Finite Group Databasebeta

← #7628631

Subgroups — #7628631

Order 512.

4990 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36640C212yesmaximal, complemented
2#36635C212yesmaximal, complemented
3#35337C212yesmaximal, complemented
4#35336C212yesmaximal, complemented
5#35335C211yesmaximal, characteristic, complemented
6#35334C211yesmaximal, characteristic
7#35333C211yesmaximal, characteristic
8#35330C211yesmaximal, characteristic, complemented
9#35282C214yesmaximal, complemented
10#35265C212yesmaximal, complemented
11#35257C212yesmaximal
12#35221C214yesmaximal, complemented
13#35175C214yesmaximal, complemented
14#35018C218yesmaximal, complemented
15#34920C214yesmaximal, complemented
16#34893C214yesmaximal, complemented
17#34840C218yesmaximal, complemented
18#34625C214yesmaximal, complemented
19C4×#544C212yesmaximal, complemented
20#34060C212yesmaximal
21C4×#533C211yesmaximal, characteristic, complemented
22C2×C4×#125C211yesmaximal, characteristic, complemented
23C42×#41C211yesmaximal, characteristic
24C2×#544C2212yes—
25C2×#533C2211yescharacteristic
26C22×#125C2211yescharacteristic
27C2×C4×#41C2211yescharacteristic
28C2×C4×#41C2211yescharacteristic
29C2×C4×#41C2211yescharacteristic
30#2864C2214yes—
31#2864C2218yes—
32#2863C2218yes—
33#2862C2212yes—
34#2859C2212yes—
35#2859C2212yes—
36#2859C2212yes—
37#2859C2214yes—
38#2857C2214yes—
39#2855C2218yes—
40#2851C2212yes—
41#2851C2212yes—
42#2851C2212yes—
43#2851C2212yes—
44#2851C2218yes—
45#2851C2214yes—
46#2667C2218yes—
47#2666C2218yes—
48#2666C2218yes—
49#2665C2218yes—
50#2660C2214yes—
51#2660C2214yes—
52#2647C2214yes—
53#2647C2214yes—
54#2629C2214yes—
55#2629C2214yes—
56#2628C2214yes—
57#2628C2214yes—
58#2590C2218yes—
59#2590C2218yes—
60#2589C2218yes—
61#2589C2218yes—
62#2588C2218yes—
63#2588C2218yes—
64#2587C2218yes—
65#2587C2218yes—
66#2586C2218yes—
67#2585C2218yes—
68#2584C2214yes—
69#2584C2214yes—
70#2583C2218yes—
71#2581C2214yes—
72#2580C2214yes—
73#2579C2218yes—
74#2574C2218yes—
75#2566C2214yes—
76#2565C2214yes—
77#2564C2218yes—
78#2556C2218yes—
79#2550C2214yes—
80#2550C2214yes—
81#2549C2218yes—
82#2522C2218yes—
83#2520C2218yes—
84#2509C2214yes—
85#2508C2214yes—
86#2507C2214yes—
87#2506C2214yes—
88#2505C2218yes—
89#2473C2218yes—
90#2465C2218yes—
91#2462C2218yes—
92#2454C2214yes—
93#2453C2214yes—
94#2452C2214yes—
95#2451C2214yes—
96#2450C2218yes—
97#2449C2218yes—
98#2402C2218yes—
99#2399C2218yes—
100#2396C2218yes—
101#2396C2218yes—
102#2331C2214yes—
103#2331C2214yes—
104#2330C2214yes—
105#2330C2214yes—
106#2329C2218yes—
107#2320C2214yes—
108#2319C2214yes—
109#2318C2218yes—
110#2317C2212yes—
111#2317C2212yes—
112#2317C2212yes—
113#2317C2212yes—
114#2316C2212yes—
115#2314C2214yes—
