Finite Group Databasebeta

← #7674378

Subgroups — #7674378

Order 512.

8144 conjugacy classes of subgroups.

The subgroup lattice has 1320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3510C211yesmaximal, characteristic, complemented
2C2×#3500C211yesmaximal, characteristic, complemented
3#45319C214yesmaximal, complemented
4#45307C214yesmaximal, complemented
5#45084C214yesmaximal, complemented
6#45057C214yesmaximal, complemented
7#38086C218yesmaximal, complemented
8#38077C218yesmaximal, complemented
9#37751C214yesmaximal, complemented
10#37750C214yesmaximal, complemented
11#37699C214yesmaximal, complemented
12#37696C214yesmaximal, complemented
13#35673C211yesmaximal, characteristic, complemented
14#35660C211yesmaximal, characteristic, complemented
15#35541C211yesmaximal, characteristic, complemented
16#35513C211yesmaximal, characteristic, complemented
17#35280C211yesmaximal, characteristic, complemented
18#35273C211yesmaximal, characteristic, complemented
19#35168C211yesmaximal, characteristic, complemented
20#35153C211yesmaximal, characteristic, complemented
21#34637C211yesmaximal, characteristic, complemented
22#34257C211yesmaximal, characteristic, complemented
23#34256C211yesmaximal, characteristic, complemented
24#34070C211yesmaximal, characteristic, complemented
25C2×#2326C211yesmaximal, characteristic, complemented
26C22×2−1+4C2211yescharacteristic
27C22×H(5,𝔽2)C2211yescharacteristic
28#3510—216no—
29#3500—216no—
30C2×#559C2214yescomplemented
31C2×#556C2214yescomplemented
32C2×#551C2218yescomplemented
33C2×#548C2214yes—
34C2×#546C2214yes—
35C2×#546C2218yes—
36C2×#542C2214yescomplemented
37C2×#537C2211yescharacteristic
38C2×#537C2211yescharacteristic, complemented
39C2×#536C2211yescharacteristic
40C2×#536C2212yes—
41C2×#536C2211yescharacteristic, complemented
42C2×#535C2211yescharacteristic
43C2×#535C2212yes—
44C2×#535C2211yescharacteristic
45C2×#533C2211yescharacteristic, complemented
46C2×#532C2211yescharacteristic
47C2×#532C2212yes—
48C2×#532C2211yescharacteristic
49C2×#529C2214yescomplemented
50C22×#124C2212yes—
51C22×#124C2211yescharacteristic
52C2×#519C2211yescharacteristic, complemented
53C2×#518C2211yescharacteristic
54C2×C4×#41C2211yescharacteristic
55C2×C4×#41C2211yescharacteristic, complemented
56C22×C4×Q8C2211yescharacteristic, complemented
57C22×C4×D4C2211yescharacteristic
58#2857C2214yescomplemented
59#2857C2212yescomplemented
60#2856C2212yescomplemented
61#2854C2214yescomplemented
62#2847C2214yescomplemented
63#2715C2218yescomplemented
64#2712C2218yescomplemented
65#2710C2218yescomplemented
66#2703C2218yescomplemented
67#2700C2218yescomplemented
68#2695C2218yescomplemented
69#2693C2218yescomplemented
70#2691C2218yescomplemented
71#2691C2218yescomplemented
72#2689C2218yescomplemented
73#2687C2218yescomplemented
74#2685C2218yescomplemented
75#2681C2218yescomplemented
76#2678C2218yescomplemented
77#2676C2218yescomplemented
78#2671C2218yescomplemented
79#2642C2212yescomplemented
80#2641C2212yescomplemented
81#2640C2212yescomplemented
82#2640C2212yescomplemented
83#2639C2214yescomplemented
84#2639C2214yescomplemented
85#2629C2214yescomplemented
86#2620C2212yescomplemented
87#2620C2212yescomplemented
88#2618C2214yescomplemented
89#2617C2214yescomplemented
90#2582C2214yescomplemented
91#2538C2214yescomplemented
92#2538C2214yescomplemented
93#2537C2214yescomplemented
94#2498C2218yescomplemented
95#2480C2218yescomplemented
96#2476C2218yescomplemented
97#2472C2218yescomplemented
98#2470C2218yescomplemented
99#2466C2218yescomplemented
100#2464C2218yescomplemented
101#2459C2218yescomplemented
102#2457C2218yescomplemented
