Finite Group Databasebeta

← #7646201

Subgroups — #7646201

Order 512.

8496 conjugacy classes of subgroups.

The subgroup lattice has 842 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#42652C214yesmaximal, complemented
4#42648C214yesmaximal, complemented
5#42430C214yesmaximal, complemented
6#42426C214yesmaximal, complemented
7#39881C218yesmaximal, complemented
8#39876C218yesmaximal, complemented
9#37446C214yesmaximal, complemented
10#36739C218yesmaximal, complemented
11#35513C214yesmaximal, complemented
12#35328C212yesmaximal, complemented
13#35166C212yesmaximal, complemented
14#35158C212yesmaximal, complemented
15#35078C214yesmaximal, complemented
16#34937C212yesmaximal, complemented
17C2×#2357C211yesmaximal, 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×#534C2214yes—
33C2×#532C2212yes—
34C2×#532C2214yescomplemented
35C2×#532C2214yescomplemented
36C2×#529C2214yescomplemented
37C2×#525C2214yescomplemented
38C22×#121C2214yes—
39C2×C4×#41C2212yescomplemented
40C22×C4×D4C2211yescharacteristic
41#2856C2218yescomplemented
42#2850C2218yescomplemented
43#2850C2218yescomplemented
44#2816C2218yescomplemented
45#2815C2218yescomplemented
46#2718C22116yescomplemented
47#2710C22116yescomplemented
48#2706C22116yescomplemented
49#2703C22116yescomplemented
50#2685C22116yescomplemented
51#2678C22116yescomplemented
52#2670C22116yescomplemented
53#2669C22116yescomplemented
54#2661C2218yescomplemented
55#2661C2218yescomplemented
56#2656C2218yescomplemented
57#2639C2218yescomplemented
58#2635C22116yescomplemented
59#2623C2218yescomplemented
60#2621C2214yescomplemented
61#2619C2214yescomplemented
62#2613C2218yescomplemented
63#2548C2212yescomplemented
64#2547C2212yescomplemented
65#2546C2212yescomplemented
66#2545C2214yescomplemented
67#2544C2214yescomplemented
68#2543C2218yescomplemented
69#2543C2218yescomplemented
70#2543C2214yescomplemented
71#2543C2214yescomplemented
72#2542C2218yescomplemented
73#2541C2218yescomplemented
74#2541C2212yescomplemented
75#2540C2218yescomplemented
76#2540C2218yescomplemented
77#2536C2214yescomplemented
78#2536C2214yescomplemented
79#2535C2214yescomplemented
80#2535C2214yescomplemented
81#2504C2214yescomplemented
82#2502C2214yescomplemented
83#2500C2218yescomplemented
84#2492C2218yescomplemented
85#2491C2218yescomplemented
86#2490C2218yescomplemented
87#2489C2218yescomplemented
88#2482C2218yescomplemented
89#2435C2214yescomplemented
90#2435C2218yescomplemented
91#2433C2214yescomplemented
92#2433C2218yescomplemented
93#2432C2218yescomplemented
94#2431C2218yescomplemented
95#2431C2218yescomplemented
96#2416C2218yescomplemented
97#2410C22116yescomplemented
98#2410C22116yescomplemented
