Finite Group Databasebeta

← #7665639

Subgroups — #7665639

Order 512.

8544 conjugacy classes of subgroups.

The subgroup lattice has 801 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3482C211yesmaximal, characteristic, complemented
2C2×D4×#41C211yesmaximal, characteristic, complemented
3#39887C2112yesmaximal, complemented
4#39881C2112yesmaximal, complemented
5#39488C213yesmaximal, complemented
6#39362C213yesmaximal, complemented
7#38957C213yesmaximal, complemented
8#38951C213yesmaximal, complemented
9#36583C211yesmaximal, characteristic, complemented
10Q8×#127C211yesmaximal, characteristic, complemented
11#36465C211yesmaximal, characteristic, complemented
12#36446C211yesmaximal, characteristic, complemented
13#36434C214yesmaximal, complemented
14#36428C214yesmaximal, complemented
15#35298C213yesmaximal, complemented
16#35240C213yesmaximal, complemented
17#35190C213yesmaximal, complemented
18#34125C211yesmaximal, characteristic, complemented
19C4×#535C213yesmaximal, complemented
20C23×#41C2212yes—
21#3482—216no—
22C2×#557C2211yescharacteristic, complemented
23C2×#556C2213yescomplemented
24C2×#552C2216yescomplemented
25D4×#41—216no—
26C2×#550C2211yescharacteristic
27C2×D4×Q8C2211yescharacteristic
28C2×D4×Q8C2211yescharacteristic, complemented
29C2×D4×Q8C2214yescomplemented
30C2×#548C2212yes—
31C2×#548C2212yes—
32C2×#548C2214yescomplemented
33C2×#547C2213yes—
34C2×#547C2213yescomplemented
35C2×#546C2216yes—
36C2×D42C2213yes—
37C2×#535C2213yes—
38C2×#533C2213yescomplemented
39C2×#532C2213yes—
40C2×#529C2216yescomplemented
41C2×#525C2216yes—
42C2×C4×#41C2211yescharacteristic
43C2×C4×#41C2213yescomplemented
44C22×C4×Q8C2212yescomplemented
45C22×C4×D4C2213yes—
46#2868C2213yescomplemented
47#2862C2213yescomplemented
48#2858C2213yescomplemented
49#2858C2213yescomplemented
50#2850C22112yescomplemented
51#2848C22112yescomplemented
52#2718C22124yescomplemented
53#2706C22124yescomplemented
54#2685C22124yescomplemented
55#2678C22124yescomplemented
56#2635C22112yescomplemented
57#2633C22112yescomplemented
58#2620C2216yescomplemented
59#2620C2216yescomplemented
60#2598C22112yescomplemented
61#2568C2213yescomplemented
62#2566C22112yescomplemented
63#2548C2213yescomplemented
64#2547C2213yes—
65#2547C2213yescomplemented
66#2545C22112yescomplemented
67#2542C2213yes—
68#2542C2213yescomplemented
69#2542C2213yescomplemented
70#2542C22112yescomplemented
71#2541C2213yescomplemented
72#2540C22112yescomplemented
73#2536C22112yescomplemented
74#2502C2216yescomplemented
75#2500C2216yescomplemented
76#2500C22112yescomplemented
77#2490C22112yescomplemented
78#2489C22112yescomplemented
79#2482C22112yescomplemented
80#2435C2216yes—
81#2435C22112yescomplemented