116#2314C2214yes—
117#2311C2212yes—
118#2311C2212yes—
119C4×C4⋊Q8C2214yes—
120C4×C4⋊Q8C2214yes—
121C4×C4⋊Q8C2212yes—
122C4×C4⋊Q8C2212yes—
123C4×#125C2211yescharacteristic
124C4×#125C2212yes—
125C4×#125C2211yescharacteristic
126C4×#125C2218yes—
127C4×#125C2211yescharacteristic
128C4×#125C2212yes—
129C4×#125C2211yescharacteristic
130C4×#125C2214yes—
131C4×#125C2214yes—
132C4×#125C2212yes—
133C4×#125C2214yes—
134C4×#125C2214yes—
135C4×#125C2212yes—
136C4×C22⋊Q8C2218yes—
137C4×C22⋊Q8C2214yes—
138C4×C22⋊Q8C2218yes—
139C4×C22⋊Q8C2214yes—
140#2296C2218yes—
141#2296C2212yes—
142#2295C2214yes—
143#2295C2218yes—
144#2295C2214yes—
145#2293C2214yes—
146C2×#389C2212yes—
147#2290C2218yes—
148C2×#387C2214yes—
149#2285C2211yescharacteristic
150#2285C2214yes—
151#2283C2214yes—
152C2×#382C2211yescharacteristic
153C42×Q8C2214yes—
154C42×Q8C2212yes—
155C42×Q8C2212yes—
156C42×D4C2214yes—
157C42×D4C2212yes—
158C42×D4C2212yes—
159C42×D4C2214yes—
160C4×#117C2211yescharacteristic
161C4×#117C2212yes—
162C4×#117C2212yes—
163C4×#117C2211yescharacteristic
164C4×#117C2212yes—
165C4×#117C2211yescharacteristic
166C4×#117C2212yes—
167C2×C4×C4⋊C4C2212yes—
168C2×C4×C4⋊C4C2214yes—
169C2×C43C2212yes—
170C2×C43C2211yescharacteristic
171C22×#41C2311yescharacteristic
172#544—216no—
173#533—28no—
174C2×C4⋊Q8C2312yes—
175C2×C4⋊Q8C2314yes—
176C2×C4⋊Q8C2314yes—
177C2×#125—28no—
178C2×#125C2314yes—
179C2×#125C2312yes—
180C2×#125C2311yescharacteristic
181C2×#125C2311yescharacteristic
182C2×#125C2312yes—
183C2×#125C2314yes—
184C2×#125C2314yes—
185C2×#125C2318yes—
186C2×C22⋊Q8C2314yes—
187C2×C22⋊Q8C2318yes—
188C2×C22⋊Q8C2318yes—
189C4×#41—28no—
190C4×#41—28no—
191C4×#41Q8116yescomplemented
192C2×C4×Q8C2312yes—
193C2×C4×Q8C2314yes—
194C2×C4×Q8C2312yes—
195C2×C4×Q8C2318yes—
196C2×C4×Q8C2314yes—
197C2×C4×Q8C2314yes—
198C2×C4×Q8C2311yescharacteristic
199C2×C4×Q8C2311yescharacteristic
200C2×C4×D4C2314yes—
201C2×C4×D4C2312yes—
202C2×C4×D4C2314yes—
203C2×C4×D4C2312yes—
204C2×C4×D4C2312yes—
205C2×C4×D4C2311yescharacteristic
206C2×C4×D4C2312yes—
207C2×C4×D4C2311yescharacteristic
208C2×#117C2312yes—
209C2×#117C2312yes—
210C2×#117C2311yescharacteristic
211C2×#117C2312yes—
212C2×#117C2312yes—
213C2×#117C2318yes—
214C2×#117C2312yes—
215C2×#117C2311yescharacteristic
216C2×#117C2311yescharacteristic
217C22×C4⋊C4C2312yes—
218C22×C4⋊C4C2312yes—
219C22×C4⋊C4C2314yes—
220C22×C4⋊C4C2314yes—
221C22×C42C2312yes—
222C22×C42C2312yes—
223C22×C42C2311yescharacteristic
224C22×C42C2314yes—
225C22×C42C2312yes—
226C22×C42C2312yes—
227C22×C42C2314yes—
228C22×C42C2314yes—
229C22×C42C2311yescharacteristic
230C22×C42C2312yes—
231C22×C42C2311yescharacteristic
232#400C2318yes—
233#400C2318yes—
234#400C2318yes—
