Finite Group Databasebeta

← #7658069

Subgroups — #7658069

Order 512.

4573 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42738C214yesmaximal, complemented
2#42733C214yesmaximal, complemented
3#41494C218yesmaximal, complemented
4#41493C218yesmaximal, complemented
5#39769C211yesmaximal, characteristic, complemented
6#39762C211yesmaximal, characteristic, complemented
7#38943C212yesmaximal, complemented
8#38057C214yesmaximal, complemented
9#37705C212yesmaximal, complemented
10#37695C212yesmaximal, complemented
11#37630C212yesmaximal, complemented
12#37495C214yesmaximal, complemented
13#36274C212yesmaximal
14D4×C4⋊Q8C211yesmaximal, characteristic, complemented
15D4×#125C211yesmaximal, characteristic, complemented
16#35961C214yesmaximal, complemented
17#35888C214yesmaximal
18#35319C211yesmaximal, characteristic, complemented
19#35315C212yesmaximal, complemented
20#34629C211yesmaximal, characteristic, complemented
21C2×#2642C212yesmaximal, complemented
22#34334C212yesmaximal, complemented
23#34123C211yesmaximal, characteristic
24C2×D4×Q8C2212yes—
25C2×#541C2212yes—
26C22×C4⋊Q8C2212yes—
27C22×#125C2212yes—
28C2×C4×#41C2211yescharacteristic
29#2868C2211yescharacteristic
30#2859C2211yescharacteristic
31#2857C2212yes—
32#2857C2212yes—
33#2855C2214yes—
34#2851C2212yes—
35#2839C2218yes—
36#2833C2218yes—
37#2831C2218yes—
38#2794C2218yes—
39#2776C2218yes—
40#2769C2218yes—
41#2762C2218yes—
42#2762C2218yes—
43#2758C2218yes—
44#2755C2218yes—
45#2744C2218yes—
46#2725C2218yes—
47#2719C2218yes—
48#2716C2218yes—
49#2713C2218yes—
50#2666C2218yes—
51#2655C2218yes—
52#2655C2214yes—
53#2652C2214yes—
54#2650C2218yes—
55#2647C2211yescharacteristic
56#2647C2214yes—
57#2646C2218yes—
58#2645C2214yes—
59#2645C2212yes—
60#2645C2214yes—
61#2643C2218yes—
62#2642C2218yes—
63#2642C2218yes—
64#2642C2214yes—
65#2642C2212yes—
66#2642C2211yescharacteristic
67#2642C2212yes—
68#2642C2214yes—
69#2642C2212yes—
70#2629C2211yescharacteristic
71#2625C2212yes—
72#2621C2211yescharacteristic
73#2621C2212yes—
74#2582C2212yes—
75#2571C2214yes—
76#2570C2214yes—
77#2569C2218yes—
78#2568C2212yes—
79#2552C2212yes—
80#2551C2214yes—
81#2546C2212yes—
82#2533C2218yes—
83#2528C2218yes—
84#2514C2214yes—
85#2514C2214yes—
86#2511C2214yes—
87#2511C2214yes—
88#2510C2218yes—
89#2509C2214yes—
90#2509C2214yes—
91#2508C2214yes—
92#2506C2214yes—
93#2506C2214yes—
94#2506C2214yes—
95#2505C2218yes—
96#2505C2218yes—
97#2505C2218yes—
98#2497C2214yes—
99#2496C2214yes—
100#2496C2214yes—
101#2495C2214yes—
102#2493C2218yes—
103#2493C2218yes—
104#2493C2218yes—
105#2489C2214yes—
106#2481C2218yes—
107#2481C2218yes—
108#2473C2218yes—
109#2473C2218yes—
110#2453C2214yes—
111#2451C2214yes—
112#2450C2218yes—
113#2446C2214yes—
114#2446C2214yes—
115#2442C2214yes—
116#2442C2218yes—
117#2440C2218yes—
118#2439C2214yes—
119#2438C2218yes—
120#2434C2214yes—
121#2429C2214yes—
122#2417C2214yes—
123#2409C2214yes—
124#2402C2214yes—
125#2401C2214yes—
126C2×#400C2218yes—
