Finite Group Databasebeta

← #7633202

Subgroups — #7633202

Order 512.

7196 conjugacy classes of subgroups.

The subgroup lattice has 1027 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3509C211yesmaximal, characteristic, complemented
2C2×#3480C211yesmaximal, characteristic
3#36560C212yesmaximal, complemented
4#36538C212yesmaximal, complemented
5#36419C212yesmaximal, complemented
6#36376C214yesmaximal, complemented
7#36188C212yesmaximal, complemented
8#36184C214yesmaximal, complemented
9#36045C218yesmaximal, complemented
10#35959C214yesmaximal, complemented
11#35938C214yesmaximal, complemented
12#35635C218yesmaximal, complemented
13#35621C214yesmaximal, complemented
14#35317C211yesmaximal, characteristic, complemented
15#35241C212yesmaximal, complemented
16#35201C212yesmaximal, complemented
17#35180C211yesmaximal, characteristic, complemented
18#34979C212yesmaximal, complemented
19#34953C211yesmaximal, characteristic, complemented
20#34947C212yesmaximal, complemented
21C2×#2568C211yesmaximal, characteristic, complemented
22#34268C214yesmaximal, complemented
23C4×#520C211yesmaximal, characteristic, complemented
24#3509—216no—
25#3480—216no—
26C2×#559C2212yes—
27C2×#559C2211yescharacteristic
28C2×#557C2212yes—
29C2×#557C2212yes—
30C2×#557C2211yescharacteristic
31C2×#556C2212yes—
32C2×#556C2212yes—
33C2×#556C2211yescharacteristic
34C2×#556C2212yes—
35C2×#553C2212yes—
36C2×#553C2214yes—
37C2×#552C2214yes—
38C2×#552C2214yes—
39C2×#550C2211yescharacteristic
40C2×#548C2212yes—
41C2×#541C2214yes—
42C2×#536C2212yes—
43C2×#536C2214yes—
44C2×#533C2211yescharacteristic
45C2×#533C2212yes—
46C2×#533C2212yes—
47C2×#532C2212yes—
48C2×#532C2211yescharacteristic
49C22×C4⋊Q8C2211yescharacteristic
50C2×#529C2214yes—
51C2×#529C2212yes—
52C2×#520C2212yes—
53C2×#519C2212yes—
54C2×C4×#41C2212yes—
55C2×C4×#41C2212yes—
56C2×C4×#41C2211yescharacteristic
57C22×C4×Q8C2211yescharacteristic
58#2868C2212yes—
59#2861C2214yes—
60#2859C2214yes—
61#2858C2212yes—
62#2857C2214yes—
63#2850C2214yes—
64#2850C2214yes—
65#2664C2218yes—
66#2663C2218yes—
67#2658C2214yes—
68#2639C2214yes—
69#2611C2218yes—
70#2604C2218yes—
71#2592C2214yes—
72#2584C2214yes—
73#2583C2214yes—
74#2568C2214yes—
75#2568C2212yes—
76#2568C2212yes—
77#2568C2212yes—
78#2568C2214yes—
79#2568C2212yes—
80#2568C2212yes—
81#2567C2211yescharacteristic
82#2567C2211yescharacteristic
83#2566C2214yes—
84#2565C2214yes—
85#2565C2214yes—
86#2564C2218yes—
87#2563C2212yes—
88#2562C2214yes—
89#2559C22116yes—
90#2558C22116yes—
91#2556C22116yes—
92#2553C22116yes—
93#2548C2212yes—
94#2547C2218yes—
95#2547C2212yes—
96#2546C2218yes—
97#2546C2211yescharacteristic
98#2546C2211yescharacteristic
99#2545C2214yes—
100#2545C2218yes—
101#2544C2218yes—
102#2542C2214yes—
103#2542C2212yes—
104#2542C2212yes—
105#2521C22116yes—
106#2519C22116yes—
107#2506C22116yes—
108#2502C2212yes—