103#2450C2218yescomplemented
104#2450C2218yescomplemented
105#2448C2214yescomplemented
106#2447C2214yescomplemented
107#2446C2214yescomplemented
108#2445C2214yescomplemented
109#2438C2218yescomplemented
110#2437C2218yescomplemented
111#2436C2212yescomplemented
112#2435C2212yes—
113#2434C2212yescomplemented
114#2433C2212yes—
115#2432C2212yes—
116#2432C2212yescomplemented
117#2431C2212yes—
118#2431C2212yescomplemented
119#2430C2218yescomplemented
120#2429C2214yescomplemented
121#2429C2214yescomplemented
122#2428C2214yescomplemented
123#2428C2214yescomplemented
124#2427C2214yescomplemented
125#2427C2214yescomplemented
126#2426C2214yescomplemented
127#2426C2214yescomplemented
128#2425C2218yescomplemented
129#2424C2218yescomplemented
130#2423C2214yescomplemented
131#2422C2214yescomplemented
132#2421C2214yescomplemented
133#2420C2214yescomplemented
134#2417C2218yescomplemented
135#2416C2218yescomplemented
136#2412C2218yescomplemented
137#2412C2218yescomplemented
138#2411C2218yescomplemented
139#2410C2218yes—
140#2409C2214yescomplemented
141#2408C2214yes—
142#2407C2214yes—
143#2407C2214yescomplemented
144#2398C2214yescomplemented
145#2398C2214yescomplemented
146#2341C2214yescomplemented
147#2341C2214yescomplemented
148Q8×C22⋊C4C2214yescomplemented
149Q8×C22⋊C4C2214yescomplemented
150#2339C2214yes—
151#2339C2214yes—
152D4×C22⋊C4C2214yes—
153D4×C22⋊C4C2214yes—
154#2328C2212yescomplemented
155#2327C2212yescomplemented
156#2326C2214yescomplemented
157#2326C2212yescomplemented
158#2326C2214yescomplemented
159#2326C2214yescomplemented
160#2326C2214yescomplemented
161#2326C2212yescomplemented
162#2325C2214yescomplemented
163#2325C2214yescomplemented
164#2316C2211yescharacteristic, complemented
165#2316C2211yescharacteristic, complemented
166#2311C2211yescharacteristic
167#2311C2211yescharacteristic
168#2311C2211yescharacteristic
169#2311C2214yescomplemented
170#2311C2211yescharacteristic, complemented
171#2308C2214yes—
172#2297C2211yescharacteristic
173#2297C2211yescharacteristic
174#2297C2211yescharacteristic
175#2297C2211yescharacteristic, complemented
176#2297C2211yescharacteristic, complemented
177#2297C2211yescharacteristic, complemented
178#2297C2214yescomplemented
179C2×#391C2211yescharacteristic, complemented
180C2×#390C2211yescharacteristic
181#2290C2214yescomplemented
182#2290C2214yescomplemented
183C2×#388C2214yescomplemented
184C2×#386C2214yes—
185C2×#385C2214yescomplemented
186#2285C2211yescharacteristic, complemented
187C2×#384C2211yescharacteristic, complemented
188C2×#376C2211yescharacteristic, complemented
189C2×2−1+4—28no—
190C2×2−1+4—28no—
191C2×2−1+4—44no—
192C2×H(5,𝔽2)—28no—
193C2×H(5,𝔽2)—28no—
194C2×H(5,𝔽2)—44no—
195C22×#41C2311yescharacteristic
196C22×#41C2311yescharacteristic
197C22×#41C2311yescharacteristic
198C22×#41C2314yes—
199C22×#41C2312yes—
200C22×#41C2312yes—
201C22×#41C2312yes—
202C22×#41C2312yes—
203C22×#41C2311yescharacteristic
204C23×Q8C2312yes—
205C23×Q8C2312yes—
206C23×Q8C2311yescharacteristic
207C23×D4C2314yes—
208C23×D4C2312yes—
209C23×D4C2312yes—
210C23×D4C2311yescharacteristic
211C24×C4C2312yes—
212#559—232no—
213#556—232no—
214#551—264no—
215#548—232no—
216#546—232no—
217#546—264no—
218#542—232no—
219#537—44no—
220#537—44no—
221#536—28no—
222#536—28no—
223#536—216no—
224#535—28no—
225#535—28no—
226#535—216no—
227#533—28no—
228#532—28no—
229#532—216no—
230#532—28no—
231C2×C4⋊Q8C2311yescharacteristic
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2312yes—
236C2×#127C2311yescharacteristic
237C2×#127C2311yescharacteristic
238C2×#127C2312yes—
239C2×#127C2312yes—
240#529—232no—
241C2×#126C2318yes—
