Finite Group Databasebeta

← #7645283

Subgroups — #7645283

Order 512.

4594 conjugacy classes of subgroups.

The subgroup lattice has 961 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41428C218yesmaximal, complemented
2#41394C214yesmaximal, complemented
3#41388C214yesmaximal, complemented
4#38113C214yesmaximal, complemented
5#38066C214yesmaximal, complemented
6#37882C214yesmaximal, complemented
7#37850C214yesmaximal, complemented
8#37504C214yesmaximal, complemented
9#36798C218yesmaximal, complemented
10#35370C212yesmaximal
11#35368C212yesmaximal, complemented
12#35231C214yesmaximal, complemented
13#35020C211yesmaximal, characteristic, complemented
14#35010C211yesmaximal, characteristic
15#34995C212yesmaximal
16#34994C212yesmaximal, complemented
17C2×#2502C211yesmaximal, characteristic, complemented
18C2×#2487C211yesmaximal, characteristic
19#34212C211yesmaximal, characteristic, complemented
20C2×#2345C211yesmaximal, characteristic, complemented
21#34057C211yesmaximal, characteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×C4×D4C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25#2855C2212yes—
26#2852C2218yes—
27#2851C2218yescomplemented
28#2851C2214yescomplemented
29#2848C2212yes—
30#2839C2218yescomplemented
31#2836C2218yescomplemented
32#2798C2218yescomplemented
33#2794C2218yescomplemented
34#2794C2218yescomplemented
35#2789C2218yescomplemented
36#2776C2218yescomplemented
37#2769C2218yescomplemented
38#2766C2218yescomplemented
39#2758C2218yescomplemented
40#2754C2218yescomplemented
41#2747C2218yescomplemented
42#2744C2218yescomplemented
43#2739C2218yescomplemented
44#2722C2218yescomplemented
45#2721C2218yescomplemented
46#2721C2218yescomplemented
47#2719C2218yescomplemented
48#2664C2218yescomplemented
49#2655C2218yescomplemented
50#2655C2218yescomplemented
51#2654C2218yescomplemented
52#2647C2214yescomplemented
53#2646C2218yescomplemented
54#2646C2214yescomplemented
55#2645C2214yescomplemented
56#2643C2218yes—
57#2629C2214yescomplemented
58#2627C2212yes—
59#2626C2212yes—
60#2625C2214yescomplemented
61#2579C2214yes—
62#2569C2218yes—
63#2569C2214yes—
64#2569C2214yescomplemented
65#2564C2214yes—
66#2524C2218yescomplemented
67#2519C2218yescomplemented
68#2514C2214yescomplemented
69#2510C2218yes—
70#2510C2218yes—
71#2510C2218yes—
72#2506C2214yescomplemented
73#2506C2214yescomplemented
74#2505C2218yes—
75#2505C2218yescomplemented
76#2505C2218yescomplemented
77#2505C2218yescomplemented
78#2502C2214yes—
79#2502C2214yes—
80#2502C2212yescomplemented
81#2502C2212yescomplemented
82#2502C2214yescomplemented
83#2496C2214yescomplemented
84#2496C2214yescomplemented
85#2493C2218yes—
86#2493C2218yes—
87#2489C2214yescomplemented
88#2487C2212yes—
89#2487C2212yes—
90#2487C2214yes—
91#2487C2212yes—
92#2487C2214yes—
93#2487C2214yes—
94#2481C2218yes—
95#2481C2218yes—
96#2481C2218yes—
97#2480C2218yes—
98#2480C2218yes—
99#2473C2218yes—
100#2473C2218yescomplemented
101#2473C2218yescomplemented
102#2473C2218yescomplemented