99#2408C2218yescomplemented
100#2408C2218yescomplemented
101#2407C2218yescomplemented
102#2407C2218yescomplemented
103#2404C2218yescomplemented
104#2392C2214yescomplemented
105#2392C2214yescomplemented
106#2357C2214yescomplemented
107#2357C2214yescomplemented
108#2357C2218yescomplemented
109#2321C22116yescomplemented
110#2311C2214yescomplemented
111C4×#121C2218yescomplemented
112#2297C2214yescomplemented
113C2×#390C2212yes—
114C2×#388C2214yescomplemented
115C2×#382C2211yescharacteristic, complemented
116C2×#381C2212yescomplemented
117C2×C4×C4⋊C4C2212yescomplemented
118C2×C4×C4⋊C4C2211yescharacteristic, complemented
119C2×C4×C22⋊C4C2212yescomplemented
120C2×H(5,𝔽2)—216no—
121C2×H(5,𝔽2)—48no—
122C2×H(5,𝔽2)—48no—
123C22×#41C2314yes—
124C22×#41C2312yes—
125C22×#41C2318yes—
126C22×#41C2314yes—
127C23×D4C2311yescharacteristic
128C23×D4C2318yes—
129C23×D4C2318yes—
130C23×D4C2314yes—
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#534—232no—
144#532—232no—
145#532—216no—
146#532—416no—
147C2×C4⋊Q8C2312yes—
148C2×C4⋊Q8C2314yes—
149C2×C4⋊Q8C2314yes—
150C2×#127C2312yes—
151C2×#127C2314yes—
152C2×#127C2314yes—
153C2×#127C2318yes—
154#529—232no—
155C2×#126C2318yes—
156C2×#125C2314yes—
157C2×#124C2314yes—
158C2×#124C2318yes—
159C2×#124C2314yes—
160C2×#124C2314yes—
161C2×#124C2314yes—
162C2×#124C2318yes—
163#525—232no—
164C2×#123C2318yes—
165C2×#123C2318yes—
166C2×#123C23116yes—
167C2×C22⋊Q8C2314yes—
168C2×C22⋊Q8C2314yes—
169C2×C22⋊Q8C2314yes—
170C2×C22⋊Q8C2318yes—
171C2×C22⋊Q8C2318yes—
172C2×C22⋊Q8C2318yes—
173C2×#121—232no—
174C2×#121C2318yes—
175C2×#121C2318yes—
176C2×#121C2314yes—
177C2×#121C2318yes—
178C2×#121C2314yes—
179C2×#121C2314yes—
180C2×#121C2314yes—
181C2×#121C2314yes—
182C2×#121C2318yes—
183C2×#121C2314yes—
184C2×#121C2314yes—
185C2×#121C2318yes—
186C2×#121C2318yes—
187C2×#121C2318yes—
188C2×#121C23116yes—
189C2×#121C2318yes—
190C2×#121C2318yes—
191C2×#121C2318yes—
192C2×#120C2318yes—
193C2×#120C23116yes—
194C2×#120C23116yes—
195C2×#120C23116yes—
196C4×#41—216no—
197C2×C4×Q8C2312yes—
198C2×C4×Q8C2312yes—
199C2×C4×D4D4116yescomplemented
200C2×C4×D4C2318yes—
201C2×C4×D4C2314yes—
202C2×C4×D4C2314yes—
203C2×C4×D4C2314yes—
204C2×C4×D4C2312yes—
205C2×C4×D4C2312yes—
206C2×C4×D4C2314yes—
207C2×C4×D4C2318yes—
208C2×C4×D4C2318yes—
209C2×C4×D4C2314yes—
210C2×C4×D4C2314yes—
211C2×#117C2312yes—
212C2×#117C2314yes—
213C2×#117C2314yes—
214C22×C4⋊C4C2312yes—
215C22×C4⋊C4C2314yes—
216C22×C4⋊C4C2312yes—
217C22×C4⋊C4C2311yescharacteristic
218C22×C22⋊C4C2318yes—
219C22×C22⋊C4C2314yes—
220C22×C22⋊C4C2314yes—
221C22×C22⋊C4C2312yes—
222C22×C42C2314yes—
223C22×C42C2312yes—
224C22×C42C2314yes—
225C22×C42C2311yescharacteristic