242C2×#126C2318yes—
243C2×#125C2312yes—
244C2×#124—216no—
245C2×#124D4116yescomplemented
246C2×#124C2311yescharacteristic
247C2×#124C2311yescharacteristic
248C2×#124C2311yescharacteristic
249C2×#124C2311yescharacteristic
250C2×#124C2312yes—
251C2×#124C2312yes—
252C2×#124C2318yes—
253C2×#124C2318yes—
254C2×#124C2312yes—
255C2×#124C2312yes—
256C2×#124C2312yes—
257C2×#124C2312yes—
258C2×#124C2314yes—
259C2×#123C2314yes—
260C2×#123C2314yes—
261C2×#123C2318yes—
262C2×#123C2318yes—
263C2×#123C2318yes—
264C2×#123C2318yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2318yes—
269C2×C22⋊Q8C2318yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2318yes—
275C2×#121C2314yes—
276C2×#121C2314yes—
277C2×#121C2314yes—
278C2×#121C2318yes—
279C2×#121C2318yes—
280C2×#121C2314yes—
281C2×#121C2314yes—
282C2×#121C2314yes—
283C2×#121C2312yes—
284C2×#121C2312yes—
285C2×#121C2312yes—
286C2×#121C2312yes—
287C2×#121C2318yes—
288C2×#121C2318yes—
289C2×#120C2314yes—
290C2×#120C2314yes—
291C2×#120C2318yes—
292C2×#120C2318yes—
293#519—28no—
294#518—28no—
295C4×#41—28no—
296C4×#41—28no—
297C2×C4×Q8—44no—
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2314yes—
301C2×C4×Q8C2314yes—
302C2×C4×Q8C2314yes—
303C2×C4×Q8C2314yes—
304C2×C4×Q8C2314yes—
305C2×C4×D4—44no—
306C2×C4×D4C2314yes—
307C2×C4×D4C2314yes—
308C2×C4×D4C2312yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2314yes—
311C2×C4×D4C2314yes—
312C2×C4×D4C2314yes—
313C2×C4×D4C2314yes—
314C2×C4×D4C2318yes—
315C2×C4×D4C2318yes—
316C2×C4×D4C2314yes—
317C2×C4×D4C2314yes—
318C2×#117C2311yescharacteristic
319C2×#117C2311yescharacteristic
320C2×#117C2311yescharacteristic
321C2×#117C2314yes—
322C2×#117C2311yescharacteristic
323C2×#117C2312yes—
324C2×#117C2312yes—
325C2×#117C2318yes—
326C22×C4⋊C4C2311yescharacteristic
327C22×C4⋊C4C2311yescharacteristic
328C22×C4⋊C4C2312yes—
329C22×C4⋊C4C2314yes—
330C22×C22⋊C4C2314yes—
331C22×C22⋊C4C2318yes—
332C22×C22⋊C4C2312yes—
333C22×C22⋊C4C2318yes—
334C22×C22⋊C4C2314yes—
335C22×C22⋊C4C2314yes—
336C22×C42C2312yes—
337C22×C42C2312yes—
338C22×C42C2311yescharacteristic
339C22×C42C2311yescharacteristic
340C22×C42C2312yes—
341C22×C42C2311yescharacteristic
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2318yes—
347#399C2318yes—
348#398C2318yes—
349#398C2318yes—
350#398C2318yes—
351#398C2318yes—
352#397C2318yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2318yes—
358#397C2318yes—
359#397C2318yes—
360#396C2318yes—
361#396C2318yes—
362#396C2318yes—
363#396C2318yes—
364#396C2318yes—
365#396C2318yes—
366#395C2318yes—
367#394C2318yes—
368#394C2318yes—
369#394C2318yes—
370#394C2318yes—
371#394C2318yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2318yes—
377#394C2318yes—
378#394C2318yes—
379#394C2318yes—
380#394C2318yes—
381#393C2314yes—
382#393C2314yes—
383#393C2314yes—
384#393C2314yes—
385#393C2318yes—
386#392C2318yes—
387#392C2318yes—
388#392C2318yes—
389#392C2318yes—
390#391C2312yes—
391#391C2312yes—
392#391C2312yes—
393#391C2312yes—
394#391C2318yes—
395#391C2314yes—
396#391C2312yes—
397#391C2312yes—
398#391C2312yes—
399#391C2312yes—
400#391C2318yes—
401#391C2312yes—
402#391C2312yes—
403#391C2318yes—
404#391C2312yes—
405#391C2312yes—
406#390C2312yes—
407#390C2312yes—
408#390C2312yes—
409#390C2312yes—
410#390C2318yes—
411#390C2314yes—
412#390C2312yes—
413#390C2312yes—
414#390C2312yes—
415#390C2312yes—
416#390C2312yes—
417#390C2312yes—
418#390C2318yes—
419#390C2318yes—
420#390C2318yes—
421#390C2312yes—
422#390C2312yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2318yes—
428#389C2318yes—
429#389C2318yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#388C2318yes—
