Finite Group Databasebeta

← #7674609

Subgroups — #7674609

Order 512.

7332 conjugacy classes of subgroups.

The subgroup lattice has 839 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3504C211yesmaximal, characteristic, complemented
2C2×#3508C211yesmaximal, characteristic, complemented
3#43103C2116yesmaximal, complemented
4#39174C214yesmaximal, complemented
5#39169C214yesmaximal, complemented
6#39164C214yesmaximal, complemented
7#39161C214yesmaximal, complemented
8#37756C218yesmaximal, complemented
9#37710C214yesmaximal, complemented
10#37706C214yesmaximal, complemented
11#35533C212yesmaximal, complemented
12#35529C212yesmaximal, complemented
13#35333C211yesmaximal, characteristic, complemented
14#35272C211yesmaximal, characteristic, complemented
15#35264C212yesmaximal, complemented
16C2×#2641C211yesmaximal, characteristic, complemented
17#34275C212yesmaximal, complemented
18#34074C211yesmaximal, characteristic, complemented
19#34070C211yesmaximal, characteristic, complemented
20#3508—216no—
21#3504—216no—
22C2×#559C2214yes—
23C2×#557C2214yescomplemented
24C2×#554C2218yes—
25C2×#554C2214yescomplemented
26C2×#550C2214yes—
27C2×#546C2218yes—
28C2×#544C2212yes—
29C2×#544C2214yescomplemented
30C2×#540C2212yes—
31C2×#540C2212yes—
32C2×#535C2212yes—
33C2×#535C2212yes—
34C2×#533C2211yescharacteristic
35C2×#533C2212yescomplemented
36C2×#532C2211yescharacteristic
37C2×#532C2214yes—
38C22×#127C2211yescharacteristic
39C22×#125C2211yescharacteristic
40C22×#125C2212yescomplemented
41C2×#520C2212yes—
42C2×#518C2212yes—
43C2×C4×#41C2211yescharacteristic
44C2×C4×#41C2211yescharacteristic
45#2861C2214yescomplemented
46#2858C2214yescomplemented
47#2856C2214yes—
48#2851C2214yescomplemented
49#2731C22116yescomplemented
50#2730C22116yescomplemented
51#2711C22116yescomplemented
52#2711C22116yescomplemented
53#2707C22116yescomplemented
54#2681C22116yescomplemented
55#2676C22116yescomplemented
56#2676C22116yescomplemented
57#2641C2214yes—
58#2641C2214yes—
59#2641C2214yes—
60#2641C2214yes—
61#2641C2214yescomplemented
62#2640C2214yescomplemented
63#2629C2214yescomplemented
64#2619C2214yes—
65#2579C2218yes—
66#2566C2214yescomplemented
67#2566C2214yescomplemented
68#2566C2214yescomplemented
69#2565C2214yescomplemented
70#2563C2214yescomplemented
71#2548C2214yes—
72#2548C2214yescomplemented
73#2545C2214yescomplemented
74#2544C2214yescomplemented
75#2542C2214yescomplemented
76#2541C2214yes—
77#2541C2214yescomplemented
78#2491C2218yescomplemented
79#2490C2218yescomplemented
80#2472C22116yes—
81#2463C22116yescomplemented
82#2460C22116yescomplemented
83#2458C22116yescomplemented
84#2454C2218yescomplemented
85#2452C2218yescomplemented
