Finite Group Databasebeta

← #7674628

Subgroups — #7674628

Order 512.

10714 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3499C211yesmaximal, characteristic, complemented
2C2×#3489C212yesmaximal, complemented
3C2×#3449C211yesmaximal, characteristic, complemented
4#44447C218yesmaximal, complemented
5#43492C218yesmaximal, complemented
6#39360C214yesmaximal, complemented
7#39357C214yesmaximal, complemented
8#37682C214yesmaximal, complemented
9#37675C214yesmaximal, complemented
10#37656C218yesmaximal, complemented
11#37651C218yesmaximal, complemented
12#35660C212yesmaximal, complemented
13#35621C212yesmaximal, complemented
14#35328C211yesmaximal, characteristic, complemented
15#35317C211yesmaximal, characteristic, complemented
16#35305C212yesmaximal, complemented
17C2×#2621C211yesmaximal, characteristic, complemented
18#34208C211yesmaximal, characteristic, complemented
19#34065C211yesmaximal, characteristic, complemented
20C22×2−1+4C2212yescomplemented
21C23×#41C2212yes—
22#3499—216no—
23#3489—232no—
24C2×D4×Q8C2214yescomplemented
25C2×D4×Q8C2214yescomplemented
26C2×#548C2214yes—
27C2×#547C2214yes—
28C2×#547C2214yescomplemented
29C2×#547C2218yescomplemented
30C2×#547C2218yescomplemented
31C2×#546C2218yes—
32C2×#546C2214yescomplemented
33#3449—216no—
34C2×#537C2214yes—
35C2×#537C2214yes—
36C2×#537C2212yescomplemented
37C2×#536C2214yes—
38C2×#536C2212yes—
39C2×#536C2212yes—
40C2×#536C2212yescomplemented
41C2×#536C2212yescomplemented
42C2×#536C2214yescomplemented
43C2×#536C2212yescomplemented
44C2×#535C2212yes—
45C2×#535C2212yes—
46C2×#534C2214yes—
47C2×#532C2211yescharacteristic
48C2×#532C2212yes—
49C2×#532C2211yescharacteristic
50C2×#532C2212yescomplemented
51C22×C4⋊Q8C2212yescomplemented
52C22×C4⋊Q8C2211yescharacteristic, complemented
53C2×#525C2218yes—
54C2×#525C2211yescharacteristic
55C2×#525C2214yescomplemented
56C22×C22⋊Q8C2212yes—
57C22×C22⋊Q8C2214yescomplemented
58C2×#520C2212yescomplemented
59C2×C4×#41C2211yescharacteristic, complemented
60C22×#117C2211yescharacteristic
61#2868C2212yescomplemented
62#2858C2212yescomplemented
63#2850C2214yescomplemented
64#2848C2218yescomplemented
65#2681C22116yescomplemented
66#2680C22116yescomplemented
67#2680C22116yescomplemented
68#2678C22116yescomplemented
69#2677C22116yescomplemented
70#2674C22116yescomplemented
71#2671C22116yescomplemented
72#2668C22116yescomplemented
73#2658C2214yescomplemented
74#2621C2212yescomplemented
75#2621C2218yescomplemented
76#2621C2214yescomplemented
77#2621C2214yescomplemented
78#2619C2212yescomplemented
79#2616C2218yes—
80#2547C2214yescomplemented
81#2546C2214yescomplemented
82#2545C2214yescomplemented
83#2544C2214yescomplemented
84#2543C2218yescomplemented
85#2542C2218yescomplemented
86#2536C2214yescomplemented
87#2535C2214yescomplemented
88#2501C2218yescomplemented
89#2472C22116yescomplemented
