
1025C2×D4—861no—
1026C2×D4—862no—
1027C2×D4—861no—
1028C2×D4C2×C22⋊D4312yes—
1029C2×D4C2×C22⋊D4311yescharacteristic
1030C2×D4C2×C22⋊D4312yes—
1031C2×D4C2×C22⋊D4311yescharacteristic
1032C2×D4C2×C22⋊D4312yes—
1033C2×D4C2×C22⋊D4312yes—
1034C2×D4C2×C22⋊D4312yes—
1035C2×D4C23×D4312yes—
1036C22×C4—22no—
1037C22×C4—22no—
1038C22×C4—21no—
1039C22×C4—21no—
1040C22×C4—21no—
1041C22×C4—22no—
1042C22×C4—22no—
1043C22×C4—42no—
1044C22×C4—42no—
1045C22×C4—44no—
1046C22×C4—862no—
1047C22×C4—861no—
1048C22×C4—862no—
1049C22×C4—861no—
1050C22×C4—862no—
1051C22×C4—861no—
1052C22×C4C2×C22⋊D4311yescharacteristic
1053C22×C4C2×C22⋊D4311yescharacteristic
1054C22×C4C2×C22⋊D4311yescharacteristic
1055C22×C4C2×C22⋊D4312yes—
1056C22×C4C2×C22⋊D4312yes—
1057C22×C4C2×C22⋊D4312yes—
1058C22×C4C23×D4312yes—
1059C22×C4C23×D4311yescharacteristic
1060C22×C4C23×D4311yescharacteristic
1061C22×C4C23×D4312yes—
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—431no—
1076C2×C8—431no—
1077C2×C8—432no—
1078C2×C8—431no—
1079C2×C8—431no—
1080C2×C8—432no—
1081C2×C8—862no—
1082C2×C8—862no—
1083C2×C8—1722no—
1084C2×C8—1722no—
1085C4⋊C4—21no—
1086C4⋊C4—21no—
1087C4⋊C4—22no—
1088C4⋊C4—22no—
1089C4⋊C4—22no—
1090C4⋊C4—22no—
1091C4⋊C4—432no—
1092C4⋊C4—431no—
1093C4⋊C4—431no—
1094C4⋊C4—862no—
1095C4⋊C4—861no—
1096C4⋊C4—862no—
1097C4⋊C4—861no—
1098C4⋊C4—862no—
1099C4⋊C4—862no—
1100C4⋊C4—862no—
1101C4⋊C4—862no—
1102C4⋊C4—861no—
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—22no—
1112C22⋊C4—22no—
1113C22⋊C4—22no—
1114C22⋊C4—22no—
1115C22⋊C4—22no—
1116C22⋊C4—22no—
1117C22⋊C4—22no—
1118C22⋊C4—22no—
1119C22⋊C4—862no—
1120C22⋊C4—861no—
1121C22⋊C4—862no—
1122C22⋊C4—862no—
1123C22⋊C4—862no—
1124C22⋊C4—862no—
1125C22⋊C4—861no—
1126C22⋊C4—862no—
1127C22⋊C4—861no—
1128C22⋊C4—861no—
1129C22⋊C4—862no—
1130C22⋊C4—861no—
1131C42—21no—
1132C42—21no—
1133C42—21no—
1134C42—21no—
1135C42—862no—
1136C42—861no—
1137C23—22no—
1138C23—22no—
1139C23—42no—
1140C23—41no—
1141C23—41no—
1142C23—42no—
1143C23—42no—
1144C23—42no—
1145C23—81no—
1146C23—81no—
1147C23—861no—
1148C23C22×C22⋊D4311yescharacteristic
1149C23C22×C22⋊D4312yes—
1150C23C22×C22⋊D4312yes—
1151C23C22×C22⋊D4311yescharacteristic
1152C23C22×C22⋊D4311yescharacteristic
1153Q8—22no—
1154Q8—22no—
1155Q8—22no—
1156Q8—22no—
1157Q8—42no—
1158Q8—42no—
1159Q8—862no—
1160Q8—861no—
1161Q8—862no—
1162Q8—861no—
1163Q8—1724no—
1164Q8—1722no—
1165D4—24no—
1166D4—24no—
1167D4—22no—
1168D4—22no—
1169D4—22no—
1170D4—22no—
1171D4—42no—
1172D4—42no—
1173D4—42no—
1174D4—44no—
1175D4—44no—
1176D4—42no—
1177D4—82no—
1178D4—82no—
1179D4—82no—
1180D4—82no—
1181D4—861no—
1182D4—861no—
1183D4—3441no—
1184D4—3442no—
1185D4—1724no—
1186D4—1722no—
1187D4—1722no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—22no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—44no—
1208C2×C4—44no—
1209C2×C4—42no—
1210C2×C4—81no—
1211C2×C4—81no—
1212C2×C4—861no—
1213C2×C4—862no—
1214C2×C4—861no—
1215C2×C4—862no—
1216C2×C4—861no—
1217C2×C4—3441no—
1218C2×C4—3442no—
1219C2×C4—1724no—
1220C2×C4—1724no—
1221C2×C4—1722no—
1222C2×C4—1722no—
1223C2×C4C22×C22⋊D4311yescharacteristic
1224C2×C4C22×C22⋊D4312yes—
1225C2×C4C22×C22⋊D4312yes—
1226C2×C4C22×C22⋊D4311yescharacteristic
1227C2×C4C22×C22⋊D4311yescharacteristic
1228C2×C4#1306337012yes—
1229C2×C4#1306337012yes—
1230C2×C4C24×D4311yescharacteristic
1231C8—861no—
1232C8—861no—
1233C8—861no—
1234C8—861no—
1235C8—862no—
1236C8—862no—
1237C22—21no—
1238C22—21no—
1239C22—21no—
1240C22—22no—
1241C22—22no—
1242C22—21no—
1243C22—21no—
1244C22—22no—
1245C22—22no—
1246C22—21no—
1247C22—21no—
1248C22—21no—
1249C22—22no—
1250C22—22no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—82no—
1255C22—84no—
1256C22—84no—
1257C22—1721no—
1258C22—1721no—
1259C22—1721no—
1260C22#1458345812yes—
