Finite Group Databasebeta

← #6574600

Subgroups — #6574600

Order 512.

1969 conjugacy classes of subgroups.

The subgroup lattice has 1324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3387C211yesmaximal, characteristic, complemented
2C2×#2947C211yesmaximal, characteristic
3#35786C211yesmaximal, characteristic, complemented
4#35748C211yesmaximal, characteristic
5#33219C211yesmaximal, characteristic, complemented
6#32968C211yesmaximal, characteristic
7#32964C211yesmaximal, characteristic, complemented
8#28545C211yesmaximal, characteristic, complemented
9#28277C211yesmaximal, characteristic, complemented
10#26486C211yesmaximal, characteristic, complemented
11#26480C211yesmaximal, characteristic, complemented
12#26397C211yesmaximal, characteristic, complemented
13#26395C211yesmaximal, characteristic, complemented
14#26389C211yesmaximal, characteristic, complemented
15#26385C211yesmaximal, characteristic, complemented
16#26077C211yesmaximal, characteristic, complemented
17#26072C211yesmaximal, characteristic, complemented
18#25963C211yesmaximal, characteristic, complemented
19#25961C211yesmaximal, characteristic
20#25955C211yesmaximal, characteristic, complemented
21#25951C211yesmaximal, characteristic
22#24821C211yesmaximal, characteristic, complemented
23#24813C211yesmaximal, characteristic, complemented
24#24334C211yesmaximal, characteristic, complemented
25#24333C211yesmaximal, characteristic, complemented
26C4⋊C4×Q16C211yesmaximal, characteristic, complemented
27#22679C211yesmaximal, characteristic, complemented
28#22679C211yesmaximal, characteristic, complemented
29#22445C211yesmaximal, characteristic
30#22445C211yesmaximal, characteristic
31#21606C211yesmaximal, characteristic, complemented
32C22×#137C2211yescharacteristic
33C2×Q82C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#520C2211yescharacteristic
36C2×#519C2211yescharacteristic
37#3387—28no—
38C2×#501C2211yescharacteristic
39C2×#501C2211yescharacteristic
40C2×#498C2211yescharacteristic
41C2×#479C2211yescharacteristic
42C2×#479C2211yescharacteristic
43C2×#477C2211yescharacteristic
44C2×#477C2211yescharacteristic
45C2×#475C2211yescharacteristic
46C2×#475C2211yescharacteristic
47C2×#475C2211yescharacteristic
48C2×#478C2211yescharacteristic
49C2×#446C2211yescharacteristic
50#2947—28no—
51C2×#441C2211yescharacteristic
52C2×#441C2211yescharacteristic
53C2×#441C2211yescharacteristic
54C2×#441C2211yescharacteristic
55C2×#440C2211yescharacteristic
56C2×#440C2211yescharacteristic
57C2×C4×Q16C2211yescharacteristic
58C2×C4×Q16C2211yescharacteristic
59C2×C4×Q16C2211yescharacteristic
60C2×C4×Q16C2211yescharacteristic
61C2×C4×SD16C2211yescharacteristic
62C2×C4×SD16C2211yescharacteristic
63C2×#428C2211yescharacteristic
64C2×#416C2211yescharacteristic
65C22×#103C2211yescharacteristic
66C2×#405C2211yescharacteristic
67#2629—21no—
68#2629C2211yescharacteristic
69#2628—21no—
70#2628C2211yescharacteristic
71#2582—21no—
72#2582C2211yescharacteristic
73#2580—21no—
74#2580C2211yescharacteristic
75#2565—21no—
76#2565C2211yescharacteristic
77#2542—21no—
