Finite Group Databasebeta

← #7647630

Subgroups — #7647630

Order 512.

6760 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×#3511C211yesmaximal, characteristic
2C2×Q8×#41C211yesmaximal, characteristic, complemented
3#42891C214yesmaximal, complemented
4#42482C214yesmaximal, complemented
5#40589C218yesmaximal, complemented
6#39617C212yesmaximal, complemented
7#39489C212yesmaximal, complemented
8#39173C212yesmaximal, complemented
9#38958C212yesmaximal, complemented
10#38085C214yesmaximal, complemented
11#37862C214yesmaximal, complemented
12#37640C212yesmaximal, complemented
13#37635C212yesmaximal, complemented
14#37275C218yesmaximal, complemented
15#35519C214yesmaximal, complemented
16#35281C211yesmaximal, characteristic, complemented
17#35255C214yesmaximal, complemented
18#35249C212yesmaximal, complemented
19#35180C211yesmaximal, characteristic, complemented
20#35179C212yesmaximal, complemented
21#34955C211yesmaximal, characteristic, complemented
22C2×#2567C211yesmaximal, characteristic, complemented
23#34060C211yesmaximal, characteristic, complemented
24#3511—216no—
25Q8×#41—216no—
26C2×Q82C2211yescharacteristic
27C2×#557C2211yescharacteristic
28C2×#557C2212yes—
29C2×#556C2212yes—
30C2×#555C2212yes—
31C2×#554C2212yes—
32C2×#554C2211yescharacteristic
33C2×#554C2214yes—
34C2×#554C2212yes—
35C2×#554C2212yes—
36C2×#553C2214yes—
37C2×D4×Q8C2211yescharacteristic
38C2×D4×Q8C2212yes—
39C2×#548C2214yes—
40C2×#547C2212yes—
41C2×#542C2214yes—
42C2×#537C2212yes—
43C2×#533C2212yes—
44C2×#533C2212yes—
45C2×#533C2211yescharacteristic
46C2×#533C2214yes—
47C2×#533C2212yes—
48C2×#532C2212yes—
49C2×#532C2211yescharacteristic
50C22×C4⋊Q8C2211yescharacteristic
51C2×#520C2212yes—
52C2×C4×#41C2212yes—
53C2×C4×#41C2211yescharacteristic
54C22×C4×Q8C2212yes—
55C22×C4×Q8C2211yescharacteristic
56#2868C2212yes—
57#2862C2212yes—
58#2855C2218yes—
59#2854C2218yes—
60#2850C2214yes—
61#2820C2218yes—
62#2817C2218yes—
63#2721C22116yes—
64#2716C22116yes—
65#2700C22116yes—
66#2690C22116yes—
67#2687C22116yes—
68#2680C22116yes—
69#2677C22116yes—
70#2674C22116yes—
71#2660C2214yes—
72#2660C2214yes—
73#2642C2214yes—
74#2639C2214yes—
75#2634C2218yes—
76#2632C2218yes—
77#2627C2218yes—
78#2625C2218yes—
79#2624C2218yes—
80#2620C2214yes—
81#2620C2214yes—
82#2616C2218yes—
83#2592C2214yes—
84#2592C2214yes—
85#2591C2214yes—
86#2582C2218yes—
87#2581C2218yes—
88#2581C2218yes—
89#2580C2218yes—
90#2568C2211yescharacteristic
91#2568C2212yes—
92#2568C2211yescharacteristic
93#2567C2212yes—
94#2567C2212yes—
95#2567C2212yes—
96#2567C2212yes—
97#2567C2212yes—
98#2567C2212yes—
99#2567C2214yes—
100#2567C2214yes—
101#2565C2214yes—
102#2565C2214yes—
103#2563C2212yes—
104#2562C2214yes—
105#2548C2211yescharacteristic
106#2548C2212yes—
