Finite Group Databasebeta

← #7632118

Subgroups — #7632118

Order 512.

8012 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#556C211yesmaximal, characteristic, complemented
2C2×C4×2−1+4C211yesmaximal, characteristic, complemented
3#36233C218yesmaximal, complemented
4#36229C218yesmaximal, complemented
5#35817C218yesmaximal, complemented
6#35787C218yesmaximal, complemented
7#35679C211yesmaximal, characteristic, complemented
8#35676C211yesmaximal, characteristic
9#35674C211yesmaximal, characteristic, complemented
10#35666C211yesmaximal, characteristic, complemented
11#35454C214yesmaximal, complemented
12#35357C214yesmaximal, complemented
13#35327C212yesmaximal, complemented
14#35143C214yesmaximal, complemented
15#34952C212yesmaximal, complemented
16#34875C214yesmaximal, complemented
17#34266C212yesmaximal, complemented
18#34265C212yesmaximal, complemented
19#34187C211yesmaximal, characteristic, complemented
20C22×2−1+4C2211yescharacteristic
21C2×#556—216no—
22C2×#556C2218yes—
23C2×#556C2218yes—
24C2×#536C2212yes—
25C2×#535C2212yes—
26C22×C4⋊Q8C2211yescharacteristic
27C22×#126C2212yes—
28C22×#126C2212yes—
29C22×#124C2211yescharacteristic
30C22×#124C2211yescharacteristic
31C22×C22⋊Q8C2212yes—
32C4×2−1+4—216no—
33C2×#520C2214yes—
34C2×#520C2212yes—
35C2×#520C2214yescomplemented
36C2×#519C2211yescharacteristic
37C2×#519C2214yescomplemented
38C2×C4×#41C2214yes—
39C2×C4×#41C2212yes—
40C2×C4×#41C2214yescomplemented
41C22×C4×Q8C2211yescharacteristic
42C22×C4×Q8C2211yescharacteristic
43C22×C4×Q8C2211yescharacteristic
44C22×C4×Q8C2214yescomplemented
45C22×C4×D4C2211yescharacteristic
46C22×#117C2212yes—
47#2852C22116yescomplemented
48#2850C2218yes—
49#2637C2218yescomplemented
50#2636C2218yescomplemented
51#2620C2218yes—
52#2609C22116yescomplemented
53#2604C2218yescomplemented
54#2603C2218yescomplemented
55#2601C22116yescomplemented
56#2599C2218yescomplemented
57#2598C2218yescomplemented
58#2582C2214yescomplemented
59#2581C2214yescomplemented
60#2580C2214yescomplemented
61#2579C2214yes—
62#2579C2214yes—
63#2545C2214yes—
64#2545C2214yes—
65#2544C2214yes—
66#2544C2214yes—
67#2538C2214yescomplemented
68#2534C2218yes—
69#2534C2218yes—
70#2487C2214yes—
71#2484C2214yes—
72#2484C2214yes—
73#2482C2214yes—
74#2482C2214yes—
75#2481C22116yescomplemented
76#2479C22116yescomplemented
77#2477C22116yescomplemented
78#2469C22116yescomplemented
79#2467C22116yescomplemented
80#2465C22116yescomplemented
81#2463C22116yescomplemented
82#2449C22116yescomplemented
83#2448C2218yes—
84#2448C2218yes—
85#2446C2218yescomplemented