109#2501C2214yes—
110#2501C2214yes—
111#2500C2214yes—
112#2499C2214yes—
113#2499C2214yes—
114#2498C2218yes—
115#2496C22116yes—
116#2434C2212yes—
117#2432C2214yes—
118#2425C22116yes—
119#2425C22116yes—
120#2417C2218yes—
121#2417C2218yes—
122#2415C2218yes—
123#2415C2218yes—
124#2399C2214yes—
125#2396C2218yes—
126#2395C2218yes—
127C2×#400C2214yes—
128#2367C2218yes—
129#2367C2218yes—
130#2365C2218yes—
131#2365C2218yes—
132#2359C22116yes—
133#2359C22116yes—
134#2323C2218yes—
135#2323C2218yes—
136#2311C2214yes—
137C4×C4⋊Q8C2214yes—
138C4×C4⋊Q8C2212yes—
139C4×C4⋊Q8C2212yes—
140C4×#124C2214yes—
141C4×C22⋊Q8C2218yes—
142C4×C22⋊Q8C2218yes—
143#2297C2214yes—
144#2296C2214yes—
145C2×#391C2212yes—
146C2×#391C2214yes—
147#2285C2214yes—
148C2×#382C2212yes—
149#2276C2212yes—
150#2275C2212yes—
151#2275C2214yes—
152#2274C2214yes—
153#2274C2212yes—
154C42×Q8C2212yes—
155C42×D4C2214yes—
156C42×D4C2212yes—
157C4×#117C2212yes—
158C4×#117C2211yescharacteristic
159C2×C4×C4⋊C4C2211yescharacteristic
160C2×C4×C4⋊C4C2212yes—
161C22×#41C2312yes—
162C22×#41C2312yes—
163C22×#41C2311yescharacteristic
164C23×Q8C2312yes—
165C23×Q8C2311yescharacteristic
166#559—28no—
167#559—216no—
168#557—28no—
169#557—216no—
170#557—216no—
171#556—216no—
172#556—28no—
173#556—216no—
174#556—216no—
175#553—216no—
176#553—232no—
177#552—232no—
178#552—232no—
179#550—28no—
180#548—216no—
181#541—232no—
182#536—216no—
183#536—232no—
184#533—28no—
185#533—216no—
186#533—216no—
187#532—216no—
188#532—28no—
189C2×C4⋊Q8—28no—
190C2×C4⋊Q8C2312yes—
191C2×C4⋊Q8C2311yescharacteristic
192C2×C4⋊Q8C2312yes—
193C2×C4⋊Q8C2311yescharacteristic
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2318yes—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2311yescharacteristic
200C2×C4⋊Q8C2314yes—
201C2×C4⋊Q8C2312yes—
202C2×#127C2311yescharacteristic
203C2×#127C2312yes—
204#529—232no—
205#529—216no—
206C2×#126C2314yes—
207C2×#126C2314yes—
208C2×#126C2314yes—
209C2×#126C2318yes—
210C2×#126C2318yes—
211C2×#125C2312yes—
212C2×#125C2312yes—
213C2×#125C2314yes—
214C2×#125C2314yes—
215C2×#125C2314yes—
216C2×#125C2318yes—
217C2×#125C2318yes—
218C2×#124C2312yes—
219C2×#124C2318yes—
220C2×#124C2312yes—
221C2×#124C2314yes—
222C2×#124C2312yes—
223C2×#124C2312yes—
224C2×#124C2314yes—
225C2×#124C2314yes—
226C2×#123C23116yes—
227C2×#123C2314yes—
228C2×#123C2314yes—
229C2×#123C2314yes—
230C2×#123C2318yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2318yes—
233C2×C22⋊Q8C2318yes—
234C2×C22⋊Q8C2312yes—
235C2×C22⋊Q8C2312yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2312yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2314yes—
241C2×#121C2312yes—
242C2×#121C2312yes—
243C2×#121C2312yes—
244C2×#121C2314yes—
245C2×#121C2314yes—
246C2×#121C2314yes—
247#520—216no—
248#519—216no—
249C4×#41—216no—
250C4×#41—216no—
251C4×#41D4116yes—
252C2×C4×Q8—28no—
253C2×C4×Q8C2312yes—