103#2453C2214yescomplemented
104#2442C2218yes—
105#2442C2214yes—
106#2442C2214yescomplemented
107#2421C2214yescomplemented
108#2417C2214yes—
109#2409C2212yes—
110C2×#400C2212yes—
111C2×#399C2212yes—
112C2×#398C2214yescomplemented
113#2368C2214yes—
114#2360C2214yes—
115#2345C2214yes—
116#2345C2214yes—
117#2345C2214yescomplemented
118#2345C2214yescomplemented
119#2345C2214yescomplemented
120#2345C2212yescomplemented
121Q8×C22⋊C4C2212yescomplemented
122#2330C2214yescomplemented
123#2329C2214yescomplemented
124#2323C2214yescomplemented
125#2320C2214yescomplemented
126#2318C2214yes—
127#2318C2214yes—
128#2315C2211yescharacteristic
129#2315C2211yescharacteristic
130#2315C2212yes—
131#2315C2212yes—
132#2315C2212yes—
133#2315C2212yes—
134#2314C2214yescomplemented
135#2313C2212yes—
136#2312C2212yes—
137#2308C2211yescharacteristic
138#2308C2211yescharacteristic
139#2308C2212yes—
140C4×C22⋊Q8C2214yescomplemented
141C2×#391C2212yescomplemented
142C2×#389C2212yes—
143C2×#389C2212yescomplemented
144#2290C2214yes—
145#2290C2214yes—
146C2×#387C2214yescomplemented
147C2×#386C2212yes—
148C2×#385C2212yes—
149C2×#385C2212yes—
150C2×#385C2212yes—
151C2×#384C2212yescomplemented
152#2283C2212yes—
153#2280C2212yes—
154C2×#380C2212yes—
155C2×#380C2211yescharacteristic
156C2×#380C2211yescharacteristic
157C2×#380C2212yes—
158#2273C2212yes—
159C2×C4×C4⋊C4C2212yescomplemented
160C2×C4×C22⋊C4C2211yescharacteristic
161C2×C4×C22⋊C4C2211yescharacteristic
162C2×C4×C22⋊C4C2212yes—
163C23×Q8C2311yescharacteristic
164C23×D4C2311yescharacteristic
165C24×C4C2311yescharacteristic
166C24×C4C2312yes—
167C24×C4C2311yescharacteristic
168C2×#126C2318yes—
169C2×#126C2318yes—
170C2×#125C2314yes—
171C2×#125C2318yes—
172C2×#125C2318yes—
173C2×C22⋊Q8—28no—
174C2×C22⋊Q8C2312yes—
175C2×C22⋊Q8C2312yes—
176C2×C22⋊Q8C2312yes—
177C2×C22⋊Q8C2312yes—
178C2×C22⋊Q8C2314yes—
179C2×C4×Q8C2314yes—
180C2×C4×D4—28no—
181C2×C4×D4C2312yes—
182C2×C4×D4C2312yes—
183C2×C4×D4C2312yes—
184C2×C4×D4C2312yes—
185C2×#117C2314yes—
186C22×C4⋊C4—28no—
187C22×C4⋊C4C2311yescharacteristic
188C22×C4⋊C4C2312yes—
189C22×C4⋊C4C2312yes—
190C22×C4⋊C4C2312yes—
191C22×C4⋊C4C2312yes—
192C22×C4⋊C4C2312yes—
193C22×C4⋊C4C2311yescharacteristic
194C22×C4⋊C4C2311yescharacteristic
195C22×C4⋊C4C2312yes—
196C22×C4⋊C4C2311yescharacteristic
197C22×C4⋊C4C2312yes—
198C22×C4⋊C4C2312yes—
199C22×C4⋊C4C2314yes—
200C22×C4⋊C4C2314yes—
201C22×C4⋊C4C2314yes—
202C22×C4⋊C4C2314yes—
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2311yescharacteristic
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2314yes—
213C22×C42C2311yescharacteristic
214C22×C42C2312yes—
215C22×C42C2312yes—
216C22×C42C2314yes—
217#401C2318yes—
218#401C2318yes—
219#400C2314yes—
220#400C2318yes—
221#400C2318yes—
222#400C2318yes—
223#400C2318yes—
224#400C2318yes—
225#400C2314yes—
226#400C2318yes—
227#400C2318yes—
228#400C2318yes—
229#400C2318yes—
230#400C2318yes—
231#400C2318yes—
232#400C2318yes—
233#400C2318yes—
234#400C2318yes—
235#400C2314yes—
236#400C2318yes—
