Finite Group Databasebeta

← #7632661

Subgroups — #7632661

Order 512.

8366 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3489C211yesmaximal, characteristic
2C2×#3428C211yesmaximal, characteristic, complemented
3#36432C214yesmaximal, complemented
4#36217C2112yesmaximal, complemented
5#35791C2112yesmaximal, complemented
6#35723C214yesmaximal, complemented
7#35619C213yesmaximal, complemented
8#35619C213yesmaximal, complemented
9#35618C213yesmaximal, complemented
10#35530C213yesmaximal, complemented
11#35311C213yesmaximal, complemented
12#35157C213yesmaximal, complemented
13#34810C213yesmaximal, complemented
14C2×#2499C213yesmaximal, complemented
15#34259C211yesmaximal, characteristic, complemented
16#34259C211yesmaximal, characteristic, complemented
17#34184C211yesmaximal, characteristic, complemented
18#34183C211yesmaximal, characteristic, complemented
19C22⋊C4×#41C211yesmaximal, characteristic, complemented
20C22×2−1+4C2211yescharacteristic
21C23×#41C2211yescharacteristic
22#3489—216no—
23C2×D4×Q8C2212yes—
24C2×#548C2212yes—
25C2×#547C2216yes—
26C2×#546C2216yes—
27C2×#537C2213yes—
28C2×#536C2213yes—
29C2×#525C2213yes—
30C22×C22⋊Q8C2213yes—
31#3428—216no—
32C2×#520C2213yes—
33C2×#520C2213yes—
34C2×#520C2211yescharacteristic
35C2×#520C2211yescharacteristic
36C2×#520C2211yescharacteristic
37C2×#519C2212yes—
38C2×#518C2216yes—
39C2×C4×#41C2211yescharacteristic
40C2×C4×#41C2211yescharacteristic
41C2×C4×#41C2212yes—
42C2×C4×#41C2216yes—
43C22×#117C2213yes—
44C22×#117C2213yes—
45#2855C22112yescomplemented
46#2853C22112yescomplemented
47#2625C22112yes—
48#2622C22112yes—
49#2504C2213yescomplemented
50#2503C2216yescomplemented
51#2503C2213yescomplemented
52#2502C2213yescomplemented
53#2502C2216yescomplemented
54#2501C2213yescomplemented
55#2500C2213yes—
56#2500C2211yescharacteristic
57#2500C2216yescomplemented
58#2499C2216yes—
59#2499C22112yes—
60#2499C2213yes—
61#2499C2213yes—
62#2499C2216yescomplemented
63#2499C2216yescomplemented
64#2499C2216yescomplemented
65#2499C22112yescomplemented
66#2498C22112yescomplemented
67#2485C22112yes—
68#2485C22112yescomplemented
69#2484C22112yescomplemented
70#2483C22112yes—
71#2447C22112yescomplemented
72#2447C22112yescomplemented
73#2446C22112yescomplemented
74#2446C22112yescomplemented
75#2444C22124yescomplemented
76#2443C22124yescomplemented
77#2423C22112yescomplemented
78#2422C22112yescomplemented
79#2421C22112yescomplemented
80#2420C22112yescomplemented
81#2419C22124yescomplemented
82#2419C22124yescomplemented
83#2412C22112yes—
84#2395C22112yes—
85C2×#397C22112yes—
86#2351C2214yescomplemented