127C2×#400C2218yes—
128#2369C2214yes—
129#2368C2218yes—
130#2365C2212yes—
131#2360C2214yes—
132#2356C2212yes—
133#2355C2212yes—
134#2353C2214yes—
135#2349C2214yes—
136#2349C2212yes—
137#2349C2214yes—
138D4×C4⋊C4C2212yes—
139D4×C4⋊C4C2214yes—
140D4×C4⋊C4C2214yes—
141#2346C2212yes—
142#2343C2214yes—
143Q8×C22⋊C4C2214yes—
144#2339C2212yes—
145#2339C2214yes—
146#2331C2214yes—
147#2330C2212yes—
148#2329C2218yes—
149#2327C2212yes—
150#2327C2212yes—
151#2320C2214yes—
152C4×C4⋊Q8C2211yescharacteristic
153C4×C4⋊Q8C2212yes—
154C4×#125C2211yescharacteristic
155C4×C22⋊Q8C2214yes—
156C4×C22⋊Q8C2212yes—
157#2295C2212yes—
158#2295C2211yescharacteristic
159#2295C2211yescharacteristic
160C2×#391C2214yes—
161C2×#391C2214yes—
162#2290C2212yes—
163#2290C2212yes—
164#2283C2211yescharacteristic
165#2283C2212yes—
166#2275C2214yes—
167C42×D4C2211yescharacteristic
168C42×D4C2211yescharacteristic
169C4×#117C2211yescharacteristic
170C2×#376C2212yes—
171C22×#41C2311yescharacteristic
172C23×Q8C2314yes—
173D4×Q8—216no—
174#541—48no—
175C2×C4⋊Q8—48no—
176C2×C4⋊Q8C2312yes—
177C2×C4⋊Q8C2311yescharacteristic
178C2×C4⋊Q8C2312yes—
179C2×C4⋊Q8C2314yes—
180C2×C4⋊Q8C2312yes—
181C2×C4⋊Q8C2314yes—
182C2×C4⋊Q8C2318yes—
183C2×#126C2318yes—
184C2×#125—48no—
185C2×#125C2311yescharacteristic
186C2×#125C2312yes—
187C2×#125C2314yes—
188C2×#125C2318yes—
189C2×#125C2318yes—
190C2×C22⋊Q8C2318yes—
191C2×C22⋊Q8C2314yes—
192C2×C22⋊Q8C2314yes—
193C2×C22⋊Q8C2312yes—
194C4×#41—28no—
195C2×C4×Q8C2312yes—
196C2×C4×Q8C2311yescharacteristic
197C2×C4×Q8C2311yescharacteristic
198C2×C4×Q8C2314yes—
199C2×C4×Q8C2314yes—
200C2×C4×D4C2312yes—
201C2×C4×D4C2314yes—
202C2×C4×D4C2314yes—
203C2×C4×D4C2312yes—
204C2×C4×D4C2311yescharacteristic
205C2×C4×D4C2312yes—
206C2×C4×D4C2312yes—
207C2×C4×D4C2311yescharacteristic
208C2×#117C2312yes—
209C2×#117C2311yescharacteristic
210C2×#117C2311yescharacteristic
211C2×#117C2311yescharacteristic
212C22×C4⋊C4C2314yes—
213C22×C4⋊C4C2318yes—
214C22×C4⋊C4C2318yes—
215C22×C42C2312yes—
216C22×C42C2312yes—
217C22×C42C2311yescharacteristic
218C22×C42C2312yes—
219#401C2318yes—
220#401C2318yes—
221#401C2314yes—
222#400C2318yes—
223#400C2314yes—
224#400C2318yes—
225#400C2318yes—
226#400C2318yes—
227#400C2318yes—
228#400C2318yes—
229#400C2318yes—
230#400C2314yes—
231#400C2318yes—
232#400C2318yes—
233#400C2318yes—
234#400C2318yes—
235#400C2318yes—
236#400C2318yes—
237#400C2318yes—
238#400C2314yes—
239#400C2314yes—
240#400C2318yes—
241#400C2318yes—
242#400C2318yes—
243#400C2318yes—
244#400C2318yes—
245#400C2318yes—
246#400C2318yes—
247#400C2318yes—
248#400C2318yes—
249#400C2318yes—
250#400C2314yes—
251#400C2314yes—
252#400C2314yes—
253#398C2318yes—
254#398C2318yes—
255#398C2318yes—
256#398C2318yes—
257#398C2318yes—
258#398C2318yes—
259#398C2318yes—
260#398C2318yes—
261#398C2318yes—
262#398C2318yes—
263#398C2314yes—
264#398C2314yes—
265#398C2314yes—
266#398C2314yes—
267#397C2314yes—
268#397C2318yes—
269#397C2318yes—
