Finite Group Databasebeta

← #7698646

Subgroups — #7698646

Order 512.

5862 conjugacy classes of subgroups.

The subgroup lattice has 807 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59375C213yesmaximal, complemented
2#59273C216yesmaximal, complemented
3#52203C213yesmaximal, complemented
4#45380C213yesmaximal, complemented
5#45365C216yesmaximal, complemented
6#45330C213yesmaximal, complemented
7#45081C216yesmaximal, complemented
8#39042C216yesmaximal, complemented
9#38054C216yesmaximal, complemented
10#37968C216yesmaximal, complemented
11#36483C211yesmaximal, characteristic, complemented
12#36432C212yesmaximal, complemented
13#36082C211yesmaximal, characteristic
14#35948C211yesmaximal, characteristic, complemented
15#35898C212yesmaximal, complemented
16#35748C212yesmaximal, complemented
17#34294C212yesmaximal, complemented
18#34258C212yesmaximal, complemented
19#34193C212yesmaximal, complemented
20C22×H(5,𝔽2)C2211yescharacteristic
21C2×Q82C2211yescharacteristic, complemented
22C2×#551C2216yescomplemented
23C2×#548C2212yes—
24C2×#548C2211yescharacteristic
25C2×#520C2212yes—
26C2×C4×#41C2212yes—
27C22×C4×Q8C2211yescharacteristic, complemented
28#2855C2216yescomplemented
29#2854C2213yescomplemented
30#2764C2213yescomplemented
31#2763C2211yescharacteristic, complemented
32#2762C2216yescomplemented
33#2761C2216yescomplemented
34#2760C2213yescomplemented
35#2757C22112yescomplemented
36#2749C2216yescomplemented
37#2746C22112yescomplemented
38#2743C2216yescomplemented
39#2737C2216yescomplemented
40#2737C22112yescomplemented
41#2736C2216yescomplemented
42#2735C22112yescomplemented
43#2728C2216yescomplemented
44#2723C22112yescomplemented
45#2706C2216yescomplemented
46#2693C2213yescomplemented
47#2684C2216yescomplemented
48#2644C2216yescomplemented
49#2640C2213yescomplemented
50#2628C2216yescomplemented
51#2616C2213yes—
52#2600C2216yescomplemented
53#2597C22112yescomplemented
54#2592C2213yescomplemented
55#2586C2216yescomplemented
56#2580C2216yescomplemented
57#2561C22112yescomplemented
58#2547C2213yescomplemented
59#2542C2216yescomplemented
60#2513C2216yescomplemented
61#2512C2216yescomplemented
62#2512C2216yescomplemented
63#2501C2213yescomplemented
64#2499C2216yescomplemented
65#2497C2216yescomplemented
66#2496C2216yescomplemented
67#2494C2216yescomplemented
68#2492C2216yescomplemented
69#2491C2216yescomplemented
70#2486C2213yescomplemented
71#2485C2216yescomplemented
72#2483C2216yescomplemented
73#2482C22112yescomplemented
74#2480C22112yescomplemented
75#2479C22112yescomplemented
76#2477C22112yescomplemented
77#2461C22112yescomplemented
78#2452C2216yescomplemented
79#2452C2216yescomplemented
80#2448C2216yescomplemented
81#2447C2216yescomplemented
