Finite Group Databasebeta

← #7647078

Subgroups — #7647078

Order 512.

8738 conjugacy classes of subgroups.

The subgroup lattice has 905 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3496C211yesmaximal, characteristic, complemented
2C2×#3460C211yesmaximal, characteristic, complemented
3#42443C218yesmaximal, complemented
4#42438C218yesmaximal, complemented
5#39471C214yesmaximal, complemented
6#39342C214yesmaximal, complemented
7#38920C214yesmaximal, complemented
8#38910C214yesmaximal, complemented
9#37439C214yesmaximal, complemented
10#36739C218yesmaximal, complemented
11#35513C214yesmaximal, complemented
12#35273C212yesmaximal, complemented
13#35252C214yesmaximal, complemented
14#35166C212yesmaximal, complemented
15#35158C212yesmaximal, complemented
16#34937C212yesmaximal, complemented
17C2×#2354C211yesmaximal, characteristic, complemented
18C22×H(5,𝔽2)C2212yes—
19#3496—216no—
20C2×#547C2214yes—
21C2×#546C2218yes—
22C2×D42C2214yes—
23#3460—216no—
24C2×#544C2211yescharacteristic, complemented
25C2×#542C2214yescomplemented
26C2×#540C2214yescomplemented
27C2×#538C2214yescomplemented
28C2×#537C2212yes—
29C2×#537C2211yescharacteristic, complemented
30C2×#537C2214yescomplemented
31C2×#535C2212yes—
32C2×#535C2214yescomplemented
33C2×#534C2214yes—
34C2×#532C2212yes—
35C2×#532C2214yescomplemented
36C2×#532C2214yescomplemented
37C2×#529C2214yescomplemented
38C2×#525C2214yescomplemented
39C22×#121C2214yes—
40C2×C4×#41C2212yescomplemented
41C22×C4×D4C2211yescharacteristic
42C22×#117C2212yescomplemented
43#2857C2214yescomplemented
44#2856C2218yescomplemented
45#2856C2214yescomplemented
46#2850C2218yescomplemented
47#2813C22116yescomplemented
48#2718C22116yescomplemented
49#2710C22116yescomplemented
50#2706C22116yescomplemented
51#2703C22116yescomplemented
52#2685C22116yescomplemented
53#2678C22116yescomplemented
54#2670C22116yescomplemented
55#2669C22116yescomplemented
56#2656C2218yescomplemented
57#2639C2218yescomplemented
58#2626C2218yescomplemented
59#2624C2218yescomplemented
60#2620C2218yescomplemented
61#2620C2218yescomplemented
62#2619C2218yescomplemented
63#2617C2218yescomplemented
64#2615C2218yescomplemented
65#2548C2212yescomplemented
66#2547C2212yescomplemented
67#2546C2212yescomplemented
68#2545C2214yescomplemented
69#2544C2214yescomplemented
70#2543C2218yescomplemented
71#2542C2218yescomplemented
72#2541C2218yescomplemented
73#2541C2212yescomplemented
74#2540C2218yescomplemented
75#2540C2218yescomplemented
76#2538C2214yescomplemented
77#2538C2214yescomplemented
78#2537C2214yescomplemented