1261C22C23×C22⋊D4311yescharacteristic
1262C4—21no—
1263C4—21no—
1264C4—22no—
1265C4—22no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—42no—
1271C4—1722no—
1272C4—1721no—
1273C4—1721no—
1274C4—1722no—
1275C4—1721no—
1276C4#1458345812yes—
1277C4C2×#1306337011yescharacteristic
1278C4C2×#1306337011yescharacteristic
1279C2—22no—
1280C2—41no—
1281C2—41no—
1282C2—42no—
1283C2—42no—
1284C2—82no—
1285C2—3441no—
1286C2C2×#1458345811yescharacteristic
1287C2#1914936611yescharacteristic
1288C2#1914938111yescharacteristic
subgroupG/H
centerC22C23×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3449C2
socleC22×C43C23×D4
hypercenter#3449D43
hypocenterC43#60761
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×#41 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. #19148275C2semidirect
2. #19145501C2semidirect
3. #19145492C2semidirect
4. #19145471C2semidirect
5. #19145471C2semidirect
6. #19145432C2semidirect
7. #19145421C2semidirect
8. #19145383C2semidirect
9. #19145372C2semidirect
10. #19144558C2semidirect
11. #19144547C2semidirect
12. #19144543C2semidirect
13. #19144508C2semidirect
14. #19144282C2semidirect
15. #19144271C2semidirect
16. #19144247C2semidirect
17. #19144231C2semidirect
18. #19143888C2semidirect
19. #19143879C2semidirect
20. #19143837C2semidirect
21. C2×#14583061C2semidirect
22. #19143044C2semidirect
23. C43×#3449C2semidirect
25. C2×#13063356C22semidirect
26. C2×#13063351C22semidirect
27. C22×#10621885C22semidirect
28. C22×#10621883C22semidirect
38. #14583477C22semidirect
40. #14583470C22semidirect
42. #14583410C22semidirect
44. C2×#13063304C22semidirect
46. #14583240C22semidirect
47. #14583240C22semidirect
48. #14583240C22semidirect
49. #14583240C22semidirect
50. #14583237C22semidirect
51. #14583237C22semidirect
52. #14583234C22semidirect
53. #14583234C22semidirect
54. #14583232C22semidirect
55. #14583229C22semidirect
56. #14583229C22semidirect
57. #14583227C22semidirect
58. #14583223C22semidirect
59. #14583223C22semidirect
60. #14583220C22semidirect
61. #14583220C22semidirect
62. #14583217C22semidirect
63. #14583215C22semidirect
64. #14583212C22semidirect
65. #14583210C22semidirect
66. #14583155C22semidirect
67. #14583155C22semidirect
68. #14583155C22semidirect
69. #14583150C22semidirect
70. #14583147C22semidirect
71. #14583143C22semidirect
72. #14583143C22semidirect
73. #14583143C22semidirect
74. #14583138C22semidirect
75. #14583138C22semidirect
76. #14583138C22semidirect
77. #14583133C22semidirect
78. #14583130C22semidirect
79. #14583126C22semidirect
80. #14583126C22semidirect
81. #14583126C22semidirect
85. #14583061C22semidirect
86. #14583061C22semidirect
87. #14583061C22semidirect
88. #14583059C22semidirect
89. #14583059C22semidirect
90. #14583054C22semidirect
91. #14583054C22semidirect
93. #14583044C22semidirect
94. #14583042C22semidirect
95. #14583042C22semidirect
96. #14583037C22semidirect
97. #14583037C22semidirect
98. #14582942C22semidirect
99. #14582942C22semidirect
100. #14582935C22semidirect
101. #14582935C22semidirect
102. #14582908C22semidirect
103. #14582907C22semidirect
104. #14582907C22semidirect
105. #14582904C22semidirect
106. #14582893C22semidirect
107. #14582893C22semidirect
108. C2×#13063249C22semidirect
109. C2×#13063246C22semidirect
112. #14582866C22semidirect
113. #14582866C22semidirect
115. #14582863C22semidirect
117. C2×C22⋊(C43⋊C8)C22semidirect
636. #3449D43semidirect
779. C43#60761semidirect

Maximal subgroups

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

subgroupindex
#191482752
#191455012
#191454922
#191454712
#191454322
#191454212
#191453832
#191453722
#191445582
#191445472
#191445432
#191445082
#191442822
#191442712
#191442472
#191442312
#191438882
#191438792
#191438372
C2×#145830612
#191430442
C43×#34492
#6076143