107#2548C2211yescharacteristic
108#2547C2214yes—
109#2547C2212yes—
110#2546C2214yes—
111#2542C2214yes—
112#2538C2218yes—
113#2504C2212yes—
114#2502C2214yes—
115#2501C2214yes—
116#2499C2214yes—
117#2499C2214yes—
118#2450C22116yes—
119#2449C22116yes—
120#2444C22116yes—
121#2443C22116yes—
122#2442C2218yes—
123#2441C2218yes—
124#2440C2218yes—
125#2439C2218yes—
126#2436C2214yes—
127#2436C2212yes—
128#2434C2214yes—
129#2423C2218yes—
130#2422C2218yes—
131#2421C2218yes—
132#2420C2218yes—
133#2406C2218yes—
134#2398C2214yes—
135C2×#395C2214yes—
136#2326C2214yes—
137#2326C2214yes—
138#2320C2212yes—
139#2319C2212yes—
140#2318C2214yes—
141#2317C2212yes—
142#2317C2214yes—
143#2317C2214yes—
144#2314C2214yes—
145#2311C2212yes—
146#2311C2214yes—
147#2310C2214yes—
148C4×#124C2212yes—
149C4×#124C2212yes—
150#2297C2214yes—
151#2295C2212yes—
152C2×#391C2212yes—
153#2293C2212yes—
154C2×#389C2214yes—
155#2290C2214yes—
156#2285C2212yes—
157C2×#384C2212yes—
158#2283C2212yes—
159C4×#117C2211yescharacteristic
160C2×C4×C4⋊C4C2211yescharacteristic
161C22×#41C2312yes—
162C22×#41C2311yescharacteristic
163C22×#41C2314yes—
164C23×Q8C2312yes—
165C23×Q8C2311yescharacteristic
166C23×Q8C2312yes—
167Q82—28no—
168#557—28no—
169#557—216no—
170#556—216no—
171#555—216no—
172#554—216no—
173#554—216no—
174#554—232no—
175#554—216no—
176#554—28no—
177#553—232no—
178D4×Q8—216no—
179D4×Q8—28no—
180#548—232no—
181#547—216no—
182#542—232no—
183#537—216no—
184#533—216no—
185#533—232no—
186#533—28no—
187#533—216no—
188#533—216no—
189#532—28no—
190#532—216no—
191C2×C4⋊Q8—28no—
192C2×C4⋊Q8C2311yescharacteristic
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2311yescharacteristic
198C2×C4⋊Q8C2311yescharacteristic
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2312yes—
201C2×C4⋊Q8C2314yes—
202C2×C4⋊Q8C2312yes—
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2314yes—
205C2×C4⋊Q8C2318yes—
206C2×#127C2311yescharacteristic
207C2×#126C2318yes—
208C2×#125C2312yes—
209C2×#125C2314yes—
210C2×#125C2314yes—
211C2×#125C2314yes—
212C2×#125C2312yes—
213C2×#125C2312yes—
214C2×#125C2314yes—
215C2×#124C2314yes—
216C2×#124C2312yes—
217C2×#124C2312yes—
218C2×#124C2318yes—
219C2×#124C2314yes—
220C2×#124C2312yes—
221C2×#123C2318yes—
222C2×#123C23116yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2318yes—
238C2×C22⋊Q8C23116yes—
239C2×#121C2312yes—
240C2×#121C2312yes—
241C2×#121C2314yes—
242C2×#121C2314yes—
243C2×#121C2314yes—
244C2×#121C2318yes—
245#520—216no—
246C4×#41—216no—
247C4×#41D4116yes—
248C2×C4×Q8—28no—
249C2×C4×Q8—216no—
250C2×C4×Q8C2312yes—
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2312yes—
255C2×C4×Q8C2312yes—
256C2×C4×Q8C2312yes—
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2311yescharacteristic
259C2×C4×Q8C2314yes—
