Finite Group Databasebeta

← #7667009

Subgroups — #7667009

Order 512.

5832 conjugacy classes of subgroups.

The subgroup lattice has 1021 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59621C214yesmaximal, complemented
2#59538C214yesmaximal, complemented
3#59510C214yesmaximal, complemented
4#59488C214yesmaximal, complemented
5#59466C211yesmaximal, characteristic, complemented
6#59436C212yesmaximal, complemented
7#59420C211yesmaximal, characteristic, complemented
8#59404C214yesmaximal, complemented
9#59382C214yesmaximal, complemented
10#59235C212yesmaximal, complemented
11#59070C211yesmaximal, characteristic, complemented
12#59041C211yesmaximal, characteristic
13#52185C214yesmaximal, complemented
14#34941C212yesmaximal, complemented
15#34917C214yesmaximal, complemented
16#34913C214yesmaximal, complemented
17#34875C214yesmaximal, complemented
18#34700C214yesmaximal, complemented
19C4×#559C211yesmaximal, characteristic, complemented
20C4×D42C211yesmaximal, characteristic, complemented
21D4×#117C214yesmaximal, complemented
22C4×#532C211yesmaximal, characteristic, complemented
23C4×#529C212yesmaximal, complemented
24C2×#559C2211yescharacteristic
25C2×D42C2211yescharacteristic
26C2×#532C2211yescharacteristic
27C2×#529C2212yes—
28C2×C4×#41C2212yescomplemented
29C22×C4×D4C2214yes—
30C22×#117C2214yescomplemented
31#2748C2214yescomplemented
32#2747C2218yescomplemented
33#2746C2218yescomplemented
34#2745C2218yescomplemented
35#2744C2218yescomplemented
36#2743C2218yescomplemented
37#2735C2218yescomplemented
38#2717C2214yescomplemented
39#2697C2214yes—
40#2684C2214yes—
41#2609C2218yescomplemented
42#2609C2218yescomplemented
43#2599C2218yescomplemented
44#2598C2218yescomplemented
45#2579C2214yescomplemented
46#2579C2214yescomplemented
47#2578C2218yescomplemented
48#2578C2218yescomplemented
49#2577C2218yescomplemented
50#2576C2218yescomplemented
51#2576C2218yescomplemented
52#2575C2218yescomplemented
53#2574C2218yescomplemented
54#2570C2214yescomplemented
55#2567C2212yescomplemented
56#2566C2214yescomplemented
57#2563C2212yes—
58#2562C2214yescomplemented
59#2552C2212yescomplemented
60#2538C2212yes—
61#2535C2214yes—
62#2534C2214yes—
63#2534C2214yescomplemented
64#2515C2218yescomplemented
65#2514C2214yescomplemented
66#2508C2214yescomplemented
67#2508C2214yescomplemented
68#2497C2214yescomplemented
69#2497C2214yescomplemented
70#2495C2214yescomplemented
71#2494C2214yescomplemented
72#2489C2214yescomplemented
73#2484C2214yescomplemented
74#2482C2214yescomplemented
75#2480C2218yescomplemented
76#2468C2218yescomplemented
77#2457C2218yescomplemented
78#2457C2218yescomplemented
79#2454C2214yes—
80#2454C2214yescomplemented
81#2454C2214yescomplemented
82#2447C2214yes—
83#2447C2214yescomplemented
84#2442C2214yescomplemented
85#2435C2214yes—
86#2427C2214yes—
87#2427C2214yescomplemented
88#2423C2214yescomplemented
89#2422C2214yescomplemented
