Finite Group Databasebeta

← #25064370

Subgroups — #25064370

Order 11008.

1074 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148430C211yesmaximal, characteristic
2#19143623C211yesmaximal, characteristic, complemented
3#19137506C211yesmaximal, characteristic, complemented
4#19133165C211yesmaximal, characteristic, complemented
5#19133161C211yesmaximal, characteristic, complemented
6#19133137C211yesmaximal, characteristic, complemented
7#19133135C211yesmaximal, characteristic, complemented
8#19133134C211yesmaximal, characteristic, complemented
9#19133133C211yesmaximal, characteristic, complemented
10#19133118C211yesmaximal, characteristic, complemented
11#19133098C211yesmaximal, characteristic, complemented
12#19133096C211yesmaximal, characteristic, complemented
13#328×D43C211yesmaximal, characteristic, complemented
14#327×D43C211yesmaximal, characteristic, complemented
15C43×#1509C211yesmaximal, characteristic, complemented
16#14583602C411yescharacteristic, complemented
17#14583600—21no—
18#14583599C411yescharacteristic, complemented
19#14583593—21no—
20#14583590C411yescharacteristic, complemented
21#14583587C411yescharacteristic, complemented
22#14583574—21no—
23#14583573—21no—
24#14583561C411yescharacteristic, complemented
25#14583557C411yescharacteristic, complemented
26#14583544C411yescharacteristic, complemented
27#14583542C411yescharacteristic, complemented
28#14583493—21no—
29#14583482—21no—
30#14583460—21no—
31#14583433C2211yescharacteristic
32#14583412C2211yescharacteristic
33#14583409C2211yescharacteristic
34C22⋊Q8×D43C2211yescharacteristic
35#121×D43C2211yescharacteristic
36#14583371—21no—
37C2×C4×D172—21no—
38C2×C4×D172C2211yescharacteristic
39#14582972—21no—
40#14582972—21no—
41#14582969—21no—
42#14582969—21no—
43#14582956C2211yescharacteristic, complemented
44#14582861C2211yescharacteristic, complemented
45#14582861C2211yescharacteristic, complemented
46C22⋊C8×D43C2211yescharacteristic
47C22⋊C8×D43C2211yescharacteristic
48#14582797—21no—
49#14582770—21no—
50#14582770—21no—
51#14582765C2211yescharacteristic, complemented
52#14582758C2211yescharacteristic
53#14582758C2211yescharacteristic, complemented
54#95×D43C2211yescharacteristic
55#95×D43C2211yescharacteristic, complemented
56#14582637C2211yescharacteristic, complemented
57#14582637C2211yescharacteristic, complemented
58#14582636C2211yescharacteristic, complemented
59#14582636C2211yescharacteristic, complemented
60#14582635C2211yescharacteristic, complemented
61#14582635C2211yescharacteristic, complemented
62#14582634C2211yescharacteristic
63#14582634C2211yescharacteristic
64#14582633C2211yescharacteristic
65#14582633C2211yescharacteristic
66#14582632C2211yescharacteristic
67#14582632C2211yescharacteristic
68C43×#529C2211yescharacteristic
69C43×#432C2211yescharacteristic, complemented
70C4×C4⋊C4×C43C2211yescharacteristic, complemented
71C43×#328C2211yescharacteristic, complemented
72C43×#328C2211yescharacteristic, complemented
73C43×#327C2211yescharacteristic
74C43×#327C2211yescharacteristic