435#388C2318yes—
436#388C2318yes—
437#388C2318yes—
438#388C2318yes—
439#388C2318yes—
440#388C2318yes—
441#388C2318yes—
442#387C2314yes—
443#387C2314yes—
444#387C2314yes—
445#387C2314yes—
446#387C2318yes—
447#387C2318yes—
448#386C2312yes—
449#386C2312yes—
450#386C2314yes—
451#386C2314yes—
452#386C2318yes—
453#386C2318yes—
454#386C2314yes—
455#386C2312yes—
456#386C2312yes—
457#386C2314yes—
458#386C2312yes—
459#386C2312yes—
460#386C2314yes—
461#386C2314yes—
462#386C2314yes—
463#386C2314yes—
464#386C2318yes—
465#386C2318yes—
466#386C2318yes—
467#386C2318yes—
468#386C2312yes—
469#386C2312yes—
470#386C2314yes—
471#386C2314yes—
472#386C2318yes—
473#386C2318yes—
474#386C2318yes—
475#386C2318yes—
476#385C2314yes—
477#385C2314yes—
478#385C2314yes—
479#385C2314yes—
480#385C2318yes—
481#385C2318yes—
482#385C2318yes—
483#385C2318yes—
484#385C2318yes—
485#385C2318yes—
486#385C2318yes—
487#385C2318yes—
488#384C2314yes—
489#384C2312yes—
490#384C2312yes—
491#384C2312yes—
492#382C2312yes—
493#381C2318yes—
494#381C2318yes—
495#380C2314yes—
496#380C2314yes—
497#380C2314yes—
498#380C2318yes—
499#380C2318yes—
500#380C2314yes—
501#380C2314yes—
502#380C2314yes—
503#380C2314yes—
504#380C2318yes—
505#380C2318yes—
506#380C2318yes—
507#379C2318yes—
508#379C2318yes—
509C4×C4⋊C4C2314yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2318yes—
514C4×C22⋊C4C2318yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2314yes—
520#376C2312yes—
521#376C2312yes—
522#376C2312yes—
523#376C2312yes—
524C2×#95C2312yes—
525C2×#95C2312yes—
526C2×#95C2318yes—
527C2×#95C2314yes—
528C25C2414yes—
529C25C2412yes—
5302−1+4—464no—
531H(5,𝔽2)—464no—
532C2×#41—28no—
533C2×#41—28no—
534C2×#41—28no—
535C2×#41—28no—
536C2×#41—28no—
537C2×#41—216no—
538C2×#41—28no—
539C2×#41—24no—
540C2×#41—24no—
541C2×#41—24no—
542C2×#41—24no—
543C2×#41—216no—
544C2×#41—24no—
545C2×#41—28no—
546C2×#41—24no—
547C2×#41—28no—
548C2×#41—24no—
549C2×#41—24no—
550C2×#41—24no—
551C2×#41—24no—
552C2×#41—24no—
553C2×#41—48no—
554C2×#41—44no—
555C2×#41—44no—
556C2×#41—44no—
557C2×#41—44no—
558C2×#41#4118yes—
559C22×Q8—28no—
560C22×Q8—28no—
561C22×Q8—28no—
562C22×Q8—24no—
563C22×Q8—28no—
564C22×Q8—24no—
565C22×Q8—44no—
566C22×Q8—44no—
567C22×Q8C2×D418yes—
568C22×Q8C2411yescharacteristic
569C22×Q8C2411yescharacteristic
570C22×Q8C2411yescharacteristic
571C22×Q8C2414yes—
572C22×Q8C2412yes—
573C22×Q8C2412yes—
574C22×Q8C2411yescharacteristic
575C22×Q8C2414yes—
576C22×D4—216no—
577C22×D4—28no—
578C22×D4—28no—
579C22×D4—28no—
580C22×D4—216no—
581C22×D4—24no—
582C22×D4—28no—
583C22×D4—24no—
584C22×D4—44no—
585C22×D4—44no—
586C22×D4—48no—
587C22×D4C2×D418yes—
588C22×D4C2412yes—
589C22×D4C2411yescharacteristic
590C22×D4C2412yes—
591C22×D4C2412yes—
592C22×D4C2411yescharacteristic
593C22×D4C2411yescharacteristic
594C22×D4C2414yes—
595C22×D4C2414yes—
596C22×D4C2414yes—
597C22×D4C2412yes—
598C22×D4C2412yes—
599C22×D4C2412yes—
600C22×D4C2411yescharacteristic
601C22×D4C2414yes—
602C22×D4C2418yes—
603C22×D4C2418yes—
604C22×D4C2414yes—
605C22×D4C2414yes—
606C22×D4C2414yes—
607C23×C4—44no—
608C23×C4—84no—
609C23×C4C2412yes—
610C23×C4C2412yes—
611C23×C4C2412yes—
612C23×C4C2414yes—
613C23×C4C2414yes—
614C23×C4C2414yes—
615C23×C4C2412yes—
616C23×C4C2412yes—
617C23×C4C2412yes—
618C23×C4C2418yes—
619C23×C4C2414yes—
620C23×C4C2412yes—
621C23×C4C2411yescharacteristic
622C23×C4C2412yes—
623C23×C4C2411yescharacteristic
624C23×C4C2414yes—
625C23×C4C2418yes—
626C23×C4C2412yes—
627C23×C4C2411yescharacteristic
628C4⋊Q8—28no—
629C4⋊Q8—28no—
630C4⋊Q8—24no—
631C4⋊Q8—24no—
632C4⋊Q8—28no—
633#127—28no—
634#127—28no—
635#127—24no—
636#127—24no—
