Finite Group Databasebeta

← #7630600

Subgroups — #7630600

Order 512.

8096 conjugacy classes of subgroups.

The subgroup lattice has 845 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#542C211yesmaximal, characteristic, complemented
2C2×C4×2−1+4C211yesmaximal, characteristic, complemented
3#35679C211yesmaximal, characteristic, complemented
4#35676C211yesmaximal, characteristic, complemented
5#35675C218yesmaximal, complemented
6#35672C211yesmaximal, characteristic, complemented
7#35659C211yesmaximal, characteristic, complemented
8#35574C212yesmaximal, complemented
9#35563C212yesmaximal, complemented
10#35539C218yesmaximal, complemented
11#35357C214yesmaximal, complemented
12#35356C214yesmaximal, complemented
13#35243C218yesmaximal, complemented
14#35195C218yesmaximal, complemented
15#35143C214yesmaximal, complemented
16#35129C214yesmaximal, complemented
17C4×#535C212yesmaximal, complemented
18#34065C212yesmaximal, complemented
19#34059C211yesmaximal, characteristic, complemented
20C22×2−1+4C2211yescharacteristic
21C2×#542—216no—
22C2×#542C2218yes—
23C2×#542C2218yes—
24C2×#535C2212yes—
25C22×C4⋊Q8C2211yescharacteristic
26C22×#126C2212yes—
27C22×#124C2212yes—
28C22×#124C2211yescharacteristic
29C2×#525C2212yes—
30C22×#123C2212yes—
31C22×C22⋊Q8C2212yes—
32C22×C22⋊Q8C2211yescharacteristic
33C22×#121C2211yescharacteristic
34C4×2−1+4—216no—
35C2×#520C2214yes—
36C2×#520C2212yes—
37C2×#520C2214yescomplemented
38C2×#519C2211yescharacteristic
39C2×#519C2214yescomplemented
40C2×C4×#41C2212yes—
41C2×C4×#41C2214yes—
42C2×C4×#41C2214yescomplemented
43C22×C4×Q8C2211yescharacteristic
44C22×C4×Q8C2214yescomplemented
45C22×C4×D4C2211yescharacteristic
46C22×#117C2211yescharacteristic
47#2852C22116yescomplemented
48#2850C22116yescomplemented
49#2637C2218yescomplemented
50#2636C2218yescomplemented
51#2632C2218yescomplemented
52#2631C2218yescomplemented
53#2610C22116yescomplemented
54#2604C2218yescomplemented
55#2603C2218yescomplemented
56#2601C22116yescomplemented
57#2592C2218yescomplemented
58#2579C2218yes—
59#2540C2218yescomplemented
60#2534C2218yes—
61#2484C2214yes—
62#2482C2214yes—
63#2482C2214yes—
64#2482C2214yes—
65#2477C22116yescomplemented
66#2471C22116yescomplemented
67#2465C22116yescomplemented
68#2463C22116yescomplemented
69#2458C22116yescomplemented
70#2456C22116yescomplemented
71#2452C2218yescomplemented
72#2451C2218yescomplemented
73#2449C22116yescomplemented
74#2448C2218yescomplemented
75#2448C2218yescomplemented
76#2443C22116yescomplemented
77#2440C2218yescomplemented
78#2439C2218yescomplemented
79#2436C2218yescomplemented
80#2431C2218yescomplemented
81#2428C2218yes—
82#2426C2218yes—
