Finite Group Databasebeta

← #7632674

Subgroups — #7632674

Order 512.

8774 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3488C211yesmaximal, characteristic
2C2×#3428C211yesmaximal, characteristic, complemented
3#36433C214yesmaximal, complemented
4#36216C2112yesmaximal, complemented
5#35801C214yesmaximal, complemented
6#35713C2112yesmaximal, complemented
7#35618C213yesmaximal, complemented
8#35531C213yesmaximal, complemented
9#35531C213yesmaximal, complemented
10#35530C213yesmaximal, complemented
11#35262C213yesmaximal, complemented
12#35157C213yesmaximal, complemented
13#34810C213yesmaximal, complemented
14C2×#2500C213yesmaximal, complemented
15#34258C211yesmaximal, characteristic, complemented
16#34258C211yesmaximal, characteristic, complemented
17#34184C211yesmaximal, characteristic, complemented
18#34183C211yesmaximal, characteristic, complemented
19C22⋊C4×#41C211yesmaximal, characteristic, complemented
20C22×H(5,𝔽2)C2211yescharacteristic
21C23×#41C2211yescharacteristic
22#3488—216no—
23C2×#550C2212yes—
24C2×#548C2212yes—
25C2×#546C2216yes—
26C2×D42C2216yes—
27C2×#537C2213yes—
28C2×#535C2213yes—
29C2×#525C2213yes—
30C22×#121C2213yes—
31#3428—216no—
32C2×#520C2211yescharacteristic
33C2×#520C2211yescharacteristic
34C2×#520C2211yescharacteristic
35C2×#520C2213yescomplemented
36C2×#520C2213yescomplemented
37C2×#519C2212yescomplemented
38C2×#518C2216yescomplemented
39C2×C4×#41C2211yescharacteristic
40C2×C4×#41C2211yescharacteristic
41C2×C4×#41C2212yescomplemented
42C2×C4×#41C2216yescomplemented
43C22×#117C2213yescomplemented
44C22×#117C2213yescomplemented
45#2854C22112yescomplemented
46#2853C22112yescomplemented
47#2624C22112yescomplemented
48#2622C22112yescomplemented
49#2504C2216yescomplemented
50#2504C2213yescomplemented
51#2503C2213yescomplemented
52#2502C2213yescomplemented
53#2501C2216yescomplemented
54#2501C2213yescomplemented
55#2500C2216yescomplemented
56#2500C22112yescomplemented
57#2500C2216yescomplemented
58#2500C2216yescomplemented
59#2500C22112yescomplemented
60#2500C2213yescomplemented
61#2500C2216yescomplemented
62#2500C2213yescomplemented
63#2499C2216yescomplemented
64#2499C2213yescomplemented
65#2499C2211yescharacteristic, complemented
66#2498C22112yescomplemented
67#2485C22112yescomplemented
68#2485C22112yescomplemented
69#2482C22112yescomplemented
70#2448C22112yescomplemented
71#2448C22112yescomplemented
72#2445C22112yescomplemented
73#2445C22112yescomplemented
74#2444C22124yescomplemented
75#2443C22124yescomplemented
76#2423C22112yescomplemented
77#2422C22112yescomplemented
78#2421C22112yescomplemented
79#2420C22112yescomplemented
80#2418C22124yescomplemented
81#2418C22124yescomplemented
82#2412C22112yescomplemented
83#2405C22112yescomplemented
84#2395C22112yescomplemented
85C2×#394C22112yescomplemented