226#400C23116yes—
227#399C23116yes—
228#399C23116yes—
229#398C2314yes—
230#398C2318yes—
231#398C2318yes—
232#398C2314yes—
233#397C2318yes—
234#397C2318yes—
235#397C2314yes—
236#397C23116yes—
237#397C2314yes—
238#396C2318yes—
239#396C2318yes—
240#394C2314yes—
241#394C2318yes—
242#394C23116yes—
243#394C23116yes—
244#394C23116yes—
245#394C2318yes—
246#394C2314yes—
247#394C2318yes—
248#394C2318yes—
249#394C23116yes—
250#394C23116yes—
251#393C23116yes—
252#392C2314yes—
253#392C2318yes—
254#392C23116yes—
255#392C2318yes—
256#392C23116yes—
257#392C23116yes—
258#392C2314yes—
259#392C23116yes—
260#392C23116yes—
261#392C23116yes—
262#391C2318yes—
263#391C2318yes—
264#391C2314yes—
265#391C2314yes—
266#390C2318yes—
267#390C23116yes—
268#390C23116yes—
269#390C2318yes—
270#390C2318yes—
271#390C2318yes—
272#390C2318yes—
273#390C2318yes—
274#390C2314yes—
275#390C2314yes—
276#390C2318yes—
277#389C2318yes—
278#388C2318yes—
279#388C23116yes—
280#388C23116yes—
281#388C23116yes—
282#388C23116yes—
283#388C23116yes—
284#388C23116yes—
285#388C2318yes—
286#386C23116yes—
287#386C2318yes—
288#386C23116yes—
289#386C23116yes—
290#386C2318yes—
291#386C23116yes—
292#386C23116yes—
293#386C2318yes—
294#386C2318yes—
295#385C23116yes—
296#385C23116yes—
297#384C2318yes—
298#382C2314yes—
299#382C2318yes—
300#382C2314yes—
301#381C2318yes—
302#381C2318yes—
303#380C2318yes—
304#380C2318yes—
305#380C2318yes—
306#379C23116yes—
307#379C23116yes—
308C4×C4⋊C4C2312yes—
309C4×C4⋊C4C2312yes—
310C4×C4⋊C4C2318yes—
311C4×C4⋊C4C2318yes—
312C4×C4⋊C4C2314yes—
313C4×C22⋊C4C2318yes—
314C4×C22⋊C4C2314yes—
315C4×C22⋊C4C2314yes—
316C4×C22⋊C4C2318yes—
317C4×C22⋊C4C2318yes—
318C2×#95C2314yes—
319C2×#95C2311yescharacteristic
320C2×#95C2312yes—
321C2×#95C2311yescharacteristic
322C2×#95C2312yes—
323C25C2412yes—
324C25C2418yes—
325H(5,𝔽2)—4128no—
326C2×#41—232no—
327C2×#41—28no—
328C2×#41—216no—
329C2×#41—216no—
330C2×#41—28no—
331C2×#41—216no—
332C2×#41—28no—
333C2×#41—216no—
334C2×#41—416no—
335C2×#41—416no—
336C2×#41—88no—
337C22×Q8C2412yes—
338C22×Q8C2414yes—
339C22×Q8C2414yes—
340C22×D4—232no—
341C22×D4—232no—
342C22×D4—216no—
343C22×D4—24no—
344C22×D4—24no—
345C22×D4—416no—
346C22×D4—416no—
347C22×D4—416no—
348C22×D4—416no—
349C22×D4—88no—
350C22×D4C2×D418yes—
351C22×D4C2414yes—
352C22×D4C2412yes—
353C22×D4C2418yes—
354C22×D4C2414yes—
355C22×D4C2414yes—
356C22×D4C2414yes—
357C22×D4C2418yes—
358C22×D4C2418yes—
359C22×D4C2414yes—
360C22×D4C2418yes—
361C22×D4C2418yes—
362C22×D4C24116yes—
363C22×D4C2414yes—
364C22×D4C2418yes—
365C22×D4C24116yes—
366C23×C4—84no—
367C23×C4C2×D4116yes—
368C23×C4C2414yes—
369C23×C4C2418yes—
370C23×C4C2412yes—
371C23×C4C2412yes—