90#2464C22116yescomplemented
91#2449C22116yescomplemented
92#2443C22116yescomplemented
93#2443C22116yescomplemented
94#2440C22116yescomplemented
95#2436C2214yescomplemented
96#2435C2214yescomplemented
97#2434C2214yescomplemented
98#2434C2214yescomplemented
99#2432C2214yes—
100#2432C2214yes—
101#2432C2214yescomplemented
102#2431C2214yescomplemented
103#2430C22116yescomplemented
104#2425C22116yescomplemented
105#2422C22116yescomplemented
106#2418C22116yescomplemented
107#2417C2218yescomplemented
108#2415C2218yescomplemented
109#2409C2218yescomplemented
110#2407C2218yescomplemented
111#2406C2218yescomplemented
112#2405C2218yes—
113C2×#398C2214yescomplemented
114C2×#397C2214yes—
115#2364C2218yescomplemented
116#2352C2218yescomplemented
117#2328C2212yescomplemented
118#2327C2212yescomplemented
119#2324C2214yescomplemented
120#2323C2214yescomplemented
121#2322C2214yescomplemented
122#2321C2214yes—
123#2311C2212yescomplemented
124#2311C2212yescomplemented
125C4×#124C2214yescomplemented
126#2297C2211yescharacteristic, complemented
127#2296C2211yescharacteristic, complemented
128C2×#391C2212yescomplemented
129#2293C2214yescomplemented
130#2290C2214yescomplemented
131C2×#382C2211yescharacteristic, complemented
132#2280C2211yescharacteristic
133C4×#117C2211yescharacteristic, complemented
134C2×2−1+4—216no—
135C2×2−1+4—216no—
136C2×2−1+4—48no—
137C22×#41—216no—
138C22×#41—216no—
139C22×#41—48no—
140C22×#41C2312yes—
141C22×#41C2314yes—
142C22×#41C2314yes—
143C22×#41C2312yes—
144C22×#41C2312yes—
145C22×#41C2314yes—
146C22×#41C2314yes—
147C22×#41C2318yes—
148C22×#41C2312yes—
149C22×#41C2311yescharacteristic
150C23×Q8C2312yes—
151C23×Q8C2312yes—
152C23×Q8C2314yes—
153C23×Q8C2314yes—
154C23×D4C2314yes—
155C23×D4C2312yes—
156C24×C4C2314yes—
157C24×C4C2311yescharacteristic
158D4×Q8—232no—
159D4×Q8—232no—
160#548—232no—
161#547—264no—
162#547—264no—
163#547—232no—
164#547—232no—
165#546—264no—
166#546—232no—
167#537—216no—
168#537—232no—
169#537—232no—
170#536—216no—
171#536—216no—
172#536—216no—
173#536—232no—
174#536—232no—
175#536—216no—
176#536—48no—
177#535—216no—
178#535—216no—
179#534—232no—
180#532—216no—
181#532—216no—
182#532—28no—
183#532D4116yescomplemented
184C2×C4⋊Q8—216no—
185C2×C4⋊Q8—28no—
186C2×C4⋊Q8C2312yes—
187C2×C4⋊Q8C2311yescharacteristic
188C2×C4⋊Q8C2314yes—
189C2×C4⋊Q8C2312yes—
190C2×C4⋊Q8C2314yes—
191C2×C4⋊Q8C2318yes—
192C2×C4⋊Q8C2314yes—
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2318yes—
195C2×C4⋊Q8C2314yes—
196C2×C4⋊Q8C2311yescharacteristic
197C2×#127C2311yescharacteristic
198C2×#127C2312yes—
199C2×#127C2311yescharacteristic
200C2×#124C2312yes—
201C2×#124C2314yes—
202C2×#124C2318yes—
203C2×#124C2312yes—
204C2×#124C2312yes—
205C2×#124C2314yes—
206C2×#124C2314yes—
207C2×#124C2312yes—
208#525—232no—
209#525—264no—
210#525D4116yescomplemented