75C2×#10621902C2×C411yescharacteristic, complemented
76C2×#10621900C2×C411yescharacteristic, complemented
77C2×Q8×D43C2×C411yescharacteristic, complemented
78C22×D172D411yescharacteristic
79C2×D4×D43—21no—
80C2×D4×D43C2×C411yescharacteristic, complemented
81C22×C4×D43—21no—
82C22×C4×D43—21no—
83C22×C4×D43C2311yescharacteristic
84C22×C4×D43C2311yescharacteristic
85C2×#10621872—21no—
86C2×#10621872—21no—
87C2×C8×D43—21no—
88C2×C8×D43—21no—
89#13063320—21no—
90#13063320—21no—
91#13063319—21no—
92#13063319—21no—
93#13063318—21no—
94#13063317C2×C411yescharacteristic, complemented
95#13063316—21no—
96#13063315—21no—
97#13063313—21no—
98#13063313C2×C411yescharacteristic, complemented
99#13063311—21no—
100#13063310—21no—
101#13063310—21no—
102#13063310—21no—
103#13063310—21no—
104#13063309—21no—
105#13063308—21no—
106#13063308—21no—
107#13063307—21no—
108#13063307—21no—
109#13063305—21no—
110#13063305C2×C411yescharacteristic, complemented
111#13063305C2×C411yescharacteristic, complemented
112#13063304C2311yescharacteristic
113#13063303—21no—
114#13063302—21no—
115#13063302—21no—
116#13063301C2×C411yescharacteristic, complemented
117#13063301C2×C411yescharacteristic, complemented
118#13063300—21no—
119#13063300—21no—
120#13063300C2×C411yescharacteristic, complemented
121#13063300C2×C411yescharacteristic, complemented
122#13063299—21no—
123#13063299C2311yescharacteristic
124#13063298—21no—
125#13063298—21no—
126#13063298—21no—
127#13063298—21no—
128#13063297—21no—
129#13063296C2×C411yescharacteristic, complemented
130#13063296C2×C411yescharacteristic, complemented
131#13063295—21no—
132#13063295—21no—
133#13063295—21no—
134#13063293—21no—
135C4×Dic86C2×C411yescharacteristic, complemented
136C4×D172—21no—
137C4×D172—44no—
138C4×D172C2×C411yescharacteristic
139C4×D172C2×C411yescharacteristic
140C4×D172C2×C411yescharacteristic
141C4×D172C2×C411yescharacteristic
142C4×D172C2×C411yescharacteristic, complemented
143C4×D172D411yescharacteristic
144C4×D172D411yescharacteristic
145C4×D172D411yescharacteristic
146C4×D172D411yescharacteristic
147D4×Dic43—21no—
148#13063287—21no—
149#13063287—21no—
150C4×C22⋊D43—21no—
151C4×C22⋊D43—21no—
152(C22⋊D43)⋊C4—21no—
153(C22⋊D43)⋊C4—21no—
154(C22⋊D43)⋊C4—21no—
155#13063283—21no—
156#13063283C2×C411yescharacteristic, complemented
157#13063283C2×C411yescharacteristic, complemented
158#13063282—21no—
159#13063282—21no—
160C2×C4⋊Dic43—21no—
161C2×C4⋊Dic43D411yescharacteristic
162C2×Dic43⋊C4—21no—
163C2×Dic43⋊C4—21no—
164C4⋊C4×D43—21no—
165C4⋊C4×D43C2×C411yescharacteristic, complemented
166C4⋊C4×D43C2×C411yescharacteristic, complemented
167C2×(C2×D43)⋊C4—21no—
168C2×(C2×D43)⋊C4—21no—
169C2×(C2×D43)⋊C4—21no—
170C2×(C2×D43)⋊C4D411yescharacteristic
171C2×(C2×D43)⋊C4D411yescharacteristic
172C22⋊C4×D43—21no—
173C22⋊C4×D43—21no—
174C22⋊C4×D43—21no—
175C4⋊(C43⋊C8)—21no—
176C22⋊(C43⋊C8)C2311yescharacteristic
177C22⋊(C43⋊C8)C2311yescharacteristic
178(C2×D43)⋊C8—21no—
179(C2×D43)⋊C8—21no—
180(C2×D43)⋊C8—21no—
181(C2×D43)⋊C8—21no—