83#2423C2218yescomplemented
84#2421C2218yescomplemented
85#2416C2218yes—
86#2414C2218yes—
87#2409C2218yes—
88#2409C2218yescomplemented
89#2408C2218yes—
90#2407C2218yescomplemented
91#2406C2214yes—
92#2404C2214yes—
93#2404C2214yes—
94#2404C2214yes—
95#2328C2214yescomplemented
96#2326C2214yescomplemented
97#2324C2214yescomplemented
98#2324C2214yescomplemented
99#2324C2218yescomplemented
100#2323C2214yescomplemented
101#2323C2214yescomplemented
102#2322C2214yes—
103#2322C2214yes—
104#2321C2214yes—
105#2321C2214yes—
106#2321C2218yes—
107#2320C2218yescomplemented
108#2317C2212yes—
109#2316C2212yes—
110#2313C2214yes—
111#2311C2212yes—
112#2310C2211yescharacteristic
113#2310C2211yescharacteristic
114#2309C2212yes—
115C4×#127C2214yescomplemented
116C4×#124C2214yescomplemented
117C4×#121C2218yescomplemented
118C4×#120C2218yes—
119#2297C2212yes—
120#2296C2212yes—
121#2295C2218yescomplemented
122#2293C2218yescomplemented
123#2290C2218yescomplemented
124#2283C2214yes—
125#2280C2212yes—
126C4×#117C2212yes—
127C2×2−1+4—216no—
128C2×2−1+4—28no—
129C22×#41C2314yes—
130C22×#41C2314yes—
131C22×#41C2312yes—
132C23×Q8C2314yes—
133C23×Q8C2311yescharacteristic
134C23×Q8C2312yes—
135C23×D4C2311yescharacteristic
136C23×D4C2312yes—
137C24×C4C2311yescharacteristic
138C24×C4C2312yes—
139#542—264no—
140#542—264no—
141#535—216no—
142C2×C4⋊Q8—28no—
143C2×C4⋊Q8C2318yes—
144C2×#127C2314yes—
145C2×#126—216no—
146C2×#126C2318yes—
147C2×#126C2318yes—
148C2×#124—28no—
149C2×#124—216no—
150C2×#124C2314yes—
151C2×#124C2318yes—
152C2×#124C2318yes—
153C2×#124C2318yes—
154#525—216no—
155C2×#123—216no—
156C2×#123C2314yes—
157C2×#123C23116yes—
158C2×C22⋊Q8—28no—
159C2×C22⋊Q8—216no—
160C2×C22⋊Q8C2314yes—
161C2×C22⋊Q8C2318yes—
162C2×C22⋊Q8C23116yes—
163C2×C22⋊Q8C23116yes—
164C2×#121—28no—
165C2×#121C2314yes—
166C2×#121C2318yes—
167C2×#121C2318yes—
168C2×#121C23116yes—
169C2×#120C2314yes—
170C2×#120C2318yes—
171#520—232no—
172#520—216no—
173#520—232no—
174#519—28no—
175#519—232no—
176C4×#41—232no—
177C4×#41—216no—
178C4×#41—232no—
179C2×C4×Q8—232no—
180C2×C4×Q8D4116yescomplemented
181C2×C4×Q8C2312yes—
182C2×C4×Q8C2312yes—
183C2×C4×Q8C2314yes—
184C2×C4×Q8C2314yes—
185C2×C4×Q8C2314yes—
186C2×C4×Q8C2314yes—
187C2×C4×Q8C2318yes—
188C2×C4×Q8C2314yes—
189C2×C4×Q8C2314yes—
190C2×C4×Q8C2314yes—
191C2×C4×D4—28no—
192C2×C4×D4C2312yes—
193C2×C4×D4C2314yes—
194C2×C4×D4C2314yes—
195C2×C4×D4C2314yes—
196C2×C4×D4C2318yes—
197C2×C4×D4C2312yes—
198C2×C4×D4C2314yes—
199C2×C4×D4C2314yes—
200C2×C4×D4C2314yes—
201C2×C4×D4C2314yes—
202C2×C4×D4C2318yes—
203C2×C4×D4C2318yes—
204C2×C4×D4C23116yes—
205C2×#117—28no—
206C2×#117C2312yes—