270#397C2314yes—
271#397C2314yes—
272#396C2318yes—
273#396C2318yes—
274#396C2314yes—
275#395C2318yes—
276#395C2318yes—
277#395C2318yes—
278#393C2318yes—
279#391C2314yes—
280#391C2312yes—
281#391C2314yes—
282#391C2314yes—
283#391C2314yes—
284#391C2318yes—
285#391C2314yes—
286#391C2314yes—
287#391C2314yes—
288#391C2314yes—
289#391C2318yes—
290#391C2318yes—
291#391C2318yes—
292#391C2312yes—
293#391C2312yes—
294#391C2312yes—
295#391C2314yes—
296#391C2314yes—
297#391C2312yes—
298#391C2312yes—
299#391C2318yes—
300#391C2318yes—
301#389C2312yes—
302#389C2314yes—
303#389C2314yes—
304#389C2314yes—
305#389C2312yes—
306#389C2314yes—
307#389C2314yes—
308#389C2314yes—
309#389C2318yes—
310#389C2312yes—
311#389C2314yes—
312#389C2314yes—
313#389C2314yes—
314#389C2318yes—
315#389C2318yes—
316#389C2314yes—
317#389C2314yes—
318#389C2318yes—
319#389C2312yes—
320#389C2314yes—
321#389C2314yes—
322#389C2314yes—
323#389C2314yes—
324#389C2312yes—
325#389C2312yes—
326#389C2318yes—
327#388C2314yes—
328#388C2314yes—
329#388C2318yes—
330#388C2318yes—
331#387C2314yes—
332#387C2318yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2314yes—
341#387C2318yes—
342#387C2318yes—
343#387C2314yes—
344#387C2314yes—
345#387C2314yes—
346#387C2318yes—
347#387C2318yes—
348#387C2318yes—
349#387C2318yes—
350#387C2318yes—
351#387C2314yes—
352#387C2314yes—
353#387C2318yes—
354#387C2318yes—
355#387C2314yes—
356#387C2318yes—
357#387C2318yes—
358#387C2318yes—
359#386C2314yes—
360#386C2314yes—
361#386C2318yes—
362#386C2318yes—
363#385C2318yes—
364#385C2318yes—
365#385C2318yes—
366#385C2318yes—
367#385C2318yes—
368#385C2314yes—
369#385C2314yes—
370#385C2318yes—
371#385C2318yes—
372#385C2318yes—
373#385C2318yes—
374#385C2314yes—
375#384C2312yes—
376#384C2311yescharacteristic
377#384C2314yes—
378#384C2314yes—
379#384C2314yes—
380#383C2318yes—
381#383C2312yes—
382#383C2314yes—
383#383C2318yes—
384#382C2311yescharacteristic
385#382C2314yes—
386#382C2312yes—
387#382C2318yes—
388#382C2314yes—
389#382C2312yes—
390#382C2314yes—
391#382C2318yes—
392#381C2314yes—
393#381C2318yes—
394#381C2312yes—
395#380C2314yes—
396#380C2318yes—
397#380C2318yes—
398#380C2314yes—
399#380C2312yes—
400#380C2314yes—
401#380C2318yes—
402#380C2314yes—
403#380C2318yes—
404#380C2312yes—
405C4×C4⋊C4C2312yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2312yes—
414C4×C4⋊C4C2312yes—
415C4×C4⋊C4C2312yes—
416C4×C4⋊C4C2312yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2318yes—
421C4×C4⋊C4C2312yes—
422C4×C4⋊C4C2312yes—
423C4×C4⋊C4C2311yescharacteristic
424C4×C22⋊C4C2318yes—
425C4×C22⋊C4C2314yes—
426C4×C22⋊C4C2318yes—
427C4×C22⋊C4C2312yes—
428C4×C22⋊C4C2314yes—
429C4×C22⋊C4C2312yes—
430C4×C22⋊C4C2318yes—
431C4×C22⋊C4C2314yes—
432C4×C22⋊C4C2312yes—
433C4×C22⋊C4C2312yes—
434C4×C22⋊C4C2312yes—
435#376C2312yes—
436#376C2311yescharacteristic
437#376C2312yes—
438#376C2314yes—
439#376C2314yes—
440#376C2314yes—
441#376C2311yescharacteristic
442#376C2312yes—
