Finite Group Databasebeta

← #7672855

Subgroups — #7672855

Order 512.

4988 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#43576C218yesmaximal, complemented
2#43151C218yesmaximal, complemented
3#39799C214yesmaximal, complemented
4#39798C214yesmaximal, complemented
5#39797C214yesmaximal, complemented
6#39796C214yesmaximal, complemented
7#37959C214yesmaximal, complemented
8#37958C214yesmaximal, complemented
9#37957C214yesmaximal, complemented
10#37956C214yesmaximal, complemented
11#35370C214yesmaximal, complemented
12#35019C212yesmaximal
13#35010C212yesmaximal, complemented
14C2×#2659C211yesmaximal, characteristic, complemented
15#34212C212yesmaximal, complemented
16#34185C212yesmaximal, complemented
17C2×#2329C211yesmaximal, characteristic, complemented
18C2×#2325C211yesmaximal, characteristic
19C22×C22⋊Q8C2212yes—
20C22×C22⋊Q8C2211yescharacteristic
21C22×#121C2211yescharacteristic
22C22×C4×D4C2212yes—
23#2855C2214yes—
24#2850C2214yes—
25#2850C2214yes—
26#2848C2214yes—
27#2789C2218yescomplemented
28#2788C2218yescomplemented
29#2787C2218yescomplemented
30#2786C2218yescomplemented
31#2783C2218yescomplemented
32#2777C2218yescomplemented
33#2775C2218yescomplemented
34#2767C2218yescomplemented
35#2762C2218yescomplemented
36#2759C2218yescomplemented
37#2758C2218yescomplemented
38#2745C2218yescomplemented
39#2740C2218yescomplemented
40#2715C2218yescomplemented
41#2700C2218yescomplemented
42#2689C2218yescomplemented
43#2659C2214yes—
44#2659C2214yes—
45#2659C2214yescomplemented
46#2659C2214yescomplemented
47#2639C2214yes—
48#2639C2214yes—
49#2627C2214yes—
50#2626C2214yes—
51#2605C2218yescomplemented
52#2604C2218yescomplemented
53#2601C2218yescomplemented
54#2599C2218yescomplemented
55#2594C2218yescomplemented
56#2591C2218yes—
57#2588C2218yescomplemented
58#2579C2218yescomplemented
59#2577C2218yescomplemented
60#2564C2218yescomplemented
61#2561C2218yes—
62#2560C2218yescomplemented
63#2532C2218yescomplemented
64#2528C2218yescomplemented
65#2524C2218yescomplemented
66#2521C2218yescomplemented
67#2510C2218yescomplemented
68#2510C2218yescomplemented
69#2510C2218yescomplemented
70#2510C2218yescomplemented
71#2504C2214yes—
72#2503C2214yes—
73#2493C2218yes—
74#2493C2218yes—
75#2487C2214yescomplemented
76#2481C2218yescomplemented
77#2481C2218yescomplemented
78#2481C2218yescomplemented
79#2481C2218yescomplemented
80#2480C2218yes—
81#2480C2218yes—
82#2478C2218yescomplemented
83#2474C2218yescomplemented
84#2469C2218yescomplemented
85#2465C2218yescomplemented
86#2436C2214yes—
87#2435C2214yes—
88#2417C2214yescomplemented
89#2417C2214yescomplemented
90#2409C2214yescomplemented
91C2×#398C2214yescomplemented
92C2×#395C2214yescomplemented
93#2368C2218yes—
94#2360C2214yes—
95#2360C2214yes—
96#2353C2218yescomplemented