79#2537C2214yescomplemented
80#2492C2218yescomplemented
81#2491C2218yescomplemented
82#2490C2218yescomplemented
83#2489C2218yescomplemented
84#2487C2218yescomplemented
85#2435C2218yescomplemented
86#2433C2218yescomplemented
87#2432C2218yescomplemented
88#2431C2218yescomplemented
89#2416C2214yescomplemented
90#2416C2218yescomplemented
91#2416C2214yescomplemented
92#2416C2218yescomplemented
93#2414C2218yescomplemented
94#2414C2218yescomplemented
95#2411C22116yescomplemented
96#2410C22116yescomplemented
97#2410C22116yescomplemented
98#2408C2218yescomplemented
99#2408C2218yescomplemented
100#2408C2218yescomplemented
101#2407C2218yescomplemented
102#2407C2218yescomplemented
103#2392C2218yescomplemented
104#2354C2214yescomplemented
105#2354C2214yescomplemented
106#2354C2218yescomplemented
107#2317C2214yescomplemented
108#2311C2214yescomplemented
109#2311C2214yescomplemented
110#2309C2214yescomplemented
111C4×#121C2214yescomplemented
112C4×#121C2214yescomplemented
113#2297C2214yescomplemented
114C2×#390C2212yes—
115C2×#388C2214yescomplemented
116C2×#384C2211yescharacteristic, complemented
117C2×#380C2212yescomplemented
118C2×C4×C4⋊C4C2212yescomplemented
119C2×C4×C4⋊C4C2211yescharacteristic, complemented
120C2×H(5,𝔽2)—216no—
121C2×H(5,𝔽2)—48no—
122C2×H(5,𝔽2)—48no—
123C22×#41C2314yes—
124C22×#41C2312yes—
125C22×#41C2314yes—
126C22×#41C2318yes—
127C23×D4C2311yescharacteristic
128C23×D4C2314yes—
129C23×D4C2318yes—
130C23×D4C2318yes—
131C24×C4C2312yes—
132#547—232no—
133#546—264no—
134D42—232no—
135#544—28no—
136#542—232no—
137#540—232no—
138#538—232no—
139#537—216no—
140#537—28no—
141#537—416no—
142#535—216no—
143#535—416no—
144#534—232no—
145#532—232no—
146#532—216no—
147#532—416no—
148C2×C4⋊Q8C2312yes—
149C2×C4⋊Q8C2314yes—
150C2×C4⋊Q8C2314yes—
151C2×#127C2312yes—
152C2×#127C2314yes—
153C2×#127C2318yes—
154C2×#127C2314yes—
155#529—232no—
156C2×#126C2318yes—
157C2×#125C2314yes—
158C2×#124C2314yes—
159C2×#124C2318yes—
160C2×#124C2314yes—
161C2×#124C2318yes—
162C2×#124C2314yes—
163C2×#124C2314yes—
164#525—232no—
165C2×#123C2318yes—
166C2×#123C2318yes—
167C2×#123C23116yes—
168C2×C22⋊Q8C2314yes—
169C2×C22⋊Q8C2314yes—
170C2×C22⋊Q8C2314yes—
171C2×C22⋊Q8C2318yes—
172C2×C22⋊Q8C2318yes—
173C2×C22⋊Q8C2318yes—
174C2×#121—232no—
175C2×#121C2318yes—
176C2×#121C2314yes—
177C2×#121C2318yes—
178C2×#121C2314yes—
179C2×#121C2318yes—
180C2×#121C2314yes—
181C2×#121C2314yes—
182C2×#121C2314yes—
183C2×#121C2318yes—
184C2×#121C2314yes—
185C2×#121C2314yes—
186C2×#121C2314yes—
187C2×#121C2318yes—
188C2×#121C2318yes—
189C2×#121C2318yes—
190C2×#121C2318yes—