237#400C2318yes—
238#400C2318yes—
239#399C2314yes—
240#399C2314yes—
241#399C2314yes—
242#399C2318yes—
243#398C2318yes—
244#398C2318yes—
245#398C2318yes—
246#398C2318yes—
247#398C2318yes—
248#398C2318yes—
249#398C2318yes—
250#398C2318yes—
251#398C2318yes—
252#398C2318yes—
253#398C2318yes—
254#398C2318yes—
255#398C2318yes—
256#398C2318yes—
257#398C2318yes—
258#397C2318yes—
259#397C2318yes—
260#397C2318yes—
261#397C2318yes—
262#397C2318yes—
263#397C2318yes—
264#396C2318yes—
265#396C2318yes—
266#396C2318yes—
267#395C2314yes—
268#393C2314yes—
269#391C2314yes—
270#391C2314yes—
271#391C2318yes—
272#391C2314yes—
273#391C2314yes—
274#391C2318yes—
275#389C2314yes—
276#389C2314yes—
277#389C2314yes—
278#389C2318yes—
279#389C2318yes—
280#389C2318yes—
281#389C2318yes—
282#389C2314yes—
283#389C2318yes—
284#389C2314yes—
285#389C2314yes—
286#389C2314yes—
287#389C2314yes—
288#389C2318yes—
289#389C2318yes—
290#388C2314yes—
291#388C2314yes—
292#388C2314yes—
293#388C2314yes—
294#388C2318yes—
295#388C2318yes—
296#388C2318yes—
297#388C2318yes—
298#388C2318yes—
299#388C2318yes—
300#387C2318yes—
301#387C2314yes—
302#387C2314yes—
303#387C2314yes—
304#387C2314yes—
305#387C2318yes—
306#387C2318yes—
307#387C2318yes—
308#387C2318yes—
309#387C2318yes—
310#387C2318yes—
311#387C2318yes—
312#387C2318yes—
313#387C2318yes—
314#387C2318yes—
315#387C2318yes—
316#387C2318yes—
317#387C2318yes—
318#387C2318yes—
319#387C2318yes—
320#387C2318yes—
321#387C2318yes—
322#387C2318yes—
323#387C2318yes—
324#387C2318yes—
325#387C2318yes—
326#387C2318yes—
327#387C2318yes—
328#386C2318yes—
329#386C2314yes—
330#386C2314yes—
331#386C2314yes—
332#386C2314yes—
333#386C2314yes—
334#386C2314yes—
335#386C2314yes—
336#386C2314yes—
337#386C2318yes—
338#385C2318yes—
339#385C2314yes—
340#385C2318yes—
341#385C2318yes—
342#385C2318yes—
343#385C2314yes—
344#385C2314yes—
345#385C2314yes—
346#385C2314yes—
347#385C2314yes—
348#385C2314yes—
349#385C2318yes—
350#385C2318yes—
351#385C2318yes—
352#385C2314yes—
353#385C2318yes—
354#385C2314yes—
355#385C2314yes—
356#385C2314yes—
357#385C2314yes—
358#385C2314yes—
359#385C2314yes—
360#385C2318yes—
361#385C2318yes—
362#384C2314yes—
363#384C2314yes—
364#384C2318yes—
365#383C2314yes—
366#383C2318yes—
367#383C2318yes—
368#382C2314yes—
369#382C2314yes—
370#382C2318yes—
371#382C2318yes—
372#381C2312yes—
373#381C2312yes—
374#381C2314yes—
375#381C2314yes—
376#380C2318yes—
377#380C2312yes—
378#380C2312yes—
379#380C2312yes—
380#380C2312yes—
381#380C2318yes—
382#380C2312yes—
383#380C2318yes—
384#380C2312yes—
385#380C2318yes—
386#380C2314yes—
387#380C2314yes—
388#380C2314yes—
389#380C2314yes—
390#380C2314yes—
391#380C2312yes—
392#380C2312yes—
393#380C2312yes—
394#380C2312yes—
395#380C2312yes—
396#380C2318yes—
397#380C2314yes—
398#380C2312yes—
399#380C2318yes—
400#379C2312yes—
401#379C2312yes—
402#379C2314yes—
403C4×C4⋊C4C2314yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2318yes—
407C4×C4⋊C4C2318yes—
408C4×C4⋊C4C2314yes—
409C4×C22⋊C4C2312yes—