90#2420C2214yes—
91#2420C2214yes—
92#2420C2214yes—
93#2418C2218yescomplemented
94#2417C2214yescomplemented
95#2408C2214yes—
96#2406C2214yescomplemented
97#2404C2214yes—
98#2401C2218yescomplemented
99#2396C2218yescomplemented
100#2395C2218yescomplemented
101#2392C2218yescomplemented
102#2374C2214yescomplemented
103#2367C2214yescomplemented
104#2366C2211yescharacteristic
105#2366C2211yescharacteristic
106#2361C2214yes—
107#2358C2214yes—
108#2357C2214yescomplemented
109#2355C2212yescomplemented
110#2354C2214yes—
111#2354C2214yes—
112#2352C2218yescomplemented
113#2352C2218yescomplemented
114D4×C4⋊C4C2212yes—
115D4×C4⋊C4C2214yescomplemented
116D4×C4⋊C4C2214yescomplemented
117#2344C2214yescomplemented
118#2344C2214yescomplemented
119#2342C2218yescomplemented
120#2342C2218yescomplemented
121D4×C22⋊C4C2214yes—
122D4×C22⋊C4C2214yes—
123D4×C22⋊C4C2214yes—
124C4×C4⋊Q8C2211yescharacteristic, complemented
125C4×C4⋊Q8C2211yescharacteristic, complemented
126C4×#127C2211yescharacteristic
127C4×#127C2211yescharacteristic
128C4×#125C2212yescomplemented
129C4×#125C2214yescomplemented
130C4×#125C2212yescomplemented
131C4×#126C2214yescomplemented
132C4×#126C2214yescomplemented
133C4×#124C2212yes—
134C4×#124C2212yes—
135C4×#124C2214yescomplemented
136C4×#124C2212yescomplemented
137C4×#124C2212yescomplemented
138C4×C22⋊Q8C2212yescomplemented
139C4×C22⋊Q8C2214yescomplemented
140C4×C22⋊Q8C2212yescomplemented
141C4×#123C2214yescomplemented
142C4×#123C2214yescomplemented
143C4×#123C2214yescomplemented
144C4×#123C2214yescomplemented
145C4×#121C2214yes—
146C4×#121C2212yes—
147C4×#121C2212yes—
148C4×#121C2214yescomplemented
149C4×#121C2214yescomplemented
150C4×#120C2214yes—
151C4×#120C2214yescomplemented
152#2298C2214yescomplemented
153#2297C2212yescomplemented
154#2295C2212yescomplemented
155#2293C2212yes—
156#2293C2214yes—
157#2293C2214yescomplemented
158#2290C2214yescomplemented
159#2290C2218yescomplemented
160#2290C2218yescomplemented
161#2285C2214yescomplemented
162#2285C2211yescharacteristic, complemented
163#2283C2214yescomplemented
164#2283C2212yescomplemented
165#2280C2218yescomplemented
166C42×Q8C2212yescomplemented
167C42×D4C2212yes—
168C42×D4C2214yescomplemented
169C42×D4C2214yescomplemented
170C42×D4C2214yescomplemented
171C4×#117C2214yescomplemented
172C2×C43C2211yescharacteristic, complemented
173C22×#41C2312yes—
174C23×D4C2314yes—
175C24×C4C2314yes—
176#559—28no—
177D42—28no—
178#532—28no—
179C2×C4⋊Q8C2311yescharacteristic
180C2×#127C2311yescharacteristic
181#529—216no—
182C2×#126C2314yes—
183C2×#125C2312yes—
184C2×#125C2314yes—
185C2×#124C2314yes—
186C2×#124C2312yes—
187C2×#124C2312yes—
188C2×#123C2314yes—
189C2×#123C2314yes—
190C2×#123C2314yes—
191C2×C22⋊Q8C2312yes—
192C2×C22⋊Q8C2314yes—
193C2×#121C2314yes—
194C2×#121C2312yes—
195C2×#121C2314yes—
196C2×#120C2314yes—
197C2×#120C2314yes—
198C4×#41—48no—
199C2×C4×Q8C2312yes—
200C2×C4×Q8C2312yes—