86#2443C22116yescomplemented
87#2437C22116yes—
88#2432C22116yescomplemented
89#2426C22116yescomplemented
90#2424C22116yes—
91#2416C22116yescomplemented
92#2416C2218yescomplemented
93#2414C2218yescomplemented
94#2408C2218yes—
95#2407C22116yescomplemented
96C2×#394C2218yes—
97#2363C2218yescomplemented
98#2361C2218yescomplemented
99#2358C22116yes—
100#2331C2214yescomplemented
101#2330C2212yescomplemented
102#2330C2212yescomplemented
103#2329C2218yes—
104#2328C2212yescomplemented
105#2328C2214yescomplemented
106#2327C2212yescomplemented
107#2326C2212yescomplemented
108#2326C2214yescomplemented
109#2326C2212yescomplemented
110#2325C2218yes—
111#2317C2212yes—
112#2311C2212yes—
113#2309C2212yes—
114C4×#127C2214yescomplemented
115C4×#124C2214yescomplemented
116#2297C2211yescharacteristic
117#2297C2211yescharacteristic
118#2296C2212yes—
119#2295C2214yescomplemented
120#2295C2214yescomplemented
121C2×#390C2212yes—
122C2×#390C2212yes—
123#2290C2214yescomplemented
124#2290C2214yescomplemented
125#2285C2211yescharacteristic
126#2285C2211yescharacteristic
127C4×#117C2212yes—
128C2×#376C2211yescharacteristic
129C22×#41C2311yescharacteristic
130C22×#41C2311yescharacteristic
131C22×#41C2318yes—
132C23×D4C2312yes—
133C23×D4C2314yes—
134#559—232no—
135#557—232no—
136#554—264no—
137#554—232no—
138#550—232no—
139#546—264no—
140#544—232no—
141#544—216no—
142#540—216no—
143#540—216no—
144#535—216no—
145#535—216no—
146#533—216no—
147#533D4116yescomplemented
148#532—28no—
149#532—232no—
150C2×C4⋊Q8C2314yes—
151C2×C4⋊Q8C2311yescharacteristic
152C2×C4⋊Q8C2314yes—
153C2×C4⋊Q8C2318yes—
154C2×C4⋊Q8C2312yes—
155C2×#127—28no—
156C2×#127C2314yes—
157C2×#127C2311yescharacteristic
158C2×#127C2312yes—
159C2×#127C2314yes—
160C2×#127C2312yes—
161C2×#127C2314yes—
162C2×#125—216no—
163C2×#125—28no—
164C2×#125C2314yes—
165C2×#125C2314yes—
166C2×#125C2312yes—
167C2×#125C2312yes—
168C2×#125C2314yes—
169C2×#125C2318yes—
170C2×#125C2318yes—
171C2×#125C2311yescharacteristic
172C2×#125C2311yescharacteristic
173C2×#124C2311yescharacteristic
174C2×#124C2311yescharacteristic
175C2×#124C2314yes—
176C2×#124C2314yes—
177C2×#124C2318yes—
178C2×#124C23116yes—
179C2×#123C2318yes—
180C2×#123C2318yes—
181C2×C22⋊Q8C2318yes—
182C2×C22⋊Q8C2318yes—
183C2×C22⋊Q8C2318yes—
184C2×C22⋊Q8C2318yes—
185C2×C22⋊Q8C23116yes—
186C2×C22⋊Q8C2314yes—
187C2×#121C2314yes—
188C2×#121C2318yes—
189C2×#121C2314yes—
190C2×#121C2314yes—
191C2×#121C2318yes—
192C2×#121C2318yes—
193C2×#121C2318yes—
194C2×#121C23116yes—
195C2×#121C23116yes—
196C2×#120C2318yes—
197C2×#120C2318yes—
198#520—216no—
199#518—216no—
200C4×#41—28no—
201C4×#41—28no—
202C2×C4×Q8C2312yes—
203C2×C4×Q8C2312yes—
204C2×C4×Q8C2314yes—
205C2×C4×Q8C2318yes—