97#2353C2218yescomplemented
98#2352C2214yescomplemented
99#2352C2214yescomplemented
100#2352C2214yescomplemented
101#2352C2214yescomplemented
102#2345C2214yescomplemented
103#2345C2218yescomplemented
104Q8×C22⋊C4C2214yescomplemented
105#2329C2214yes—
106#2329C2214yes—
107#2329C2218yescomplemented
108#2329C2214yescomplemented
109#2329C2214yescomplemented
110#2325C2218yes—
111#2325C2214yes—
112#2325C2214yes—
113#2315C2214yes—
114#2313C2214yes—
115#2312C2214yes—
116#2308C2214yes—
117#2308C2214yes—
118C4×C22⋊Q8C2214yescomplemented
119C4×C22⋊Q8C2214yescomplemented
120C2×#391C2212yescomplemented
121C2×#389C2212yescomplemented
122C2×#388C2212yes—
123C2×#387C2212yes—
124C2×#387C2212yescomplemented
125C2×#387C2212yescomplemented
126C2×#386C2212yes—
127C2×#386C2212yes—
128C2×#385C2212yes—
129C2×#385C2212yes—
130#2283C2214yes—
131#2280C2214yes—
132C2×#380C2212yes—
133C2×#380C2212yes—
134C2×#380C2211yescharacteristic
135C2×#380C2211yescharacteristic
136#2273C2214yes—
137C2×C4×C22⋊C4C2212yes—
138C22×#95C2211yescharacteristic
139C23×Q8C2312yes—
140C23×Q8C2311yescharacteristic
141C23×D4C2312yes—
142C23×D4C2311yescharacteristic
143C24×C4C2312yes—
144C24×C4C2311yescharacteristic
145C24×C4C2311yescharacteristic
146C24×C4C2311yescharacteristic
147C2×#126C2318yes—
148C2×#126C2318yes—
149C2×#124C2314yes—
150C2×#124C2314yes—
151C2×C22⋊Q8—28no—
152C2×C22⋊Q8—216no—
153C2×C22⋊Q8C2314yes—
154C2×C22⋊Q8C2314yes—
155C2×C22⋊Q8C2314yes—
156C2×C22⋊Q8C2314yes—
157C2×C22⋊Q8C2314yes—
158C2×C22⋊Q8C2314yes—
159C2×C22⋊Q8C2314yes—
160C2×C22⋊Q8C2314yes—
161C2×#121—28no—
162C2×#121C2314yes—
163C2×#121C2314yes—
164C2×C4×Q8C2314yes—
165C2×C4×Q8C2314yes—
166C2×C4×D4—216no—
167C2×C4×D4C2314yes—
168C2×C4×D4C2314yes—
169C2×C4×D4C2314yes—
170C2×C4×D4C2314yes—
171C2×#117C2314yes—
172C2×#117C2314yes—
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2314yes—
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2312yes—
182C22×C4⋊C4C2312yes—
183C22×C4⋊C4C2311yescharacteristic
184C22×C4⋊C4C2311yescharacteristic
185C22×C4⋊C4C2312yes—
186C22×C4⋊C4C2312yes—
187C22×C4⋊C4C2312yes—
188C22×C4⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2314yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C42C2312yes—
198C22×C42C2312yes—
199C22×C42C2312yes—
200#401C2318yes—
201#401C2318yes—
202#400C2318yes—
203#400C2318yes—
204#400C2318yes—
205#400C2318yes—
206#400C2318yes—
207#400C2318yes—
208#400C2318yes—
209#400C2318yes—
210#400C2318yes—
211#399C2318yes—
212#398C2318yes—
213#398C2318yes—
214#398C2318yes—
215#398C2318yes—
216#398C2318yes—
217#398C2318yes—
218#397C2318yes—
219#397C2318yes—
220#397C2318yes—
221#397C2318yes—
222#397C2318yes—
223#397C2318yes—
224#397C2318yes—
225#397C2318yes—
226#396C2318yes—
227#396C2318yes—
228#396C2318yes—
229#396C2318yes—