201C2×C4×Q8C2312yes—
202C2×C4×Q8C2312yes—
203C2×C4×Q8C2312yes—
204C2×C4×D4—232no—
205C2×C4×D4C2314yes—
206C2×C4×D4C2312yes—
207C2×C4×D4C2314yes—
208C2×C4×D4C2314yes—
209C2×C4×D4C2314yes—
210C2×C4×D4C2314yes—
211C2×C4×D4C2318yes—
212C2×C4×D4C2314yes—
213C2×C4×D4C2318yes—
214C2×C4×D4C2312yes—
215C2×C4×D4C2314yes—
216C2×C4×D4C2312yes—
217C2×C4×D4C2314yes—
218C2×C4×D4C2314yes—
219C2×C4×D4C2314yes—
220C2×C4×D4C2312yes—
221C2×C4×D4C2314yes—
222C2×C4×D4C2314yes—
223C2×C4×D4C2312yes—
224C2×#117—416no—
225C2×#117C2314yes—
226C2×#117C2314yes—
227C2×#117C2318yes—
228C2×#117C2318yes—
229C2×#117C2312yes—
230C2×#117C2314yes—
231C2×#117C2318yes—
232C22×C4⋊C4C2314yes—
233C22×C4⋊C4C2314yes—
234C22×C4⋊C4C2314yes—
235C22×C22⋊C4C2318yes—
236C22×C22⋊C4C2314yes—
237C22×C22⋊C4C2314yes—
238C22×C42C2314yes—
239C22×C42C2314yes—
240C22×C42C2311yescharacteristic
241C22×C42C2312yes—
242C22×C42C2311yescharacteristic
243C22×C42C2314yes—
244C22×C42C2311yescharacteristic
245C22×C42C2312yes—
246#401C2318yes—
247#400C2318yes—
248#400C2318yes—
249#400C2318yes—
250#400C2318yes—
251#400C2318yes—
252#399C2318yes—
253#399C2318yes—
254#398C2318yes—
255#398C2318yes—
256#398C2318yes—
257#398C2318yes—
258#397C2318yes—
259#397C2318yes—
260#397C2318yes—
261#397C2318yes—
262#397C2318yes—
263#397C2318yes—
264#397C2318yes—
265#396C2318yes—
266#396C2318yes—
267#396C2318yes—
268#396C2318yes—
269#396C2318yes—
270#395C2318yes—
271#394C2318yes—
272#394C2318yes—
273#394C2318yes—
274#394C2318yes—
275#394C2318yes—
276#393C2318yes—
277#392C2318yes—
278#391C2312yes—
279#391C2312yes—
280#391C2314yes—
281#391C2314yes—
282#391C2312yes—
283#391C2312yes—
284#390C2314yes—
285#390C2314yes—
286#390C2312yes—
287#390C2312yes—
288#390C2314yes—
289#390C2314yes—
290#390C2312yes—
291#390C2312yes—
292#390C2314yes—
293#390C2314yes—
294#389C2314yes—
295#389C2312yes—
296#389C2312yes—
297#389C2312yes—
298#389C2314yes—
299#389C2312yes—
300#389C2314yes—
301#389C2314yes—
302#389C2314yes—
303#389C2314yes—
304#389C2314yes—
305#389C2314yes—
306#388C2314yes—
307#388C2314yes—
308#388C2314yes—
309#388C2314yes—
310#388C2314yes—
311#388C2314yes—
312#388C2318yes—
313#388C2318yes—
314#388C2318yes—
315#388C2318yes—
316#388C2318yes—
317#388C2318yes—
318#388C2318yes—
319#388C2318yes—
320#388C2318yes—
321#388C2318yes—
322#388C2318yes—
323#388C2318yes—
324#388C2314yes—
325#388C2314yes—
326#388C2318yes—
327#387C2314yes—
328#387C2314yes—
329#387C2314yes—
330#387C2314yes—
331#387C2314yes—
332#387C2314yes—
333#387C2318yes—
334#387C2318yes—
335#387C2314yes—
336#387C2314yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2318yes—
344#386C2314yes—
345#386C2318yes—
346#386C2318yes—
347#386C2318yes—
348#386C2318yes—
349#386C2318yes—
350#386C2314yes—
351#386C2314yes—
352#386C2314yes—
353#386C2318yes—
354#386C2318yes—
355#386C2314yes—
356#386C2318yes—
357#386C2314yes—
358#385C2314yes—
359#385C2318yes—
360#385C2318yes—
361#385C2318yes—