206C2×C4×Q8C2314yes—
207C2×C4×D4C2314yes—
208C2×C4×D4C2314yes—
209C2×C4×D4C2312yes—
210C2×C4×D4C2314yes—
211C2×C4×D4C2314yes—
212C2×C4×D4C2314yes—
213C2×C4×D4C2312yes—
214C2×C4×D4C2318yes—
215C2×C4×D4C2314yes—
216C2×C4×D4C2314yes—
217C2×C4×D4C2314yes—
218C2×C4×D4C2318yes—
219C2×C4×D4C23116yes—
220C2×#117C2311yescharacteristic
221C2×#117C2312yes—
222C2×#117C2311yescharacteristic
223C2×#117C2314yes—
224C2×#117C2312yes—
225C2×#117C2312yes—
226C2×#117C2312yes—
227C22×C4⋊C4C2312yes—
228C22×C4⋊C4C2314yes—
229C22×C4⋊C4C2314yes—
230C22×C4⋊C4C2318yes—
231C22×C22⋊C4C2318yes—
232C22×C22⋊C4C2318yes—
233C22×C22⋊C4C2318yes—
234C22×C42C2312yes—
235C22×C42C2312yes—
236C22×C42C2311yescharacteristic
237C22×C42C2311yescharacteristic
238C22×C42C2311yescharacteristic
239#399C23116yes—
240#398C23116yes—
241#397C23116yes—
242#396C23116yes—
243#396C23116yes—
244#396C23116yes—
245#396C23116yes—
246#394C23116yes—
247#394C23116yes—
248#394C23116yes—
249#394C23116yes—
250#394C23116yes—
251#394C23116yes—
252#394C23116yes—
253#394C23116yes—
254#394C23116yes—
255#393C23116yes—
256#393C23116yes—
257#392C23116yes—
258#392C23116yes—
259#391C2314yes—
260#391C2312yes—
261#391C2312yes—
262#391C2318yes—
263#391C2318yes—
264#390C2312yes—
265#390C23116yes—
266#390C2314yes—
267#390C2314yes—
268#390C2314yes—
269#390C2314yes—
270#390C2318yes—
271#390C2314yes—
272#390C2314yes—
273#390C2312yes—
274#390C2314yes—
275#390C23116yes—
276#390C23116yes—
277#390C2318yes—
278#390C2318yes—
279#390C23116yes—
280#389C2318yes—
281#389C2318yes—
282#389C2318yes—
283#389C2314yes—
284#389C2314yes—
285#388C2318yes—
286#388C2318yes—
287#388C23116yes—
288#388C23116yes—
289#388C23116yes—
290#388C23116yes—
291#388C23116yes—
292#387C23116yes—
293#387C2318yes—
294#387C2318yes—
295#387C2318yes—
296#387C2318yes—
297#387C2318yes—
298#387C2318yes—
299#386C2318yes—
300#386C2314yes—
301#386C2314yes—
302#386C2318yes—
303#386C2318yes—
304#386C23116yes—
305#386C23116yes—
306#386C23116yes—
307#385C23116yes—
308#385C23116yes—
309#385C23116yes—
310#385C2318yes—
311#385C2318yes—
312#385C2318yes—
313#385C23116yes—
314#385C2318yes—
315#384C2314yes—
316#384C2312yes—
317#384C2312yes—
318#382C2312yes—
319#382C2314yes—
320#382C2312yes—
321#380C23116yes—
322#380C2318yes—
323#380C2314yes—
324#380C2314yes—
325#379C2318yes—
326C4×C4⋊C4C2314yes—
327C4×C4⋊C4C2314yes—
328C4×C4⋊C4C2314yes—
329C4×C4⋊C4C2314yes—
330C4×C4⋊C4C2314yes—
331C4×C4⋊C4C2314yes—
332C4×C22⋊C4C2318yes—
333C4×C22⋊C4C23116yes—
334C4×C22⋊C4C2314yes—
335C4×C22⋊C4C2314yes—
336#376C2312yes—
337#376C2314yes—
338#376C2312yes—
339#376C2312yes—
340#376C2312yes—
341C2×#95C2314yes—
342C43C2314yes—
343C25C2414yes—
344C2×#41—232no—
345C2×#41—24no—