87Q8×C4⋊C4C2214yescomplemented
88#2349C22112yescomplemented
89D4×C4⋊C4C22112yescomplemented
90#2341C2212yes—
91Q8×C22⋊C4C2212yes—
92Q8×C22⋊C4C2214yescomplemented
93Q8×C22⋊C4C2214yescomplemented
94#2339C2216yes—
95#2339C22112yescomplemented
96#2339C22112yescomplemented
97D4×C22⋊C4C2216yes—
98#2317C2213yescomplemented
99#2317C2213yescomplemented
100#2317C2213yescomplemented
101#2317C2213yescomplemented
102#2311C2213yescomplemented
103#2311C2213yescomplemented
104#2310C2213yescomplemented
105#2310C2213yescomplemented
106C4×#123C22112yescomplemented
107#2297C2213yes—
108#2297C2213yes—
109#2297C2213yescomplemented
110#2297C2213yescomplemented
111C2×#391C2213yescomplemented
112C2×#391C2213yescomplemented
113C2×#387C22112yescomplemented
114#2285C2213yescomplemented
115#2285C2213yescomplemented
116C2×#384C2213yescomplemented
117C2×#382C2213yescomplemented
118#2280C2213yes—
119C2×C4×C22⋊C4C2213yes—
120C2×2−1+4—28no—
121C2×2−1+4—28no—
122C2×2−1+4—28no—
123C22×#41—28no—
124C22×#41—28no—
125C22×#41D4116yes—
126C22×#41C2313yes—
127C22×#41C2316yes—
128C22×#41C2313yes—
129C22×#41C2311yescharacteristic
130C22×#41C2313yes—
131C22×#41C2311yescharacteristic
132C23×Q8C2313yes—
133C23×Q8C2312yes—
134C23×Q8C2311yescharacteristic
135C23×D4C2313yes—
136C24×C4C2313yes—
137D4×Q8—216no—
138#548—216no—
139#547—248no—
140#546—248no—
141#537—224no—
142#536—224no—
143C2×C4⋊Q8C2316yes—
144C2×#124C2316yes—
145#525—224no—
146C2×#123C2316yes—
147C2×#123C23112yes—
148C2×#123C23112yes—
149C2×C22⋊Q8—224no—
150C2×C22⋊Q8C2316yes—
151C2×C22⋊Q8C2316yes—
152C2×C22⋊Q8C2313yes—
153C2×C22⋊Q8C2316yes—
154C2×C22⋊Q8C2313yes—
155C2×C22⋊Q8C2316yes—
156C2×#121C2311yescharacteristic
157C2×#121C2313yes—
158C2×#121C2316yes—
159C2×#121C23112yes—
160C2×#120C2316yes—
161#520—224no—
162#520—224no—
163#520—28no—
164#520—28no—
165#520—28no—
166#519—216no—
167#518—248no—
168C4×#41—248no—
169C4×#41—216no—
170C4×#41—28no—
171C4×#41—28no—
172C2×C4×Q8C2312yes—
173C2×C4×Q8C2312yes—
174C2×C4×Q8C2312yes—
175C2×C4×Q8C2312yes—
176C2×C4×Q8C2312yes—
177C2×C4×Q8C2316yes—
178C2×C4×Q8C2316yes—
179C2×C4×D4C2316yes—
180C2×C4×D4C2316yes—
181C2×C4×D4C2316yes—
182C2×C4×D4C2316yes—
183C2×C4×D4C2316yes—
184C2×C4×D4C2316yes—
185C2×C4×D4C23112yes—
186C2×C4×D4C23112yes—
187C2×C4×D4C2316yes—
188C2×C4×D4C2316yes—
189C2×C4×D4C2316yes—
190C2×#117—224no—
191C2×#117—224no—
192C2×#117C2313yes—
193C2×#117C2313yes—
194C2×#117C2313yes—
195C2×#117C2313yes—
196C2×#117C2313yes—
197C2×#117C2316yes—
198C2×#117C2313yes—
199C2×#117C2311yescharacteristic
200C2×#117C2316yes—
201C2×#117C2316yes—
202C2×#117C2316yes—
203C2×#117C2316yes—
204C22×C4⋊C4C2313yes—
