Finite Group Databasebeta

← #25064392

Subgroups — #25064392

Order 11008.

898 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148451C211yesmaximal, characteristic
2#19143679C211yesmaximal, characteristic, complemented
3#19137558C211yesmaximal, characteristic, complemented
4#19133171C211yesmaximal, characteristic, complemented
5#19133169C211yesmaximal, characteristic, complemented
6#19133144C211yesmaximal, characteristic, complemented
7#19133140C211yesmaximal, characteristic
8#19133134C211yesmaximal, characteristic, complemented
9#19133133C211yesmaximal, characteristic, complemented
10#19133118C211yesmaximal, characteristic, complemented
11#19133105C211yesmaximal, characteristic, complemented
12#19133101C211yesmaximal, characteristic
13#19133080C211yesmaximal, characteristic, complemented
14#19133078C211yesmaximal, characteristic, complemented
15C43×#1509C211yesmaximal, characteristic, complemented
16#14583632C411yescharacteristic, complemented
17#14583631C411yescharacteristic, complemented
18#14583626C411yescharacteristic, complemented
19#14583625C411yescharacteristic, complemented
20#14583621C411yescharacteristic, complemented
21#14583618C411yescharacteristic, complemented
22#14583617—21no—
23#14583616—21no—
24#14583608C411yescharacteristic, complemented
25#14583605C411yescharacteristic, complemented
26#14583585—21no—
27#14583582—21no—
28#14583493—21no—
29#14583491—21no—
30#14583471—21no—
31#14583451C2211yescharacteristic
32#14583444C2211yescharacteristic
33#14583435C2211yescharacteristic
34#14583433C2211yescharacteristic
35#14583430C2211yescharacteristic
36#14583378—21no—
37C2×C4×Dic86C2211yescharacteristic
38#14583028—21no—
39#14583028—21no—
40#14583027—21no—
41#14583027—21no—
42#14582956C2211yescharacteristic
43#14582953C2211yescharacteristic
44#14582953C2211yescharacteristic
45#14582949C2211yescharacteristic
46#14582949C2211yescharacteristic
47#14582805—21no—
48#14582780—21no—
49#14582780—21no—
50#14582766C2211yescharacteristic
51#14582766C2211yescharacteristic
52#14582765C2211yescharacteristic
53C4×C4⋊Dic43—21no—
54#14582744C2211yescharacteristic
55#14582744C2211yescharacteristic
56#14582637C2211yescharacteristic
57#14582637C2211yescharacteristic
58#14582636C2211yescharacteristic
59#14582636C2211yescharacteristic
60#14582635C2211yescharacteristic
61#14582635C2211yescharacteristic
62#14582634C2211yescharacteristic
63#14582634C2211yescharacteristic
64#14582633C2211yescharacteristic
65#14582633C2211yescharacteristic
66#14582632C2211yescharacteristic
67#14582632C2211yescharacteristic
68C43×#529C2211yescharacteristic
69C43×#432C2211yescharacteristic
70C4×C4⋊C4×C43C2211yescharacteristic
71C43×#328C2211yescharacteristic
72C43×#328C2211yescharacteristic
73C43×#327C2211yescharacteristic
74C43×#327C2211yescharacteristic
75C2×#10621900—21no—
76C22×Dic86D411yescharacteristic