637#126—232no—
638#126—232no—
639#125—28no—
640#124—28no—
641#124—28no—
642#124—24no—
643#124—28no—
644#124—28no—
645#124—24no—
646#124—232no—
647#124—232no—
648#124—24no—
649#124—24no—
650#124C2×D4116yes—
651#124C2×D4116yes—
652#124C2×D4132yes—
653#123—216no—
654#123—216no—
655#123—232no—
656#123—232no—
657#123—232no—
658#123—88no—
659C22⋊Q8—216no—
660C22⋊Q8—216no—
661C22⋊Q8—216no—
662C22⋊Q8—232no—
663C22⋊Q8—232no—
664C22⋊Q8—44no—
665C22⋊Q8—44no—
666C22⋊Q8—44no—
667C22⋊Q8—44no—
668C22⋊Q8—88no—
669#121—216no—
670#121—216no—
671#121—216no—
672#121—216no—
673#121—232no—
674#121—232no—
675#121—44no—
676#121—44no—
677#121—44no—
678#121—44no—
679#121—48no—
680#121—48no—
681#121—88no—
682#121—88no—
683#120—216no—
684#120—216no—
685#120—232no—
686#120—88no—
687C4×Q8—216no—
688C4×Q8—216no—
689C4×Q8—28no—
690C4×Q8—28no—
691C4×Q8—216no—
692C4×Q8—48no—
693C4×Q8—48no—
694C4×D4—216no—
695C4×D4—216no—
696C4×D4—216no—
697C4×D4—216no—
698C4×D4—216no—
699C4×D4—232no—
700C4×D4—232no—
701C4×D4—28no—
702C4×D4—28no—
703C4×D4—216no—
704C4×D4—48no—
705C4×D4—48no—
706#117—24no—
707#117—24no—
708#117—24no—
709#117—24no—
710#117—216no—
711#117—232no—
712#117—28no—
713#117—28no—
714C2×C4⋊C4—24no—
715C2×C4⋊C4—24no—
716C2×C4⋊C4—44no—
717C2×C4⋊C4—84no—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2418yes—
730C2×C4⋊C4C2418yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2418yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2418yes—
737C2×C4⋊C4C2418yes—
738C2×C4⋊C4C2418yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2418yes—
742C2×C4⋊C4C2418yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C22⋊C4—216no—
746C2×C22⋊C4—232no—
747C2×C22⋊C4—44no—
748C2×C22⋊C4—88no—
749C2×C22⋊C4—84no—
750C2×C22⋊C4C2×D4132yes—
751C2×C22⋊C4C2412yes—
752C2×C22⋊C4C2412yes—
753C2×C22⋊C4C2414yes—
754C2×C22⋊C4C2418yes—
755C2×C22⋊C4C2418yes—
756C2×C22⋊C4C2418yes—
757C2×C22⋊C4C2412yes—
758C2×C22⋊C4C2412yes—
759C2×C22⋊C4C2414yes—
760C2×C22⋊C4C2414yes—
761C2×C22⋊C4C2418yes—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2418yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2418yes—
769C2×C22⋊C4C2418yes—
770C2×C22⋊C4C2418yes—
771C2×C22⋊C4C2418yes—
772C2×C22⋊C4C2418yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2418yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2418yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2418yes—
790C2×C22⋊C4C2418yes—
791C2×C42—24no—
792C2×C42—24no—
793C2×C42—28no—
794C2×C42—28no—
795C2×C42—44no—
796C2×C42C2×D418yes—
797C2×C42C2412yes—
798C2×C42C2418yes—
799C2×C42C2414yes—
800C2×C42C2412yes—
801C2×C42C2412yes—
802C2×C42C2412yes—
803C2×C42C2414yes—
804C2×C42C2412yes—
805C2×C42C2412yes—
806C2×C42C2412yes—
807C2×C42C2411yescharacteristic
808C2×C42C2411yescharacteristic
809C2×C42C2418yes—
810C2×C42C2411yescharacteristic
811C2×C42C2411yescharacteristic
812C2×C42C2412yes—
813#95C2414yes—
814#95C2414yes—
815#95C2412yes—
816#95C2412yes—
817#95C2412yes—
818#95C2412yes—
819#95C2412yes—
820#95C2412yes—
821#95C2412yes—
822#95C2412yes—
823#95C2418yes—
824#95C2418yes—
825#95C2418yes—
826#95C2418yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2418yes—
831#95C2414yes—
832#95C2418yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2418yes—
842#95C2418yes—
843C24—24no—
844C24—24no—
845C24—28no—
846C24—28no—
847C24—44no—
848C24—44no—
849C24—44no—
850C24—48no—
851C24—48no—
852C24C22×D418yes—
853C24C2512yes—
854C24C2512yes—
855C24C2512yes—
856C24C2514yes—
857C24C2512yes—
858C24C2511yescharacteristic
859#41—232no—
860#41—432no—
861#41—464no—
862#41—432no—
863#41—432no—
864#41—432no—
865#41—416no—
866#41—416no—
867#41—416no—
868C2×Q8—232no—