182#13063236—21no—
183C43⋊#95—21no—
184C43⋊#95—21no—
185C43⋊#95—21no—
186C43⋊#95C2311yescharacteristic
187C43⋊#95C2311yescharacteristic
188#126×C43—21no—
189#125×C43C2×C411yescharacteristic, complemented
190#124×C43C2×C411yescharacteristic, complemented
191#123×C43—21no—
192C22⋊Q8×C43C2311yescharacteristic
193#121×C43C2311yescharacteristic
194C4×Q8×C43C2×C411yescharacteristic, complemented
195C4×D4×C43—21no—
196C4×D4×C43C2×C411yescharacteristic, complemented
197#117×C43—21no—
198C2×C4⋊C4×C43—21no—
199C2×C42×C43—21no—
200C2×C42×C43C2311yescharacteristic
201C4⋊C8×C43—21no—
202C22⋊C8×C43C2311yescharacteristic
203C22⋊C8×C43C2311yescharacteristic
204#97×C43—21no—
205#95×C43C2311yescharacteristic
206#95×C43C2311yescharacteristic
207C23×D43—21no—
208C23×D43C2×D411yescharacteristic
209C23×D43C2×D411yescharacteristic
210C2×Q8×C43C22×C411yescharacteristic
211C2×D4×C43—21no—
212C2×D4×C43C22×C411yescharacteristic
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2411yescharacteristic
219C2×C22⋊D43—21no—
220C2×C22⋊D43—21no—
221C2×C22⋊D43—21no—
222C2×C22⋊D43—21no—
223C2×C22⋊D43—21no—
224C22×Dic43—21no—
225C22×Dic43—21no—
226C22×Dic43—21no—
227C22×Dic43C2×D411yescharacteristic
228C22×Dic43C2×D411yescharacteristic
229#10621902—81no—
230Q8×D43—81no—
231#10621900—81no—
232D4×D43—42no—
233D4×D43—42no—
234D4×D43—81no—
235C2×D172—21no—
236C2×D172—21no—
237C2×D172—21no—
238C2×D172—22no—
239C2×D172—22no—
240C2×D172C22⋊C411yescharacteristic
241C2×D172C22⋊C411yescharacteristic
242C2×D172C22⋊C411yescharacteristic
243C2×D172C22⋊C411yescharacteristic
244C2×D172C22×C411yescharacteristic
245C2×C4×D43—21no—
246C2×C4×D43—21no—
247C2×C4×D43—21no—
248C2×C4×D43—21no—
249C2×C4×D43—21no—
250C2×C4×D43—42no—
251C2×C4×D43—42no—
252C2×C4×D43—42no—
253C2×C4×D43—42no—
254C2×C4×D43—81no—
255C2×C4×D43—81no—
256C2×C4×D43—81no—
257C2×C4×D43—81no—
258C2×C4×D43C22×C411yescharacteristic
259C2×C4×D43C22×C411yescharacteristic
260C2×C4×D43C22×C411yescharacteristic
261C2×C4×D43C22×C411yescharacteristic
262C2×C4×D43C2×D411yescharacteristic
263C2×C4×D43C2×D411yescharacteristic
264C2×C4×D43C2×D411yescharacteristic
265C2×C4×D43C2×D411yescharacteristic
266C2×Dic86—21no—
267C2×Dic86C22×C411yescharacteristic
268C2×C8×C43—21no—
269C2×C8×C43—21no—
270C4⋊C4×C43—21no—
271C4⋊C4×C43—21no—
272C4⋊C4×C43—21no—
273C4⋊C4×C43—21no—
274C4⋊C4×C43—42no—
275C4⋊C4×C43C22×C411yescharacteristic
276C4⋊C4×C43C22×C411yescharacteristic
277C22⋊C4×C43—21no—
278C22⋊C4×C43—21no—
279C22⋊C4×C43—21no—
280C22⋊C4×C43—21no—
281C22⋊C4×C43—21no—
282C42×C43—21no—
283C42×C43—42no—
284C42×C43C22×C411yescharacteristic
285C42×C43C22×C411yescharacteristic
286C42×C43C2×D411yescharacteristic
287C42×C43C2×D411yescharacteristic
288C22⋊Dic43—21no—
289C22⋊Dic43—21no—
290C22⋊Dic43—21no—
291(C2×D43)⋊C4—21no—
292(C2×D43)⋊C4—21no—
293(C2×D43)⋊C4—21no—
294(C2×D43)⋊C4—21no—
295(C2×D43)⋊C4—21no—
296(C2×D43)⋊C4—21no—
297(C2×D43)⋊C4—21no—
298(C2×D43)⋊C4—21no—
299(C2×D43)⋊C4—21no—
300(C2×D43)⋊C4—21no—
301(C2×D43)⋊C4—21no—
302(C2×D43)⋊C4—21no—
303(C2×D43)⋊C4—42no—