78#2542C2211yescharacteristic
79#2453—21no—
80#2453C2211yescharacteristic
81#2452—21no—
82#2452—21no—
83#2452C2211yescharacteristic
84#2452C2211yescharacteristic
85#2451—21no—
86#2451C2211yescharacteristic
87#2441—21no—
88#2441C2211yescharacteristic
89#2440—21no—
90#2440—21no—
91#2440C2211yescharacteristic
92#2440C2211yescharacteristic
93#2439—21no—
94#2439C2211yescharacteristic
95#2396—21no—
96#2396—21no—
97#2396C2211yescharacteristic
98#2351C2211yescharacteristic
99#2351C2211yescharacteristic
100Q8×C4⋊C4C2211yescharacteristic
101Q8×C4⋊C4C2211yescharacteristic
102Q8×C4⋊C4C2211yescharacteristic
103Q8×C4⋊C4C2211yescharacteristic
104#2341C2211yescharacteristic
105#2341C2211yescharacteristic
106Q8×C22⋊C4C2211yescharacteristic
107Q8×C22⋊C4C2211yescharacteristic
108#2096C2211yescharacteristic
109#2095C2211yescharacteristic
110#2093C2211yescharacteristic
111#2092C2211yescharacteristic
112#2085C2211yescharacteristic
113#2084C2211yescharacteristic
114#2084C2211yescharacteristic
115#2083C2211yescharacteristic
116#2068C2211yescharacteristic
117#2068C2211yescharacteristic
118#2067C2211yescharacteristic
119#2066C2211yescharacteristic
120#2066C2211yescharacteristic
121#2065C2211yescharacteristic
122#2065C2211yescharacteristic
123#2065C2211yescharacteristic
124#2059C2211yescharacteristic
125#2058C2211yescharacteristic
126#2057C2211yescharacteristic
127#2057C2211yescharacteristic
128#2025C2211yescharacteristic
129#2024C2211yescharacteristic
130#2024C2211yescharacteristic
131#2023C2211yescharacteristic
132#1991C2211yescharacteristic
133#1990C2211yescharacteristic
134#1984C2211yescharacteristic
135#1973C2211yescharacteristic
136#1973C2211yescharacteristic
137#1968C2211yescharacteristic
138#1968C2211yescharacteristic
139#1944C2211yescharacteristic
140#1944C2211yescharacteristic
141#1944C2211yescharacteristic
142#1943C2211yescharacteristic
143#1942C2211yescharacteristic
144#1942C2211yescharacteristic
145#1941C2211yescharacteristic
146#1941C2211yescharacteristic
147#1939C2211yescharacteristic
148#1917C2211yescharacteristic
149#1917C2211yescharacteristic
150#1880C2211yescharacteristic
151#1880C2211yescharacteristic
152#1880C2211yescharacteristic
153#1880C2211yescharacteristic
154#1878C2211yescharacteristic
155#1878C2211yescharacteristic
156#1878C2211yescharacteristic
157#1878C2211yescharacteristic
158#1865C2211yescharacteristic
159#1865C2211yescharacteristic
160#1865C2211yescharacteristic
161#1865C2211yescharacteristic
162#1865C2211yescharacteristic
163#1865C2211yescharacteristic
164#1864C2211yescharacteristic
165#1863C2211yescharacteristic
166#1863C2211yescharacteristic
167#1863C2211yescharacteristic
168#1863C2211yescharacteristic
169#1863C2211yescharacteristic
170#1863C2211yescharacteristic
171#1863C2211yescharacteristic
172#1863C2211yescharacteristic
173#1862C2211yescharacteristic
174#1854C2211yescharacteristic
175#1854C2211yescharacteristic
176#1853C2211yescharacteristic
177#1852C2211yescharacteristic
178#1850C2211yescharacteristic
179#1850C2211yescharacteristic
180#1847C2211yescharacteristic
181#1847C2211yescharacteristic