869C2×Q8—22no—
870C2×Q8—22no—
871C2×Q8—28no—
872C2×Q8—22no—
873C2×Q8—22no—
874C2×Q8—28no—
875C2×Q8—24no—
876C2×Q8—24no—
877C2×Q8—22no—
878C2×Q8—28no—
879C2×Q8—22no—
880C2×Q8—22no—
881C2×Q8—24no—
882C2×Q8—24no—
883C2×Q8—22no—
884C2×Q8—22no—
885C2×Q8—22no—
886C2×Q8—22no—
887C2×Q8—44no—
888C2×Q8—44no—
889C2×Q8—44no—
890C2×Q8—432no—
891C2×Q8—432no—
892C2×Q8C22×D418yes—
893C2×Q8C22×D418yes—
894C2×Q8C2×#4114yes—
895C2×D4—24no—
896C2×D4—24no—
897C2×D4—24no—
898C2×D4—24no—
899C2×D4—28no—
900C2×D4—24no—
901C2×D4—28no—
902C2×D4—24no—
903C2×D4—28no—
904C2×D4—24no—
905C2×D4—28no—
906C2×D4—24no—
907C2×D4—24no—
908C2×D4—24no—
909C2×D4—24no—
910C2×D4—216no—
911C2×D4—216no—
912C2×D4—28no—
913C2×D4—232no—
914C2×D4—22no—
915C2×D4—22no—
916C2×D4—28no—
917C2×D4—22no—
918C2×D4—22no—
919C2×D4—28no—
920C2×D4—24no—
921C2×D4—24no—
922C2×D4—22no—
923C2×D4—28no—
924C2×D4—22no—
925C2×D4—22no—
926C2×D4—24no—
927C2×D4—24no—
928C2×D4—22no—
929C2×D4—22no—
930C2×D4—22no—
931C2×D4—22no—
932C2×D4—432no—
933C2×D4—44no—
934C2×D4—44no—
935C2×D4—44no—
936C2×D4—44no—
937C2×D4—48no—
938C2×D4—44no—
939C2×D4—48no—
940C2×D4—44no—
941C2×D4—44no—
942C2×D4—48no—
943C2×D4—48no—
944C2×D4—48no—
945C2×D4—44no—
946C2×D4—44no—
947C2×D4—48no—
948C2×D4—432no—
949C2×D4—464no—
950C2×D4C22×D418yes—
951C2×D4C22×D418yes—
952C2×D4C2×#4118yes—
953C2×D4C2×#4114yes—
954C22×C4—24no—
955C22×C4—24no—
956C22×C4—24no—
957C22×C4—24no—
958C22×C4—28no—
959C22×C4—28no—
960C22×C4—22no—
961C22×C4—22no—
962C22×C4—216no—
963C22×C4—24no—
964C22×C4—24no—
965C22×C4—24no—
966C22×C4—24no—
967C22×C4—28no—
968C22×C4—28no—
969C22×C4—24no—
970C22×C4—24no—
971C22×C4—24no—
972C22×C4—28no—
973C22×C4—24no—
974C22×C4—28no—
975C22×C4—24no—
976C22×C4—24no—
977C22×C4—24no—
978C22×C4—24no—
979C22×C4—28no—
980C22×C4—28no—
981C22×C4—42no—
982C22×C4—42no—
983C22×C4—42no—
984C22×C4—42no—
985C22×C4—44no—
986C22×C4—44no—
987C22×C4—44no—
988C22×C4—42no—
989C22×C4—44no—
990C22×C4—48no—
991C22×C4—48no—
992C22×C4—44no—
993C22×C4—48no—
994C22×C4—44no—
995C22×C4—48no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4—44no—
999C22×C4—42no—
1000C22×C4—48no—
1001C22×C4—816no—
1002C22×C4C22×D418yes—
1003C22×C4C22×D418yes—
1004C22×C4C22×D414yes—
1005C22×C4C2×#4118yes—
1006C22×C4C2×#4114yes—
1007C22×C4H(5,𝔽2)14yes—
1008C22×C4C2512yes—
1009C22×C4C2512yes—
1010C22×C4C2512yes—
1011C22×C4C2512yes—
1012C22×C4C2512yes—
1013C22×C4C2512yes—
1014C22×C4C2514yes—
1015C22×C4C2514yes—
1016C22×C4C2514yes—
1017C22×C4C2514yes—
1018C22×C4C2514yes—
1019C22×C4C2514yes—
1020C22×C4C2512yes—
1021C22×C4C2512yes—
1022C22×C4C2514yes—
1023C22×C4C2512yes—
1024C22×C4C2512yes—
1025C22×C4C2511yescharacteristic
1026C22×C4C2511yescharacteristic
1027C4⋊C4—28no—
1028C4⋊C4—24no—
1029C4⋊C4—24no—
1030C4⋊C4—28no—
1031C4⋊C4—24no—
1032C4⋊C4—28no—
1033C4⋊C4—24no—
1034C4⋊C4—216no—
1035C4⋊C4—216no—
1036C4⋊C4—28no—
1037C4⋊C4—216no—
1038C4⋊C4—28no—
1039C4⋊C4—28no—
1040C4⋊C4—28no—
1041C4⋊C4—24no—
1042C4⋊C4—24no—
1043C4⋊C4—24no—
1044C4⋊C4—24no—
1045C4⋊C4—48no—
1046C4⋊C4—48no—
1047C4⋊C4—48no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—48no—
1052C4⋊C4—48no—
1053C4⋊C4—44no—
1054C22⋊C4—24no—
1055C22⋊C4—24no—
1056C22⋊C4—216no—
1057C22⋊C4—216no—
1058C22⋊C4—24no—
1059C22⋊C4—24no—
1060C22⋊C4—216no—
1061C22⋊C4—28no—
1062C22⋊C4—28no—
1063C22⋊C4—216no—
1064C22⋊C4—28no—
1065C22⋊C4—28no—
1066C22⋊C4—28no—
1067C22⋊C4—216no—
1068C22⋊C4—28no—
1069C22⋊C4—48no—
1070C22⋊C4—44no—
1071C22⋊C4—44no—
1072C22⋊C4—48no—
1073C22⋊C4—48no—
1074C22⋊C4—48no—
1075C22⋊C4—48no—
1076C22⋊C4—44no—
1077C22⋊C4—44no—
1078C22⋊C4—44no—
1079C22⋊C4—44no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C4—48no—
1084C22⋊C4—44no—