211C2×#123C2318yes—
212C2×#123C2318yes—
213C2×#123C2318yes—
214C2×#123C2318yes—
215C2×#123C2318yes—
216C2×#123C23116yes—
217C2×#123C2318yes—
218C2×#123C2318yes—
219C2×#123C2318yes—
220C2×#123C2312yes—
221C2×C22⋊Q8—216no—
222C2×C22⋊Q8—232no—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2318yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2318yes—
232C2×C22⋊Q8C2318yes—
233C2×C22⋊Q8C2318yes—
234C2×C22⋊Q8C2318yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C23116yes—
237C2×C22⋊Q8C2318yes—
238C2×C22⋊Q8C2318yes—
239C2×C22⋊Q8C2312yes—
240C2×#121C2314yes—
241C2×#121C2314yes—
242C2×#121C2318yes—
243C2×#121C2318yes—
244C2×#121C2318yes—
245C2×#121C2318yes—
246C2×#121C2318yes—
247C2×#121C2318yes—
248C2×#121C2314yes—
249C2×#121C2318yes—
250C2×#121C2318yes—
251C2×#121C2312yes—
252C2×#121C2314yes—
253C2×#120C2318yes—
254C2×#120C2318yes—
255C2×#120C2318yes—
256C2×#120C2312yes—
257#520—216no—
258C4×#41—28no—
259C2×C4×Q8C2312yes—
260C2×C4×Q8C2314yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2312yes—
263C2×C4×D4C2314yes—
264C2×C4×D4C2318yes—
265C2×C4×D4C2318yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2318yes—
268C2×C4×D4C2318yes—
269C2×C4×D4C2318yes—
270C2×C4×D4C2314yes—
271C2×C4×D4C2314yes—
272C2×#117—28no—
273C2×#117C2311yescharacteristic
274C2×#117C2311yescharacteristic
275C2×#117C2314yes—
276C2×#117C2314yes—
277C2×#117C2312yes—
278C2×#117C2312yes—
279C2×#117C2312yes—
280C2×#117C2311yescharacteristic
281C22×C4⋊C4C2312yes—
282C22×C4⋊C4C2312yes—
283C22×C4⋊C4C2314yes—
284C22×C4⋊C4C2314yes—
285C22×C4⋊C4C2314yes—
286C22×C4⋊C4C2318yes—
287C22×C4⋊C4C2318yes—
288C22×C22⋊C4C2312yes—
289C22×C22⋊C4C2314yes—
290C22×C22⋊C4C2318yes—
291C22×C42C2312yes—
292C22×C42C2311yescharacteristic
293C22×C42C2311yescharacteristic
294#399C23116yes—
295#399C23116yes—
296#398C23116yes—
297#398C23116yes—
298#398C2318yes—
299#398C23116yes—
300#397C23116yes—
301#397C23116yes—
302#397C2318yes—
303#397C23116yes—
304#396C23116yes—
305#395C23116yes—
306#395C23116yes—
307#394C23116yes—
308#394C23116yes—
309#394C23116yes—
310#394C2318yes—
311#394C23116yes—
312#394C23116yes—
313#393C23116yes—
314#392C2318yes—
315#392C23116yes—
316#391C2314yes—
317#391C2314yes—
318#391C2312yes—
319#391C2318yes—
320#391C2314yes—
321#391C2314yes—
322#390C2314yes—
323#390C2314yes—
324#390C2318yes—
325#390C2312yes—
326#390C23116yes—
327#389C2318yes—
328#389C2314yes—
329#389C23116yes—
330#388C2318yes—
331#388C2318yes—
332#388C2318yes—
333#388C23116yes—
334#388C23116yes—
335#388C23116yes—
336#387C2318yes—
337#387C23116yes—
338#386C2318yes—
339#386C2318yes—
340#386C2314yes—
341#386C2318yes—
342#386C23116yes—
343#386C23116yes—
344#386C23116yes—
345#386C23116yes—
346#386C23116yes—
347#385C2314yes—
348#385C2318yes—
349#385C23116yes—
350#385C23116yes—
351#385C23116yes—
352#385C23116yes—
353#385C23116yes—