77#13063324—21no—
78#13063324—21no—
79#13063324C2×C411yescharacteristic
80#13063324C2×C411yescharacteristic
81#13063323C2×C411yescharacteristic
82#13063321C2×C411yescharacteristic
83#13063320—21no—
84#13063320—21no—
85#13063319—21no—
86#13063319—21no—
87#13063318—21no—
88#13063318—21no—
89#13063318—21no—
90#13063317—21no—
91#13063317C2×C411yescharacteristic
92#13063316—21no—
93#13063316C2×C411yescharacteristic
94#13063316C2×C411yescharacteristic
95#13063315—21no—
96#13063315—21no—
97#13063315—21no—
98#13063314C2×C411yescharacteristic
99#13063313C2×C411yescharacteristic
100#13063312C2×C411yescharacteristic
101#13063311—21no—
102#13063311—21no—
103#13063311—21no—
104#13063309—21no—
105#13063309—21no—
106#13063308—21no—
107#13063308—21no—
108#13063307—21no—
109#13063307—21no—
110#13063306—21no—
111#13063305—21no—
112#13063304—21no—
113#13063304C2311yescharacteristic
114#13063303—21no—
115#13063303—21no—
116#13063303—21no—
117#13063302—21no—
118#13063302—21no—
119#13063302—21no—
120#13063302—21no—
121#13063299C2311yescharacteristic
122#13063297—21no—
123Q8×Dic43C2×C411yescharacteristic
124Q8×Dic43C2×C411yescharacteristic
125C4×Dic86—21no—
126C4×Dic86C2×C411yescharacteristic
127C4×Dic86C2×C411yescharacteristic
128C4×Dic86C2×C411yescharacteristic
129C4×Dic86C2×C411yescharacteristic
130C4×Dic86C2×C411yescharacteristic
131C4×Dic86D411yescharacteristic
132C4×Dic86D411yescharacteristic
133C4×Dic86D411yescharacteristic
134C4×Dic86D411yescharacteristic
135#13063290—21no—
136#13063290—21no—
137#13063290C2×C411yescharacteristic
138#13063290C2×C411yescharacteristic
139C4×D172C2×C411yescharacteristic
140D4×Dic43—21no—
141D4×Dic43C2×C411yescharacteristic
142D4×Dic43C2×C411yescharacteristic
143#13063287C2×C411yescharacteristic
144#13063287C2×C411yescharacteristic
145C4×C22⋊D43—21no—
146C4×C22⋊D43—21no—
147(C22⋊D43)⋊C4—21no—
148(C22⋊D43)⋊C4—21no—
149(C22⋊D43)⋊C4—21no—
150#13063283—21no—
151#13063282—21no—
152#13063282—21no—
153#13063281—21no—
154#13063281—21no—
155#13063281—21no—
156C2×C4⋊Dic43—21no—
157C2×C4⋊Dic43D411yescharacteristic
158C2×Dic43⋊C4—21no—
159C2×Dic43⋊C4D411yescharacteristic
160C2×Dic43⋊C4D411yescharacteristic
161C4⋊C4×D43—21no—
162C2×C4×Dic43—21no—
163C2×C4×Dic43—21no—
164C2×C4×Dic43C2311yescharacteristic
165C2×C4×Dic43C2311yescharacteristic
166C4⋊(C43⋊C8)—21no—
167Dic43⋊C8—21no—
168Dic43⋊C8—21no—
169Dic43⋊C8—21no—
170Dic43⋊C8—21no—
171C22⋊(C43⋊C8)C2311yescharacteristic
172C22⋊(C43⋊C8)C2311yescharacteristic
173#13063236—21no—
174#13063235—21no—
175#13063235—21no—
176C8×Dic43—21no—
177C8×Dic43—21no—
178C43⋊#95—21no—
179C43⋊#95—21no—
180C43⋊#95—21no—
181C43⋊#95—21no—
182C43⋊#95—21no—
183C43⋊#95—21no—
184C43⋊#95—21no—
185C43⋊#95C2311yescharacteristic
186C43⋊#95C2311yescharacteristic
187#126×C43—21no—
188#125×C43C2×C411yescharacteristic
189#124×C43C2×C411yescharacteristic
190#123×C43—21no—