346C2×#41—24no—
347C2×#41—24no—
348C2×#41—24no—
349C2×#41—24no—
350C2×#41—816no—
351C2×#41#4118yescomplemented
352C22×Q8C2411yescharacteristic
353C22×Q8C2411yescharacteristic
354C22×Q8C2418yes—
355C22×Q8C2414yes—
356C22×D4—28no—
357C22×D4—216no—
358C22×D4—28no—
359C22×D4—28no—
360C22×D4—88no—
361C22×D4C2412yes—
362C22×D4C2414yes—
363C22×D4C2414yes—
364C22×D4C2411yescharacteristic
365C22×D4C2412yes—
366C22×D4C2411yescharacteristic
367C22×D4C24116yes—
368C22×D4C2414yes—
369C22×D4C2418yes—
370C22×D4C2418yes—
371C22×D4C2418yes—
372C22×D4C2418yes—
373C23×C4C2412yes—
374C23×C4C2412yes—
375C23×C4C2414yes—
376C23×C4C2412yes—
377C23×C4C2412yes—
378C23×C4C2418yes—
379C23×C4C2418yes—
380C23×C4C2418yes—
381C23×C4C2414yes—
382C23×C4C2414yes—
383C23×C4C2412yes—
384C23×C4C2411yescharacteristic
385C4⋊Q8—232no—
386C4⋊Q8—24no—
387C4⋊Q8—216no—
388C4⋊Q8—216no—
389C4⋊Q8C2×D4116yes—
390#127—24no—
391#127—216no—
392#127—28no—
393#127—28no—
394#127—216no—
395#127—216no—
396#125—216no—
397#125—232no—
398#125—232no—
399#125—28no—
400#125—28no—
401#125—216no—
402#125—216no—
403#125C2×D418yes—
404#125C2×D418yes—
405#124—232no—
406#124—24no—
407#124—216no—
408#124—24no—
409#124—216no—
410#124—816no—
411#123—232no—
412#123—232no—
413C22⋊Q8—232no—
414C22⋊Q8—232no—
415C22⋊Q8—232no—
416C22⋊Q8—232no—
417C22⋊Q8—816no—
418C22⋊Q8C2×D4132yes—
419#121—216no—
420#121—232no—
421#121—216no—
422#121—216no—
423#121—232no—
424#121—232no—
425#121—232no—
426#121—816no—
427#121—816no—
428#120—232no—
429#120—232no—
430C4×Q8—232no—
431C4×Q8—28no—
432C4×Q8—28no—
433C4×Q8—216no—
434C4×Q8C2×D4132yes—
435C4×D4—216no—
436C4×D4—216no—
437C4×D4—216no—
438C4×D4—216no—
439C4×D4—216no—
440C4×D4—232no—
441C4×D4—232no—
442C4×D4—28no—
443C4×D4—28no—
444C4×D4—216no—
445C4×D4—216no—
446C4×D4—216no—
447C4×D4—816no—
448#117—24no—
449#117—24no—
450#117—28no—
451#117—216no—
452#117—28no—
453#117—28no—
454#117C2×D4116yes—
455C2×C4⋊C4—28no—
456C2×C4⋊C4—216no—
457C2×C4⋊C4—216no—
458C2×C4⋊C4—232no—
459C2×C4⋊C4C2414yes—
460C2×C4⋊C4C2418yes—
461C2×C4⋊C4C2414yes—
462C2×C4⋊C4C2418yes—
463C2×C4⋊C4C2418yes—
464C2×C4⋊C4C2418yes—
465C2×C4⋊C4C2418yes—
466C2×C4⋊C4C2412yes—
467C2×C4⋊C4C2414yes—
468C2×C4⋊C4C2412yes—
469C2×C4⋊C4C2414yes—
470C2×C4⋊C4C2414yes—
471C2×C4⋊C4C2414yes—
472C2×C4⋊C4C2418yes—
473C2×C4⋊C4C24116yes—
474C2×C4⋊C4C2418yes—
475C2×C4⋊C4C2418yes—
476C2×C4⋊C4C2418yes—
477C2×C4⋊C4C2418yes—
478C2×C4⋊C4C2412yes—
479C2×C4⋊C4C2414yes—
480C2×C4⋊C4C2412yes—
481C2×C4⋊C4C2414yes—
482C2×C4⋊C4C2414yes—
483C2×C22⋊C4—232no—
484C2×C22⋊C4—88no—
485C2×C22⋊C4—88no—
486C2×C22⋊C4C2412yes—
487C2×C22⋊C4C2418yes—
488C2×C22⋊C4C2418yes—
489C2×C22⋊C4C2414yes—
490C2×C22⋊C4C2412yes—
491C2×C22⋊C4C2414yes—
492C2×C22⋊C4C2418yes—