354#384C23116yes—
355#382C2312yes—
356#382C2314yes—
357#382C2312yes—
358#381C2312yes—
359#380C2318yes—
360#380C2318yes—
361#380C2314yes—
362#380C23116yes—
363#379C2312yes—
364#379C23116yes—
365C4×C4⋊C4C2314yes—
366C4×C4⋊C4C2314yes—
367C4×C22⋊C4C2314yes—
368C4×C22⋊C4C23116yes—
369C4×C22⋊C4C2314yes—
370C4×C22⋊C4C2314yes—
371#376C2312yes—
372C2×#95C2314yes—
373C2×#95C2318yes—
374C43C2312yes—
375C25C2414yes—
376C25C2411yescharacteristic
3772−1+4—4128no—
378C2×#41—28no—
379C2×#41—216no—
380C2×#41—216no—
381C2×#41—28no—
382C2×#41—216no—
383C2×#41—232no—
384C2×#41—232no—
385C2×#41—24no—
386C2×#41—28no—
387C2×#41—216no—
388C2×#41—28no—
389C2×#41—216no—
390C2×#41—28no—
391C2×#41—216no—
392C2×#41—28no—
393C2×#41—216no—
394C2×#41—216no—
395C2×#41—28no—
396C2×#41—28no—
397C2×#41—24no—
398C2×#41—28no—
399C2×#41—48no—
400C2×#41—48no—
401C2×#41—416no—
402C2×#41—44no—
403C2×#41—44no—
404C2×#41—48no—
405C2×#41—48no—
406C2×#41—4128no—
407C2×#41C2×D418yes—
408C2×#41C2×D4116yes—
409C22×Q8—216no—
410C22×Q8—216no—
411C22×Q8—28no—
412C22×Q8—28no—
413C22×Q8—28no—
414C22×Q8—216no—
415C22×Q8—28no—
416C22×Q8—216no—
417C22×Q8—28no—
418C22×Q8—44no—
419C22×Q8—48no—
420C22×Q8—48no—
421C22×Q8C2414yes—
422C22×Q8C2414yes—
423C22×Q8C2412yes—
424C22×Q8C2414yes—
425C22×Q8C2418yes—
426C22×Q8C2411yescharacteristic
427C22×Q8C2412yes—
428C22×D4—216no—
429C22×D4—216no—
430C22×D4—28no—
431C22×D4—28no—
432C22×D4—44no—
433C22×D4—48no—
434C22×D4C2414yes—
435C22×D4C2412yes—
436C22×D4C2414yes—
437C22×D4C2414yes—
438C22×D4C2418yes—
439C22×D4C2414yes—
440C22×D4C2412yes—
441C22×D4C2411yescharacteristic
442C22×D4C2414yes—
443C22×D4C2412yes—
444C22×D4C2418yes—
445C22×D4C2414yes—
446C22×D4C2418yes—
447C22×D4C2414yes—
448C22×D4C2414yes—
449C23×C4—24no—
450C23×C4—24no—
451C23×C4—216no—
452C23×C4—216no—
453C23×C4—48no—
454C23×C4C2×D418yes—
455C23×C4C2414yes—
456C23×C4C2414yes—
457C23×C4C2418yes—
458C23×C4C2418yes—
459C23×C4C2414yes—
460C23×C4C2414yes—
461C23×C4C2414yes—
462C23×C4C2411yescharacteristic
463C23×C4C2414yes—
464C23×C4C2412yes—
465C23×C4C2412yes—
466C23×C4C2412yes—
467C23×C4C2414yes—
468C23×C4C2418yes—
469C23×C4C2412yes—
470C23×C4C2414yes—
471C23×C4C2412yes—
472C23×C4C2411yescharacteristic
473C4⋊Q8—216no—
474C4⋊Q8—28no—
475C4⋊Q8—232no—
476C4⋊Q8—232no—
477C4⋊Q8—28no—
478C4⋊Q8—28no—
479C4⋊Q8—216no—
480C4⋊Q8—24no—
481C4⋊Q8—216no—
482C4⋊Q8—48no—
483C4⋊Q8C2×D418yes—
484#127—28no—
485#127—24no—
486#127C2×D418yes—
487#124—28no—
488#124—28no—
489#124—216no—
490#124—232no—
491#124—28no—
492#124—216no—
493#124—48no—
494#124C2×D4116yes—
495#123—232no—
496#123—232no—
497#123—232no—
498#123—232no—
499#123—232no—
500#123—232no—
501#123—232no—
502#123—264no—
503#123—416no—
504#123C2×D4116yes—
505C22⋊Q8—216no—
506C22⋊Q8—216no—
507C22⋊Q8—216no—
508C22⋊Q8—216no—
509C22⋊Q8—216no—
510C22⋊Q8—232no—
511C22⋊Q8—216no—
512C22⋊Q8—216no—