372C23×C4C2414yes—
373C23×C4C2418yes—
374C23×C4C2414yes—
375C23×C4C2414yes—
376C23×C4C2411yescharacteristic
377C23×C4C2414yes—
378C23×C4C2412yes—
379C23×C4C2414yes—
380C23×C4C2411yescharacteristic
381C23×C4C2411yescharacteristic
382C4⋊Q8—216no—
383C4⋊Q8—28no—
384C4⋊Q8—48no—
385#127—216no—
386#127—28no—
387#127—48no—
388#127—88no—
389#126—232no—
390#125—216no—
391#124—216no—
392#124—232no—
393#124—216no—
394#124—48no—
395#124—48no—
396#124—88no—
397#123—232no—
398#123—232no—
399#123—264no—
400C22⋊Q8—216no—
401C22⋊Q8—216no—
402C22⋊Q8—216no—
403C22⋊Q8—232no—
404C22⋊Q8—416no—
405C22⋊Q8—416no—
406#121—216no—
407#121—216no—
408#121—216no—
409#121—232no—
410#121—232no—
411#121—232no—
412#121—216no—
413#121—216no—
414#121—216no—
415#121—216no—
416#121—232no—
417#121—232no—
418#121—416no—
419#121—416no—
420#121—416no—
421#121—416no—
422#121—416no—
423#121—432no—
424#120—232no—
425#120—264no—
426#120—432no—
427#120—816no—
428C4×Q8—28no—
429C4×Q8—28no—
430C4×D4—216no—
431C4×D4—216no—
432C4×D4—232no—
433C4×D4—28no—
434C4×D4—28no—
435C4×D4—216no—
436C4×D4—216no—
437C4×D4—416no—
438C4×D4—416no—
439C4×D4C2×D4132yes—
440C4×D4C2×D4132yes—
441#117—28no—
442#117—216no—
443#117—216no—
444C2×C4⋊C4—216no—
445C2×C4⋊C4—28no—
446C2×C4⋊C4—44no—
447C2×C4⋊C4C2×D418yes—
448C2×C4⋊C4C2414yes—
449C2×C4⋊C4C2418yes—
450C2×C4⋊C4C2418yes—
451C2×C4⋊C4C2414yes—
452C2×C4⋊C4C2412yes—
453C2×C4⋊C4C2412yes—
454C2×C4⋊C4C2414yes—
455C2×C4⋊C4C2414yes—
456C2×C4⋊C4C2414yes—
457C2×C4⋊C4C2414yes—
458C2×C4⋊C4C2418yes—
459C2×C4⋊C4C2414yes—
460C2×C4⋊C4C2414yes—
461C2×C4⋊C4C2418yes—
462C2×C4⋊C4C2418yes—
463C2×C4⋊C4C24116yes—
464C2×C4⋊C4C2414yes—
465C2×C22⋊C4—232no—
466C2×C22⋊C4—48no—
467C2×C22⋊C4—84no—
468C2×C22⋊C4C2×D4116yes—
469C2×C22⋊C4C2418yes—
470C2×C22⋊C4C2418yes—
471C2×C22⋊C4C24116yes—
472C2×C22⋊C4C2414yes—
473C2×C22⋊C4C2414yes—
474C2×C22⋊C4C2414yes—
475C2×C22⋊C4C2418yes—
476C2×C22⋊C4C2418yes—
477C2×C22⋊C4C2418yes—
478C2×C22⋊C4C2418yes—
479C2×C22⋊C4C2418yes—
480C2×C22⋊C4C24116yes—
481C2×C22⋊C4C2418yes—
482C2×C22⋊C4C2418yes—
483C2×C22⋊C4C2418yes—
484C2×C22⋊C4C2418yes—
485C2×C22⋊C4C2418yes—
486C2×C22⋊C4C2418yes—
487C2×C22⋊C4C24116yes—
488C2×C22⋊C4C24116yes—
489C2×C22⋊C4C24116yes—
490C2×C22⋊C4C24116yes—
491C2×C22⋊C4C2418yes—
492C2×C22⋊C4C2418yes—
493C2×C22⋊C4C2418yes—
494C2×C42—28no—
495C2×C42—216no—
496C2×C42—84no—
497C2×C42C2×D418yes—
498C2×C42C2414yes—
499C2×C42C2414yes—
500C2×C42C2414yes—
501C2×C42C2414yes—
502C2×C42C2414yes—
503C2×C42C2418yes—
504C2×C42C2418yes—
505C2×C42C2412yes—
506C2×C42C2412yes—
507#95C2412yes—
508#95C2411yescharacteristic
509#95C2411yescharacteristic
510#95C2414yes—
511#95C2414yes—
512#95C2412yes—
513#95C2412yes—
514#95C24116yes—