1085C22⋊C4—44no—
1086C22⋊C4—44no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C22⋊C4—44no—
1090C22⋊C4—48no—
1091C22⋊C4—44no—
1092C22⋊C4C22×D4132yes—
1093C22⋊C4C22×D4132yes—
1094C42—24no—
1095C42—28no—
1096C42—24no—
1097C42—28no—
1098C42—216no—
1099C42—24no—
1100C42—24no—
1101C42—24no—
1102C42—22no—
1103C42—22no—
1104C42—24no—
1105C42—24no—
1106C42—48no—
1107C42C22×D414yes—
1108C42C22×D414yes—
1109C42C22×D418yes—
1110C23—22no—
1111C23—22no—
1112C23—22no—
1113C23—24no—
1114C23—24no—
1115C23—22no—
1116C23—24no—
1117C23—28no—
1118C23—24no—
1119C23—28no—
1120C23—216no—
1121C23—22no—
1122C23—22no—
1123C23—22no—
1124C23—22no—
1125C23—22no—
1126C23—22no—
1127C23—22no—
1128C23—22no—
1129C23—22no—
1130C23—24no—
1131C23—24no—
1132C23—24no—
1133C23—24no—
1134C23—24no—
1135C23—24no—
1136C23—416no—
1137C23—416no—
1138C23—84no—
1139C23—88no—
1140C23—84no—
1141C23—816no—
1142C23—816no—
1143C23—164no—
1144C23—164no—
1145C23C23×D418yes—
1146C23C23×D412yes—
1147C23C22×#4114yes—
1148C23C22×#4112yes—
1149C23C2×H(5,𝔽2)12yes—
1150C23C2611yescharacteristic
1151Q8—216no—
1152Q8—216no—
1153Q8—28no—
1154Q8—416no—
1155Q8—44no—
1156Q8—44no—
1157Q8—44no—
1158Q8—88no—
1159D4—216no—
1160D4—216no—
1161D4—216no—
1162D4—28no—
1163D4—416no—
1164D4—416no—
1165D4—416no—
1166D4—48no—
1167D4—48no—
1168D4—48no—
1169D4—44no—
1170D4—44no—
1171D4—44no—
1172D4—88no—
1173D4—816no—
1174D4—816no—
1175D4—88no—
1176D4—164no—
1177D4—164no—
1178C2×C4—22no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—216no—
1187C2×C4—216no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—22no—
1192C2×C4—24no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—24no—
1210C2×C4—28no—
1211C2×C4—24no—
1212C2×C4—24no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—28no—
1216C2×C4—24no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—24no—
1221C2×C4—22no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—24no—
1225C2×C4—48no—
1226C2×C4—416no—
1227C2×C4—416no—
1228C2×C4—416no—
1229C2×C4—44no—
1230C2×C4—44no—
1231C2×C4—48no—
1232C2×C4—48no—
1233C2×C4—48no—
1234C2×C4—88no—
1235C2×C4—88no—
1236C2×C4—816no—
1237C2×C4—84no—
1238C2×C4—84no—
1239C2×C4—84no—
1240C2×C4—816no—
1241C2×C4#546116yes—
1242C2×C4C23×D414yes—
1243C2×C4C23×D414yes—
1244C2×C4C23×D418yes—
1245C2×C4C23×D412yes—
1246C2×C4C23×D412yes—
1247C2×C4C22×#4114yes—
1248C2×C4C22×#4112yes—
1249C2×C4C22×#4112yes—
1250C2×C4C2×H(5,𝔽2)12yes—
1251C2×C4C2×H(5,𝔽2)12yes—
1252C22—24no—
1253C22—24no—
1254C22—22no—
1255C22—22no—
1256C22—216no—
1257C22—28no—
1258C22—24no—
1259C22—28no—
1260C22—44no—
1261C22—48no—
1262C22—44no—
1263C22—42no—
1264C22—44no—
1265C22—42no—
1266C22—44no—
1267C22—44no—
1268C22—44no—
1269C22—44no—
1270C22—44no—
1271C22—44no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—816no—
1282C22—1616no—
1283C22C2×#54614yes—
1284C22C24×D411yescharacteristic
1285C22C23×#4111yescharacteristic
1286C22C22×H(5,𝔽2)11yescharacteristic
1287C22H(7,𝔽2)12yes—
1288C222−1+612yes—
1289C4—24no—
1290C4—24no—
1291C4—24no—
1292C4—28no—
1293C4—44no—
1294C4—44no—
1295C4—44no—
1296C4—44no—
1297C4—42no—
1298C4—42no—
1299C4—42no—
1300C4—44no—
1301C4—44no—
1302C4—42no—
1303C4—42no—
1304C4—42no—
1305C4—42no—
1306C4C2×#54614yes—
1307C4C2×#54614yes—
1308C2—24no—
1309C2—48no—
1310C2—44no—
1311C2—82no—
1312C2—82no—
1313C2—82no—
1314C2C22×#54611yescharacteristic
1315C2#6285312yes—
1316C2#6285712yes—
1317C2#6287611yescharacteristic
1318C2#6288711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3510C2semidirect
2. C2×#3500C2semidirect
3. #45319C2semidirect
4. #45307C2semidirect
5. #45084C2semidirect
6. #45057C2semidirect
7. #38086C2semidirect