513C22⋊Q8—232no—
514C22⋊Q8—216no—
515C22⋊Q8—232no—
516C22⋊Q8—232no—
517C22⋊Q8—232no—
518C22⋊Q8—264no—
519C22⋊Q8—232no—
520C22⋊Q8—416no—
521C22⋊Q8C2×D4116yes—
522#121—232no—
523#121—216no—
524#121—232no—
525#121—232no—
526#121—232no—
527#121—232no—
528#121—232no—
529#121—216no—
530#121—216no—
531#121—232no—
532#121—232no—
533#121C2×D4116yes—
534#121C2×D4132yes—
535#120—232no—
536#120—232no—
537#120—232no—
538#120C2×D4116yes—
539C4×Q8—28no—
540C4×Q8—216no—
541C4×D4—232no—
542C4×D4—232no—
543C4×D4—216no—
544C4×D4—232no—
545C4×D4—232no—
546C4×D4—232no—
547C4×D4—28no—
548C4×D4—216no—
549C4×D4—216no—
550C4×D4C2×D4132yes—
551C4×D4C2×D4132yes—
552#117—24no—
553#117—24no—
554#117—216no—
555#117—216no—
556#117—28no—
557#117—28no—
558#117—28no—
559#117C2×D418yes—
560C2×C4⋊C4—28no—
561C2×C4⋊C4—28no—
562C2×C4⋊C4—216no—
563C2×C4⋊C4—216no—
564C2×C4⋊C4—216no—
565C2×C4⋊C4—232no—
566C2×C4⋊C4—232no—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2418yes—
569C2×C4⋊C4C2418yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2418yes—
574C2×C4⋊C4C2418yes—
575C2×C4⋊C4C2418yes—
576C2×C4⋊C4C2418yes—
577C2×C4⋊C4C2418yes—
578C2×C4⋊C4C24116yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2418yes—
584C2×C4⋊C4C2418yes—
585C2×C4⋊C4C24116yes—
586C2×C4⋊C4C2418yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2414yes—
590C2×C22⋊C4—216no—
591C2×C22⋊C4—28no—
592C2×C22⋊C4—232no—
593C2×C22⋊C4C2418yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2418yes—
598C2×C22⋊C4C2418yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2412yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2412yes—
603C2×C22⋊C4C2418yes—
604C2×C22⋊C4C2418yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C24116yes—
609C2×C22⋊C4C24116yes—
610C2×C22⋊C4C2418yes—
611C2×C22⋊C4C24116yes—
612C2×C22⋊C4C2418yes—
613C2×C22⋊C4C24116yes—
614C2×C22⋊C4C2414yes—
615C2×C22⋊C4C2412yes—
616C2×C22⋊C4C2414yes—
617C2×C22⋊C4C2418yes—
618C2×C42—24no—
619C2×C42—28no—
620C2×C42C2×D418yes—
621C2×C42C2412yes—
622C2×C42C2412yes—
623C2×C42C2412yes—
624C2×C42C2418yes—
625C2×C42C2412yes—
626C2×C42C2414yes—
627C2×C42C2418yes—
628C2×C42C2411yescharacteristic
629C2×C42C2412yes—
630C2×C42C2411yescharacteristic
631C2×C42C2412yes—
632#95C2418yes—
633#95C24116yes—
634#95C2418yes—
635#95C24116yes—
636#95C2418yes—
637#95C2418yes—
638#95C24116yes—
639#95C2418yes—
640#95C2418yes—
641#95C24116yes—
642C24—22no—
643C24—22no—
644C24—28no—
645C24—28no—
646C24—44no—
647C24—44no—
648C24—48no—
649C24—48no—
650C24C22×D414yes—
651C24C2514yes—
652C24C2512yes—
653C24C2514yes—
654C24C2512yes—
655C24C2511yescharacteristic
656#41—264no—
657#41—232no—
658#41—464no—
659#41—464no—
660#41—432no—
661#41—464no—
662#41—464no—
663#41—432no—
664#41—4128no—
665#41—432no—
666C2×Q8—22no—
667C2×Q8—24no—
668C2×Q8—28no—
669C2×Q8—28no—
670C2×Q8—216no—
671C2×Q8—28no—
672C2×Q8—216no—