515#95C2418yes—
516#95C2418yes—
517#95C2418yes—
518#95C2418yes—
519#95C2418yes—
520#95C24116yes—
521#95C24116yes—
522C24—24no—
523C24—24no—
524C24—216no—
525C24—44no—
526C24—44no—
527C24—48no—
528C24—48no—
529C24—416no—
530C24—416no—
531C24C22×D418yes—
532C24C2518yes—
533C24C2514yes—
534C24C2514yes—
535C24C2511yescharacteristic
536#41—4128no—
537#41—432no—
538#41—464no—
539#41—832no—
540C2×Q8—24no—
541C2×Q8—28no—
542C2×Q8—28no—
543C2×Q8—24no—
544C2×Q8—28no—
545C2×Q8—24no—
546C2×Q8—28no—
547C2×Q8—48no—
548C2×D4—28no—
549C2×D4—232no—
550C2×D4—216no—
551C2×D4—28no—
552C2×D4—28no—
553C2×D4—216no—
554C2×D4—216no—
555C2×D4—216no—
556C2×D4—216no—
557C2×D4—232no—
558C2×D4—24no—
559C2×D4—28no—
560C2×D4—28no—
561C2×D4—28no—
562C2×D4—216no—
563C2×D4—28no—
564C2×D4—28no—
565C2×D4—28no—
566C2×D4—24no—
567C2×D4—28no—
568C2×D4—24no—
569C2×D4—28no—
570C2×D4—216no—
571C2×D4—416no—
572C2×D4—416no—
573C2×D4—48no—
574C2×D4—48no—
575C2×D4—48no—
576C2×D4—416no—
577C2×D4—48no—
578C2×D4—416no—
579C2×D4—48no—
580C2×D4—48no—
581C2×D4—48no—
582C2×D4—48no—
583C2×D4—48no—
584C2×D4—48no—
585C2×D4—416no—
586C2×D4—416no—
587C2×D4—416no—
588C2×D4—4128no—
589C2×D4—4128no—
590C2×D4—832no—
591C2×D4C22×D4116yes—
592C22×C4—216no—
593C22×C4—24no—
594C22×C4—24no—
595C22×C4—28no—
596C22×C4—28no—
597C22×C4—28no—
598C22×C4—216no—
599C22×C4—28no—
600C22×C4—216no—
601C22×C4—28no—
602C22×C4—216no—
603C22×C4—24no—
604C22×C4—28no—
605C22×C4—42no—
606C22×C4—44no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—48no—
610C22×C4—48no—
611C22×C4—48no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—44no—
615C22×C4—44no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—48no—
619C22×C4—816no—
620C22×C4C22×D414yes—
621C22×C4C22×D414yes—
622C22×C4C22×D4116yes—
623C22×C4C22×D418yes—
624C22×C4C22×D4116yes—
625C22×C4C22×D414yes—
626C22×C4H(5,𝔽2)14yes—
627C22×C4H(5,𝔽2)14yes—
628C22×C4C2514yes—
629C22×C4C2518yes—
630C22×C4C2514yes—
631C22×C4C2514yes—
632C22×C4C2518yes—
633C22×C4C2512yes—
634C22×C4C2514yes—
635C22×C4C2511yescharacteristic
636C22×C4C2511yescharacteristic
637C22×C4C2512yes—
638C22×C4C2514yes—
639C22×C4C2512yes—
640C22×C4C2512yes—
641C4⋊C4—28no—
642C4⋊C4—216no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—28no—
646C4⋊C4—28no—
647C4⋊C4—28no—
648C4⋊C4—28no—
649C4⋊C4—216no—
650C4⋊C4—28no—
651C4⋊C4—216no—
652C4⋊C4—28no—
653C4⋊C4—44no—
654C4⋊C4—48no—
655C4⋊C4—48no—
656C4⋊C4—416no—
657C4⋊C4C22×D4116yes—
658C22⋊C4—28no—
659C22⋊C4—216no—
660C22⋊C4—216no—
661C22⋊C4—216no—
662C22⋊C4—232no—
663C22⋊C4—28no—
664C22⋊C4—28no—
665C22⋊C4—216no—
666C22⋊C4—216no—
667C22⋊C4—216no—
668C22⋊C4—216no—
669C22⋊C4—48no—
670C22⋊C4—416no—
671C22⋊C4—48no—
672C22⋊C4—48no—