86#2446C2218yescomplemented
87#2436C2218yes—
88#2434C2218yescomplemented
89#2432C2218yescomplemented
90#2431C2218yes—
91#2409C2214yes—
92#2406C2214yes—
93#2406C2214yes—
94#2404C2214yes—
95#2404C2214yes—
96#2396C2218yescomplemented
97#2396C2218yescomplemented
98#2392C2218yescomplemented
99#2367C2218yes—
100#2367C2218yescomplemented
101#2366C2218yes—
102#2365C2218yescomplemented
103#2363C2218yes—
104#2362C2218yescomplemented
105#2361C2218yes—
106#2360C2218yescomplemented
107#2356C2218yescomplemented
108#2355C2218yescomplemented
109#2322C2218yes—
110#2321C2218yes—
111#2313C2214yes—
112#2310C2211yescharacteristic
113#2310C2211yescharacteristic
114#2310C2212yes—
115#2309C2212yes—
116C4×C22⋊Q8C2218yescomplemented
117C4×#123C2218yes—
118C4×#120C2218yes—
119#2297C2212yes—
120#2297C2212yes—
121#2296C2212yes—
122#2296C2212yes—
123#2290C22116yescomplemented
124#2285C2212yes—
125#2283C2214yes—
126#2274C2212yes—
127C2×2−1+4—216no—
128C2×2−1+4—28no—
129C22×#41C2314yes—
130C22×#41C2314yes—
131C22×#41C2312yes—
132C23×Q8C2311yescharacteristic
133C23×Q8C2314yes—
134C23×Q8C2311yescharacteristic
135C23×Q8C2311yescharacteristic
136C23×D4C2311yescharacteristic
137C24×C4C2312yes—
138#556—264no—
139#556—264no—
140#536—216no—
141#535—216no—
142C2×C4⋊Q8—28no—
143C2×C4⋊Q8C2314yes—
144C2×C4⋊Q8C2318yes—
145C2×#127C2314yes—
146C2×#126—216no—
147C2×#126—216no—
148C2×#126C2318yes—
149C2×#126C2318yes—
150C2×#126C23116yes—
151C2×#124—28no—
152C2×#124—28no—
153C2×#124C2314yes—
154C2×#124C2314yes—
155C2×#124C2314yes—
156C2×#124C2314yes—
157C2×#124C2318yes—
158C2×#123C2318yes—
159C2×C22⋊Q8—216no—
160C2×C22⋊Q8C2318yes—
161C2×C22⋊Q8C23116yes—
162C2×C22⋊Q8C2318yes—
163C2×#121C2318yes—
164C2×#120C2318yes—
165#520—232no—
166#520—216no—
167#520—232no—
168#519—28no—
169#519—232no—
170C4×#41—232no—
171C4×#41—232no—
172C4×#41—216no—
173C2×C4×Q8—232no—
174C2×C4×Q8—28no—
175C2×C4×Q8—28no—
176C2×C4×Q8D4116yescomplemented
177C2×C4×Q8C2314yes—
178C2×C4×Q8C2312yes—
179C2×C4×Q8C2312yes—
180C2×C4×Q8C2314yes—
181C2×C4×Q8C2314yes—
182C2×C4×Q8C2318yes—
183C2×C4×Q8C2314yes—
184C2×C4×Q8C2314yes—
185C2×C4×Q8C2314yes—
186C2×C4×Q8C2318yes—
187C2×C4×Q8C2314yes—
188C2×C4×Q8C2314yes—
189C2×C4×Q8C2314yes—
190C2×C4×D4—28no—
191C2×C4×D4C2318yes—
192C2×C4×D4C2314yes—
193C2×C4×D4C2312yes—
194C2×C4×D4C2314yes—
195C2×C4×D4C2318yes—
196C2×C4×D4C2314yes—
197C2×C4×D4C2314yes—
198C2×C4×D4C2314yes—
199C2×C4×D4C2312yes—
200C2×C4×D4C2318yes—
201C2×C4×D4C23116yes—
202C2×#117—216no—
203C2×#117C2312yes—
204C2×#117C2312yes—
205C2×#117C2312yes—