304(C2×D43)⋊C4—42no—
305(C2×D43)⋊C4C22⋊C411yescharacteristic
306(C2×D43)⋊C4C22⋊C411yescharacteristic
307(C2×D43)⋊C4C22⋊C411yescharacteristic
308(C2×D43)⋊C4C22⋊C411yescharacteristic
309(C2×D43)⋊C4C22⋊C411yescharacteristic
310(C2×D43)⋊C4C22⋊C411yescharacteristic
311(C2×D43)⋊C4C22⋊C411yescharacteristic
312(C2×D43)⋊C4C22⋊C411yescharacteristic
313C4⋊Dic43—21no—
314C4⋊Dic43—21no—
315C4⋊Dic43—42no—
316C4⋊Dic43C22⋊C411yescharacteristic
317C4⋊Dic43C22⋊C411yescharacteristic
318C4⋊Dic43C22⋊C411yescharacteristic
319C4⋊Dic43C22⋊C411yescharacteristic
320C4⋊Dic43C22×C411yescharacteristic
321C4⋊Dic43C22×C411yescharacteristic
322Dic43⋊C4—21no—
323Dic43⋊C4—21no—
324Dic43⋊C4—21no—
325Dic43⋊C4—21no—
326Dic43⋊C4—21no—
327Dic43⋊C4—21no—
328Dic43⋊C4—21no—
329Dic43⋊C4—21no—
330Dic43⋊C4—81no—
331Dic43⋊C4—81no—
332C4×Dic43—21no—
333C4×Dic43—21no—
334C4×Dic43—21no—
335C2×C43⋊C8—21no—
336C2×C43⋊C8—21no—
337#10621872—81no—
338#10621872—81no—
339C8×D43—81no—
340C8×D43—81no—
341C23×C43—21no—
342C23×C43C22×D411yescharacteristic
343C22×D43—21no—
344C22×D43—21no—
345C22×D43—21no—
346C22×D43—41no—
347C22×D43—41no—
348C22×D43—41no—
349C22×D43—41no—
350C22×D43—42no—
351C22×D43—81no—
352C22×D43—81no—
353C22×D43C2×C22⋊C411yescharacteristic
354C22×D43C2×C22⋊C411yescharacteristic
355C22×D43C2×C22⋊C411yescharacteristic
356C22×D43C2×C22⋊C411yescharacteristic
357C22×D43AGL(1,ℤ/8)12yes—
358C22×D43#13712yes—
359Q8×C43—41no—
360D4×C43—41no—
361D4×C43—41no—
362D4×C43—41no—
363C2×C4×C43—21no—
364C2×C4×C43—21no—
365C2×C4×C43—22no—
366C2×C4×C43—21no—
367C2×C4×C43—21no—
368C2×C4×C43—21no—
369C2×C4×C43—41no—
370C2×C4×C43—41no—
371C2×C4×C43—41no—
372C2×C4×C43—41no—
373C2×C4×C43—41no—
374C2×C4×C43—41no—
375C2×C4×C43—41no—
376C2×C4×C43—81no—
377C2×C4×C43C2×C22⋊C411yescharacteristic
378C2×C4×C43C2×C22⋊C411yescharacteristic
379C2×C4×C43C2×C22⋊C411yescharacteristic
380C2×C4×C43C2×C22⋊C411yescharacteristic
381C2×C4×C43C23×C411yescharacteristic
382C2×C4×C43C22×D411yescharacteristic
383C22⋊D43—41no—
384C22⋊D43—41no—
385C22⋊D43—42no—
386C22⋊D43—81no—
387C22⋊D43—81no—
388C22⋊D43—81no—
389C2×Dic43—21no—
390C2×Dic43—21no—
391C2×Dic43—21no—
392C2×Dic43—41no—
393C2×Dic43—41no—
394C2×Dic43—41no—
395C2×Dic43—41no—
396C2×Dic43—41no—
397C2×Dic43—41no—
398C2×Dic43—41no—
399C2×Dic43—41no—
400C2×Dic43—81no—
401C2×Dic43C2×C22⋊C411yescharacteristic
402C2×Dic43C2×C22⋊C411yescharacteristic
403C2×Dic43C2×C22⋊C411yescharacteristic
404C2×Dic43C2×C22⋊C411yescharacteristic
405D172—22no—
406D172—22no—
407D172—22no—
408D172—22no—
409D172—41no—
410D172—42no—
411D172—81no—
412D172—81no—
413C4×D43—41no—
414C4×D43—41no—
415C4×D43—41no—
416C4×D43—41no—
417C4×D43—41no—
418C4×D43—41no—
419C4×D43—41no—
420C4×D43—41no—
421C4×D43—42no—
422C4×D43—81no—
423C4×D43—81no—
424C4×D43—81no—
425C4×D43—81no—
426C4×D43—84no—
427C4×D43—84no—
428Dic86—41no—
429Dic86—81no—
430C8×C43—41no—
431C8×C43—41no—
432C43⋊C8—41no—
433C43⋊C8—41no—
434#17622—431nomaximal, Sylow
435C22×C43—21no—
436C22×C43—21no—
437C22×C43—41no—
438C22×C43—41no—
439C22×C43—41no—
