Finite Group Databasebeta

← #7336236

Subgroups — #7336236

Order 512.

1624 conjugacy classes of subgroups.

The subgroup lattice has 1364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59094C211yesmaximal, characteristic
2#45525C211yesmaximal, characteristic, complemented
3#32053C211yesmaximal, characteristic, complemented
4#31584C211yesmaximal, characteristic, complemented
5#31519C211yesmaximal, characteristic, complemented
6#31211C211yesmaximal, characteristic, complemented
7#31195C211yesmaximal, characteristic, complemented
8#30996C211yesmaximal, characteristic, complemented
9#30881C211yesmaximal, characteristic, complemented
10#30854C211yesmaximal, characteristic, complemented
11#30644C211yesmaximal, characteristic, complemented
12#30569C211yesmaximal, characteristic, complemented
13#30531C211yesmaximal, characteristic, complemented
14#30520C211yesmaximal, characteristic, complemented
15#29950C211yesmaximal, characteristic, complemented
16#29664C211yesmaximal, characteristic, complemented
17#28407C211yesmaximal, characteristic, complemented
18#28338C211yesmaximal, characteristic, complemented
19#28302C211yesmaximal, characteristic, complemented
20#27787C211yesmaximal, characteristic, complemented
21#26789C211yesmaximal, characteristic, complemented
22#26595C211yesmaximal, characteristic, complemented
23#26558C211yesmaximal, characteristic, complemented
24#26534C211yesmaximal, characteristic, complemented
25#26480C211yesmaximal, characteristic, complemented
26#25953C211yesmaximal, characteristic, complemented
27#25672C211yesmaximal, characteristic, complemented
28#25151C211yesmaximal, characteristic, complemented
29#24436C211yesmaximal, characteristic
30#24247C211yesmaximal, characteristic
31#22357C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#533C2211yescharacteristic
34C2×#498C2211yescharacteristic, complemented
35C2×#488C2211yescharacteristic
36C2×#487C2211yescharacteristic, complemented
37C2×#485C2211yescharacteristic, complemented
38C2×#483C2211yescharacteristic
39C2×#483C2211yescharacteristic
40C2×#479C2211yescharacteristic, complemented
41C2×#467C2211yescharacteristic, complemented
42C2×#465C2211yescharacteristic
43C2×#464C2211yescharacteristic
44C2×#464C2211yescharacteristic
45C2×#462C2211yescharacteristic, complemented
46C2×#462C2211yescharacteristic, complemented
47C2×#452C2211yescharacteristic
48C2×#452C2211yescharacteristic
49C2×#450C2211yescharacteristic
50C2×#450C2211yescharacteristic
51C2×C4×Q16C2211yescharacteristic, complemented
52C2×C4×SD16C2211yescharacteristic
53C2×#416C2211yescharacteristic
54#2857C2211yescharacteristic
55#2857C2211yescharacteristic
56#2814—21no—
57#2802—21no—
58#2798—21no—
59#2783—21no—
60#2755—21no—
61#2747—21no—
62#2741—21no—
63#2711—21no—
64#2707—21no—
65#2570C2211yescharacteristic, complemented
66#2565C2211yescharacteristic, complemented
67#2545C2211yescharacteristic
68#2536C2211yescharacteristic
69#2499C2211yescharacteristic, complemented
70#2492C2211yescharacteristic, complemented
71#2491C2211yescharacteristic
72#2489C2211yescharacteristic
73#2472—21no—
74#2458—21no—
75#2452C2211yescharacteristic
76#2451C2211yescharacteristic, complemented
77#2448C2211yescharacteristic
78#2446C2211yescharacteristic, complemented
79#2441C2211yescharacteristic, complemented