673C22⋊C4—48no—
674C22⋊C4—48no—
675C22⋊C4—416no—
676C22⋊C4—48no—
677C22⋊C4—416no—
678C22⋊C4—48no—
679C22⋊C4—416no—
680C22⋊C4—416no—
681C22⋊C4—48no—
682C22⋊C4C22×D4132yes—
683C42—28no—
684C42—28no—
685C42—28no—
686C42—28no—
687C42—28no—
688C42—48no—
689C42—48no—
690C42C22×D418yes—
691C42C22×D418yes—
692C23—22no—
693C23—22no—
694C23—24no—
695C23—24no—
696C23—28no—
697C23—28no—
698C23—216no—
699C23—24no—
700C23—28no—
701C23—24no—
702C23—24no—
703C23—28no—
704C23—28no—
705C23—28no—
706C23—28no—
707C23—28no—
708C23—28no—
709C23—28no—
710C23—28no—
711C23—48no—
712C23—48no—
713C23—432no—
714C23—88no—
715C23—88no—
716C23—816no—
717C23—816no—
718C23—1616no—
719C23—1616no—
720C23C23×D418yes—
721C23C23×D412yes—
722C23C2×H(5,𝔽2)12yes—
723C23C2×H(5,𝔽2)12yes—
724C23C2611yescharacteristic
725Q8—48no—
726Q8—416no—
727Q8—88no—
728D4—232no—
729D4—416no—
730D4—464no—
731D4—432no—
732D4—416no—
733D4—416no—
734D4—48no—
735D4—88no—
736D4—816no—
737D4—816no—
738D4—88no—
739D4—816no—
740D4—816no—
741D4—816no—
742D4—1616no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—28no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—28no—
753C2×C4—22no—
754C2×C4—24no—
755C2×C4—28no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—28no—
759C2×C4—28no—
760C2×C4—28no—
761C2×C4—28no—
762C2×C4—22no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—28no—
766C2×C4—24no—
767C2×C4—28no—
768C2×C4—44no—
769C2×C4—48no—
770C2×C4—416no—
771C2×C4—416no—
772C2×C4—44no—
773C2×C4—48no—
774C2×C4—416no—
775C2×C4—432no—
776C2×C4—432no—
777C2×C4—416no—
778C2×C4—88no—
779C2×C4—84no—
780C2×C4—88no—
781C2×C4#535116yes—
782C2×C4C23×D412yes—
783C2×C4C23×D414yes—
784C2×C4C23×D412yes—
785C2×C4C23×D418yes—
786C2×C4C23×D414yes—
787C2×C4C2×H(5,𝔽2)14yes—
788C2×C4C2×H(5,𝔽2)14yes—
789C2×C4#58514yes—
790C22—22no—
791C22—22no—
792C22—24no—
793C22—24no—
794C22—28no—
795C22—28no—
796C22—28no—
797C22—48no—
798C22—48no—
799C22—44no—
800C22—48no—
801C22—44no—
802C22—48no—
803C22—48no—
804C22—44no—
805C22—48no—
806C22—48no—
807C22—48no—
808C22—48no—
809C22—48no—
810C22—48no—
811C22—816no—
812C22—1632no—
813C22C2×#53514yes—
814C22C24×D411yescharacteristic
815C22C22×H(5,𝔽2)11yescharacteristic
816C22C22×H(5,𝔽2)11yescharacteristic
817C22C2×#58512yes—
818C22H(7,𝔽2)12yes—
819C4—24no—
820C4—22no—
821C4—22no—
822C4—28no—
823C4—24no—
824C4—44no—
825C4—44no—
826C4—48no—
827C4—44no—
828C4—42no—
829C4—44no—
830C4—48no—
831C4C2×#53518yes—
832C2—24no—
833C2—48no—
834C2—84no—
835C2—88no—
836C2C22×#53511yescharacteristic
837C2#6281211yescharacteristic
838C2#6284211yescharacteristic
839C2#6295712yes—
840C2#6296112yes—
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. #42652C2semidirect
