Finite Group Databasebeta

← #7677907

Subgroups — #7677907

Order 512.

4754 conjugacy classes of subgroups.

The subgroup lattice has 981 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59961C214yesmaximal, complemented
2#59893C214yesmaximal, complemented
3#59751C214yesmaximal, complemented
4#59749C214yesmaximal, complemented
5#45407C214yesmaximal, complemented
6#45403C214yesmaximal, complemented
7#45189C214yesmaximal, complemented
8#45021C214yesmaximal, complemented
9#39543C214yesmaximal, complemented
10#37933C214yesmaximal, complemented
11#37885C214yesmaximal, complemented
12#36207C214yesmaximal, complemented
13#35679C212yesmaximal
14#35558C212yesmaximal
15#35174C211yesmaximal, characteristic
16#35159C211yesmaximal, characteristic, complemented
17#35154C211yesmaximal, characteristic, complemented
18#34815C212yesmaximal, complemented
19#34271C211yesmaximal, characteristic, complemented
20#34254C212yesmaximal, complemented
21#34182C211yesmaximal, characteristic, complemented
22C2×#2367C211yesmaximal, characteristic
23#34058C211yesmaximal, characteristic
24C2×#544C2211yescharacteristic
25C22×#124C2211yescharacteristic
26C2×#519C2212yes—
27C22×C4×Q8C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29#2855C2214yes—
30#2851C2214yes—
31#2848C2214yes—
32#2793C2218yescomplemented
33#2777C2218yescomplemented
34#2775C2218yescomplemented
35#2773C2218yescomplemented
36#2773C2218yescomplemented
37#2772C2218yescomplemented
38#2770C2218yescomplemented
39#2768C2218yescomplemented
40#2754C2218yescomplemented
41#2738C2218yescomplemented
42#2721C2218yescomplemented
43#2698C2218yescomplemented
44#2646C2214yes—
45#2627C2214yes—
46#2626C2214yes—
47#2611C2218yescomplemented
48#2604C2218yescomplemented
49#2596C2218yescomplemented
50#2575C2218yescomplemented
51#2556C2218yescomplemented
52#2532C2218yescomplemented
53#2530C2218yescomplemented
54#2529C2218yescomplemented
55#2529C2218yescomplemented
56#2525C2218yescomplemented
57#2519C2218yescomplemented
58#2519C2218yescomplemented
59#2517C2218yescomplemented
60#2515C2218yescomplemented
61#2513C2214yes—
62#2513C2214yes—
63#2513C2214yes—
64#2513C2214yes—
65#2512C2214yes—
66#2512C2214yes—
67#2512C2214yes—
68#2512C2214yes—
69#2509C2214yescomplemented
70#2509C2212yescomplemented
71#2509C2212yescomplemented
72#2508C2214yescomplemented
73#2508C2212yescomplemented
74#2508C2212yescomplemented
75#2507C2214yescomplemented
76#2507C2212yescomplemented
77#2507C2212yescomplemented
78#2506C2212yescomplemented
79#2506C2214yescomplemented
80#2506C2212yescomplemented
81#2505C2214yes—
82#2505C2214yes—
83#2499C2214yescomplemented
84#2496C2214yescomplemented
85#2495C2214yescomplemented
86#2489C2214yescomplemented
87#2482C2218yes—
88#2482C2218yes—
89#2480C2218yes—
90#2480C2218yes—
91#2478C2218yescomplemented
92#2473C2214yes—
93#2473C2214yes—
94#2454C2214yes—
95#2454C2214yes—
96#2453C2214yescomplemented
97#2453C2214yescomplemented
98#2452C2214yes—
99#2452C2214yes—
100#2451C2214yescomplemented