82#2447C2216yescomplemented
83#2440C2216yescomplemented
84#2440C2216yescomplemented
85#2437C22112yescomplemented
86#2435C2213yes—
87#2435C2216yes—
88#2423C2216yescomplemented
89#2422C2216yescomplemented
90#2420C2216yescomplemented
91#2418C22112yescomplemented
92#2408C2213yes—
93#2408C2216yes—
94#2401C2216yescomplemented
95#2398C2213yescomplemented
96#2396C2216yescomplemented
97#2388C2213yes—
98#2367C2216yescomplemented
99#2361C2216yescomplemented
100#2360C2216yescomplemented
101#2354C2216yescomplemented
102#2354C2216yescomplemented
103#2351C2212yescomplemented
104Q8×C4⋊C4C2212yescomplemented
105Q8×C4⋊C4C2212yescomplemented
106Q8×C4⋊C4C2212yescomplemented
107D4×C4⋊C4C2216yescomplemented
108#2347C2216yescomplemented
109#2347C2216yescomplemented
110#2341C2211yescharacteristic
111#2341C2212yes—
112#2341C2212yes—
113#2341C2212yes—
114#2341C2212yes—
115#2341C2212yes—
116Q8×C22⋊C4C2211yescharacteristic, complemented
117Q8×C22⋊C4C2212yescomplemented
118D4×C22⋊C4C2216yes—
119D4×C22⋊C4C2216yes—
120D4×C22⋊C4C2216yes—
121D4×C22⋊C4C2216yes—
122#2326C2216yescomplemented
123#2323C2216yescomplemented
124#2319C2216yescomplemented
125#2319C2216yescomplemented
126#2311C2216yes—
127#2309C2216yes—
128C4×#123C2216yescomplemented
129C4×#123C2213yescomplemented
130C4×#121C2216yescomplemented
131#2297C2216yes—
132C2×#390C2216yes—
133#2290C2216yescomplemented
134#2285C2216yescomplemented
135#2283C2216yescomplemented
136#2276C2212yescomplemented
137#2276C2211yescharacteristic, complemented
138C2×H(5,𝔽2)—216no—
139C2×H(5,𝔽2)—44no—
140C22×#41C2311yescharacteristic
141C22×#41C2313yes—
142C22×#41C2312yes—
143C23×Q8C2311yescharacteristic
144C23×D4C2316yes—
145C23×D4C2313yes—
146Q82—44no—
147#551—424no—
148#548—216no—
149#548—44no—
150C2×C4⋊Q8C2316yes—
151C2×C4⋊Q8C2313yes—
152C2×#126C23112yes—
153C2×#124C2316yes—
154C2×#124C2313yes—
155C2×#124C2316yes—
156C2×#123C2316yes—
157C2×#123C2313yes—
158C2×#123C2316yes—
159C2×C22⋊Q8C2316yes—
160C2×C22⋊Q8C2313yes—
161C2×C22⋊Q8C23112yes—
162C2×C22⋊Q8C23112yes—
163C2×#121C2316yes—
164C2×#121C2313yes—
165C2×#120C2316yes—
166#520—48no—
167C4×#41—216no—
168C2×C4×Q8—44no—
169C2×C4×Q8C2312yes—
170C2×C4×Q8C2312yes—
171C2×C4×Q8C2312yes—
172C2×C4×Q8C2312yes—
173C2×C4×Q8C2312yes—
174C2×C4×Q8C2311yescharacteristic
175C2×C4×Q8C2316yes—
176C2×C4×Q8C2313yes—
177C2×C4×D4C2316yes—
178C2×C4×D4C2316yes—
179C2×C4×D4C2316yes—
180C2×C4×D4C2316yes—
181C2×C4×D4C2316yes—
182C2×C4×D4C23112yes—
183C2×C4×D4C2313yes—
184C2×#117C2316yes—
185C2×#117C2316yes—
186C2×#117C23112yes—
187C22×C4⋊C4C2316yes—
188C22×C4⋊C4C2313yes—
189C22×C22⋊C4C23112yes—
190C22×C22⋊C4C23112yes—
191C22×C42C2316yes—
192C22×C42C2313yes—
193#401C2316yes—
194#400C2316yes—
195#400C2316yes—
196#400C2312yes—