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2312yes—
257C2×C4×Q8C2314yes—
258C2×C4×Q8C2311yescharacteristic
259C2×C4×Q8C2311yescharacteristic
260C2×C4×Q8C2312yes—
261C2×C4×Q8C2312yes—
262C2×C4×Q8C2314yes—
263C2×C4×Q8C2314yes—
264C2×C4×Q8C2312yes—
265C2×C4×Q8C2314yes—
266C2×C4×Q8C2312yes—
267C2×C4×Q8C2312yes—
268C2×C4×Q8C2314yes—
269C2×C4×Q8C2314yes—
270C2×C4×Q8C2314yes—
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2311yescharacteristic
273C2×C4×D4C2312yes—
274C2×C4×D4C2312yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2312yes—
277C2×C4×D4C2314yes—
278C2×C4×D4C2314yes—
279C2×C4×D4C2312yes—
280C2×C4×D4C2312yes—
281C2×C4×D4C2314yes—
282C2×C4×D4C2318yes—
283C2×C4×D4C2314yes—
284C2×C4×D4C2314yes—
285C2×C4×D4C2312yes—
286C2×C4×D4C2311yescharacteristic
287C2×C4×D4C2312yes—
288C2×C4×D4C2311yescharacteristic
289C2×#117C2312yes—
290C2×#117C2314yes—
291C2×#117C2314yes—
292C2×#117C2318yes—
293C2×#117C2314yes—
294C2×#117C2312yes—
295C2×#117C2314yes—
296C2×#117C2314yes—
297C2×#117C2311yescharacteristic
298C2×#117C2312yes—
299C2×#117C2312yes—
300C22×C4⋊C4C2312yes—
301C22×C4⋊C4C2312yes—
302C22×C4⋊C4C2312yes—
303C22×C4⋊C4C2311yescharacteristic
304C22×C4⋊C4C2314yes—
305C22×C4⋊C4C2312yes—
306C22×C42C2312yes—
307C22×C42C2314yes—
308C22×C42C2312yes—
309C22×C42C2314yes—
310C22×C42C2311yescharacteristic
311C22×C42C2312yes—
312#400C2318yes—
313#400C2318yes—
314#400C2318yes—
315#400C2318yes—
316#400C2318yes—
317#399C2318yes—
318#399C2318yes—
319#399C23116yes—
320#398C23116yes—
321#398C23116yes—
322#398C2314yes—
323#398C2314yes—
324#398C2318yes—
325#397C2318yes—
326#397C23116yes—
327#397C23116yes—
328#396C23116yes—
329#396C23116yes—
330#395C2314yes—
331#395C2314yes—
332#395C2318yes—
333#394C2318yes—
334#394C23116yes—
335#394C23116yes—
336#393C2318yes—
337#391C2312yes—
338#391C2312yes—
339#391C2314yes—
340#391C2314yes—
341#391C2312yes—
342#391C2312yes—
343#391C2318yes—
344#391C2318yes—
345#391C2314yes—
346#391C2318yes—
347#391C2318yes—
348#391C2318yes—
349#391C2318yes—
350#390C2314yes—
351#390C2314yes—
352#390C2318yes—
353#390C2314yes—
354#390C2318yes—
355#389C2318yes—
356#389C2318yes—
357#389C23116yes—
358#389C2314yes—
359#389C2314yes—
360#389C2314yes—
361#389C23116yes—
362#389C23116yes—
363#389C2314yes—
364#389C23116yes—
365#388C23116yes—
366#388C23116yes—
367#388C23116yes—
368#388C23116yes—
369#388C23116yes—
370#388C23116yes—
371#388C23116yes—
372#387C23116yes—
373#387C23116yes—
374#387C23116yes—
375#387C23116yes—
376#386C23116yes—
377#386C23116yes—
378#386C23116yes—
379#385C23116yes—
380#385C2318yes—
381#385C2318yes—
382#385C23116yes—
383#384C2312yes—
384#384C2312yes—
385#384C2314yes—
386#384C2314yes—
387#384C2318yes—
388#382C2314yes—
389#382C2314yes—
390#382C2314yes—
391#382C2318yes—
392#380C2318yes—
393#380C2318yes—
394#380C23116yes—
395#380C23116yes—
396C4×C4⋊C4C2312yes—