101#2451C2214yescomplemented
102#2448C2214yes—
103#2448C2214yes—
104#2448C2214yes—
105#2448C2214yes—
106#2448C2214yes—
107#2448C2214yes—
108#2448C2214yes—
109#2448C2214yes—
110#2441C2214yescomplemented
111#2423C2214yescomplemented
112#2402C2214yescomplemented
113#2402C2214yescomplemented
114#2373C2218yescomplemented
115#2370C2214yescomplemented
116#2370C2214yescomplemented
117#2369C2214yescomplemented
118#2367C2214yes—
119#2367C2214yes—
120#2367C2214yes—
121#2367C2214yes—
122#2365C2214yescomplemented
123#2362C2214yescomplemented
124#2356C2214yescomplemented
125#2356C2214yescomplemented
126#2355C2214yescomplemented
127#2355C2214yescomplemented
128#2351C2214yescomplemented
129#2351C2214yescomplemented
130Q8×C4⋊C4C2214yescomplemented
131Q8×C4⋊C4C2214yescomplemented
132#2346C2214yescomplemented
133#2343C2218yes—
134#2343C2218yes—
135#2329C2214yes—
136#2320C2214yescomplemented
137#2320C2214yescomplemented
138#2319C2214yes—
139#2319C2214yes—
140#2317C2212yes—
141#2316C2211yescharacteristic
142#2316C2211yescharacteristic
143#2316C2214yes—
144#2316C2211yescharacteristic
145#2312C2214yes—
146#2310C2212yes—
147#2309C2212yes—
148#2309C2212yes—
149C4×#125C2214yescomplemented
150C4×#125C2214yescomplemented
151C4×C22⋊Q8C2214yes—
152#2296C2212yes—
153#2296C2212yes—
154#2296C2212yes—
155#2296C2212yes—
156#2295C2214yescomplemented
157#2295C2214yescomplemented
158C2×#391C2211yescharacteristic
159#2293C2214yes—
160#2293C2214yes—
161C2×#390C2211yescharacteristic
162C2×#388C2212yes—
163C2×#388C2212yes—
164C2×#385C2212yes—
165#2285C2214yes—
166#2285C2212yes—
167#2280C2214yes—
168#2274C2212yes—
169C4×#117C2212yes—
170C2×C4×C4⋊C4C2211yescharacteristic
171C2×C4×C4⋊C4C2211yescharacteristic
172C2×C4×C22⋊C4C2212yes—
173C23×Q8C2311yescharacteristic
174C23×D4C2311yescharacteristic
175C24×C4C2312yes—
176#544—28no—
177C2×C4⋊Q8C2314yes—
178C2×#126C2318yes—
179C2×#126C2318yes—
180C2×#125C2314yes—
181C2×#125C2314yes—
182C2×#125C2314yes—
183C2×#125C2314yes—
184C2×#124—28no—
185C2×#124C2314yes—
186C2×#124C2314yes—
187C2×C22⋊Q8C2314yes—
188C2×C22⋊Q8C2314yes—
189C2×C22⋊Q8C2314yes—
190#519—216no—
191C2×C4×Q8—28no—
192C2×C4×Q8C2314yes—
193C2×C4×Q8C2314yes—
194C2×C4×Q8C2314yes—
195C2×C4×Q8C2314yes—
196C2×C4×Q8C2314yes—
197C2×C4×Q8C2314yes—
198C2×C4×Q8C2314yes—
199C2×C4×D4—28no—
200C2×C4×D4C2314yes—
201C2×C4×D4C2314yes—
202C2×#117C2312yes—
203C2×#117C2312yes—
204C2×#117C2312yes—
205C2×#117C2312yes—
206C2×#117C2318yes—
207C2×#117C2314yes—
208C2×#117C2314yes—
209C22×C4⋊C4C2312yes—
210C22×C4⋊C4C2311yescharacteristic
211C22×C4⋊C4C2311yescharacteristic
212C22×C4⋊C4C2311yescharacteristic
213C22×C4⋊C4C2311yescharacteristic
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C42C2312yes—
220C22×C42C2311yescharacteristic
221C22×C42C2311yescharacteristic
222C22×C42C2311yescharacteristic
223C22×C42C2312yes—
224#400C2314yes—
225#400C2314yes—
226#400C2314yes—
227#400C2318yes—
228#400C2314yes—
229#400C2318yes—
230#400C2318yes—
231#400C2314yes—