230#395C2318yes—
231#395C2318yes—
232#395C2318yes—
233#395C2318yes—
234#395C2318yes—
235#394C2318yes—
236#394C2318yes—
237#393C2318yes—
238#393C2318yes—
239#393C2318yes—
240#391C2318yes—
241#391C2318yes—
242#391C2318yes—
243#391C2318yes—
244#391C2314yes—
245#391C2314yes—
246#391C2314yes—
247#391C2314yes—
248#391C2314yes—
249#391C2314yes—
250#390C2314yes—
251#390C2314yes—
252#389C2318yes—
253#389C2318yes—
254#389C2318yes—
255#389C2318yes—
256#389C2314yes—
257#389C2314yes—
258#389C2314yes—
259#389C2314yes—
260#388C2318yes—
261#388C2318yes—
262#388C2318yes—
263#388C2318yes—
264#388C2318yes—
265#388C2318yes—
266#388C2318yes—
267#388C2318yes—
268#388C2318yes—
269#388C2318yes—
270#388C2318yes—
271#388C2318yes—
272#388C2318yes—
273#388C2318yes—
274#388C2318yes—
275#388C2318yes—
276#387C2318yes—
277#387C2318yes—
278#387C2318yes—
279#387C2318yes—
280#387C2318yes—
281#387C2318yes—
282#387C2318yes—
283#387C2318yes—
284#387C2318yes—
285#387C2318yes—
286#387C2318yes—
287#387C2318yes—
288#387C2318yes—
289#387C2318yes—
290#387C2318yes—
291#387C2318yes—
292#387C2318yes—
293#387C2318yes—
294#387C2318yes—
295#387C2318yes—
296#387C2318yes—
297#387C2318yes—
298#387C2318yes—
299#387C2318yes—
300#386C2318yes—
301#386C2318yes—
302#386C2318yes—
303#386C2318yes—
304#386C2318yes—
305#386C2318yes—
306#386C2318yes—
307#386C2318yes—
308#386C2318yes—
309#386C2318yes—
310#386C2318yes—
311#386C2318yes—
312#385C2318yes—
313#385C2318yes—
314#385C2318yes—
315#385C2318yes—
316#385C2318yes—
317#385C2318yes—
318#385C2318yes—
319#385C2318yes—
320#385C2318yes—
321#385C2318yes—
322#383C2318yes—
323#383C2318yes—
324#383C2318yes—
325#382C2314yes—
326#382C2314yes—
327#382C2314yes—
328#382C2314yes—
329#381C2318yes—
330#381C2318yes—
331#381C2318yes—
332#380C2318yes—
333#380C2318yes—
334#380C2314yes—
335#380C2314yes—
336#380C2314yes—
337#380C2314yes—
338#380C2314yes—
339#380C2314yes—
340#380C2314yes—
341#380C2314yes—
342#380C2314yes—
343#380C2314yes—
344#380C2314yes—
345#380C2314yes—
346#380C2318yes—
347#380C2318yes—
348#379C2318yes—
349#379C2318yes—
350C4×C4⋊C4C2318yes—
351C4×C4⋊C4C2314yes—
352C4×C4⋊C4C2314yes—
353C4×C4⋊C4C2318yes—
354C4×C4⋊C4C2314yes—
355C4×C4⋊C4C2314yes—
356C4×C22⋊C4C2318yes—
357C4×C22⋊C4C2314yes—
358C4×C22⋊C4C2318yes—
359C4×C22⋊C4C2318yes—
360C4×C22⋊C4C2314yes—
361C4×C22⋊C4C2314yes—
362C4×C22⋊C4C2314yes—
363C4×C22⋊C4C2318yes—
364C4×C22⋊C4C2318yes—
365C4×C22⋊C4C2318yes—
366C4×C22⋊C4C2318yes—
367#376C2318yes—
368C2×#95C2314yes—
369C2×#95C2314yes—
370C2×#95C2312yes—
371C2×#95C2312yes—
372C2×#95C2312yes—
373C2×#95C2312yes—
374C2×#95C2312yes—
375C2×#95C2312yes—
376C2×#95C2312yes—
377C2×#95C2312yes—
378C2×#95C2314yes—
379C2×#95C2312yes—
380C2×#95C2312yes—
381C2×#95C2312yes—
382C2×#95C2312yes—
383C25C2412yes—
384C25C2411yescharacteristic