191C2×#121C23116yes—
192C2×#121C2314yes—
193C2×#121C2318yes—
194C2×#121C2318yes—
195C2×#121C2318yes—
196C2×#120C2318yes—
197C2×#120C23116yes—
198C2×#120C23116yes—
199C2×#120C23116yes—
200C4×#41—216no—
201C2×C4×Q8C2312yes—
202C2×C4×Q8C2312yes—
203C2×C4×D4D4116yescomplemented
204C2×C4×D4C2314yes—
205C2×C4×D4C2314yes—
206C2×C4×D4C2314yes—
207C2×C4×D4C2312yes—
208C2×C4×D4C2312yes—
209C2×C4×D4C2318yes—
210C2×C4×D4C2314yes—
211C2×C4×D4C2318yes—
212C2×C4×D4C2318yes—
213C2×C4×D4C2314yes—
214C2×C4×D4C2314yes—
215C2×#117—48no—
216C2×#117C2314yes—
217C2×#117C2312yes—
218C2×#117C2314yes—
219C2×#117C2314yes—
220C2×#117C2314yes—
221C2×#117C2318yes—
222C22×C4⋊C4C2312yes—
223C22×C4⋊C4C2314yes—
224C22×C4⋊C4C2311yescharacteristic
225C22×C4⋊C4C2312yes—
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2312yes—
228C22×C4⋊C4C2311yescharacteristic
229C22×C22⋊C4C2318yes—
230C22×C22⋊C4C2314yes—
231C22×C22⋊C4C2314yes—
232C22×C22⋊C4C2312yes—
233C22×C42C2314yes—
234C22×C42C2312yes—
235C22×C42C2314yes—
236C22×C42C2311yescharacteristic
237#400C23116yes—
238#399C23116yes—
239#399C23116yes—
240#398C2318yes—
241#397C23116yes—
242#397C2318yes—
243#396C23116yes—
244#396C2318yes—
245#396C23116yes—
246#396C2318yes—
247#394C2318yes—
248#394C23116yes—
249#394C2318yes—
250#394C23116yes—
251#394C23116yes—
252#394C23116yes—
253#394C23116yes—
254#394C23116yes—
255#394C23116yes—
256#394C2318yes—
257#393C23116yes—
258#392C23116yes—
259#392C23116yes—
260#392C23116yes—
261#392C23116yes—
262#392C23116yes—
263#392C2318yes—
264#392C23116yes—
265#391C2318yes—
266#391C2318yes—
267#391C2314yes—
268#391C2314yes—
269#390C2314yes—
270#390C2318yes—
271#390C2318yes—
272#390C2318yes—
273#390C2318yes—
274#390C2318yes—
275#390C23116yes—
276#390C23116yes—
277#390C2318yes—
278#390C2318yes—
279#390C2318yes—
280#390C2314yes—
281#390C2314yes—
282#390C2314yes—
283#389C2314yes—
284#389C2318yes—
285#389C2318yes—
286#389C2314yes—
287#388C23116yes—
288#388C23116yes—
289#388C23116yes—
290#388C23116yes—
291#388C2318yes—
292#388C2318yes—
293#386C23116yes—
294#386C23116yes—
295#386C2318yes—
296#386C23116yes—
297#386C2318yes—
298#386C2318yes—
299#386C2318yes—
300#385C23116yes—
301#385C23116yes—
302#384C2318yes—
303#384C2314yes—
304#384C2314yes—
305#382C2318yes—
306#380C2314yes—
307#380C2318yes—
308#380C2318yes—
309#380C2318yes—
310#380C2318yes—
311#380C2318yes—
312#380C2318yes—
313#380C2314yes—
314#379C23116yes—
315#379C23116yes—
316C4×C4⋊C4C2314yes—
317C4×C4⋊C4C2318yes—
318C4×C4⋊C4C2318yes—
319C4×C4⋊C4C2312yes—
320C4×C4⋊C4C2312yes—
321C4×C22⋊C4C2318yes—
322C4×C22⋊C4C2318yes—
