Finite Group Databasebeta

← #7629013

Subgroups — #7629013

Order 512.

5426 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35612C214yesmaximal, complemented
2#35602C214yesmaximal, complemented
3#35585C212yesmaximal, complemented
4#35581C214yesmaximal, complemented
5#35580C214yesmaximal, complemented
6#35566C212yesmaximal, complemented
7#35529C212yesmaximal
8#35515C212yesmaximal
9#35402C218yesmaximal, complemented
10#34958C214yesmaximal, complemented
11#34941C214yesmaximal, complemented
12#34929C214yesmaximal, complemented
13#34893C214yesmaximal, complemented
14#34893C214yesmaximal, complemented
15#34739C214yesmaximal, complemented
16C4×#544C212yesmaximal, complemented
17#34058C211yesmaximal, characteristic
18C4×#533C212yesmaximal, complemented
19C2×#2293C211yesmaximal, characteristic
20C4×#518C211yesmaximal, characteristic
21C2×#544C2212yes—
22C2×#533C2212yes—
23C2×#533C2214yescomplemented
24C2×#518C2212yes—
25C22×C4×D4C2211yescharacteristic
26C22×#117C2212yes—
27#2608C2214yescomplemented
28#2608C2214yescomplemented
29#2607C2214yescomplemented
30#2607C2214yescomplemented
31#2589C2218yescomplemented
32#2589C2218yescomplemented
33#2587C2218yescomplemented
34#2587C2218yescomplemented
35#2584C2214yescomplemented
36#2584C2214yescomplemented
37#2580C2214yes—
38#2580C2214yes—
39#2574C2218yescomplemented
40#2574C2218yescomplemented
41#2569C2218yes—
42#2569C2218yescomplemented
43#2567C2214yescomplemented
44#2566C2214yes—
45#2566C2214yes—
46#2563C2214yes—
47#2556C2218yescomplemented
48#2556C2218yescomplemented
49#2552C2214yescomplemented
50#2551C2214yescomplemented
51#2550C2214yescomplemented
52#2550C2214yescomplemented
53#2549C2218yes—
54#2549C2218yescomplemented
55#2546C2214yescomplemented
56#2542C2214yes—
57#2538C2214yes—
58#2538C2214yes—
59#2522C2218yescomplemented
60#2522C2218yescomplemented
61#2509C2214yescomplemented
62#2509C2214yescomplemented
63#2508C2214yescomplemented
64#2508C2214yescomplemented
65#2507C2214yescomplemented
66#2507C2214yescomplemented
67#2506C2214yescomplemented
68#2506C2214yescomplemented
69#2497C2218yescomplemented
70#2492C2218yescomplemented
71#2465C2218yescomplemented
72#2465C2218yescomplemented
73#2454C2214yes—
74#2454C2214yes—
75#2454C2214yes—
76#2454C2214yes—
77#2452C2214yes—
78#2452C2214yes—
79#2452C2214yes—
80#2452C2214yes—
81#2442C2218yes—
82#2441C2218yescomplemented
83#2440C2218yes—
84#2439C2218yescomplemented
85#2438C2218yescomplemented
86#2438C2218yescomplemented
87#2437C2218yes—
88#2437C2218yes—
89#2437C2218yes—
90#2437C2218yes—
91#2429C2218yescomplemented