80#2437—21no—
81#2435C2211yescharacteristic
82#2432C2211yescharacteristic
83#2429C2211yescharacteristic, complemented
84#2426—21no—
85#2426C2211yescharacteristic
86#2421C2211yescharacteristic
87#2417C2211yescharacteristic
88#2415C2211yescharacteristic
89#2411—21no—
90#2378—21no—
91#2367C2211yescharacteristic
92#2360C2211yescharacteristic
93#2342—21no—
94#2341C2211yescharacteristic
95C4×#123C2211yescharacteristic
96C2×#390C2211yescharacteristic
97#2097C2211yescharacteristic, complemented
98#2097C2211yescharacteristic, complemented
99#2094C2211yescharacteristic
100#2094C2211yescharacteristic
101#2093C2211yescharacteristic
102#2093C2211yescharacteristic
103#2085C2211yescharacteristic, complemented
104#2073C2211yescharacteristic
105#2068C2211yescharacteristic, complemented
106#2067C2211yescharacteristic
107#2067C2211yescharacteristic
108#2067C2211yescharacteristic
109#2067C2211yescharacteristic
110#2066C2211yescharacteristic, complemented
111#2066C2211yescharacteristic, complemented
112#2065C2211yescharacteristic
113#2059C2211yescharacteristic, complemented
114#2056C2211yescharacteristic, complemented
115#2055C2211yescharacteristic
116#2042C2211yescharacteristic
117#2042C2211yescharacteristic
118#2036C2211yescharacteristic, complemented
119#2035C2211yescharacteristic
120#2035C2211yescharacteristic
121#2035C2211yescharacteristic
122#2035C2211yescharacteristic
123#2035C2211yescharacteristic, complemented
124#2035C2211yescharacteristic, complemented
125#2034C2211yescharacteristic
126#2025C2211yescharacteristic
127#2024C2211yescharacteristic, complemented
128#2024C2211yescharacteristic, complemented
129#2023C2211yescharacteristic
130#2023C2211yescharacteristic
131#2016C2211yescharacteristic, complemented
132#2016C2211yescharacteristic, complemented
133#2015C2211yescharacteristic
134#2015C2211yescharacteristic
135#2015C2211yescharacteristic
136#2015C2211yescharacteristic
137#2013C2211yescharacteristic
138#2013C2211yescharacteristic
139#2001C2211yescharacteristic
140#2001C2211yescharacteristic
141#2001C2211yescharacteristic
142#2001C2211yescharacteristic
143#2001C2211yescharacteristic, complemented
144#2000C2211yescharacteristic
145#1990C2211yescharacteristic, complemented
146#1983C2211yescharacteristic
147#1969C2211yescharacteristic, complemented
148#1969C2211yescharacteristic, complemented
149#1968C2211yescharacteristic
150#1968C2211yescharacteristic
151#1968C2211yescharacteristic
152#1968C2211yescharacteristic
153#1968C2211yescharacteristic
154#1968C2211yescharacteristic
155#1958C2211yescharacteristic
156#1958C2211yescharacteristic
157#1956C2211yescharacteristic, complemented
158#1954C2211yescharacteristic
159#1949C2211yescharacteristic, complemented
160#1941C2211yescharacteristic, complemented
161#1941C2211yescharacteristic, complemented
162#1939C2211yescharacteristic, complemented
163#1928C2211yescharacteristic, complemented
164#1927C2211yescharacteristic, complemented
165#1927C2211yescharacteristic, complemented
166#1926C2211yescharacteristic
167#1923C2211yescharacteristic
168#1923C2211yescharacteristic
169#1923C2211yescharacteristic, complemented
170#1923C2211yescharacteristic, complemented
171#1916C2211yescharacteristic, complemented
172#1916C2211yescharacteristic, complemented
173#1880C2211yescharacteristic