82#2432C22112yescomplemented
83#2432C22112yescomplemented
84#2431C2216yescomplemented
85#2429C22112yescomplemented
86#2426C22112yescomplemented
87#2417C22112yescomplemented
88#2416C22112yescomplemented
89#2408C22112yescomplemented
90#2407C22112yescomplemented
91#2407C22112yescomplemented
92#2357C2216yescomplemented
93#2351C2212yescomplemented
94#2347C2216yescomplemented
95#2341C2212yes—
96#2341C2214yescomplemented
97Q8×C22⋊C4C2214yescomplemented
98#2328C2211yescharacteristic
99#2328C2213yescomplemented
100#2326C2213yes—
101#2326C2213yescomplemented
102#2326C2216yescomplemented
103#2324C22112yescomplemented
104#2321C22112yescomplemented
105#2317C2213yescomplemented
106#2311C2213yescomplemented
107#2309C2213yes—
108C4×#127C2213yes—
109C4×#127C2213yescomplemented
110C4×#124C2213yes—
111C4×#124C2213yescomplemented
112C4×#121C22112yescomplemented
113C4×#120C22112yescomplemented
114#2293C2213yescomplemented
115#2293C2213yescomplemented
116#2283C2213yescomplemented
117C42×Q8C2211yescharacteristic, complemented
118C42×Q8C2211yescharacteristic, complemented
119C4×#117C2213yescomplemented
120C22×#41—216no—
121C22×#41—416no—
122C22×#41C2312yes—
123C22×#41C2313yes—
124C22×#41C2311yescharacteristic
125C22×#41C2316yes—
126C22×#41C2316yes—
127C23×Q8C2312yes—
128C23×Q8C2312yes—
129C23×D4C2313yes—
130C23×D4C2316yes—
131C24×C4C2316yes—
132#557—28no—
133#556—224no—
134#552—248no—
135#550—28no—
136D4×Q8—28no—
137D4×Q8—28no—
138D4×Q8—416no—
139#548—216no—
140#548—216no—
141#548—416no—
142#547—224no—
143#547—224no—
144#546—248no—
145D42—224no—
146#535—224no—
147#533—224no—
148#532—224no—
149C2×C4⋊Q8C2313yes—
150C2×C4⋊Q8C2313yes—
151C2×C4⋊Q8C2313yes—
152C2×C4⋊Q8C23112yes—
153C2×#127C2313yes—
154C2×#127C2313yes—
155C2×#127C2311yescharacteristic
156#529—248no—
157C2×#126C23112yes—
158C2×#125C2316yes—
159C2×#125C2316yes—
160C2×#124C2313yes—
161C2×#124C2313yes—
162C2×#124C2316yes—
163C2×#124C2316yes—
164C2×#124C2316yes—
165C2×#124C23112yes—
166#525—248no—
167C2×#123C23112yes—
168C2×#123C23112yes—
169C2×C22⋊Q8C2316yes—
170C2×C22⋊Q8C2316yes—
171C2×C22⋊Q8C2316yes—
172C2×C22⋊Q8C2316yes—
173C2×C22⋊Q8C2316yes—
174C2×C22⋊Q8C23112yes—
175C2×C22⋊Q8C23112yes—
176C2×C22⋊Q8C23112yes—
177C2×#121C23112yes—
178C2×#121C2316yes—
179C2×#121C2316yes—
180C2×#121C2316yes—
181C2×#121C2316yes—
182C2×#121C2316yes—
183C2×#121C23112yes—
184C2×#120C23112yes—
185C2×#120C23112yes—
186C4×#41—224no—
187C4×#41D4116yescomplemented
188C2×C4×Q8—216no—
189C2×C4×Q8C2313yes—
190C2×C4×Q8C2313yes—
191C2×C4×Q8C2312yes—
192C2×C4×Q8C2312yes—
193C2×C4×Q8C2312yes—
194C2×C4×Q8C2316yes—
195C2×C4×Q8C2316yes—
196C2×C4×Q8C2311yescharacteristic
197C2×C4×Q8C2311yescharacteristic
198C2×C4×D4—224no—