92#2423C2218yescomplemented
93#2396C2218yescomplemented
94#2396C2218yescomplemented
95#2396C2218yescomplemented
96#2396C2218yescomplemented
97#2331C2214yescomplemented
98#2331C2214yescomplemented
99#2330C2214yescomplemented
100#2330C2214yescomplemented
101#2329C2218yes—
102#2319C2214yes—
103#2319C2214yes—
104#2317C2212yes—
105#2317C2212yes—
106#2316C2212yes—
107#2316C2212yes—
108#2312C2214yes—
109#2309C2211yescharacteristic
110#2309C2211yescharacteristic
111C4×C4⋊Q8C2214yescomplemented
112C4×C4⋊Q8C2214yescomplemented
113C4×C4⋊Q8C2212yescomplemented
114C4×C4⋊Q8C2212yescomplemented
115C4×C4⋊Q8C2212yescomplemented
116C4×C4⋊Q8C2212yescomplemented
117C4×#125C2212yescomplemented
118C4×#125C2212yescomplemented
119C4×#125C2214yescomplemented
120C4×#125C2214yescomplemented
121C4×#125C2212yescomplemented
122C4×#125C2212yescomplemented
123C4×C22⋊Q8C2218yes—
124C4×C22⋊Q8C2214yes—
125C4×C22⋊Q8C2214yes—
126C4×C22⋊Q8C2214yes—
127C4×C22⋊Q8C2214yes—
128C4×C22⋊Q8C2218yescomplemented
129C4×C22⋊Q8C2218yescomplemented
130#2296C2212yes—
131#2296C2212yes—
132#2296C2214yescomplemented
133#2296C2214yescomplemented
134#2295C2214yescomplemented
135#2295C2214yescomplemented
136#2293C2214yes—
137#2293C2214yes—
138#2293C2214yes—
139#2293C2214yes—
140#2293C2214yes—
141#2293C2214yes—
142C2×#390C2212yes—
143C2×#389C2212yes—
144C2×#388C2214yes—
145#2285C2212yes—
146#2285C2214yescomplemented
147#2280C2214yes—
148#2275C2214yes—
149#2275C2214yes—
150#2274C2211yescharacteristic
151#2274C2211yescharacteristic
152#2273C2214yes—
153C42×Q8C2214yescomplemented
154C42×Q8C2214yescomplemented
155C42×D4C2214yes—
156C42×D4C2214yes—
157C4×#117C2212yes—
158C4×#117C2212yes—
159C2×C4×C4⋊C4C2211yescharacteristic
160C2×C4×C22⋊C4C2212yes—
161C2×C4×C22⋊C4C2214yes—
162C2×C43C2211yescharacteristic
163C23×D4C2311yescharacteristic
164C24×C4C2312yes—
165#544—216no—
166#533—216no—
167#533—416no—
168C2×C4⋊Q8C2312yes—
169C2×C4⋊Q8C2312yes—
170C2×C4⋊Q8C2314yes—
171C2×C4⋊Q8C2314yes—
172C2×C4⋊Q8C2318yes—
173C2×#125C2312yes—
174C2×#125C2312yes—
175C2×#125C2314yes—
176C2×#125C2314yes—
177C2×#125C2318yes—
178C2×C22⋊Q8C2318yes—
179C2×C22⋊Q8C2314yes—
180C2×C22⋊Q8C2314yes—
181C2×C22⋊Q8C2318yes—
182C2×C22⋊Q8C2318yes—
183C2×C22⋊Q8C2318yes—
184C2×C22⋊Q8C2318yes—
185#518—216no—
186C2×C4×Q8C2314yes—
187C2×C4×Q8C2314yes—
188C2×C4×Q8C2314yes—
189C2×C4×Q8C2318yes—
190C2×C4×Q8C2314yes—
191C2×C4×Q8C2314yes—
192C2×C4×Q8C2314yes—
193C2×C4×D4Q8116yescomplemented
194C2×C4×D4C2314yes—
195C2×C4×D4C2314yes—
196C2×C4×D4C2314yes—
197C2×C4×D4C2314yes—
198C2×C4×D4C2314yes—
199C2×C4×D4C2314yes—