235#400C2318yes—
236#400C2318yes—
237#400C2318yes—
238#399C2318yes—
239#399C2318yes—
240#398C2318yes—
241#398C2318yes—
242#398C2318yes—
243#398C2318yes—
244#398C2318yes—
245#398C2318yes—
246#398C2318yes—
247#398C2318yes—
248#398C2318yes—
249#398C2318yes—
250#398C2318yes—
251#398C2318yes—
252#396C2318yes—
253#396C2318yes—
254#396C2318yes—
255#396C2318yes—
256#395C2318yes—
257#395C2318yes—
258#395C2318yes—
259#395C2318yes—
260#395C2318yes—
261#395C2318yes—
262#393C2318yes—
263#393C2318yes—
264#391C2314yes—
265#391C2318yes—
266#391C2318yes—
267#391C2314yes—
268#391C2314yes—
269#391C2314yes—
270#391C2318yes—
271#391C2318yes—
272#391C2318yes—
273#391C2318yes—
274#390C2314yes—
275#390C2314yes—
276#389C2314yes—
277#389C2314yes—
278#389C2314yes—
279#389C2314yes—
280#389C2312yes—
281#389C2312yes—
282#389C2312yes—
283#389C2312yes—
284#389C2314yes—
285#389C2314yes—
286#389C2314yes—
287#389C2314yes—
288#389C2318yes—
289#389C2318yes—
290#389C2314yes—
291#389C2314yes—
292#389C2314yes—
293#389C2314yes—
294#389C2318yes—
295#389C2318yes—
296#389C2314yes—
297#389C2314yes—
298#389C2314yes—
299#389C2314yes—
300#389C2314yes—
301#389C2314yes—
302#389C2318yes—
303#389C2318yes—
304#389C2318yes—
305#389C2318yes—
306#389C2318yes—
307#389C2318yes—
308#389C2318yes—
309#389C2318yes—
310#388C2318yes—
311#388C2318yes—
312#388C2318yes—
313#388C2318yes—
314#387C2318yes—
315#387C2318yes—
316#387C2318yes—
317#387C2318yes—
318#387C2318yes—
319#387C2318yes—
320#387C2318yes—
321#387C2318yes—
322#387C2318yes—
323#387C2318yes—
324#387C2318yes—
325#387C2318yes—
326#387C2314yes—
327#387C2314yes—
328#387C2314yes—
329#387C2314yes—
330#387C2318yes—
331#387C2318yes—
332#387C2318yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#386C2318yes—
343#386C2318yes—
344#385C2318yes—
345#385C2318yes—
346#385C2318yes—
347#385C2318yes—
348#385C2318yes—
349#385C2318yes—
350#385C2318yes—
351#385C2318yes—
352#385C2318yes—
353#385C2318yes—
354#385C2314yes—
355#385C2314yes—
356#384C2312yes—
357#384C2314yes—
358#384C2314yes—
359#384C2314yes—
360#384C2314yes—
361#383C2318yes—
362#382C2314yes—
363#382C2311yescharacteristic
364#382C2312yes—
365#382C2311yescharacteristic
366#382C2312yes—
367#382C2314yes—
368#382C2314yes—
369#382C2318yes—
370#382C2314yes—
371#382C2314yes—
372#382C2318yes—
373#381C2318yes—
374#380C2318yes—
375#380C2314yes—
376#380C2314yes—
377#380C2314yes—
378#380C2314yes—
379#380C2318yes—
380#380C2318yes—
381#380C2314yes—
382C4×C4⋊C4C2314yes—
383C4×C4⋊C4C2314yes—
384C4×C4⋊C4C2312yes—
385C4×C4⋊C4C2318yes—
386C4×C4⋊C4C2318yes—
387C4×C4⋊C4C2314yes—
388C4×C4⋊C4C2312yes—
389C4×C4⋊C4C2318yes—
390C4×C4⋊C4C2314yes—
391C4×C4⋊C4C2318yes—
392C4×C4⋊C4C2314yes—
393C4×C4⋊C4C2318yes—