440C22×C43C22×C22⋊C411yescharacteristic
441C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
442C22×C43C2×#13711yescharacteristic
443C2×D43—21no—
444C2×D43—21no—
445C2×D43—21no—
446C2×D43—21no—
447C2×D43—21no—
448C2×D43—21no—
449C2×D43—21no—
450C2×D43—21no—
451C2×D43—21no—
452C2×D43—21no—
453C2×D43—42no—
454C2×D43—42no—
455C2×D43—42no—
456C2×D43—42no—
457C2×D43—41no—
458C2×D43—41no—
459C2×D43—41no—
460C2×D43—162no—
461C2×D43#41712yes—
462C2×D43#41712yes—
463C4×C43—21no—
464C4×C43—21no—
465C4×C43—21no—
466C4×C43—21no—
467C4×C43—21no—
468C4×C43—21no—
469C4×C43—42no—
470C4×C43—41no—
471C4×C43—41no—
472C4×C43—41no—
473C4×C43—81no—
474Dic43—21no—
475Dic43—21no—
476Dic43—21no—
477Dic43—21no—
478Dic43—41no—
479Dic43—41no—
480Dic43—41no—
481Dic43—81no—
482Dic43—81no—
483#3505—431no—
484#2973—431no—
485#2349—431no—
486#1520—431no—
487#1519—431no—
488#1513—431no—
489#1513—431no—
490#1512—431no—
491#1512—431no—
492#1509—431no—
493#1509D4311yescharacteristic, complemented
494#1504—431no—
495#1504—431no—
496C2×#328—431no—
497C2×#327—431no—
498C2×C43—21no—
499C2×C43—21no—
500C2×C43—81no—
501C2×C43#288311yescharacteristic
502C2×C43C2×#41711yescharacteristic
503C2×C43#290111yescharacteristic
504D43—22no—
505D43—22no—
506D43—41no—
507D43—41no—
508D43—81no—
509#553—431no—
510#553—431no—
511#553—861no—
512#553—861no—
513#552—431no—
514#552—431no—
515#551—861no—
516#551—861no—
517#548—431no—
518#548—431no—
519#546—431no—
520#546—431no—
521#539—861no—
522#538—861no—
523#534—861no—
524#529—431no—
525#529C2×D4311yescharacteristic
526#525—431no—
527#525—431no—
528C2×C22⋊Q8—431no—
529C2×#121—431no—
530#518—861no—
531C2×C4×D4—431no—
532C2×C4×D4—861no—
533#435—861no—
534#435—861no—
535#435—861no—
536#435—861no—
537#432—431no—
538#432C2×D4311yescharacteristic, complemented
539#407—431no—
540#407—431no—
541C2×C22⋊C8—431no—
542C2×C22⋊C8—431no—
543#389—861no—
544#385—861no—
545#385—861no—
546#382—431no—
547#380—431no—
548#380—431no—
549C4×C4⋊C4C2×D4311yescharacteristic, complemented
550C2×#95—431no—
551C2×#95—431no—
552#328—431no—
553#328—431no—
554#328—431no—
555#328—431no—
556#328—431no—
557#328—431no—
558#328C2×D4311yescharacteristic, complemented
559#328C2×D4311yescharacteristic, complemented
560#327—431no—
561#327—431no—
562#327—431no—
563#327—431no—
564#327—431no—
565#327—431no—
566#327C2×D4311yescharacteristic
567#327C2×D4311yescharacteristic
568C43#1762211yescharacteristic, complemented, Sylow
569C2×#41—431no—
570C2×#41—431no—
571C22×Q8—431no—
572C22×D4—431no—
573C22×D4—431no—
574C22×D4—861no—
575C23×C4—431no—
576C23×C4—431no—
577C23×C4—861no—
578C23×C4—861no—
579C2×M16—861no—
580C2×M16—861no—
581C22×C8—861no—
582C22×C8—861no—
583#126—21no—
584#126—861no—
585#126—861no—
586#126—861no—
587#126—861no—
588#126—861no—
589#125—431no—
590#125—861no—
591#125—861no—
592#125C4×D4311yescharacteristic, complemented
593#124—431no—
594#124—861no—
595#124—861no—
596#124C4×D4311yescharacteristic, complemented
597#123—21no—
598#123—861no—
599#123—861no—
600#123—861no—
601#123—861no—
602#123—861no—