200C2×#117—48no—
201C2×#117C2312yes—
202C2×#117C2312yes—
203C2×#117C2312yes—
204C2×#117C2314yes—
205C2×#117C2314yes—
206C2×#117C2314yes—
207C2×#117C2314yes—
208C2×#117C2318yes—
209C2×#117C2312yes—
210C22×C4⋊C4C2312yes—
211C22×C4⋊C4C2314yes—
212C22×C4⋊C4C2311yescharacteristic
213C22×C22⋊C4C2318yes—
214C22×C22⋊C4C2314yes—
215C22×C22⋊C4C2314yes—
216C22×C22⋊C4C2312yes—
217C22×C42C2311yescharacteristic
218C22×C42C2312yes—
219C22×C42C2312yes—
220C22×C42C2314yes—
221C22×C42C2311yescharacteristic
222C22×C42C2312yes—
223C22×C42C2314yes—
224C22×C42C2311yescharacteristic
225#400C2318yes—
226#400C2318yes—
227#400C2318yes—
228#400C2318yes—
229#399C2318yes—
230#399C2318yes—
231#399C2318yes—
232#399C2318yes—
233#398C2318yes—
234#398C2318yes—
235#398C2318yes—
236#398C2318yes—
237#398C2318yes—
238#398C2318yes—
239#398C2318yes—
240#398C2318yes—
241#396C2318yes—
242#396C2318yes—
243#396C2318yes—
244#396C2318yes—
245#396C2318yes—
246#396C2318yes—
247#396C2318yes—
248#396C2318yes—
249#395C2318yes—
250#395C2318yes—
251#395C2318yes—
252#395C2318yes—
253#393C2318yes—
254#393C2318yes—
255#393C2318yes—
256#393C2318yes—
257#391C2318yes—
258#391C2318yes—
259#391C2314yes—
260#391C2314yes—
261#391C2314yes—
262#391C2314yes—
263#391C2318yes—
264#391C2318yes—
265#391C2318yes—
266#390C2314yes—
267#390C2314yes—
268#390C2314yes—
269#390C2314yes—
270#390C2314yes—
271#390C2314yes—
272#390C2314yes—
273#390C2314yes—
274#389C2312yes—
275#389C2312yes—
276#389C2312yes—
277#389C2312yes—
278#389C2312yes—
279#389C2312yes—
280#389C2312yes—
281#389C2312yes—
282#389C2314yes—
283#389C2314yes—
284#389C2314yes—
285#389C2314yes—
286#389C2314yes—
287#389C2314yes—
288#389C2314yes—
289#389C2314yes—
290#389C2318yes—
291#389C2318yes—
292#389C2314yes—
293#389C2314yes—
294#389C2314yes—
295#389C2314yes—
296#389C2314yes—
297#389C2314yes—
298#389C2314yes—
299#389C2314yes—
300#389C2314yes—
301#389C2318yes—
302#389C2318yes—
303#389C2318yes—
304#389C2318yes—
305#389C2314yes—
306#389C2318yes—
307#389C2318yes—
308#389C2318yes—
309#389C2314yes—
310#389C2314yes—
311#388C2318yes—
312#388C2318yes—
313#388C2318yes—
314#388C2318yes—
315#388C2318yes—
316#388C2318yes—
317#388C2318yes—
318#388C2318yes—
319#387C2314yes—
320#387C2314yes—
321#387C2314yes—
322#387C2314yes—
323#387C2318yes—
324#387C2318yes—
325#387C2318yes—
326#387C2318yes—
327#387C2314yes—
328#387C2314yes—
329#387C2314yes—
330#387C2314yes—
331#387C2318yes—
332#387C2318yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#385C2318yes—
338#385C2318yes—
339#385C2318yes—
340#385C2318yes—
341#385C2314yes—