323C2×#95C2314yes—
324C2×#95C2312yes—
325C25C2412yes—
326C25C2418yes—
327H(5,𝔽2)—4128no—
328C2×#41—232no—
329C2×#41—28no—
330C2×#41—216no—
331C2×#41—216no—
332C2×#41—28no—
333C2×#41—216no—
334C2×#41—28no—
335C2×#41—216no—
336C2×#41—48no—
337C2×#41—48no—
338C2×#41—416no—
339C2×#41—416no—
340C22×Q8C2412yes—
341C22×Q8C2414yes—
342C22×Q8C2414yes—
343C22×D4—232no—
344C22×D4—232no—
345C22×D4—216no—
346C22×D4—24no—
347C22×D4—24no—
348C22×D4—416no—
349C22×D4—416no—
350C22×D4—48no—
351C22×D4—48no—
352C22×D4—416no—
353C22×D4—416no—
354C22×D4C2×D418yes—
355C22×D4C2414yes—
356C22×D4C2412yes—
357C22×D4C2414yes—
358C22×D4C2418yes—
359C22×D4C2414yes—
360C22×D4C2414yes—
361C22×D4C2414yes—
362C22×D4C2418yes—
363C22×D4C2418yes—
364C22×D4C2418yes—
365C22×D4C2418yes—
366C22×D4C24116yes—
367C22×D4C2414yes—
368C22×D4C2418yes—
369C22×D4C24116yes—
370C23×C4—44no—
371C23×C4—44no—
372C23×C4C2×D4116yes—
373C23×C4C2414yes—
374C23×C4C2414yes—
375C23×C4C2418yes—
376C23×C4C2412yes—
377C23×C4C2411yescharacteristic
378C23×C4C2414yes—
379C23×C4C2414yes—
380C23×C4C2412yes—
381C23×C4C2418yes—
382C23×C4C2414yes—
383C23×C4C2411yescharacteristic
384C23×C4C2414yes—
385C23×C4C2412yes—
386C23×C4C2411yescharacteristic
387C4⋊Q8—216no—
388C4⋊Q8—28no—
389C4⋊Q8—48no—
390#127—216no—
391#127—28no—
392#127—48no—
393#127—416no—
394#126—232no—
395#125—216no—
396#124—216no—
397#124—232no—
398#124—216no—
399#124—416no—
400#124—48no—
401#124—48no—
402#123—232no—
403#123—232no—
404#123—264no—
405C22⋊Q8—216no—
406C22⋊Q8—216no—
407C22⋊Q8—216no—
408C22⋊Q8—232no—
409C22⋊Q8—416no—
410C22⋊Q8—416no—
411#121—216no—
412#121—216no—
413#121—216no—
414#121—232no—
415#121—232no—
416#121—232no—
417#121—216no—
418#121—216no—
419#121—216no—
420#121—216no—
421#121—232no—
422#121—216no—
423#121—232no—
424#121—48no—
425#121—416no—
426#121—416no—
427#121—416no—
428#121—416no—
429#121—416no—
430#121—432no—
431#121—88no—
432#120—232no—
433#120—264no—
434#120—432no—
435#120—816no—
436C4×Q8—28no—
437C4×Q8—28no—
438C4×D4—216no—
439C4×D4—216no—
440C4×D4—232no—
441C4×D4—28no—
442C4×D4—28no—
443C4×D4—216no—
444C4×D4—216no—
445C4×D4—416no—
446C4×D4—416no—
447C4×D4C2×D4132yes—
448C4×D4C2×D4132yes—
449#117—28no—
450#117—216no—
451#117—216no—
452#117—216no—
453#117—416no—
454#117—48no—
455C2×C4⋊C4—216no—
456C2×C4⋊C4—28no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—42no—
459C2×C4⋊C4—44no—
460C2×C4⋊C4—82no—
461C2×C4⋊C4C2×D418yes—
462C2×C4⋊C4C2414yes—
463C2×C4⋊C4C2411yescharacteristic
464C2×C4⋊C4C2412yes—
465C2×C4⋊C4C2414yes—
466C2×C4⋊C4C2418yes—
467C2×C4⋊C4C2418yes—