207C2×#117C2312yes—
208C2×#117C2312yes—
209C2×#117C2314yes—
210C2×#117C2314yes—
211C2×#117C2314yes—
212C2×#117C2318yes—
213C2×#117C2314yes—
214C2×#117C2314yes—
215C2×#117C2318yes—
216C22×C4⋊C4C2311yescharacteristic
217C22×C4⋊C4C2311yescharacteristic
218C22×C4⋊C4C2311yescharacteristic
219C22×C4⋊C4C2312yes—
220C22×C4⋊C4C2314yes—
221C22×C4⋊C4C2318yes—
222C22×C4⋊C4C2312yes—
223C22×C4⋊C4C2312yes—
224C22×C4⋊C4C2311yescharacteristic
225C22×C22⋊C4C2311yescharacteristic
226C22×C22⋊C4C2311yescharacteristic
227C22×C22⋊C4C2312yes—
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2312yes—
230C22×C22⋊C4C2312yes—
231C22×C22⋊C4C2312yes—
232C22×C42C2318yes—
233C22×C42C2311yescharacteristic
234C22×C42C2314yes—
235C22×C42C2311yescharacteristic
236C22×C42C2312yes—
237#400C2318yes—
238#399C2318yes—
239#399C2318yes—
240#399C2318yes—
241#398C23116yes—
242#398C2318yes—
243#397C2318yes—
244#397C2318yes—
245#397C2318yes—
246#396C23116yes—
247#396C23116yes—
248#395C2318yes—
249#395C23116yes—
250#394C23116yes—
251#394C2318yes—
252#394C23116yes—
253#393C2318yes—
254#393C2318yes—
255#393C2318yes—
256#393C23116yes—
257#392C2318yes—
258#392C23116yes—
259#392C2318yes—
260#392C2318yes—
261#391C2318yes—
262#391C2318yes—
263#391C2314yes—
264#391C2314yes—
265#391C23116yes—
266#390C2314yes—
267#390C2314yes—
268#390C23116yes—
269#390C2318yes—
270#390C2314yes—
271#390C2318yes—
272#390C2318yes—
273#390C2314yes—
274#390C23116yes—
275#389C2318yes—
276#389C2318yes—
277#389C2318yes—
278#389C2318yes—
279#389C2318yes—
280#389C2314yes—
281#389C2314yes—
282#388C2318yes—
283#388C2318yes—
284#388C2318yes—
285#388C2318yes—
286#388C23116yes—
287#388C23116yes—
288#388C2318yes—
289#388C2318yes—
290#388C23116yes—
291#388C23116yes—
292#388C23116yes—
293#388C23116yes—
294#387C23116yes—
295#387C23116yes—
296#387C2318yes—
297#387C2318yes—
298#387C23116yes—
299#387C23116yes—
300#386C2318yes—
301#386C2314yes—
302#386C2314yes—
303#386C2318yes—
304#386C2318yes—
305#386C23116yes—
306#386C23116yes—
307#386C23116yes—
308#386C23116yes—
309#386C23116yes—
310#386C23116yes—
311#385C2318yes—
312#385C2314yes—
313#385C2314yes—
314#385C2318yes—
315#385C2318yes—
316#385C23116yes—
317#385C23116yes—
318#385C23116yes—
319#384C2314yes—
320#383C2318yes—
321#382C2314yes—
322#382C2318yes—
323#381C2314yes—
324#381C2314yes—
325#381C2314yes—
326#380C2318yes—
327#380C2318yes—
328#380C2314yes—
329#380C2314yes—
330#379C2318yes—
331#379C2314yes—
332C4×C4⋊C4C2314yes—
333C4×C4⋊C4C2314yes—
334C4×C4⋊C4C2318yes—
335C4×C4⋊C4C2318yes—
336C4×C22⋊C4C2314yes—
337C4×C22⋊C4C2314yes—
338C4×C22⋊C4C2318yes—
339C4×C22⋊C4C2318yes—
340C4×C22⋊C4C23116yes—
341#376C2314yes—
342#376C2318yes—