191C22⋊Q8×C43C2311yescharacteristic
192#121×C43C2311yescharacteristic
193C4×Q8×C43C2×C411yescharacteristic
194C4×D4×C43—21no—
195C4×D4×C43C2×C411yescharacteristic
196#117×C43—21no—
197C2×C4⋊C4×C43—21no—
198C2×C42×C43—21no—
199C2×C42×C43C2311yescharacteristic
200C4⋊C8×C43—21no—
201C22⋊C8×C43C2311yescharacteristic
202C22⋊C8×C43C2311yescharacteristic
203#97×C43—21no—
204#95×C43C2311yescharacteristic
205#95×C43C2311yescharacteristic
206C2×Q8×C43C22×C411yescharacteristic
207C2×D4×C43—21no—
208C2×D4×C43C22×C411yescharacteristic
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43C2×D411yescharacteristic
213C22×C4×C43C2×D411yescharacteristic
214C22×C4×C43C2411yescharacteristic
215C2×C22⋊D43—21no—
216C2×C22⋊D43—21no—
217C2×C22⋊D43—21no—
218C22×Dic43—21no—
219C22×Dic43—21no—
220C22×Dic43—21no—
221C22×Dic43—21no—
222C22×Dic43C2×D411yescharacteristic
223C22×Dic43C2×D411yescharacteristic
224C22×Dic43C2×D411yescharacteristic
225C22×Dic43C2×D411yescharacteristic
226#10621900—42no—
227#10621900—42no—
228C2×D172C22×C411yescharacteristic
229C2×C4×D43—21no—
230C2×C4×D43—21no—
231C2×C4×D43—21no—
232C2×Dic86—21no—
233C2×Dic86—21no—
234C2×Dic86—41no—
235C2×Dic86—41no—
236C2×Dic86C22⋊C411yescharacteristic
237C2×Dic86C22⋊C411yescharacteristic
238C2×Dic86C22⋊C411yescharacteristic
239C2×Dic86C22⋊C411yescharacteristic
240C2×Dic86C22×C411yescharacteristic
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C4⋊C4×C43—21no—
244C4⋊C4×C43—21no—
245C4⋊C4×C43—21no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—42no—
248C4⋊C4×C43C22×C411yescharacteristic
249C4⋊C4×C43C22×C411yescharacteristic
250C22⋊C4×C43—21no—
251C22⋊C4×C43—21no—
252C22⋊C4×C43—21no—
253C22⋊C4×C43—21no—
254C22⋊C4×C43—21no—
255C42×C43—21no—
256C42×C43—42no—
257C42×C43C22×C411yescharacteristic
258C42×C43C22×C411yescharacteristic
259C42×C43C2×D411yescharacteristic
260C42×C43C2×D411yescharacteristic
261C22⋊Dic43—21no—
262C22⋊Dic43—21no—
263C22⋊Dic43—21no—
264C22⋊Dic43—21no—
265C22⋊Dic43—21no—
266(C2×D43)⋊C4—21no—
267(C2×D43)⋊C4—21no—
268(C2×D43)⋊C4—21no—
269(C2×D43)⋊C4—21no—
270(C2×D43)⋊C4—21no—
271(C2×D43)⋊C4—21no—
272(C2×D43)⋊C4—21no—
273(C2×D43)⋊C4—21no—
274C4⋊Dic43—21no—
275C4⋊Dic43—21no—
276C4⋊Dic43—21no—
277C4⋊Dic43—21no—
278C4⋊Dic43—42no—
279C4⋊Dic43C22⋊C411yescharacteristic
280C4⋊Dic43C22⋊C411yescharacteristic
281C4⋊Dic43C22⋊C411yescharacteristic
282C4⋊Dic43C22⋊C411yescharacteristic
283C4⋊Dic43C22×C411yescharacteristic
284C4⋊Dic43C22×C411yescharacteristic
285Dic43⋊C4—21no—
286Dic43⋊C4—21no—
287Dic43⋊C4—21no—
288Dic43⋊C4—21no—
289Dic43⋊C4—21no—
290Dic43⋊C4—21no—
291Dic43⋊C4—21no—
292Dic43⋊C4—21no—
293Dic43⋊C4—21no—
294Dic43⋊C4—21no—
295Dic43⋊C4—21no—
296Dic43⋊C4—21no—
297Dic43⋊C4C22⋊C411yescharacteristic
298Dic43⋊C4C22⋊C411yescharacteristic
299Dic43⋊C4C22⋊C411yescharacteristic
300Dic43⋊C4C22⋊C411yescharacteristic
301Dic43⋊C4C22⋊C411yescharacteristic
