Finite Group Databasebeta

← #7646117

Subgroups — #7646117

Order 512.

6944 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#554C211yesmaximal, characteristic, complemented
2C2×#3460C211yesmaximal, characteristic
3#42442C218yesmaximal, complemented
4#42439C218yesmaximal, complemented
5#39880C218yesmaximal, complemented
6#39877C218yesmaximal, complemented
7#37449C214yesmaximal, complemented
8#36716C214yesmaximal, complemented
9#36705C214yesmaximal, complemented
10#35649C211yesmaximal, characteristic, complemented
11#35640C211yesmaximal, characteristic, complemented
12#35592C211yesmaximal, characteristic, complemented
13#35576C211yesmaximal, characteristic, complemented
14#35333C212yesmaximal, complemented
15#35152C212yesmaximal, complemented
16#35152C212yesmaximal, complemented
17#35057C214yesmaximal, complemented
18#34952C212yesmaximal, complemented
19#34186C211yesmaximal, characteristic, complemented
20C2×#554—216no—
21C2×#554C2218yes—
22C2×#554C2218yes—
23#3460—216no—
24C2×#544C2211yescharacteristic
25C2×#542C2214yes—
26C2×#540C2214yes—
27C2×#538C2214yes—
28C2×#537C2211yescharacteristic
29C2×#535C2212yes—
30C2×#532C2214yes—
31C22×C4⋊Q8C2211yescharacteristic
32C2×#529C2214yes—
33C22×#125C2211yescharacteristic
34C22×#125C2211yescharacteristic
35C2×#525C2214yes—
36C22×C22⋊Q8C2212yes—
37C22×C22⋊Q8C2212yes—
38C22×C22⋊Q8C2212yes—
39C2×C4×#41C2212yes—
40C22×C4×Q8C2211yescharacteristic
41C22×C4×D4C2211yescharacteristic
42C22×C4×D4C2211yescharacteristic
43C22×C4×D4C2211yescharacteristic
44C23×C4⋊C4C2212yes—
45#2851C2218yescomplemented
46#2849C2218yes—
47#2849C2218yes—
48#2814C22116yescomplemented
49#2700C22116yescomplemented
50#2698C22116yescomplemented
51#2689C22116yescomplemented
52#2687C22116yescomplemented
53#2681C22116yescomplemented
54#2680C22116yescomplemented
55#2674C22116yescomplemented
56#2672C22116yescomplemented
57#2638C22116yescomplemented
58#2629C2218yescomplemented
59#2627C2218yescomplemented
60#2622C2218yes—
61#2622C2218yes—
62#2621C2218yescomplemented
63#2620C2218yescomplemented
64#2618C2218yescomplemented
65#2591C2214yes—
66#2591C2214yes—
67#2583C2214yes—
68#2583C2214yes—
69#2582C2214yescomplemented
70#2581C2214yescomplemented
71#2580C2214yescomplemented
72#2579C2218yes—
73#2579C2218yes—
74#2579C2214yes—
75#2579C2214yes—
76#2566C2214yescomplemented
77#2566C2214yescomplemented
78#2565C2214yescomplemented
79#2565C2214yescomplemented
80#2552C2218yescomplemented
81#2551C2218yescomplemented
82#2550C2218yescomplemented
83#2550C2218yescomplemented
84#2538C2214yescomplemented
85#2504C2214yes—
86#2502C2214yes—
87#2499C2218yescomplemented
88#2492C2218yescomplemented
89#2491C2218yescomplemented
90#2490C2218yescomplemented
91#2489C2218yescomplemented
92#2487C2214yes—
93#2484C2218yescomplemented
94#2447C2218yes—
95#2447C2218yes—
96#2445C2218yes—
97#2445C2218yes—
98#2436C2214yes—
99#2434C2214yes—
100#2432C2218yescomplemented