468C2×C4⋊C4C2412yes—
469C2×C4⋊C4C2412yes—
470C2×C4⋊C4C2412yes—
471C2×C4⋊C4C2414yes—
472C2×C4⋊C4C2414yes—
473C2×C4⋊C4C2414yes—
474C2×C4⋊C4C2414yes—
475C2×C4⋊C4C2418yes—
476C2×C4⋊C4C2414yes—
477C2×C4⋊C4C2414yes—
478C2×C4⋊C4C2418yes—
479C2×C4⋊C4C2412yes—
480C2×C4⋊C4C2418yes—
481C2×C4⋊C4C2418yes—
482C2×C4⋊C4C24116yes—
483C2×C4⋊C4C2414yes—
484C2×C4⋊C4C2411yescharacteristic
485C2×C22⋊C4—232no—
486C2×C22⋊C4—48no—
487C2×C22⋊C4—84no—
488C2×C22⋊C4C2×D4116yes—
489C2×C22⋊C4C2418yes—
490C2×C22⋊C4C2418yes—
491C2×C22⋊C4C24116yes—
492C2×C22⋊C4C2414yes—
493C2×C22⋊C4C2414yes—
494C2×C22⋊C4C2414yes—
495C2×C22⋊C4C2418yes—
496C2×C22⋊C4C2418yes—
497C2×C22⋊C4C2418yes—
498C2×C22⋊C4C2418yes—
499C2×C22⋊C4C2418yes—
500C2×C22⋊C4C2418yes—
501C2×C22⋊C4C24116yes—
502C2×C22⋊C4C2418yes—
503C2×C22⋊C4C2418yes—
504C2×C22⋊C4C2418yes—
505C2×C22⋊C4C2418yes—
506C2×C22⋊C4C2418yes—
507C2×C22⋊C4C24116yes—
508C2×C22⋊C4C24116yes—
509C2×C22⋊C4C24116yes—
510C2×C22⋊C4C24116yes—
511C2×C22⋊C4C2418yes—
512C2×C22⋊C4C2418yes—
513C2×C22⋊C4C2418yes—
514C2×C42—28no—
515C2×C42—216no—
516C2×C42—48no—
517C2×C42C2×D418yes—
518C2×C42C2414yes—
519C2×C42C2414yes—
520C2×C42C2418yes—
521C2×C42C2414yes—
522C2×C42C2414yes—
523C2×C42C2414yes—
524C2×C42C2418yes—
525C2×C42C2412yes—
526C2×C42C2412yes—
527#95C24116yes—
528#95C2414yes—
529#95C2414yes—
530#95C2418yes—
531#95C2418yes—
532#95C2418yes—
533#95C2418yes—
534#95C24116yes—
535#95C24116yes—
536C24—24no—
537C24—24no—
538C24—216no—
539C24—42no—
540C24—42no—
541C24—42no—
542C24—42no—
543C24—48no—
544C24—48no—
545C24—48no—
546C24—48no—
547C24—48no—
548C24—48no—
549C24C22×D418yes—
550C24C2518yes—
551C24C2514yes—
552C24C2514yes—
553C24C2511yescharacteristic
554#41—4128no—
555#41—432no—
556#41—464no—
557#41—832no—
558C2×Q8—24no—
559C2×Q8—28no—
560C2×Q8—28no—
561C2×Q8—24no—
562C2×Q8—28no—
563C2×Q8—24no—
564C2×Q8—28no—
565C2×Q8—44no—
566C2×Q8—44no—
567C2×D4—28no—
568C2×D4—232no—
569C2×D4—216no—
570C2×D4—28no—
571C2×D4—28no—
572C2×D4—216no—
573C2×D4—216no—
574C2×D4—216no—
575C2×D4—216no—
576C2×D4—232no—
577C2×D4—24no—
578C2×D4—28no—
579C2×D4—28no—
580C2×D4—28no—
581C2×D4—216no—
582C2×D4—28no—
583C2×D4—28no—
584C2×D4—28no—
585C2×D4—28no—
586C2×D4—24no—
587C2×D4—28no—
588C2×D4—24no—
589C2×D4—28no—
590C2×D4—216no—
591C2×D4—28no—
592C2×D4—416no—
593C2×D4—416no—
594C2×D4—48no—
595C2×D4—48no—
596C2×D4—48no—
597C2×D4—48no—
598C2×D4—48no—
599C2×D4—48no—
600C2×D4—44no—
601C2×D4—48no—
602C2×D4—44no—
603C2×D4—48no—
604C2×D4—44no—
605C2×D4—48no—
606C2×D4—48no—
607C2×D4—44no—
608C2×D4—48no—
609C2×D4—416no—
610C2×D4—416no—
611C2×D4—416no—
612C2×D4—4128no—