199C2×C4×D4C2313yes—
200C2×C4×D4C2313yes—
201C2×C4×D4C2313yes—
202C2×C4×D4C2316yes—
203C2×C4×D4C2316yes—
204C2×C4×D4C2316yes—
205C2×C4×D4C2311yescharacteristic
206C2×C4×D4C2313yes—
207C2×C4×D4C2311yescharacteristic
208C2×C4×D4C2316yes—
209C2×C4×D4C2316yes—
210C2×C4×D4C23112yes—
211C2×C4×D4C23112yes—
212C2×C4×D4C2313yes—
213C2×C4×D4C2313yes—
214C2×#117C2313yes—
215C2×#117C2313yes—
216C2×#117C2316yes—
217C2×#117C2316yes—
218C2×#117C2313yes—
219C2×#117C2313yes—
220C22×C4⋊C4C2313yes—
221C22×C4⋊C4C2316yes—
222C22×C22⋊C4C2316yes—
223C22×C42C2316yes—
224C22×C42C2313yes—
225#400C23112yes—
226#399C23112yes—
227#399C23112yes—
228#399C23112yes—
229#398C23124yes—
230#397C23112yes—
231#397C23112yes—
232#396C23124yes—
233#396C23124yes—
234#394C23112yes—
235#394C23124yes—
236#394C23124yes—
237#394C23124yes—
238#394C23124yes—
239#392C23112yes—
240#392C23124yes—
241#391C2313yes—
242#391C2313yes—
243#391C2316yes—
244#391C23112yes—
245#391C23112yes—
246#390C2313yes—
247#390C2313yes—
248#390C23112yes—
249#390C2311yescharacteristic
250#390C2313yes—
251#390C23112yes—
252#390C2311yescharacteristic
253#390C23112yes—
254#390C2313yes—
255#390C23112yes—
256#390C23112yes—
257#390C2316yes—
258#390C23112yes—
259#390C2316yes—
260#390C2316yes—
261#390C23112yes—
262#389C23112yes—
263#389C2316yes—
264#389C2316yes—
265#388C23112yes—
266#388C23112yes—
267#388C23112yes—
268#388C23112yes—
269#388C23124yes—
270#388C23124yes—
271#388C23112yes—
272#388C23112yes—
273#386C23112yes—
274#386C2314yes—
275#386C23112yes—
276#386C2314yes—
277#386C23112yes—
278#386C23124yes—
279#385C23112yes—
280#385C23124yes—
281#385C23112yes—
282#385C23112yes—
283#385C23124yes—
284#384C2313yes—
285#384C2313yes—
286#384C23112yes—
287#384C2316yes—
288#383C2316yes—
289#382C23112yes—
290#382C2313yes—
291#382C2311yescharacteristic
292#382C2316yes—
293#381C2316yes—
294#380C23112yes—
295#380C2316yes—
296#380C23112yes—
297#380C23112yes—
298#379C23112yes—
299#379C23124yes—
300C4×C4⋊C4C2316yes—
301C4×C4⋊C4C2313yes—
302C4×C4⋊C4C2316yes—
303C4×C4⋊C4C2316yes—
304C4×C4⋊C4C2316yes—
305C4×C4⋊C4C2313yes—
306C4×C22⋊C4C2316yes—
307C4×C22⋊C4C23112yes—
308C4×C22⋊C4C2316yes—
309C4×C22⋊C4C23112yes—
310C4×C22⋊C4C2316yes—
311#376C2313yes—
312#376C2311yescharacteristic
313C43C2313yes—
314C43C2313yes—
315C25C2416yes—
316C2×#41—28no—
317C2×#41—28no—
318C2×#41—216no—
319C2×#41—224no—
320C2×#41—212no—
321C2×#41—212no—
322C2×#41—224no—
323C2×#41—424no—
324C2×#41—424no—
325C2×#41—46no—
326C2×#41—4128no—
327C2×#41C2×D418yes—
328C22×Q8—28no—
329C22×Q8—28no—
330C22×Q8—216no—
331C22×Q8—216no—
332C22×Q8C2416yes—
333C22×Q8C2413yes—
334C22×Q8C2416yes—
335C22×Q8C2411yescharacteristic
336C22×D4—224no—
337C22×D4—212no—
338C22×D4—212no—