342#385C2318yes—
343#385C2318yes—
344#385C2318yes—
345#385C2318yes—
346#385C2318yes—
347#385C2318yes—
348#385C2314yes—
349#385C2314yes—
350#385C2314yes—
351#384C2312yes—
352#384C2312yes—
353#384C2314yes—
354#384C2314yes—
355#384C2318yes—
356#382C2312yes—
357#382C2312yes—
358#382C2314yes—
359#382C2314yes—
360#382C2318yes—
361#381C2314yes—
362#381C2314yes—
363#380C2318yes—
364#380C2318yes—
365#380C2318yes—
366#380C2314yes—
367#380C2318yes—
368#380C2318yes—
369#380C2318yes—
370#380C2318yes—
371#380C2314yes—
372#379C2314yes—
373#379C2314yes—
374C4×C4⋊C4C2312yes—
375C4×C4⋊C4C2312yes—
376C4×C4⋊C4C2314yes—
377C4×C4⋊C4C2318yes—
378C4×C4⋊C4C2312yes—
379C4×C4⋊C4C2312yes—
380C4×C4⋊C4C2312yes—
381C4×C4⋊C4C2312yes—
382C4×C4⋊C4C2312yes—
383C4×C4⋊C4C2312yes—
384C4×C4⋊C4C2318yes—
385C4×C4⋊C4C2318yes—
386C4×C4⋊C4C2314yes—
387C4×C4⋊C4C2314yes—
388C4×C4⋊C4C2314yes—
389C4×C4⋊C4C2314yes—
390C4×C4⋊C4C2314yes—
391C4×C4⋊C4C2314yes—
392C4×C4⋊C4C2314yes—
393C4×C4⋊C4C2314yes—
394C4×C4⋊C4C2314yes—
395C4×C4⋊C4C2314yes—
396C4×C4⋊C4C2314yes—
397C4×C4⋊C4C2314yes—
398C4×C4⋊C4C2314yes—
399C4×C4⋊C4C2314yes—
400C4×C4⋊C4C2314yes—
401C4×C4⋊C4C2314yes—
402C4×C4⋊C4C2314yes—
403C4×C4⋊C4C2314yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2314yes—
409C4×C22⋊C4C2314yes—
410C4×C22⋊C4C2314yes—
411C4×C22⋊C4C2314yes—
412C4×C22⋊C4C2318yes—
413C4×C22⋊C4C2314yes—
414C4×C22⋊C4C2318yes—
415C4×C22⋊C4C2318yes—
416C4×C22⋊C4C2314yes—
417C4×C22⋊C4C2314yes—
418C4×C22⋊C4C2314yes—
419C4×C22⋊C4C2318yes—
420C4×C22⋊C4C2318yes—
421C4×C22⋊C4C2318yes—
422C4×C22⋊C4C2314yes—
423C4×C22⋊C4C2318yes—
424C4×C22⋊C4C2314yes—
425C4×C22⋊C4C2314yes—
426#376C2314yes—
427#376C2314yes—
428C2×#95C2314yes—
429C2×#95C2318yes—
430C2×#95C2312yes—
431C43C2312yes—
432C43C2312yes—
433C43C2314yes—
434C43C2314yes—
435C43C2312yes—
436C43C2312yes—
437C25C2412yes—
438C22×Q8C2414yes—
439C22×Q8C2414yes—
440C22×Q8C2418yes—
441C22×D4—28no—
442C22×D4C2×Q818yes—
443C22×D4C2414yes—
444C23×C4—44no—
445C23×C4—44no—
446C23×C4C2×Q8116yes—
447C23×C4C2412yes—
448C23×C4C2412yes—
449C23×C4C2414yes—
450C23×C4C2411yescharacteristic
451C23×C4C2414yes—
452C23×C4C2418yes—
453C23×C4C2418yes—
454C23×C4C2411yescharacteristic
455C23×C4C2412yes—
456C23×C4C2414yes—
457C23×C4C2411yescharacteristic
458C4⋊Q8—28no—
459C4⋊Q8—28no—
460C4⋊Q8—216no—
461C4⋊Q8—216no—
462C4⋊Q8—416no—
463#125—28no—
464#125—28no—
465#125—216no—
466#125—216no—
467#125—416no—
468C22⋊Q8—216no—
469C22⋊Q8—216no—
470C22⋊Q8—232no—
471C22⋊Q8—416no—
472C22⋊Q8—416no—
473C22⋊Q8—416no—
474C22⋊Q8—416no—
475C4×Q8—216no—
476C4×Q8—216no—
477C4×Q8—216no—