613C2×D4—4128no—
614C2×D4—832no—
615C2×D4C22×D4116yes—
616C22×C4—22no—
617C22×C4—28no—
618C22×C4—22no—
619C22×C4—28no—
620C22×C4—216no—
621C22×C4—24no—
622C22×C4—24no—
623C22×C4—28no—
624C22×C4—28no—
625C22×C4—28no—
626C22×C4—216no—
627C22×C4—24no—
628C22×C4—28no—
629C22×C4—216no—
630C22×C4—28no—
631C22×C4—28no—
632C22×C4—216no—
633C22×C4—28no—
634C22×C4—28no—
635C22×C4—432no—
636C22×C4—42no—
637C22×C4—41no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4—42no—
641C22×C4—41no—
642C22×C4—42no—
643C22×C4—48no—
644C22×C4—48no—
645C22×C4—44no—
646C22×C4—42no—
647C22×C4—44no—
648C22×C4—42no—
649C22×C4—44no—
650C22×C4—44no—
651C22×C4C22×D414yes—
652C22×C4C22×D4116yes—
653C22×C4C22×D414yes—
654C22×C4C22×D4116yes—
655C22×C4C22×D418yes—
656C22×C4C22×D414yes—
657C22×C4H(5,𝔽2)14yes—
658C22×C4H(5,𝔽2)14yes—
659C22×C4C2514yes—
660C22×C4C2514yes—
661C22×C4C2514yes—
662C22×C4C2518yes—
663C22×C4C2512yes—
664C22×C4C2518yes—
665C22×C4C2514yes—
666C22×C4C2512yes—
667C22×C4C2514yes—
668C22×C4C2511yescharacteristic
669C22×C4C2512yes—
670C22×C4C2512yes—
671C22×C4C2511yescharacteristic
672C4⋊C4—28no—
673C4⋊C4—216no—
674C4⋊C4—24no—
675C4⋊C4—24no—
676C4⋊C4—28no—
677C4⋊C4—28no—
678C4⋊C4—28no—
679C4⋊C4—28no—
680C4⋊C4—216no—
681C4⋊C4—28no—
682C4⋊C4—24no—
683C4⋊C4—22no—
684C4⋊C4—216no—
685C4⋊C4—28no—
686C4⋊C4—24no—
687C4⋊C4—42no—
688C4⋊C4—44no—
689C4⋊C4—48no—
690C4⋊C4—48no—
691C4⋊C4—48no—
692C4⋊C4—416no—
693C4⋊C4C22×D4116yes—
694C4⋊C4H(5,𝔽2)14yescomplemented
695C22⋊C4—28no—
696C22⋊C4—216no—
697C22⋊C4—216no—
698C22⋊C4—216no—
699C22⋊C4—232no—
700C22⋊C4—28no—
701C22⋊C4—28no—
702C22⋊C4—216no—
703C22⋊C4—216no—
704C22⋊C4—216no—
705C22⋊C4—216no—
706C22⋊C4—48no—
707C22⋊C4—416no—
708C22⋊C4—48no—
709C22⋊C4—48no—
710C22⋊C4—48no—
711C22⋊C4—48no—
712C22⋊C4—48no—
713C22⋊C4—416no—
714C22⋊C4—48no—
715C22⋊C4—416no—
716C22⋊C4—48no—
717C22⋊C4—416no—
718C22⋊C4—416no—
719C22⋊C4C22×D4132yes—
720C42—28no—
721C42—28no—
722C42—28no—
723C42—28no—
724C42—28no—
725C42—216no—
726C42—48no—
727C42C22×D418yes—
728C42C22×D418yes—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—24no—
734C23—24no—
735C23—24no—
736C23—24no—
737C23—24no—
738C23—24no—
739C23—216no—
740C23—24no—
741C23—28no—
742C23—28no—
743C23—24no—
744C23—24no—
745C23—28no—
746C23—28no—
747C23—24no—
748C23—28no—
749C23—24no—
750C23—28no—
751C23—24no—
752C23—28no—
753C23—24no—
754C23—48no—
755C23—48no—
756C23—432no—
757C23—84no—
758C23—84no—
759C23—84no—
760C23—84no—
761C23—816no—
762C23—816no—
763C23—168no—
764C23—168no—
765C23—168no—
766C23—168no—
767C23C23×D418yes—
768C23C23×D412yes—