673C2×Q8—28no—
674C2×Q8—28no—
675C2×Q8—24no—
676C2×Q8—24no—
677C2×Q8—28no—
678C2×Q8—22no—
679C2×Q8—24no—
680C2×Q8—28no—
681C2×Q8—28no—
682C2×Q8—24no—
683C2×Q8—48no—
684C2×Q8—44no—
685C2×Q8—432no—
686C2×Q8—464no—
687C2×Q8—464no—
688C2×Q8—432no—
689C2×Q8C22×D414yes—
690C2×Q8C22×D418yes—
691C2×D4—28no—
692C2×D4—24no—
693C2×D4—28no—
694C2×D4—24no—
695C2×D4—28no—
696C2×D4—216no—
697C2×D4—28no—
698C2×D4—28no—
699C2×D4—28no—
700C2×D4—28no—
701C2×D4—216no—
702C2×D4—28no—
703C2×D4—28no—
704C2×D4—216no—
705C2×D4—216no—
706C2×D4—24no—
707C2×D4—22no—
708C2×D4—28no—
709C2×D4—28no—
710C2×D4—24no—
711C2×D4—24no—
712C2×D4—28no—
713C2×D4—24no—
714C2×D4—22no—
715C2×D4—24no—
716C2×D4—432no—
717C2×D4—44no—
718C2×D4—44no—
719C2×D4—44no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—416no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—464no—
728C2×D4C22×D418yes—
729C2×D4C22×D414yes—
730C2×D4C22×D4116yes—
731C2×D4C22×D418yes—
732C2×D4C22×D4116yes—
733C2×D4C22×D4116yes—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—232no—
737C22×C4—24no—
738C22×C4—28no—
739C22×C4—24no—
740C22×C4—24no—
741C22×C4—24no—
742C22×C4—24no—
743C22×C4—28no—
744C22×C4—24no—
745C22×C4—28no—
746C22×C4—28no—
747C22×C4—216no—
748C22×C4—28no—
749C22×C4—216no—
750C22×C4—28no—
751C22×C4—28no—
752C22×C4—24no—
753C22×C4—28no—
754C22×C4—28no—
755C22×C4—216no—
756C22×C4—28no—
757C22×C4—216no—
758C22×C4—28no—
759C22×C4—28no—
760C22×C4—28no—
761C22×C4—28no—
762C22×C4—28no—
763C22×C4—28no—
764C22×C4—216no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4—48no—
770C22×C4—48no—
771C22×C4—48no—
772C22×C4—464no—
773C22×C4—416no—
774C22×C4—48no—
775C22×C4—44no—
776C22×C4C22×D414yes—
777C22×C4C22×D4116yes—
778C22×C4C22×D418yes—
779C22×C4C22×D418yes—
780C22×C4C22×D418yes—
781C22×C4C22×D418yes—
782C22×C4C22×D414yes—
783C22×C4C22×D414yes—
784C22×C4H(5,𝔽2)14yes—
785C22×C4C2514yes—
786C22×C4C2518yes—
787C22×C4C2514yes—
788C22×C4C2514yes—
789C22×C4C2518yes—
790C22×C4C2514yes—
791C22×C4C2512yes—
792C22×C4C2512yes—
793C22×C4C2514yes—
794C22×C4C2512yes—
795C22×C4C2514yes—
796C22×C4C2512yes—
797C22×C4C2511yescharacteristic
798C22×C4C2511yescharacteristic
799C4⋊C4—28no—
800C4⋊C4—216no—
801C4⋊C4—216no—
802C4⋊C4—28no—
803C4⋊C4—28no—
804C4⋊C4—216no—
805C4⋊C4—28no—
806C4⋊C4—216no—
807C4⋊C4—216no—
808C4⋊C4—216no—
809C4⋊C4—232no—
810C4⋊C4—216no—
811C4⋊C4—28no—
812C4⋊C4—24no—
813C4⋊C4—216no—
814C4⋊C4—28no—
815C4⋊C4—216no—
816C4⋊C4—24no—
817C4⋊C4—48no—
818C4⋊C4—416no—
819C4⋊C4C22×D418yes—
820C4⋊C4C22×D4116yes—
821C4⋊C4C22×D4116yes—
822C22⋊C4—216no—
823C22⋊C4—216no—
824C22⋊C4—24no—
825C22⋊C4—216no—
826C22⋊C4—216no—
827C22⋊C4—232no—
828C22⋊C4—24no—
829C22⋊C4—28no—
830C22⋊C4—28no—
831C22⋊C4—216no—
832C22⋊C4—216no—
833C22⋊C4—216no—
834C22⋊C4—28no—
835C22⋊C4—216no—
836C22⋊C4—216no—
837C22⋊C4—216no—
838C22⋊C4—48no—
839C22⋊C4—416no—