362#385C2318yes—
363#385C2314yes—
364#385C2314yes—
365#385C2314yes—
366#385C2314yes—
367#385C2318yes—
368#385C2318yes—
369#385C2318yes—
370#385C2314yes—
371#384C2311yescharacteristic
372#384C2311yescharacteristic
373#384C2314yes—
374#384C2314yes—
375#383C2314yes—
376#383C2318yes—
377#382C2314yes—
378#382C2312yes—
379#382C2312yes—
380#382C2318yes—
381#382C2318yes—
382#382C2314yes—
383#382C2312yes—
384#381C2314yes—
385#381C2314yes—
386#381C2314yes—
387#381C2318yes—
388#381C2318yes—
389#381C2314yes—
390#381C2314yes—
391#380C2312yes—
392#380C2314yes—
393#380C2314yes—
394#380C2314yes—
395#380C2314yes—
396#380C2314yes—
397#380C2318yes—
398#380C2314yes—
399#380C2314yes—
400#380C2318yes—
401#380C2318yes—
402#380C2318yes—
403#380C2318yes—
404#380C2312yes—
405#379C2314yes—
406#379C2318yes—
407#379C2318yes—
408#379C2314yes—
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2312yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2312yes—
418C4×C4⋊C4C2312yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2312yes—
422C4×C4⋊C4C2312yes—
423C4×C4⋊C4C2318yes—
424C4×C4⋊C4C2318yes—
425C4×C4⋊C4C2314yes—
426C4×C4⋊C4C2314yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2314yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2312yes—
432C4×C22⋊C4C2314yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2314yes—
435C4×C22⋊C4C2314yes—
436C4×C22⋊C4C2314yes—
437C4×C22⋊C4C2314yes—
438C4×C22⋊C4C2318yes—
439C4×C22⋊C4C2314yes—
440C4×C22⋊C4C2314yes—
441C4×C22⋊C4C2318yes—
442C4×C22⋊C4C2318yes—
443C4×C22⋊C4C2314yes—
444C4×C22⋊C4C2318yes—
445C4×C22⋊C4C2314yes—
446C4×C22⋊C4C2318yes—
447C4×C22⋊C4C2314yes—
448C4×C22⋊C4C2318yes—
449C4×C22⋊C4C2318yes—
450C4×C22⋊C4C2314yes—
451C4×C22⋊C4C2314yes—
452C4×C22⋊C4C2314yes—
453C4×C22⋊C4C2314yes—
454#376C2314yes—
455#376C2314yes—
456C43C2311yescharacteristic
457C43C2312yes—
458C43C2311yescharacteristic
459C43C2314yes—
460C43C2311yescharacteristic
461C43C2312yes—
462C43C2311yescharacteristic
463C25C2414yes—
464C2×#41—28no—
465C2×#41—44no—
466C2×#41—44no—
467C22×Q8C2412yes—
468C22×Q8C2412yes—
469C22×D4—216no—
470C22×D4—216no—
471C22×D4—48no—
472C22×D4C2414yes—
473C22×D4C2414yes—
474C22×D4C2418yes—
475C22×D4C2414yes—
476C22×D4C2412yes—
477C22×D4C2412yes—
478C23×C4—232no—
479C23×C4—48no—
480C23×C4C2414yes—
481C23×C4C2411yescharacteristic
482C23×C4C2412yes—
483C23×C4C2411yescharacteristic
484C23×C4C2414yes—
485C23×C4C2418yes—
486C23×C4C2414yes—
487C23×C4C2414yes—
488C23×C4C2412yes—
489C23×C4C2414yes—
490C23×C4C2414yes—
491C23×C4C2414yes—
492C23×C4C2414yes—
493C23×C4C2411yescharacteristic
494C23×C4C2414yes—
495C4⋊Q8—24no—
496#127#4118yes—
497#126—216no—
498#125—28no—
499#125—48no—
500#124—28no—
501#124—28no—
502#124—216no—
503#123—216no—
504#123—216no—
505#123—48no—
506C22⋊Q8—28no—
507C22⋊Q8—48no—
508#121—28no—
509#121—216no—
510#121—216no—
511#120—216no—
512#120—48no—
513C4×Q8—28no—
514C4×Q8—28no—
515C4×Q8—44no—
516C4×Q8—44no—