394C4×C4⋊C4C2318yes—
395C4×C4⋊C4C2318yes—
396C4×C4⋊C4C2312yes—
397C4×C4⋊C4C2312yes—
398C4×C4⋊C4C2312yes—
399C4×C4⋊C4C2318yes—
400C4×C4⋊C4C2314yes—
401C4×C4⋊C4C2314yes—
402C4×C4⋊C4C2314yes—
403C4×C4⋊C4C2314yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2312yes—
407C4×C4⋊C4C2312yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2312yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2312yes—
418C4×C4⋊C4C2312yes—
419C4×C22⋊C4C2314yes—
420C4×C22⋊C4C2314yes—
421C4×C22⋊C4C2314yes—
422C4×C22⋊C4C2312yes—
423C4×C22⋊C4C2314yes—
424C4×C22⋊C4C2314yes—
425C4×C22⋊C4C2314yes—
426C4×C22⋊C4C2318yes—
427C4×C22⋊C4C2314yes—
428C4×C22⋊C4C2314yes—
429C4×C22⋊C4C2314yes—
430C4×C22⋊C4C2312yes—
431C4×C22⋊C4C2314yes—
432#376C2314yes—
433#376C2312yes—
434#376C2312yes—
435#376C2318yes—
436#376C2312yes—
437C2×#95C2314yes—
438C2×#95C2314yes—
439C2×#95C2314yes—
440C43C2311yescharacteristic
441C43C2311yescharacteristic
442C43C2312yes—
443C43C2311yescharacteristic
444C43C2311yescharacteristic
445C43C2312yes—
446C43C2312yes—
447C43C2314yes—
448C43C2314yes—
449C43C2312yes—
450C43C2312yes—
451C43C2314yes—
452C2×#41—24no—
453C2×#41—24no—
454C2×#41C2×Q818yes—
455C22×Q8C2411yescharacteristic
456C22×Q8C2414yes—
457C22×Q8C2418yes—
458C22×D4C2412yes—
459C22×D4C2411yescharacteristic
460C23×C4C2412yes—
461C23×C4C2414yes—
462C23×C4C2412yes—
463C23×C4C2412yes—
464C23×C4C2411yescharacteristic
465C23×C4C2414yes—
466C23×C4C2414yes—
467C23×C4C2414yes—
468C23×C4C2411yescharacteristic
469C23×C4C2412yes—
470C23×C4C2412yes—
471C23×C4C2411yescharacteristic
472C4⋊Q8—216no—
473C4⋊Q8—28no—
474C4⋊Q8—216no—
475#125—216no—
476#125—28no—
477#125—28no—
478#125—216no—
479#125—24no—
480#125—24no—
481#125—216no—
482#125—416no—
483C22⋊Q8—216no—
484C22⋊Q8—232no—
485C22⋊Q8—416no—
486C4×Q8—28no—
487C4×Q8—28no—
488C4×Q8—216no—
489C4×Q8—416no—
490C4×Q8—48no—
491C4×Q8—48no—
492C4×Q8C2×Q818yes—
493C4×Q8C2×Q818yes—
494C4×D4—216no—
495C4×D4—28no—
496C4×D4—216no—
497C4×D4—28no—
498C4×D4C2×Q8116yes—
499C4×D4C2×Q818yes—
500C4×D4C2×Q8116yes—
501C4×D4C2×Q818yes—
502#117—24no—
503#117—28no—
504#117—28no—
505#117—28no—
506#117—28no—
507#117—416no—
508#117C2×Q8116yes—
509#117C2×Q818yes—
510#117#4118yes—
511C2×C4⋊C4—216no—
512C2×C4⋊C4—28no—
513C2×C4⋊C4—28no—
514C2×C4⋊C4—48no—
515C2×C4⋊C4C2418yes—
516C2×C4⋊C4C2414yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2418yes—
519C2×C4⋊C4C2418yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2412yes—
523C2×C4⋊C4C2414yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2412yes—
526C2×C4⋊C4C2412yes—
527C2×C4⋊C4C2412yes—
528C2×C4⋊C4C2412yes—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2414yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2414yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2418yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2418yes—