410C4×C22⋊C4C2312yes—
411C4×C22⋊C4C2318yes—
412C4×C22⋊C4C2312yes—
413C4×C22⋊C4C2312yes—
414C4×C22⋊C4C2318yes—
415C4×C22⋊C4C2312yes—
416C4×C22⋊C4C2314yes—
417C4×C22⋊C4C2312yes—
418C4×C22⋊C4C2318yes—
419C4×C22⋊C4C2314yes—
420C4×C22⋊C4C2318yes—
421C4×C22⋊C4C2314yes—
422C4×C22⋊C4C2312yes—
423C4×C22⋊C4C2312yes—
424#376C2314yes—
425C2×#95C2312yes—
426C2×#95C2312yes—
427C2×#95C2314yes—
428C2×#95C2312yes—
429C2×#95C2312yes—
430C2×#95C2314yes—
431C2×#95C2314yes—
432C2×#95C2314yes—
433C2×#95C2314yes—
434C2×#95C2314yes—
435C25C2411yescharacteristic
436C25C2411yescharacteristic
437C22×Q8—24no—
438C22×Q8—44no—
439C22×Q8C2412yes—
440C22×Q8C2412yes—
441C22×D4—24no—
442C22×D4—24no—
443C22×D4—24no—
444C22×D4C2412yes—
445C22×D4C2412yes—
446C23×C4—28no—
447C23×C4—24no—
448C23×C4—44no—
449C23×C4—44no—
450C23×C4—84no—
451C23×C4#4118yes—
452C23×C4C2411yescharacteristic
453C23×C4C2412yes—
454C23×C4C2411yescharacteristic
455C23×C4C2411yescharacteristic
456C23×C4C2411yescharacteristic
457C23×C4C2411yescharacteristic
458C23×C4C2414yes—
459C23×C4C2412yes—
460C23×C4C2414yes—
461C23×C4C2412yes—
462C23×C4C2414yes—
463C23×C4C2412yes—
464C23×C4C2412yes—
465C23×C4C2411yescharacteristic
466C23×C4C2412yes—
467C23×C4C2412yes—
468C23×C4C2414yes—
469C23×C4C2412yes—
470C23×C4C2412yes—
471C23×C4C2412yes—
472C23×C4C2411yescharacteristic
473C23×C4C2411yescharacteristic
474C23×C4C2411yescharacteristic
475#126—88no—
476#126—88no—
477#125—48no—
478#125—88no—
479#125—88no—
480C22⋊Q8—28no—
481C22⋊Q8—28no—
482C22⋊Q8—28no—
483C22⋊Q8—28no—
484C22⋊Q8—48no—
485C4×Q8—48no—
486C4×D4—28no—
487C4×D4—28no—
488C4×D4—28no—
489C4×D4—28no—
490#117—48no—
491C2×C4⋊C4—24no—
492C2×C4⋊C4—24no—
493C2×C4⋊C4—28no—
494C2×C4⋊C4—28no—
495C2×C4⋊C4—28no—
496C2×C4⋊C4—28no—
497C2×C4⋊C4—28no—
498C2×C4⋊C4—24no—
499C2×C4⋊C4—24no—
500C2×C4⋊C4—28no—
501C2×C4⋊C4—44no—
502C2×C4⋊C4—44no—
503C2×C4⋊C4—84no—
504C2×C4⋊C4—84no—
505C2×C4⋊C4—84no—
506C2×C4⋊C4—84no—
507C2×C4⋊C4C2412yes—
508C2×C4⋊C4C2412yes—
509C2×C4⋊C4C2412yes—
510C2×C4⋊C4C2414yes—
511C2×C4⋊C4C2414yes—
512C2×C4⋊C4C2412yes—
513C2×C4⋊C4C2412yes—
514C2×C4⋊C4C2412yes—
515C2×C4⋊C4C2414yes—
516C2×C4⋊C4C2412yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2412yes—
519C2×C4⋊C4C2414yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2418yes—
522C2×C4⋊C4C2418yes—
523C2×C4⋊C4C2418yes—
524C2×C4⋊C4C2418yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2418yes—
527C2×C4⋊C4C2418yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2414yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2414yes—
533C2×C4⋊C4C2418yes—
534C2×C4⋊C4C2418yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2418yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2418yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2418yes—
543C2×C22⋊C4—24no—
544C2×C22⋊C4—28no—
545C2×C22⋊C4—24no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—24no—
548C2×C22⋊C4—28no—
549C2×C22⋊C4—24no—
550C2×C22⋊C4—28no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—84no—
553C2×C22⋊C4C2412yes—