517C4×Q8—44no—
518C4×D4—216no—
519C4×D4—216no—
520C4×D4—216no—
521C4×D4—232no—
522C4×D4—216no—
523C4×D4—216no—
524C4×D4—232no—
525C4×D4—216no—
526C4×D4—28no—
527C4×D4—48no—
528C4×D4—44no—
529C4×D4—48no—
530C4×D4—48no—
531C4×D4—48no—
532C4×D4—48no—
533C4×D4—44no—
534C4×D4—44no—
535C4×D4—48no—
536C4×D4#41116yescomplemented
537#117—216no—
538#117—216no—
539#117—416no—
540#117—44no—
541#117—48no—
542#117—416no—
543#117—416no—
544C2×C4⋊C4—216no—
545C2×C4⋊C4—48no—
546C2×C4⋊C4—48no—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2418yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2412yes—
554C2×C4⋊C4C2412yes—
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2412yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2412yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2418yes—
564C2×C4⋊C4C2418yes—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2412yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2418yes—
573C2×C4⋊C4C2418yes—
574C2×C4⋊C4C2418yes—
575C2×C4⋊C4C2418yes—
576C2×C4⋊C4C2412yes—
577C2×C22⋊C4—232no—
578C2×C22⋊C4—48no—
579C2×C22⋊C4—48no—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2414yes—
588C2×C22⋊C4C2418yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2414yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2414yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2418yes—
604C2×C22⋊C4C2418yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2418yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2414yes—
611C2×C42—216no—
612C2×C42—28no—
613C2×C42—24no—
614C2×C42—216no—
615C2×C42—24no—
616C2×C42—48no—
617C2×C42—44no—
618C2×C42—42no—
619C2×C42C2411yescharacteristic
620C2×C42C2414yes—
621C2×C42C2414yes—
622C2×C42C2411yescharacteristic
623C2×C42C2414yes—
624C2×C42C2412yes—
625C2×C42C2412yes—
626C2×C42C2414yes—
627C2×C42C2414yes—
628C2×C42C2414yes—
629C2×C42C2412yes—
630C2×C42C2411yescharacteristic
631C2×C42C2412yes—
632C2×C42C2412yes—
633C2×C42C2414yes—
634C2×C42C2414yes—
635C2×C42C2412yes—
636C2×C42C2414yes—
637C2×C42C2411yescharacteristic
638C2×C42C2414yes—
639C2×C42C2418yes—
640C2×C42C2414yes—
641C2×C42C2414yes—
642C2×C42C2412yes—
643C2×C42C2412yes—
644C2×C42C2411yescharacteristic
645C2×C42C2412yes—
646C2×C42C2411yescharacteristic
647C2×C42C2411yescharacteristic
648C2×C42C2412yes—
649C2×C42C2411yescharacteristic
650#95C2414yes—
651#95C2414yes—
652#95C2414yes—
653#95C2414yes—
654#95C2414yes—
655#95C2414yes—
656#95C2414yes—
657#95C2414yes—
658#95C2414yes—
659#95C2414yes—
660#95C2414yes—
661#95C2418yes—
662#95C2418yes—
663#95C2418yes—
664#95C2418yes—
665#95C2418yes—
666#95C2414yes—
667#95C2414yes—
668#95C2414yes—
669#95C2414yes—
670#95C2414yes—
671#95C2414yes—
672#95C2414yes—
673#95C2418yes—
674#95C2418yes—
675#95C2418yes—
676#95C2418yes—
677#95C2414yes—
678#95C2414yes—
679#95C2418yes—
680#95C2418yes—
681#95C2418yes—
682#95C2418yes—
683C24—216no—
684C24—28no—
685C24—44no—
686C24—48no—