174#1878C2211yescharacteristic, complemented
175#1878C2211yescharacteristic, complemented
176#1877C2211yescharacteristic
177#1875C2211yescharacteristic
178#1869C2211yescharacteristic
179#1865C2211yescharacteristic, complemented
180#1865C2211yescharacteristic, complemented
181#1865C2211yescharacteristic, complemented
182#1865C2211yescharacteristic, complemented
183#1865C2211yescharacteristic, complemented
184#1865C2211yescharacteristic, complemented
185#1864C2211yescharacteristic
186#1863C2211yescharacteristic, complemented
187#1854C2211yescharacteristic, complemented
188#1852C2211yescharacteristic
189#1852C2211yescharacteristic
190#1850C2211yescharacteristic, complemented
191#1807C2211yescharacteristic, complemented
192#1804C2211yescharacteristic
193#1803C2211yescharacteristic, complemented
194#1803C2211yescharacteristic, complemented
195#1797C2211yescharacteristic
196#1788C2211yescharacteristic
197#1786C2211yescharacteristic
198#1786C2211yescharacteristic
199C4×#106C2211yescharacteristic, complemented
200C8×C4⋊C4C2211yescharacteristic, complemented
201C8×C22⋊C4C2211yescharacteristic, complemented
202C4×C22⋊C8C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C23×C8C2311yescharacteristic
214#546—42no—
215#546—42no—
216#533—42no—
217#533—42no—
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222C2×#125—21no—
223C2×#125C2311yescharacteristic
224C2×#124—21no—
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×#123—21no—
229C2×#123D411yescharacteristic
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×C22⋊Q8C2311yescharacteristic
239C2×C22⋊Q8C2311yescharacteristic
240C2×#121—21no—
241C2×#121C2311yescharacteristic
242C2×#120—21no—
243C2×C4×Q8—21no—
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×#117—21no—
252C2×#117C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C22⋊C4—21no—
255C22×C22⋊C4—21no—
256C22×C22⋊C4—21no—
257C22×C42C2311yescharacteristic
258#498—42no—
259#488—42no—
260#487—42no—
261#485—42no—
262#483—42no—
263#483—42no—
264#479—42no—
265#467—42no—
266#465—42no—
267#464—42no—
268#464—42no—
269#462—42no—
270#462—42no—
271#452—42no—
272#452—42no—
273#450—42no—
274#450—42no—
275C4×Q16—42no—
276C4×SD16—42no—
277C2×#107C2311yescharacteristic
278C2×#107C2311yescharacteristic
279C2×#107C2311yescharacteristic
280C2×#107C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×#106C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×#106C2311yescharacteristic
287C2×#106C2311yescharacteristic
288C2×#106C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291C2×C4⋊C8C2311yescharacteristic
292C2×C4⋊C8C2311yescharacteristic
293C2×C4⋊C8C2311yescharacteristic
294#416—42no—
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#103C2311yescharacteristic
312C2×#103C2311yescharacteristic
313C2×#103C2311yescharacteristic
314C2×#103C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×#102C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×C22⋊C8C2311yescharacteristic
333C2×C22⋊C8C2311yescharacteristic
334C2×C4×C8C2311yescharacteristic
335C2×C4×C8C2311yescharacteristic
336C2×C4×C8C2311yescharacteristic
337C2×C4×C8C2311yescharacteristic
338C2×C4×C8C2311yescharacteristic
339#400—21no—
340#400—21no—
341#400—21no—
342#400—21no—
343#400—21no—
344#399—21no—
345#399—21no—
346#398—21no—
347#398—21no—
348#398—21no—
349#398—21no—