603#123—861no—
604#123—861no—
605#123—861no—
606#123—861no—
607C22⋊Q8—431no—
608C22⋊Q8—431no—
609C22⋊Q8—431no—
610C22⋊Q8—431no—
611C22⋊Q8—431no—
612C22⋊Q8—861no—
613C22⋊Q8—861no—
614C22⋊Q8—861no—
615C22⋊Q8—861no—
616C22⋊Q8C22×D4311yescharacteristic
617#121—431no—
618#121—431no—
619#121—431no—
620#121—431no—
621#121—431no—
622#121—861no—
623#121—861no—
624#121—861no—
625#121—861no—
626#121—861no—
627#121—861no—
628#121—861no—
629#121—861no—
630#121C22×D4311yescharacteristic
631#120—861no—
632#120—861no—
633#120—861no—
634#120—861no—
635C4×Q8—431no—
636C4×Q8C4×D4311yescharacteristic, complemented
637C4×D4—21no—
638C4×D4—431no—
639C4×D4—431no—
640C4×D4—431no—
641C4×D4—431no—
642C4×D4—431no—
643C4×D4—431no—
644C4×D4—431no—
645C4×D4—431no—
646C4×D4—431no—
647C4×D4—861no—
648C4×D4—861no—
649C4×D4—861no—
650C4×D4—861no—
651C4×D4—861no—
652C4×D4—861no—
653C4×D4—861no—
654C4×D4—861no—
655C4×D4—861no—
656C4×D4—1724no—
657C4×D4C4×D4311yescharacteristic, complemented
658#117—21no—
659#117—431no—
660#117—431no—
661#117—861no—
662#117—861no—
663#117—861no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—431no—
666C2×C4⋊C4—431no—
667C2×C4⋊C4—431no—
668C2×C4⋊C4—861no—
669C2×C4⋊C4—861no—
670C2×C4⋊C4—861no—
671C2×C4⋊C4—861no—
672C2×C22⋊C4—431no—
673C2×C22⋊C4—431no—
674C2×C22⋊C4—861no—
675C2×C22⋊C4—861no—
676C2×C22⋊C4—861no—
677C2×C22⋊C4—861no—
678C2×C22⋊C4—861no—
679C2×C22⋊C4—861no—
680C2×C42—21no—
681C2×C42C22×D4311yescharacteristic
682C4⋊C8—21no—
683C4⋊C8—861no—
684C22⋊C8—431no—
685C22⋊C8—431no—
686C22⋊C8—861no—
687C22⋊C8—861no—
688C22⋊C8—861no—
689C22⋊C8—861no—
690C22⋊C8C22×D4311yescharacteristic
691C22⋊C8C22×D4311yescharacteristic
692#97—21no—
693#97—861no—
694#95—431no—
695#95—431no—
696#95—861no—
697#95—861no—
698#95—861no—
699#95C22×D4311yescharacteristic
700#95C22×D4311yescharacteristic
701C24—431no—
702C24—431no—
703C24—861no—
704#41—3441no—
705#41—3441no—
706C2×Q8—431no—
707C2×Q8—861no—
708C2×Q8—3441no—
709C2×Q8C2×C4×D4311yescharacteristic
710C2×D4—21no—
711C2×D4—431no—
712C2×D4—431no—
713C2×D4—431no—
714C2×D4—431no—
715C2×D4—431no—
716C2×D4—862no—
717C2×D4—862no—
718C2×D4—861no—
719C2×D4—861no—
720C2×D4—861no—
721C2×D4—861no—
722C2×D4—861no—
723C2×D4—861no—
724C2×D4—861no—
725C2×D4—861no—
726C2×D4—3441no—
727C2×D4—1722no—
728C2×D4—1722no—
729C2×D4C2×C4×D4311yescharacteristic
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—431no—
734C22×C4—431no—
735C22×C4—431no—
736C22×C4—431no—
737C22×C4—431no—
738C22×C4—431no—
739C22×C4—431no—
740C22×C4—431no—
741C22×C4—431no—
742C22×C4—431no—
743C22×C4—861no—
744C22×C4—861no—
745C22×C4—861no—
746C22×C4—861no—
747C22×C4—861no—
748C22×C4—861no—
749C22×C4—861no—
750C22×C4—861no—
751C22×C4—3441no—
752C22×C4—3441no—
753C22×C4—3441no—
754C22×C4—3441no—
755C22×C4—1722no—
756C22×C4—1722no—
757C22×C4—1722no—
758C22×C4—1722no—
759C22×C4D4×D4311yescharacteristic
760C22×C4D4×D4311yescharacteristic
761C22×C4C23×D4311yescharacteristic
762M16—3441no—
763M16—3441no—
764C2×C8—21no—
765C2×C8—21no—
766C2×C8—861no—
767C2×C8—861no—