302Dic43⋊C4C22⋊C411yescharacteristic
303Dic43⋊C4C22⋊C411yescharacteristic
304Dic43⋊C4C22⋊C411yescharacteristic
305C4×Dic43—21no—
306C4×Dic43—21no—
307C4×Dic43—21no—
308C4×Dic43—21no—
309C4×Dic43—21no—
310C4×Dic43—42no—
311C4×Dic43—42no—
312C4×Dic43C22×C411yescharacteristic
313C4×Dic43C22×C411yescharacteristic
314C4×Dic43C22×C411yescharacteristic
315C4×Dic43C22×C411yescharacteristic
316C4×Dic43C2×D411yescharacteristic
317C4×Dic43C2×D411yescharacteristic
318C4×Dic43C2×D411yescharacteristic
319C4×Dic43C2×D411yescharacteristic
320C2×C43⋊C8—21no—
321C2×C43⋊C8—21no—
322C23×C43—21no—
323C23×C43C22×D411yescharacteristic
324C22×D43—21no—
325Q8×C43—41no—
326D4×C43—41no—
327D4×C43—41no—
328D4×C43—41no—
329C2×C4×C43—21no—
330C2×C4×C43—21no—
331C2×C4×C43—22no—
332C2×C4×C43—21no—
333C2×C4×C43—21no—
334C2×C4×C43—21no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43—41no—
342C2×C4×C43—81no—
343C2×C4×C43C2×C22⋊C411yescharacteristic
344C2×C4×C43C2×C22⋊C411yescharacteristic
345C2×C4×C43C2×C22⋊C411yescharacteristic
346C2×C4×C43C2×C22⋊C411yescharacteristic
347C2×C4×C43C23×C411yescharacteristic
348C2×C4×C43C22×D411yescharacteristic
349C22⋊D43—42no—
350C22⋊D43—41no—
351C22⋊D43—41no—
352C22⋊D43—81no—
353C2×Dic43—21no—
354C2×Dic43—21no—
355C2×Dic43—21no—
356C2×Dic43—21no—
357C2×Dic43—21no—
358C2×Dic43—21no—
359C2×Dic43—21no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43—42no—
363C2×Dic43—41no—
364C2×Dic43—41no—
365C2×Dic43—41no—
366C2×Dic43—41no—
367C2×Dic43—41no—
368C2×Dic43—41no—
369C2×Dic43—81no—
370C2×Dic43C2×C22⋊C411yescharacteristic
371C2×Dic43C2×C22⋊C411yescharacteristic
372C2×Dic43C2×C22⋊C411yescharacteristic
373C2×Dic43C2×C22⋊C411yescharacteristic
374C2×Dic43C2×C22⋊C411yescharacteristic
375C2×Dic43C2×C22⋊C411yescharacteristic
376C2×Dic43C2×C22⋊C411yescharacteristic
377C2×Dic43C2×C22⋊C411yescharacteristic
378D172—41no—
379C4×D43—42no—
380C4×D43—81no—
381C4×D43—81no—
382Dic86—41no—
383Dic86—41no—
384Dic86—41no—
385Dic86—41no—
386Dic86—42no—
387Dic86—41no—
388Dic86—81no—
389C8×C43—41no—
390C8×C43—41no—
391C43⋊C8—41no—
392C43⋊C8—41no—
393#17624—431nomaximal, Sylow
394C22×C43—21no—
395C22×C43—21no—
396C22×C43—41no—
397C22×C43—41no—
398C22×C43—41no—
399C22×C43C22×C22⋊C411yescharacteristic
400C22×C43#57511yescharacteristic
401C22×C43#57511yescharacteristic
402C2×D43—41no—
403C2×D43—41no—
404C2×D43—41no—
405C4×C43—21no—
406C4×C43—21no—
407C4×C43—21no—
408C4×C43—21no—
409C4×C43—21no—
410C4×C43—21no—
411C4×C43—42no—
412C4×C43—41no—
413C4×C43—41no—
414C4×C43—41no—
415C4×C43—81no—
416Dic43—21no—
417Dic43—21no—
418Dic43—21no—
419Dic43—21no—
420Dic43—21no—
421Dic43—21no—
422Dic43—21no—
423Dic43—21no—
424Dic43—41no—
425Dic43—41no—
426Dic43—41no—
427Dic43—81no—
428Dic43—81no—
429#3507—431no—
430#2983—431no—
431#2356—431no—
432#1521—431no—
433#1521—431no—
434#1515—431no—
435#1514—431no—