769C23C2×H(5,𝔽2)12yes—
770C23C2×H(5,𝔽2)12yes—
771C23C2611yescharacteristic
772Q8—48no—
773Q8—416no—
774Q8—88no—
775D4—232no—
776D4—464no—
777D4—432no—
778D4—416no—
779D4—416no—
780D4—48no—
781D4—416no—
782D4—88no—
783D4—816no—
784D4—816no—
785D4—88no—
786D4—816no—
787D4—816no—
788D4—816no—
789D4—1616no—
790C2×C4—24no—
791C2×C4—22no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—24no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—28no—
799C2×C4—232no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—28no—
804C2×C4—22no—
805C2×C4—24no—
806C2×C4—28no—
807C2×C4—22no—
808C2×C4—24no—
809C2×C4—28no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—28no—
813C2×C4—28no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—28no—
819C2×C4—22no—
820C2×C4—24no—
821C2×C4—416no—
822C2×C4—48no—
823C2×C4—44no—
824C2×C4—48no—
825C2×C4—432no—
826C2×C4—432no—
827C2×C4—416no—
828C2×C4—416no—
829C2×C4—88no—
830C2×C4—88no—
831C2×C4—84no—
832C2×C4#535116yescomplemented
833C2×C4C23×D414yes—
834C2×C4C23×D412yes—
835C2×C4C23×D418yes—
836C2×C4C23×D414yes—
837C2×C4C23×D412yes—
838C2×C4C2×H(5,𝔽2)14yes—
839C2×C4C2×H(5,𝔽2)14yes—
840C2×C4C2×H(5,𝔽2)14yes—
841C2×C4C2×H(5,𝔽2)12yes—
842C2×C4#58512yes—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—28no—
850C22—28no—
851C22—28no—
852C22—44no—
853C22—44no—
854C22—44no—
855C22—44no—
856C22—44no—
857C22—48no—
858C22—44no—
859C22—48no—
860C22—44no—
861C22—48no—
862C22—44no—
863C22—48no—
864C22—48no—
865C22—44no—
866C22—44no—
867C22—48no—
868C22—44no—
869C22—48no—
870C22—816no—
871C22—1632no—
872C22C2×#53514yes—
873C22C24×D411yescharacteristic
874C22C22×H(5,𝔽2)11yescharacteristic
875C22C22×H(5,𝔽2)11yescharacteristic
876C22C22×H(5,𝔽2)11yescharacteristic
877C22C2×#58511yescharacteristic
878C22H(7,𝔽2)11yescharacteristic
879C222−1+611yescharacteristic
880C4—22no—
881C4—28no—
882C4—24no—
883C4—24no—
884C4—44no—
885C4—44no—
886C4—42no—
887C4—48no—
888C4—48no—
889C4—44no—
890C4—44no—
891C4C2×#53518yes—
892C4#349614yes—
893C2—24no—
894C2—48no—
895C2—84no—
896C2—88no—
897C2C22×#53511yescharacteristic
898C2C2×#349611yescharacteristic
899C2#6285311yescharacteristic
900C2#6291411yescharacteristic
901C2#6291611yescharacteristic
902C2#6293011yescharacteristic
903C2#6293111yescharacteristic
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×#3496C2semidirect
2. C2×#3460C2semidirect
3. #42443C2semidirect
4. #42438C2semidirect
5. #39471C2semidirect
6. #39342C2semidirect
7. #38920C2semidirect
8. #38910C2semidirect
9. #37439C2semidirect
10. #36739C2semidirect
11. #35513C2semidirect
12. #35273C2semidirect
