Finite Group Databasebeta

← #7631649

Subgroups — #7631649

Order 512.

5140 conjugacy classes of subgroups.

The subgroup lattice has 981 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36307C214yesmaximal, complemented
2#36304C214yesmaximal, complemented
3#36171C214yesmaximal, complemented
4#36167C214yesmaximal, complemented
5#36043C218yesmaximal, complemented
6#36023C214yesmaximal, complemented
7#36013C214yesmaximal, complemented
8#35461C218yesmaximal, complemented
9#35456C212yesmaximal, complemented
10#35448C212yesmaximal
11#35026C214yesmaximal, complemented
12#35020C211yesmaximal, characteristic, complemented
13#35010C211yesmaximal, characteristic
14#34780C214yesmaximal, complemented
15C2×#2503C211yesmaximal, characteristic, complemented
16C2×#2486C211yesmaximal, characteristic
17#34212C211yesmaximal, characteristic, complemented
18#34199C212yesmaximal
19#34177C212yesmaximal, complemented
20C2×#2344C211yesmaximal, characteristic, complemented
21C4×#518C211yesmaximal, characteristic
22C22×#123C2212yes—
23C22×C22⋊Q8C2211yescharacteristic
24C2×#518C2211yescharacteristic
25C2×#518C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C22×#117C2212yes—
28C23×C4⋊C4C2211yescharacteristic
29#2864C2214yescomplemented
30#2863C2214yescomplemented
31#2855C2212yes—
32#2855C2214yescomplemented
33#2851C2214yescomplemented
34#2851C2214yescomplemented
35#2848C2212yes—
36#2655C2218yescomplemented
37#2652C2218yescomplemented
38#2646C2214yescomplemented
39#2627C2212yes—
40#2626C2212yes—
41#2590C2218yescomplemented
42#2588C2218yescomplemented
43#2585C2218yescomplemented
44#2579C2214yes—
45#2577C2218yescomplemented
46#2575C2218yescomplemented
47#2573C2218yescomplemented
48#2569C2214yes—
49#2569C2214yescomplemented
50#2564C2214yes—
51#2533C2218yescomplemented
52#2533C2218yescomplemented
53#2530C2218yescomplemented
54#2528C2218yescomplemented
55#2528C2218yescomplemented
56#2527C2218yescomplemented
57#2524C2218yescomplemented
58#2524C2218yescomplemented
59#2523C2218yescomplemented
60#2520C2218yescomplemented
61#2517C2218yescomplemented
62#2515C2218yescomplemented
63#2514C2214yescomplemented
64#2509C2214yescomplemented
65#2508C2214yescomplemented
66#2505C2218yescomplemented
67#2503C2214yes—
68#2503C2214yes—
69#2503C2214yescomplemented
70#2503C2212yescomplemented
71#2503C2212yescomplemented
72#2495C2214yescomplemented
73#2494C2214yescomplemented
74#2493C2218yes—
75#2493C2218yes—
76#2493C2218yescomplemented
77#2493C2218yescomplemented
78#2493C2218yescomplemented
79#2493C2218yescomplemented
80#2493C2218yescomplemented
81#2489C2214yescomplemented
82#2487C2212yes—
83#2486C2214yes—
84#2486C2214yes—
85#2486C2214yes—
86#2486C2212yes—
87#2486C2212yes—
88#2484C2218yes—
89#2483C2218yes—
90#2453C2214yescomplemented
91#2442C2214yes—
92#2442C2214yescomplemented
93#2421C2214yescomplemented
94#2419C2218yes—
95#2419C2218yes—
96#2419C2218yes—
97#2419C2218yes—
98#2417C2214yes—
99#2409C2212yes—
100#2402C2218yescomplemented
101#2401C2218yescomplemented
102C2×#400C2214yescomplemented
103C2×#398C2212yes—
104C2×#397C2212yes—
105#2368C2214yes—
106#2360C2214yes—
107#2359C2218yes—
108#2359C2218yes—
109#2345C2212yescomplemented
110#2345C2214yescomplemented
111#2344C2214yes—
112#2344C2214yes—
113#2344C2218yes—
114#2344C2214yescomplemented
115#2344C2214yescomplemented
116#2343C2218yes—
117#2343C2218yes—
118#2343C2218yescomplemented
119#2343C2218yescomplemented
120#2342C2218yes—
121Q8×C22⋊C4C2212yescomplemented