86#2351C2214yescomplemented
87Q8×C4⋊C4C2214yescomplemented
88#2349C22112yescomplemented
89D4×C4⋊C4C22112yescomplemented
90#2341C2212yescomplemented
91#2341C2214yescomplemented
92#2341C2214yescomplemented
93Q8×C22⋊C4C2212yescomplemented
94#2339C2216yescomplemented
95D4×C22⋊C4C2216yescomplemented
96D4×C22⋊C4C22112yescomplemented
97D4×C22⋊C4C22112yescomplemented
98#2317C2213yescomplemented
99#2317C2213yescomplemented
100#2317C2213yescomplemented
101#2317C2213yescomplemented
102#2311C2213yescomplemented
103#2311C2213yescomplemented
104#2309C2213yescomplemented
105#2309C2213yescomplemented
106C4×#123C22112yescomplemented
107#2297C2213yescomplemented
108#2297C2213yescomplemented
109#2297C2213yescomplemented
110#2297C2213yescomplemented
111C2×#390C2213yescomplemented
112C2×#390C2213yescomplemented
113C2×#388C22112yescomplemented
114#2285C2213yescomplemented
115#2285C2213yescomplemented
116C2×#384C2213yescomplemented
117C2×#382C2213yescomplemented
118#2280C2213yescomplemented
119C2×C4×C22⋊C4C2213yescomplemented
120C2×H(5,𝔽2)—28no—
121C2×H(5,𝔽2)—28no—
122C2×H(5,𝔽2)—28no—
123C22×#41—28no—
124C22×#41—28no—
125C22×#41D4116yes—
126C22×#41C2313yes—
127C22×#41C2312yes—
128C22×#41C2313yes—
129C22×#41C2311yescharacteristic
130C22×#41C2313yes—
131C22×#41C2311yescharacteristic
132C23×Q8C2311yescharacteristic
133C23×D4C2313yes—
134C23×D4C2316yes—
135C23×D4C2313yes—
136C23×D4C2316yes—
137C24×C4C2313yes—
138#550—216no—
139#548—216no—
140#546—248no—
141D42—248no—
142#537—224no—
143#535—224no—
144C2×#127C2316yes—
145C2×#124C2316yes—
146#525—224no—
147C2×#123C2316yes—
148C2×#123C23112yes—
149C2×#123C23124yes—
150C2×C22⋊Q8C2311yescharacteristic
151C2×C22⋊Q8C2313yes—
152C2×C22⋊Q8C2316yes—
153C2×#121—224no—
154C2×#121C2316yes—
155C2×#121C2316yes—
156C2×#121C2313yes—
157C2×#121C2316yes—
158C2×#121C2313yes—
159C2×#121C2316yes—
160C2×#121C23112yes—
161C2×#120C2316yes—
162C2×#120C23112yes—
163#520—28no—
164#520—28no—
165#520—28no—
166#520—224no—
167#520—224no—
168#519—216no—
169#518—248no—
170C4×#41—248no—
171C4×#41—216no—
172C4×#41—28no—
173C4×#41—28no—
174C2×C4×Q8C2312yes—
175C2×C4×Q8C2312yes—
176C2×C4×Q8C2312yes—
177C2×C4×Q8C2312yes—
178C2×C4×Q8C2312yes—
179C2×C4×Q8C2316yes—
180C2×C4×Q8C2316yes—
181C2×C4×D4C2316yes—
182C2×C4×D4C2316yes—
183C2×C4×D4C2316yes—
184C2×C4×D4C2316yes—
185C2×C4×D4C2316yes—
186C2×C4×D4C2316yes—
187C2×C4×D4C23112yes—
188C2×C4×D4C23112yes—
189C2×C4×D4C2316yes—
190C2×C4×D4C2316yes—
191C2×C4×D4C2316yes—
192C2×#117—224no—
193C2×#117—224no—
194C2×#117C2313yes—
195C2×#117C2313yes—
196C2×#117C2313yes—
197C2×#117C2313yes—
198C2×#117C2313yes—
199C2×#117C2316yes—
200C2×#117C2313yes—
201C2×#117C2311yescharacteristic
202C2×#117C2316yes—
203C2×#117C2316yes—
204C2×#117C2316yes—
205C2×#117C2316yes—
206C22×C4⋊C4C2313yes—