554C2×C22⋊C4C2412yes—
555C2×C22⋊C4C2412yes—
556C2×C22⋊C4C2412yes—
557C2×C22⋊C4C2414yes—
558C2×C22⋊C4C2414yes—
559C2×C22⋊C4C2412yes—
560C2×C22⋊C4C2412yes—
561C2×C22⋊C4C2412yes—
562C2×C22⋊C4C2412yes—
563C2×C22⋊C4C2414yes—
564C2×C22⋊C4C2412yes—
565C2×C22⋊C4C2412yes—
566C2×C22⋊C4C2414yes—
567C2×C22⋊C4C2412yes—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2412yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2418yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2418yes—
576C2×C22⋊C4C2414yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2418yes—
579C2×C42—24no—
580C2×C42—44no—
581C2×C42—44no—
582C2×C42—84no—
583C2×C42C2414yes—
584C2×C42C2414yes—
585C2×C42C2412yes—
586C2×C42C2412yes—
587C2×C42C2418yes—
588C2×C42C2418yes—
589C2×C42C2418yes—
590C2×C42C2418yes—
591C2×C42C2414yes—
592C2×C42C2414yes—
593#95C2414yes—
594#95C2414yes—
595#95C2414yes—
596#95C2414yes—
597#95C2418yes—
598#95C2418yes—
599#95C2418yes—
600#95C2418yes—
601#95C2414yes—
602#95C2418yes—
603#95C2414yes—
604#95C2418yes—
605#95C2414yes—
606#95C2414yes—
607#95C2418yes—
608#95C2418yes—
609#95C2418yes—
610#95C2418yes—
611#95C2418yes—
612#95C2418yes—
613#95C2414yes—
614#95C2414yes—
615#95C2414yes—
616#95C2414yes—
617#95C2418yes—
618#95C2418yes—
619#95C2414yes—
620#95C2414yes—
621#95C2418yes—
622#95C2418yes—
623#95C2414yes—
624#95C2414yes—
625#95C2418yes—
626#95C2418yes—
627#95C2418yes—
628#95C2418yes—
629#95C2418yes—
630#95C2418yes—
631#95C2418yes—
632#95C2418yes—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—42no—
637C24—42no—
638C24—42no—
639C24—42no—
640C24C2×#4114yes—
641C242−1+414yes—
642C242−1+414yes—
643C24C2512yes—
644C24C2511yescharacteristic
645C24C2511yescharacteristic
646C24C2511yescharacteristic
647C2×Q8—24no—
648C2×Q8—24no—
649C2×Q8—28no—
650C2×Q8—44no—
651C2×Q8—88no—
652C2×D4—24no—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—24no—
656C2×D4—24no—
657C2×D4—24no—
658C2×D4—416no—
659C22×C4—24no—
660C22×C4—24no—
661C22×C4—24no—
662C22×C4—22no—
663C22×C4—24no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—24no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—24no—
672C22×C4—22no—
673C22×C4—24no—
674C22×C4—28no—
675C22×C4—28no—
676C22×C4—28no—
677C22×C4—24no—
678C22×C4—28no—
679C22×C4—24no—
680C22×C4—28no—
681C22×C4—24no—
682C22×C4—416no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—44no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—44no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—42no—
695C22×C4—44no—
696C22×C4—44no—
697C22×C4—44no—
698C22×C4—44no—
699C22×C4—44no—
700C22×C4—42no—
701C22×C4—44no—
702C22×C4—42no—
703C22×C4—44no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—42no—
708C22×C4—44no—
709C22×C4—88no—
710C22×C4—816no—
711C22×C4C2×#4114yes—
712C22×C4C2×#4114yes—
713C22×C4C2×#4114yes—
714C22×C4C2×#4114yes—
715C22×C4C2×#4114yes—
716C22×C4C2×#4114yes—
717C22×C4C2512yes—
718C22×C4C2514yes—
719C22×C4C2512yes—
720C22×C4C2514yes—
721C22×C4C2514yes—
722C22×C4C2514yes—
723C22×C4C2514yes—