478C4×Q8—48no—
479C4×Q8—416no—
480C4×Q8—48no—
481C4×Q8—48no—
482C4×D4—216no—
483C4×D4—216no—
484C4×D4—216no—
485C4×D4—216no—
486C4×D4C2×Q8132yes—
487C4×D4C2×Q8132yes—
488#117—28no—
489#117—28no—
490#117—28no—
491#117—216no—
492#117—48no—
493#117—48no—
494#117—48no—
495#117—416no—
496#117#41116yes—
497C2×C4⋊C4—28no—
498C2×C4⋊C4—48no—
499C2×C4⋊C4C2×Q818yes—
500C2×C4⋊C4C2418yes—
501C2×C4⋊C4C2414yes—
502C2×C4⋊C4C2414yes—
503C2×C4⋊C4C2412yes—
504C2×C4⋊C4C2412yes—
505C2×C4⋊C4C2412yes—
506C2×C4⋊C4C2412yes—
507C2×C4⋊C4C2412yes—
508C2×C4⋊C4C2412yes—
509C2×C4⋊C4C2414yes—
510C2×C4⋊C4C2414yes—
511C2×C4⋊C4C2414yes—
512C2×C4⋊C4C2414yes—
513C2×C4⋊C4C2414yes—
514C2×C4⋊C4C2414yes—
515C2×C4⋊C4C2414yes—
516C2×C4⋊C4C2414yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2414yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2418yes—
522C2×C4⋊C4C2418yes—
523C2×C4⋊C4C2418yes—
524C2×C4⋊C4C2418yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2418yes—
527C2×C4⋊C4C2418yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2414yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2414yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2418yes—
537C2×C4⋊C4C2418yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2412yes—
541C2×C4⋊C4C2412yes—
542C2×C22⋊C4—232no—
543C2×C22⋊C4—48no—
544C2×C22⋊C4—48no—
545C2×C22⋊C4C2×Q8116yes—
546C2×C22⋊C4C2414yes—
547C2×C22⋊C4C2418yes—
548C2×C22⋊C4C2418yes—
549C2×C22⋊C4C2418yes—
550C2×C22⋊C4C2418yes—
551C2×C22⋊C4C2414yes—
552C2×C22⋊C4C2414yes—
553C2×C22⋊C4C2418yes—
554C2×C22⋊C4C2418yes—
555C2×C22⋊C4C2414yes—
556C2×C22⋊C4C2414yes—
557C2×C22⋊C4C2414yes—
558C2×C22⋊C4C2414yes—
559C2×C22⋊C4C2418yes—
560C2×C22⋊C4C2418yes—
561C2×C22⋊C4C2418yes—
562C2×C22⋊C4C2414yes—
563C2×C42—28no—
564C2×C42—24no—
565C2×C42—44no—
566C2×C42—48no—
567C2×C42—48no—
568C2×C42—42no—
569C2×C42—44no—
570C2×C42C2×Q818yes—
571C2×C42C2412yes—
572C2×C42C2414yes—
573C2×C42C2414yes—
574C2×C42C2414yes—
575C2×C42C2412yes—
576C2×C42C2412yes—
577C2×C42C2412yes—
578C2×C42C2412yes—
579C2×C42C2412yes—
580C2×C42C2412yes—
581C2×C42C2411yescharacteristic
582C2×C42C2414yes—
583C2×C42C2414yes—
584C2×C42C2414yes—
585C2×C42C2414yes—
586C2×C42C2412yes—
587C2×C42C2414yes—
588C2×C42C2414yes—
589C2×C42C2414yes—
590C2×C42C2414yes—
591C2×C42C2414yes—
592C2×C42C2414yes—
593C2×C42C2414yes—
594C2×C42C2414yes—
595C2×C42C2411yescharacteristic
596C2×C42C2411yescharacteristic
597C2×C42C2412yes—
598C2×C42C2412yes—
599C2×C42C2414yes—
600C2×C42C2414yes—
601C2×C42C2412yes—
602C2×C42C2412yes—
603C2×C42C2414yes—
604C2×C42C2411yescharacteristic
605#95C2414yes—