343C43C2314yes—
344C25C2411yescharacteristic
345C25C2412yes—
3462−1+4—2128no—
347C2×#41—216no—
348C2×#41—232no—
349C2×#41—216no—
350C2×#41—216no—
351C2×#41—28no—
352C2×#41—216no—
353C2×#41—28no—
354C2×#41#41116yes—
355C22×Q8—216no—
356C22×Q8—216no—
357C22×Q8—28no—
358C22×Q8—216no—
359C22×Q8—28no—
360C22×Q8—84no—
361C22×Q8C2×D418yes—
362C22×Q8C2414yes—
363C22×Q8C2414yes—
364C22×Q8C2412yes—
365C22×Q8C2418yes—
366C22×D4—24no—
367C22×D4—28no—
368C22×D4—28no—
369C22×D4—84no—
370C22×D4C2414yes—
371C22×D4C2414yes—
372C22×D4C2414yes—
373C22×D4C2412yes—
374C22×D4C2418yes—
375C22×D4C24116yes—
376C22×D4C2418yes—
377C23×C4—24no—
378C23×C4—28no—
379C23×C4—28no—
380C23×C4—84no—
381C23×C4C2411yescharacteristic
382C23×C4C2418yes—
383C23×C4C2414yes—
384C23×C4C2412yes—
385C23×C4C2414yes—
386C23×C4C2411yescharacteristic
387C23×C4C2411yescharacteristic
388C23×C4C2412yes—
389C23×C4C2414yes—
390C23×C4C2418yes—
391C23×C4C2418yes—
392C23×C4C2414yes—
393C23×C4C2411yescharacteristic
394C23×C4C2411yescharacteristic
395C23×C4C2412yes—
396C23×C4C2411yescharacteristic
397C4⋊Q8—232no—
398#127—216no—
399#126—232no—
400#126—232no—
401#124—232no—
402#124—216no—
403#124—232no—
404#124—232no—
405#123—216no—
406#123—264no—
407C22⋊Q8—232no—
408C22⋊Q8—216no—
409C22⋊Q8—264no—
410C22⋊Q8—816no—
411#121—216no—
412#121—232no—
413#121—232no—
414#121—816no—
415#120—216no—
416#120—232no—
417C4×Q8—216no—
418C4×Q8—216no—
419C4×Q8—216no—
420C4×Q8—232no—
421C4×Q8—28no—
422C4×Q8—216no—
423C4×Q8—28no—
424C4×Q8—216no—
425C4×Q8C2×D4132yes—
426C4×Q8C2×D4132yes—
427C4×D4—216no—
428C4×D4—216no—
429C4×D4—232no—
430C4×D4—232no—
431C4×D4—216no—
432C4×D4—232no—
433C4×D4—216no—
434C4×D4—216no—
435C4×D4—28no—
436C4×D4—216no—
437C4×D4—28no—
438C4×D4—216no—
439C4×D4—816no—
440#117—216no—
441#117—28no—
442#117—28no—
443#117—28no—
444#117—216no—
445#117—232no—
446#117—216no—
447#117—216no—
448#117—216no—
449#117—232no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—28no—
454C2×C4⋊C4—28no—
455C2×C4⋊C4—216no—
456C2×C4⋊C4—232no—
457C2×C4⋊C4C2×D418yes—
458C2×C4⋊C4C2×D4116yes—
459C2×C4⋊C4C2412yes—
460C2×C4⋊C4C2414yes—
461C2×C4⋊C4C2418yes—
462C2×C4⋊C4C2414yes—
463C2×C4⋊C4C2414yes—
464C2×C4⋊C4C2412yes—
465C2×C4⋊C4C2412yes—
466C2×C4⋊C4C2414yes—
467C2×C4⋊C4C2418yes—
468C2×C4⋊C4C2418yes—
469C2×C4⋊C4C2412yes—
470C2×C4⋊C4C2414yes—
471C2×C4⋊C4C2414yes—
472C2×C4⋊C4C2414yes—
473C2×C4⋊C4C2414yes—
474C2×C4⋊C4C2418yes—
475C2×C4⋊C4C24116yes—
476C2×C4⋊C4C24116yes—
477C2×C4⋊C4C2418yes—
478C2×C4⋊C4C2418yes—
479C2×C4⋊C4C2414yes—
480C2×C4⋊C4C2418yes—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—28no—
484C2×C22⋊C4—28no—
485C2×C22⋊C4—28no—
486C2×C22⋊C4—28no—