8. #38077C2semidirect
9. #37751C2semidirect
10. #37750C2semidirect
11. #37699C2semidirect
12. #37696C2semidirect
13. #35673C2semidirect
14. #35660C2semidirect
15. #35541C2semidirect
16. #35513C2semidirect
17. #35280C2semidirect
18. #35273C2semidirect
19. #35168C2semidirect
20. #35153C2semidirect
21. #34637C2semidirect
22. #34257C2semidirect
23. #34256C2semidirect
24. #34070C2semidirect
25. C2×#2326C2semidirect
30. C2×#559C22semidirect
31. C2×#556C22semidirect
32. C2×#551C22semidirect
36. C2×#542C22semidirect
38. C2×#537C22semidirect
41. C2×#536C22semidirect
45. C2×#533C22semidirect
49. C2×#529C22semidirect
52. C2×#519C22semidirect
55. C2×C4×#41C22semidirect
56. C22×C4×Q8C22semidirect
58. #2857C22semidirect
59. #2857C22semidirect
60. #2856C22semidirect
61. #2854C22semidirect
62. #2847C22semidirect
63. #2715C22semidirect
64. #2712C22semidirect
65. #2710C22semidirect
66. #2703C22semidirect
67. #2700C22semidirect
68. #2695C22semidirect
69. #2693C22semidirect
70. #2691C22semidirect
71. #2691C22semidirect
72. #2689C22semidirect
73. #2687C22semidirect
74. #2685C22semidirect
75. #2681C22semidirect
76. #2678C22semidirect
77. #2676C22semidirect
78. #2671C22semidirect
79. #2642C22semidirect
80. #2641C22semidirect
81. #2640C22semidirect
82. #2640C22semidirect
83. #2639C22semidirect
84. #2639C22semidirect
85. #2629C22semidirect
86. #2620C22semidirect
87. #2620C22semidirect
88. #2618C22semidirect
89. #2617C22semidirect
90. #2582C22semidirect
91. #2538C22semidirect
92. #2538C22semidirect
93. #2537C22semidirect
94. #2498C22semidirect
95. #2480C22semidirect
96. #2476C22semidirect
97. #2472C22semidirect
98. #2470C22semidirect
99. #2466C22semidirect
100. #2464C22semidirect
101. #2459C22semidirect
102. #2457C22semidirect
103. #2450C22semidirect
104. #2450C22semidirect
105. #2448C22semidirect
106. #2447C22semidirect
107. #2446C22semidirect
108. #2445C22semidirect
109. #2438C22semidirect
110. #2437C22semidirect
111. #2436C22semidirect
113. #2434C22semidirect
116. #2432C22semidirect
118. #2431C22semidirect
119. #2430C22semidirect
120. #2429C22semidirect
121. #2429C22semidirect
122. #2428C22semidirect
123. #2428C22semidirect
124. #2427C22semidirect
125. #2427C22semidirect
126. #2426C22semidirect
127. #2426C22semidirect
128. #2425C22semidirect
129. #2424C22semidirect
130. #2423C22semidirect
131. #2422C22semidirect
132. #2421C22semidirect
133. #2420C22semidirect
134. #2417C22semidirect
135. #2416C22semidirect
136. #2412C22semidirect
137. #2412C22semidirect
138. #2411C22semidirect
140. #2409C22semidirect
143. #2407C22semidirect
144. #2398C22semidirect
145. #2398C22semidirect
146. #2341C22semidirect
147. #2341C22semidirect
148. Q8×C22⋊C4C22semidirect
149. Q8×C22⋊C4C22semidirect
154. #2328C22semidirect
155. #2327C22semidirect
156. #2326C22semidirect
157. #2326C22semidirect
158. #2326C22semidirect
159. #2326C22semidirect
160. #2326C22semidirect
161. #2326C22semidirect
162. #2325C22semidirect
163. #2325C22semidirect
164. #2316C22semidirect
165. #2316C22semidirect
169. #2311C22semidirect
170. #2311C22semidirect
175. #2297C22semidirect
176. #2297C22semidirect
177. #2297C22semidirect
178. #2297C22semidirect
179. C2×#391C22semidirect
181. #2290C22semidirect
182. #2290C22semidirect
183. C2×#388C22semidirect
185. C2×#385C22semidirect
186. #2285C22semidirect
187. C2×#384C22semidirect
188. C2×#376C22semidirect
245. C2×#124D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35102
C2×#35002
#453192
#453072
#450842
#450572
#380862
#380772
#377512
#377502
#376992
#376962
#356732
#356602
#355412
#355132
#352802
#352732
#351682
#351532
#346372
#342572
#342562
#340702
C2×#23262