493C2×C22⋊C4C2414yes—
494C2×C22⋊C4C2418yes—
495C2×C22⋊C4C2418yes—
496C2×C22⋊C4C2414yes—
497C2×C22⋊C4C2414yes—
498C2×C22⋊C4C24116yes—
499C2×C22⋊C4C24116yes—
500C2×C22⋊C4C24116yes—
501C2×C22⋊C4C24116yes—
502C2×C22⋊C4C24116yes—
503C2×C22⋊C4C2418yes—
504C2×C22⋊C4C24116yes—
505C2×C22⋊C4C24116yes—
506C2×C22⋊C4C24116yes—
507C2×C22⋊C4C2418yes—
508C2×C22⋊C4C2414yes—
509C2×C42—24no—
510C2×C42—24no—
511C2×C42—28no—
512C2×C42—28no—
513C2×C42C2×D418yes—
514C2×C42C2412yes—
515C2×C42C2412yes—
516C2×C42C2418yes—
517C2×C42C2414yes—
518C2×C42C2414yes—
519C2×C42C2412yes—
520C2×C42C2414yes—
521C2×C42C2411yescharacteristic
522C2×C42C2411yescharacteristic
523C2×C42C2412yes—
524C2×C42C2412yes—
525C2×C42C2418yes—
526C2×C42C2418yes—
527C2×C42C2411yescharacteristic
528C2×C42C2411yescharacteristic
529C2×C42C2414yes—
530C2×C42C2412yes—
531#95C2414yes—
532#95C2414yes—
533#95C2414yes—
534#95C2414yes—
535#95C2418yes—
536#95C2418yes—
537#95C2418yes—
538#95C24116yes—
539#95C2418yes—
540#95C2418yes—
541#95C2418yes—
542#95C2418yes—
543#95C2418yes—
544#95C24116yes—
545C24—28no—
546C24—28no—
547C24—28no—
548C24—48no—
549C24—48no—
550C24C2518yes—
551C24C2512yes—
552C24C2512yes—
553C24C2511yescharacteristic
554#41—232no—
555#41—416no—
556#41—864no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—216no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8—48no—
564C2×Q8—416no—
565C2×Q8C22×D4116yes—
566C2×Q8C2×#4114yes—
567C2×D4—24no—
568C2×D4—24no—
569C2×D4—24no—
570C2×D4—24no—
571C2×D4—24no—
572C2×D4—28no—
573C2×D4—232no—
574C2×D4—22no—
575C2×D4—28no—
576C2×D4—28no—
577C2×D4—22no—
578C2×D4—216no—
579C2×D4—216no—
580C2×D4—216no—
581C2×D4—216no—
582C2×D4—28no—
583C2×D4—28no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—28no—
587C2×D4—28no—
588C2×D4—22no—
589C2×D4—416no—
590C2×D4—416no—
591C2×D4—416no—
592C2×D4—48no—
593C2×D4—416no—
594C2×D4—416no—
595C2×D4—416no—
596C2×D4—432no—
597C2×D4—832no—
598C2×D4C2×#4118yes—
599C2×D4C2×#4114yes—
600C22×C4—24no—
601C22×C4—24no—
602C22×C4—28no—
603C22×C4—24no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—28no—
607C22×C4—24no—
608C22×C4—24no—
609C22×C4—28no—
610C22×C4—216no—
611C22×C4—216no—
612C22×C4—216no—
613C22×C4—44no—
614C22×C4—48no—
615C22×C4—44no—
616C22×C4—48no—
617C22×C4—44no—
618C22×C4—416no—
619C22×C4—416no—
620C22×C4—48no—
621C22×C4—416no—
622C22×C4C22×D418yes—
623C22×C4C22×D414yes—
624C22×C4C2×#4118yes—
625C22×C4C2×#4114yes—
626C22×C42−1+414yes—
627C22×C4C2514yes—
628C22×C4C2512yes—
629C22×C4C2512yes—
630C22×C4C2518yes—
631C22×C4C2512yes—
632C22×C4C2514yes—
633C22×C4C2514yes—
634C22×C4C2518yes—
635C22×C4C2512yes—
636C22×C4C2514yes—
637C22×C4C2512yes—
638C22×C4C2514yes—
639C22×C4C2512yes—