101#2422C2218yes—
102#2422C2218yes—
103#2420C2218yes—
104#2420C2218yes—
105#2413C22116yescomplemented
106#2409C2214yes—
107#2406C2218yescomplemented
108#2396C2218yescomplemented
109#2357C2218yes—
110#2354C2218yes—
111#2322C22116yescomplemented
112#2317C2212yes—
113#2317C2212yes—
114#2312C2214yes—
115#2311C2212yes—
116#2311C2212yes—
117#2309C2212yes—
118C4×C22⋊Q8C2218yescomplemented
119#2297C2212yes—
120#2297C2212yes—
121#2296C2212yes—
122#2296C2212yes—
123#2285C2212yes—
124#2280C2214yes—
125#2274C2211yescharacteristic
126#2274C2211yescharacteristic
127C22×#41C2312yes—
128C22×#41C2314yes—
129C23×Q8C2311yescharacteristic
130C23×Q8C2312yes—
131C23×D4C2311yescharacteristic
132C24×C4C2312yes—
133C24×C4C2312yes—
134C24×C4C2312yes—
135#554—264no—
136#554—264no—
137#544—28no—
138#542—232no—
139#540—232no—
140#538—232no—
141#537—28no—
142#535—216no—
143#532—232no—
144C2×C4⋊Q8—28no—
145C2×C4⋊Q8C2318yes—
146C2×C4⋊Q8C2314yes—
147C2×C4⋊Q8C2318yes—
148C2×#127C2314yes—
149#529—232no—
150C2×#126C2318yes—
151C2×#125—28no—
152C2×#125—28no—
153C2×#125C2314yes—
154C2×#125C2314yes—
155C2×#125C2318yes—
156C2×#125C2314yes—
157C2×#124C2314yes—
158C2×#124C2318yes—
159C2×#124C2318yes—
160#525—232no—
161C2×#123C2318yes—
162C2×#123C2318yes—
163C2×#123C23116yes—
164C2×#123C23116yes—
165C2×C22⋊Q8—216no—
166C2×C22⋊Q8—216no—
167C2×C22⋊Q8—216no—
168C2×C22⋊Q8C2314yes—
169C2×C22⋊Q8C2318yes—
170C2×C22⋊Q8C2314yes—
171C2×C22⋊Q8C2318yes—
172C2×C22⋊Q8C23116yes—
173C2×C22⋊Q8C23116yes—
174C2×C22⋊Q8C2314yes—
175C2×C22⋊Q8C2318yes—
176C2×#121C2314yes—
177C2×#121C2314yes—
178C2×#121C2314yes—
179C2×#121C2318yes—
180C2×#121C2314yes—
181C2×#121C2314yes—
182C2×#120C2318yes—
183C4×#41—216no—
184C2×C4×Q8—28no—
185C2×C4×Q8C2312yes—
186C2×C4×Q8C2312yes—
187C2×C4×Q8C2314yes—
188C2×C4×Q8C2314yes—
189C2×C4×D4—28no—
190C2×C4×D4—28no—
191C2×C4×D4D4116yes—
192C2×C4×D4C2312yes—
193C2×C4×D4C2312yes—
194C2×C4×D4C2318yes—
195C2×C4×D4C2314yes—
196C2×C4×D4C2314yes—
197C2×C4×D4C2318yes—
198C2×C4×D4C2318yes—
199C2×C4×D4C2314yes—
200C2×C4×D4C2314yes—
201C2×#117C2312yes—
202C2×#117C2312yes—
203C2×#117C2312yes—
204C2×#117C2314yes—
205C2×#117C2314yes—
206C2×#117C2318yes—
207C22×C4⋊C4—216no—
208C22×C4⋊C4C2311yescharacteristic
209C22×C4⋊C4C2311yescharacteristic
210C22×C4⋊C4C2318yes—
211C22×C4⋊C4C2311yescharacteristic
212C22×C4⋊C4C2312yes—
213C22×C4⋊C4C2311yescharacteristic
214C22×C4⋊C4C2312yes—
215C22×C4⋊C4C2312yes—
216C22×C4⋊C4C2312yes—
217C22×C4⋊C4C2318yes—
218C22×C4⋊C4C2311yescharacteristic
219C22×C4⋊C4C2312yes—
220C22×C4⋊C4C2311yescharacteristic
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2312yes—
223C22×C22⋊C4C2312yes—
224C22×C42C2314yes—
225C22×C42C2311yescharacteristic
226C22×C42C2311yescharacteristic
227C22×C42C2311yescharacteristic
228#400C2318yes—
229#400C2318yes—
230#400C2318yes—
231#399C2318yes—
232#398C23116yes—
233#398C23116yes—
234#398C2318yes—
235#398C2318yes—