724C22×C4C2518yes—
725C22×C4C2518yes—
726C22×C4C2514yes—
727C22×C4C2514yes—
728C22×C4C2512yes—
729C22×C4C2514yes—
730C22×C4C2511yescharacteristic
731C22×C4C2511yescharacteristic
732C22×C4C2511yescharacteristic
733C22×C4C2511yescharacteristic
734C4⋊C4—28no—
735C4⋊C4—24no—
736C4⋊C4—24no—
737C4⋊C4—28no—
738C4⋊C4—24no—
739C4⋊C4—24no—
740C4⋊C4—24no—
741C4⋊C4—24no—
742C4⋊C4—24no—
743C4⋊C4—24no—
744C4⋊C4—28no—
745C4⋊C4—28no—
746C4⋊C4—28no—
747C4⋊C4—28no—
748C4⋊C4—44no—
749C4⋊C4—44no—
750C4⋊C4—48no—
751C4⋊C4—48no—
752C4⋊C4—48no—
753C4⋊C4—48no—
754C4⋊C4—48no—
755C4⋊C4—48no—
756C4⋊C4—48no—
757C4⋊C4—48no—
758C4⋊C4—44no—
759C4⋊C4—44no—
760C4⋊C4—48no—
761C4⋊C4—48no—
762C4⋊C4—48no—
763C4⋊C4—48no—
764C4⋊C4—44no—
765C4⋊C4—48no—
766C4⋊C4—44no—
767C4⋊C4—48no—
768C4⋊C4—48no—
769C4⋊C4—48no—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—28no—
773C22⋊C4—28no—
774C22⋊C4—24no—
775C22⋊C4—24no—
776C22⋊C4—28no—
777C22⋊C4—24no—
778C22⋊C4—24no—
779C22⋊C4—24no—
780C22⋊C4—28no—
781C22⋊C4—28no—
782C22⋊C4—28no—
783C22⋊C4—24no—
784C22⋊C4—24no—
785C22⋊C4—24no—
786C22⋊C4—24no—
787C22⋊C4—24no—
788C22⋊C4—48no—
789C22⋊C4—48no—
790C22⋊C4—44no—
791C22⋊C4—44no—
792C22⋊C4—48no—
793C22⋊C4—44no—
794C22⋊C4—48no—
795C22⋊C4—44no—
796C42—24no—
797C42—24no—
798C42—28no—
799C42—28no—
800C42—44no—
801C42—44no—
802C42—48no—
803C42—48no—
804C42—48no—
805C42—48no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—24no—
816C23—24no—
817C23—44no—
818C23—44no—
819C23—48no—
820C23—48no—
821C23—48no—
822C23—44no—
823C23—82no—
824C23—82no—
825C23—84no—
826C23#541116yes—
827C23C22×#4112yes—
828C23C22×#4112yes—
829C23C22×#4112yes—
830C23C2×2−1+412yes—
831C23C2×2−1+412yes—
832C23C2×2−1+412yes—
833C23C2×2−1+412yes—
834C23C2×2−1+412yes—
835C23C2×2−1+412yes—
836C23C2611yescharacteristic
837Q8—48no—
838Q8—84no—
839D4—48no—
840D4—48no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—28no—
845C2×C4—28no—
846C2×C4—28no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—24no—
850C2×C4—22no—
851C2×C4—24no—
852C2×C4—24no—
853C2×C4—24no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—24no—
858C2×C4—28no—
859C2×C4—28no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—24no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—28no—
867C2×C4—28no—
868C2×C4—28no—
869C2×C4—24no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—28no—
873C2×C4—24no—
874C2×C4—24no—
875C2×C4—28no—
876C2×C4—28no—
877C2×C4—24no—
878C2×C4—24no—
879C2×C4—24no—
880C2×C4—24no—
881C2×C4—24no—
882C2×C4—44no—
883C2×C4—44no—
884C2×C4—44no—
885C2×C4—48no—
886C2×C4—48no—
887C2×C4—48no—
888C2×C4—48no—
889C2×C4—48no—
890C2×C4—44no—
891C2×C4—48no—
892C2×C4—84no—
893C2×C4—84no—
894C2×C4—82no—
895C2×C4—84no—
896C2×C4—88no—
897C2×C4—88no—
898C2×C4—82no—
899C2×C4—88no—
900C2×C4—88no—
901C2×C4—84no—
902C2×C4C22×#4112yes—
903C2×C4C22×#4112yes—
904C2×C4C22×#4112yes—
905C2×C4C22×#4112yes—
906C2×C4#58514yes—
907C22—22no—
908C22—22no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—22no—
913C22—24no—