436#1512—431no—
437#1512—431no—
438#1509—431no—
439#1509D4311yescharacteristic, complemented
440#1506—431no—
441#1505—431no—
442#1500—431no—
443#1500—431no—
444C2×C43—21no—
445C2×C43—21no—
446C2×C43—81no—
447C2×C43#288411yescharacteristic
448C2×C43#289611yescharacteristic
449C2×C43#290111yescharacteristic
450D43—81no—
451#559—431no—
452#559—431no—
453#557—431no—
454#557—431no—
455#556—431no—
456#556—431no—
457#556—861no—
458#556—861no—
459#554—431no—
460#554—431no—
461#552—861no—
462#552—861no—
463#539—861no—
464#539—861no—
465#536—861no—
466#533—431no—
467#532—431no—
468#529—431no—
469#529—431no—
470#529—431no—
471#529C2×D4311yescharacteristic
472#520—861no—
473C2×C4×Q8—431no—
474#446—861no—
475#446—861no—
476#446—861no—
477#446—861no—
478#432—431no—
479#432—431no—
480#432—431no—
481#432C2×D4311yescharacteristic
482#431—431no—
483#431—431no—
484#391—861no—
485#387—861no—
486#387—861no—
487#383—431no—
488#383—431no—
489#382—431no—
490C4×C4⋊C4—861no—
491C4×C4⋊C4C2×D4311yescharacteristic
492#376—431no—
493#376—431no—
494#328—431no—
495#328—431no—
496#328—431no—
497#328—431no—
498#328—431no—
499#328—431no—
500#328C2×D4311yescharacteristic
501#328C2×D4311yescharacteristic
502#327—431no—
503#327—431no—
504#327—431no—
505#327—431no—
506#327—431no—
507#327—431no—
508#327C2×D4311yescharacteristic
509#327C2×D4311yescharacteristic
510C43#1762411yescharacteristic, complemented, Sylow
511C2×#41—861no—
512C22×Q8—431no—
513C4⋊Q8—431no—
514C4⋊Q8—431no—
515C4⋊Q8—431no—
516C4⋊Q8—861no—
517C4⋊Q8—861no—
518#127—431no—
519#126—21no—
520#126—861no—
521#126—861no—
522#126—861no—
523#126—861no—
524#126—861no—
525#126—861no—
526#126—861no—
527#125—431no—
528#125—431no—
529#125—431no—
530#125—861no—
531#125—861no—
532#125—861no—
533#125—861no—
534#125—861no—
535#125C4×D4311yescharacteristic
536#124—431no—
537#124—431no—
538#124—431no—
539#124—861no—
540#124—861no—
541#124—861no—
542#124C4×D4311yescharacteristic
543#123—21no—
544#123—861no—
545#123—861no—
546#123—861no—
547#123—861no—
548#123—861no—
549#123—861no—
550#123—861no—
551C22⋊Q8—431no—
552C22⋊Q8—861no—
553C22⋊Q8—861no—
554C22⋊Q8—861no—
555C22⋊Q8—861no—
556C22⋊Q8—861no—
557C22⋊Q8—861no—
558C22⋊Q8—861no—
559C22⋊Q8—861no—
560C22⋊Q8—861no—
561C22⋊Q8C22×D4311yescharacteristic
562#121—431no—
563#121—861no—
564#121C22×D4311yescharacteristic
565C4×Q8—431no—
566C4×Q8—431no—
567C4×Q8—431no—
568C4×Q8—431no—
569C4×Q8—431no—
570C4×Q8—431no—
571C4×Q8—431no—
572C4×Q8—431no—
573C4×Q8—431no—
574C4×Q8—431no—
575C4×Q8—431no—
576C4×Q8—431no—
577C4×Q8—431no—
578C4×Q8—861no—
579C4×Q8—861no—
580C4×Q8—861no—
581C4×Q8C4×D4311yescharacteristic
582C4×D4—21no—
583C4×D4—431no—
584C4×D4—431no—
585C4×D4—431no—
586C4×D4—431no—
587C4×D4—431no—
588C4×D4—861no—
589C4×D4—861no—
590C4×D4—861no—
591C4×D4—861no—
592C4×D4—861no—
593C4×D4—861no—
594C4×D4C4×D4311yescharacteristic