487C2×C22⋊C4—28no—
488C2×C22⋊C4C2414yes—
489C2×C22⋊C4C2412yes—
490C2×C22⋊C4C2412yes—
491C2×C22⋊C4C2414yes—
492C2×C22⋊C4C2414yes—
493C2×C22⋊C4C2418yes—
494C2×C22⋊C4C2418yes—
495C2×C22⋊C4C2418yes—
496C2×C22⋊C4C2418yes—
497C2×C22⋊C4C2414yes—
498C2×C22⋊C4C2414yes—
499C2×C22⋊C4C2414yes—
500C2×C22⋊C4C2418yes—
501C2×C22⋊C4C2414yes—
502C2×C22⋊C4C2414yes—
503C2×C22⋊C4C2418yes—
504C2×C22⋊C4C2418yes—
505C2×C22⋊C4C24116yes—
506C2×C22⋊C4C24116yes—
507C2×C22⋊C4C24116yes—
508C2×C22⋊C4C2418yes—
509C2×C22⋊C4C2418yes—
510C2×C22⋊C4C2418yes—
511C2×C22⋊C4C24116yes—
512C2×C22⋊C4C2418yes—
513C2×C42—24no—
514C2×C42—216no—
515C2×C42—232no—
516C2×C42C2×D418yes—
517C2×C42C2×D4116yes—
518C2×C42C2414yes—
519C2×C42C2414yes—
520C2×C42C2418yes—
521C2×C42C2418yes—
522C2×C42C2414yes—
523C2×C42C2414yes—
524C2×C42C2414yes—
525C2×C42C2414yes—
526C2×C42C2418yes—
527C2×C42C2418yes—
528C2×C42C2412yes—
529C2×C42C2412yes—
530C2×C42C2414yes—
531C2×C42C2414yes—
532#95C2418yes—
533#95C2418yes—
534#95C24116yes—
535#95C2418yes—
536#95C2418yes—
537#95C2418yes—
538#95C2418yes—
539#95C24116yes—
540#95C24116yes—
541#95C2418yes—
542#95C2418yes—
543#95C2418yes—
544#95C2418yes—
545#95C2418yes—
546#95C2418yes—
547C24—24no—
548C24—22no—
549C24—24no—
550C24—28no—
551C24—44no—
552C24—42no—
553C24—42no—
554C24—44no—
555C24C2512yes—
556C24C2514yes—
557C24C2514yes—
558C24C2511yescharacteristic
559#41—2128no—
560#41—2128no—
561#41—264no—
562C2×Q8—2128no—
563C2×Q8—232no—
564C2×Q8—28no—
565C2×Q8—24no—
566C2×Q8—216no—
567C2×Q8—216no—
568C2×Q8—28no—
569C2×Q8—28no—
570C2×Q8—24no—
571C2×Q8—416no—
572C2×Q8—816no—
573C2×Q8C22×D4116yes—
574C2×Q8C2×#4118yes—
575C2×D4—28no—
576C2×D4—216no—
577C2×D4—28no—
578C2×D4—216no—
579C2×D4—232no—
580C2×D4—28no—
581C2×D4—24no—
582C2×D4—28no—
583C2×D4—216no—
584C2×D4—24no—
585C2×D4—28no—
586C2×D4—28no—
587C2×D4—416no—
588C2×D4—48no—
589C2×D4—416no—
590C2×D4—48no—
591C2×D4—416no—
592C2×D4—416no—
593C2×D4—816no—
594C2×D4C2×#41116yes—
595C2×D4C2×#4118yes—
596C22×C4—216no—
597C22×C4—28no—
598C22×C4—216no—
599C22×C4—28no—
600C22×C4—216no—
601C22×C4—28no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—24no—
606C22×C4—24no—
607C22×C4—28no—
608C22×C4—28no—
609C22×C4—28no—
610C22×C4—28no—
611C22×C4—28no—
612C22×C4—216no—
613C22×C4—216no—
614C22×C4—42no—
615C22×C4—44no—
616C22×C4—42no—
617C22×C4—48no—
618C22×C4—42no—
619C22×C4—44no—
620C22×C4—42no—
621C22×C4—48no—
622C22×C4—416no—
623C22×C4—416no—
624C22×C4—416no—
625C22×C4—816no—
626C22×C4C22×D418yes—
627C22×C4C22×D414yes—
628C22×C4C22×D414yes—
629C22×C4C22×D418yes—
630C22×C4C22×D414yes—
631C22×C4C2×#41116yes—
632C22×C4C2×#4118yes—
633C22×C4C2518yes—
634C22×C4C2518yes—