768C2×C8—3441no—
769C2×C8—3441no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—42no—
775C4⋊C4—431no—
776C4⋊C4—431no—
777C4⋊C4—431no—
778C4⋊C4—431no—
779C4⋊C4—431no—
780C4⋊C4—431no—
781C4⋊C4—861no—
782C4⋊C4—861no—
783C4⋊C4—861no—
784C4⋊C4—861no—
785C4⋊C4—861no—
786C4⋊C4—861no—
787C4⋊C4—861no—
788C4⋊C4—861no—
789C4⋊C4—861no—
790C4⋊C4—861no—
791C4⋊C4—3441no—
792C4⋊C4—3441no—
793C4⋊C4—1722no—
794C4⋊C4C2×C4×D4311yescharacteristic
795C4⋊C4C2×C4×D4311yescharacteristic
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—431no—
802C22⋊C4—431no—
803C22⋊C4—431no—
804C22⋊C4—431no—
805C22⋊C4—431no—
806C22⋊C4—431no—
807C22⋊C4—431no—
808C22⋊C4—431no—
809C22⋊C4—861no—
810C22⋊C4—861no—
811C22⋊C4—861no—
812C22⋊C4—861no—
813C22⋊C4—861no—
814C22⋊C4—861no—
815C22⋊C4—861no—
816C22⋊C4—861no—
817C22⋊C4—861no—
818C22⋊C4—861no—
819C22⋊C4—861no—
820C22⋊C4—861no—
821C22⋊C4—861no—
822C22⋊C4—861no—
823C22⋊C4—861no—
824C22⋊C4—1722no—
825C22⋊C4—1722no—
826C42—21no—
827C42—42no—
828C42—861no—
829C42—861no—
830C42—861no—
831C42C2×C4×D4311yescharacteristic
832C42C2×C4×D4311yescharacteristic
833C42D4×D4311yescharacteristic
834C42D4×D4311yescharacteristic
835C23—21no—
836C23—431no—
837C23—431no—
838C23—432no—
839C23—432no—
840C23—431no—
841C23—431no—
842C23—861no—
843C23—861no—
844C23—861no—
845C23—3441no—
846C23—3441no—
847C23—1721no—
848C23—1721no—
849C23—1721no—
850C23—1721no—
851C23—1722no—
852C23C2×D4×D4311yescharacteristic
853Q8—41no—
854Q8—3441no—
855Q8—1721no—
856D4—41no—
857D4—41no—
858D4—41no—
859D4—862no—
860D4—862no—
861D4—862no—
862D4—862no—
863D4—3441no—
864D4—3441no—
865D4—3441no—
866D4—3441no—
867D4—3441no—
868D4—1721no—
869D4—1722no—
870D4—1722no—
871D4—1721no—
872D4—1721no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—22no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—81no—
887C2×C4—431no—
888C2×C4—431no—
889C2×C4—431no—
890C2×C4—431no—
891C2×C4—861no—
892C2×C4—861no—
893C2×C4—861no—
894C2×C4—3441no—
895C2×C4—3441no—
896C2×C4—3444no—
897C2×C4—3444no—
898C2×C4—3441no—
899C2×C4—3441no—
900C2×C4—3441no—
901C2×C4—1721no—
902C2×C4—1721no—
903C2×C4—1721no—
904C2×C4—1721no—
905C2×C4—1721no—
906C2×C4—1721no—
907C2×C4—1721no—
908C2×C4—1721no—
909C2×C4—1722no—
910C2×C4—1721no—
911C2×C4—1721no—
912C2×C4—1721no—
913C2×C4—1721no—
914C2×C4—1721no—
915C2×C4—1721no—
916C2×C4—1721no—
917C2×C4—1721no—
918C2×C4C22⋊C4×D4311yescharacteristic
919C2×C4C22⋊C4×D4311yescharacteristic
920C2×C4C22⋊C4×D4311yescharacteristic
921C2×C4C22⋊C4×D4311yescharacteristic
922C2×C4C22×C4×D4311yescharacteristic
923C2×C4C2×D4×D4311yescharacteristic
924C8—41no—
925C8—41no—
926C8—1721no—
927C8—1721no—
928C22—21no—
929C22—21no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—432no—
934C22—432no—
935C22—861no—
936C22—861no—
937C22—861no—
938C22—861no—
939C22—861no—
940C22—861no—
941C22—861no—
942C22—861no—
943C22—861no—
944C22—861no—
945C22—1722no—
946C22—1722no—
947C22—1722no—
948C22—1722no—
949C22—1721no—
950C22—1721no—
951C22—1721no—
952C22—6882no—
953C22C2×C22⋊C4×D4311yescharacteristic