207C22×C4⋊C4C2313yes—
208C22×C4⋊C4C2313yes—
209C22×C4⋊C4C2313yes—
210C22×C4⋊C4C2313yes—
211C22×C4⋊C4C23112yes—
212C22×C22⋊C4C2316yes—
213C22×C22⋊C4C2316yes—
214C22×C22⋊C4C2316yes—
215C22×C22⋊C4C2316yes—
216C22×C22⋊C4C23112yes—
217C22×C22⋊C4C23112yes—
218C22×C42C2316yes—
219C22×C42C2316yes—
220C22×C42C2313yes—
221C22×C42C2313yes—
222#400C23112yes—
223#399C23124yes—
224#399C23112yes—
225#398C23112yes—
226#397C23112yes—
227#397C23124yes—
228#397C23124yes—
229#397C2314yes—
230#397C23112yes—
231#394C23124yes—
232#394C23124yes—
233#394C23112yes—
234#394C23112yes—
235#394C23124yes—
236#394C23124yes—
237#391C2313yes—
238#391C2313yes—
239#391C2316yes—
240#391C2316yes—
241#391C2311yescharacteristic
242#391C2311yescharacteristic
243#390C2313yes—
244#390C2313yes—
245#390C2316yes—
246#390C2316yes—
247#390C23112yes—
248#390C23112yes—
249#390C2316yes—
250#390C2316yes—
251#390C23112yes—
252#390C23112yes—
253#390C2313yes—
254#390C2313yes—
255#389C23112yes—
256#389C23112yes—
257#389C23112yes—
258#389C23112yes—
259#388C23124yes—
260#388C23124yes—
261#388C23112yes—
262#388C23124yes—
263#388C23124yes—
264#388C23112yes—
265#387C23112yes—
266#387C23124yes—
267#387C2314yes—
268#386C23112yes—
269#386C23112yes—
270#386C23112yes—
271#386C23112yes—
272#386C23112yes—
273#386C23112yes—
274#386C23124yes—
275#386C23112yes—
276#385C23112yes—
277#385C23112yes—
278#385C23112yes—
279#385C23112yes—
280#385C23112yes—
281#384C2316yes—
282#384C2313yes—
283#384C2313yes—
284#384C23112yes—
285#384C2311yescharacteristic
286#384C2313yes—
287#382C2316yes—
288#382C2313yes—
289#382C2313yes—
290#382C23112yes—
291#382C2311yescharacteristic
292#382C2313yes—
293#381C2316yes—
294#381C23112yes—
295#380C23112yes—
296#380C23112yes—
297#380C2316yes—
298#380C2316yes—
299#380C23112yes—
300#380C23112yes—
301#379C23112yes—
302#379C23112yes—
303#379C2316yes—
304C4×C4⋊C4C23112yes—
305C4×C4⋊C4C23112yes—
306C4×C22⋊C4C2316yes—
307C4×C22⋊C4C23112yes—
308C4×C22⋊C4C23112yes—
309C4×C22⋊C4C2316yes—
310C4×C22⋊C4C2311yescharacteristic
311C4×C22⋊C4C2313yes—
312C4×C22⋊C4C2316yes—
313C4×C22⋊C4C2313yes—
314C4×C22⋊C4C2313yes—
315C2×#95C2316yes—
316C2×#95C23112yes—
317C25C2416yes—
318C25C2413yes—
319H(5,𝔽2)—464no—
320C2×#41—2128no—
321C2×#41—28no—
322C2×#41—24no—
323C2×#41—24no—
324C2×#41—28no—
325C2×#41—28no—
326C2×#41—212no—
327C2×#41—212no—
328C2×#41—212no—
329C2×#41—212no—
330C2×#41—212no—
331C2×#41—212no—
332C2×#41—212no—
333C2×#41C2×D4124yes—
334C2×#41C2×D418yes—
335C2×#41C2×D4124yes—
336C2×#41C2×D418yes—
337C2×#41#4118yes—
338C2×#41#4118yes—
339C22×Q8—24no—
340C22×Q8—24no—
341C22×Q8C2×D418yes—
342C22×Q8C2411yescharacteristic
343C22×Q8C2413yes—
344C22×Q8C2411yescharacteristic
345C22×D4—212no—
346C22×D4—212no—
347C22×D4—224no—
348C22×D4—224no—
349C22×D4—224no—
350C22×D4—224no—
351C22×D4—212no—