537C2×C4⋊C4C2418yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2418yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C2418yes—
551C2×C4⋊C4C2418yes—
552C2×C4⋊C4C2412yes—
553C2×C4⋊C4C2412yes—
554C2×C4⋊C4C2411yescharacteristic
555C2×C4⋊C4C2411yescharacteristic
556C2×C4⋊C4C2412yes—
557C2×C22⋊C4C2412yes—
558C2×C22⋊C4C2414yes—
559C2×C22⋊C4C2414yes—
560C2×C22⋊C4C2414yes—
561C2×C22⋊C4C2414yes—
562C2×C22⋊C4C2418yes—
563C2×C22⋊C4C2418yes—
564C2×C22⋊C4C2418yes—
565C2×C22⋊C4C2418yes—
566C2×C22⋊C4C2412yes—
567C2×C22⋊C4C2412yes—
568C2×C22⋊C4C2412yes—
569C2×C22⋊C4C2412yes—
570C2×C42—24no—
571C2×C42—28no—
572C2×C42—28no—
573C2×C42—44no—
574C2×C42—48no—
575C2×C42—44no—
576C2×C42—48no—
577C2×C42—48no—
578C2×C42C2×Q8116yes—
579C2×C42C2×Q818yes—
580C2×C42#4118yes—
581C2×C42C2412yes—
582C2×C42C2411yescharacteristic
583C2×C42C2414yes—
584C2×C42C2414yes—
585C2×C42C2412yes—
586C2×C42C2414yes—
587C2×C42C2414yes—
588C2×C42C2412yes—
589C2×C42C2414yes—
590C2×C42C2412yes—
591C2×C42C2411yescharacteristic
592C2×C42C2414yes—
593C2×C42C2418yes—
594C2×C42C2414yes—
595C2×C42C2414yes—
596C2×C42C2412yes—
597C2×C42C2412yes—
598C2×C42C2414yes—
599C2×C42C2414yes—
600C2×C42C2412yes—
601C2×C42C2412yes—
602C2×C42C2412yes—
603C2×C42C2414yes—
604C2×C42C2412yes—
605C2×C42C2414yes—
606C2×C42C2414yes—
607C2×C42C2414yes—
608C2×C42C2418yes—
609C2×C42C2411yescharacteristic
610C2×C42C2412yes—
611C2×C42C2411yescharacteristic
612C2×C42C2412yes—
613C2×C42C2411yescharacteristic
614C2×C42C2412yes—
615C2×C42C2411yescharacteristic
616C2×C42C2412yes—
617C2×C42C2411yescharacteristic
618C2×C42C2412yes—
619C2×C42C2411yescharacteristic
620#95C2418yes—
621#95C2418yes—
622#95C2418yes—
623#95C2418yes—
624#95C2418yes—
625#95C2418yes—
626#95C2414yes—
627#95C2414yes—
628#95C2414yes—
629#95C2414yes—
630#95C2414yes—
631#95C2414yes—
632#95C2414yes—
633#95C2414yes—
634#95C2414yes—
635#95C2414yes—
636#95C2418yes—
637#95C2418yes—
638#95C2418yes—
639#95C2418yes—
640#95C2418yes—
641#95C2418yes—
642#95C2414yes—
643#95C2414yes—
644#95C2414yes—
645#95C2414yes—
646#95C2414yes—
647#95C2414yes—
648#95C2418yes—
649#95C2418yes—
650#95C2418yes—
651#95C2418yes—
652#95C2418yes—
653#95C2418yes—
654#95C2418yes—
655#95C2418yes—
656C24C2512yes—
657C24C2511yescharacteristic
658#41—232no—
659C2×Q8—22no—
660C2×Q8—22no—
661C2×Q8—28no—
662C2×Q8—216no—
663C2×Q8—44no—
664C2×Q8—44no—
665C2×Q8—48no—
666C2×Q8—48no—
667C2×Q8C22×Q814yes—
668C2×D4—24no—
669C2×D4—24no—
670C2×D4—22no—
671C2×D4—22no—
672C2×D4C22×Q818yes—
673C2×D4C22×Q814yes—
674C22×C4—24no—
675C22×C4—24no—
676C22×C4—24no—
677C22×C4—28no—