197#400C2316yes—
198#400C2316yes—
199#399C23112yes—
200#399C2316yes—
201#399C23112yes—
202#398C2316yes—
203#398C2316yes—
204#398C2316yes—
205#397C2316yes—
206#397C23112yes—
207#397C2316yes—
208#397C23112yes—
209#397C23112yes—
210#397C2313yes—
211#397C2313yes—
212#397C23112yes—
213#397C2316yes—
214#397C2316yes—
215#397C23112yes—
216#397C2316yes—
217#396C23112yes—
218#396C2316yes—
219#396C2316yes—
220#396C2316yes—
221#395C2313yes—
222#395C23112yes—
223#395C2312yes—
224#394C23112yes—
225#394C23112yes—
226#394C2316yes—
227#394C2313yes—
228#394C2316yes—
229#394C2316yes—
230#393C23112yes—
231#393C23112yes—
232#393C2316yes—
233#393C2313yes—
234#393C2311yescharacteristic
235#393C2311yescharacteristic
236#392C2313yes—
237#392C2316yes—
238#391C2316yes—
239#391C2316yes—
240#391C2316yes—
241#391C2316yes—
242#391C2316yes—
243#391C2312yes—
244#390C2316yes—
245#390C23112yes—
246#390C2316yes—
247#390C2316yes—
248#390C2316yes—
249#390C2316yes—
250#390C2316yes—
251#390C2316yes—
252#390C2316yes—
253#390C2316yes—
254#390C2316yes—
255#390C2316yes—
256#390C2316yes—
257#390C2316yes—
258#389C2316yes—
259#389C2316yes—
260#389C2316yes—
261#389C2316yes—
262#389C2316yes—
263#389C23112yes—
264#389C2316yes—
265#389C2316yes—
266#389C2316yes—
267#388C2316yes—
268#388C23112yes—
269#388C23112yes—
270#388C23112yes—
271#388C23112yes—
272#388C23112yes—
273#388C23112yes—
274#388C23112yes—
275#388C23112yes—
276#388C23112yes—
277#388C23112yes—
278#388C2316yes—
279#388C2316yes—
280#388C2312yes—
281#388C2316yes—
282#387C2316yes—
283#387C23112yes—
284#387C23112yes—
285#387C2316yes—
286#387C2316yes—
287#387C2316yes—
288#387C2316yes—
289#386C23112yes—
290#386C23112yes—
291#386C2316yes—
292#386C2316yes—
293#386C2316yes—
294#386C2316yes—
295#386C2313yes—
296#386C2316yes—
297#386C2316yes—
298#386C2316yes—
299#385C23112yes—
300#385C23112yes—
301#385C23112yes—
302#385C23112yes—
303#385C23112yes—
304#385C2316yes—
305#385C2316yes—
306#385C2311yescharacteristic
307#385C2312yes—
308#384C2316yes—
309#384C2316yes—
310#384C2316yes—
311#383C2316yes—
312#383C2316yes—
313#382C2316yes—
314#382C2316yes—
315#382C2312yes—
316#381C2316yes—
317#381C23112yes—
318#381C2316yes—
319#381C2313yes—
320#381C2316yes—
321#380C2316yes—
322#380C2316yes—
323#380C2316yes—
324#380C2316yes—
325#380C23112yes—
326#380C2313yes—
327#380C2316yes—
328#380C2316yes—
329#380C2313yes—
330#380C2316yes—
331#380C2316yes—
332#379C23112yes—
333#379C23112yes—
334#379C23112yes—
335#379C2316yes—
336C4×C4⋊C4C2316yes—
337C4×C4⋊C4C2316yes—
338C4×C4⋊C4C2316yes—
339C4×C4⋊C4C23112yes—
340C4×C4⋊C4C2313yes—
341C4×C4⋊C4C2316yes—
342C4×C4⋊C4C2316yes—
343C4×C4⋊C4C2316yes—
344C4×C4⋊C4C2316yes—
345C4×C4⋊C4C2316yes—
346C4×C22⋊C4C23112yes—
347C4×C22⋊C4C2316yes—
348C4×C22⋊C4C2316yes—