236#398C2318yes—
237#398C2318yes—
238#398C23116yes—
239#397C23116yes—
240#397C23116yes—
241#397C23116yes—
242#397C23116yes—
243#397C23116yes—
244#396C23116yes—
245#396C23116yes—
246#396C2318yes—
247#396C2318yes—
248#395C2318yes—
249#395C2318yes—
250#395C2318yes—
251#395C23116yes—
252#394C2318yes—
253#394C2318yes—
254#394C23116yes—
255#394C23116yes—
256#394C23116yes—
257#394C23116yes—
258#393C2318yes—
259#393C23116yes—
260#391C2314yes—
261#391C2314yes—
262#391C2314yes—
263#391C2314yes—
264#391C2318yes—
265#391C2318yes—
266#391C2318yes—
267#391C2318yes—
268#390C2318yes—
269#390C2318yes—
270#390C2314yes—
271#390C2314yes—
272#390C2314yes—
273#390C2314yes—
274#390C2318yes—
275#389C2318yes—
276#389C2318yes—
277#389C23116yes—
278#389C23116yes—
279#389C2314yes—
280#389C2314yes—
281#389C2314yes—
282#389C2314yes—
283#389C2318yes—
284#388C23116yes—
285#388C23116yes—
286#388C23116yes—
287#388C23116yes—
288#387C23116yes—
289#387C23116yes—
290#387C2318yes—
291#387C2318yes—
292#386C2318yes—
293#386C2318yes—
294#386C23116yes—
295#386C2314yes—
296#386C2314yes—
297#386C2314yes—
298#386C2314yes—
299#386C23116yes—
300#385C23116yes—
301#385C23116yes—
302#385C2318yes—
303#385C2318yes—
304#385C2318yes—
305#385C23116yes—
306#385C2318yes—
307#385C2314yes—
308#385C2314yes—
309#385C2314yes—
310#385C2314yes—
311#385C23116yes—
312#384C2314yes—
313#384C2314yes—
314#384C2314yes—
315#384C2318yes—
316#382C2314yes—
317#382C2314yes—
318#382C2314yes—
319#382C2318yes—
320#381C23116yes—
321#381C23116yes—
322#381C2318yes—
323#380C2318yes—
324#380C2318yes—
325#380C2314yes—
326#380C2314yes—
327#380C2318yes—
328#380C2318yes—
329#379C2318yes—
330C4×C4⋊C4C2314yes—
331C4×C4⋊C4C2314yes—
332C4×C4⋊C4C2318yes—
333C4×C4⋊C4C2318yes—
334C4×C4⋊C4C2318yes—
335C4×C4⋊C4C2318yes—
336C4×C22⋊C4C2314yes—
337C4×C22⋊C4C2314yes—
338C4×C22⋊C4C2318yes—
339C4×C22⋊C4C2318yes—
340C4×C22⋊C4C2318yes—
341C25C2412yes—
342C2×#41—28no—
343C2×#41—216no—
344C2×#41—28no—
345C2×#41—28no—
346C2×#41—88no—
347C22×Q8—24no—
348C22×Q8—28no—
349C22×Q8—44no—
350C22×Q8—84no—
351C22×Q8C2412yes—
352C22×Q8C2414yes—
353C22×Q8C2418yes—
354C22×Q8C2414yes—
355C22×D4—28no—
356C22×D4C2×D418yes—
357C22×D4C2414yes—
358C22×D4C2412yes—
359C22×D4C2414yes—
360C22×D4C2418yes—
361C22×D4C2418yes—
362C22×D4C2414yes—
363C23×C4—28no—
364C23×C4—28no—
365C23×C4—48no—
366C23×C4—84no—
367C23×C4—84no—
368C23×C4C2×D4116yes—
369C23×C4C2411yescharacteristic
370C23×C4C2414yes—
371C23×C4C2418yes—
372C23×C4C2411yescharacteristic
373C23×C4C2411yescharacteristic
374C23×C4C2412yes—
375C23×C4C2412yes—
376C23×C4C2411yescharacteristic
377C23×C4C2418yes—
378C23×C4C2414yes—
379C23×C4C2414yes—
380C23×C4C2411yescharacteristic
381C23×C4C2412yes—
382C23×C4C2411yescharacteristic
383C23×C4C2414yes—
384C23×C4C2414yes—
385C23×C4C2411yescharacteristic
386C4⋊Q8—232no—
387C4⋊Q8—216no—
388C4⋊Q8—88no—
389#127—216no—
390#126—232no—
391#125—232no—