260C2×C4×Q8C2314yes—
261C2×C4×Q8C2314yes—
262C2×C4×Q8C2314yes—
263C2×C4×Q8C2314yes—
264C2×C4×Q8C2312yes—
265C2×C4×Q8C2312yes—
266C2×C4×Q8C2312yes—
267C2×C4×Q8C2311yescharacteristic
268C2×C4×Q8C2311yescharacteristic
269C2×C4×D4C2312yes—
270C2×C4×D4C2312yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2312yes—
274C2×C4×D4C2312yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2318yes—
278C2×C4×D4C2312yes—
279C2×C4×D4C2311yescharacteristic
280C2×C4×D4C2312yes—
281C2×C4×D4C2311yescharacteristic
282C2×#117C2314yes—
283C2×#117C2312yes—
284C2×#117C2312yes—
285C2×#117C2314yes—
286C2×#117C2314yes—
287C2×#117C2314yes—
288C2×#117C2312yes—
289C2×#117C2311yescharacteristic
290C22×C4⋊C4C2312yes—
291C22×C4⋊C4C2312yes—
292C22×C4⋊C4C2312yes—
293C22×C4⋊C4C2312yes—
294C22×C4⋊C4C2314yes—
295C22×C4⋊C4C2311yescharacteristic
296C22×C4⋊C4C2314yes—
297C22×C4⋊C4C2312yes—
298C22×C4⋊C4C2318yes—
299C22×C42C2314yes—
300C22×C42C2312yes—
301C22×C42C2312yes—
302C22×C42C2311yescharacteristic
303C22×C42C2312yes—
304#400C2314yes—
305#400C2318yes—
306#400C23116yes—
307#400C2314yes—
308#400C23116yes—
309#399C23116yes—
310#399C23116yes—
311#398C23116yes—
312#398C23116yes—
313#398C23116yes—
314#398C23116yes—
315#397C23116yes—
316#397C23116yes—
317#397C23116yes—
318#397C2318yes—
319#397C2318yes—
320#396C23116yes—
321#396C23116yes—
322#395C2318yes—
323#395C2318yes—
324#395C23116yes—
325#395C2318yes—
326#395C2318yes—
327#395C2318yes—
328#395C2318yes—
329#394C2318yes—
330#394C2314yes—
331#394C2314yes—
332#394C23116yes—
333#394C23116yes—
334#393C2318yes—
335#393C23116yes—
336#393C2318yes—
337#391C2312yes—
338#391C2314yes—
339#391C2314yes—
340#391C2314yes—
341#391C23116yes—
342#391C2318yes—
343#391C2314yes—
344#391C2314yes—
345#391C2318yes—
346#391C2314yes—
347#391C2314yes—
348#391C2314yes—
349#391C2312yes—
350#391C2318yes—
351#390C2314yes—
352#390C2314yes—
353#390C2318yes—
354#390C2314yes—
355#390C2312yes—
356#390C2314yes—
357#390C2312yes—
358#389C2318yes—
359#389C2318yes—
360#389C2318yes—
361#389C2318yes—
362#389C2318yes—
363#389C2318yes—
364#389C2314yes—
365#389C2314yes—
366#389C23116yes—
367#388C23116yes—
368#388C2318yes—
369#388C2318yes—
370#388C23116yes—
371#388C23116yes—
372#388C2318yes—
373#388C2318yes—
374#387C23116yes—
375#387C23116yes—
376#387C2318yes—
377#387C2318yes—
378#387C23116yes—
379#387C23116yes—
380#386C2318yes—
381#386C23116yes—
382#386C2318yes—
383#386C2318yes—
384#386C23116yes—
385#385C2318yes—
386#385C23116yes—
387#385C23116yes—
388#385C23116yes—
389#385C23116yes—
390#384C2314yes—
391#384C2314yes—
392#384C2314yes—
393#384C2318yes—
394#384C2314yes—
395#384C2314yes—
396#384C2318yes—
397#383C2314yes—
398#382C2314yes—
399#382C2314yes—
400#382C2312yes—
401#382C2312yes—
402#382C2314yes—
403#382C2318yes—