232#400C2314yes—
233#400C2314yes—
234#400C2314yes—
235#399C2318yes—
236#399C2318yes—
237#399C2318yes—
238#399C2318yes—
239#399C2318yes—
240#398C2318yes—
241#398C2318yes—
242#398C2318yes—
243#398C2318yes—
244#398C2314yes—
245#398C2314yes—
246#398C2314yes—
247#398C2314yes—
248#398C2314yes—
249#398C2314yes—
250#398C2314yes—
251#398C2314yes—
252#397C2318yes—
253#397C2318yes—
254#397C2318yes—
255#397C2318yes—
256#397C2318yes—
257#397C2318yes—
258#397C2318yes—
259#397C2318yes—
260#397C2318yes—
261#397C2318yes—
262#396C2318yes—
263#396C2318yes—
264#396C2318yes—
265#396C2318yes—
266#395C2318yes—
267#393C2318yes—
268#391C2314yes—
269#391C2314yes—
270#391C2314yes—
271#391C2314yes—
272#391C2314yes—
273#391C2318yes—
274#391C2314yes—
275#391C2314yes—
276#391C2314yes—
277#391C2314yes—
278#390C2314yes—
279#390C2314yes—
280#390C2314yes—
281#390C2314yes—
282#390C2314yes—
283#390C2314yes—
284#390C2314yes—
285#390C2314yes—
286#390C2314yes—
287#390C2314yes—
288#389C2314yes—
289#389C2314yes—
290#389C2314yes—
291#389C2314yes—
292#389C2314yes—
293#389C2314yes—
294#389C2314yes—
295#389C2314yes—
296#389C2318yes—
297#389C2318yes—
298#389C2318yes—
299#389C2314yes—
300#389C2314yes—
301#389C2318yes—
302#389C2314yes—
303#389C2314yes—
304#389C2312yes—
305#389C2312yes—
306#389C2318yes—
307#389C2314yes—
308#389C2314yes—
309#389C2314yes—
310#389C2314yes—
311#389C2312yes—
312#389C2312yes—
313#389C2314yes—
314#389C2312yes—
315#389C2312yes—
316#389C2312yes—
317#389C2312yes—
318#389C2312yes—
319#389C2312yes—
320#389C2312yes—
321#389C2312yes—
322#389C2312yes—
323#389C2312yes—
324#389C2312yes—
325#389C2312yes—
326#388C2318yes—
327#388C2318yes—
328#388C2318yes—
329#388C2318yes—
330#388C2318yes—
331#388C2318yes—
332#388C2318yes—
333#388C2318yes—
334#388C2318yes—
335#388C2318yes—
336#388C2318yes—
337#388C2318yes—
338#388C2318yes—
339#388C2318yes—
340#388C2318yes—
341#388C2318yes—
342#388C2318yes—
343#388C2318yes—
344#388C2318yes—
345#388C2318yes—
346#388C2318yes—
347#388C2318yes—
348#387C2314yes—
349#387C2314yes—
350#387C2314yes—
351#387C2314yes—
352#387C2314yes—
353#387C2314yes—
354#387C2314yes—
355#387C2314yes—
356#387C2318yes—
357#387C2318yes—
358#387C2318yes—
359#387C2318yes—
360#387C2318yes—
361#387C2318yes—
362#387C2318yes—
363#387C2318yes—
364#387C2318yes—
365#387C2318yes—
366#387C2318yes—
367#387C2318yes—
368#387C2318yes—
369#387C2318yes—
370#387C2318yes—
371#385C2318yes—
372#385C2318yes—
373#385C2314yes—
374#385C2314yes—
375#385C2318yes—
376#385C2314yes—
377#385C2314yes—
378#385C2314yes—
379#385C2318yes—
380#385C2318yes—
381#385C2314yes—
382#385C2314yes—
383#385C2314yes—
384#384C2314yes—
385#384C2314yes—
386#384C2314yes—
387#384C2312yes—
388#384C2312yes—
389#383C2318yes—
390#383C2318yes—
391#382C2314yes—
392#382C2314yes—
393#382C2314yes—
394#382C2318yes—
395#382C2318yes—
396#382C2318yes—
397#382C2314yes—
398#382C2312yes—
399#382C2312yes—
400#381C2318yes—
401#381C2318yes—
402#380C2314yes—
403#380C2314yes—
404#380C2314yes—