678C22×C4—24no—
679C22×C4—28no—
680C22×C4—28no—
681C22×C4—28no—
682C22×C4—28no—
683C22×C4—24no—
684C22×C4—28no—
685C22×C4—42no—
686C22×C4—44no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—44no—
690C22×C4—42no—
691C22×C4—44no—
692C22×C4—44no—
693C22×C4—44no—
694C22×C4—44no—
695C22×C4—44no—
696C22×C4—44no—
697C22×C4C22×Q818yes—
698C22×C4C22×Q818yes—
699C22×C4C22×Q814yes—
700C22×C4C22×Q818yes—
701C22×C4C22×Q814yes—
702C22×C4C22×Q814yes—
703C22×C4C2×#4118yes—
704C22×C4C2×#4114yes—
705C22×C4C2×#4114yes—
706C22×C4C2514yes—
707C22×C4C2518yes—
708C22×C4C2514yes—
709C22×C4C2512yes—
710C22×C4C2514yes—
711C22×C4C2514yes—
712C22×C4C2518yes—
713C22×C4C2514yes—
714C22×C4C2511yescharacteristic
715C22×C4C2512yes—
716C22×C4C2511yescharacteristic
717C22×C4C2511yescharacteristic
718C22×C4C2512yes—
719C22×C4C2512yes—
720C22×C4C2512yes—
721C22×C4C2512yes—
722C22×C4C2514yes—
723C22×C4C2512yes—
724C22×C4C2511yescharacteristic
725C22×C4C2511yescharacteristic
726C22×C4C2511yescharacteristic
727C4⋊C4—216no—
728C4⋊C4—216no—
729C4⋊C4—28no—
730C4⋊C4—28no—
731C4⋊C4—28no—
732C4⋊C4—28no—
733C4⋊C4—28no—
734C4⋊C4—28no—
735C4⋊C4—24no—
736C4⋊C4—24no—
737C4⋊C4—24no—
738C4⋊C4—24no—
739C4⋊C4—24no—
740C4⋊C4—28no—
741C4⋊C4—28no—
742C4⋊C4—28no—
743C4⋊C4—216no—
744C4⋊C4—216no—
745C4⋊C4—216no—
746C4⋊C4—216no—
747C4⋊C4—28no—
748C4⋊C4—28no—
749C4⋊C4—48no—
750C4⋊C4—48no—
751C4⋊C4—48no—
752C4⋊C4—48no—
753C4⋊C4—44no—
754C4⋊C4—44no—
755C4⋊C4—48no—
756C4⋊C4—48no—
757C4⋊C4—44no—
758C4⋊C4—44no—
759C4⋊C4—48no—
760C4⋊C4—48no—
761C4⋊C4—48no—
762C4⋊C4—48no—
763C4⋊C4—48no—
764C4⋊C4C22×Q818yes—
765C4⋊C4C22×Q818yes—
766C4⋊C4C22×Q814yes—
767C4⋊C4C22×Q814yes—
768C4⋊C4C2×#4118yes—
769C22⋊C4—24no—
770C22⋊C4—28no—
771C22⋊C4—28no—
772C22⋊C4—28no—
773C22⋊C4—28no—
774C22⋊C4—48no—
775C22⋊C4—48no—
776C22⋊C4—48no—
777C22⋊C4—48no—
778C22⋊C4C22×Q818yes—
779C22⋊C4C22×Q818yes—
780C22⋊C4C22×Q818yes—
781C22⋊C4C2×#4118yes—
782C42—22no—
783C42—22no—
784C42—24no—
785C42—28no—
786C42—24no—
787C42—28no—
788C42—28no—
789C42—28no—
790C42—24no—
791C42—24no—
792C42—216no—
793C42—24no—
794C42—28no—
795C42—24no—
796C42—28no—
797C42—28no—
798C42—28no—
799C42—42no—
800C42—44no—
801C42—42no—
802C42—44no—
803C42—42no—
804C42—42no—
805C42—44no—
806C42—44no—
807C42—48no—
808C42—44no—
809C42—44no—
810C42C22×Q814yes—
811C42C22×Q814yes—
812C42C22×Q818yes—
813C42C22×Q818yes—
814C42C22×Q814yes—
815C42C22×Q818yes—
816C42C22×Q814yes—
817C42C2×#4114yes—
818C42C2×#4118yes—
819C42C2×#4114yes—
820C42C2×#4118yes—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—24no—
826C23—24no—
827C23C23×Q814yes—
828C23C23×Q812yes—
829C23C22×#4112yes—
830C23C22×#4112yes—
831C23C2611yescharacteristic
832Q8—28no—
833Q8—416no—
834Q8—816no—