206C2×#117C2318yes—
207C2×#117C2318yes—
208C2×#117C2318yes—
209C2×#117C2314yes—
210C2×#117C2314yes—
211C2×#117C2314yes—
212C2×#117C2318yes—
213C22×C4⋊C4C2312yes—
214C22×C4⋊C4C2311yescharacteristic
215C22×C4⋊C4C2311yescharacteristic
216C22×C4⋊C4C2314yes—
217C22×C4⋊C4C2312yes—
218C22×C4⋊C4C2311yescharacteristic
219C22×C4⋊C4C2318yes—
220C22×C4⋊C4C2312yes—
221C22×C4⋊C4C2312yes—
222C22×C4⋊C4C2311yescharacteristic
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2312yes—
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2312yes—
228C22×C42C2314yes—
229C22×C42C2318yes—
230C22×C42C2312yes—
231C22×C42C2311yescharacteristic
232C22×C42C2311yescharacteristic
233C22×C42C2312yes—
234C22×C42C2311yescharacteristic
235#400C2318yes—
236#400C2318yes—
237#400C2318yes—
238#399C2318yes—
239#399C2318yes—
240#399C2318yes—
241#398C2318yes—
242#398C2318yes—
243#398C2318yes—
244#398C2318yes—
245#397C2318yes—
246#397C2318yes—
247#396C2318yes—
248#396C2318yes—
249#396C23116yes—
250#396C23116yes—
251#395C2318yes—
252#395C2318yes—
253#395C2318yes—
254#394C2318yes—
255#394C23116yes—
256#394C2318yes—
257#394C23116yes—
258#393C2318yes—
259#393C2318yes—
260#393C2318yes—
261#392C2318yes—
262#392C2318yes—
263#391C2318yes—
264#391C2318yes—
265#391C2318yes—
266#391C2314yes—
267#391C2314yes—
268#391C2314yes—
269#391C2314yes—
270#391C2318yes—
271#390C2318yes—
272#390C2314yes—
273#390C2314yes—
274#390C23116yes—
275#390C2314yes—
276#390C2314yes—
277#389C23116yes—
278#389C2314yes—
279#389C2314yes—
280#389C2314yes—
281#389C2314yes—
282#389C2318yes—
283#388C23116yes—
284#388C23116yes—
285#388C23116yes—
286#388C23116yes—
287#388C23116yes—
288#388C23116yes—
289#388C23116yes—
290#388C23116yes—
291#387C23116yes—
292#387C23116yes—
293#387C23116yes—
294#387C2318yes—
295#387C2318yes—
296#387C23116yes—
297#387C23116yes—
298#387C23116yes—
299#386C2314yes—
300#386C23116yes—
301#386C2314yes—
302#386C2314yes—
303#386C2314yes—
304#386C23116yes—
305#386C23116yes—
306#386C23116yes—
307#386C23116yes—
308#386C23116yes—
309#385C2314yes—
310#385C2314yes—
311#385C23116yes—
312#385C2318yes—
313#385C2318yes—
314#385C2314yes—
315#385C2314yes—
316#385C23116yes—
317#385C23116yes—
318#385C23116yes—
319#384C2314yes—
320#383C2318yes—
321#382C2314yes—
322#382C2318yes—
323#381C2314yes—
324#381C2314yes—
325#381C2318yes—
326#380C2314yes—
327#380C2314yes—
328#380C2318yes—
329#379C2318yes—
330C4×C4⋊C4C2318yes—
331C4×C4⋊C4C2314yes—
332C4×C4⋊C4C2318yes—
333C4×C4⋊C4C2318yes—
334C4×C4⋊C4C2314yes—
335C4×C4⋊C4C23116yes—
336C4×C4⋊C4C2318yes—
337C4×C4⋊C4C2318yes—