182#1845C2211yescharacteristic
183#1809C2211yescharacteristic
184#1809C2211yescharacteristic
185#1808C2211yescharacteristic
186#1807C2211yescharacteristic
187#1805C2211yescharacteristic
188#1805C2211yescharacteristic
189#1805C2211yescharacteristic
190#1803C2211yescharacteristic
191#1803C2211yescharacteristic
192#1803C2211yescharacteristic
193#1803C2211yescharacteristic
194#1802C2211yescharacteristic
195#1798C2211yescharacteristic
196#1788C2211yescharacteristic
197#1788C2211yescharacteristic
198#1787C2211yescharacteristic
199#1787C2211yescharacteristic
200#1771C2211yescharacteristic
201#1771C2211yescharacteristic
202C8×C4⋊C4C2211yescharacteristic
203#1753C2211yescharacteristic
204#1753C2211yescharacteristic
205C22×#41C2311yescharacteristic
206C23×Q8C2311yescharacteristic
207C2×#137—24no—
208C2×#137—24no—
209C2×#137Q818yescomplemented
210C22×Q16C2311yescharacteristic
211C22×Q16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×M16C2311yescharacteristic
215C23×C8C2311yescharacteristic
216Q82—24no—
217Q82—42no—
218#557—24no—
219#557—42no—
220C2×C4⋊Q8—21no—
221C2×C4⋊Q8—21no—
222C2×C4⋊Q8—21no—
223C2×C4⋊Q8—21no—
224C2×C4⋊Q8C2311yescharacteristic
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2311yescharacteristic
227C2×C4⋊Q8C2311yescharacteristic
228C2×#125—21no—
229C2×#125—21no—
230C2×#125C2311yescharacteristic
231C2×#125C2311yescharacteristic
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8—21no—
237C2×C22⋊Q8—21no—
238#520—24no—
239#520—42no—
240#519—24no—
241#519—42no—
242C2×C4×Q8—21no—
243C2×C4×Q8—21no—
244C2×C4×Q8—21no—
245C2×C4×Q8—21no—
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2311yescharacteristic
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2311yescharacteristic
259C2×C4×Q8C2311yescharacteristic
260C2×C4×Q8C2311yescharacteristic
261C2×C4×D4—21no—
262C2×C4×D4—21no—
263C2×C4×D4C2311yescharacteristic
264C2×C4×D4C2311yescharacteristic
265C2×#117—21no—
266C2×#117—21no—
267C2×#117—21no—
268C2×#117C2311yescharacteristic
269C2×#117C2311yescharacteristic
270C22×C4⋊C4—21no—
271C22×C4⋊C4C2311yescharacteristic
272#501—24no—
273#501—24no—
274#498—24no—
275#479—24no—
276#479—24no—
277#478—42no—
278#477—24no—
279#477—42no—
280#475—24no—
281#475—24no—
282#475—24no—
283#446—24no—
284#441—24no—
285#441—24no—
286#441—24no—
287#441D418yes—
288#440—24no—
289#440—24no—
290C4×Q16—24no—
291C4×Q16—24no—
292C4×Q16—24no—
293C4×Q16—24no—
294C4×SD16—24no—
295C4×SD16—24no—
296#428—24no—
297C2×#107C2311yescharacteristic
298C2×#107C2311yescharacteristic
299C2×#107C2311yescharacteristic
300C2×#107C2311yescharacteristic
301C2×#107C2311yescharacteristic
302C2×#107C2311yescharacteristic
303C2×#107C2311yescharacteristic
304C2×#107C2311yescharacteristic
305C2×#107C2311yescharacteristic
306C2×#107C2311yescharacteristic
307C2×#106C2311yescharacteristic
308C2×#106C2311yescharacteristic
309C2×#106C2311yescharacteristic
310C2×#106C2311yescharacteristic
311C2×#106C2311yescharacteristic
312C2×#106C2311yescharacteristic
313C2×#106C2311yescharacteristic
314C2×#106C2311yescharacteristic
315C2×#106C2311yescharacteristic