205C22×C4⋊C4C2313yes—
206C22×C4⋊C4C2313yes—
207C22×C4⋊C4C2313yes—
208C22×C4⋊C4C2313yes—
209C22×C4⋊C4C2316yes—
210C22×C4⋊C4C23112yes—
211C22×C22⋊C4C2316yes—
212C22×C22⋊C4C2316yes—
213C22×C22⋊C4C2316yes—
214C22×C22⋊C4C2316yes—
215C22×C42C2316yes—
216C22×C42C2316yes—
217C22×C42C2313yes—
218C22×C42C2313yes—
219#400C23124yes—
220#400C23112yes—
221#399C23112yes—
222#398C23124yes—
223#398C23112yes—
224#397C23124yes—
225#397C23124yes—
226#397C23112yes—
227#397C23112yes—
228#397C23124yes—
229#397C23124yes—
230#397C23112yes—
231#394C23112yes—
232#394C23124yes—
233#394C2314yes—
234#391C2313yes—
235#391C2313yes—
236#391C2316yes—
237#391C2316yes—
238#391C23112yes—
239#391C23112yes—
240#391C2316yes—
241#391C2316yes—
242#391C23112yes—
243#391C23112yes—
244#391C2313yes—
245#391C2313yes—
246#390C2313yes—
247#390C2313yes—
248#390C2316yes—
249#390C2316yes—
250#390C2311yescharacteristic
251#390C2311yescharacteristic
252#389C23112yes—
253#389C23112yes—
254#389C23112yes—
255#389C23112yes—
256#388C23112yes—
257#388C23124yes—
258#388C2314yes—
259#387C23124yes—
260#387C23124yes—
261#387C23112yes—
262#387C23124yes—
263#387C23124yes—
264#387C23112yes—
265#386C23112yes—
266#386C23112yes—
267#386C23112yes—
268#386C23112yes—
269#386C23112yes—
270#386C23112yes—
271#386C23112yes—
272#385C23112yes—
273#385C23112yes—
274#385C23112yes—
275#385C23112yes—
276#385C23124yes—
277#385C23112yes—
278#384C2316yes—
279#384C2313yes—
280#384C2313yes—
281#384C23112yes—
282#384C2313yes—
283#384C2311yescharacteristic
284#382C2316yes—
285#382C2313yes—
286#382C2313yes—
287#382C23112yes—
288#382C2313yes—
289#382C2311yescharacteristic
290#381C23112yes—
291#381C23112yes—
292#381C2316yes—
293#381C23124yes—
294#381C23112yes—
295#380C23112yes—
296#380C23112yes—
297#380C2316yes—
298#380C2316yes—
299#380C23112yes—
300#380C23112yes—
301#379C2316yes—
302C4×C4⋊C4C23112yes—
303C4×C4⋊C4C23112yes—
304C4×C22⋊C4C2316yes—
305C4×C22⋊C4C2316yes—
306C4×C22⋊C4C23112yes—
307C4×C22⋊C4C23112yes—
308C4×C22⋊C4C2311yescharacteristic
309C4×C22⋊C4C2313yes—
310C4×C22⋊C4C2313yes—
311C4×C22⋊C4C2313yes—
312C4×C22⋊C4C2316yes—
313C2×#95C2316yes—
314C2×#95C23112yes—
315C2×#95C23112yes—
316C2×#95C23112yes—
317C25C2413yes—
3182−1+4—464no—
319C2×#41—2128no—
320C2×#41—24no—
321C2×#41—24no—
322C2×#41—224no—
323C2×#41—212no—
324C2×#41—212no—
325C2×#41—224no—
326C2×#41—224no—
327C2×#41—212no—
328C2×#41—212no—
329C2×#41—212no—
330C2×#41—212no—
331C2×#41—212no—
332C2×#41C2×D4124yes—
333C2×#41C2×D418yes—
334C2×#41C2×D4124yes—
335C2×#41C2×D418yes—
336C2×#41#4118yes—
337C2×#41#4118yes—
338C22×Q8—24no—
339C22×Q8—24no—
340C22×Q8—28no—
341C22×Q8—28no—