404#381C2314yes—
405#381C23116yes—
406#380C2318yes—
407#380C2318yes—
408#380C2314yes—
409#380C2314yes—
410#380C2314yes—
411#380C23116yes—
412C4×C4⋊C4C2312yes—
413C4×C4⋊C4C2312yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2312yes—
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2311yescharacteristic
418C4×C4⋊C4C2312yes—
419C4×C4⋊C4C2312yes—
420C4×C22⋊C4C2312yes—
421C4×C22⋊C4C2318yes—
422C4×C22⋊C4C2318yes—
423C4×C22⋊C4C2314yes—
424C4×C22⋊C4C2312yes—
425#376C2312yes—
426#376C2314yes—
427C2×#95C2312yes—
428C2×#95C2318yes—
429C43C2312yes—
430C2×#41—28no—
431C2×#41—216no—
432C2×#41—28no—
433C2×#41—216no—
434C2×#41—88no—
435C2×#41C2×D418yes—
436C22×Q8—28no—
437C22×Q8—24no—
438C22×Q8—24no—
439C22×Q8—28no—
440C22×Q8—28no—
441C22×Q8—42no—
442C22×Q8—44no—
443C22×Q8—84no—
444C22×Q8C2412yes—
445C22×Q8C2411yescharacteristic
446C22×Q8C2412yes—
447C22×Q8C2412yes—
448C22×Q8C2414yes—
449C22×Q8C2411yescharacteristic
450C22×Q8C2411yescharacteristic
451C22×Q8C2414yes—
452C22×Q8C2412yes—
453C22×Q8C2414yes—
454C22×Q8C2414yes—
455C22×D4C2412yes—
456C22×D4C2414yes—
457C22×D4C2412yes—
458C22×D4C2412yes—
459C22×D4C2411yescharacteristic
460C22×D4C2412yes—
461C22×D4C2418yes—
462C23×C4C2414yes—
463C23×C4C2412yes—
464C23×C4C2414yes—
465C23×C4C2411yescharacteristic
466C23×C4C2412yes—
467C23×C4C2412yes—
468C23×C4C2412yes—
469C23×C4C2414yes—
470C23×C4C2414yes—
471C23×C4C2414yes—
472C23×C4C2418yes—
473C23×C4C2411yescharacteristic
474C23×C4C2412yes—
475C23×C4C2411yescharacteristic
476C4⋊Q8—28no—
477C4⋊Q8—216no—
478C4⋊Q8—28no—
479C4⋊Q8—216no—
480C4⋊Q8—28no—
481C4⋊Q8—28no—
482C4⋊Q8—28no—
483C4⋊Q8—28no—
484C4⋊Q8—24no—
485C4⋊Q8—28no—
486C4⋊Q8—24no—
487C4⋊Q8—28no—
488C4⋊Q8—24no—
489C4⋊Q8—88no—
490#127—24no—
491#126—232no—
492#125—28no—
493#125—28no—
494#125—216no—
495#125—216no—
496#125—216no—
497#125—28no—
498#125—216no—
499#124—28no—
500#124—232no—
501#124—28no—
502#124—216no—
503#124—48no—
504#124—44no—
505#123—232no—
506#123—816no—
507C22⋊Q8—216no—
508C22⋊Q8—216no—
509C22⋊Q8—216no—
510C22⋊Q8—28no—
511C22⋊Q8—28no—
512C22⋊Q8—28no—
513C22⋊Q8—28no—
514C22⋊Q8—216no—
515C22⋊Q8—232no—
516C22⋊Q8—216no—
517C22⋊Q8—216no—
518C22⋊Q8—216no—
519C22⋊Q8—216no—
520C22⋊Q8—216no—
521C22⋊Q8—216no—
522C22⋊Q8—816no—
523#121—216no—
524#121—232no—
525#121—216no—
526#121—28no—
527#121—28no—
528#121—216no—
529C4×Q8—28no—
530C4×Q8—28no—
531C4×Q8—24no—
532C4×Q8—216no—
533C4×Q8—28no—
534C4×Q8—24no—
535C4×Q8—28no—
536C4×Q8—28no—
537C4×Q8—24no—
538C4×Q8—28no—
539C4×Q8—24no—
540C4×Q8—28no—
541C4×Q8—216no—
542C4×Q8—216no—
543C4×Q8—216no—
544C4×Q8—28no—
545C4×Q8—216no—
546C4×Q8C2×D418yes—
547C4×Q8C2×D418yes—
548C4×D4—28no—
549C4×D4—216no—
550C4×D4—28no—
551C4×D4—216no—
552C4×D4—232no—
553C4×D4—216no—
554C4×D4—28no—
555C4×D4—216no—