840C22⋊C4—48no—
841C22⋊C4—416no—
842C22⋊C4—416no—
843C22⋊C4C22×D4116yes—
844C22⋊C4C22×D418yes—
845C22⋊C4C22×D4116yes—
846C22⋊C4C22×D4132yes—
847C42—24no—
848C42—24no—
849C42—24no—
850C42—28no—
851C42—216no—
852C42—24no—
853C42—48no—
854C42C22×D414yes—
855C42C22×D414yes—
856C42C22×D418yes—
857C42C22×D418yes—
858C23—24no—
859C23—22no—
860C23—22no—
861C23—24no—
862C23—22no—
863C23—22no—
864C23—24no—
865C23—28no—
866C23—24no—
867C23—28no—
868C23—28no—
869C23—24no—
870C23—28no—
871C23—24no—
872C23—24no—
873C23—24no—
874C23—28no—
875C23—28no—
876C23—48no—
877C23—416no—
878C23—416no—
879C23—84no—
880C23—84no—
881C23—816no—
882C23—88no—
883C23—816no—
884C23C23×D414yes—
885C23C23×D418yes—
886C23C23×D414yes—
887C23C23×D412yes—
888C23C23×D412yes—
889C23C2×H(5,𝔽2)12yes—
890C23C2611yescharacteristic
891Q8—28no—
892Q8—216no—
893Q8—432no—
894Q8—416no—
895Q8—416no—
896Q8—416no—
897Q8—48no—
898D4—232no—
899D4—216no—
900D4—216no—
901D4—28no—
902D4—416no—
903D4—416no—
904D4—416no—
905D4—416no—
906D4—416no—
907D4—432no—
908D4—416no—
909D4—48no—
910D4—88no—
911D4—816no—
912D4—816no—
913C2×C4—24no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—24no—
918C2×C4—22no—
919C2×C4—24no—
920C2×C4—28no—
921C2×C4—24no—
922C2×C4—28no—
923C2×C4—216no—
924C2×C4—216no—
925C2×C4—232no—
926C2×C4—216no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—28no—
930C2×C4—24no—
931C2×C4—28no—
932C2×C4—24no—
933C2×C4—28no—
934C2×C4—24no—
935C2×C4—28no—
936C2×C4—24no—
937C2×C4—28no—
938C2×C4—28no—
939C2×C4—216no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—48no—
943C2×C4—416no—
944C2×C4—416no—
945C2×C4—416no—
946C2×C4—432no—
947C2×C4—432no—
948C2×C4—416no—
949C2×C4—416no—
950C2×C4—416no—
951C2×C4—816no—
952C2×C4—88no—
953C2×C4—84no—
954C2×C4D42116yes—
955C2×C4C23×D414yes—
956C2×C4C23×D418yes—
957C2×C4C23×D414yes—
958C2×C4C23×D414yes—
959C2×C4C23×D418yes—
960C2×C4C23×D414yes—
961C2×C4C23×D412yes—
962C2×C4C23×D412yes—
963C2×C4C23×D412yes—
964C2×C4C23×D412yes—
965C2×C4C2×H(5,𝔽2)12yes—
966C2×C4C2×H(5,𝔽2)12yes—
967C22—24no—
968C22—24no—
969C22—24no—
970C22—24no—
971C22—28no—
972C22—216no—
973C22—24no—
974C22—24no—
975C22—24no—
976C22—28no—
977C22—44no—
978C22—44no—
979C22—44no—
980C22—44no—
981C22—44no—
982C22—48no—
983C22—44no—
984C22—48no—
985C22—44no—
986C22—44no—
987C22—48no—
988C22—44no—
989C22—88no—
990C22—832no—
991C22C2×D4214yes—
992C22C24×D411yescharacteristic
993C22C24×D411yescharacteristic
994C22C22×H(5,𝔽2)11yescharacteristic
995C222−1+614yes—
996C4—24no—
997C4—24no—
998C4—28no—
999C4—24no—
1000C4—28no—
1001C4—24no—
1002C4—44no—
1003C4—48no—
1004C4—44no—
1005C4—44no—
1006C4—44no—
1007C4—48no—
1008C4C2×D4214yes—
1009C4C2×D4214yes—
1010C2—24no—
1011C2—44no—
1012C2—48no—
1013C2—44no—
1014C2—84no—
1015C2C22×D4211yescharacteristic
1016C2#6285912yes—
1017C2#6285912yes—
1018C2#6288812yes—