687C24—44no—
688C24C2514yes—
689C24C2514yes—
690C24C2511yescharacteristic
691#41—432no—
692C2×Q8—24no—
693C2×Q8—24no—
694C2×Q8—24no—
695C2×Q8—24no—
696C2×Q8—42no—
697C2×Q8—42no—
698C2×D4—216no—
699C2×D4—28no—
700C2×D4—216no—
701C2×D4—28no—
702C2×D4—28no—
703C2×D4—28no—
704C2×D4—28no—
705C2×D4—24no—
706C2×D4—28no—
707C2×D4—24no—
708C2×D4—42no—
709C2×D4—44no—
710C2×D4—44no—
711C2×D4—48no—
712C2×D4—42no—
713C2×D4—464no—
714C2×D4C2×#4118yes—
715C2×D4C2×#41116yes—
716C2×D4C2×#4118yes—
717C22×C4—22no—
718C22×C4—28no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—28no—
722C22×C4—216no—
723C22×C4—28no—
724C22×C4—24no—
725C22×C4—28no—
726C22×C4—28no—
727C22×C4—24no—
728C22×C4—24no—
729C22×C4—24no—
730C22×C4—24no—
731C22×C4—216no—
732C22×C4—216no—
733C22×C4—216no—
734C22×C4—28no—
735C22×C4—28no—
736C22×C4—28no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—24no—
740C22×C4—28no—
741C22×C4—28no—
742C22×C4—28no—
743C22×C4—42no—
744C22×C4—42no—
745C22×C4—44no—
746C22×C4—48no—
747C22×C4—44no—
748C22×C4—464no—
749C22×C4—44no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4—48no—
753C22×C4—44no—
754C22×C4—48no—
755C22×C4—44no—
756C22×C4C2×#41116yes—
757C22×C4C2514yes—
758C22×C4C2512yes—
759C22×C4C2512yes—
760C22×C4C2514yes—
761C22×C4C2514yes—
762C22×C4C2514yes—
763C22×C4C2514yes—
764C22×C4C2514yes—
765C22×C4C2514yes—
766C22×C4C2514yes—
767C22×C4C2511yescharacteristic
768C22×C4C2511yescharacteristic
769C22×C4C2514yes—
770C22×C4C2512yes—
771C22×C4C2511yescharacteristic
772C22×C4C2514yes—
773C22×C4C2511yescharacteristic
774C22×C4C2511yescharacteristic
775C22×C4C2512yes—
776C22×C4C2511yescharacteristic
777C4⋊C4—216no—
778C4⋊C4—28no—
779C4⋊C4—28no—
780C4⋊C4—28no—
781C4⋊C4—24no—
782C4⋊C4—24no—
783C4⋊C4—28no—
784C4⋊C4—28no—
785C4⋊C4—24no—
786C4⋊C4—28no—
787C4⋊C4—28no—
788C4⋊C4—28no—
789C4⋊C4—28no—
790C4⋊C4—24no—
791C4⋊C4—28no—
792C4⋊C4—24no—
793C4⋊C4—48no—
794C4⋊C4—48no—
795C4⋊C4—42no—
796C4⋊C4—42no—
797C4⋊C4—44no—
798C4⋊C4—44no—
799C4⋊C4—44no—
800C4⋊C4—44no—
801C4⋊C4—44no—
802C4⋊C4—48no—
803C4⋊C4—48no—
804C4⋊C4—48no—
805C4⋊C4—48no—
806C4⋊C4C2×#4118yes—
807C22⋊C4—216no—
808C22⋊C4—28no—
809C22⋊C4—28no—
810C22⋊C4—216no—
811C22⋊C4—216no—
812C22⋊C4—28no—
813C22⋊C4—28no—
814C22⋊C4—28no—
815C22⋊C4—28no—
816C22⋊C4—216no—
817C22⋊C4—216no—
818C22⋊C4—28no—
819C22⋊C4—28no—
820C22⋊C4—28no—
821C22⋊C4—28no—
822C22⋊C4—48no—
823C22⋊C4—48no—
824C22⋊C4—44no—
825C22⋊C4—44no—
826C22⋊C4—44no—
827C22⋊C4—48no—
828C22⋊C4—44no—
829C22⋊C4—48no—
830C22⋊C4—44no—
831C22⋊C4—44no—
832C22⋊C4—44no—
833C22⋊C4—44no—
834C22⋊C4—48no—
835C22⋊C4—48no—
836C22⋊C4—44no—
837C22⋊C4C2×#41116yes—
838C42—24no—
839C42—24no—
840C42—28no—
841C42—28no—
842C42—28no—
843C42—22no—
844C42—24no—
845C42—24no—
846C42—28no—
847C42—28no—
848C42—28no—
849C42—22no—
850C42—28no—
851C42—28no—
852C42—22no—
853C42—22no—
854C42—28no—
855C42—24no—
856C42—24no—
857C42—28no—
858C42—42no—
859C42—41no—