349C4×C22⋊C4C2316yes—
350C4×C22⋊C4C2316yes—
351C4×C22⋊C4C2316yes—
352C4×C22⋊C4C2313yes—
353C4×C22⋊C4C2316yes—
354C4×C22⋊C4C2313yes—
355#376C2313yes—
356#376C2316yes—
357C25C2416yes—
358H(5,𝔽2)—464no—
359C2×#41—28no—
360C2×#41—28no—
361C2×#41—28no—
362C2×#41—24no—
363C2×#41—224no—
364C2×#41—46no—
365C2×#41#41116yes—
366C22×Q8—28no—
367C22×Q8—24no—
368C22×Q8C2413yes—
369C22×Q8C2411yescharacteristic
370C22×Q8C2411yescharacteristic
371C22×Q8C2416yes—
372C22×Q8C2411yescharacteristic
373C22×D4—224no—
374C22×D4—224no—
375C22×D4—224no—
376C22×D4—412no—
377C22×D4—46no—
378C22×D4C2413yes—
379C22×D4C2416yes—
380C22×D4C2413yes—
381C22×D4C2416yes—
382C22×D4C2416yes—
383C22×D4C2413yes—
384C23×C4C2413yes—
385C23×C4C2413yes—
386C23×C4C2416yes—
387C23×C4C2416yes—
388C23×C4C2416yes—
389C23×C4C2413yes—
390C23×C4C24112yes—
391C23×C4C2411yescharacteristic
392C4⋊Q8—412no—
393C4⋊Q8—46no—
394#126—424no—
395#124—224no—
396#124—46no—
397#124—412no—
398#123—224no—
399#123—212no—
400#123—86no—
401C22⋊Q8—224no—
402C22⋊Q8—424no—
403C22⋊Q8—46no—
404C22⋊Q8—812no—
405#121—224no—
406#121—46no—
407#120—412no—
408C4×Q8—28no—
409C4×Q8—28no—
410C4×Q8—28no—
411C4×Q8—28no—
412C4×Q8—28no—
413C4×Q8—24no—
414C4×Q8—46no—
415C4×Q8—412no—
416C4×D4—224no—
417C4×D4—224no—
418C4×D4—224no—
419C4×D4—412no—
420C4×D4—412no—
421C4×D4—46no—
422C4×D4—424no—
423#117—224no—
424#117—412no—
425#117—424no—
426C2×C4⋊C4—46no—
427C2×C4⋊C4—412no—
428C2×C4⋊C4C2416yes—
429C2×C4⋊C4C2416yes—
430C2×C4⋊C4C2416yes—
431C2×C4⋊C4C2416yes—
432C2×C4⋊C4C2416yes—
433C2×C4⋊C4C2416yes—
434C2×C4⋊C4C2416yes—
435C2×C4⋊C4C2413yes—
436C2×C4⋊C4C2416yes—
437C2×C4⋊C4C2416yes—
438C2×C4⋊C4C2416yes—
439C2×C4⋊C4C2416yes—
440C2×C4⋊C4C2412yes—
441C2×C4⋊C4C2413yes—
442C2×C4⋊C4C24112yes—
443C2×C4⋊C4C2413yes—
444C2×C4⋊C4C2416yes—
445C2×C4⋊C4C2416yes—
446C2×C4⋊C4C2416yes—
447C2×C4⋊C4C24112yes—
448C2×C4⋊C4C2412yes—
449C2×C4⋊C4C2412yes—
450C2×C4⋊C4C2412yes—
451C2×C4⋊C4C24112yes—
452C2×C22⋊C4—424no—
453C2×C22⋊C4—812no—
454C2×C22⋊C4C2416yes—
455C2×C22⋊C4C2416yes—
456C2×C22⋊C4C24112yes—
457C2×C22⋊C4C2412yes—
458C2×C22⋊C4C2416yes—
459C2×C22⋊C4C2416yes—
460C2×C22⋊C4C24112yes—
461C2×C22⋊C4C2416yes—
462C2×C22⋊C4C2416yes—
463C2×C22⋊C4C24112yes—
464C2×C22⋊C4C24112yes—
465C2×C22⋊C4C24112yes—
466C2×C22⋊C4C24112yes—
467C2×C22⋊C4C2416yes—
468C2×C22⋊C4C2416yes—
469C2×C22⋊C4C24112yes—
470C2×C22⋊C4C2411yescharacteristic
471C2×C22⋊C4C2413yes—
472C2×C22⋊C4C2416yes—
473C2×C22⋊C4C2416yes—
474C2×C22⋊C4C2416yes—
475C2×C22⋊C4C2413yes—
476C2×C22⋊C4C2416yes—
477C2×C22⋊C4C2412yes—
478C2×C22⋊C4C2416yes—
479C2×C22⋊C4C2416yes—
480C2×C22⋊C4C2416yes—
481C2×C22⋊C4C2416yes—
482C2×C22⋊C4C2416yes—
483C2×C22⋊C4C2411yescharacteristic
484C2×C42—224no—
485C2×C42—46no—
486C2×C42C2416yes—