385C22×Q8—24no—
386C22×Q8—28no—
387C22×Q8—81no—
388C22×Q8—81no—
389C22×Q8—82no—
390C22×Q8—82no—
391C22×Q8C2414yes—
392C22×Q8C2414yes—
393C22×Q8C2414yes—
394C22×D4—28no—
395C22×D4—28no—
396C22×D4—28no—
397C22×D4—24no—
398C22×D4—81no—
399C22×D4—81no—
400C22×D4C2414yes—
401C22×D4C2414yes—
402C22×D4C2414yes—
403C23×C4—24no—
404C23×C4—28no—
405C23×C4—81no—
406C23×C4—81no—
407C23×C4—81no—
408C23×C4—81no—
409C23×C4—81no—
410C23×C4—81no—
411C23×C4—82no—
412C23×C4—82no—
413C23×C4#4118yes—
414C23×C4#4118yes—
415C23×C4C2412yes—
416C23×C4C2412yes—
417C23×C4C2412yes—
418C23×C4C2412yes—
419C23×C4C2414yes—
420C23×C4C2414yes—
421C23×C4C2412yes—
422C23×C4C2412yes—
423C23×C4C2412yes—
424C23×C4C2412yes—
425C23×C4C2412yes—
426C23×C4C2412yes—
427C23×C4C2414yes—
428C23×C4C2414yes—
429C23×C4C2411yescharacteristic
430C23×C4C2412yes—
431C23×C4C2411yescharacteristic
432C23×C4C2412yes—
433C23×C4C2412yes—
434C23×C4C2411yescharacteristic
435C23×C4C2411yescharacteristic
436C23×C4C2412yes—
437#126—88no—
438#126—88no—
439#124—84no—
440#124—84no—
441C22⋊Q8—216no—
442C22⋊Q8—216no—
443C22⋊Q8—216no—
444C22⋊Q8—216no—
445C22⋊Q8—216no—
446C22⋊Q8—216no—
447C22⋊Q8—84no—
448C22⋊Q8—84no—
449#121—216no—
450#121—216no—
451C4×Q8—84no—
452C4×Q8—84no—
453C4×D4—216no—
454C4×D4—216no—
455C4×D4—216no—
456C4×D4—216no—
457#117—84no—
458#117—84no—
459C2×C4⋊C4—28no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—28no—
463C2×C4⋊C4—28no—
464C2×C4⋊C4—216no—
465C2×C4⋊C4—81no—
466C2×C4⋊C4—81no—
467C2×C4⋊C4—82no—
468C2×C4⋊C4—82no—
469C2×C4⋊C4—81no—
470C2×C4⋊C4—81no—
471C2×C4⋊C4—82no—
472C2×C4⋊C4—82no—
473C2×C4⋊C4—82no—
474C2×C4⋊C4—82no—
475C2×C4⋊C4C2414yes—
476C2×C4⋊C4C2414yes—
477C2×C4⋊C4C2414yes—
478C2×C4⋊C4C2418yes—
479C2×C4⋊C4C2414yes—
480C2×C4⋊C4C2414yes—
481C2×C4⋊C4C2414yes—
482C2×C4⋊C4C2418yes—
483C2×C4⋊C4C2418yes—
484C2×C4⋊C4C2414yes—
485C2×C4⋊C4C2414yes—
486C2×C4⋊C4C2414yes—
487C2×C4⋊C4C2414yes—
488C2×C4⋊C4C2414yes—
489C2×C4⋊C4C2414yes—
490C2×C4⋊C4C2414yes—
491C2×C4⋊C4C2414yes—
492C2×C4⋊C4C2418yes—
493C2×C4⋊C4C2418yes—
494C2×C4⋊C4C2418yes—
495C2×C4⋊C4C2418yes—
496C2×C4⋊C4C2418yes—
497C2×C4⋊C4C2418yes—
498C2×C4⋊C4C2418yes—
499C2×C4⋊C4C2418yes—
500C2×C22⋊C4—28no—
501C2×C22⋊C4—28no—
502C2×C22⋊C4—216no—
503C2×C22⋊C4—28no—
504C2×C22⋊C4—28no—
505C2×C22⋊C4—28no—
506C2×C22⋊C4—82no—
507C2×C22⋊C4—82no—
508C2×C22⋊C4C2414yes—
509C2×C22⋊C4C2414yes—
510C2×C22⋊C4C2414yes—
511C2×C22⋊C4C2414yes—
512C2×C22⋊C4C2418yes—
513C2×C22⋊C4C2418yes—
514C2×C22⋊C4C2414yes—
515C2×C22⋊C4C2414yes—
516C2×C22⋊C4C2418yes—
517C2×C22⋊C4C2414yes—
518C2×C22⋊C4C2414yes—
519C2×C22⋊C4C2418yes—
520C2×C22⋊C4C2418yes—
521C2×C22⋊C4C2418yes—
522C2×C22⋊C4C2418yes—
523C2×C22⋊C4C2418yes—
524C2×C22⋊C4C2418yes—
525C2×C22⋊C4C2418yes—
526C2×C22⋊C4C2418yes—
527C2×C22⋊C4C2418yes—