342C22×Q8—28no—
343C22×Q8—212no—
344C22×Q8—212no—
345C22×Q8—212no—
346C22×Q8C2×D418yes—
347C22×Q8C2413yes—
348C22×Q8C2416yes—
349C22×Q8C2413yes—
350C22×Q8C2411yescharacteristic
351C22×D4—212no—
352C22×D4—212no—
353C22×D4C2×D4124yes—
354C22×D4C2416yes—
355C22×D4C2411yescharacteristic
356C22×D4C2416yes—
357C22×D4C2413yes—
358C22×D4C2412yes—
359C22×D4C2416yes—
360C22×D4C2413yes—
361C23×C4—212no—
362C23×C4—212no—
363C23×C4C2×D4124yes—
364C23×C4C2416yes—
365C23×C4C2416yes—
366C23×C4C2416yes—
367C23×C4C2413yes—
368C23×C4C2413yes—
369C23×C4C2413yes—
370C23×C4C2411yescharacteristic
371C23×C4C2413yes—
372C23×C4C2416yes—
373C23×C4C2416yes—
374C23×C4C2416yes—
375C23×C4C2416yes—
376C23×C4C2416yes—
377C23×C4C2416yes—
378C23×C4C2413yes—
379C4⋊Q8—224no—
380#124—224no—
381#123—248no—
382#123—224no—
383#123—424no—
384C22⋊Q8—224no—
385C22⋊Q8—212no—
386C22⋊Q8—224no—
387C22⋊Q8—224no—
388C22⋊Q8—224no—
389C22⋊Q8—212no—
390#121—248no—
391#121—224no—
392#121—24no—
393#121—212no—
394#120—224no—
395C4×Q8—224no—
396C4×Q8—224no—
397C4×Q8—28no—
398C4×Q8—28no—
399C4×Q8—28no—
400C4×Q8—28no—
401C4×Q8—28no—
402C4×D4—248no—
403C4×D4—248no—
404C4×D4—224no—
405C4×D4—224no—
406C4×D4—224no—
407C4×D4—224no—
408C4×D4—224no—
409C4×D4—224no—
410C4×D4—224no—
411C4×D4—224no—
412C4×D4—224no—
413#117—212no—
414#117—24no—
415#117—224no—
416#117—224no—
417#117—224no—
418#117—224no—
419#117—224no—
420#117—212no—
421#117—212no—
422#117—212no—
423#117—212no—
424#117—212no—
425C2×C4⋊C4—212no—
426C2×C4⋊C4—212no—
427C2×C4⋊C4—212no—
428C2×C4⋊C4—212no—
429C2×C4⋊C4—212no—
430C2×C4⋊C4—224no—
431C2×C4⋊C4—424no—
432C2×C4⋊C4C2413yes—
433C2×C4⋊C4C2411yescharacteristic
434C2×C4⋊C4C2413yes—
435C2×C4⋊C4C2411yescharacteristic
436C2×C4⋊C4C2413yes—
437C2×C4⋊C4C2416yes—
438C2×C4⋊C4C24112yes—
439C2×C4⋊C4C2416yes—
440C2×C4⋊C4C2416yes—
441C2×C4⋊C4C2416yes—
442C2×C4⋊C4C2416yes—
443C2×C4⋊C4C2416yes—
444C2×C4⋊C4C24112yes—
445C2×C4⋊C4C2411yescharacteristic
446C2×C4⋊C4C2416yes—
447C2×C4⋊C4C2416yes—
448C2×C4⋊C4C2416yes—
449C2×C4⋊C4C24124yes—
450C2×C4⋊C4C24112yes—
451C2×C4⋊C4C2414yes—
452C2×C4⋊C4C24112yes—
453C2×C22⋊C4—224no—
454C2×C22⋊C4—224no—
455C2×C22⋊C4—224no—
456C2×C22⋊C4—412no—
457C2×C22⋊C4C2416yes—
458C2×C22⋊C4C2412yes—
459C2×C22⋊C4C2412yes—
460C2×C22⋊C4C2416yes—
461C2×C22⋊C4C2416yes—
462C2×C22⋊C4C2416yes—
463C2×C22⋊C4C24112yes—
464C2×C22⋊C4C24112yes—
465C2×C22⋊C4C2416yes—
466C2×C22⋊C4C2416yes—
467C2×C22⋊C4C2416yes—
468C2×C22⋊C4C2416yes—
469C2×C22⋊C4C2412yes—
470C2×C22⋊C4C2416yes—
471C2×C22⋊C4C2416yes—
472C2×C22⋊C4C2414yes—
473C2×C22⋊C4C2416yes—
474C2×C22⋊C4C2416yes—
475C2×C22⋊C4C24112yes—
476C2×C22⋊C4C2414yes—