556C4×D4—28no—
557C4×D4C2×D418yes—
558C4×D4C2×D4116yes—
559C4×D4C2×D4116yes—
560C4×D4C2×D418yes—
561#117—216no—
562#117—28no—
563#117—216no—
564#117—28no—
565#117—216no—
566#117—48no—
567#117C2×D418yes—
568#117C2×D4116yes—
569C2×C4⋊C4—28no—
570C2×C4⋊C4—216no—
571C2×C4⋊C4—24no—
572C2×C4⋊C4—28no—
573C2×C4⋊C4—28no—
574C2×C4⋊C4—28no—
575C2×C4⋊C4—28no—
576C2×C4⋊C4—216no—
577C2×C4⋊C4—88no—
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2418yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C24116yes—
612C2×C4⋊C4C24116yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C24116yes—
616C2×C4⋊C4C24116yes—
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C22⋊C4C2418yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2418yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C24116yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C24116yes—
638C2×C22⋊C4C2412yes—
639C2×C22⋊C4C2412yes—
640C2×C22⋊C4C2412yes—
641C2×C42—216no—
642C2×C42—28no—
643C2×C42—44no—
644C2×C42C2×D418yes—
645C2×C42C2×D4116yes—
646C2×C42C2418yes—
647C2×C42C2414yes—
648C2×C42C2412yes—
649C2×C42C2412yes—
650C2×C42C2414yes—
651C2×C42C2414yes—
652C2×C42C2412yes—
653C2×C42C2414yes—
654C2×C42C2412yes—
655C2×C42C2414yes—
656C2×C42C2412yes—
657C2×C42C2412yes—
658C2×C42C2414yes—
659C2×C42C2414yes—
660C2×C42C2412yes—
661C2×C42C2411yescharacteristic
662C2×C42C2412yes—
663C2×C42C2411yescharacteristic
664C2×C42C2411yescharacteristic
665C2×C42C2412yes—
666C2×C42C2411yescharacteristic
667#95C2414yes—
668#95C2414yes—
669#95C24116yes—
670#95C24116yes—
671#95C2412yes—
672#95C2412yes—
673#95C2414yes—
674#95C2418yes—
675#95C2418yes—
676#95C2418yes—
677#95C2418yes—
678#95C2418yes—
679#95C2418yes—
680#95C2418yes—
681#95C2418yes—
682#95C24116yes—
683#95C24116yes—
684#95C24116yes—
685#95C24116yes—
686C24C2514yes—
687C24C2512yes—
688C24C2511yescharacteristic
689#41—232no—
690#41—432no—
691#41—832no—
692C2×Q8—22no—
693C2×Q8—24no—
694C2×Q8—28no—
695C2×Q8—24no—
696C2×Q8—24no—
697C2×Q8—22no—
698C2×Q8—28no—
699C2×Q8—24no—
700C2×Q8—28no—
701C2×Q8—28no—
702C2×Q8—24no—
703C2×Q8—28no—
704C2×Q8—24no—
705C2×Q8—24no—
706C2×Q8—22no—
707C2×Q8—28no—
708C2×Q8—22no—
709C2×Q8—24no—
710C2×Q8—22no—
711C2×Q8—42no—
712C2×Q8—44no—
713C2×Q8—48no—
714C2×Q8—48no—
715C2×Q8—44no—
716C2×Q8—48no—
717C2×Q8—416no—
718C2×Q8—432no—
719C2×Q8—816no—
720C2×Q8C22×D414yes—
721C2×Q82−1+414yes—
722C2×D4—28no—
723C2×D4—28no—
724C2×D4—216no—
725C2×D4—216no—
726C2×D4—24no—
727C2×D4—24no—
728C2×D4—24no—
729C2×D4—24no—
730C2×D4—24no—
731C2×D4—28no—
732C2×D4—24no—
733C2×D4—44no—
734C2×D4—416no—
735C2×D4C22×D418yes—
736C2×D4C22×D414yes—
737C22×C4—22no—
738C22×C4—24no—
739C22×C4—28no—
740C22×C4—22no—
741C22×C4—24no—
742C22×C4—28no—
743C22×C4—24no—
744C22×C4—28no—
745C22×C4—28no—