640C22×C4C2511yescharacteristic
641C22×C4C2511yescharacteristic
642C4⋊C4—28no—
643C4⋊C4—216no—
644C4⋊C4—216no—
645C4⋊C4—28no—
646C4⋊C4—216no—
647C4⋊C4—216no—
648C4⋊C4—216no—
649C4⋊C4—24no—
650C4⋊C4—28no—
651C4⋊C4—28no—
652C4⋊C4—24no—
653C4⋊C4—216no—
654C4⋊C4—28no—
655C4⋊C4—28no—
656C4⋊C4—416no—
657C4⋊C4—48no—
658C4⋊C4—48no—
659C4⋊C4—48no—
660C4⋊C4—48no—
661C4⋊C4C22×D418yes—
662C4⋊C4C22×D4116yes—
663C4⋊C4C22×D418yes—
664C4⋊C4C22×D4116yes—
665C4⋊C4C22×D4116yes—
666C22⋊C4—24no—
667C22⋊C4—24no—
668C22⋊C4—28no—
669C22⋊C4—28no—
670C22⋊C4—216no—
671C22⋊C4—216no—
672C22⋊C4—28no—
673C22⋊C4—28no—
674C22⋊C4—216no—
675C22⋊C4—216no—
676C22⋊C4—216no—
677C22⋊C4—28no—
678C22⋊C4—232no—
679C22⋊C4—416no—
680C22⋊C4—416no—
681C22⋊C4—416no—
682C22⋊C4—416no—
683C22⋊C4—48no—
684C22⋊C4—416no—
685C22⋊C4—416no—
686C22⋊C4—416no—
687C22⋊C4—48no—
688C22⋊C4C22×D4116yes—
689C42—24no—
690C42—24no—
691C42—28no—
692C42—28no—
693C42—216no—
694C42—24no—
695C42—22no—
696C42—22no—
697C42—28no—
698C42—24no—
699C42—24no—
700C42—48no—
701C42—48no—
702C42C22×D414yes—
703C42C22×D414yes—
704C42C22×D418yes—
705C42C22×D4116yes—
706C23—24no—
707C23—22no—
708C23—22no—
709C23—28no—
710C23—28no—
711C23—22no—
712C23—22no—
713C23—28no—
714C23—22no—
715C23—28no—
716C23—28no—
717C23—216no—
718C23—216no—
719C23—416no—
720C23—88no—
721C23—88no—
722C23—816no—
723C23—816no—
724C23C23×D412yes—
725C23C22×#4114yes—
726C23C22×#4112yes—
727C23C2×2−1+412yes—
728C23C2611yescharacteristic
729Q8—28no—
730Q8—416no—
731Q8—44no—
732Q8—816no—
733D4—216no—
734D4—28no—
735D4—432no—
736D4—48no—
737D4—416no—
738D4—416no—
739D4—44no—
740D4—816no—
741D4—816no—
742D4—816no—
743D4—88no—
744D4—832no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—28no—
748C2×C4—28no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—216no—
752C2×C4—22no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—28no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—28no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—216no—
767C2×C4—28no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—28no—
771C2×C4—48no—
772C2×C4—416no—
773C2×C4—48no—
774C2×C4—88no—
775C2×C4—816no—
776C2×C4—816no—
777C2×C4—816no—
778C2×C4—88no—
779C2×C4—84no—
780C2×C4—84no—
781C2×C4#548116yes—
782C2×C4C23×D414yes—
783C2×C4C23×D414yes—
784C2×C4C23×D418yes—
785C2×C4C23×D418yes—
786C2×C4C23×D412yes—
787C2×C4C23×D412yes—
788C2×C4C22×#4114yes—
789C2×C4C22×#4112yes—
790C2×C4C22×#4112yes—
791C2×C4C2×2−1+412yes—
792C2×C4C2×2−1+412yes—
793C22—24no—
794C22—24no—
795C22—24no—
796C22—28no—
797C22—24no—
798C22—44no—
799C22—44no—
800C22—44no—
801C22—48no—
802C22—48no—
803C22—44no—
804C22—416no—
805C22—44no—
806C22—416no—
807C22—42no—
808C22—48no—