316C2×#106C2311yescharacteristic
317C2×C4⋊C8C2311yescharacteristic
318C2×C4⋊C8C2311yescharacteristic
319C2×C4⋊C8C2311yescharacteristic
320C2×C4⋊C8C2311yescharacteristic
321C2×C4⋊C8C2311yescharacteristic
322C2×C4⋊C8C2311yescharacteristic
323#416—24no—
324C2×#103—24no—
325C2×#103C2311yescharacteristic
326C2×#103C2311yescharacteristic
327C2×#103C2311yescharacteristic
328C2×#103C2311yescharacteristic
329C2×#103C2311yescharacteristic
330C2×#103C2311yescharacteristic
331C2×#103C2311yescharacteristic
332C2×#103C2311yescharacteristic
333C2×#103C2311yescharacteristic
334C2×#103C2311yescharacteristic
335C2×#103C2311yescharacteristic
336C2×#103C2311yescharacteristic
337C2×#103C2311yescharacteristic
338C2×#103C2311yescharacteristic
339C2×#103C2311yescharacteristic
340C2×#103C2311yescharacteristic
341C2×#103C2311yescharacteristic
342C2×#103C2311yescharacteristic
343C2×#102C2311yescharacteristic
344C2×#102C2311yescharacteristic
345C2×#102C2311yescharacteristic
346C2×#102C2311yescharacteristic
347C2×#102C2311yescharacteristic
348C2×#102C2311yescharacteristic
349C2×C22⋊C8C2311yescharacteristic
350C2×C22⋊C8C2311yescharacteristic
351#405—24no—
352C2×#97C2311yescharacteristic
353C2×#97C2311yescharacteristic
354C2×#97C2311yescharacteristic
355C2×#97C2311yescharacteristic
356C2×C4×C8C2311yescharacteristic
357C2×C4×C8C2311yescharacteristic
358C2×C4×C8C2311yescharacteristic
359C2×C4×C8C2311yescharacteristic
360#400—21no—
361#400—21no—
362#400D411yescharacteristic
363#399—21no—
364#399—21no—
365#399—21no—
366#399—21no—
367#399—21no—
368#399D411yescharacteristic
369#398—21no—
370#398—21no—
371#398—21no—
372#398—21no—
373#398—21no—
374#398—21no—
375#398—21no—
376#398—21no—
377#398—21no—
378#398—21no—
379#398D411yescharacteristic
380#398D411yescharacteristic
381#396—21no—
382#396—21no—
383#396—21no—
384#396—21no—
385#396—21no—
386#396—21no—
387#396D411yescharacteristic
388#396D411yescharacteristic
389#395—21no—
390#395—21no—
391#395—21no—
392#395—21no—
393#395D411yescharacteristic
394#393—21no—
395#393—21no—
396#393—21no—
397#393—21no—
398#393—21no—
399#393D411yescharacteristic
400#391—21no—
401#391—21no—
402#391—21no—
403#391—21no—
404#391—21no—
405#391—21no—
406#391—21no—
407#391C2311yescharacteristic
408#391C2311yescharacteristic
409#391C2311yescharacteristic
410#391C2311yescharacteristic
411#390—21no—
412#390—21no—
413#390—21no—
414#390—21no—
415#390C2311yescharacteristic
416#390C2311yescharacteristic
417#390C2311yescharacteristic
418#390C2311yescharacteristic
419#389—21no—
420#389—21no—
421#389—21no—
422#389—21no—
423#389—21no—
424#389—21no—
425#389—21no—
426#389—21no—
427#389—21no—
428#389—21no—
429#389—21no—
430#389—21no—
431#389—21no—
432#389—21no—
433#389—21no—
434#389C2311yescharacteristic
435#389C2311yescharacteristic
436#389C2311yescharacteristic
437#389C2311yescharacteristic
438#389C2311yescharacteristic
439#389C2311yescharacteristic
440#389C2311yescharacteristic
441#389C2311yescharacteristic
442#389C2311yescharacteristic
443#389C2311yescharacteristic
444#389C2311yescharacteristic
445#389C2311yescharacteristic