339C22×D4—46no—
340C22×D4—424no—
341C22×D4C2413yes—
342C22×D4C2416yes—
343C22×D4C2416yes—
344C22×D4C2416yes—
345C22×D4C2413yes—
346C22×D4C2411yescharacteristic
347C22×D4C2411yescharacteristic
348C22×D4C2416yes—
349C22×D4C24112yes—
350C22×D4C24112yes—
351C22×D4C2414yes—
352C23×C4—224no—
353C23×C4—424no—
354C23×C4C2416yes—
355C23×C4C2416yes—
356C23×C4C2416yes—
357C23×C4C2416yes—
358C23×C4C2413yes—
359C23×C4C2413yes—
360C23×C4C2416yes—
361C23×C4C2412yes—
362C23×C4C2416yes—
363C23×C4C2412yes—
364C23×C4C2413yes—
365C4⋊Q8—212no—
366C4⋊Q8—212no—
367C4⋊Q8—212no—
368C4⋊Q8—424no—
369#127—212no—
370#127—212no—
371#127#4118yescomplemented
372#126—248no—
373#125—224no—
374#125—224no—
375#124—224no—
376#124—212no—
377#124—224no—
378#124—212no—
379#124—412no—
380#124—424no—
381#123—248no—
382#123—248no—
383C22⋊Q8—224no—
384C22⋊Q8—224no—
385C22⋊Q8—224no—
386C22⋊Q8—224no—
387C22⋊Q8—224no—
388C22⋊Q8—424no—
389C22⋊Q8—424no—
390C22⋊Q8—424no—
391#121—224no—
392#121—248no—
393#121—224no—
394#121—224no—
395#121—224no—
396#121—224no—
397#121—424no—
398#120—248no—
399#120—248no—
400C4×Q8—28no—
401C4×Q8—28no—
402C4×Q8—28no—
403C4×Q8—224no—
404C4×Q8—224no—
405C4×Q8—212no—
406C4×Q8—212no—
407C4×Q8C2×D418yes—
408C4×Q8C2×D418yes—
409C4×D4—224no—
410C4×D4—224no—
411C4×D4—24no—
412C4×D4—224no—
413C4×D4—212no—
414C4×D4—212no—
415C4×D4—224no—
416C4×D4—212no—
417C4×D4—24no—
418C4×D4—212no—
419C4×D4—224no—
420C4×D4—424no—
421C4×D4—424no—
422C4×D4C2×D4124yes—
423C4×D4C2×D4124yes—
424#117—212no—
425#117—224no—
426#117—224no—
427#117—212no—
428#117—46no—
429#117C2×D4124yes—
430C2×C4⋊C4—212no—
431C2×C4⋊C4—224no—
432C2×C4⋊C4C2411yescharacteristic
433C2×C4⋊C4C2413yes—
434C2×C4⋊C4C2416yes—
435C2×C4⋊C4C2416yes—
436C2×C4⋊C4C24112yes—
437C2×C4⋊C4C2411yescharacteristic
438C2×C4⋊C4C2416yes—
439C2×C4⋊C4C2413yes—
440C2×C4⋊C4C2416yes—
441C2×C4⋊C4C2416yes—
442C2×C4⋊C4C2416yes—
443C2×C4⋊C4C2416yes—
444C2×C4⋊C4C2416yes—
445C2×C4⋊C4C2416yes—
446C2×C4⋊C4C2416yes—
447C2×C4⋊C4C2416yes—
448C2×C4⋊C4C24112yes—
449C2×C4⋊C4C24112yes—
450C2×C4⋊C4C24124yes—
451C2×C4⋊C4C2413yes—
452C2×C4⋊C4C2413yes—
453C2×C22⋊C4—224no—
454C2×C22⋊C4C2412yes—
455C2×C22⋊C4C2416yes—
456C2×C22⋊C4C2416yes—
457C2×C22⋊C4C2416yes—
458C2×C22⋊C4C2412yes—
459C2×C22⋊C4C2416yes—
460C2×C22⋊C4C2416yes—
461C2×C22⋊C4C2416yes—
462C2×C22⋊C4C24112yes—
463C2×C22⋊C4C24112yes—
464C2×C22⋊C4C24112yes—
465C2×C22⋊C4C24112yes—
466C2×C22⋊C4C2416yes—
467C2×C22⋊C4C2414yes—
468C2×C22⋊C4C24112yes—
469C2×C22⋊C4C24112yes—
470C2×C22⋊C4C24112yes—
471C2×C22⋊C4C24124yes—
472C2×C22⋊C4C24124yes—
473C2×C22⋊C4C2414yes—
474C2×C22⋊C4C24112yes—
475C2×C22⋊C4C24112yes—
476C2×C22⋊C4C2416yes—
477C2×C42—224no—
478C2×C42C2×D4124yes—
479C2×C42C2411yescharacteristic