350#398—21no—
351#398—21no—
352#398—21no—
353#398—21no—
354#397—21no—
355#397—21no—
356#397—21no—
357#397—21no—
358#397—21no—
359#397—21no—
360#396—21no—
361#396—21no—
362#396—21no—
363#396—21no—
364#396—21no—
365#396—21no—
366#396—21no—
367#395—21no—
368#394—21no—
369#394—21no—
370#394—21no—
371#394—21no—
372#394—21no—
373#394—21no—
374#394—21no—
375#394—21no—
376#393—21no—
377#393—21no—
378#393—21no—
379#391—21no—
380#391—21no—
381#391—21no—
382#391C2311yescharacteristic
383#391C2311yescharacteristic
384#391C2311yescharacteristic
385#391C2311yescharacteristic
386#391C2311yescharacteristic
387#391C2311yescharacteristic
388#391C2311yescharacteristic
389#391C2311yescharacteristic
390#390—21no—
391#390—21no—
392#390—21no—
393#390—21no—
394#390—21no—
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#390C2311yescharacteristic
399#390C2311yescharacteristic
400#390C2311yescharacteristic
401#389—21no—
402#389—21no—
403#389—21no—
404#389—21no—
405#389—21no—
406#389—21no—
407#389—21no—
408#389C2311yescharacteristic
409#389C2311yescharacteristic
410#389C2311yescharacteristic
411#389C2311yescharacteristic
412#389C2311yescharacteristic
413#389C2311yescharacteristic
414#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#388—21no—
419#388—21no—
420#388—21no—
421#388—21no—
422#388—21no—
423#388—21no—
424#388—21no—
425#388—21no—
426#388—21no—
427#388—21no—
428#388—21no—
429#388D411yescharacteristic
430#388D411yescharacteristic
431#387—21no—
432#387—21no—
433#387—21no—
434#387—21no—
435#387—21no—
436#387—21no—
437#387—21no—
438#387—21no—
439#387—21no—
440#387—21no—
441#387—21no—
442#387—21no—
443#387D411yescharacteristic
444#387D411yescharacteristic
445#386—21no—
446#386D411yescharacteristic
447#385—21no—
448#385—21no—
449#385—21no—
450#385—21no—
451#385—21no—
452#385D411yescharacteristic
453#384C2311yescharacteristic
454#384C2311yescharacteristic
455#382—21no—
456#382C2311yescharacteristic
457#382C2311yescharacteristic
458#381D411yescharacteristic
459#380—21no—
460#380—21no—
461#380—21no—
462#380—21no—
463#380—21no—
464#380C2311yescharacteristic
465#380C2311yescharacteristic
466#380C2311yescharacteristic
467#380C2311yescharacteristic
468#379—21no—
469#379—21no—
470C4×C4⋊C4C2311yescharacteristic
471C4×C4⋊C4C2311yescharacteristic
472C4×C4⋊C4C2311yescharacteristic
473C4×C4⋊C4C2311yescharacteristic
474C4×C22⋊C4—21no—
475C4×C22⋊C4—21no—
476C4×C22⋊C4—21no—
477C4×C22⋊C4C2311yescharacteristic
478C4×C22⋊C4C2311yescharacteristic
479C4×C22⋊C4C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502C25—21no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C22×Q8—21no—
510C22×Q8—21no—
511C22×Q8C2411yescharacteristic
512C22×Q8C2411yescharacteristic
513C22×Q8C2411yescharacteristic
514C22×Q8C2411yescharacteristic
515C22×D4—22no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4C2×D411yescharacteristic
525C22×D4C2411yescharacteristic
526C22×D4C2411yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4C2×D411yescharacteristic
531C23×C4C2×D411yescharacteristic
532C23×C4C2411yescharacteristic
533C23×C4C2411yescharacteristic
534C2×Q16—22no—
535C2×Q16—22no—
536C2×Q16—41no—
537C2×Q16—41no—
538C2×Q16—41no—
539C2×Q16—41no—
540C2×Q16—41no—
541C2×Q16—41no—
542C2×Q16—41no—
543C2×Q16—41no—
544C2×Q16—41no—
545C2×Q16—41no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×SD16—41no—