446#387—21no—
447#387—21no—
448#387—21no—
449#387—21no—
450#387—21no—
451#387—21no—
452#385—21no—
453#385—21no—
454#385—21no—
455#385—21no—
456#385—21no—
457#385—21no—
458#384—21no—
459#384—21no—
460#384—21no—
461#384—21no—
462#384C2311yescharacteristic
463#384C2311yescharacteristic
464#384C2311yescharacteristic
465#384C2311yescharacteristic
466#382—21no—
467#382—21no—
468#382C2311yescharacteristic
469#382C2311yescharacteristic
470#380—21no—
471#380—21no—
472#380—21no—
473#380—21no—
474#380C2311yescharacteristic
475#380C2311yescharacteristic
476#380C2311yescharacteristic
477#380C2311yescharacteristic
478C4×C4⋊C4—21no—
479C4×C4⋊C4—21no—
480C4×C4⋊C4—21no—
481C4×C4⋊C4—21no—
482C4×C4⋊C4—21no—
483C4×C4⋊C4—21no—
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2311yescharacteristic
487C4×C22⋊C4—21no—
488C4×C22⋊C4—21no—
489C4×C22⋊C4—21no—
490C4×C22⋊C4—21no—
491C4×C22⋊C4C2311yescharacteristic
492C4×C22⋊C4C2311yescharacteristic
493#340C2311yescharacteristic
494#340C2311yescharacteristic
495#340C2311yescharacteristic
496#340C2311yescharacteristic
497#340C2311yescharacteristic
498#340C2311yescharacteristic
499#340C2311yescharacteristic
500#340C2311yescharacteristic
501#340C2311yescharacteristic
502#340C2311yescharacteristic
503#340C2311yescharacteristic
504#340C2311yescharacteristic
505#340C2311yescharacteristic
506#340C2311yescharacteristic
507#340C2311yescharacteristic
508#340C2311yescharacteristic
509#336C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515#336C2311yescharacteristic
516#336C2311yescharacteristic
517#336C2311yescharacteristic
518#336C2311yescharacteristic
519C2×#41—22no—
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—41no—
523C2×#41—41no—
524C2×#41C2×Q814yes—
525C22×Q8—21no—
526C22×Q8—21no—
527C22×Q8—21no—
528C22×Q8—21no—
529C22×Q8—21no—
530C22×Q8—22no—
531C22×Q8—22no—
532C22×Q8—22no—
533C22×Q8—41no—
534C22×Q8—41no—
535C22×Q8C2×D411yescharacteristic
536C22×Q8C2×Q814yes—
537C22×Q8C2411yescharacteristic
538C22×Q8C2411yescharacteristic
539C22×Q8C2411yescharacteristic
540C22×D4—21no—
541C22×D4C2411yescharacteristic
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—21no—
546C23×C4—21no—
547C23×C4C2411yescharacteristic
548#137—232no—
549C2×Q16—22no—
550C2×Q16—22no—
551C2×Q16C2×D414yes—
552C2×Q16C2×Q814yes—
553C2×Q16C2×Q814yes—
554C2×Q16#4114yes—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16C2×Q814yes—
560C2×SD16C2×Q814yes—
561C2×M16—22no—
562C2×M16—22no—
563C2×M16C2×Q814yes—
564C22×C8—22no—
565C22×C8—22no—
566C22×C8—41no—
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C4⋊Q8—22no—
576C4⋊Q8—22no—
577C4⋊Q8—22no—
578C4⋊Q8—22no—
579C4⋊Q8—22no—
580C4⋊Q8—41no—
581C4⋊Q8—41no—
582C4⋊Q8—41no—
583C4⋊Q8—44no—
584C4⋊Q8—44no—
585C4⋊Q8—44no—
586C4⋊Q8—44no—
587#125—22no—
588#125—22no—
589#125—22no—
590#125—41no—
591#125—44no—
592#125—44no—
593C22⋊Q8—82no—
594C22⋊Q8—82no—
595C22⋊Q8—82no—
596C22⋊Q8—82no—
597C22⋊Q8—82no—
598C22⋊Q8—82no—
599C4×Q8—22no—
600C4×Q8—22no—
601C4×Q8—22no—
602C4×Q8—22no—
603C4×Q8—22no—
604C4×Q8—22no—
605C4×Q8—22no—
606C4×Q8—22no—
607C4×Q8—22no—
608C4×Q8—22no—