746C22×C4—24no—
747C22×C4—28no—
748C22×C4—28no—
749C22×C4—24no—
750C22×C4—28no—
751C22×C4—216no—
752C22×C4—216no—
753C22×C4—44no—
754C22×C4—44no—
755C22×C4—42no—
756C22×C4—44no—
757C22×C4—42no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4—48no—
761C22×C4—416no—
762C22×C4—48no—
763C22×C4C22×D418yes—
764C22×C4C22×D414yes—
765C22×C4C22×D418yes—
766C22×C4C22×D414yes—
767C22×C4C22×D418yes—
768C22×C4C22×D414yes—
769C22×C42−1+418yes—
770C22×C4C2514yes—
771C22×C4C2514yes—
772C22×C4C2518yes—
773C22×C4C2514yes—
774C22×C4C2512yes—
775C22×C4C2514yes—
776C22×C4C2518yes—
777C22×C4C2512yes—
778C22×C4C2512yes—
779C22×C4C2514yes—
780C22×C4C2512yes—
781C22×C4C2511yescharacteristic
782C22×C4C2511yescharacteristic
783C22×C4C2512yes—
784C22×C4C2511yescharacteristic
785C22×C4C2512yes—
786C22×C4C2512yes—
787C22×C4C2511yescharacteristic
788C22×C4C2511yescharacteristic
789C22×C4C2511yescharacteristic
790C4⋊C4—24no—
791C4⋊C4—22no—
792C4⋊C4—28no—
793C4⋊C4—28no—
794C4⋊C4—28no—
795C4⋊C4—216no—
796C4⋊C4—28no—
797C4⋊C4—24no—
798C4⋊C4—24no—
799C4⋊C4—28no—
800C4⋊C4—24no—
801C4⋊C4—28no—
802C4⋊C4—24no—
803C4⋊C4—28no—
804C4⋊C4—22no—
805C4⋊C4—24no—
806C4⋊C4—28no—
807C4⋊C4—24no—
808C4⋊C4—28no—
809C4⋊C4—28no—
810C4⋊C4—24no—
811C4⋊C4—24no—
812C4⋊C4—24no—
813C4⋊C4—216no—
814C4⋊C4—28no—
815C4⋊C4—28no—
816C4⋊C4—28no—
817C4⋊C4—24no—
818C4⋊C4—28no—
819C4⋊C4—28no—
820C4⋊C4—28no—
821C4⋊C4—24no—
822C4⋊C4—24no—
823C4⋊C4—416no—
824C4⋊C4—416no—
825C4⋊C4—48no—
826C4⋊C4—48no—
827C4⋊C4—416no—
828C4⋊C4—416no—
829C4⋊C4C22×D414yes—
830C4⋊C4C22×D414yes—
831C4⋊C4C22×D418yes—
832C4⋊C4C22×D418yes—
833C22⋊C4—28no—
834C22⋊C4—28no—
835C22⋊C4—28no—
836C22⋊C4—216no—
837C22⋊C4—28no—
838C22⋊C4—216no—
839C22⋊C4—216no—
840C22⋊C4—28no—
841C22⋊C4—28no—
842C22⋊C4—216no—
843C22⋊C4—48no—
844C22⋊C4—48no—
845C22⋊C4—416no—
846C22⋊C4—48no—
847C22⋊C4—48no—
848C22⋊C4—416no—
849C22⋊C4—48no—
850C22⋊C4C22×D418yes—
851C22⋊C4C22×D418yes—
852C22⋊C4C22×D418yes—
853C42—24no—
854C42—28no—
855C42—24no—
856C42—28no—
857C42—24no—
858C42—28no—
859C42—24no—
860C42—216no—
861C42—28no—
862C42—24no—
863C42—28no—
864C42—24no—
865C42—44no—
866C42—44no—
867C42C22×D414yes—
868C42C22×D418yes—
869C42C22×D414yes—
870C42C22×D418yes—
871C42C22×D414yes—
872C42C22×D414yes—
873C42C22×D418yes—
874C23—21no—
875C23—21no—
876C23—22no—
877C23—22no—
878C23—24no—
879C23—22no—
880C23—24no—
881C23—24no—
882C23—24no—
883C23—28no—
884C23—24no—
885C23—28no—
886C23C23×D414yes—
887C23C23×D412yes—
888C23C2×2−1+414yes—
889C23C2611yescharacteristic
890Q8—28no—
891Q8—28no—
892Q8—48no—
893Q8—416no—
894Q8—416no—
895Q8—48no—
896Q8—44no—
897Q8—48no—
898Q8—88no—
899Q8—84no—
900Q8—88no—
901D4—216no—
902D4—28no—
903D4—48no—
904D4—416no—
905D4—48no—
906D4—48no—
907D4—816no—
908C2×C4—22no—
909C2×C4—24no—
910C2×C4—21no—