405#380C2314yes—
406#380C2314yes—
407#380C2314yes—
408#380C2314yes—
409#380C2314yes—
410#380C2314yes—
411#379C2318yes—
412#379C2318yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2312yes—
415C4×C4⋊C4C2312yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2314yes—
424C4×C4⋊C4C2312yes—
425C4×C4⋊C4C2312yes—
426C4×C4⋊C4C2318yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2314yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2318yes—
431C4×C4⋊C4C2318yes—
432C4×C4⋊C4C2314yes—
433C4×C4⋊C4C2318yes—
434C4×C4⋊C4C2314yes—
435C4×C4⋊C4C2312yes—
436C4×C4⋊C4C2314yes—
437C4×C4⋊C4C2314yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2312yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2312yes—
443C4×C4⋊C4C2312yes—
444C4×C22⋊C4C2314yes—
445C4×C22⋊C4C2314yes—
446C4×C22⋊C4C2318yes—
447C4×C22⋊C4C2314yes—
448C4×C22⋊C4C2314yes—
449C4×C22⋊C4C2314yes—
450C4×C22⋊C4C2314yes—
451C4×C22⋊C4C2318yes—
452#376C2314yes—
453#376C2318yes—
454#376C2318yes—
455C2×#95C2312yes—
456C2×#95C2312yes—
457C2×#95C2312yes—
458C2×#95C2311yescharacteristic
459C2×#95C2311yescharacteristic
460C43C2314yes—
461C25C2412yes—
462C22×Q8—24no—
463C22×Q8—24no—
464C22×Q8#4118yes—
465C22×Q8C2414yes—
466C22×Q8C2414yes—
467C22×D4—24no—
468C22×D4—24no—
469C22×D4—24no—
470C22×D4C2414yes—
471C23×C4—28no—
472C23×C4—44no—
473C23×C4—82no—
474C23×C4C2411yescharacteristic
475C23×C4C2411yescharacteristic
476C23×C4C2414yes—
477C23×C4C2412yes—
478C23×C4C2411yescharacteristic
479C23×C4C2411yescharacteristic
480C23×C4C2411yescharacteristic
481C23×C4C2412yes—
482C23×C4C2411yescharacteristic
483C23×C4C2414yes—
484C23×C4C2412yes—
485C23×C4C2411yescharacteristic
486C4⋊Q8—216no—
487#126—416no—
488#126—88no—
489#125—216no—
490#125—48no—
491#125—48no—
492#125—84no—
493#124—216no—
494#124—216no—
495C22⋊Q8—216no—
496C22⋊Q8—48no—
497C22⋊Q8—84no—
498C4×Q8—216no—
499C4×Q8—216no—
500C4×Q8—216no—
501C4×Q8—216no—
502C4×Q8—216no—
503C4×Q8—216no—
504C4×Q8—84no—
505C4×D4—216no—
506C4×D4—216no—
507#117—232no—
508#117—28no—
509#117—28no—
510#117—28no—
511#117—28no—
512#117—48no—
513#117—84no—
514C2×C4⋊C4—28no—
515C2×C4⋊C4—24no—
516C2×C4⋊C4—42no—
517C2×C4⋊C4—42no—
518C2×C4⋊C4#4118yes—
519C2×C4⋊C4C2418yes—
520C2×C4⋊C4C2412yes—
521C2×C4⋊C4C2412yes—
522C2×C4⋊C4C2414yes—
523C2×C4⋊C4C2412yes—
524C2×C4⋊C4C2412yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2418yes—
527C2×C4⋊C4C2412yes—
528C2×C4⋊C4C2412yes—
529C2×C4⋊C4C2412yes—
530C2×C4⋊C4C2412yes—
531C2×C4⋊C4C2412yes—
532C2×C4⋊C4C2412yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2412yes—
539C2×C4⋊C4C2412yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2414yes—
566C2×C22⋊C4—28no—
567C2×C22⋊C4—28no—
568C2×C22⋊C4—28no—
569C2×C22⋊C4—44no—
570C2×C22⋊C4—82no—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2414yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2418yes—
575C2×C22⋊C4C2414yes—
576C2×C22⋊C4C2414yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C2418yes—