13. #35252C2semidirect
14. #35166C2semidirect
15. #35158C2semidirect
16. #34937C2semidirect
17. C2×#2354C2semidirect
24. C2×#544C22semidirect
25. C2×#542C22semidirect
26. C2×#540C22semidirect
27. C2×#538C22semidirect
29. C2×#537C22semidirect
30. C2×#537C22semidirect
32. C2×#535C22semidirect
35. C2×#532C22semidirect
36. C2×#532C22semidirect
37. C2×#529C22semidirect
38. C2×#525C22semidirect
40. C2×C4×#41C22semidirect
42. C22×#117C22semidirect
43. #2857C22semidirect
44. #2856C22semidirect
45. #2856C22semidirect
46. #2850C22semidirect
47. #2813C22semidirect
48. #2718C22semidirect
49. #2710C22semidirect
50. #2706C22semidirect
51. #2703C22semidirect
52. #2685C22semidirect
53. #2678C22semidirect
54. #2670C22semidirect
55. #2669C22semidirect
56. #2656C22semidirect
57. #2639C22semidirect
58. #2626C22semidirect
59. #2624C22semidirect
60. #2620C22semidirect
61. #2620C22semidirect
62. #2619C22semidirect
63. #2617C22semidirect
64. #2615C22semidirect
65. #2548C22semidirect
66. #2547C22semidirect
67. #2546C22semidirect
68. #2545C22semidirect
69. #2544C22semidirect
70. #2543C22semidirect
71. #2542C22semidirect
72. #2541C22semidirect
73. #2541C22semidirect
74. #2540C22semidirect
75. #2540C22semidirect
76. #2538C22semidirect
77. #2538C22semidirect
78. #2537C22semidirect
79. #2537C22semidirect
80. #2492C22semidirect
81. #2491C22semidirect
82. #2490C22semidirect
83. #2489C22semidirect
84. #2487C22semidirect
85. #2435C22semidirect
86. #2433C22semidirect
87. #2432C22semidirect
88. #2431C22semidirect
89. #2416C22semidirect
90. #2416C22semidirect
91. #2416C22semidirect
92. #2416C22semidirect
93. #2414C22semidirect
94. #2414C22semidirect
95. #2411C22semidirect
96. #2410C22semidirect
97. #2410C22semidirect
98. #2408C22semidirect
99. #2408C22semidirect
100. #2408C22semidirect
101. #2407C22semidirect
102. #2407C22semidirect
103. #2392C22semidirect
104. #2354C22semidirect
105. #2354C22semidirect
106. #2354C22semidirect
107. #2317C22semidirect
108. #2311C22semidirect
109. #2311C22semidirect
110. #2309C22semidirect
111. C4×#121C22semidirect
112. C4×#121C22semidirect
113. #2297C22semidirect
115. C2×#388C22semidirect
116. C2×#384C22semidirect
117. C2×#380C22semidirect
118. C2×C4×C4⋊C4C22semidirect
119. C2×C4×C4⋊C4C22semidirect
203. C2×C4×D4D4semidirect
694. C4⋊C4H(5,𝔽2)semidirect
832. C2×C4#535semidirect

Maximal subgroups

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

subgroupindex
C2×#34962
C2×#34602
#424432
#424382
#394712
#393422
#389202
#389102
#374392
#367392
#355132
#352732
#352522
#351662
#351582
#349372
C2×#23542