392#125—216no—
393#125—216no—
394#125—216no—
395#124—216no—
396#124—232no—
397#124—88no—
398#123—232no—
399#123—232no—
400#123—432no—
401#123—816no—
402C22⋊Q8—232no—
403C22⋊Q8—232no—
404C22⋊Q8—216no—
405C22⋊Q8—216no—
406C22⋊Q8—216no—
407C22⋊Q8—264no—
408C22⋊Q8—264no—
409C22⋊Q8—416no—
410#121—216no—
411#121—216no—
412#121—216no—
413#121—216no—
414#121—216no—
415#121—232no—
416#120—232no—
417C4×Q8—216no—
418C4×Q8—216no—
419C4×Q8—28no—
420C4×Q8—28no—
421C4×D4—232no—
422C4×D4—232no—
423C4×D4—216no—
424C4×D4—216no—
425C4×D4—232no—
426C4×D4—28no—
427C4×D4—28no—
428C4×D4C2×D4132yes—
429C4×D4C2×D4132yes—
430#117—28no—
431#117—216no—
432#117—28no—
433#117—28no—
434#117—216no—
435#117—88no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—28no—
438C2×C4⋊C4—28no—
439C2×C4⋊C4—28no—
440C2×C4⋊C4—232no—
441C2×C4⋊C4—232no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—28no—
447C2×C4⋊C4—28no—
448C2×C4⋊C4C2×D418yes—
449C2×C4⋊C4C2412yes—
450C2×C4⋊C4C2412yes—
451C2×C4⋊C4C2414yes—
452C2×C4⋊C4C2418yes—
453C2×C4⋊C4C2414yes—
454C2×C4⋊C4C2418yes—
455C2×C4⋊C4C2414yes—
456C2×C4⋊C4C2414yes—
457C2×C4⋊C4C2414yes—
458C2×C4⋊C4C2412yes—
459C2×C4⋊C4C2412yes—
460C2×C4⋊C4C2418yes—
461C2×C4⋊C4C2418yes—
462C2×C4⋊C4C2412yes—
463C2×C4⋊C4C2412yes—
464C2×C4⋊C4C2414yes—
465C2×C4⋊C4C2414yes—
466C2×C4⋊C4C2414yes—
467C2×C4⋊C4C2414yes—
468C2×C4⋊C4C2414yes—
469C2×C4⋊C4C2414yes—
470C2×C4⋊C4C2418yes—
471C2×C4⋊C4C2418yes—
472C2×C4⋊C4C2418yes—
473C2×C4⋊C4C2418yes—
474C2×C4⋊C4C2418yes—
475C2×C4⋊C4C2418yes—
476C2×C4⋊C4C24116yes—
477C2×C4⋊C4C24116yes—
478C2×C4⋊C4C2418yes—
479C2×C4⋊C4C2414yes—
480C2×C22⋊C4—28no—
481C2×C22⋊C4—28no—
482C2×C22⋊C4C2×D4116yes—
483C2×C22⋊C4C2418yes—
484C2×C22⋊C4C2418yes—
485C2×C22⋊C4C2414yes—
486C2×C22⋊C4C2414yes—
487C2×C22⋊C4C2414yes—
488C2×C22⋊C4C2418yes—
489C2×C22⋊C4C2414yes—
490C2×C22⋊C4C2414yes—
491C2×C22⋊C4C2418yes—
492C2×C22⋊C4C2418yes—
493C2×C22⋊C4C2418yes—
494C2×C22⋊C4C24116yes—
495C2×C22⋊C4C2418yes—
496C2×C22⋊C4C2418yes—
497C2×C22⋊C4C24116yes—
498C2×C22⋊C4C24116yes—
499C2×C22⋊C4C24116yes—
500C2×C22⋊C4C2418yes—
501C2×C22⋊C4C2418yes—
502C2×C42—24no—
503C2×C42—24no—
504C2×C42—216no—
505C2×C42C2×D418yes—
506C2×C42C2414yes—
507C2×C42C2414yes—
508C2×C42C2414yes—
509C2×C42C2414yes—
510C2×C42C2414yes—
511C2×C42C2414yes—
512C2×C42C2414yes—
513C2×C42C2418yes—
514C2×C42C2418yes—
515C2×C42C2412yes—
516C2×C42C2412yes—
517#95C2418yes—
518#95C2418yes—
519#95C2418yes—
520#95C2418yes—
521#95C2418yes—
522#95C2418yes—
523#95C2418yes—
524#95C2418yes—
525#95C2418yes—
526#95C2418yes—
527#95C2418yes—
528#95C2418yes—
529#95C24116yes—
530#95C24116yes—
531#95C24116yes—
532#95C24116yes—
533C24—28no—
534C24—44no—
535C24—44no—
536C24C22×D418yes—
537C24C2514yes—
538C24C2514yes—
539C24C2511yescharacteristic
540#41—432no—
541#41—832no—
542C2×Q8—28no—
543C2×Q8—24no—
544C2×Q8—216no—
545C2×Q8—28no—
546C2×Q8—24no—
547C2×Q8—24no—
548C2×Q8—28no—
549C2×Q8—44no—