809C22—1616no—
810C22C2×#54814yes—
811C22C24×D411yescharacteristic
812C22C23×#4111yescharacteristic
813C22C22×2−1+411yescharacteristic
814C22H(7,𝔽2)14yes—
815C4—24no—
816C4—24no—
817C4—28no—
818C4—28no—
819C4—24no—
820C4—44no—
821C4—48no—
822C4—44no—
823C4—42no—
824C4—42no—
825C4—48no—
826C4—44no—
827C4—42no—
828C4C2×#54814yes—
829C4C2×#54814yes—
830C2—24no—
831C2—44no—
832C2—82no—
833C2—88no—
834C2C22×#54811yescharacteristic
835C2#6285212yes—
836C2#6285812yes—
837C2#6288112yes—
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×#3504C2semidirect
2. C2×#3508C2semidirect
3. #43103C2semidirect
4. #39174C2semidirect
5. #39169C2semidirect
6. #39164C2semidirect
7. #39161C2semidirect
8. #37756C2semidirect
9. #37710C2semidirect
10. #37706C2semidirect
11. #35533C2semidirect
12. #35529C2semidirect
13. #35333C2semidirect
14. #35272C2semidirect
15. #35264C2semidirect
16. C2×#2641C2semidirect
17. #34275C2semidirect
18. #34074C2semidirect
19. #34070C2semidirect
23. C2×#557C22semidirect
25. C2×#554C22semidirect
29. C2×#544C22semidirect
35. C2×#533C22semidirect
40. C22×#125C22semidirect
45. #2861C22semidirect
46. #2858C22semidirect
48. #2851C22semidirect
49. #2731C22semidirect
50. #2730C22semidirect
51. #2711C22semidirect
52. #2711C22semidirect
53. #2707C22semidirect
54. #2681C22semidirect
55. #2676C22semidirect
56. #2676C22semidirect
61. #2641C22semidirect
62. #2640C22semidirect
63. #2629C22semidirect
66. #2566C22semidirect
67. #2566C22semidirect
68. #2566C22semidirect
69. #2565C22semidirect
70. #2563C22semidirect
72. #2548C22semidirect
73. #2545C22semidirect
74. #2544C22semidirect
75. #2542C22semidirect
77. #2541C22semidirect
78. #2491C22semidirect
79. #2490C22semidirect
81. #2463C22semidirect
82. #2460C22semidirect
83. #2458C22semidirect
84. #2454C22semidirect
85. #2452C22semidirect
86. #2443C22semidirect
88. #2432C22semidirect
89. #2426C22semidirect
91. #2416C22semidirect
92. #2416C22semidirect
93. #2414C22semidirect
95. #2407C22semidirect
97. #2363C22semidirect
98. #2361C22semidirect
100. #2331C22semidirect
101. #2330C22semidirect
102. #2330C22semidirect
104. #2328C22semidirect
105. #2328C22semidirect
106. #2327C22semidirect
107. #2326C22semidirect
108. #2326C22semidirect
109. #2326C22semidirect
114. C4×#127C22semidirect
115. C4×#124C22semidirect
119. #2295C22semidirect
120. #2295C22semidirect
123. #2290C22semidirect
124. #2290C22semidirect
147. #533D4semidirect
351. C2×#41#41semidirect

Maximal subgroups

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

subgroupindex
C2×#35042
C2×#35082
#431032
#391742
#391692
#391642
#391612
#377562
#377102
#377062
#355332
#355292
#353332
#352722
#352642
C2×#26412
#342752
#340742
#340702