528C2×C22⋊C4C2418yes—
529C2×C42—28no—
530C2×C42—82no—
531C2×C42—82no—
532C2×C42C2414yes—
533C2×C42C2414yes—
534C2×C42C2418yes—
535C2×C42C2418yes—
536C2×C42C2418yes—
537C2×C42C2414yes—
538C2×C42C2414yes—
539C2×C42C2414yes—
540C2×C42C2414yes—
541C2×C42C2418yes—
542#95C2414yes—
543#95C2414yes—
544#95C2414yes—
545#95C2414yes—
546#95C2418yes—
547#95C2418yes—
548#95C2414yes—
549#95C2414yes—
550#95C2414yes—
551#95C2414yes—
552#95C2418yes—
553#95C2418yes—
554#95C2418yes—
555#95C2418yes—
556#95C2418yes—
557#95C2418yes—
558#95C2418yes—
559#95C2418yes—
560#95C2418yes—
561#95C2418yes—
562#95C2418yes—
563#95C2418yes—
564#95C2418yes—
565#95C2418yes—
566#95C2418yes—
567#95C2418yes—
568#95C2418yes—
569#95C2418yes—
570#95C2418yes—
571#95C2418yes—
572#95C2418yes—
573#95C2418yes—
574#95C2418yes—
575#95C2418yes—
576C24—24no—
577C24—24no—
578C24—24no—
579C24—41no—
580C24—41no—
581C24—41no—
582C24—41no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24C2×#4114yes—
588C24C2×#4114yes—
589C242−1+414yes—
590C24C2514yes—
591C24C2511yescharacteristic
592C24C2511yescharacteristic
593C24C2511yescharacteristic
594C2×Q8—28no—
595C2×Q8—28no—
596C2×Q8—28no—
597C2×Q8—44no—
598C2×Q8—44no—
599C2×Q8—44no—
600C2×Q8—44no—
601C2×Q8—44no—
602C2×Q8—44no—
603C2×Q8—88no—
604C2×Q8—816no—
605C2×D4—28no—
606C2×D4—28no—
607C2×D4—28no—
608C2×D4—28no—
609C2×D4—28no—
610C2×D4—28no—
611C2×D4—28no—
612C2×D4—44no—
613C2×D4—44no—
614C2×D4—432no—
615C2×D4—88no—
616C22×C4—24no—
617C22×C4—24no—
618C22×C4—24no—
619C22×C4—24no—
620C22×C4—24no—
621C22×C4—24no—
622C22×C4—24no—
623C22×C4—28no—
624C22×C4—24no—
625C22×C4—28no—
626C22×C4—24no—
627C22×C4—24no—
628C22×C4—24no—
629C22×C4—24no—
630C22×C4—28no—
631C22×C4—28no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—41no—
637C22×C4—41no—
638C22×C4—41no—
639C22×C4—41no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—44no—
646C22×C4—44no—
647C22×C4—42no—
648C22×C4—42no—
649C22×C4—41no—
650C22×C4—41no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—41no—
654C22×C4—41no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—44no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—44no—
668C22×C4—44no—
669C22×C4—44no—
670C22×C4—44no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—44no—
674C22×C4—88no—
675C22×C4—88no—
676C22×C4—816no—
677C22×C4—88no—
678C22×C4C2×#4118yes—
679C22×C4C2×#4114yes—
680C22×C4C2×#4118yes—
681C22×C4C2×#4114yes—
682C22×C4C2×#4114yes—
683C22×C4C2×#4114yes—
684C22×C4C2×#4118yes—
685C22×C4C2×#4118yes—
686C22×C4C2514yes—
687C22×C4C2514yes—
688C22×C4C2514yes—
689C22×C4C2514yes—
690C22×C4C2514yes—
691C22×C4C2514yes—
692C22×C4C2514yes—
693C22×C4C2518yes—
694C22×C4C2514yes—
695C22×C4C2518yes—
696C22×C4C2512yes—
697C22×C4C2512yes—
698C22×C4C2512yes—
699C22×C4C2512yes—
700C4⋊C4—28no—