477C2×C22⋊C4C24112yes—
478C2×C22⋊C4C24112yes—
479C2×C42—224no—
480C2×C42—224no—
481C2×C42—212no—
482C2×C42—212no—
483C2×C42C2412yes—
484C2×C42C2416yes—
485C2×C42C2416yes—
486C2×C42C2416yes—
487C2×C42C24112yes—
488C2×C42C2413yes—
489C2×C42C2413yes—
490C2×C42C2416yes—
491C2×C42C2416yes—
492C2×C42C2416yes—
493C2×C42C2411yescharacteristic
494C2×C42C2411yescharacteristic
495#95C2412yes—
496#95C24112yes—
497#95C24112yes—
498#95C24112yes—
499#95C2416yes—
500#95C2416yes—
501#95C2416yes—
502#95C24124yes—
503#95C24124yes—
504#95C24124yes—
505#95C24112yes—
506#95C24112yes—
507#95C24112yes—
508#95C2414yes—
509#95C24112yes—
510#95C24112yes—
511C24—26no—
512C24—26no—
513C24—46no—
514C24—46no—
515C24C22×D4112yes—
516C24C2512yes—
517C24C2511yescharacteristic
518C24C2513yes—
519C24C2513yes—
520#41—232no—
521#41—296no—
522#41—296no—
523#41—496no—
524#41—448no—
525#41#123164yescomplemented
526C2×Q8—232no—
527C2×Q8—26no—
528C2×Q8—212no—
529C2×Q8—26no—
530C2×Q8—26no—
531C2×Q8—26no—
532C2×Q8—26no—
533C2×Q8—212no—
534C2×Q8—212no—
535C2×Q8—432no—
536C2×Q8—448no—
537C2×Q8C22×D4112yes—
538C2×Q8C22×D414yes—
539C2×Q8C2×#4114yes—
540C2×Q8C2×#4114yes—
541C2×D4—212no—
542C2×D4—212no—
543C2×D4—296no—
544C2×D4—24no—
545C2×D4—212no—
546C2×D4—212no—
547C2×D4—212no—
548C2×D4—212no—
549C2×D4—22no—
550C2×D4—26no—
551C2×D4—26no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—44no—
555C2×D4—412no—
556C2×D4C22×D4124yes—
557C2×D4C22×D4112yes—
558C2×D4C22×D4112yes—
559C2×D4C2×#41112yes—
560C2×D4C2×#41112yes—
561C22×C4—26no—
562C22×C4—26no—
563C22×C4—296no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—26no—
567C22×C4—26no—
568C22×C4—26no—
569C22×C4—26no—
570C22×C4—26no—
571C22×C4—26no—
572C22×C4—212no—
573C22×C4—212no—
574C22×C4—212no—
575C22×C4—212no—
576C22×C4—212no—
577C22×C4—212no—
578C22×C4—212no—
579C22×C4—212no—
580C22×C4—212no—
581C22×C4—212no—
582C22×C4—212no—
583C22×C4—212no—
584C22×C4—212no—
585C22×C4—212no—
586C22×C4—46no—
587C22×C4—46no—
588C22×C4—412no—
589C22×C4—412no—
590C22×C4—412no—
591C22×C4—46no—
592C22×C4—412no—
593C22×C4—412no—
594C22×C4C22×D4112yes—
595C22×C4C22×D4112yes—
596C22×C4C22×D4112yes—
597C22×C4C22×D4112yes—
598C22×C4C22×D414yes—
599C22×C4C22×D4112yes—
600C22×C4C2×#41112yes—
601C22×C4C2×#41112yes—
602C22×C4C2512yes—
603C22×C4C2516yes—
604C22×C4C2516yes—
605C22×C4C2516yes—
606C22×C4C2516yes—
607C22×C4C2512yes—
608C22×C4C2512yes—
609C22×C4C2516yes—
610C22×C4C2512yes—
611C22×C4C2516yes—
612C22×C4C2511yescharacteristic
613C22×C4C2513yes—
614C22×C4C2512yes—
615C22×C4C2513yes—
616C22×C4C2511yescharacteristic
617C4⋊C4—22no—
618C4⋊C4—26no—