860C42—42no—
861C42—41no—
862C42—42no—
863C42—48no—
864C42—44no—
865C42—44no—
866C42C2×#4118yes—
867C42C2×#4114yes—
868C42H(5,𝔽2)14yes—
869C23—22no—
870C23—28no—
871C23—24no—
872C23—24no—
873C23—21no—
874C23—24no—
875C23—21no—
876C23—24no—
877C23—24no—
878C23—24no—
879C23—22no—
880C23—24no—
881C23—28no—
882C23—24no—
883C23—416no—
884C23—432no—
885C23—88no—
886C23—816no—
887C23—88no—
888C23C22×#4118yes—
889C23C22×#4118yes—
890C23#58512yes—
891C23C2611yescharacteristic
892Q8—48no—
893Q8—48no—
894D4—216no—
895D4—232no—
896D4—48no—
897D4—416no—
898D4—432no—
899D4—416no—
900C2×C4—28no—
901C2×C4—21no—
902C2×C4—24no—
903C2×C4—21no—
904C2×C4—24no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—232no—
911C2×C4—24no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—24no—
922C2×C4—28no—
923C2×C4—24no—
924C2×C4—24no—
925C2×C4—21no—
926C2×C4—24no—
927C2×C4—21no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—28no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—416no—
947C2×C4—48no—
948C2×C4—432no—
949C2×C4—416no—
950C2×C4—44no—
951C2×C4—48no—
952C2×C4—416no—
953C2×C4—44no—
954C2×C4—416no—
955C2×C4—88no—
956C2×C4—88no—
957C2×C4—88no—
958C2×C4—88no—
959C2×C4C22×#4114yes—
960C2×C4C22×#4112yes—
961C2×C4C22×#4118yes—
962C2×C4C22×#4114yes—
963C2×C4C22×#4114yes—
964C2×C4C22×#4114yes—
965C2×C4C2×H(5,𝔽2)12yes—
966C2×C4C2×H(5,𝔽2)12yes—
967C2×C4C2×H(5,𝔽2)12yes—
968C2×C4#58514yes—
969C22—22no—
970C22—28no—
971C22—24no—
972C22—28no—
973C22—28no—
974C22—216no—
975C22—28no—
976C22—41no—
977C22—44no—
978C22—44no—
979C22—44no—
980C22—44no—
981C22—48no—
982C22—42no—
983C22—44no—
984C22—44no—
985C22—41no—
986C22—832no—
987C22C23×#4111yescharacteristic
988C22C23×#4112yes—
989C22C22×H(5,𝔽2)11yescharacteristic
990C22C2×#58512yes—
991C22C2×#58511yescharacteristic
992C4—22no—
993C4—22no—
994C4—22no—
995C4—24no—
996C4—28no—
997C4—41no—
998C4—44no—
999C4—44no—
1000C4—44no—
1001C4—44no—
1002C4—42no—
1003C4—44no—
1004C4—44no—
1005C4—42no—
1006C4—44no—
1007C4—44no—
1008C4—41no—
1009C4—44no—
1010C4#347518yes—
1011C4#348114yes—
1012C2—42no—
1013C2—48no—
1014C2—48no—
1015C2C2×#347512yes—
1016C2C2×#348111yescharacteristic
1017C2#6275911yescharacteristic
1018C2#6277311yescharacteristic
1019C2#6281612yes—
subgroupG/H
centerC22×C4C25
commutator, Frattini, socle, cosocleC23C26
prime radical#59041C2
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. #59621C2semidirect
2. #59538C2semidirect
3. #59510C2semidirect
4. #59488C2semidirect
5. #59466C2semidirect
6. #59436C2semidirect
7. #59420C2semidirect
8. #59404C2semidirect
9. #59382C2semidirect
10. #59235C2semidirect
11. #59070C2semidirect
13. #52185C2semidirect
14. #34941C2semidirect
15. #34917C2semidirect
16. #34913C2semidirect
17. #34875C2semidirect
18. #34700C2semidirect
19. C4×#559C2semidirect
20. C4×D42C2semidirect
21. D4×#117C2semidirect
22. C4×#532C2semidirect
23. C4×#529C2semidirect
28. C2×C4×#41C22semidirect