701C4⋊C4—28no—
702C4⋊C4—28no—
703C4⋊C4—28no—
704C4⋊C4—28no—
705C4⋊C4—28no—
706C4⋊C4—216no—
707C4⋊C4—216no—
708C4⋊C4—216no—
709C4⋊C4—44no—
710C4⋊C4—44no—
711C4⋊C4—44no—
712C4⋊C4—44no—
713C4⋊C4—44no—
714C4⋊C4—44no—
715C4⋊C4—44no—
716C4⋊C4—44no—
717C4⋊C4—48no—
718C4⋊C4—48no—
719C4⋊C4—48no—
720C4⋊C4—48no—
721C4⋊C4—48no—
722C4⋊C4—48no—
723C4⋊C4—48no—
724C4⋊C4—48no—
725C22⋊C4—28no—
726C22⋊C4—28no—
727C22⋊C4—216no—
728C22⋊C4—28no—
729C22⋊C4—216no—
730C22⋊C4—28no—
731C22⋊C4—28no—
732C22⋊C4—28no—
733C22⋊C4—28no—
734C22⋊C4—28no—
735C22⋊C4—216no—
736C22⋊C4—48no—
737C22⋊C4—48no—
738C22⋊C4—48no—
739C22⋊C4—48no—
740C22⋊C4—48no—
741C22⋊C4—48no—
742C22⋊C4—48no—
743C22⋊C4—48no—
744C22⋊C4—48no—
745C22⋊C4—48no—
746C42—28no—
747C42—28no—
748C42—44no—
749C42—44no—
750C42—44no—
751C42—44no—
752C42—48no—
753C42—48no—
754C42—48no—
755C42—48no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—24no—
769C23—24no—
770C23—24no—
771C23—24no—
772C23—24no—
773C23—24no—
774C23—24no—
775C23—44no—
776C23—44no—
777C23—44no—
778C23—44no—
779C23—44no—
780C23—44no—
781C23—48no—
782C23—48no—
783C23—48no—
784C23—84no—
785C23—84no—
786C23—84no—
787C23—84no—
788C23#556116yes—
789C23C22×#4112yes—
790C23C22×#4112yes—
791C23C22×#4112yes—
792C23C22×#4112yes—
793C23C22×#4112yes—
794C23C22×#4112yes—
795C23C2×2−1+412yes—
796C23C2×2−1+412yes—
797C23C2×2−1+412yes—
798C23C2611yescharacteristic
799Q8—416no—
800Q8—88no—
801Q8—88no—
802D4—416no—
803D4—416no—
804D4—88no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—28no—
817C2×C4—24no—
818C2×C4—24no—
819C2×C4—24no—
820C2×C4—28no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—24no—
831C2×C4—24no—
832C2×C4—24no—
833C2×C4—28no—
834C2×C4—28no—
835C2×C4—28no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—28no—
842C2×C4—24no—
843C2×C4—48no—
844C2×C4—44no—
845C2×C4—48no—
846C2×C4—48no—
847C2×C4—44no—
848C2×C4—44no—
849C2×C4—44no—
850C2×C4—48no—
851C2×C4—416no—
852C2×C4—48no—
853C2×C4—48no—
854C2×C4—48no—
855C2×C4—48no—
856C2×C4—88no—
857C2×C4—88no—
858C2×C4—84no—
859C2×C4—84no—
860C2×C4—84no—
861C2×C4—84no—
862C2×C4—84no—
863C2×C4—84no—
864C2×C4—88no—
865C2×C4C22×#4114yes—
866C2×C4C22×#4114yes—
867C2×C4C22×#4114yes—
868C2×C4C22×#4114yes—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—22no—
878C22—22no—
879C22—22no—
880C22—22no—
881C22—22no—
882C22—22no—
883C22—22no—
884C22—22no—
885C22—22no—
886C22—22no—
887C22—416no—
888C22—44no—
889C22—44no—
890C22—44no—
891C22—44no—
892C22—44no—
893C22—44no—
894C22—44no—
895C22—816no—
896C22C2×#55614yes—
897C22C2×#55614yes—
898C22C2×#55614yes—
899C22C23×#4111yescharacteristic
900C22C23×#4111yescharacteristic
901C22C22×2−1+411yescharacteristic
902C22H(7,𝔽2)11yescharacteristic
903C22H(7,𝔽2)11yescharacteristic
904C22H(7,𝔽2)11yescharacteristic