911C2×C4—22no—
912C2×C4—21no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—24no—
917C2×C4—22no—
918C2×C4—216no—
919C2×C4—28no—
920C2×C4—216no—
921C2×C4—22no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—22no—
925C2×C4—24no—
926C2×C4—22no—
927C2×C4—28no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—28no—
932C2×C4—28no—
933C2×C4—22no—
934C2×C4—24no—
935C2×C4—28no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—22no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—28no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—28no—
945C2×C4—216no—
946C2×C4—44no—
947C2×C4—48no—
948C2×C4—48no—
949C2×C4—416no—
950C2×C4—416no—
951C2×C4—416no—
952C2×C4—816no—
953C2×C4—84no—
954C2×C4—88no—
955C2×C4—88no—
956C2×C4#536116yes—
957C2×C4C23×D414yes—
958C2×C4C23×D414yes—
959C2×C4C23×D412yes—
960C2×C4C23×D412yes—
961C2×C4C23×D412yes—
962C2×C4C23×D414yes—
963C2×C4C23×D412yes—
964C2×C4C23×D412yes—
965C2×C4C23×D412yes—
966C2×C4C2×2−1+414yes—
967C2×C4C2×2−1+414yes—
968C2×C4C2×2−1+414yes—
969C2×C4C2×2−1+412yes—
970C2×C4#58512yes—
971C22—22no—
972C22—22no—
973C22—24no—
974C22—24no—
975C22—24no—
976C22—24no—
977C22—24no—
978C22—44no—
979C22—44no—
980C22—44no—
981C22—44no—
982C22—48no—
983C22—44no—
984C22—48no—
985C22C2×#53614yes—
986C22C24×D411yescharacteristic
987C22C22×2−1+411yescharacteristic
988C22C22×2−1+412yes—
989C22C2×#58511yescharacteristic
990C22H(7,𝔽2)12yes—
991C4—22no—
992C4—24no—
993C4—24no—
994C4—22no—
995C4—24no—
996C4—22no—
997C4—24no—
998C4—42no—
999C4—44no—
1000C4—42no—
1001C4—48no—
1002C4—42no—
1003C4—44no—
1004C4—44no—
1005C4—48no—
1006C4—44no—
1007C4—44no—
1008C4C2×#53614yes—
1009C4C2×#53614yes—
1010C4#348914yes—
1011C2—24no—
1012C2—44no—
1013C2—84no—
1014C2C22×#53611yescharacteristic
1015C2C2×#348911yescharacteristic
1016C2#6285211yescharacteristic
1017C2#6292612yes—
1018C2#6294312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3511C2
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×Q8×#41C2semidirect
3. #42891C2semidirect
4. #42482C2semidirect
5. #40589C2semidirect
6. #39617C2semidirect
7. #39489C2semidirect
8. #39173C2semidirect
9. #38958C2semidirect
10. #38085C2semidirect
11. #37862C2semidirect
12. #37640C2semidirect
13. #37635C2semidirect
14. #37275C2semidirect
15. #35519C2semidirect
16. #35281C2semidirect
17. #35255C2semidirect
18. #35249C2semidirect
19. #35180C2semidirect
20. #35179C2semidirect
21. #34955C2semidirect
22. C2×#2567C2semidirect
23. #34060C2semidirect

Maximal subgroups

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

subgroupindex
C2×#35112
C2×Q8×#412
#428912
#424822
#405892
#396172
#394892
#391732
#389582
#380852
#378622
#376402
#376352
#372752
#355192
#352812
#352552
#352492
#351802
#351792
#349552
C2×#25672
#340602