619C4⋊C4—22no—
620C4⋊C4—26no—
621C4⋊C4—26no—
622C4⋊C4—212no—
623C4⋊C4—212no—
624C4⋊C4—212no—
625C4⋊C4—212no—
626C4⋊C4—212no—
627C4⋊C4—212no—
628C4⋊C4—224no—
629C4⋊C4—22no—
630C4⋊C4—212no—
631C4⋊C4—212no—
632C4⋊C4—212no—
633C4⋊C4—224no—
634C4⋊C4—424no—
635C4⋊C4—44no—
636C4⋊C4—412no—
637C4⋊C4—412no—
638C22⋊C4—212no—
639C22⋊C4—24no—
640C22⋊C4—212no—
641C22⋊C4—224no—
642C22⋊C4—212no—
643C22⋊C4—212no—
644C22⋊C4—224no—
645C22⋊C4—212no—
646C22⋊C4—212no—
647C22⋊C4—212no—
648C22⋊C4—212no—
649C22⋊C4—24no—
650C22⋊C4—212no—
651C22⋊C4—24no—
652C22⋊C4—212no—
653C22⋊C4—28no—
654C22⋊C4—46no—
655C22⋊C4—46no—
656C22⋊C4—412no—
657C22⋊C4—412no—
658C22⋊C4—44no—
659C22⋊C4—412no—
660C42—212no—
661C42—24no—
662C42—224no—
663C42—212no—
664C42—212no—
665C42—212no—
666C42—22no—
667C42—22no—
668C42—26no—
669C42—26no—
670C42—212no—
671C42—212no—
672C23—26no—
673C23—26no—
674C23—21no—
675C23—21no—
676C23—23no—
677C23—23no—
678C23—22no—
679C23—26no—
680C23—26no—
681C23—22no—
682C23—224no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—24no—
687C23—24no—
688C23—412no—
689C23—412no—
690C23—812no—
691C23—812no—
692C23C23×D412yes—
693C23C23×D416yes—
694C23C23×D416yes—
695C23C22×#4116yes—
696C23C22×#4116yes—
697C23C2611yescharacteristic
698Q8—224no—
699Q8—412no—
700Q8—424no—
701Q8C2×#123116yes—
702D4—248no—
703D4—224no—
704D4—48no—
705D4—424no—
706D4—44no—
707D4—812no—
708D4C2×#123148yes—
709C2×C4—22no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—23no—
713C2×C4—23no—
714C2×C4—22no—
715C2×C4—224no—
716C2×C4—28no—
717C2×C4—224no—
718C2×C4—224no—
719C2×C4—224no—
720C2×C4—22no—
721C2×C4—26no—
722C2×C4—26no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—26no—
726C2×C4—26no—
727C2×C4—22no—
728C2×C4—26no—
729C2×C4—26no—
730C2×C4—26no—
731C2×C4—26no—
732C2×C4—26no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—26no—
736C2×C4—212no—
737C2×C4—212no—
738C2×C4—26no—
739C2×C4—26no—
740C2×C4—22no—
741C2×C4—212no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—424no—
745C2×C4—424no—
746C2×C4—424no—
747C2×C4—812no—
748C2×C4—812no—
749C2×C4—812no—
750C2×C4—812no—
751C2×C4—812no—
752C2×C4—812no—
753C2×C4C2×#123148yes—
754C2×C4C23×D412yes—
755C2×C4C23×D416yes—
756C2×C4C23×D416yes—
757C2×C4C23×D412yes—
758C2×C4C22×#4112yes—
759C2×C4C22×#4112yes—
760C2×C4C22×#4116yes—
761C2×C4C22×#4116yes—
762C2×C4#58514yes—
763C22—212no—
764C22—212no—
765C22—26no—
766C22—26no—
767C22—26no—
768C22—22no—
769C22—26no—
770C22—22no—
771C22—22no—
772C22—26no—
773C22—46no—
774C22—42no—
775C22—46no—
776C22—42no—
777C22—44no—
778C22—44no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—824no—