905C222−1+611yescharacteristic
906C4—24no—
907C4—24no—
908C4—24no—
909C4—24no—
910C4—44no—
911C4—44no—
912C4—48no—
913C4—44no—
914C4—44no—
915C4—48no—
916C4—44no—
917C4—44no—
918C4—44no—
919C4—44no—
920C2—24no—
921C2—24no—
922C2—24no—
923C2—84no—
924C2C22×#55611yescharacteristic
925C2#6284411yescharacteristic
926C2#6284411yescharacteristic
927C2#6285611yescharacteristic
928C2#6285611yescharacteristic
929C2#6286411yescharacteristic
930C2#6286511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#121C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #43576C2semidirect
2. #43151C2semidirect
3. #39799C2semidirect
4. #39798C2semidirect
5. #39797C2semidirect
6. #39796C2semidirect
7. #37959C2semidirect
8. #37958C2semidirect
9. #37957C2semidirect
10. #37956C2semidirect
11. #35370C2semidirect
13. #35010C2semidirect
14. C2×#2659C2semidirect
15. #34212C2semidirect
16. #34185C2semidirect
17. C2×#2329C2semidirect
27. #2789C22semidirect
28. #2788C22semidirect
29. #2787C22semidirect
30. #2786C22semidirect
31. #2783C22semidirect
32. #2777C22semidirect
33. #2775C22semidirect
34. #2767C22semidirect
35. #2762C22semidirect
36. #2759C22semidirect
37. #2758C22semidirect
38. #2745C22semidirect
39. #2740C22semidirect
40. #2715C22semidirect
41. #2700C22semidirect
42. #2689C22semidirect
45. #2659C22semidirect
46. #2659C22semidirect
51. #2605C22semidirect
52. #2604C22semidirect
53. #2601C22semidirect
54. #2599C22semidirect
55. #2594C22semidirect
57. #2588C22semidirect
58. #2579C22semidirect
59. #2577C22semidirect
60. #2564C22semidirect
62. #2560C22semidirect
63. #2532C22semidirect
64. #2528C22semidirect
65. #2524C22semidirect
66. #2521C22semidirect
67. #2510C22semidirect
68. #2510C22semidirect
69. #2510C22semidirect
70. #2510C22semidirect
75. #2487C22semidirect
76. #2481C22semidirect
77. #2481C22semidirect
78. #2481C22semidirect
79. #2481C22semidirect
82. #2478C22semidirect
83. #2474C22semidirect
84. #2469C22semidirect
85. #2465C22semidirect
88. #2417C22semidirect
89. #2417C22semidirect
90. #2409C22semidirect
91. C2×#398C22semidirect
92. C2×#395C22semidirect
96. #2353C22semidirect
97. #2353C22semidirect
98. #2352C22semidirect
99. #2352C22semidirect
100. #2352C22semidirect
101. #2352C22semidirect
102. #2345C22semidirect
103. #2345C22semidirect
104. Q8×C22⋊C4C22semidirect
107. #2329C22semidirect
108. #2329C22semidirect
109. #2329C22semidirect
118. C4×C22⋊Q8C22semidirect
119. C4×C22⋊Q8C22semidirect
120. C2×#391C22semidirect
121. C2×#389C22semidirect
124. C2×#387C22semidirect
125. C2×#387C22semidirect

Maximal subgroups

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

subgroupindex
#435762
#431512
#397992
#397982
#397972
#397962
#379592
#379582
#379572
#379562
#353702
#350192
#350102
C2×#26592
#342122
#341852
C2×#23292
C2×#23252