122#2329C2214yescomplemented
123#2322C2218yes—
124#2315C2212yes—
125#2315C2212yes—
126#2315C2212yes—
127#2315C2212yes—
128#2313C2218yescomplemented
129#2308C2212yes—
130C4×#125C2214yescomplemented
131C4×C22⋊Q8C2214yescomplemented
132C4×C22⋊Q8C2214yescomplemented
133C4×#123C2218yes—
134#2295C2214yescomplemented
135C2×#391C2212yescomplemented
136C2×#389C2212yes—
137C2×#389C2212yescomplemented
138C2×#387C2214yescomplemented
139#2283C2214yescomplemented
140#2283C2218yescomplemented
141C2×#382C2212yescomplemented
142C2×#381C2212yes—
143C2×#381C2212yes—
144C2×#381C2212yes—
145C2×#381C2212yes—
146C2×#380C2211yescharacteristic
147C2×#380C2212yes—
148C2×#380C2211yescharacteristic
149#2275C2214yes—
150#2275C2214yes—
151#2274C2212yes—
152#2273C2211yescharacteristic
153#2273C2211yescharacteristic
154#2273C2212yes—
155#2273C2212yes—
156C42×D4C2214yes—
157C42×D4C2214yes—
158C4×#117C2212yes—
159C2×C4×C4⋊C4C2212yescomplemented
160C2×C4×C22⋊C4C2211yescharacteristic
161C2×C4×C22⋊C4C2212yes—
162C2×C4×C22⋊C4C2211yescharacteristic
163C23×Q8C2311yescharacteristic
164C23×D4C2311yescharacteristic
165C24×C4C2312yes—
166C24×C4C2311yescharacteristic
167C24×C4C2311yescharacteristic
168C2×#125C2314yes—
169C2×#123—216no—
170C2×#123C2314yes—
171C2×#123C2318yes—
172C2×#123C2314yes—
173C2×C22⋊Q8—28no—
174C2×C22⋊Q8C2312yes—
175C2×C22⋊Q8C2312yes—
176C2×C22⋊Q8C2312yes—
177C2×C22⋊Q8C2312yes—
178C2×C22⋊Q8C2314yes—
179#518—28no—
180#518—28no—
181C2×C4×Q8C2314yes—
182C2×C4×D4—28no—
183C2×C4×D4C2312yes—
184C2×C4×D4C2314yes—
185C2×C4×D4C2312yes—
186C2×C4×D4C2314yes—
187C2×C4×D4C2312yes—
188C2×C4×D4C2312yes—
189C2×C4×D4C2314yes—
190C2×C4×D4C2314yes—
191C2×#117—216no—
192C2×#117C2318yes—
193C2×#117C2318yes—
194C2×#117C2312yes—
195C2×#117C2312yes—
196C22×C4⋊C4—28no—
197C22×C4⋊C4C2314yes—
198C22×C4⋊C4C2312yes—
199C22×C4⋊C4C2312yes—
200C22×C4⋊C4C2314yes—
201C22×C4⋊C4C2312yes—
202C22×C4⋊C4C2312yes—
203C22×C4⋊C4C2312yes—
204C22×C4⋊C4C2311yescharacteristic
205C22×C4⋊C4C2311yescharacteristic
206C22×C4⋊C4C2311yescharacteristic
207C22×C4⋊C4C2312yes—
208C22×C4⋊C4C2311yescharacteristic
209C22×C4⋊C4C2312yes—
210C22×C4⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2311yescharacteristic
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2314yes—
220C22×C22⋊C4C2311yescharacteristic
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2311yescharacteristic
223C22×C42C2311yescharacteristic
224C22×C42C2314yes—
225C22×C42C2312yes—
226C22×C42C2314yes—
227C22×C42C2312yes—
228#401C2318yes—
229#401C2318yes—
230#400C2314yes—
231#400C2318yes—
232#400C2318yes—
233#400C2318yes—
234#400C2318yes—
235#400C2318yes—
236#400C2318yes—
237#400C2318yes—
238#400C2318yes—
239#400C2318yes—
240#400C2318yes—
241#400C2318yes—
242#400C2318yes—
243#400C2318yes—
244#400C2318yes—
245#399C2314yes—
246#398C2318yes—
247#398C2318yes—
248#398C2318yes—
249#398C2314yes—
250#398C2318yes—
251#398C2318yes—
252#398C2318yes—
253#398C2314yes—
254#397C2314yes—
255#397C2318yes—
256#397C2318yes—
257#397C2318yes—
258#397C2314yes—
259#397C2318yes—
260#397C2318yes—
261#396C2318yes—
262#395C2314yes—
263#393C2314yes—
264#391C2318yes—
265#391C2318yes—
266#391C2314yes—
267#391C2314yes—
268#391C2314yes—
269#391C2314yes—
270#389C2314yes—
271#389C2314yes—
272#389C2318yes—
273#389C2318yes—
274#389C2318yes—
275#389C2318yes—
276#389C2318yes—
277#389C2314yes—
278#389C2314yes—
279#389C2314yes—
280#389C2314yes—
281#389C2314yes—
282#389C2314yes—
283#388C2318yes—
284#388C2318yes—