635C22×C4C2514yes—
636C22×C4C2512yes—
637C22×C4C2512yes—
638C22×C4C2512yes—
639C22×C4C2514yes—
640C22×C4C2514yes—
641C22×C4C2511yescharacteristic
642C22×C4C2514yes—
643C22×C4C2512yes—
644C22×C4C2514yes—
645C22×C4C2511yescharacteristic
646C22×C4C2514yes—
647C22×C4C2512yes—
648C4⋊C4—28no—
649C4⋊C4—216no—
650C4⋊C4—28no—
651C4⋊C4—24no—
652C4⋊C4—28no—
653C4⋊C4—24no—
654C4⋊C4—24no—
655C4⋊C4—28no—
656C4⋊C4—216no—
657C4⋊C4—216no—
658C4⋊C4—28no—
659C4⋊C4—28no—
660C4⋊C4—24no—
661C4⋊C4—28no—
662C4⋊C4—28no—
663C4⋊C4—216no—
664C4⋊C4—48no—
665C4⋊C4—416no—
666C4⋊C4—416no—
667C4⋊C4—48no—
668C4⋊C4C22×D4116yes—
669C4⋊C4C22×D4132yes—
670C22⋊C4—28no—
671C22⋊C4—28no—
672C22⋊C4—28no—
673C22⋊C4—216no—
674C22⋊C4—28no—
675C22⋊C4—24no—
676C22⋊C4—24no—
677C22⋊C4—28no—
678C22⋊C4—28no—
679C22⋊C4—216no—
680C22⋊C4—216no—
681C22⋊C4—216no—
682C22⋊C4—216no—
683C22⋊C4—28no—
684C22⋊C4—216no—
685C22⋊C4—28no—
686C22⋊C4—216no—
687C22⋊C4—232no—
688C22⋊C4—416no—
689C22⋊C4—48no—
690C22⋊C4—48no—
691C22⋊C4—416no—
692C22⋊C4—416no—
693C22⋊C4—48no—
694C22⋊C4—48no—
695C42—28no—
696C42—28no—
697C42—216no—
698C42—216no—
699C42—28no—
700C42—28no—
701C42—28no—
702C42—28no—
703C42—48no—
704C42—48no—
705C42C22×D418yes—
706C42C22×D4116yes—
707C42C22×D418yes—
708C42C22×D4116yes—
709C23—22no—
710C23—22no—
711C23—24no—
712C23—24no—
713C23—28no—
714C23—28no—
715C23—24no—
716C23—22no—
717C23—24no—
718C23—28no—
719C23—28no—
720C23—24no—
721C23—22no—
722C23—28no—
723C23—22no—
724C23—48no—
725C23—44no—
726C23—44no—
727C23—48no—
728C23—44no—
729C23—48no—
730C23—88no—
731C23—816no—
732C23C23×D412yes—
733C23C22×#4118yes—
734C23C22×#4114yes—
735C23C2611yescharacteristic
736Q8—232no—
737Q8—232no—
738Q8—216no—
739Q8—816no—
740D4—232no—
741D4—232no—
742D4—216no—
743D4—416no—
744D4—816no—
745D4—816no—
746D4—832no—
747C2×C4—264no—
748C2×C4—24no—
749C2×C4—28no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—28no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—216no—
756C2×C4—232no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—28no—
764C2×C4—28no—
765C2×C4—24no—
766C2×C4—28no—
767C2×C4—28no—
768C2×C4—28no—
769C2×C4—28no—
770C2×C4—24no—
771C2×C4—28no—
772C2×C4—28no—
773C2×C4—28no—
774C2×C4—24no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—48no—
778C2×C4—416no—
779C2×C4—44no—
780C2×C4—48no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—416no—
784C2×C4—88no—
785C2×C4—816no—
786C2×C4—816no—
787C2×C4#525116yes—
788C2×C4C23×D412yes—
789C2×C4C23×D418yes—
790C2×C4C23×D414yes—
791C2×C4C23×D418yes—
792C2×C4C23×D412yes—
793C2×C4C23×D414yes—
794C2×C4C22×#4118yes—
795C2×C4C22×#4114yes—
796C2×C4C22×#4114yes—
797C22—22no—
798C22—22no—