606#95C2414yes—
607#95C2418yes—
608#95C2418yes—
609#95C2418yes—
610#95C2418yes—
611#95C2418yes—
612#95C2414yes—
613#95C2414yes—
614#95C2414yes—
615#95C2414yes—
616#95C2414yes—
617#95C2414yes—
618#95C2418yes—
619#95C2418yes—
620#95C2414yes—
621#95C2414yes—
622#95C2414yes—
623#95C2414yes—
624#95C2414yes—
625#95C2414yes—
626#95C2414yes—
627#95C2414yes—
628#95C2414yes—
629#95C2414yes—
630#95C2414yes—
631#95C2414yes—
632#95C2418yes—
633#95C2418yes—
634#95C2418yes—
635#95C2418yes—
636#95C2418yes—
637#95C2418yes—
638C24—28no—
639C24—42no—
640C24—44no—
641C24—42no—
642C24C22×Q818yes—
643C24C2514yes—
644C24C2511yescharacteristic
645C2×Q8—28no—
646C2×Q8—28no—
647C2×Q8—216no—
648C2×Q8—28no—
649C2×Q8—28no—
650C2×Q8—44no—
651C2×Q8—44no—
652C2×Q8—48no—
653C2×Q8—48no—
654C2×D4—232no—
655C2×D4—28no—
656C2×D4—28no—
657C2×D4C22×Q8116yes—
658C22×C4—22no—
659C22×C4—28no—
660C22×C4—28no—
661C22×C4—22no—
662C22×C4—24no—
663C22×C4—24no—
664C22×C4—28no—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—216no—
668C22×C4—216no—
669C22×C4—432no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—42no—
674C22×C4—44no—
675C22×C4—42no—
676C22×C4—44no—
677C22×C4—44no—
678C22×C4—48no—
679C22×C4—48no—
680C22×C4—44no—
681C22×C4—48no—
682C22×C4—48no—
683C22×C4C22×Q814yes—
684C22×C4C22×Q8116yes—
685C22×C4C22×Q814yes—
686C22×C4C22×Q818yes—
687C22×C4C22×Q8116yes—
688C22×C4C22×Q814yes—
689C22×C4C2×#4118yes—
690C22×C4C2514yes—
691C22×C4C2512yes—
692C22×C4C2514yes—
693C22×C4C2514yes—
694C22×C4C2514yes—
695C22×C4C2514yes—
696C22×C4C2518yes—
697C22×C4C2512yes—
698C22×C4C2514yes—
699C22×C4C2511yescharacteristic
700C22×C4C2512yes—
701C22×C4C2514yes—
702C22×C4C2514yes—
703C22×C4C2514yes—
704C22×C4C2512yes—
705C22×C4C2512yes—
706C22×C4C2512yes—
707C22×C4C2511yescharacteristic
708C4⋊C4—28no—
709C4⋊C4—28no—
710C4⋊C4—24no—
711C4⋊C4—24no—
712C4⋊C4—24no—
713C4⋊C4—24no—
714C4⋊C4—24no—
715C4⋊C4—24no—
716C4⋊C4—28no—
717C4⋊C4—28no—
718C4⋊C4—28no—
719C4⋊C4—28no—
720C4⋊C4—28no—
721C4⋊C4—28no—
722C4⋊C4—216no—
723C4⋊C4—216no—
724C4⋊C4—216no—
725C4⋊C4—216no—
726C4⋊C4—28no—
727C4⋊C4—28no—
728C4⋊C4—28no—
729C4⋊C4—28no—
730C4⋊C4—28no—
731C4⋊C4—28no—
732C4⋊C4—48no—
733C4⋊C4—48no—
734C4⋊C4—48no—
735C4⋊C4—44no—
736C4⋊C4—44no—
737C4⋊C4—44no—
738C4⋊C4—44no—
739C4⋊C4—44no—
740C4⋊C4—44no—
741C4⋊C4—48no—
742C4⋊C4—48no—
743C4⋊C4—48no—
744C4⋊C4—48no—
745C4⋊C4—48no—
746C4⋊C4—48no—
747C4⋊C4C22×Q8116yes—
748C4⋊C4C2×#4118yes—
749C4⋊C4C2×#4118yes—
750C22⋊C4—28no—
751C22⋊C4—28no—
752C22⋊C4—28no—
753C22⋊C4—216no—
754C22⋊C4—216no—
755C22⋊C4—216no—
756C22⋊C4—216no—