338C4×C22⋊C4C2318yes—
339C4×C22⋊C4C2318yes—
340C4×C22⋊C4C23116yes—
341C4×C22⋊C4C2318yes—
342C4×C22⋊C4C23116yes—
343#376C2318yes—
344C25C2412yes—
3452−1+4—2128no—
346C2×#41—216no—
347C2×#41—232no—
348C2×#41—216no—
349C2×#41—216no—
350C2×#41—28no—
351C2×#41—216no—
352C2×#41—28no—
353C2×#41#41116yes—
354C22×Q8—216no—
355C22×Q8—216no—
356C22×Q8—24no—
357C22×Q8—24no—
358C22×Q8—216no—
359C22×Q8—28no—
360C22×Q8—28no—
361C22×Q8—44no—
362C22×Q8C2×D418yes—
363C22×Q8C2414yes—
364C22×Q8C2414yes—
365C22×Q8C2414yes—
366C22×Q8C2414yes—
367C22×Q8C2412yes—
368C22×D4—24no—
369C22×D4—28no—
370C22×D4C2414yes—
371C22×D4C2414yes—
372C22×D4C2414yes—
373C22×D4C2412yes—
374C22×D4C24116yes—
375C23×C4—28no—
376C23×C4—48no—
377C23×C4C2412yes—
378C23×C4C2411yescharacteristic
379C23×C4C2418yes—
380C23×C4C2418yes—
381C23×C4C2412yes—
382C23×C4C2414yes—
383C23×C4C2411yescharacteristic
384C23×C4C2411yescharacteristic
385C23×C4C2411yescharacteristic
386C23×C4C2418yes—
387C23×C4C2414yes—
388C23×C4C2414yes—
389C23×C4C2411yescharacteristic
390C23×C4C2411yescharacteristic
391C23×C4C2412yes—
392C23×C4C2411yescharacteristic
393C4⋊Q8—232no—
394C4⋊Q8—216no—
395#127—216no—
396#126—264no—
397#126—232no—
398#126—232no—
399#124—232no—
400#124—216no—
401#124—216no—
402#124—216no—
403#124—216no—
404#123—232no—
405C22⋊Q8—232no—
406C22⋊Q8—264no—
407C22⋊Q8—416no—
408#121—232no—
409#120—232no—
410C4×Q8—216no—
411C4×Q8—216no—
412C4×Q8—216no—
413C4×Q8—232no—
414C4×Q8—232no—
415C4×Q8—216no—
416C4×Q8—28no—
417C4×Q8—216no—
418C4×Q8—216no—
419C4×Q8—216no—
420C4×Q8—28no—
421C4×Q8C2×D4132yes—
422C4×Q8C2×D4132yes—
423C4×D4—216no—
424C4×D4—232no—
425C4×D4—216no—
426C4×D4—232no—
427C4×D4—216no—
428C4×D4—232no—
429C4×D4—216no—
430C4×D4—28no—
431C4×D4—216no—
432C4×D4—28no—
433C4×D4—432no—
434#117—216no—
435#117—28no—
436#117—28no—
437#117—28no—
438#117—216no—
439#117—232no—
440#117—232no—
441#117—232no—
442#117—232no—
443#117—216no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—28no—
446C2×C4⋊C4—28no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—28no—
450C2×C4⋊C4—216no—
451C2×C4⋊C4—232no—
452C2×C4⋊C4C2×D418yes—
453C2×C4⋊C4C2×D4116yes—
454C2×C4⋊C4C2418yes—
455C2×C4⋊C4C2412yes—
456C2×C4⋊C4C2414yes—
457C2×C4⋊C4C2414yes—
458C2×C4⋊C4C2412yes—
459C2×C4⋊C4C2412yes—
460C2×C4⋊C4C2418yes—
461C2×C4⋊C4C2418yes—
462C2×C4⋊C4C2414yes—
463C2×C4⋊C4C2412yes—
464C2×C4⋊C4C2412yes—
465C2×C4⋊C4C2418yes—
466C2×C4⋊C4C2412yes—
467C2×C4⋊C4C2414yes—
468C2×C4⋊C4C2414yes—
469C2×C4⋊C4C2414yes—
470C2×C4⋊C4C2414yes—
471C2×C4⋊C4C2418yes—
472C2×C4⋊C4C24116yes—
473C2×C4⋊C4C2418yes—