556C2×SD16—41no—
557C2×SD16—41no—
558C22×C8—22no—
559C22×C8—41no—
560C22×C8—41no—
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C4⋊Q8—22no—
570C4⋊Q8—22no—
571C4⋊Q8—41no—
572C4⋊Q8—41no—
573C4⋊Q8—41no—
574C4⋊Q8—41no—
575C4⋊Q8—41no—
576C4⋊Q8—41no—
577#125—41no—
578#125—41no—
579#125—44no—
580#124—22no—
581#124—22no—
582#124—41no—
583#124—41no—
584#124—41no—
585#124—41no—
586#124—82no—
587#123—24no—
588#123—44no—
589C22⋊Q8—22no—
590C22⋊Q8—22no—
591C22⋊Q8—44no—
592C22⋊Q8—41no—
593C22⋊Q8—41no—
594C22⋊Q8—44no—
595C22⋊Q8—41no—
596C22⋊Q8—41no—
597C22⋊Q8—41no—
598C22⋊Q8—41no—
599C22⋊Q8—41no—
600C22⋊Q8—41no—
601C22⋊Q8—41no—
602C22⋊Q8—41no—
603C22⋊Q8—41no—
604C22⋊Q8—41no—
605C22⋊Q8—82no—
606#121—22no—
607#121—41no—
608#121—44no—
609#120—44no—
610C4×Q8—22no—
611C4×Q8—22no—
612C4×Q8—41no—
613C4×Q8—41no—
614C4×Q8—41no—
615C4×Q8—41no—
616C4×Q8—41no—
617C4×Q8—41no—
618C4×Q8—41no—
619C4×Q8—41no—
620C4×Q8—44no—
621C4×D4—22no—
622C4×D4—41no—
623C4×D4—41no—
624C4×D4—41no—
625#117—44no—
626#117—41no—
627#117—41no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
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—41no—
660C2×C4⋊C4—41no—
661C2×C4⋊C4C2×D411yescharacteristic
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—44no—
709C2×C22⋊C4—44no—
710C2×C22⋊C4—82no—
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C42—21no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42—21no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—41no—
728C2×C42—41no—
729C2×C42C2×D411yescharacteristic
730C2×C42C2×D411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736#107—41no—
737#107—41no—
738#107—41no—
739#107—41no—
740#106—22no—
741#106—22no—
742#106—22no—
743#106—22no—
744#106—41no—
745#106—41no—
746#106—41no—
747#106—41no—
748C4⋊C8—22no—
749C4⋊C8—41no—
750C4⋊C8—41no—
751C4⋊C8—41no—
752C4⋊C8—41no—
753#103—22no—
754#103—22no—
755#103—22no—
756#103—22no—
757#103—22no—
758#103—22no—
759#103—22no—
760#103—22no—
761#103—22no—
762#103—22no—
763#103—41no—
764#103—41no—
765#103—41no—
766#103—41no—
767#103—41no—
768#103—41no—
769#103—41no—
770#103—41no—
771#103—41no—
772#103—41no—
773#102—22no—
774#102—22no—
775#102—41no—
776#102—41no—
777#102—41no—
778#102—41no—
779#102—41no—
780#102—41no—
781#102—41no—
782#102—41no—
783#102—41no—
784#102—41no—
785C22⋊C8—22no—
786C22⋊C8—22no—
787C22⋊C8—22no—
788C22⋊C8—41no—
789C22⋊C8—41no—
790C22⋊C8—41no—
791C22⋊C8—41no—
792C4×C8—22no—
793C4×C8—41no—
794C4×C8—41no—
795C4×C8—41no—
796C4×C8—41no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
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#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834#95C2×D411yescharacteristic
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837#95C2×D411yescharacteristic
838#95C2×D411yescharacteristic
839C24—21no—
840C24—21no—
841C24—42no—
842C24—42no—
843C24—42no—
844C24—42no—
845C24—81no—
846C24—81no—
847C24—81no—
848C24C22×D411yescharacteristic
849C24C22×D411yescharacteristic
850#41—44no—
851#41—82no—
852#41—82no—
853#41—82no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—21no—
874C2×Q8—21no—
875C2×Q8—21no—
876C2×Q8—21no—
877C2×Q8—42no—
878C2×Q8—42no—
879C2×Q8—42no—
880C2×Q8—81no—
881C2×Q8—81no—
882C2×Q8—81no—
883C2×Q8H(5,𝔽2)12yes—
884C2×D4—22no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—41no—