443C2×#95C2318yes—
444C2×#95C2318yes—
445C2×#95C2314yes—
446C2×#95C2318yes—
447C2×#95C2314yes—
448C2×#95C2318yes—
449C43C2311yescharacteristic
450C43C2311yescharacteristic
451C2×#41—24no—
452C2×#41—28no—
453C22×Q8—216no—
454C22×Q8—48no—
455C22×Q8—48no—
456C22×Q8C2414yes—
457C22×Q8C2411yescharacteristic
458C22×Q8C2412yes—
459C22×Q8C2418yes—
460C22×D4C2412yes—
461C22×D4C2411yescharacteristic
462C23×C4C2411yescharacteristic
463C23×C4C2412yes—
464C23×C4C2411yescharacteristic
465C23×C4C2414yes—
466C23×C4C2412yes—
467C23×C4C2418yes—
468C23×C4C2418yes—
469C23×C4C2412yes—
470C23×C4C2411yescharacteristic
471C23×C4C2414yes—
472C4⋊Q8—216no—
473C4⋊Q8—28no—
474C4⋊Q8—24no—
475C4⋊Q8—28no—
476C4⋊Q8—416no—
477C4⋊Q8—48no—
478C4⋊Q8—44no—
479#126—416no—
480#125—24no—
481#125—28no—
482#125—48no—
483#125—416no—
484#125—416no—
485C22⋊Q8—216no—
486C22⋊Q8—232no—
487C22⋊Q8—44no—
488C22⋊Q8—48no—
489C4×Q8—24no—
490C4×Q8—24no—
491C4×Q8—28no—
492C4×Q8—48no—
493C4×Q8—48no—
494C4×D4—24no—
495C4×D4—216no—
496C4×D4—28no—
497C4×D4—216no—
498C4×D4—28no—
499C4×D4—28no—
500C4×D4—28no—
501C4×D4#4118yes—
502#117—24no—
503#117—28no—
504#117—24no—
505#117—42no—
506C2×C4⋊C4—48no—
507C2×C4⋊C4—416no—
508C2×C4⋊C4—416no—
509C2×C4⋊C4C2412yes—
510C2×C4⋊C4C2414yes—
511C2×C4⋊C4C2414yes—
512C2×C4⋊C4C2414yes—
513C2×C4⋊C4C2418yes—
514C2×C4⋊C4C2418yes—
515C2×C4⋊C4C2411yescharacteristic
516C2×C4⋊C4C2412yes—
517C2×C4⋊C4C2412yes—
518C2×C4⋊C4C2412yes—
519C2×C4⋊C4C2414yes—
520C2×C4⋊C4C2412yes—
521C2×C4⋊C4C2412yes—
522C2×C4⋊C4C2414yes—
523C2×C4⋊C4C2412yes—
524C2×C4⋊C4C2412yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2418yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2418yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2412yes—
534C2×C4⋊C4C2418yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2418yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2411yescharacteristic
550C2×C22⋊C4C2412yes—
551C2×C22⋊C4C2412yes—
552C2×C22⋊C4C2412yes—
553C2×C22⋊C4C2418yes—
554C2×C22⋊C4C2414yes—
555C2×C22⋊C4C2414yes—
556C2×C22⋊C4C2418yes—
557C2×C22⋊C4C2412yes—
558C2×C22⋊C4C2418yes—
559C2×C22⋊C4C2414yes—
560C2×C22⋊C4C2414yes—
561C2×C22⋊C4C2414yes—
562C2×C22⋊C4C2412yes—
563C2×C42—28no—
564C2×C42—24no—
565C2×C42—28no—
566C2×C42—44no—
567C2×C42C2412yes—
568C2×C42C2411yescharacteristic
569C2×C42C2411yescharacteristic
570C2×C42C2411yescharacteristic
571C2×C42C2411yescharacteristic
572C2×C42C2414yes—
573C2×C42C2412yes—
574C2×C42C2412yes—
575C2×C42C2411yescharacteristic
576C2×C42C2412yes—
577C2×C42C2412yes—
578C2×C42C2414yes—
579C2×C42C2412yes—
580C2×C42C2412yes—
581C2×C42C2414yes—
582C2×C42C2411yescharacteristic
583C2×C42C2418yes—
584C2×C42C2418yes—
585C2×C42C2412yes—
586C2×C42C2412yes—
587C2×C42C2414yes—
588C2×C42C2418yes—
589C2×C42C2411yescharacteristic
590C2×C42C2411yescharacteristic
591#95C2412yes—
592#95C2412yes—
593#95C2414yes—
594#95C2414yes—
595#95C2414yes—
596#95C2414yes—
597#95C2414yes—
598#95C2414yes—
599#95C2414yes—
600#95C2414yes—