352C22×D4—212no—
353C22×D4—212no—
354C22×D4—812no—
355C22×D4C2×D4124yes—
356C22×D4C2416yes—
357C22×D4C2413yes—
358C22×D4C2416yes—
359C22×D4C2416yes—
360C22×D4C2413yes—
361C22×D4C2416yes—
362C22×D4C2416yes—
363C22×D4C24112yes—
364C22×D4C2413yes—
365C23×C4—212no—
366C23×C4—212no—
367C23×C4C2×D4124yes—
368C23×C4C2416yes—
369C23×C4C2416yes—
370C23×C4C2413yes—
371C23×C4C2413yes—
372C23×C4C2413yes—
373C23×C4C2411yescharacteristic
374C23×C4C2413yes—
375C23×C4C2416yes—
376C23×C4C2416yes—
377C23×C4C2416yes—
378C23×C4C2416yes—
379C23×C4C2416yes—
380C23×C4C2416yes—
381C23×C4C2413yes—
382#127—224no—
383#124—224no—
384#123—224no—
385#123—424no—
386#123—824no—
387C22⋊Q8—224no—
388C22⋊Q8—24no—
389C22⋊Q8—212no—
390#121—248no—
391#121—224no—
392#121—212no—
393#121—224no—
394#121—224no—
395#121—224no—
396#121—212no—
397#120—224no—
398#120—248no—
399C4×Q8—224no—
400C4×Q8—224no—
401C4×Q8—28no—
402C4×Q8—28no—
403C4×Q8—28no—
404C4×Q8—28no—
405C4×Q8—28no—
406C4×D4—248no—
407C4×D4—248no—
408C4×D4—224no—
409C4×D4—224no—
410C4×D4—224no—
411C4×D4—224no—
412C4×D4—224no—
413C4×D4—224no—
414C4×D4—224no—
415C4×D4—224no—
416C4×D4—224no—
417#117—212no—
418#117—24no—
419#117—224no—
420#117—224no—
421#117—224no—
422#117—224no—
423#117—224no—
424#117—212no—
425#117—212no—
426#117—212no—
427#117—212no—
428#117—212no—
429C2×C4⋊C4—212no—
430C2×C4⋊C4—212no—
431C2×C4⋊C4—212no—
432C2×C4⋊C4—212no—
433C2×C4⋊C4—212no—
434C2×C4⋊C4—812no—
435C2×C4⋊C4C2413yes—
436C2×C4⋊C4C2411yescharacteristic
437C2×C4⋊C4C2413yes—
438C2×C4⋊C4C2411yescharacteristic
439C2×C4⋊C4C2413yes—
440C2×C4⋊C4C2416yes—
441C2×C4⋊C4C2416yes—
442C2×C4⋊C4C2416yes—
443C2×C4⋊C4C2416yes—
444C2×C4⋊C4C2416yes—
445C2×C4⋊C4C2411yescharacteristic
446C2×C4⋊C4C2416yes—
447C2×C4⋊C4C2416yes—
448C2×C4⋊C4C2412yes—
449C2×C4⋊C4C2416yes—
450C2×C4⋊C4C2414yes—
451C2×C4⋊C4C24112yes—
452C2×C4⋊C4C24124yes—
453C2×C4⋊C4C24112yes—
454C2×C4⋊C4C24112yes—
455C2×C22⋊C4—224no—
456C2×C22⋊C4—224no—
457C2×C22⋊C4—224no—
458C2×C22⋊C4—412no—
459C2×C22⋊C4—424no—
460C2×C22⋊C4—812no—
461C2×C22⋊C4C2416yes—
462C2×C22⋊C4C2412yes—
463C2×C22⋊C4C2412yes—
464C2×C22⋊C4C2416yes—
465C2×C22⋊C4C24112yes—
466C2×C22⋊C4C2416yes—
467C2×C22⋊C4C2416yes—
468C2×C22⋊C4C24112yes—
469C2×C22⋊C4C24112yes—
470C2×C22⋊C4C2416yes—
471C2×C22⋊C4C2416yes—
472C2×C22⋊C4C2416yes—
473C2×C22⋊C4C2416yes—
474C2×C22⋊C4C2412yes—
475C2×C22⋊C4C2416yes—
476C2×C22⋊C4C2416yes—
477C2×C22⋊C4C24112yes—
478C2×C22⋊C4C24124yes—
479C2×C22⋊C4C2416yes—
480C2×C22⋊C4C2416yes—
481C2×C22⋊C4C24124yes—
482C2×C22⋊C4C24112yes—
483C2×C22⋊C4C24112yes—
484C2×C22⋊C4C24112yes—
485C2×C42—224no—
486C2×C42—224no—
487C2×C42—212no—
488C2×C42—212no—
489C2×C42C2412yes—
490C2×C42C2416yes—
491C2×C42C2416yes—
492C2×C42C2416yes—
493C2×C42C24112yes—
494C2×C42C2413yes—
495C2×C42C2413yes—
496C2×C42C2416yes—
497C2×C42C2416yes—