397C4×C4⋊C4C23116yes—
398C4×C4⋊C4C2318yes—
399C4×C4⋊C4C2318yes—
400C4×C4⋊C4C2312yes—
401C4×C4⋊C4C2314yes—
402C4×C4⋊C4C2311yescharacteristic
403C4×C4⋊C4C2311yescharacteristic
404C4×C4⋊C4C2312yes—
405C4×C4⋊C4C2312yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2312yes—
409C4×C4⋊C4C23116yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2318yes—
414C4×C4⋊C4C2318yes—
415C4×C22⋊C4C2312yes—
416C4×C22⋊C4C2318yes—
417C4×C22⋊C4C23116yes—
418C4×C22⋊C4C23116yes—
419C4×C22⋊C4C2314yes—
420C4×C22⋊C4C2314yes—
421C4×C22⋊C4C2312yes—
422C4×C22⋊C4C2318yes—
423C4×C22⋊C4C2318yes—
424#376C2314yes—
425#376C2312yes—
426C2×#95C2314yes—
427C2×#95C2318yes—
428C2×#95C2318yes—
429C2×#95C2312yes—
430C43C2312yes—
431C43C2314yes—
432C2×#41—28no—
433C2×#41—28no—
434C2×#41—28no—
435C2×#41—28no—
436C2×#41—216no—
437C2×#41—44no—
438C2×#41C2×D418yes—
439C22×Q8—24no—
440C22×Q8—24no—
441C22×Q8—28no—
442C22×Q8—216no—
443C22×Q8—42no—
444C22×Q8C2412yes—
445C22×Q8C2414yes—
446C22×Q8C2411yescharacteristic
447C22×Q8C2414yes—
448C22×Q8C2412yes—
449C22×Q8C2412yes—
450C22×Q8C2411yescharacteristic
451C22×Q8C2411yescharacteristic
452C22×Q8C2412yes—
453C22×D4C2414yes—
454C22×D4C2412yes—
455C22×D4C2412yes—
456C22×D4C2414yes—
457C22×D4C2412yes—
458C22×D4C2411yescharacteristic
459C22×D4C2414yes—
460C22×D4C2412yes—
461C23×C4C2414yes—
462C23×C4C2414yes—
463C23×C4C2412yes—
464C23×C4C2414yes—
465C23×C4C2411yescharacteristic
466C23×C4C2412yes—
467C23×C4C2412yes—
468C23×C4C2412yes—
469C23×C4C2414yes—
470C23×C4C2418yes—
471C23×C4C2414yes—
472C23×C4C2411yescharacteristic
473C23×C4C2412yes—
474C23×C4C2411yescharacteristic
475C4⋊Q8—28no—
476C4⋊Q8—216no—
477C4⋊Q8—28no—
478C4⋊Q8—28no—
479C4⋊Q8—28no—
480C4⋊Q8—28no—
481C4⋊Q8—28no—
482C4⋊Q8—24no—
483C4⋊Q8—24no—
484C4⋊Q8—24no—
485C4⋊Q8—232no—
486C4⋊Q8—44no—
487#127—28no—
488#127—24no—
489#126—216no—
490#126—216no—
491#126—232no—
492#126—232no—
493#126—216no—
494#125—216no—
495#125—232no—
496#125—232no—
497#125—28no—
498#125—28no—
499#125—216no—
500#125—216no—
501#124—28no—
502#124—28no—
503#124—216no—
504#124—216no—
505#124—28no—
506#124—28no—
507#124—232no—
508#124—48no—
509#123—232no—
510#123—216no—
511#123—216no—
512#123—216no—
513#123—264no—
514C22⋊Q8—28no—
515C22⋊Q8—216no—
516C22⋊Q8—216no—
517C22⋊Q8—28no—
518C22⋊Q8—28no—
519C22⋊Q8—216no—
520C22⋊Q8—216no—
521C22⋊Q8—216no—
522C22⋊Q8—232no—
523C22⋊Q8—232no—
524#121—216no—
525#121—216no—
526#121—28no—
527#121—28no—
528#121—28no—
529#121—216no—
530C4×Q8—28no—
531C4×Q8—28no—
532C4×Q8—216no—
533C4×Q8—216no—
534C4×Q8—24no—
535C4×Q8—28no—
536C4×Q8—24no—
537C4×Q8—24no—
538C4×Q8—24no—
539C4×Q8—28no—
540C4×Q8—28no—
541C4×Q8—216no—
542C4×Q8—216no—
543C4×Q8—216no—
544C4×Q8—216no—
545C4×Q8—28no—
546C4×Q8—28no—
547C4×Q8—216no—
548C4×Q8C2×D418yes—
549C4×Q8C2×D418yes—
550C4×D4—216no—
551C4×D4—216no—
552C4×D4—216no—
553C4×D4—28no—
554C4×D4—28no—
555C4×D4—216no—