550C2×Q8—48no—
551C2×Q8—48no—
552C2×Q8—48no—
553C2×Q8—416no—
554C2×Q8—816no—
555C2×D4—28no—
556C2×D4—28no—
557C2×D4—28no—
558C2×D4—216no—
559C2×D4—216no—
560C2×D4—232no—
561C2×D4—24no—
562C2×D4—28no—
563C2×D4—28no—
564C2×D4—28no—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—416no—
568C2×D4—416no—
569C2×D4—48no—
570C2×D4C22×D4116yes—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—216no—
579C22×C4—216no—
580C22×C4—28no—
581C22×C4—28no—
582C22×C4—28no—
583C22×C4—28no—
584C22×C4—216no—
585C22×C4—28no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—44no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—48no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—48no—
598C22×C4—48no—
599C22×C4—416no—
600C22×C4—432no—
601C22×C4—816no—
602C22×C4—816no—
603C22×C4C22×D414yes—
604C22×C4C22×D414yes—
605C22×C4C22×D418yes—
606C22×C4C22×D4116yes—
607C22×C4C22×D4116yes—
608C22×C4C22×D414yes—
609C22×C42−1+418yes—
610C22×C4C2514yes—
611C22×C4C2518yes—
612C22×C4C2518yes—
613C22×C4C2512yes—
614C22×C4C2512yes—
615C22×C4C2514yes—
616C22×C4C2512yes—
617C22×C4C2514yes—
618C22×C4C2514yes—
619C22×C4C2514yes—
620C22×C4C2511yescharacteristic
621C22×C4C2512yes—
622C22×C4C2514yes—
623C22×C4C2511yescharacteristic
624C22×C4C2512yes—
625C22×C4C2512yes—
626C4⋊C4—24no—
627C4⋊C4—24no—
628C4⋊C4—216no—
629C4⋊C4—28no—
630C4⋊C4—28no—
631C4⋊C4—216no—
632C4⋊C4—28no—
633C4⋊C4—28no—
634C4⋊C4—24no—
635C4⋊C4—24no—
636C4⋊C4—28no—
637C4⋊C4—216no—
638C4⋊C4—216no—
639C4⋊C4—24no—
640C4⋊C4—24no—
641C4⋊C4—28no—
642C4⋊C4—28no—
643C4⋊C4—28no—
644C4⋊C4—28no—
645C4⋊C4—216no—
646C4⋊C4—28no—
647C4⋊C4—28no—
648C4⋊C4—216no—
649C4⋊C4—48no—
650C4⋊C4—48no—
651C4⋊C4—48no—
652C4⋊C4—416no—
653C4⋊C4—48no—
654C4⋊C4—416no—
655C4⋊C4—48no—
656C4⋊C4C22×D4116yes—
657C22⋊C4—216no—
658C22⋊C4—216no—
659C22⋊C4—28no—
660C22⋊C4—216no—
661C22⋊C4—216no—
662C22⋊C4—28no—
663C22⋊C4—28no—
664C22⋊C4—28no—
665C22⋊C4—28no—
666C22⋊C4—216no—
667C22⋊C4—216no—
668C22⋊C4—416no—
669C22⋊C4—48no—
670C22⋊C4—416no—
671C22⋊C4—416no—
672C22⋊C4—48no—
673C22⋊C4—416no—
674C22⋊C4—48no—
675C22⋊C4C22×D4132yes—
676C42—28no—
677C42—28no—
678C42—28no—
679C42—28no—
680C42—28no—
681C42—28no—
682C42—28no—
683C42—48no—
684C42—48no—
685C42C22×D418yes—
686C42C22×D418yes—
687C23—22no—
688C23—22no—
689C23—28no—
690C23—28no—
691C23—28no—
692C23—216no—
693C23—24no—
694C23—24no—
695C23—24no—
696C23—28no—
697C23—28no—
698C23—48no—
699C23—48no—
700C23—432no—
701C23C23×D418yes—
702C23C23×D412yes—
703C23C2×2−1+414yes—
704C23C2611yescharacteristic
705Q8—416no—
706Q8—48no—
707Q8—816no—
708Q8—88no—
709D4—232no—
710D4—416no—
711D4—48no—
712D4—88no—
713D4—816no—
714D4—816no—
715C2×C4—28no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—28no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—28no—
731C2×C4—28no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—28no—
735C2×C4—28no—
736C2×C4—28no—
737C2×C4—24no—
738C2×C4—28no—