498C2×C42C2416yes—
499C2×C42C2411yescharacteristic
500C2×C42C2411yescharacteristic
501#95C2412yes—
502#95C24112yes—
503#95C2416yes—
504#95C2416yes—
505#95C2416yes—
506#95C24124yes—
507#95C2414yes—
508#95C2414yes—
509#95C24112yes—
510#95C24112yes—
511#95C24112yes—
512#95C2414yes—
513#95C24112yes—
514#95C24112yes—
515C24—26no—
516C24—26no—
517C24—212no—
518C24—212no—
519C24—212no—
520C24—46no—
521C24—46no—
522C24—412no—
523C24—412no—
524C24C22×D4112yes—
525C24C2516yes—
526C24C2511yescharacteristic
527C24C2513yes—
528C24C2513yes—
529#41—232no—
530#41—296no—
531#41—296no—
532#41—432no—
533#41—448no—
534#41#123164yescomplemented
535C2×Q8—232no—
536C2×Q8—22no—
537C2×Q8—26no—
538C2×Q8—26no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8C22×D4112yes—
542C2×Q8C22×D414yes—
543C2×Q8C2×#4114yes—
544C2×Q8C2×#4114yes—
545C2×D4—212no—
546C2×D4—212no—
547C2×D4—296no—
548C2×D4—212no—
549C2×D4—212no—
550C2×D4—212no—
551C2×D4—212no—
552C2×D4—212no—
553C2×D4—224no—
554C2×D4—26no—
555C2×D4—212no—
556C2×D4—26no—
557C2×D4—26no—
558C2×D4—26no—
559C2×D4—26no—
560C2×D4—212no—
561C2×D4—212no—
562C2×D4—412no—
563C2×D4—412no—
564C2×D4—424no—
565C2×D4—496no—
566C2×D4—448no—
567C2×D4—848no—
568C2×D4C22×D4124yes—
569C2×D4C22×D4112yes—
570C2×D4C22×D4112yes—
571C2×D4C2×#41112yes—
572C2×D4C2×#41112yes—
573C22×C4—26no—
574C22×C4—26no—
575C22×C4—296no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—26no—
579C22×C4—26no—
580C22×C4—26no—
581C22×C4—26no—
582C22×C4—26no—
583C22×C4—26no—
584C22×C4—212no—
585C22×C4—212no—
586C22×C4—212no—
587C22×C4—212no—
588C22×C4—212no—
589C22×C4—212no—
590C22×C4—212no—
591C22×C4—212no—
592C22×C4—212no—
593C22×C4—212no—
594C22×C4—212no—
595C22×C4—46no—
596C22×C4—46no—
597C22×C4—412no—
598C22×C4—46no—
599C22×C4—412no—
600C22×C4—412no—
601C22×C4—412no—
602C22×C4—412no—
603C22×C4C22×D4112yes—
604C22×C4C22×D4112yes—
605C22×C4C22×D4112yes—
606C22×C4C22×D4112yes—
607C22×C4C22×D414yes—
608C22×C4C22×D4112yes—
609C22×C4C2×#41112yes—
610C22×C4C2×#41112yes—
611C22×C4C2512yes—
612C22×C4C2512yes—
613C22×C4C2516yes—
614C22×C4C2516yes—
615C22×C4C2516yes—
616C22×C4C2512yes—
617C22×C4C2512yes—
618C22×C4C2516yes—
619C22×C4C2512yes—
620C22×C4C2516yes—
621C22×C4C2511yescharacteristic
622C22×C4C2513yes—
623C22×C4C2512yes—
624C22×C4C2513yes—
625C22×C4C2511yescharacteristic
626C4⋊C4—22no—
627C4⋊C4—26no—
628C4⋊C4—22no—
629C4⋊C4—26no—
630C4⋊C4—26no—
631C4⋊C4—212no—
632C4⋊C4—212no—
633C4⋊C4—212no—
634C4⋊C4—212no—
635C4⋊C4—212no—
636C4⋊C4—22no—
637C4⋊C4—24no—
638C4⋊C4—212no—
639C4⋊C4—212no—
640C4⋊C4—212no—
641C4⋊C4—28no—
642C4⋊C4—412no—
643C4⋊C4—424no—
644C4⋊C4—412no—
645C4⋊C4—412no—
646C22⋊C4—212no—
647C22⋊C4—24no—
648C22⋊C4—224no—
649C22⋊C4—212no—
650C22⋊C4—212no—
651C22⋊C4—212no—
652C22⋊C4—24no—
653C22⋊C4—212no—
654C22⋊C4—212no—