480C2×C42C2416yes—
481C2×C42C2416yes—
482C2×C42C2413yes—
483C2×C42C2413yes—
484C2×C42C2416yes—
485C2×C42C2416yes—
486C2×C42C2416yes—
487C2×C42C2416yes—
488C2×C42C2416yes—
489C2×C42C2413yes—
490C2×C42C2411yescharacteristic
491C2×C42C2413yes—
492C2×C42C2413yes—
493C2×C42C2411yescharacteristic
494#95C2412yes—
495#95C2412yes—
496#95C2416yes—
497#95C2416yes—
498#95C2414yes—
499#95C24112yes—
500#95C24112yes—
501#95C24112yes—
502#95C24112yes—
503#95C2416yes—
504#95C2416yes—
505#95C24124yes—
506C24—212no—
507C24—212no—
508C24—412no—
509C24—46no—
510C24—412no—
511C24C2516yes—
512C24C2513yes—
513C24C2512yes—
514C24C2512yes—
515#41—232no—
516#41—448no—
517#41—496no—
518#41—496no—
519#41—432no—
520C2×Q8—212no—
521C2×Q8—26no—
522C2×Q8—212no—
523C2×Q8—26no—
524C2×Q8—224no—
525C2×Q8—224no—
526C2×Q8—26no—
527C2×Q8—432no—
528C2×Q8—432no—
529C2×Q8C22×D414yes—
530C2×Q8H(5,𝔽2)18yes—
531C2×D4—212no—
532C2×D4—224no—
533C2×D4—212no—
534C2×D4—212no—
535C2×D4—224no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—212no—
539C2×D4—26no—
540C2×D4—212no—
541C2×D4—212no—
542C2×D4—26no—
543C2×D4—212no—
544C2×D4—224no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—26no—
548C2×D4—448no—
549C2×D4—44no—
550C2×D4—46no—
551C2×D4—424no—
552C2×D4—44no—
553C2×D4—46no—
554C2×D4—412no—
555C2×D4—412no—
556C2×D4—412no—
557C2×D4—496no—
558C2×D4C22×D4112yes—
559C2×D4C2×#4114yes—
560C2×D4C2×#4114yescomplemented
561C2×D4C2×#41116yescomplemented
562C22×C4—26no—
563C22×C4—212no—
564C22×C4—26no—
565C22×C4—212no—
566C22×C4—212no—
567C22×C4—24no—
568C22×C4—212no—
569C22×C4—212no—
570C22×C4—24no—
571C22×C4—212no—
572C22×C4—212no—
573C22×C4—212no—
574C22×C4—224no—
575C22×C4—224no—
576C22×C4—224no—
577C22×C4—44no—
578C22×C4—412no—
579C22×C4—412no—
580C22×C4—46no—
581C22×C4—44no—
582C22×C4—46no—
583C22×C4—496no—
584C22×C4C22×D4112yes—
585C22×C4C22×D4112yes—
586C22×C4C22×D4112yes—
587C22×C4C2516yes—
588C22×C4C2512yes—
589C22×C4C2512yes—
590C22×C4C2516yes—
591C22×C4C2516yes—
592C22×C4C2512yes—
593C22×C4C2516yes—
594C22×C4C2516yes—
595C22×C4C2511yescharacteristic
596C22×C4C2511yescharacteristic
597C22×C4C2513yes—
598C22×C4C2513yes—
599C22×C4C2512yes—
600C22×C4C2511yescharacteristic
601C22×C4C2513yes—
602C4⋊C4—22no—
603C4⋊C4—26no—
604C4⋊C4—212no—
605C4⋊C4—212no—
606C4⋊C4—224no—
607C4⋊C4—22no—
608C4⋊C4—212no—
609C4⋊C4—26no—
610C4⋊C4—212no—
611C4⋊C4—212no—
612C4⋊C4—212no—
613C4⋊C4—212no—
614C4⋊C4—212no—
615C4⋊C4—212no—
616C4⋊C4—212no—
617C4⋊C4—46no—
618C4⋊C4—412no—
619C4⋊C4—412no—
620C4⋊C4—424no—
621C4⋊C4C22×D4112yes—
622C4⋊C4C22×D4112yes—
623C22⋊C4—212no—
624C22⋊C4—224no—
625C22⋊C4—224no—
626C22⋊C4—24no—
627C22⋊C4—212no—
628C22⋊C4—212no—
629C22⋊C4—212no—
630C22⋊C4—24no—
631C22⋊C4—212no—