609C4×Q8—22no—
610C4×Q8—22no—
611C4×Q8—22no—
612C4×Q8—22no—
613C4×Q8—22no—
614C4×Q8—22no—
615C4×Q8—22no—
616C4×Q8—41no—
617C4×Q8—41no—
618C4×Q8—41no—
619C4×Q8—41no—
620C4×Q8—41no—
621C4×Q8—41no—
622C4×Q8—41no—
623C4×Q8—41no—
624C4×Q8—41no—
625C4×Q8—41no—
626C4×Q8—41no—
627C4×Q8—44no—
628C4×Q8—44no—
629C4×Q8—44no—
630C4×Q8—44no—
631C4×Q8C2×D414yes—
632C4×Q8C2×D414yes—
633C4×D4—22no—
634C4×D4—22no—
635C4×D4—22no—
636C4×D4—44no—
637C4×D4—41no—
638C4×D4—44no—
639#117—22no—
640#117—22no—
641#117—22no—
642#117—44no—
643#117—44no—
644#117—44no—
645#117—41no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—22no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—21no—
679C2×C4⋊C4—21no—
680C2×C4⋊C4—21no—
681C2×C4⋊C4—21no—
682C2×C4⋊C4—21no—
683C2×C4⋊C4—21no—
684C2×C4⋊C4—21no—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—21no—
688C2×C4⋊C4—21no—
689C2×C4⋊C4—21no—
690C2×C4⋊C4—41no—
691C2×C4⋊C4—44no—
692C2×C4⋊C4C2×D411yescharacteristic
693C2×C4⋊C4C2×D411yescharacteristic
694C2×C4⋊C4C2×D411yescharacteristic
695C2×C4⋊C4C2×D411yescharacteristic
696C2×C4⋊C4C2×D411yescharacteristic
697C2×C4⋊C4C2×D411yescharacteristic
698C2×C4⋊C4C2×D411yescharacteristic
699C2×C4⋊C4C2×D411yescharacteristic
700C2×C4⋊C4C2×D411yescharacteristic
701C2×C4⋊C4C2×D411yescharacteristic
702C2×C4⋊C4C2×D411yescharacteristic
703C2×C4⋊C4C2411yescharacteristic
704C2×C4⋊C4C2411yescharacteristic
705C2×C4⋊C4C2411yescharacteristic
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2411yescharacteristic
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4C2×D411yescharacteristic
731C2×C22⋊C4C2×D411yescharacteristic
732C2×C22⋊C4C2×D411yescharacteristic
733C2×C22⋊C4C2×D411yescharacteristic
734C2×C22⋊C4C2×D411yescharacteristic
735C2×C22⋊C4C2×D411yescharacteristic
736C2×C42—21no—
737C2×C42—21no—
738C2×C42—21no—
739C2×C42—21no—
740C2×C42—21no—
741C2×C42—21no—
742C2×C42—21no—
743C2×C42—21no—
744C2×C42—21no—
745C2×C42—21no—
746C2×C42—21no—
747C2×C42—21no—
748C2×C42—21no—
749C2×C42—21no—
750C2×C42—21no—
751C2×C42C2411yescharacteristic
752C2×C42C2411yescharacteristic
753C2×C42C2411yescharacteristic
754C2×C42C2411yescharacteristic
755C2×C42C2411yescharacteristic
756C2×C42C2411yescharacteristic
757#107—22no—
758#107—22no—
759#107—22no—
760#107—22no—
761#107—22no—
762#107—22no—
763#107—41no—
764#107—41no—
765#107—41no—
766#107—41no—
767#106—22no—
768#106—22no—
769#106—22no—
770#106—22no—
771#106—22no—
772#106—22no—
773#106—22no—
774#106—41no—
775#106—41no—
776#106C2×D414yes—
777C4⋊C8—22no—
778C4⋊C8—22no—
779C4⋊C8—22no—
780C4⋊C8—22no—
781C4⋊C8—41no—
782C4⋊C8—41no—
783#103—22no—
784#103—22no—
785#103—22no—
786#103—22no—
787#103—22no—
788#103—22no—
789#103—22no—
790#103—22no—
791#103—22no—
792#103—22no—
793#103—22no—
794#103—22no—
795#103—41no—
796#103—41no—
797#103—41no—
798#103—41no—
799#103C2×D414yes—
800#103C2×D414yes—
801#102—22no—
802#102—22no—
803#102—41no—
804#102—41no—
805#102—41no—
806#102—41no—
807C22⋊C8—22no—
808C22⋊C8—22no—
809#97—22no—
810#97—22no—
811#97—22no—
812#97C2×D414yes—
813C4×C8—22no—
814C4×C8—22no—
815C4×C8—22no—