556C4×D4—216no—
557C4×D4—232no—
558C4×D4—28no—
559C4×D4—28no—
560C4×D4—28no—
561C4×D4—216no—
562C4×D4C2×D4116yes—
563C4×D4C2×D418yes—
564C4×D4C2×D4116yes—
565C4×D4C2×D418yes—
566#117—28no—
567#117—28no—
568#117—216no—
569#117—216no—
570#117—216no—
571#117—232no—
572#117—216no—
573#117—216no—
574#117C2×D418yes—
575#117C2×D4116yes—
576#117#41116yescomplemented
577C2×C4⋊C4—28no—
578C2×C4⋊C4—24no—
579C2×C4⋊C4—28no—
580C2×C4⋊C4—28no—
581C2×C4⋊C4—28no—
582C2×C4⋊C4—216no—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2418yes—
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C2418yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C24116yes—
614C2×C4⋊C4C24116yes—
615C2×C4⋊C4C2418yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2418yes—
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C22⋊C4C2414yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2414yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C24116yes—
638C2×C22⋊C4C24116yes—
639C2×C22⋊C4C24116yes—
640C2×C22⋊C4C24116yes—
641C2×C22⋊C4C2412yes—
642C2×C22⋊C4C2412yes—
643C2×C22⋊C4C2412yes—
644C2×C22⋊C4C2414yes—
645C2×C42—28no—
646C2×C42—216no—
647C2×C42—44no—
648C2×C42—48no—
649C2×C42C2×D418yes—
650C2×C42C2×D4116yes—
651C2×C42C2412yes—
652C2×C42C2414yes—
653C2×C42C2418yes—
654C2×C42C2418yes—
655C2×C42C2418yes—
656C2×C42C2414yes—
657C2×C42C2414yes—
658C2×C42C2412yes—
659C2×C42C2412yes—
660C2×C42C2412yes—
661C2×C42C2414yes—
662C2×C42C2412yes—
663C2×C42C2412yes—
664C2×C42C2418yes—
665C2×C42C2414yes—
666C2×C42C2418yes—
667C2×C42C2414yes—
668C2×C42C2412yes—
669C2×C42C2411yescharacteristic
670C2×C42C2412yes—
671C2×C42C2412yes—
672C2×C42C2411yescharacteristic
673C2×C42C2411yescharacteristic
674C2×C42C2411yescharacteristic
675C2×C42C2414yes—
676#95C2414yes—
677#95C2412yes—
678#95C2418yes—
679#95C2414yes—
680#95C24116yes—
681#95C24116yes—
682#95C24116yes—
683#95C24116yes—
684#95C2412yes—
685#95C2418yes—
686#95C2414yes—
687#95C2418yes—
688#95C2418yes—
689#95C24116yes—
690#95C24116yes—
691#95C2418yes—
692#95C2418yes—
693C24C2514yes—
694C24C2512yes—
695C24C2511yescharacteristic
696#41—232no—
697#41—432no—
698#41—432no—
699C2×Q8—22no—
700C2×Q8—24no—
701C2×Q8—24no—
702C2×Q8—24no—
703C2×Q8—22no—
704C2×Q8—28no—
705C2×Q8—24no—
706C2×Q8—28no—
707C2×Q8—24no—
708C2×Q8—216no—
709C2×Q8—216no—
710C2×Q8—28no—
711C2×Q8—24no—
712C2×Q8—24no—
713C2×Q8—22no—
714C2×Q8—22no—
715C2×Q8—24no—
716C2×Q8—22no—
717C2×Q8—42no—
718C2×Q8—44no—
719C2×Q8—416no—
720C2×Q8—432no—
721C2×Q8C22×D414yes—
722C2×Q82−1+414yes—
723C2×D4—28no—
724C2×D4—28no—
725C2×D4—28no—
726C2×D4—216no—
727C2×D4—28no—
728C2×D4—24no—
729C2×D4—24no—
730C2×D4—24no—
731C2×D4—24no—
732C2×D4—28no—
733C2×D4—28no—
734C2×D4—24no—
735C2×D4—24no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—48no—
739C2×D4C22×D418yes—
740C2×D4C22×D414yes—
741C22×C4—28no—
742C22×C4—22no—
743C22×C4—24no—