739C2×C4—28no—
740C2×C4—28no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—28no—
744C2×C4—28no—
745C2×C4—22no—
746C2×C4—44no—
747C2×C4—416no—
748C2×C4—48no—
749C2×C4—416no—
750C2×C4—44no—
751C2×C4—432no—
752C2×C4—416no—
753C2×C4—48no—
754C2×C4—44no—
755C2×C4—48no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—416no—
759C2×C4—88no—
760C2×C4—816no—
761C2×C4#536116yes—
762C2×C4C23×D412yes—
763C2×C4C23×D414yes—
764C2×C4C23×D412yes—
765C2×C4C23×D418yes—
766C2×C4C23×D414yes—
767C2×C4C2×2−1+414yes—
768C2×C4C2×2−1+414yes—
769C2×C4#58514yes—
770C22—22no—
771C22—22no—
772C22—28no—
773C22—28no—
774C22—28no—
775C22—28no—
776C22—432no—
777C22—416no—
778C22—44no—
779C22—44no—
780C22—48no—
781C22—48no—
782C22—44no—
783C22C2×#53614yes—
784C22C24×D411yescharacteristic
785C22C22×2−1+412yes—
786C22C2×#58512yes—
787C22H(7,𝔽2)12yes—
788C4—24no—
789C4—24no—
790C4—22no—
791C4—22no—
792C4—28no—
793C4—44no—
794C4—42no—
795C4—44no—
796C4—42no—
797C4—44no—
798C4—44no—
799C4—42no—
800C4—48no—
801C4—48no—
802C4—44no—
803C4C2×#53618yes—
804C2—24no—
805C2—48no—
806C2—84no—
807C2C22×#53611yescharacteristic
808C2#6281111yescharacteristic
809C2#6284211yescharacteristic
810C2#6292614yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3460C2
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×#554C2semidirect
3. #42442C2semidirect
4. #42439C2semidirect
5. #39880C2semidirect
6. #39877C2semidirect
7. #37449C2semidirect
8. #36716C2semidirect
9. #36705C2semidirect
10. #35649C2semidirect
11. #35640C2semidirect
12. #35592C2semidirect
13. #35576C2semidirect
14. #35333C2semidirect
15. #35152C2semidirect
16. #35152C2semidirect
17. #35057C2semidirect
18. #34952C2semidirect
19. #34186C2semidirect
45. #2851C22semidirect
48. #2814C22semidirect
49. #2700C22semidirect
50. #2698C22semidirect
51. #2689C22semidirect
52. #2687C22semidirect
53. #2681C22semidirect
54. #2680C22semidirect
55. #2674C22semidirect
56. #2672C22semidirect
57. #2638C22semidirect
58. #2629C22semidirect
59. #2627C22semidirect
62. #2621C22semidirect
63. #2620C22semidirect
64. #2618C22semidirect
69. #2582C22semidirect
70. #2581C22semidirect
71. #2580C22semidirect
76. #2566C22semidirect
77. #2566C22semidirect
78. #2565C22semidirect
79. #2565C22semidirect
80. #2552C22semidirect
81. #2551C22semidirect
82. #2550C22semidirect
83. #2550C22semidirect
84. #2538C22semidirect
87. #2499C22semidirect
88. #2492C22semidirect
89. #2491C22semidirect
90. #2490C22semidirect
91. #2489C22semidirect
93. #2484C22semidirect
100. #2432C22semidirect
105. #2413C22semidirect
107. #2406C22semidirect
108. #2396C22semidirect
111. #2322C22semidirect
118. C4×C22⋊Q8C22semidirect

Maximal subgroups

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

subgroupindex
C22×#5542
C2×#34602
#424422
#424392
#398802
#398772
#374492
#367162
#367052
#356492
#356402
#355922
#355762
#353332
#351522
#350572
#349522
#341862