655C22⋊C4—212no—
656C22⋊C4—212no—
657C22⋊C4—224no—
658C22⋊C4—212no—
659C22⋊C4—24no—
660C22⋊C4—224no—
661C22⋊C4—212no—
662C22⋊C4—46no—
663C22⋊C4—46no—
664C22⋊C4—424no—
665C22⋊C4—412no—
666C22⋊C4—424no—
667C22⋊C4—412no—
668C22⋊C4—412no—
669C22⋊C4—412no—
670C42—212no—
671C42—24no—
672C42—224no—
673C42—212no—
674C42—212no—
675C42—212no—
676C42—22no—
677C42—22no—
678C42—26no—
679C42—26no—
680C42—212no—
681C42—212no—
682C23—26no—
683C23—26no—
684C23—21no—
685C23—21no—
686C23—23no—
687C23—23no—
688C23—22no—
689C23—26no—
690C23—26no—
691C23—22no—
692C23—224no—
693C23—26no—
694C23—26no—
695C23—26no—
696C23—212no—
697C23—212no—
698C23—412no—
699C23—412no—
700C23—424no—
701C23—812no—
702C23—812no—
703C23—812no—
704C23—824no—
705C23—824no—
706C23—812no—
707C23C23×D412yes—
708C23C23×D416yes—
709C23C23×D416yes—
710C23C22×#4116yes—
711C23C22×#4116yes—
712C23C2611yescharacteristic
713Q8—224no—
714Q8—44no—
715Q8C2×#123116yes—
716D4—248no—
717D4—224no—
718D4—424no—
719D4—424no—
720D4—412no—
721D4—424no—
722D4—812no—
723D4—824no—
724D4C2×#123148yes—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—23no—
729C2×C4—23no—
730C2×C4—22no—
731C2×C4—224no—
732C2×C4—28no—
733C2×C4—224no—
734C2×C4—224no—
735C2×C4—224no—
736C2×C4—26no—
737C2×C4—22no—
738C2×C4—26no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—26no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—26no—
745C2×C4—26no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—26no—
749C2×C4—22no—
750C2×C4—212no—
751C2×C4—26no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—26no—
755C2×C4—22no—
756C2×C4—26no—
757C2×C4—212no—
758C2×C4—24no—
759C2×C4—212no—
760C2×C4—424no—
761C2×C4—424no—
762C2×C4—812no—
763C2×C4—812no—
764C2×C4—812no—
765C2×C4—812no—
766C2×C4—812no—
767C2×C4—812no—
768C2×C4C2×#123148yes—
769C2×C4C23×D412yes—
770C2×C4C23×D416yes—
771C2×C4C23×D416yes—
772C2×C4C23×D412yes—
773C2×C4C22×#4112yes—
774C2×C4C22×#4112yes—
775C2×C4C22×#4116yes—
776C2×C4C22×#4116yes—
777C2×C4#58514yes—
778C22—212no—
779C22—212no—
780C22—26no—
781C22—26no—
782C22—26no—
783C22—22no—
784C22—26no—
785C22—22no—
786C22—22no—
787C22—26no—
788C22—46no—
789C22—42no—
790C22—46no—
791C22—42no—
792C22—412no—
793C22—412no—
794C22—46no—
795C22—46no—
796C22—46no—
797C22—824no—
798C22—1624no—
799C22C22×#123112yes—
800C22C24×D411yescharacteristic
801C22C23×#4111yescharacteristic
802C22C23×#4111yescharacteristic
803C22C2×#58512yes—
804C22H(7,𝔽2)12yes—
805C4—24no—
806C4—22no—
807C4—26no—
808C4—46no—
809C4—42no—
810C4—46no—
811C4—46no—
812C4—42no—
813C4—42no—
814C4—46no—
815C4—42no—
816C4—46no—
817C4—42no—
818C4C22×#12314yes—
819C4C22×#123112yes—
820C2—212no—
821C2—46no—
822C2—42no—
823C2—86no—
824C2C23×#12311yescharacteristic
825C2#6281211yescharacteristic
826C2#6285211yescharacteristic
827C2#6299412yes—