474C2×C4⋊C4C2418yes—
475C2×C4⋊C4C2418yes—
476C2×C4⋊C4C2418yes—
477C2×C4⋊C4C2418yes—
478C2×C4⋊C4C2414yes—
479C2×C4⋊C4C2418yes—
480C2×C22⋊C4—28no—
481C2×C22⋊C4—28no—
482C2×C22⋊C4—28no—
483C2×C22⋊C4—28no—
484C2×C22⋊C4—28no—
485C2×C22⋊C4C2414yes—
486C2×C22⋊C4C2418yes—
487C2×C22⋊C4C2414yes—
488C2×C22⋊C4C2418yes—
489C2×C22⋊C4C2418yes—
490C2×C22⋊C4C2418yes—
491C2×C22⋊C4C2414yes—
492C2×C22⋊C4C2418yes—
493C2×C22⋊C4C2414yes—
494C2×C22⋊C4C2414yes—
495C2×C22⋊C4C2414yes—
496C2×C22⋊C4C2414yes—
497C2×C22⋊C4C2418yes—
498C2×C22⋊C4C24116yes—
499C2×C22⋊C4C24116yes—
500C2×C22⋊C4C24116yes—
501C2×C22⋊C4C2418yes—
502C2×C22⋊C4C2418yes—
503C2×C22⋊C4C24116yes—
504C2×C22⋊C4C2418yes—
505C2×C42—28no—
506C2×C42—24no—
507C2×C42—24no—
508C2×C42—232no—
509C2×C42—216no—
510C2×C42C2×D4116yes—
511C2×C42C2×D418yes—
512C2×C42C2418yes—
513C2×C42C2414yes—
514C2×C42C2418yes—
515C2×C42C2414yes—
516C2×C42C2418yes—
517C2×C42C2414yes—
518C2×C42C2414yes—
519C2×C42C2414yes—
520C2×C42C2414yes—
521C2×C42C2414yes—
522C2×C42C24116yes—
523C2×C42C2414yes—
524C2×C42C2412yes—
525C2×C42C2414yes—
526C2×C42C2412yes—
527#95C2418yes—
528#95C2418yes—
529#95C2418yes—
530#95C2418yes—
531#95C2418yes—
532#95C2418yes—
533#95C24116yes—
534#95C2418yes—
535#95C24116yes—
536#95C2418yes—
537#95C2418yes—
538#95C2418yes—
539#95C2418yes—
540#95C2418yes—
541#95C2418yes—
542#95C24116yes—
543#95C2418yes—
544C24—24no—
545C24—28no—
546C24—44no—
547C24—44no—
548C24C2514yes—
549C24C2514yes—
550C24C2511yescharacteristic
551#41—2128no—
552#41—2128no—
553#41—264no—
554C2×Q8—2128no—
555C2×Q8—232no—
556C2×Q8—28no—
557C2×Q8—24no—
558C2×Q8—28no—
559C2×Q8—28no—
560C2×Q8—216no—
561C2×Q8—28no—
562C2×Q8—28no—
563C2×Q8—24no—
564C2×Q8—28no—
565C2×Q8—28no—
566C2×Q8—28no—
567C2×Q8—44no—
568C2×Q8—416no—
569C2×Q8—416no—
570C2×Q8C22×D4116yes—
571C2×Q8C2×#4118yes—
572C2×D4—28no—
573C2×D4—216no—
574C2×D4—28no—
575C2×D4—232no—
576C2×D4—28no—
577C2×D4—24no—
578C2×D4—28no—
579C2×D4—24no—
580C2×D4—28no—
581C2×D4—28no—
582C2×D4—416no—
583C2×D4—416no—
584C2×D4—416no—
585C2×D4C2×#41116yes—
586C2×D4C2×#4118yes—
587C22×C4—22no—
588C22×C4—216no—
589C22×C4—28no—
590C22×C4—216no—
591C22×C4—28no—
592C22×C4—216no—
593C22×C4—28no—
594C22×C4—24no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—24no—
599C22×C4—28no—
600C22×C4—28no—
601C22×C4—216no—
602C22×C4—216no—
603C22×C4—216no—
604C22×C4—28no—
605C22×C4—44no—
606C22×C4—48no—
607C22×C4—42no—
608C22×C4—48no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—416no—
614C22×C4—48no—
615C22×C4—432no—
616C22×C4C22×D418yes—