632C22⋊C4—224no—
633C22⋊C4—212no—
634C22⋊C4—224no—
635C22⋊C4—44no—
636C22⋊C4—412no—
637C22⋊C4—412no—
638C22⋊C4—46no—
639C22⋊C4—44no—
640C22⋊C4—412no—
641C22⋊C4—412no—
642C22⋊C4—412no—
643C22⋊C4—424no—
644C22⋊C4—424no—
645C22⋊C4C22×D4124yes—
646C42—212no—
647C42—212no—
648C42—212no—
649C42—26no—
650C42—212no—
651C42—212no—
652C42—22no—
653C42—26no—
654C42—46no—
655C42—46no—
656C42C22×D4112yes—
657C42C22×D414yes—
658C42C22×D4112yes—
659C42C22×D4112yes—
660C42C2×#4114yescomplemented
661C23—22no—
662C23—22no—
663C23—23no—
664C23—24no—
665C23—24no—
666C23—26no—
667C23—23no—
668C23—22no—
669C23—22no—
670C23—26no—
671C23—24no—
672C23—24no—
673C23—26no—
674C23—26no—
675C23—212no—
676C23—26no—
677C23—212no—
678C23—424no—
679C23—424no—
680C23—824no—
681C23—812no—
682C23—824no—
683C23C23×D416yes—
684C23C22×#4114yes—
685C23C22×#4114yes—
686C23C2611yescharacteristic
687Q8—424no—
688Q8—424no—
689Q8—412no—
690Q8#535116yescomplemented
691D4—224no—
692D4—28no—
693D4—28no—
694D4—416no—
695D4—424no—
696D4—424no—
697D4—448no—
698D4—424no—
699D4—412no—
700D4—812no—
701D4—824no—
702C2×C4—23no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—23no—
706C2×C4—22no—
707C2×C4—26no—
708C2×C4—22no—
709C2×C4—224no—
710C2×C4—224no—
711C2×C4—22no—
712C2×C4—26no—
713C2×C4—26no—
714C2×C4—22no—
715C2×C4—26no—
716C2×C4—26no—
717C2×C4—26no—
718C2×C4—22no—
719C2×C4—26no—
720C2×C4—26no—
721C2×C4—212no—
722C2×C4—24no—
723C2×C4—212no—
724C2×C4—26no—
725C2×C4—22no—
726C2×C4—26no—
727C2×C4—22no—
728C2×C4—26no—
729C2×C4—26no—
730C2×C4—24no—
731C2×C4—412no—
732C2×C4—424no—
733C2×C4—48no—
734C2×C4—48no—
735C2×C4—424no—
736C2×C4—424no—
737C2×C4—424no—
738C2×C4—424no—
739C2×C4—424no—
740C2×C4C23×D412yes—
741C2×C4C23×D416yes—
742C2×C4C23×D412yes—
743C2×C4C23×D416yes—
744C2×C4C23×D416yes—
745C2×C4C23×D412yes—
746C2×C4C22×#4114yes—
747C2×C4C22×#4112yes—
748C2×C4C2×H(5,𝔽2)112yes—
749C2×C4#58512yes—
750C22—28no—
751C22—28no—
752C22—26no—
753C22—26no—
754C22—26no—
755C22—24no—
756C22—24no—
757C22—46no—
758C22—42no—
759C22—42no—
760C22—44no—
761C22—46no—
762C22—44no—
763C22—42no—
764C22—42no—
765C22—412no—
766C22—46no—
767C22—412no—
768C22—46no—
769C22—46no—
770C22—848no—
771C22C24×D411yescharacteristic
772C22C23×#4111yescharacteristic
773C22C22×H(5,𝔽2)12yes—
774C22C2×#58511yescharacteristic
775C222−1+612yes—
776C4—24no—
777C4—22no—
778C4—26no—
779C4—22no—
780C4—26no—
781C4—46no—
782C4—42no—
783C4—42no—
784C4—46no—
785C4—42no—
786C4—46no—
787C4—46no—
788C4—46no—
789C4C2×#535112yes—
790C4D4×#4114yes—
791C2—44no—
792C2—46no—
793C2—44no—
794C2—86no—
795C2C22×#53511yescharacteristic
796C2C2×D4×#4111yescharacteristic
797C2#6285911yescharacteristic
798C2#6292212yes—
799C2#6298412yes—