30. C22×#117C22semidirect
31. #2748C22semidirect
32. #2747C22semidirect
33. #2746C22semidirect
34. #2745C22semidirect
35. #2744C22semidirect
36. #2743C22semidirect
37. #2735C22semidirect
38. #2717C22semidirect
41. #2609C22semidirect
42. #2609C22semidirect
43. #2599C22semidirect
44. #2598C22semidirect
45. #2579C22semidirect
46. #2579C22semidirect
47. #2578C22semidirect
48. #2578C22semidirect
49. #2577C22semidirect
50. #2576C22semidirect
51. #2576C22semidirect
52. #2575C22semidirect
53. #2574C22semidirect
54. #2570C22semidirect
55. #2567C22semidirect
56. #2566C22semidirect
58. #2562C22semidirect
59. #2552C22semidirect
63. #2534C22semidirect
64. #2515C22semidirect
65. #2514C22semidirect
66. #2508C22semidirect
67. #2508C22semidirect
68. #2497C22semidirect
69. #2497C22semidirect
70. #2495C22semidirect
71. #2494C22semidirect
72. #2489C22semidirect
73. #2484C22semidirect
74. #2482C22semidirect
75. #2480C22semidirect
76. #2468C22semidirect
77. #2457C22semidirect
78. #2457C22semidirect
80. #2454C22semidirect
81. #2454C22semidirect
83. #2447C22semidirect
84. #2442C22semidirect
87. #2427C22semidirect
88. #2423C22semidirect
89. #2422C22semidirect
93. #2418C22semidirect
94. #2417C22semidirect
96. #2406C22semidirect
98. #2401C22semidirect
99. #2396C22semidirect
100. #2395C22semidirect
101. #2392C22semidirect
102. #2374C22semidirect
103. #2367C22semidirect
108. #2357C22semidirect
109. #2355C22semidirect
112. #2352C22semidirect
113. #2352C22semidirect
115. D4×C4⋊C4C22semidirect
116. D4×C4⋊C4C22semidirect
117. #2344C22semidirect
118. #2344C22semidirect
119. #2342C22semidirect
120. #2342C22semidirect
124. C4×C4⋊Q8C22semidirect
125. C4×C4⋊Q8C22semidirect
128. C4×#125C22semidirect
129. C4×#125C22semidirect
130. C4×#125C22semidirect
131. C4×#126C22semidirect
132. C4×#126C22semidirect
135. C4×#124C22semidirect
136. C4×#124C22semidirect
137. C4×#124C22semidirect
138. C4×C22⋊Q8C22semidirect
139. C4×C22⋊Q8C22semidirect
140. C4×C22⋊Q8C22semidirect
141. C4×#123C22semidirect
142. C4×#123C22semidirect
143. C4×#123C22semidirect
144. C4×#123C22semidirect
148. C4×#121C22semidirect
149. C4×#121C22semidirect
151. C4×#120C22semidirect
152. #2298C22semidirect
153. #2297C22semidirect
154. #2295C22semidirect
157. #2293C22semidirect
158. #2290C22semidirect
159. #2290C22semidirect
160. #2290C22semidirect
161. #2285C22semidirect
162. #2285C22semidirect
163. #2283C22semidirect
164. #2283C22semidirect
165. #2280C22semidirect
166. C42×Q8C22semidirect
168. C42×D4C22semidirect
169. C42×D4C22semidirect
170. C42×D4C22semidirect
171. C4×#117C22semidirect
172. C2×C43C22semidirect
536. C4×D4#41semidirect

Maximal subgroups

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

subgroupindex
#596212
#595382
#595102
#594882
#594662
#594362
#594202
#594042
#593822
#592352
#590702
#590412
#521852
#349412
#349172
#349132
#348752
#347002
C4×#5592
C4×D422
D4×#1172
C4×#5322
C4×#5292