744C22×C4—22no—
745C22×C4—24no—
746C22×C4—24no—
747C22×C4—28no—
748C22×C4—216no—
749C22×C4—24no—
750C22×C4—28no—
751C22×C4—28no—
752C22×C4—28no—
753C22×C4—216no—
754C22×C4—24no—
755C22×C4—28no—
756C22×C4—28no—
757C22×C4—216no—
758C22×C4—44no—
759C22×C4—42no—
760C22×C4—42no—
761C22×C4—44no—
762C22×C4—48no—
763C22×C4—44no—
764C22×C4—48no—
765C22×C4—48no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4C22×D414yes—
769C22×C4C22×D418yes—
770C22×C4C22×D418yes—
771C22×C4C22×D414yes—
772C22×C4C22×D418yes—
773C22×C4C22×D414yes—
774C22×C4C2×#4118yes—
775C22×C4C2518yes—
776C22×C4C2512yes—
777C22×C4C2512yes—
778C22×C4C2512yes—
779C22×C4C2514yes—
780C22×C4C2514yes—
781C22×C4C2518yes—
782C22×C4C2514yes—
783C22×C4C2511yescharacteristic
784C22×C4C2512yes—
785C22×C4C2512yes—
786C22×C4C2511yescharacteristic
787C22×C4C2511yescharacteristic
788C22×C4C2512yes—
789C22×C4C2514yes—
790C22×C4C2514yes—
791C22×C4C2512yes—
792C22×C4C2511yescharacteristic
793C22×C4C2511yescharacteristic
794C22×C4C2511yescharacteristic
795C4⋊C4—24no—
796C4⋊C4—22no—
797C4⋊C4—28no—
798C4⋊C4—28no—
799C4⋊C4—24no—
800C4⋊C4—22no—
801C4⋊C4—24no—
802C4⋊C4—24no—
803C4⋊C4—24no—
804C4⋊C4—28no—
805C4⋊C4—28no—
806C4⋊C4—24no—
807C4⋊C4—24no—
808C4⋊C4—28no—
809C4⋊C4—24no—
810C4⋊C4—28no—
811C4⋊C4—28no—
812C4⋊C4—24no—
813C4⋊C4—24no—
814C4⋊C4—216no—
815C4⋊C4—216no—
816C4⋊C4—24no—
817C4⋊C4—28no—
818C4⋊C4—216no—
819C4⋊C4—216no—
820C4⋊C4—28no—
821C4⋊C4—28no—
822C4⋊C4—28no—
823C4⋊C4—216no—
824C4⋊C4—28no—
825C4⋊C4—232no—
826C4⋊C4—232no—
827C4⋊C4—216no—
828C4⋊C4—48no—
829C4⋊C4—48no—
830C4⋊C4—48no—
831C4⋊C4C22×D414yes—
832C4⋊C4C22×D414yes—
833C4⋊C4C22×D418yes—
834C4⋊C4C22×D418yes—
835C4⋊C4C2×#4118yes—
836C4⋊C4C2×#4118yes—
837C22⋊C4—28no—
838C22⋊C4—28no—
839C22⋊C4—216no—
840C22⋊C4—216no—
841C22⋊C4—28no—
842C22⋊C4—28no—
843C22⋊C4—28no—
844C22⋊C4—28no—
845C22⋊C4—28no—
846C22⋊C4—28no—
847C22⋊C4—28no—
848C22⋊C4—216no—
849C22⋊C4—232no—
850C22⋊C4—232no—
851C22⋊C4—416no—
852C22⋊C4—416no—
853C22⋊C4C22×D418yes—
854C22⋊C4C22×D418yes—
855C22⋊C4C22×D418yes—
856C22⋊C4C2×#41116yes—
857C42—24no—
858C42—24no—
859C42—28no—
860C42—28no—
861C42—24no—
862C42—24no—
863C42—216no—
864C42—216no—
865C42—28no—
866C42—216no—
867C42—24no—
868C42—28no—
869C42—24no—
870C42—48no—
871C42—44no—
872C42—48no—
873C42—44no—
874C42C22×D418yes—
875C42C22×D414yes—
876C42C22×D418yes—
877C42C22×D414yes—
878C42C22×D418yes—
879C42C22×D414yes—
880C42C22×D414yes—
881C42C2×#41116yes—
882C23—21no—
883C23—21no—
884C23—22no—
885C23—24no—
886C23—22no—
887C23—22no—
888C23—24no—
889C23—24no—
890C23—28no—
891C23—24no—
892C23—24no—
893C23—28no—
894C23C23×D414yes—
895C23C23×D412yes—
896C23C22×#4114yes—
897C23C2611yescharacteristic
898Q8—28no—
899Q8—28no—
900Q8—48no—
901Q8—48no—
902Q8—416no—
903Q8—416no—
904Q8—48no—
905Q8—48no—
906Q8—44no—
907D4—216no—
908D4—28no—
909D4—416no—
910D4—416no—
911D4—48no—
912D4—48no—