757C22⋊C4—48no—
758C22⋊C4—48no—
759C22⋊C4—44no—
760C22⋊C4—44no—
761C22⋊C4—44no—
762C22⋊C4—44no—
763C22⋊C4—48no—
764C22⋊C4—48no—
765C22⋊C4C22×Q8132yes—
766C22⋊C4C2×#41116yes—
767C42—24no—
768C42—24no—
769C42—24no—
770C42—24no—
771C42—28no—
772C42—28no—
773C42—28no—
774C42—24no—
775C42—22no—
776C42—28no—
777C42—28no—
778C42—28no—
779C42—28no—
780C42—24no—
781C42—24no—
782C42—24no—
783C42—28no—
784C42—42no—
785C42—42no—
786C42—44no—
787C42—41no—
788C42—44no—
789C42—41no—
790C42—44no—
791C42—44no—
792C42—44no—
793C42—44no—
794C42—44no—
795C42—44no—
796C42—44no—
797C42C22×Q818yes—
798C42C22×Q818yes—
799C42C2×#41116yes—
800C42H(5,𝔽2)14yes—
801C23—21no—
802C23—21no—
803C23—22no—
804C23—28no—
805C23—24no—
806C23—28no—
807C23—24no—
808C23—216no—
809C23—48no—
810C23—48no—
811C23—88no—
812C23—88no—
813C23C23×Q818yes—
814C23C23×Q812yes—
815C23C22×#4114yes—
816C23C2611yescharacteristic
817Q8—416no—
818Q8—416no—
819Q8—816no—
820D4—232no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—21no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—24no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—24no—
832C2×C4—21no—
833C2×C4—24no—
834C2×C4—24no—
835C2×C4—28no—
836C2×C4—232no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—24no—
845C2×C4—28no—
846C2×C4—22no—
847C2×C4—24no—
848C2×C4—28no—
849C2×C4—24no—
850C2×C4—24no—
851C2×C4—24no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—22no—
857C2×C4—24no—
858C2×C4—24no—
859C2×C4—24no—
860C2×C4—24no—
861C2×C4—24no—
862C2×C4—24no—
863C2×C4—28no—
864C2×C4—416no—
865C2×C4—48no—
866C2×C4—44no—
867C2×C4—48no—
868C2×C4—48no—
869C2×C4—816no—
870C2×C4—816no—
871C2×C4—88no—
872C2×C4#533116yescomplemented
873C2×C4C23×Q814yes—
874C2×C4C23×Q812yes—
875C2×C4C23×Q818yes—
876C2×C4C23×Q814yes—
877C2×C4C23×Q812yes—
878C2×C4C22×#4118yes—
879C2×C4C22×#4118yes—
880C2×C4C22×#4114yes—
881C2×C4C22×#4114yes—
882C2×C4C2×H(5,𝔽2)14yes—
883C2×C4C2×H(5,𝔽2)12yes—
884C2×C4#58514yes—
885C2×C4#58512yes—
886C22—22no—
887C22—24no—
888C22—24no—
889C22—22no—
890C22—28no—
891C22—28no—
892C22—28no—
893C22—48no—
894C22—48no—
895C22—816no—
896C22C2×#53314yes—
897C22C24×Q811yescharacteristic
898C22C23×#4112yes—
899C22C22×H(5,𝔽2)11yescharacteristic
900C22C2×#58511yescharacteristic
901C22C2×#58512yes—
902C4—22no—
903C4—28no—
904C4—24no—
905C4—28no—
906C4—24no—
907C4—28no—
908C4—24no—
909C4—42no—
910C4—44no—
911C4—48no—
912C4—44no—
913C4—44no—
914C4—44no—
915C4—42no—
916C4—44no—
917C4—44no—
918C4C2×#53318yes—
919C4#350114yes—
920C2—24no—
921C2—48no—
922C2C22×#53311yescharacteristic
923C2C2×#350111yescharacteristic