595#117—21no—
596#117—861no—
597#117—861no—
598#117—861no—
599#117—861no—
600#117—861no—
601#117—861no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—431no—
604C2×C4⋊C4—431no—
605C2×C4⋊C4—431no—
606C2×C4⋊C4—861no—
607C2×C4⋊C4—861no—
608C2×C4⋊C4—861no—
609C2×C42—21no—
610C2×C42—431no—
611C2×C42—431no—
612C2×C42—861no—
613C2×C42—861no—
614C2×C42C22×D4311yescharacteristic
615C4⋊C8—21no—
616C4⋊C8—861no—
617C4⋊C8—861no—
618C4⋊C8—861no—
619C4⋊C8—861no—
620C4⋊C8—861no—
621C22⋊C8—431no—
622C22⋊C8—431no—
623C22⋊C8C22×D4311yescharacteristic
624C22⋊C8C22×D4311yescharacteristic
625#97—21no—
626#97—861no—
627#97—861no—
628#97—861no—
629C4×C8—861no—
630C4×C8—861no—
631#95—431no—
632#95—431no—
633#95—861no—
634#95—861no—
635#95—861no—
636#95—861no—
637#95—861no—
638#95—861no—
639#95—861no—
640#95C22×D4311yescharacteristic
641#95C22×D4311yescharacteristic
642#41—1722no—
643#41—1722no—
644C2×Q8—431no—
645C2×Q8—431no—
646C2×Q8—431no—
647C2×Q8—431no—
648C2×Q8—431no—
649C2×Q8—861no—
650C2×Q8—861no—
651C2×Q8—1721no—
652C2×Q8—1721no—
653C2×Q8C2×C4×D4311yescharacteristic
654C2×D4—21no—
655C2×D4—431no—
656C2×D4—861no—
657C2×D4—861no—
658C2×D4—861no—
659C2×D4C2×C4×D4311yescharacteristic
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—431no—
664C22×C4—431no—
665C22×C4—431no—
666C22×C4—431no—
667C22×C4—861no—
668C22×C4—861no—
669C22×C4—861no—
670C22×C4—861no—
671C22×C4—861no—
672C22×C4—861no—
673C22×C4—861no—
674C22×C4D4×D4311yescharacteristic
675C22×C4D4×D4311yescharacteristic
676C22×C4C23×D4311yescharacteristic
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—861no—
680C2×C8—861no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—42no—
686C4⋊C4—431no—
687C4⋊C4—431no—
688C4⋊C4—431no—
689C4⋊C4—431no—
690C4⋊C4—431no—
691C4⋊C4—431no—
692C4⋊C4—431no—
693C4⋊C4—431no—
694C4⋊C4—431no—
695C4⋊C4—431no—
696C4⋊C4—431no—
697C4⋊C4—431no—
698C4⋊C4—431no—
699C4⋊C4—431no—
700C4⋊C4—861no—
701C4⋊C4—861no—
702C4⋊C4—861no—
703C4⋊C4—861no—
704C4⋊C4—861no—
705C4⋊C4—861no—
706C4⋊C4—861no—
707C4⋊C4—861no—
708C4⋊C4—861no—
709C4⋊C4—861no—
710C4⋊C4—861no—
711C4⋊C4—861no—
712C4⋊C4—861no—
713C4⋊C4—861no—
714C4⋊C4—861no—
715C4⋊C4—861no—
716C4⋊C4—1722no—
717C4⋊C4C2×C4×D4311yescharacteristic
718C4⋊C4C2×C4×D4311yescharacteristic
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—861no—
725C22⋊C4—861no—
726C22⋊C4—861no—
727C22⋊C4—861no—
728C22⋊C4—861no—
729C22⋊C4—861no—
730C22⋊C4—861no—
731C22⋊C4—861no—
732C22⋊C4—861no—
733C22⋊C4—861no—
734C22⋊C4—861no—
735C22⋊C4—861no—
736C22⋊C4—861no—
737C42—21no—
738C42—42no—
739C42—431no—
740C42—431no—
741C42—431no—
742C42—431no—
743C42—431no—
744C42—431no—
745C42—431no—
746C42—431no—
747C42—861no—
748C42—861no—
749C42—861no—
750C42—861no—
751C42—861no—
752C42—1722no—
753C42—1722no—
754C42C2×C4×D4311yescharacteristic
755C42C2×C4×D4311yescharacteristic
756C42D4×D4311yescharacteristic