835D4—216no—
836D4—28no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—24no—
846C2×C4—24no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—24no—
851C2×C4—24no—
852C2×C4—216no—
853C2×C4—28no—
854C2×C4—216no—
855C2×C4—22no—
856C2×C4—24no—
857C2×C4—24no—
858C2×C4—24no—
859C2×C4—24no—
860C2×C4—24no—
861C2×C4—28no—
862C2×C4—28no—
863C2×C4—28no—
864C2×C4—28no—
865C2×C4—22no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—24no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—22no—
873C2×C4—24no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—24no—
877C2×C4—28no—
878C2×C4—28no—
879C2×C4—44no—
880C2×C4—48no—
881C2×C4—48no—
882C2×C4—416no—
883C2×C4—48no—
884C2×C4—416no—
885C2×C4—416no—
886C2×C4—88no—
887C2×C4#533116yes—
888C2×C4C23×Q812yes—
889C2×C4C23×Q812yes—
890C2×C4C23×Q814yes—
891C2×C4C23×Q812yes—
892C2×C4C23×Q814yes—
893C2×C4C23×Q814yes—
894C2×C4C23×Q812yes—
895C2×C4C23×Q812yes—
896C2×C4C23×Q812yes—
897C2×C4C22×#4114yes—
898C2×C4C22×#4118yes—
899C2×C4C22×#4114yes—
900C2×C4C22×#4112yes—
901C2×C4C22×#4112yes—
902C2×C4C22×#4112yes—
903C2×C4C22×#4112yes—
904C2×C4#58514yes—
905C2×C4#58514yes—
906C22—22no—
907C22—24no—
908C22—22no—
909C22—24no—
910C22—24no—
911C22—24no—
912C22—24no—
913C22—44no—
914C22—44no—
915C22C2×#53314yes—
916C22C24×Q811yescharacteristic
917C22C23×#4111yescharacteristic
918C22C23×#4111yescharacteristic
919C22C2×#58512yes—
920C22C2×#58512yes—
921C4—22no—
922C4—24no—
923C4—24no—
924C4—28no—
925C4—22no—
926C4—22no—
927C4—24no—
928C4—24no—
929C4—24no—
930C4—24no—
931C4—44no—
932C4—42no—
933C4—48no—
934C4—44no—
935C4—44no—
936C4—48no—
937C4—44no—
938C4—44no—
939C4C2×#53314yes—
940C4C2×#53314yes—
941C4#350414yes—
942C2—24no—
943C2—44no—
944C2C22×#53311yescharacteristic
945C2#6268612yes—
946C2C2×#350411yescharacteristic
947C2#6281012yes—
948C2#6281311yescharacteristic
subgroupG/H
centerC22×C4C25
commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
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. #36640C2semidirect
2. #36635C2semidirect
3. #35337C2semidirect
4. #35336C2semidirect
5. #35335C2semidirect
8. #35330C2semidirect
9. #35282C2semidirect
10. #35265C2semidirect
12. #35221C2semidirect
13. #35175C2semidirect
14. #35018C2semidirect
15. #34920C2semidirect
16. #34893C2semidirect
17. #34840C2semidirect
18. #34625C2semidirect
19. C4×#544C2semidirect
21. C4×#533C2semidirect
22. C2×C4×#125C2semidirect
191. C4×#41Q8semidirect

Maximal subgroups

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

subgroupindex
#366402
#366352
#353372
#353362
#353352
#353342
#353332
#353302
#352822
#352652
#352572
#352212
#351752
#350182
#349202
#348932
#348402
#346252
C4×#5442
#340602
C4×#5332
C2×C4×#1252
C42×#412