914C22—24no—
915C22—24no—
916C22—24no—
917C22—24no—
918C22—24no—
919C22—416no—
920C22—42no—
921C22—42no—
922C22—44no—
923C22—44no—
924C22—42no—
925C22—88no—
926C22C2×#54114yes—
927C22C2×#54114yes—
928C22C2×#54114yes—
929C22C23×#4111yescharacteristic
930C22C22×2−1+411yescharacteristic
931C22C22×2−1+411yescharacteristic
932C22C2×#58512yes—
933C22H(7,𝔽2)12yes—
934C4—22no—
935C4—22no—
936C4—22no—
937C4—42no—
938C4—44no—
939C4—44no—
940C4—44no—
941C4—42no—
942C4—44no—
943C4—44no—
944C4—44no—
945C4—44no—
946C4—44no—
947C4—48no—
948C4—48no—
949C4—42no—
950C4#349114yes—
951C2—24no—
952C2—24no—
953C2—24no—
954C2—82no—
955C2C22×#54111yescharacteristic
956C2C2×#349111yescharacteristic
957C2#6285511yescharacteristic
958C2#6290212yes—
959C2#6290212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #41428C2semidirect
2. #41394C2semidirect
3. #41388C2semidirect
4. #38113C2semidirect
5. #38066C2semidirect
6. #37882C2semidirect
7. #37850C2semidirect
8. #37504C2semidirect
9. #36798C2semidirect
11. #35368C2semidirect
12. #35231C2semidirect
13. #35020C2semidirect
16. #34994C2semidirect
17. C2×#2502C2semidirect
19. #34212C2semidirect
20. C2×#2345C2semidirect
27. #2851C22semidirect
28. #2851C22semidirect
30. #2839C22semidirect
31. #2836C22semidirect
32. #2798C22semidirect
33. #2794C22semidirect
34. #2794C22semidirect
35. #2789C22semidirect
36. #2776C22semidirect
37. #2769C22semidirect
38. #2766C22semidirect
39. #2758C22semidirect
40. #2754C22semidirect
41. #2747C22semidirect
42. #2744C22semidirect
43. #2739C22semidirect
44. #2722C22semidirect
45. #2721C22semidirect
46. #2721C22semidirect
47. #2719C22semidirect
48. #2664C22semidirect
49. #2655C22semidirect
50. #2655C22semidirect
51. #2654C22semidirect
52. #2647C22semidirect
53. #2646C22semidirect
54. #2646C22semidirect
55. #2645C22semidirect
57. #2629C22semidirect
60. #2625C22semidirect
64. #2569C22semidirect
66. #2524C22semidirect
67. #2519C22semidirect
68. #2514C22semidirect
72. #2506C22semidirect
73. #2506C22semidirect
75. #2505C22semidirect
76. #2505C22semidirect
77. #2505C22semidirect
80. #2502C22semidirect
81. #2502C22semidirect
82. #2502C22semidirect
83. #2496C22semidirect
84. #2496C22semidirect
87. #2489C22semidirect
100. #2473C22semidirect
101. #2473C22semidirect
102. #2473C22semidirect
103. #2453C22semidirect
106. #2442C22semidirect
107. #2421C22semidirect
112. C2×#398C22semidirect
117. #2345C22semidirect
118. #2345C22semidirect
119. #2345C22semidirect
120. #2345C22semidirect
121. Q8×C22⋊C4C22semidirect
122. #2330C22semidirect
123. #2329C22semidirect
124. #2323C22semidirect
125. #2320C22semidirect
134. #2314C22semidirect
140. C4×C22⋊Q8C22semidirect
141. C2×#391C22semidirect
143. C2×#389C22semidirect
146. C2×#387C22semidirect
151. C2×#384C22semidirect
159. C2×C4×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#414282
#413942
#413882
#381132
#380662
#378822
#378502
#375042
#367982
#353702
#353682
#352312
#350202
#350102
#349952
#349942
C2×#25022
C2×#24872
#342122
C2×#23452
#340572