783C22C22×#123112yes—
784C22C24×D411yescharacteristic
785C22C23×#4111yescharacteristic
786C22C23×#4111yescharacteristic
787C22C2×#58512yes—
788C222−1+612yes—
789C4—24no—
790C4—22no—
791C4—26no—
792C4—46no—
793C4—46no—
794C4—42no—
795C4—42no—
796C4—46no—
797C4—46no—
798C4—46no—
799C4—42no—
800C4—42no—
801C4—46no—
802C4C22×#12314yes—
803C4C22×#123112yes—
804C2—212no—
805C2—46no—
806C2—42no—
807C2—82no—
808C2C23×#12311yescharacteristic
809C2#6281211yescharacteristic
810C2#6285911yescharacteristic
811C2#6299312yes—
812C2#6300912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3489C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3428C2semidirect
3. #36432C2semidirect
4. #36217C2semidirect
5. #35791C2semidirect
6. #35723C2semidirect
7. #35619C2semidirect
8. #35619C2semidirect
9. #35618C2semidirect
10. #35530C2semidirect
11. #35311C2semidirect
12. #35157C2semidirect
13. #34810C2semidirect
14. C2×#2499C2semidirect
15. #34259C2semidirect
16. #34259C2semidirect
17. #34184C2semidirect
18. #34183C2semidirect
19. C22⋊C4×#41C2semidirect
45. #2855C22semidirect
46. #2853C22semidirect
49. #2504C22semidirect
50. #2503C22semidirect
51. #2503C22semidirect
52. #2502C22semidirect
53. #2502C22semidirect
54. #2501C22semidirect
57. #2500C22semidirect
62. #2499C22semidirect
63. #2499C22semidirect
64. #2499C22semidirect
65. #2499C22semidirect
66. #2498C22semidirect
68. #2485C22semidirect
69. #2484C22semidirect
71. #2447C22semidirect
72. #2447C22semidirect
73. #2446C22semidirect
74. #2446C22semidirect
75. #2444C22semidirect
76. #2443C22semidirect
77. #2423C22semidirect
78. #2422C22semidirect
79. #2421C22semidirect
80. #2420C22semidirect
81. #2419C22semidirect
82. #2419C22semidirect
86. #2351C22semidirect
87. Q8×C4⋊C4C22semidirect
88. #2349C22semidirect
89. D4×C4⋊C4C22semidirect
92. Q8×C22⋊C4C22semidirect
93. Q8×C22⋊C4C22semidirect
95. #2339C22semidirect
96. #2339C22semidirect
98. #2317C22semidirect
99. #2317C22semidirect
100. #2317C22semidirect
101. #2317C22semidirect
102. #2311C22semidirect
103. #2311C22semidirect
104. #2310C22semidirect
105. #2310C22semidirect
106. C4×#123C22semidirect
109. #2297C22semidirect
110. #2297C22semidirect
111. C2×#391C22semidirect
112. C2×#391C22semidirect
113. C2×#387C22semidirect
114. #2285C22semidirect
115. #2285C22semidirect
116. C2×#384C22semidirect
117. C2×#382C22semidirect
525. #41#123semidirect

Maximal subgroups

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

subgroupindex
C2×#34892
C2×#34282
#364322
#362172
#357912
#357232
#356192
#356182
#355302
#353112
#351572
#348102
C2×#24992
#342592
#341842
#341832
C22⋊C4×#412