487C2×C42C2416yes—
488C2×C42C2416yes—
489C2×C42C2413yes—
490C2×C42C2416yes—
491C2×C42C2416yes—
492C2×C42C2416yes—
493C2×C42C2412yes—
494C2×C42C2416yes—
495C2×C42C24112yes—
496C2×C42C2416yes—
497#95C2411yescharacteristic
498#95C2412yes—
499#95C2416yes—
500#95C2416yes—
501#95C2413yes—
502#95C2416yes—
503#95C2416yes—
504#95C2412yes—
505#95C2412yes—
506#95C2412yes—
507#95C2412yes—
508#95C2412yes—
509#95C2411yescharacteristic
510#95C2416yes—
511#95C2416yes—
512#95C2416yes—
513#95C2416yes—
514#95C2416yes—
515#95C2416yes—
516#95C2413yes—
517#95C24112yes—
518#95C2416yes—
519#95C2416yes—
520#95C2416yes—
521#95C2412yes—
522#95C2416yes—
523#95C2416yes—
524#95C2416yes—
525#95C2416yes—
526#95C2416yes—
527#95C2416yes—
528#95C2416yes—
529#95C24112yes—
530C24—224no—
531C24—46no—
532C24—46no—
533C24—46no—
534C24—412no—
535C24C2513yes—
536C24C2516yes—
537C24C2511yescharacteristic
538#41—264no—
539#41—448no—
540#41—416no—
541C2×Q8—212no—
542C2×Q8—24no—
543C2×Q8—26no—
544C2×Q8—41no—
545C2×Q8—42no—
546C2×Q8—41no—
547C2×Q8—46no—
548C2×Q8—46no—
549C2×Q8—46no—
550C2×Q8—416no—
551C2×Q8C2×#4118yes—
552C2×Q8H(5,𝔽2)14yes—
553C2×D4—212no—
554C2×D4—212no—
555C2×D4—212no—
556C2×D4—212no—
557C2×D4—26no—
558C2×D4—212no—
559C2×D4—212no—
560C2×D4—212no—
561C2×D4—212no—
562C2×D4—26no—
563C2×D4—496no—
564C2×D4—46no—
565C2×D4—43no—
566C2×D4—46no—
567C2×D4—43no—
568C2×D4—43no—
569C2×D4—448no—
570C2×D4C2×#41124yes—
571C22×C4—212no—
572C22×C4—212no—
573C22×C4—212no—
574C22×C4—212no—
575C22×C4—26no—
576C22×C4—212no—
577C22×C4—212no—
578C22×C4—26no—
579C22×C4—212no—
580C22×C4—26no—
581C22×C4—41no—
582C22×C4—46no—
583C22×C4—42no—
584C22×C4—43no—
585C22×C4—46no—
586C22×C4—43no—
587C22×C4—46no—
588C22×C4—412no—
589C22×C4—412no—
590C22×C4—412no—
591C22×C4C2×#41124yes—
592C22×C4C2511yescharacteristic
593C22×C4C2512yes—
594C22×C4C2512yes—
595C22×C4C2511yescharacteristic
596C22×C4C2512yes—
597C22×C4C2516yes—
598C22×C4C2513yes—
599C22×C4C2516yes—
600C22×C4C2512yes—
601C22×C4C2516yes—
602C22×C4C2516yes—
603C22×C4C2516yes—
604C22×C4C2513yes—
605C22×C4C2512yes—
606C22×C4C2512yes—
607C22×C4C2513yes—
608C4⋊C4—212no—
609C4⋊C4—212no—
610C4⋊C4—212no—
611C4⋊C4—212no—
612C4⋊C4—212no—
613C4⋊C4—212no—
614C4⋊C4—212no—
615C4⋊C4—212no—
616C4⋊C4—26no—
617C4⋊C4—212no—
618C4⋊C4—46no—
619C4⋊C4—46no—
620C4⋊C4—42no—
621C4⋊C4—42no—
622C4⋊C4—42no—
623C4⋊C4—412no—
624C4⋊C4—42no—
625C4⋊C4—43no—
626C4⋊C4—412no—
627C4⋊C4—43no—
628C4⋊C4—46no—
629C4⋊C4—46no—
630C4⋊C4—46no—
631C4⋊C4—412no—
632C22⋊C4—224no—
633C22⋊C4—212no—
634C22⋊C4—224no—
635C22⋊C4—212no—
636C22⋊C4—24no—
637C22⋊C4—212no—
638C22⋊C4—212no—
639C22⋊C4—412no—
640C22⋊C4—412no—
641C22⋊C4—46no—
642C22⋊C4—46no—
643C22⋊C4—412no—
644C22⋊C4—412no—
645C22⋊C4—46no—
646C22⋊C4—42no—