757C42D4×D4311yescharacteristic
758C23—21no—
759C23—861no—
760C23C2×D4×D4311yescharacteristic
761Q8—41no—
762Q8—3441no—
763Q8—1721no—
764Q8—1721no—
765Q8—1721no—
766Q8—1721no—
767Q8—1721no—
768Q8—1722no—
769D4—41no—
770D4—41no—
771D4—41no—
772D4—3441no—
773D4—1721no—
774D4—1722no—
775D4—1721no—
776D4—1721no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—81no—
791C2×C4—431no—
792C2×C4—431no—
793C2×C4—431no—
794C2×C4—431no—
795C2×C4—431no—
796C2×C4—431no—
797C2×C4—431no—
798C2×C4—431no—
799C2×C4—861no—
800C2×C4—861no—
801C2×C4—861no—
802C2×C4—861no—
803C2×C4—861no—
804C2×C4—861no—
805C2×C4—861no—
806C2×C4—3441no—
807C2×C4—3441no—
808C2×C4—3441no—
809C2×C4—1722no—
810C2×C4—1721no—
811C2×C4—1721no—
812C2×C4—1722no—
813C2×C4—1721no—
814C2×C4—1721no—
815C2×C4—1721no—
816C2×C4—1721no—
817C2×C4—1721no—
818C2×C4—1721no—
819C2×C4C22⋊C4×D4311yescharacteristic
820C2×C4C22⋊C4×D4311yescharacteristic
821C2×C4C22⋊C4×D4311yescharacteristic
822C2×C4C22⋊C4×D4311yescharacteristic
823C2×C4C22×C4×D4311yescharacteristic
824C2×C4C2×D4×D4311yescharacteristic
825C8—41no—
826C8—41no—
827C8—1721no—
828C8—1721no—
829C22—21no—
830C22—21no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—1721no—
835C22—1721no—
836C22—1721no—
837C22C2×C22⋊C4×D4311yescharacteristic
838C22#1458369511yescharacteristic
839C22#1458369811yescharacteristic
840C4—21no—
841C4—21no—
842C4—21no—
843C4—21no—
844C4—21no—
845C4—21no—
846C4—42no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—81no—
851C4—861no—
852C4—861no—
853C4—861no—
854C4—861no—
855C4—861no—
856C4—861no—
857C4—861no—
858C4—861no—
859C4—3441no—
860C4—3441no—
861C4—1721no—
862C4—1721no—
863C4—1721no—
864C2—21no—
865C2—21no—
866C2—81no—
867C2—3441no—
868C2#1914305711yescharacteristic
869C2#1914311111yescharacteristic
870C2#1914313911yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1509C2
socleC22×C43C22×C22⋊C4
prime radical#14583444C22
cosocleC22×C4×C43C24
hypercenter#1509D43
hypocenterC43#17624
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. #19143679C2semidirect
3. #19137558C2semidirect
4. #19133171C2semidirect
5. #19133169C2semidirect
6. #19133144C2semidirect
8. #19133134C2semidirect
9. #19133133C2semidirect
10. #19133118C2semidirect
11. #19133105C2semidirect
13. #19133080C2semidirect
14. #19133078C2semidirect
15. C43×#1509C2semidirect
16. #14583632C4semidirect
17. #14583631C4semidirect
18. #14583626C4semidirect
19. #14583625C4semidirect
20. #14583621C4semidirect
21. #14583618C4semidirect
24. #14583608C4semidirect
25. #14583605C4semidirect
439. #1509D43semidirect
510. C43#17624semidirect

Maximal subgroups

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

subgroupindex
#191484512
#191436792
#191375582
#191331712
#191331692
#191331442
#191331402
#191331342
#191331332
#191331182
#191331052
#191331012
#191330802
#191330782
C43×#15092
#1762443