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×#3482C2semidirect
2. C2×D4×#41C2semidirect
3. #39887C2semidirect
4. #39881C2semidirect
5. #39488C2semidirect
6. #39362C2semidirect
7. #38957C2semidirect
8. #38951C2semidirect
9. #36583C2semidirect
10. Q8×#127C2semidirect
11. #36465C2semidirect
12. #36446C2semidirect
13. #36434C2semidirect
14. #36428C2semidirect
15. #35298C2semidirect
16. #35240C2semidirect
17. #35190C2semidirect
18. #34125C2semidirect
19. C4×#535C2semidirect
22. C2×#557C22semidirect
23. C2×#556C22semidirect
24. C2×#552C22semidirect
28. C2×D4×Q8C22semidirect
29. C2×D4×Q8C22semidirect
32. C2×#548C22semidirect
34. C2×#547C22semidirect
38. C2×#533C22semidirect
40. C2×#529C22semidirect
43. C2×C4×#41C22semidirect
44. C22×C4×Q8C22semidirect
46. #2868C22semidirect
47. #2862C22semidirect
48. #2858C22semidirect
49. #2858C22semidirect
50. #2850C22semidirect
51. #2848C22semidirect
52. #2718C22semidirect
53. #2706C22semidirect
54. #2685C22semidirect
55. #2678C22semidirect
56. #2635C22semidirect
57. #2633C22semidirect
58. #2620C22semidirect
59. #2620C22semidirect
60. #2598C22semidirect
61. #2568C22semidirect
62. #2566C22semidirect
63. #2548C22semidirect
65. #2547C22semidirect
66. #2545C22semidirect
68. #2542C22semidirect
69. #2542C22semidirect
70. #2542C22semidirect
71. #2541C22semidirect
72. #2540C22semidirect
73. #2536C22semidirect
74. #2502C22semidirect
75. #2500C22semidirect
76. #2500C22semidirect
77. #2490C22semidirect
78. #2489C22semidirect
79. #2482C22semidirect
81. #2435C22semidirect
82. #2432C22semidirect
83. #2432C22semidirect
84. #2431C22semidirect
85. #2429C22semidirect
86. #2426C22semidirect
87. #2417C22semidirect
88. #2416C22semidirect
89. #2408C22semidirect
90. #2407C22semidirect
91. #2407C22semidirect
92. #2357C22semidirect
93. #2351C22semidirect
94. #2347C22semidirect
96. #2341C22semidirect
97. Q8×C22⋊C4C22semidirect
99. #2328C22semidirect
101. #2326C22semidirect
102. #2326C22semidirect
103. #2324C22semidirect
104. #2321C22semidirect
105. #2317C22semidirect
106. #2311C22semidirect
109. C4×#127C22semidirect
111. C4×#124C22semidirect
112. C4×#121C22semidirect
113. C4×#120C22semidirect
114. #2293C22semidirect
115. #2293C22semidirect
116. #2283C22semidirect
117. C42×Q8C22semidirect
118. C42×Q8C22semidirect
119. C4×#117C22semidirect
187. C4×#41D4semidirect
371. #127#41semidirect
560. C2×D4C2×#41semidirect
561. C2×D4C2×#41semidirect
660. C42C2×#41semidirect
690. Q8#535semidirect

Maximal subgroups

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

subgroupindex
C2×#34822
C2×D4×#412
#398872
#398812
#394882
#393622
#389572
#389512
#365832
Q8×#1272
#364652
#364462
#364342
#364282
#352982
#352402
#351902
#341252
C4×#5352