828C2#6300812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3488C2
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. #36433C2semidirect
4. #36216C2semidirect
5. #35801C2semidirect
6. #35713C2semidirect
7. #35618C2semidirect
8. #35531C2semidirect
9. #35531C2semidirect
10. #35530C2semidirect
11. #35262C2semidirect
12. #35157C2semidirect
13. #34810C2semidirect
14. C2×#2500C2semidirect
15. #34258C2semidirect
16. #34258C2semidirect
17. #34184C2semidirect
18. #34183C2semidirect
19. C22⋊C4×#41C2semidirect
35. C2×#520C22semidirect
36. C2×#520C22semidirect
37. C2×#519C22semidirect
38. C2×#518C22semidirect
41. C2×C4×#41C22semidirect
42. C2×C4×#41C22semidirect
43. C22×#117C22semidirect
44. C22×#117C22semidirect
45. #2854C22semidirect
46. #2853C22semidirect
47. #2624C22semidirect
48. #2622C22semidirect
49. #2504C22semidirect
50. #2504C22semidirect
51. #2503C22semidirect
52. #2502C22semidirect
53. #2501C22semidirect
54. #2501C22semidirect
55. #2500C22semidirect
56. #2500C22semidirect
57. #2500C22semidirect
58. #2500C22semidirect
59. #2500C22semidirect
60. #2500C22semidirect
61. #2500C22semidirect
62. #2500C22semidirect
63. #2499C22semidirect
64. #2499C22semidirect
65. #2499C22semidirect
66. #2498C22semidirect
67. #2485C22semidirect
68. #2485C22semidirect
69. #2482C22semidirect
70. #2448C22semidirect
71. #2448C22semidirect
72. #2445C22semidirect
73. #2445C22semidirect
74. #2444C22semidirect
75. #2443C22semidirect
76. #2423C22semidirect
77. #2422C22semidirect
78. #2421C22semidirect
79. #2420C22semidirect
80. #2418C22semidirect
81. #2418C22semidirect
82. #2412C22semidirect
83. #2405C22semidirect
84. #2395C22semidirect
85. C2×#394C22semidirect
86. #2351C22semidirect
87. Q8×C4⋊C4C22semidirect
88. #2349C22semidirect
89. D4×C4⋊C4C22semidirect
90. #2341C22semidirect
91. #2341C22semidirect
92. #2341C22semidirect
93. Q8×C22⋊C4C22semidirect
94. #2339C22semidirect
95. D4×C22⋊C4C22semidirect
96. D4×C22⋊C4C22semidirect
97. D4×C22⋊C4C22semidirect
98. #2317C22semidirect
99. #2317C22semidirect
100. #2317C22semidirect
101. #2317C22semidirect
102. #2311C22semidirect
103. #2311C22semidirect
104. #2309C22semidirect
105. #2309C22semidirect
106. C4×#123C22semidirect
107. #2297C22semidirect
108. #2297C22semidirect
109. #2297C22semidirect
110. #2297C22semidirect
111. C2×#390C22semidirect
112. C2×#390C22semidirect
113. C2×#388C22semidirect
114. #2285C22semidirect
115. #2285C22semidirect
116. C2×#384C22semidirect
117. C2×#382C22semidirect
118. #2280C22semidirect
119. C2×C4×C22⋊C4C22semidirect
534. #41#123semidirect

Maximal subgroups

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

subgroupindex
C2×#34882
C2×#34282
#364332
#362162
#358012
#357132
#356182
#355312
#355302
#352622
#351572
#348102
C2×#25002
#342582
#341842
#341832
C22⋊C4×#412