617C22×C4C22×D418yes—
618C22×C4C22×D414yes—
619C22×C4C22×D414yes—
620C22×C4C22×D414yes—
621C22×C4C2×#41116yes—
622C22×C4C2×#4118yes—
623C22×C4C2518yes—
624C22×C4C2518yes—
625C22×C4C2512yes—
626C22×C4C2514yes—
627C22×C4C2514yes—
628C22×C4C2512yes—
629C22×C4C2514yes—
630C22×C4C2512yes—
631C22×C4C2511yescharacteristic
632C22×C4C2514yes—
633C22×C4C2514yes—
634C22×C4C2512yes—
635C22×C4C2511yescharacteristic
636C22×C4C2514yes—
637C22×C4C2512yes—
638C22×C4C2512yes—
639C4⋊C4—216no—
640C4⋊C4—28no—
641C4⋊C4—28no—
642C4⋊C4—24no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—216no—
646C4⋊C4—216no—
647C4⋊C4—28no—
648C4⋊C4—24no—
649C4⋊C4—24no—
650C4⋊C4—216no—
651C4⋊C4—28no—
652C4⋊C4—28no—
653C4⋊C4—24no—
654C4⋊C4—28no—
655C4⋊C4—28no—
656C4⋊C4—232no—
657C4⋊C4—216no—
658C4⋊C4—48no—
659C4⋊C4—48no—
660C4⋊C4—48no—
661C4⋊C4—48no—
662C4⋊C4—48no—
663C4⋊C4C22×D4116yes—
664C4⋊C4C22×D4132yes—
665C22⋊C4—28no—
666C22⋊C4—28no—
667C22⋊C4—28no—
668C22⋊C4—232no—
669C22⋊C4—216no—
670C22⋊C4—28no—
671C22⋊C4—28no—
672C22⋊C4—216no—
673C22⋊C4—216no—
674C22⋊C4—216no—
675C22⋊C4—216no—
676C22⋊C4—28no—
677C22⋊C4—28no—
678C22⋊C4—232no—
679C22⋊C4—216no—
680C22⋊C4—48no—
681C22⋊C4—416no—
682C22⋊C4—48no—
683C22⋊C4—416no—
684C22⋊C4—48no—
685C42—28no—
686C42—216no—
687C42—28no—
688C42—216no—
689C42—28no—
690C42—216no—
691C42—28no—
692C42—28no—
693C42—28no—
694C42—28no—
695C42—416no—
696C42C22×D4116yes—
697C42C22×D418yes—
698C42C22×D4116yes—
699C42C22×D418yes—
700C23—22no—
701C23—22no—
702C23—24no—
703C23—24no—
704C23—28no—
705C23—28no—
706C23—24no—
707C23—28no—
708C23—28no—
709C23—28no—
710C23—48no—
711C23—48no—
712C23—48no—
713C23—816no—
714C23C23×D412yes—
715C23C22×#4118yes—
716C23C22×#4114yes—
717C23C2611yescharacteristic
718Q8—232no—
719Q8—232no—
720Q8—216no—
721Q8—416no—
722Q8—416no—
723D4—232no—
724D4—232no—
725D4—216no—
726D4—416no—
727D4—832no—
728C2×C4—28no—
729C2×C4—264no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—28no—
733C2×C4—24no—
734C2×C4—28no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—216no—
740C2×C4—232no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—28no—
748C2×C4—28no—
749C2×C4—28no—
750C2×C4—28no—
751C2×C4—28no—
752C2×C4—28no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—28no—
756C2×C4—28no—
757C2×C4—24no—
758C2×C4—28no—
759C2×C4—22no—
760C2×C4—48no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—432no—
764C2×C4—416no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—48no—
769C2×C4—816no—
770C2×C4—88no—
771C2×C4#525116yes—
772C2×C4C23×D412yes—
773C2×C4C23×D418yes—