924C2#6280012yes—
925C2#6281012yes—
926C2#6281311yescharacteristic
subgroupG/H
centerC22×C4C25
commutator, Frattini, socle, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #35612C2semidirect
2. #35602C2semidirect
3. #35585C2semidirect
4. #35581C2semidirect
5. #35580C2semidirect
6. #35566C2semidirect
9. #35402C2semidirect
10. #34958C2semidirect
11. #34941C2semidirect
12. #34929C2semidirect
13. #34893C2semidirect
14. #34893C2semidirect
15. #34739C2semidirect
16. C4×#544C2semidirect
18. C4×#533C2semidirect
23. C2×#533C22semidirect
27. #2608C22semidirect
28. #2608C22semidirect
29. #2607C22semidirect
30. #2607C22semidirect
31. #2589C22semidirect
32. #2589C22semidirect
33. #2587C22semidirect
34. #2587C22semidirect
35. #2584C22semidirect
36. #2584C22semidirect
39. #2574C22semidirect
40. #2574C22semidirect
42. #2569C22semidirect
43. #2567C22semidirect
47. #2556C22semidirect
48. #2556C22semidirect
49. #2552C22semidirect
50. #2551C22semidirect
51. #2550C22semidirect
52. #2550C22semidirect
54. #2549C22semidirect
55. #2546C22semidirect
59. #2522C22semidirect
60. #2522C22semidirect
61. #2509C22semidirect
62. #2509C22semidirect
63. #2508C22semidirect
64. #2508C22semidirect
65. #2507C22semidirect
66. #2507C22semidirect
67. #2506C22semidirect
68. #2506C22semidirect
69. #2497C22semidirect
70. #2492C22semidirect
71. #2465C22semidirect
72. #2465C22semidirect
82. #2441C22semidirect
84. #2439C22semidirect
85. #2438C22semidirect
86. #2438C22semidirect
91. #2429C22semidirect
92. #2423C22semidirect
93. #2396C22semidirect
94. #2396C22semidirect
95. #2396C22semidirect
96. #2396C22semidirect
97. #2331C22semidirect
98. #2331C22semidirect
99. #2330C22semidirect
100. #2330C22semidirect
111. C4×C4⋊Q8C22semidirect
112. C4×C4⋊Q8C22semidirect
113. C4×C4⋊Q8C22semidirect
114. C4×C4⋊Q8C22semidirect
115. C4×C4⋊Q8C22semidirect
116. C4×C4⋊Q8C22semidirect
117. C4×#125C22semidirect
118. C4×#125C22semidirect
119. C4×#125C22semidirect
120. C4×#125C22semidirect
121. C4×#125C22semidirect
122. C4×#125C22semidirect
128. C4×C22⋊Q8C22semidirect
129. C4×C22⋊Q8C22semidirect
132. #2296C22semidirect
133. #2296C22semidirect
134. #2295C22semidirect
135. #2295C22semidirect
146. #2285C22semidirect
153. C42×Q8C22semidirect
154. C42×Q8C22semidirect
193. C2×C4×D4Q8semidirect
872. C2×C4#533semidirect

Maximal subgroups

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

subgroupindex
#356122
#356022
#355852
#355812
#355802
#355662
#355292
#355152
#354022
#349582
#349412
#349292
#348932
#347392
C4×#5442
#340582
C4×#5332
C2×#22932
C4×#5182