601#95C2414yes—
602#95C2414yes—
603#95C2418yes—
604#95C2418yes—
605#95C2418yes—
606#95C2418yes—
607#95C2418yes—
608#95C2418yes—
609#95C2418yes—
610#95C2418yes—
611#95C2418yes—
612#95C2418yes—
613#95C2418yes—
614#95C2418yes—
615#95C2414yes—
616#95C2414yes—
617#95C2414yes—
618#95C2412yes—
619#95C2412yes—
620#95C2412yes—
621#95C2412yes—
622#95C2414yes—
623#95C2414yes—
624#95C2414yes—
625#95C2414yes—
626#95C2414yes—
627#95C2414yes—
628#95C2418yes—
629#95C2414yes—
630#95C2414yes—
631#95C2418yes—
632#95C2414yes—
633#95C2414yes—
634#95C2414yes—
635#95C2414yes—
636#95C2414yes—
637#95C2418yes—
638#95C2418yes—
639#95C2418yes—
640#95C2418yes—
641#95C2418yes—
642#95C2418yes—
643#95C2418yes—
644C24C2511yescharacteristic
645C24C2512yes—
646#41—416no—
647C2×Q8—22no—
648C2×Q8—24no—
649C2×Q8—28no—
650C2×Q8—216no—
651C2×Q8—28no—
652C2×Q8—24no—
653C2×Q8—24no—
654C2×Q8—28no—
655C2×Q8—24no—
656C2×Q8—48no—
657C2×Q8—48no—
658C2×Q8—832no—
659C2×D4—24no—
660C2×D4—28no—
661C2×D4C2×#4114yes—
662C2×D42−1+418yes—
663C22×C4—24no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—28no—
667C22×C4—28no—
668C22×C4—24no—
669C22×C4—216no—
670C22×C4—216no—
671C22×C4—28no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—28no—
675C22×C4—22no—
676C22×C4—24no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—44no—
680C22×C4—44no—
681C22×C4—48no—
682C22×C4—48no—
683C22×C4—42no—
684C22×C4—44no—
685C22×C4—48no—
686C22×C4—44no—
687C22×C4—48no—
688C22×C4C2×#4118yes—
689C22×C4C2511yescharacteristic
690C22×C4C2512yes—
691C22×C4C2512yes—
692C22×C4C2511yescharacteristic
693C22×C4C2514yes—
694C22×C4C2512yes—
695C22×C4C2514yes—
696C22×C4C2512yes—
697C22×C4C2514yes—
698C22×C4C2514yes—
699C22×C4C2514yes—
700C22×C4C2514yes—
701C22×C4C2518yes—
702C22×C4C2512yes—
703C22×C4C2518yes—
704C22×C4C2511yescharacteristic
705C22×C4C2511yescharacteristic
706C22×C4C2512yes—
707C22×C4C2512yes—
708C22×C4C2511yescharacteristic
709C22×C4C2511yescharacteristic
710C4⋊C4—22no—
711C4⋊C4—24no—
712C4⋊C4—24no—
713C4⋊C4—28no—
714C4⋊C4—24no—
715C4⋊C4—28no—
716C4⋊C4—216no—
717C4⋊C4—28no—
718C4⋊C4—28no—
719C4⋊C4—24no—
720C4⋊C4—28no—
721C4⋊C4—28no—
722C4⋊C4—216no—
723C4⋊C4—216no—
724C4⋊C4—24no—
725C4⋊C4—24no—
726C4⋊C4—24no—
727C4⋊C4—28no—
728C4⋊C4—24no—
729C4⋊C4—48no—
730C4⋊C4—48no—
731C4⋊C4—48no—
732C4⋊C4—48no—
733C4⋊C4—48no—
734C4⋊C4—44no—
735C4⋊C4—44no—
736C4⋊C4—44no—
737C4⋊C4—44no—
738C4⋊C4—44no—
739C4⋊C4—44no—
740C4⋊C4—44no—
741C4⋊C4—48no—
742C4⋊C4—48no—
743C4⋊C4—44no—
744C4⋊C4—42no—
745C4⋊C4—48no—
746C4⋊C4—48no—
747C4⋊C4—44no—
748C4⋊C4—48no—
749C4⋊C4—48no—
750C4⋊C4C2×#4114yes—
751C22⋊C4—24no—
752C22⋊C4—216no—
753C22⋊C4—28no—
754C22⋊C4—28no—
755C22⋊C4—216no—
756C22⋊C4—24no—
757C22⋊C4—24no—
758C22⋊C4—44no—
759C22⋊C4—44no—
760C22⋊C4—42no—
761C22⋊C4—44no—
762C22⋊C4—48no—
763C22⋊C4C2×#4118yes—
764C42—22no—
765C42—24no—
766C42—22no—
767C42—22no—
768C42—24no—
769C42—24no—
770C42—28no—
771C42—28no—
772C42—24no—
773C42—22no—
774C42—24no—