586C2×C22⋊C4C2418yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2418yes—
589C2×C22⋊C4C2418yes—
590C2×C42—24no—
591C2×C42—28no—
592C2×C42—24no—
593C2×C42—24no—
594C2×C42—82no—
595C2×C42C2414yes—
596C2×C42C2414yes—
597C2×C42C2418yes—
598C2×C42C2418yes—
599C2×C42C2414yes—
600C2×C42C2414yes—
601C2×C42C2414yes—
602C2×C42C2412yes—
603C2×C42C2412yes—
604C2×C42C2414yes—
605C2×C42C2414yes—
606C2×C42C2412yes—
607C2×C42C2412yes—
608C2×C42C2412yes—
609C2×C42C2412yes—
610C2×C42C2414yes—
611C2×C42C2418yes—
612C2×C42C2414yes—
613C2×C42C2414yes—
614C2×C42C2414yes—
615C2×C42C2418yes—
616C2×C42C2414yes—
617#95C2414yes—
618#95C2418yes—
619#95C2411yescharacteristic
620#95C2411yescharacteristic
621#95C2411yescharacteristic
622#95C2411yescharacteristic
623#95C2414yes—
624#95C2412yes—
625#95C2418yes—
626#95C2412yes—
627#95C2414yes—
628#95C2414yes—
629#95C2414yes—
630#95C2414yes—
631#95C2414yes—
632#95C2414yes—
633#95C2418yes—
634#95C2418yes—
635#95C2418yes—
636#95C2418yes—
637#95C2418yes—
638#95C2418yes—
639#95C2418yes—
640#95C2418yes—
641#95C2414yes—
642#95C2414yes—
643#95C2414yes—
644#95C2414yes—
645#95C2414yes—
646#95C2414yes—
647#95C2418yes—
648#95C2414yes—
649#95C2418yes—
650#95C2418yes—
651#95C2414yes—
652#95C2414yes—
653#95C2414yes—
654#95C2414yes—
655#95C2414yes—
656#95C2414yes—
657#95C2414yes—
658#95C2414yes—
659#95C2414yes—
660#95C2414yes—
661#95C2414yes—
662C24—24no—
663C24—24no—
664C24—24no—
665C24—42no—
666C24—42no—
667C24—42no—
668C24—42no—
669C24C2514yes—
670C24C2511yescharacteristic
671C2×Q8—232no—
672C2×Q8—28no—
673C2×Q8—28no—
674C2×Q8—28no—
675C2×Q8—44no—
676C2×Q8—44no—
677C2×Q8C2×#41116yes—
678C2×D4—28no—
679C2×D4—28no—
680C2×D4—28no—
681C2×D4—416no—
682C22×C4—24no—
683C22×C4—24no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—24no—
691C22×C4—28no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—28no—
695C22×C4—28no—
696C22×C4—41no—
697C22×C4—42no—
698C22×C4—41no—
699C22×C4—41no—
700C22×C4—44no—
701C22×C4—42no—
702C22×C4—41no—
703C22×C4—41no—
704C22×C4—41no—
705C22×C4—42no—
706C22×C4—42no—
707C22×C4—41no—
708C22×C4—41no—
709C22×C4—41no—
710C22×C4—44no—
711C22×C4—44no—
712C22×C4—41no—
713C22×C4—816no—
714C22×C4C2×#4118yes—
715C22×C4C2×#4118yes—
716C22×C4C2×#4114yes—
717C22×C4C2×#4114yes—
718C22×C42−1+414yes—
719C22×C4C2511yescharacteristic
720C22×C4C2514yes—
721C22×C4C2511yescharacteristic
722C22×C4C2512yes—
723C22×C4C2514yes—
724C22×C4C2511yescharacteristic
725C22×C4C2511yescharacteristic
726C22×C4C2514yes—
727C22×C4C2514yes—
728C22×C4C2514yes—
729C22×C4C2512yes—
730C22×C4C2514yes—
731C22×C4C2514yes—
732C22×C4C2514yes—
733C22×C4C2514yes—
734C22×C4C2512yes—
735C22×C4C2514yes—
736C22×C4C2514yes—
737C22×C4C2511yescharacteristic
738C22×C4C2511yescharacteristic
739C22×C4C2512yes—
740C4⋊C4—216no—
741C4⋊C4—216no—
742C4⋊C4—216no—
743C4⋊C4—24no—
744C4⋊C4—24no—
745C4⋊C4—24no—
746C4⋊C4—24no—
747C4⋊C4—24no—
748C4⋊C4—24no—
749C4⋊C4—28no—
750C4⋊C4—216no—
751C4⋊C4—28no—
752C4⋊C4—24no—
753C4⋊C4—24no—
754C4⋊C4—24no—
755C4⋊C4—24no—