647C22⋊C4—46no—
648C22⋊C4—46no—
649C22⋊C4—46no—
650C22⋊C4—46no—
651C22⋊C4—46no—
652C22⋊C4—46no—
653C22⋊C4—46no—
654C22⋊C4—412no—
655C22⋊C4—41no—
656C22⋊C4—43no—
657C22⋊C4—46no—
658C22⋊C4—46no—
659C22⋊C4—46no—
660C22⋊C4—43no—
661C22⋊C4H(5,𝔽2)14yescomplemented
662C42—24no—
663C42—212no—
664C42—212no—
665C42—212no—
666C42—212no—
667C42—212no—
668C42—212no—
669C42—26no—
670C42—46no—
671C42—46no—
672C42—412no—
673C23—22no—
674C23—26no—
675C23—26no—
676C23—26no—
677C23—21no—
678C23—26no—
679C23—21no—
680C23—26no—
681C23—22no—
682C23—26no—
683C23—26no—
684C23—23no—
685C23—23no—
686C23—23no—
687C23—26no—
688C23—424no—
689C23—824no—
690C23—824no—
691C23—166no—
692C23—166no—
693C23C22×#41112yes—
694C23C2×H(5,𝔽2)12yes—
695C23C2611yescharacteristic
696Q8—44no—
697Q8—44no—
698Q8—412no—
699Q8—166no—
700Q8#551116yescomplemented
701D4—248no—
702D4—424no—
703D4—424no—
704D4—412no—
705D4—412no—
706D4—86no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—248no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—26no—
715C2×C4—26no—
716C2×C4—26no—
717C2×C4—26no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—22no—
722C2×C4—26no—
723C2×C4—23no—
724C2×C4—26no—
725C2×C4—26no—
726C2×C4—26no—
727C2×C4—26no—
728C2×C4—23no—
729C2×C4—23no—
730C2×C4—26no—
731C2×C4—21no—
732C2×C4—22no—
733C2×C4—26no—
734C2×C4—22no—
735C2×C4—26no—
736C2×C4—26no—
737C2×C4—23no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—26no—
745C2×C4—26no—
746C2×C4—26no—
747C2×C4—22no—
748C2×C4—424no—
749C2×C4—44no—
750C2×C4—412no—
751C2×C4—412no—
752C2×C4—812no—
753C2×C4—86no—
754C2×C4—1612no—
755C2×C4C22×#4114yes—
756C2×C4C22×#41112yes—
757C2×C4C2×H(5,𝔽2)14yes—
758C2×C4C2×H(5,𝔽2)16yes—
759C22—212no—
760C22—24no—
761C22—212no—
762C22—22no—
763C22—212no—
764C22—46no—
765C22—41no—
766C22—46no—
767C22—42no—
768C22—46no—
769C22—46no—
770C22—41no—
771C22—46no—
772C22—43no—
773C22—46no—
774C22—43no—
775C22—43no—
776C22—1624no—
777C22C23×#4112yes—
778C22C22×H(5,𝔽2)11yescharacteristic
779C22C22×H(5,𝔽2)11yescharacteristic
780C22H(7,𝔽2)11yescharacteristic
781C222−1+612yes—
782C4—24no—
783C4—24no—
784C4—46no—
785C4—46no—
786C4—42no—
787C4—41no—
788C4—42no—
789C4—42no—
790C4—46no—
791C4—42no—
792C4—46no—
793C4—46no—
794C4—43no—
795C4—41no—
796C4—43no—
797C4C2×#551112yes—
798C2—42no—
799C2—412no—
800C2—83no—
801C2C22×#55111yescharacteristic
802C2#6285712yes—
803C2#6291611yescharacteristic
804C2#6298512yes—
805C2#6304811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36082C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59375C2semidirect
2. #59273C2semidirect
3. #52203C2semidirect
4. #45380C2semidirect
5. #45365C2semidirect
6. #45330C2semidirect
7. #45081C2semidirect
8. #39042C2semidirect
9. #38054C2semidirect