897C2×D4—41no—
898C2×D4—42no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—81no—
904C2×D4—82no—
905C2×D4—82no—
906C2×D4—82no—
907C2×D4—82no—
908C2×D4—81no—
909C2×D4—81no—
910C2×D4—81no—
911C2×D42−1+412yes—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—22no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—41no—
940C22×C4—41no—
941C22×C4—41no—
942C22×C4—41no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4#13514yes—
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C22×D411yescharacteristic
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C2511yescharacteristic
966Q16—44no—
967Q16—82no—
968Q16—82no—
969Q16—82no—
970SD16—44no—
971SD16—82no—
972SD16—82no—
973SD16—82no—
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—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—82no—
997C2×C8H(5,𝔽2)12yes—
998C2×C8H(5,𝔽2)12yes—
999C4⋊C4—24no—
1000C4⋊C4—22no—
1001C4⋊C4—22no—
1002C4⋊C4—22no—
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—42no—
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—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4—81no—
1052C4⋊C4—81no—
1053C4⋊C4—81no—
1054C4⋊C4H(5,𝔽2)12yes—
1055C22⋊C4—24no—
1056C22⋊C4—22no—
1057C22⋊C4—22no—
1058C22⋊C4—22no—
1059C22⋊C4—22no—
1060C22⋊C4—41no—
1061C22⋊C4—41no—
1062C22⋊C4—41no—
1063C22⋊C4—41no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—21no—
1102C42—21no—
1103C42—21no—
1104C42—21no—
1105C42—41no—
1106C42—41no—
1107C42—42no—
1108C42—42no—
1109C42—81no—
1110C42—81no—
1111C42—81no—
1112C42—81no—
1113C42—81no—
1114C42—81no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—22no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—84no—
1143C23—84no—
1144C23—84no—
1145C23—84no—
1146C23—162no—
1147C23—162no—
1148C23—162no—
1149C23C2×#13512yes—
1150C23C23×D411yescharacteristic
1151Q8—22no—
1152Q8—22no—
1153Q8—41no—
1154Q8—41no—
1155Q8—41no—
1156Q8—41no—
1157Q8—41no—
1158Q8—41no—
1159Q8—41no—
1160Q8—41no—
1161Q8—41no—
1162Q8—41no—
1163Q8—41no—
1164Q8—41no—
1165Q8—41no—
1166Q8—41no—
1167Q8—84no—
1168Q8—162no—
1169D4—22no—
1170D4—22no—
1171D4—41no—
1172D4—41no—
1173D4—41no—
1174D4—41no—
1175D4—41no—
1176D4—41no—
1177D4—82no—
1178D4—84no—
1179D4—84no—
1180D4—162no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—44no—
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—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—82no—
1266C2×C4—84no—
1267C2×C4—162no—
1268C2×C4—162no—
1269C2×C4C2×#13512yes—
1270C2×C4C2×#13512yes—
1271C2×C4#57712yes—
1272C2×C4C2×H(5,𝔽2)11yescharacteristic
1273C2×C4C2×H(5,𝔽2)11yescharacteristic
1274C2×C4C2×H(5,𝔽2)11yescharacteristic
1275C2×C4C2×H(5,𝔽2)11yescharacteristic
1276C2×C4C2×2−1+411yescharacteristic
1277C2×C4#58511yescharacteristic
1278C8—22no—
1279C8—22no—
1280C8—41no—
1281C8—41no—
1282C8—41no—
1283C8—41no—
1284C8—41no—
1285C8—41no—
1286C22—22no—
1287C22—22no—
1288C22—22no—
1289C22—41no—
1290C22—41no—
1291C22—41no—
1292C22—41no—
1293C22—41no—
1294C22—42no—
1295C22—41no—
1296C22—41no—
1297C22—42no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—42no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—168no—
1315C22#348411yescharacteristic
1316C22#348911yescharacteristic
1317C22#349811yescharacteristic
1318C22C22×#13511yescharacteristic
1319C22C2×#57711yescharacteristic