756C4⋊C4—28no—
757C4⋊C4—28no—
758C4⋊C4—28no—
759C4⋊C4—42no—
760C4⋊C4—42no—
761C4⋊C4—44no—
762C4⋊C4—44no—
763C4⋊C4—44no—
764C4⋊C4—44no—
765C4⋊C4—44no—
766C4⋊C4—44no—
767C4⋊C4—44no—
768C4⋊C4—44no—
769C4⋊C4—44no—
770C4⋊C4—44no—
771C4⋊C4—44no—
772C4⋊C4—44no—
773C4⋊C4—44no—
774C4⋊C4—44no—
775C4⋊C4—44no—
776C4⋊C4—44no—
777C4⋊C4—44no—
778C4⋊C4—44no—
779C4⋊C4—44no—
780C4⋊C4—44no—
781C4⋊C4—44no—
782C4⋊C4—48no—
783C4⋊C4—48no—
784C4⋊C4—44no—
785C4⋊C4—44no—
786C4⋊C4C2×#41116yes—
787C22⋊C4—28no—
788C22⋊C4—28no—
789C22⋊C4—28no—
790C22⋊C4—28no—
791C22⋊C4—216no—
792C22⋊C4—28no—
793C22⋊C4—28no—
794C22⋊C4—216no—
795C22⋊C4—28no—
796C22⋊C4—44no—
797C22⋊C4—48no—
798C22⋊C4—48no—
799C22⋊C4—48no—
800C22⋊C4—48no—
801C22⋊C4—48no—
802C22⋊C4—48no—
803C22⋊C4—48no—
804C22⋊C4—48no—
805C22⋊C4—48no—
806C42—24no—
807C42—24no—
808C42—28no—
809C42—24no—
810C42—28no—
811C42—24no—
812C42—24no—
813C42—24no—
814C42—216no—
815C42—216no—
816C42—28no—
817C42—28no—
818C42—28no—
819C42—28no—
820C42—28no—
821C42—44no—
822C42—44no—
823C42—44no—
824C42—44no—
825C42—48no—
826C42—44no—
827C42—48no—
828C23—21no—
829C23—21no—
830C23—21no—
831C23—21no—
832C23—24no—
833C23—24no—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—24no—
839C23—48no—
840C23—48no—
841C23—48no—
842C23—84no—
843C23—84no—
844C23—84no—
845C23—84no—
846C23C22×#4112yes—
847C23C22×#4112yes—
848C23C2×2−1+412yes—
849C23C2611yescharacteristic
850Q8—232no—
851Q8—88no—
852D4—416no—
853C2×C4—21no—
854C2×C4—24no—
855C2×C4—21no—
856C2×C4—24no—
857C2×C4—24no—
858C2×C4—21no—
859C2×C4—24no—
860C2×C4—21no—
861C2×C4—216no—
862C2×C4—21no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—22no—
872C2×C4—21no—
873C2×C4—24no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—24no—
877C2×C4—24no—
878C2×C4—24no—
879C2×C4—24no—
880C2×C4—24no—
881C2×C4—24no—
882C2×C4—24no—
883C2×C4—22no—
884C2×C4—24no—
885C2×C4—21no—
886C2×C4—24no—
887C2×C4—24no—
888C2×C4—24no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—21no—
893C2×C4—24no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—24no—
897C2×C4—24no—
898C2×C4—24no—
899C2×C4—22no—
900C2×C4—24no—
901C2×C4—21no—
902C2×C4—22no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—24no—
906C2×C4—24no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—48no—
911C2×C4—416no—
912C2×C4—44no—
913C2×C4—44no—
914C2×C4—44no—
915C2×C4—44no—
916C2×C4—88no—
917C2×C4—82no—
918C2×C4—82no—
919C2×C4—84no—
920C2×C4#552116yes—
921C2×C4C22×#4118yes—
922C2×C4C22×#4118yes—
923C2×C4C22×#4114yes—
924C2×C4C22×#4114yes—
925C2×C4C2×2−1+414yes—
926C2×C4#58512yes—
927C2×C4#58512yes—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—22no—
934C22—44no—
935C22—44no—
936C22—44no—
937C22—44no—
938C22—44no—
939C22—44no—
940C22—44no—
941C22—816no—
942C22C2×#55214yes—
943C22C23×#4111yescharacteristic
944C22C23×#4111yescharacteristic
945C22C22×2−1+411yescharacteristic
946C22C2×#58511yescharacteristic
947C22C2×#58511yescharacteristic
948C22H(7,𝔽2)11yescharacteristic