816C4×C8—22no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95—21no—
834#95—21no—
835#95—21no—
836#95—21no—
837#95—21no—
838#95—21no—
839#95—21no—
840#95—21no—
841#95—21no—
842#95—21no—
843#95—21no—
844#95—21no—
845#95C2×D411yescharacteristic
846#95C2×D411yescharacteristic
847#95C2×D411yescharacteristic
848#95C2×D411yescharacteristic
849#95C2×D411yescharacteristic
850#95C2×D411yescharacteristic
851#95C2×D411yescharacteristic
852#95C2×D411yescharacteristic
853#95C2×D411yescharacteristic
854#95C2×D411yescharacteristic
855C24—21no—
856C24C22×D411yescharacteristic
857#41—28no—
858#41—44no—
859#41—44no—
860#41—44no—
861C2×Q8—22no—
862C2×Q8—24no—
863C2×Q8—22no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—28no—
872C2×Q8—21no—
873C2×Q8—21no—
874C2×Q8—21no—
875C2×Q8—21no—
876C2×Q8—41no—
877C2×Q8—42no—
878C2×Q8—42no—
879C2×Q8—42no—
880C2×Q8—42no—
881C2×Q8—42no—
882C2×Q8—44no—
883C2×Q8—44no—
884C2×Q8—44no—
885C2×Q8—42no—
886C2×Q8—42no—
887C2×Q8—81no—
888C2×Q8—81no—
889C2×Q8—81no—
890C2×Q8—81no—
891C2×Q8—81no—
892C2×Q8—81no—
893C2×Q8—81no—
894C2×Q8C22×D412yes—
895C2×Q8C22×D412yes—
896C2×Q8C22×Q812yes—
897C2×Q8C22×Q812yes—
898C2×Q8C22×Q812yes—
899C2×Q8C2×#4112yes—
900C2×Q8C2×#4112yes—
901C2×D4—24no—
902C2×D4—21no—
903C2×D4—21no—
904C2×D4—21no—
905C2×D4—21no—
906C2×D4—21no—
907C2×D4—42no—
908C2×D4—42no—
909C2×D4C22×Q812yes—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—24no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—24no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×Q812yes—
958C22×C42−1+412yes—
959C22×C4C2511yescharacteristic
960Q16—28no—
961Q16C22⋊Q8116yescomplemented
962SD16—28no—
963SD16—28no—
964M16—28no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—44no—
985C2×C8C22×D412yes—
986C2×C8C22×D412yes—
987C2×C8C22×Q812yes—
988C2×C8C22×Q812yes—
989C2×C8C2×#4112yes—
990C4⋊C4—24no—
991C4⋊C4—24no—
992C4⋊C4—22no—
993C4⋊C4—22no—
994C4⋊C4—22no—
995C4⋊C4—22no—
996C4⋊C4—22no—
997C4⋊C4—22no—
998C4⋊C4—22no—
999C4⋊C4—22no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—41no—
1023C4⋊C4—41no—
1024C4⋊C4—41no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—81no—
1052C4⋊C4—81no—
1053C4⋊C4—81no—
1054C4⋊C4—81no—
1055C4⋊C4—81no—
1056C4⋊C4—81no—
1057C4⋊C4—81no—
1058C4⋊C4—81no—
1059C4⋊C4—81no—
1060C4⋊C4—81no—
1061C4⋊C4—81no—
1062C4⋊C4—81no—
1063C4⋊C4—81no—
1064C4⋊C4—81no—
1065C4⋊C4—81no—
1066C4⋊C4C22×D412yes—
1067C4⋊C4C22×D412yes—
1068C22⋊C4—22no—
1069C22⋊C4—22no—
1070C22⋊C4—22no—
1071C22⋊C4—22no—
1072C22⋊C4—41no—
1073C22⋊C4—41no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C42—24no—
1090C42—24no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—42no—
1102C42—42no—
1103C42—42no—
1104C42—42no—
1105C42—42no—
1106C42—42no—
1107C42—42no—
1108C42—42no—
1109C42—42no—
1110C42—42no—
1111C42—42no—
1112C42—42no—
1113C42—42no—
1114C42C22×D412yes—
1115C42H(5,𝔽2)12yes—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—22no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23D4×Q812yes—
1130C23C23×D411yescharacteristic
1131Q8—22no—
1132Q8—22no—
1133Q8—22no—
1134Q8—22no—
1135Q8—22no—
1136Q8—22no—
1137Q8—22no—