799C22—28no—
800C22—216no—
801C22—28no—
802C22—44no—
803C22—44no—
804C22—48no—
805C22—42no—
806C22—44no—
807C22—44no—
808C22—42no—
809C22—44no—
810C22—416no—
811C22—44no—
812C22—42no—
813C22—44no—
814C22—816no—
815C22—88no—
816C22C2×#52514yes—
817C22C24×D411yescharacteristic
818C22C23×#4112yes—
819C22H(7,𝔽2)12yes—
820C222−1+612yes—
821C4—22no—
822C4—22no—
823C4—24no—
824C4—28no—
825C4—28no—
826C4—28no—
827C4—44no—
828C4—42no—
829C4—44no—
830C4—42no—
831C4—44no—
832C4—48no—
833C4—48no—
834C4—42no—
835C4C2×#52518yes—
836C2—24no—
837C2—48no—
838C2—84no—
839C2—82no—
840C2C22×#52511yescharacteristic
841C2#6284811yescharacteristic
842C2#6285211yescharacteristic
843C2#6285714yes—
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. C22×#542C2semidirect
2. C2×C4×2−1+4C2semidirect
3. #35679C2semidirect
4. #35676C2semidirect
5. #35675C2semidirect
6. #35672C2semidirect
7. #35659C2semidirect
8. #35574C2semidirect
9. #35563C2semidirect
10. #35539C2semidirect
11. #35357C2semidirect
12. #35356C2semidirect
13. #35243C2semidirect
14. #35195C2semidirect
15. #35143C2semidirect
16. #35129C2semidirect
17. C4×#535C2semidirect
18. #34065C2semidirect
19. #34059C2semidirect
37. C2×#520C22semidirect
39. C2×#519C22semidirect
42. C2×C4×#41C22semidirect
44. C22×C4×Q8C22semidirect
47. #2852C22semidirect
48. #2850C22semidirect
49. #2637C22semidirect
50. #2636C22semidirect
51. #2632C22semidirect
52. #2631C22semidirect
53. #2610C22semidirect
54. #2604C22semidirect
55. #2603C22semidirect
56. #2601C22semidirect
57. #2592C22semidirect
59. #2540C22semidirect
65. #2477C22semidirect
66. #2471C22semidirect
67. #2465C22semidirect
68. #2463C22semidirect
69. #2458C22semidirect
70. #2456C22semidirect
71. #2452C22semidirect
72. #2451C22semidirect
73. #2449C22semidirect
74. #2448C22semidirect
75. #2448C22semidirect
76. #2443C22semidirect
77. #2440C22semidirect
78. #2439C22semidirect
79. #2436C22semidirect
80. #2431C22semidirect
83. #2423C22semidirect
84. #2421C22semidirect
88. #2409C22semidirect
90. #2407C22semidirect
95. #2328C22semidirect
96. #2326C22semidirect
97. #2324C22semidirect
98. #2324C22semidirect
99. #2324C22semidirect
100. #2323C22semidirect
101. #2323C22semidirect
107. #2320C22semidirect
115. C4×#127C22semidirect
116. C4×#124C22semidirect
117. C4×#121C22semidirect
121. #2295C22semidirect
122. #2293C22semidirect
123. #2290C22semidirect
180. C2×C4×Q8D4semidirect

Maximal subgroups

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

subgroupindex
C22×#5422
C2×C4×2−1+42
#356792
#356762
#356752
#356722
#356592
#355742
#355632
#355392
#353572
#353562
#352432
#351952
#351432
#351292
C4×#5352
#340652
#340592