949C222−1+611yescharacteristic
950C4—22no—
951C4—28no—
952C4—22no—
953C4—28no—
954C4—41no—
955C4—42no—
956C4—44no—
957C4—44no—
958C4—41no—
959C4—42no—
960C4—44no—
961C4—44no—
962C4—42no—
963C4—44no—
964C4—44no—
965C4—41no—
966C4—41no—
967C4—44no—
968C4—44no—
969C4—44no—
970C4C2×#55218yes—
971C2—24no—
972C2—84no—
973C2C22×#55211yescharacteristic
974C2#6279311yescharacteristic
975C2#6285111yescharacteristic
976C2#6293211yescharacteristic
977C2#6296211yescharacteristic
978C2#6299011yescharacteristic
979C2#6300511yescharacteristic
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. #59961C2semidirect
2. #59893C2semidirect
3. #59751C2semidirect
4. #59749C2semidirect
5. #45407C2semidirect
6. #45403C2semidirect
7. #45189C2semidirect
8. #45021C2semidirect
9. #39543C2semidirect
10. #37933C2semidirect
11. #37885C2semidirect
12. #36207C2semidirect
16. #35159C2semidirect
17. #35154C2semidirect
18. #34815C2semidirect
19. #34271C2semidirect
20. #34254C2semidirect
21. #34182C2semidirect
32. #2793C22semidirect
33. #2777C22semidirect
34. #2775C22semidirect
35. #2773C22semidirect
36. #2773C22semidirect
37. #2772C22semidirect
38. #2770C22semidirect
39. #2768C22semidirect
40. #2754C22semidirect
41. #2738C22semidirect
42. #2721C22semidirect
43. #2698C22semidirect
47. #2611C22semidirect
48. #2604C22semidirect
49. #2596C22semidirect
50. #2575C22semidirect
51. #2556C22semidirect
52. #2532C22semidirect
53. #2530C22semidirect
54. #2529C22semidirect
55. #2529C22semidirect
56. #2525C22semidirect
57. #2519C22semidirect
58. #2519C22semidirect
59. #2517C22semidirect
60. #2515C22semidirect
69. #2509C22semidirect
70. #2509C22semidirect
71. #2509C22semidirect
72. #2508C22semidirect
73. #2508C22semidirect
74. #2508C22semidirect
75. #2507C22semidirect
76. #2507C22semidirect
77. #2507C22semidirect
78. #2506C22semidirect
79. #2506C22semidirect
80. #2506C22semidirect
83. #2499C22semidirect
84. #2496C22semidirect
85. #2495C22semidirect
86. #2489C22semidirect
91. #2478C22semidirect
96. #2453C22semidirect
97. #2453C22semidirect
100. #2451C22semidirect
101. #2451C22semidirect
110. #2441C22semidirect
111. #2423C22semidirect
112. #2402C22semidirect
113. #2402C22semidirect
114. #2373C22semidirect
115. #2370C22semidirect
116. #2370C22semidirect
117. #2369C22semidirect
122. #2365C22semidirect
123. #2362C22semidirect
124. #2356C22semidirect
125. #2356C22semidirect
126. #2355C22semidirect
127. #2355C22semidirect
128. #2351C22semidirect
129. #2351C22semidirect
130. Q8×C4⋊C4C22semidirect
131. Q8×C4⋊C4C22semidirect
132. #2346C22semidirect
136. #2320C22semidirect
137. #2320C22semidirect
149. C4×#125C22semidirect
150. C4×#125C22semidirect
156. #2295C22semidirect
157. #2295C22semidirect

Maximal subgroups

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

subgroupindex
#599612
#598932
#597512
#597492
#454072
#454032
#451892
#450212
#395432
#379332
#378852
#362072
#356792
#355582
#351742
#351592
#351542
#348152
#342712
#342542
#341822
C2×#23672
#340582