954C22AGL(1,ℤ/8)×D4311yescharacteristic
955C22#137×D4311yescharacteristic
956C4—21no—
957C4—21no—
958C4—21no—
959C4—21no—
960C4—21no—
961C4—21no—
962C4—42no—
963C4—41no—
964C4—41no—
965C4—41no—
966C4—81no—
967C4—861no—
968C4—861no—
969C4—861no—
970C4—861no—
971C4—3441no—
972C4—3441no—
973C4—1721no—
974C4—1721no—
975C4—1721no—
976C2—21no—
977C2—21no—
978C2—81no—
979C2—862no—
980C2—862no—
981C2—3441no—
982C2—1721no—
983C2—1721no—
984C2#1914305411yescharacteristic
985C2#417×D4311yescharacteristic
986C2#1914313911yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1509C2
socleC22×C43C22×C22⋊C4
prime radical#19148430C2
cosocleC22×C4×C43C24
hypercenter#1509D43
hypocenterC43#17622
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1509

Complements

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

NH ≅ G/Ntype
2. #19143623C2semidirect
3. #19137506C2semidirect
4. #19133165C2semidirect
5. #19133161C2semidirect
6. #19133137C2semidirect
7. #19133135C2semidirect
8. #19133134C2semidirect
9. #19133133C2semidirect
10. #19133118C2semidirect
11. #19133098C2semidirect
12. #19133096C2semidirect
13. #328×D43C2semidirect
14. #327×D43C2semidirect
15. C43×#1509C2semidirect
16. #14583602C4semidirect
18. #14583599C4semidirect
20. #14583590C4semidirect
21. #14583587C4semidirect
24. #14583561C4semidirect
25. #14583557C4semidirect
26. #14583544C4semidirect
27. #14583542C4semidirect
43. #14582956C22semidirect
44. #14582861C22semidirect
45. #14582861C22semidirect
51. #14582765C22semidirect
53. #14582758C22semidirect
55. #95×D43C22semidirect
56. #14582637C22semidirect
57. #14582637C22semidirect
58. #14582636C22semidirect
59. #14582636C22semidirect
60. #14582635C22semidirect
61. #14582635C22semidirect
69. C43×#432C22semidirect
70. C4×C4⋊C4×C43C22semidirect
71. C43×#328C22semidirect
72. C43×#328C22semidirect
75. C2×#10621902C2×C4semidirect
76. C2×#10621900C2×C4semidirect
77. C2×Q8×D43C2×C4semidirect
80. C2×D4×D43C2×C4semidirect
94. #13063317C2×C4semidirect
98. #13063313C2×C4semidirect
110. #13063305C2×C4semidirect
111. #13063305C2×C4semidirect
116. #13063301C2×C4semidirect
117. #13063301C2×C4semidirect
120. #13063300C2×C4semidirect
121. #13063300C2×C4semidirect
129. #13063296C2×C4semidirect
130. #13063296C2×C4semidirect
135. C4×Dic86C2×C4semidirect
142. C4×D172C2×C4semidirect
156. #13063283C2×C4semidirect
157. #13063283C2×C4semidirect
165. C4⋊C4×D43C2×C4semidirect
166. C4⋊C4×D43C2×C4semidirect
189. #125×C43C2×C4semidirect
190. #124×C43C2×C4semidirect
194. C4×Q8×C43C2×C4semidirect
196. C4×D4×C43C2×C4semidirect
493. #1509D43semidirect
538. #432C2×D43semidirect
549. C4×C4⋊C4C2×D43semidirect
558. #328C2×D43semidirect
559. #328C2×D43semidirect
568. C43#17622semidirect
592. #125C4×D43semidirect
596. #124C4×D43semidirect
636. C4×Q8C4×D43semidirect
657. C4×D4C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191484302
#191436232
#191375062
#191331652
#191331612
#191331372
#191331352
#191331342
#191331332
#191331182
#191330982
#191330962
#328×D432
#327×D432
C43×#15092
#1762243