774C2×C4C23×D414yes—
775C2×C4C23×D418yes—
776C2×C4C23×D412yes—
777C2×C4C23×D414yes—
778C2×C4C22×#4118yes—
779C2×C4C22×#4114yes—
780C2×C4C22×#4114yes—
781C2×C4#58514yes—
782C22—28no—
783C22—22no—
784C22—22no—
785C22—216no—
786C22—28no—
787C22—48no—
788C22—44no—
789C22—44no—
790C22—416no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—816no—
795C22C2×#52514yes—
796C22C24×D411yescharacteristic
797C22C23×#4112yes—
798C22C2×#58512yes—
799C222−1+612yes—
800C4—24no—
801C4—28no—
802C4—24no—
803C4—22no—
804C4—22no—
805C4—28no—
806C4—28no—
807C4—48no—
808C4—48no—
809C4—42no—
810C4—44no—
811C4—44no—
812C4—42no—
813C4—42no—
814C4—44no—
815C4C2×#52518yes—
816C2—24no—
817C2—48no—
818C2—84no—
819C2C22×#52511yescharacteristic
820C2#6281111yescharacteristic
821C2#6284811yescharacteristic
822C2#6299514yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35676C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#556C2semidirect
2. C2×C4×2−1+4C2semidirect
3. #36233C2semidirect
4. #36229C2semidirect
5. #35817C2semidirect
6. #35787C2semidirect
7. #35679C2semidirect
9. #35674C2semidirect
10. #35666C2semidirect
11. #35454C2semidirect
12. #35357C2semidirect
13. #35327C2semidirect
14. #35143C2semidirect
15. #34952C2semidirect
16. #34875C2semidirect
17. #34266C2semidirect
18. #34265C2semidirect
19. #34187C2semidirect
35. C2×#520C22semidirect
37. C2×#519C22semidirect
40. C2×C4×#41C22semidirect
44. C22×C4×Q8C22semidirect
47. #2852C22semidirect
49. #2637C22semidirect
50. #2636C22semidirect
52. #2609C22semidirect
53. #2604C22semidirect
54. #2603C22semidirect
55. #2601C22semidirect
56. #2599C22semidirect
57. #2598C22semidirect
58. #2582C22semidirect
59. #2581C22semidirect
60. #2580C22semidirect
67. #2538C22semidirect
75. #2481C22semidirect
76. #2479C22semidirect
77. #2477C22semidirect
78. #2469C22semidirect
79. #2467C22semidirect
80. #2465C22semidirect
81. #2463C22semidirect
82. #2449C22semidirect
85. #2446C22semidirect
86. #2446C22semidirect
88. #2434C22semidirect
89. #2432C22semidirect
96. #2396C22semidirect
97. #2396C22semidirect
98. #2392C22semidirect
100. #2367C22semidirect
102. #2365C22semidirect
104. #2362C22semidirect
106. #2360C22semidirect
107. #2356C22semidirect
108. #2355C22semidirect
116. C4×C22⋊Q8C22semidirect
123. #2290C22semidirect
176. C2×C4×Q8D4semidirect

Maximal subgroups

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

subgroupindex
C22×#5562
C2×C4×2−1+42
#362332
#362292
#358172
#357872
#356792
#356762
#356742
#356662
#354542
#353572
#353272
#351432
#349522
#348752
#342662
#342652
#341872