775C42—24no—
776C42—28no—
777C42—22no—
778C42—24no—
779C42—22no—
780C42—44no—
781C42—42no—
782C42—42no—
783C42—48no—
784C42—48no—
785C42—48no—
786C42C2×#4114yes—
787C42H(5,𝔽2)14yes—
788C23—22no—
789C23—22no—
790C23—24no—
791C23—21no—
792C23—21no—
793C23—22no—
794C23—21no—
795C23—22no—
796C23C22×#4114yes—
797C23C2×2−1+418yes—
798C23C2611yescharacteristic
799Q8—44no—
800Q8—416no—
801Q8—48no—
802Q8—816no—
803D4—48no—
804D4#541116yescomplemented
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—216no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—28no—
819C2×C4—24no—
820C2×C4—22no—
821C2×C4—28no—
822C2×C4—28no—
823C2×C4—24no—
824C2×C4—21no—
825C2×C4—24no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—22no—
831C2×C4—24no—
832C2×C4—28no—
833C2×C4—24no—
834C2×C4—22no—
835C2×C4—24no—
836C2×C4—24no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—24no—
840C2×C4—28no—
841C2×C4—24no—
842C2×C4—21no—
843C2×C4—24no—
844C2×C4—24no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—28no—
848C2×C4—22no—
849C2×C4—24no—
850C2×C4—24no—
851C2×C4—24no—
852C2×C4—24no—
853C2×C4—24no—
854C2×C4—22no—
855C2×C4—416no—
856C2×C4—48no—
857C2×C4—44no—
858C2×C4—44no—
859C2×C4—82no—
860C2×C4—84no—
861C2×C4—816no—
862C2×C4—88no—
863C2×C4—816no—
864C2×C4C22×#4114yes—
865C2×C4C22×#4112yes—
866C2×C4C22×#4112yes—
867C2×C4C22×#4112yes—
868C2×C4C2×H(5,𝔽2)14yes—
869C2×C4C2×H(5,𝔽2)12yes—
870C2×C4C2×2−1+414yes—
871C2×C4#58512yes—
872C22—24no—
873C22—24no—
874C22—28no—
875C22—28no—
876C22—41no—
877C22—41no—
878C22—41no—
879C22—42no—
880C22—42no—
881C22C2×#54118yes—
882C22C23×#4111yescharacteristic
883C22C22×H(5,𝔽2)11yescharacteristic
884C22C22×2−1+412yes—
885C22C2×#58511yescharacteristic
886C222−1+612yes—
887C4—24no—
888C4—22no—
889C4—24no—
890C4—41no—
891C4—44no—
892C4—48no—
893C4—44no—
894C4—42no—
895C4—41no—
896C4—41no—
897C4—42no—
898C4—42no—
899C4—44no—
900C4—48no—
901C4—44no—
902C4—42no—
903C4—44no—
904C4—44no—
905C4—42no—
906C4C2×#54114yes—
907C4#351414yes—
908C2—28no—
909C2—81no—
910C2C22×#54111yescharacteristic
911C2C2×#351411yescharacteristic
912C2#6286111yescharacteristic
913C2#6294212yes—
914C2#6295012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42738C2semidirect
2. #42733C2semidirect
3. #41494C2semidirect
4. #41493C2semidirect
5. #39769C2semidirect
6. #39762C2semidirect
7. #38943C2semidirect
8. #38057C2semidirect
9. #37705C2semidirect
10. #37695C2semidirect
11. #37630C2semidirect
12. #37495C2semidirect
14. D4×C4⋊Q8C2semidirect
15. D4×#125C2semidirect
16. #35961C2semidirect
18. #35319C2semidirect
19. #35315C2semidirect
20. #34629C2semidirect
21. C2×#2642C2semidirect
22. #34334C2semidirect
804. D4#541semidirect

Maximal subgroups

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

subgroupindex
#427382
#427332
#414942
#414932
#397692
#397622
#389432
#380572
#377052
#376952
#376302
#374952
#362742
D4×C4⋊Q82
D4×#1252
#359612
#358882
#353192
#353152
#346292
C2×#26422
#343342
#341232