4. #42648C2semidirect
5. #42430C2semidirect
6. #42426C2semidirect
7. #39881C2semidirect
8. #39876C2semidirect
9. #37446C2semidirect
10. #36739C2semidirect
11. #35513C2semidirect
12. #35328C2semidirect
13. #35166C2semidirect
14. #35158C2semidirect
15. #35078C2semidirect
16. #34937C2semidirect
17. C2×#2357C2semidirect
24. C2×#544C22semidirect
25. C2×#542C22semidirect
26. C2×#540C22semidirect
27. C2×#538C22semidirect
29. C2×#537C22semidirect
30. C2×#537C22semidirect
34. C2×#532C22semidirect
35. C2×#532C22semidirect
36. C2×#529C22semidirect
37. C2×#525C22semidirect
39. C2×C4×#41C22semidirect
41. #2856C22semidirect
42. #2850C22semidirect
43. #2850C22semidirect
44. #2816C22semidirect
45. #2815C22semidirect
46. #2718C22semidirect
47. #2710C22semidirect
48. #2706C22semidirect
49. #2703C22semidirect
50. #2685C22semidirect
51. #2678C22semidirect
52. #2670C22semidirect
53. #2669C22semidirect
54. #2661C22semidirect
55. #2661C22semidirect
56. #2656C22semidirect
57. #2639C22semidirect
58. #2635C22semidirect
59. #2623C22semidirect
60. #2621C22semidirect
61. #2619C22semidirect
62. #2613C22semidirect
63. #2548C22semidirect
64. #2547C22semidirect
65. #2546C22semidirect
66. #2545C22semidirect
67. #2544C22semidirect
68. #2543C22semidirect
69. #2543C22semidirect
70. #2543C22semidirect
71. #2543C22semidirect
72. #2542C22semidirect
73. #2541C22semidirect
74. #2541C22semidirect
75. #2540C22semidirect
76. #2540C22semidirect
77. #2536C22semidirect
78. #2536C22semidirect
79. #2535C22semidirect
80. #2535C22semidirect
81. #2504C22semidirect
82. #2502C22semidirect
83. #2500C22semidirect
84. #2492C22semidirect
85. #2491C22semidirect
86. #2490C22semidirect
87. #2489C22semidirect
88. #2482C22semidirect
89. #2435C22semidirect
90. #2435C22semidirect
91. #2433C22semidirect
92. #2433C22semidirect
93. #2432C22semidirect
94. #2431C22semidirect
95. #2431C22semidirect
96. #2416C22semidirect
97. #2410C22semidirect
98. #2410C22semidirect
99. #2408C22semidirect
100. #2408C22semidirect
101. #2407C22semidirect
102. #2407C22semidirect
103. #2404C22semidirect
104. #2392C22semidirect
105. #2392C22semidirect
106. #2357C22semidirect
107. #2357C22semidirect
108. #2357C22semidirect
109. #2321C22semidirect
110. #2311C22semidirect
111. C4×#121C22semidirect
112. #2297C22semidirect
114. C2×#388C22semidirect
115. C2×#382C22semidirect
116. C2×#381C22semidirect
117. C2×C4×C4⋊C4C22semidirect
118. C2×C4×C4⋊C4C22semidirect
119. C2×C4×C22⋊C4C22semidirect
199. C2×C4×D4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#34962
C2×#34602
#426522
#426482
#424302
#424262
#398812
#398762
#374462
#367392
#355132
#353282
#351662
#351582
#350782
#349372
C2×#23572