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×#3499C2semidirect
2. C2×#3489C2semidirect
3. C2×#3449C2semidirect
4. #44447C2semidirect
5. #43492C2semidirect
6. #39360C2semidirect
7. #39357C2semidirect
8. #37682C2semidirect
9. #37675C2semidirect
10. #37656C2semidirect
11. #37651C2semidirect
12. #35660C2semidirect
13. #35621C2semidirect
14. #35328C2semidirect
15. #35317C2semidirect
16. #35305C2semidirect
17. C2×#2621C2semidirect
18. #34208C2semidirect
19. #34065C2semidirect
20. C22×2−1+4C22semidirect
24. C2×D4×Q8C22semidirect
25. C2×D4×Q8C22semidirect
28. C2×#547C22semidirect
29. C2×#547C22semidirect
30. C2×#547C22semidirect
32. C2×#546C22semidirect
36. C2×#537C22semidirect
40. C2×#536C22semidirect
41. C2×#536C22semidirect
42. C2×#536C22semidirect
43. C2×#536C22semidirect
50. C2×#532C22semidirect
51. C22×C4⋊Q8C22semidirect
52. C22×C4⋊Q8C22semidirect
55. C2×#525C22semidirect
57. C22×C22⋊Q8C22semidirect
58. C2×#520C22semidirect
59. C2×C4×#41C22semidirect
61. #2868C22semidirect
62. #2858C22semidirect
63. #2850C22semidirect
64. #2848C22semidirect
65. #2681C22semidirect
66. #2680C22semidirect
67. #2680C22semidirect
68. #2678C22semidirect
69. #2677C22semidirect
70. #2674C22semidirect
71. #2671C22semidirect
72. #2668C22semidirect
73. #2658C22semidirect
74. #2621C22semidirect
75. #2621C22semidirect
76. #2621C22semidirect
77. #2621C22semidirect
78. #2619C22semidirect
80. #2547C22semidirect
81. #2546C22semidirect
82. #2545C22semidirect
83. #2544C22semidirect
84. #2543C22semidirect
85. #2542C22semidirect
86. #2536C22semidirect
87. #2535C22semidirect
88. #2501C22semidirect
89. #2472C22semidirect
90. #2464C22semidirect
91. #2449C22semidirect
92. #2443C22semidirect
93. #2443C22semidirect
94. #2440C22semidirect
95. #2436C22semidirect
96. #2435C22semidirect
97. #2434C22semidirect
98. #2434C22semidirect
101. #2432C22semidirect
102. #2431C22semidirect
103. #2430C22semidirect
104. #2425C22semidirect
105. #2422C22semidirect
106. #2418C22semidirect
107. #2417C22semidirect
108. #2415C22semidirect
109. #2409C22semidirect
110. #2407C22semidirect
111. #2406C22semidirect
113. C2×#398C22semidirect
115. #2364C22semidirect
116. #2352C22semidirect
117. #2328C22semidirect
118. #2327C22semidirect
119. #2324C22semidirect
120. #2323C22semidirect
121. #2322C22semidirect
123. #2311C22semidirect
124. #2311C22semidirect
125. C4×#124C22semidirect
126. #2297C22semidirect
127. #2296C22semidirect
128. C2×#391C22semidirect
129. #2293C22semidirect
130. #2290C22semidirect
131. C2×#382C22semidirect
133. C4×#117C22semidirect
183. #532D4semidirect
210. #525D4semidirect

Maximal subgroups

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

subgroupindex
C2×#34992
C2×#34892
C2×#34492
#444472
#434922
#393602
#393572
#376822
#376752
#376562
#376512
#356602
#356212
#353282
#353172
#353052
C2×#26212
#342082
#340652