1320C22#358611yescharacteristic
1321C22#358611yescharacteristic
1322C4—22no—
1323C4—22no—
1324C4—22no—
1325C4—41no—
1326C4—41no—
1327C4—42no—
1328C4—41no—
1329C4—41no—
1330C4—41no—
1331C4—41no—
1332C4—42no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—81no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4#353611yescharacteristic
1349C4#353611yescharacteristic
1350C4#354211yescharacteristic
1351C4#355811yescharacteristic
1352C2—42no—
1353C2—81no—
1354C2—82no—
1355C2—161no—
1356C2#4795111yescharacteristic
1357C2#6156411yescharacteristic
1358C2#6161811yescharacteristic
1359C2#6209711yescharacteristic
1360C2#6218911yescharacteristic
1361C2#6241411yescharacteristic
1362C2#6244411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#546C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #45525C2semidirect
3. #32053C2semidirect
4. #31584C2semidirect
5. #31519C2semidirect
6. #31211C2semidirect
7. #31195C2semidirect
8. #30996C2semidirect
9. #30881C2semidirect
10. #30854C2semidirect
11. #30644C2semidirect
12. #30569C2semidirect
13. #30531C2semidirect
14. #30520C2semidirect
15. #29950C2semidirect
16. #29664C2semidirect
17. #28407C2semidirect
18. #28338C2semidirect
19. #28302C2semidirect
20. #27787C2semidirect
21. #26789C2semidirect
22. #26595C2semidirect
23. #26558C2semidirect
24. #26534C2semidirect
25. #26480C2semidirect
26. #25953C2semidirect
27. #25672C2semidirect
28. #25151C2semidirect
31. #22357C2semidirect
34. C2×#498C22semidirect
36. C2×#487C22semidirect
37. C2×#485C22semidirect
40. C2×#479C22semidirect
41. C2×#467C22semidirect
45. C2×#462C22semidirect
46. C2×#462C22semidirect
51. C2×C4×Q16C22semidirect
65. #2570C22semidirect
66. #2565C22semidirect
69. #2499C22semidirect
70. #2492C22semidirect
76. #2451C22semidirect
78. #2446C22semidirect
79. #2441C22semidirect
83. #2429C22semidirect
97. #2097C22semidirect
98. #2097C22semidirect
103. #2085C22semidirect
105. #2068C22semidirect
110. #2066C22semidirect
111. #2066C22semidirect
113. #2059C22semidirect
114. #2056C22semidirect
118. #2036C22semidirect
123. #2035C22semidirect
124. #2035C22semidirect
127. #2024C22semidirect
128. #2024C22semidirect
131. #2016C22semidirect
132. #2016C22semidirect
143. #2001C22semidirect
145. #1990C22semidirect
147. #1969C22semidirect
148. #1969C22semidirect
157. #1956C22semidirect
159. #1949C22semidirect
160. #1941C22semidirect
161. #1941C22semidirect
162. #1939C22semidirect
163. #1928C22semidirect
164. #1927C22semidirect
165. #1927C22semidirect
169. #1923C22semidirect
170. #1923C22semidirect
171. #1916C22semidirect
172. #1916C22semidirect
174. #1878C22semidirect
175. #1878C22semidirect
179. #1865C22semidirect
180. #1865C22semidirect
181. #1865C22semidirect
182. #1865C22semidirect
183. #1865C22semidirect
184. #1865C22semidirect
186. #1863C22semidirect
187. #1854C22semidirect
190. #1850C22semidirect
191. #1807C22semidirect
193. #1803C22semidirect
194. #1803C22semidirect
199. C4×#106C22semidirect
200. C8×C4⋊C4C22semidirect
201. C8×C22⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#590942
#455252
#320532
#315842
#315192
#312112
#311952
#309962
#308812
#308542
#306442
#305692
#305312
#305202
#299502
#296642
#284072
#283382
#283022
#277872
#267892
#265952
#265582
#265342
#264802
#259532
#256722
#251512
#244362
#242472
#223572