10. #37968C2semidirect
11. #36483C2semidirect
12. #36432C2semidirect
14. #35948C2semidirect
15. #35898C2semidirect
16. #35748C2semidirect
17. #34294C2semidirect
18. #34258C2semidirect
19. #34193C2semidirect
21. C2×Q82C22semidirect
22. C2×#551C22semidirect
27. C22×C4×Q8C22semidirect
28. #2855C22semidirect
29. #2854C22semidirect
30. #2764C22semidirect
31. #2763C22semidirect
32. #2762C22semidirect
33. #2761C22semidirect
34. #2760C22semidirect
35. #2757C22semidirect
36. #2749C22semidirect
37. #2746C22semidirect
38. #2743C22semidirect
39. #2737C22semidirect
40. #2737C22semidirect
41. #2736C22semidirect
42. #2735C22semidirect
43. #2728C22semidirect
44. #2723C22semidirect
45. #2706C22semidirect
46. #2693C22semidirect
47. #2684C22semidirect
48. #2644C22semidirect
49. #2640C22semidirect
50. #2628C22semidirect
52. #2600C22semidirect
53. #2597C22semidirect
54. #2592C22semidirect
55. #2586C22semidirect
56. #2580C22semidirect
57. #2561C22semidirect
58. #2547C22semidirect
59. #2542C22semidirect
60. #2513C22semidirect
61. #2512C22semidirect
62. #2512C22semidirect
63. #2501C22semidirect
64. #2499C22semidirect
65. #2497C22semidirect
66. #2496C22semidirect
67. #2494C22semidirect
68. #2492C22semidirect
69. #2491C22semidirect
70. #2486C22semidirect
71. #2485C22semidirect
72. #2483C22semidirect
73. #2482C22semidirect
74. #2480C22semidirect
75. #2479C22semidirect
76. #2477C22semidirect
77. #2461C22semidirect
78. #2452C22semidirect
79. #2452C22semidirect
80. #2448C22semidirect
81. #2447C22semidirect
82. #2447C22semidirect
83. #2440C22semidirect
84. #2440C22semidirect
85. #2437C22semidirect
88. #2423C22semidirect
89. #2422C22semidirect
90. #2420C22semidirect
91. #2418C22semidirect
94. #2401C22semidirect
95. #2398C22semidirect
96. #2396C22semidirect
98. #2367C22semidirect
99. #2361C22semidirect
100. #2360C22semidirect
101. #2354C22semidirect
102. #2354C22semidirect
103. #2351C22semidirect
104. Q8×C4⋊C4C22semidirect
105. Q8×C4⋊C4C22semidirect
106. Q8×C4⋊C4C22semidirect
107. D4×C4⋊C4C22semidirect
108. #2347C22semidirect
109. #2347C22semidirect
116. Q8×C22⋊C4C22semidirect
117. Q8×C22⋊C4C22semidirect
122. #2326C22semidirect
123. #2323C22semidirect
124. #2319C22semidirect
125. #2319C22semidirect
128. C4×#123C22semidirect
129. C4×#123C22semidirect
130. C4×#121C22semidirect
133. #2290C22semidirect
134. #2285C22semidirect
135. #2283C22semidirect
136. #2276C22semidirect
137. #2276C22semidirect
661. C22⋊C4H(5,𝔽2)semidirect
700. Q8#551semidirect

Maximal subgroups

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

subgroupindex
#593752
#592732
#522032
#453802
#453652
#453302
#450812
#390422
#380542
#379682
#364832
#364322
#360822
#359482
#358982
#357482
#342942
#342582
#341932