1138Q8—22no—
1139Q8—44no—
1140Q8—48no—
1141Q8—41no—
1142Q8—41no—
1143Q8—84no—
1144Q8—162no—
1145Q8—162no—
1146Q8—162no—
1147Q8C2×C22⋊Q814yes—
1148Q8C2×C22⋊Q814yes—
1149D4—22no—
1150D4—22no—
1151D4—48no—
1152D4—41no—
1153D4—41no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—21no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—21no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—22no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—22no—
1189C2×C4—21no—
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—48no—
1202C2×C4—48no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—162no—
1240C2×C4—162no—
1241C2×C4—162no—
1242C2×C4D4212yes—
1243C2×C4D4212yes—
1244C2×C4D4×Q812yes—
1245C2×C4#57712yes—
1246C2×C4#57812yes—
1247C2×C4C23×D411yescharacteristic
1248C2×C4C23×Q811yescharacteristic
1249C2×C4C22×#4111yescharacteristic
1250C2×C4C2×H(5,𝔽2)11yescharacteristic
1251C2×C4C2×2−1+411yescharacteristic
1252C2×C4#58511yescharacteristic
1253C8—22no—
1254C8—22no—
1255C8—41no—
1256C8—41no—
1257C8—41no—
1258C8—41no—
1259C8—41no—
1260C8C2×C22⋊Q814yes—
1261C22—22no—
1262C22—22no—
1263C22—22no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—41no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22C2×D4211yescharacteristic
1276C22C2×D4×Q811yescharacteristic
1277C22D4×#4111yescharacteristic
1278C22C2×#57711yescharacteristic
1279C22C2×#57811yescharacteristic
1280C22#358511yescharacteristic
1281C22#358611yescharacteristic
1282C4—22no—
1283C4—22no—
1284C4—22no—
1285C4—22no—
1286C4—22no—
1287C4—24no—
1288C4—24no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—42no—
1295C4—41no—
1296C4—41no—
1297C4—41no—
1298C4—42no—
1299C4—42no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4C22×C22⋊Q811yescharacteristic
1311C4#348911yescharacteristic
1312C4#350111yescharacteristic
1313C4#352011yescharacteristic
1314C2—42no—
1315C2—82no—
1316C2D4×C22⋊Q811yescharacteristic
1317C2#6107611yescharacteristic
1318C2#6109511yescharacteristic
1319C2#6138311yescharacteristic
1320C2#6138411yescharacteristic
1321C2#6149911yescharacteristic
1322C2#6151611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#41C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3387C2semidirect
3. #35786C2semidirect
5. #33219C2semidirect
7. #32964C2semidirect
8. #28545C2semidirect
9. #28277C2semidirect
10. #26486C2semidirect
11. #26480C2semidirect
12. #26397C2semidirect
13. #26395C2semidirect
14. #26389C2semidirect
15. #26385C2semidirect
16. #26077C2semidirect
17. #26072C2semidirect
18. #25963C2semidirect
20. #25955C2semidirect
22. #24821C2semidirect
23. #24813C2semidirect
24. #24334C2semidirect
25. #24333C2semidirect
26. C4⋊C4×Q16C2semidirect
27. #22679C2semidirect
28. #22679C2semidirect
31. #21606C2semidirect
209. C2×#137Q8semidirect
961. Q16C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#33872
C2×#29472
#357862
#357482
#332192
#329682
#329642
#285452
#282772
#264862
#264802
#263972
#263952
#263892
#263852
#260772
#260722
#259632
#259612
#259552
#259512
#248212
#248132
#243342
#243332
C4⋊C4×Q162
#226792
#224452
#216062