913D4—84no—
914D4—88no—
915C2×C4—22no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—22no—
919C2×C4—21no—
920C2×C4—24no—
921C2×C4—22no—
922C2×C4—21no—
923C2×C4—22no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—22no—
927C2×C4—24no—
928C2×C4—22no—
929C2×C4—216no—
930C2×C4—28no—
931C2×C4—216no—
932C2×C4—22no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—22no—
936C2×C4—24no—
937C2×C4—22no—
938C2×C4—28no—
939C2×C4—28no—
940C2×C4—216no—
941C2×C4—28no—
942C2×C4—24no—
943C2×C4—22no—
944C2×C4—28no—
945C2×C4—24no—
946C2×C4—22no—
947C2×C4—28no—
948C2×C4—28no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—48no—
952C2×C4—44no—
953C2×C4—416no—
954C2×C4—48no—
955C2×C4—416no—
956C2×C4—416no—
957C2×C4—816no—
958C2×C4—88no—
959C2×C4—88no—
960C2×C4—84no—
961C2×C4#532116yes—
962C2×C4C23×D414yes—
963C2×C4C23×D414yes—
964C2×C4C23×D412yes—
965C2×C4C23×D412yes—
966C2×C4C23×D414yes—
967C2×C4C23×D412yes—
968C2×C4C23×D412yes—
969C2×C4C23×D412yes—
970C2×C4C23×D412yes—
971C2×C4C22×#4118yes—
972C2×C4C22×#4118yes—
973C2×C4C22×#4114yes—
974C2×C4C22×#4114yes—
975C2×C4C2×2−1+414yes—
976C2×C4C2×2−1+412yes—
977C2×C4#58512yes—
978C22—24no—
979C22—24no—
980C22—22no—
981C22—22no—
982C22—24no—
983C22—24no—
984C22—24no—
985C22—44no—
986C22—44no—
987C22—48no—
988C22—48no—
989C22—44no—
990C22—44no—
991C22—44no—
992C22C2×#53214yes—
993C22C24×D411yescharacteristic
994C22C23×#4112yes—
995C22C22×2−1+411yescharacteristic
996C22C2×#58511yescharacteristic
997C222−1+612yes—
998C4—28no—
999C4—28no—
1000C4—24no—
1001C4—22no—
1002C4—24no—
1003C4—22no—
1004C4—24no—
1005C4—22no—
1006C4—24no—
1007C4—48no—
1008C4—42no—
1009C4—44no—
1010C4—42no—
1011C4—42no—
1012C4—44no—
1013C4—44no—
1014C4—48no—
1015C4C2×#53214yes—
1016C4C2×#53214yes—
1017C4#348914yes—
1018C2—24no—
1019C2—44no—
1020C2—84no—
1021C2C22×#53211yescharacteristic
1022C2C2×#348911yescharacteristic
1023C2#6285911yescharacteristic
1024C2#6299512yes—
1025C2#6300112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3480C2
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×#3509C2semidirect
3. #36560C2semidirect
4. #36538C2semidirect
5. #36419C2semidirect
6. #36376C2semidirect
7. #36188C2semidirect
8. #36184C2semidirect
9. #36045C2semidirect
10. #35959C2semidirect
11. #35938C2semidirect
12. #35635C2semidirect
13. #35621C2semidirect
14. #35317C2semidirect
15. #35241C2semidirect
16. #35201C2semidirect
17. #35180C2semidirect
18. #34979C2semidirect
19. #34953C2semidirect
20. #34947C2semidirect
21. C2×#2568C2semidirect
22. #34268C2semidirect
23. C4×#520C2semidirect
576. #117#41semidirect

Maximal subgroups

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

subgroupindex
C2×#35092
C2×#34802
#365602
#365382
#364192
#363762
#361882
#361842
#360452
#359592
#359382
#356352
#356212
#353172
#352412
#352012
#351802
#349792
#349532
#349472
C2×#25682
#342682
C4×#5202