285#388C2318yes—
286#388C2318yes—
287#387C2318yes—
288#387C2318yes—
289#387C2318yes—
290#387C2318yes—
291#387C2318yes—
292#387C2318yes—
293#387C2318yes—
294#387C2318yes—
295#387C2318yes—
296#387C2318yes—
297#387C2318yes—
298#387C2318yes—
299#387C2318yes—
300#387C2318yes—
301#387C2318yes—
302#387C2318yes—
303#387C2318yes—
304#387C2318yes—
305#387C2318yes—
306#387C2318yes—
307#387C2318yes—
308#387C2318yes—
309#387C2318yes—
310#387C2318yes—
311#387C2318yes—
312#387C2318yes—
313#387C2318yes—
314#387C2318yes—
315#387C2318yes—
316#387C2318yes—
317#387C2318yes—
318#387C2318yes—
319#386C2318yes—
320#386C2314yes—
321#386C2314yes—
322#385C2318yes—
323#385C2318yes—
324#385C2318yes—
325#385C2314yes—
326#385C2314yes—
327#385C2318yes—
328#385C2314yes—
329#385C2318yes—
330#385C2318yes—
331#385C2314yes—
332#385C2318yes—
333#385C2318yes—
334#385C2318yes—
335#385C2318yes—
336#385C2318yes—
337#383C2318yes—
338#383C2318yes—
339#383C2318yes—
340#383C2318yes—
341#382C2314yes—
342#382C2318yes—
343#382C2314yes—
344#382C2314yes—
345#382C2318yes—
346#382C2318yes—
347#381C2314yes—
348#381C2314yes—
349#381C2314yes—
350#381C2318yes—
351#381C2318yes—
352#381C2314yes—
353#381C2318yes—
354#381C2318yes—
355#381C2318yes—
356#381C2318yes—
357#381C2318yes—
358#381C2314yes—
359#381C2314yes—
360#381C2314yes—
361#380C2318yes—
362#380C2318yes—
363#380C2312yes—
364#380C2318yes—
365#380C2312yes—
366#380C2314yes—
367#380C2314yes—
368#380C2318yes—
369#380C2312yes—
370#380C2314yes—
371#380C2312yes—
372#380C2312yes—
373#380C2312yes—
374#380C2314yes—
375#380C2312yes—
376#380C2312yes—
377#380C2314yes—
378#379C2314yes—
379C4×C4⋊C4C2318yes—
380C4×C4⋊C4C2314yes—
381C4×C4⋊C4C2318yes—
382C4×C4⋊C4C2314yes—
383C4×C4⋊C4C2318yes—
384C4×C4⋊C4C2318yes—
385C4×C4⋊C4C2314yes—
386C4×C4⋊C4C2314yes—
387C4×C4⋊C4C2314yes—
388C4×C4⋊C4C2318yes—
389C4×C4⋊C4C2314yes—
390C4×C4⋊C4C2318yes—
391C4×C4⋊C4C2314yes—
392C4×C4⋊C4C2314yes—
393C4×C4⋊C4C2314yes—
394C4×C22⋊C4C2314yes—
395C4×C22⋊C4C2318yes—
396C4×C22⋊C4C2312yes—
397C4×C22⋊C4C2312yes—
398C4×C22⋊C4C2314yes—
399C4×C22⋊C4C2314yes—
400C4×C22⋊C4C2314yes—
401C4×C22⋊C4C2314yes—
402C4×C22⋊C4C2312yes—
403C4×C22⋊C4C2318yes—
404C4×C22⋊C4C2318yes—
405C4×C22⋊C4C2318yes—
406C4×C22⋊C4C2312yes—
407C4×C22⋊C4C2312yes—
408C4×C22⋊C4C2314yes—
409C4×C22⋊C4C2314yes—
410C4×C22⋊C4C2312yes—
411C4×C22⋊C4C2312yes—
412C4×C22⋊C4C2312yes—
413C4×C22⋊C4C2314yes—
414C4×C22⋊C4C2314yes—
415C4×C22⋊C4C2312yes—
416C4×C22⋊C4C2312yes—
417C4×C22⋊C4C2312yes—
418C4×C22⋊C4C2312yes—
419C4×C22⋊C4C2314yes—
420C4×C22⋊C4C2314yes—
421C4×C22⋊C4C2314yes—
422#376C2318yes—
423#376C2318yes—
424#376C2314yes—
425C2×#95C2312yes—
426C2×#95C2312yes—
427C2×#95C2312yes—
428C2×#95C2314yes—
429C2×#95C2314yes—
430C2×#95C2314yes—
431C2×#95C2314yes—
432C2×#95C2314yes—
433C2×#95C2314yes—
434C2×#95C2312yes—
435C2×#95C2314yes—
436C2×#95C2314yes—
437C2×#95C2314yes—
438C43C2314yes—
439C25C2411yescharacteristic
440C25C2411yescharacteristic
441C22×Q8—24no—
442C22×Q8—44no—
443C22×Q8C2412yes—
444C22×Q8C2412yes—
445C22×D4—24no—
446C22×D4—24no—
447C22×D4#4118yes—
448C22×D4C2412yes—
449C22×D4C2412yes—
450C23×C4—28no—
451C23×C4—28no—
452C23×C4—28no—
453C23×C4—24no—
454C23×C4—44no—
455C23×C4—44no—
456C23×C4#4118yes—
457C23×C4C2414yes—
458C23×C4C2412yes—
459C23×C4C2414yes—
460C23×C4C2412yes—
461C23×C4C2412yes—
462C23×C4C2411yescharacteristic
463C23×C4C2411yescharacteristic
464C23×C4C2411yescharacteristic
465C23×C4C2411yescharacteristic
466C23×C4C2414yes—
467C23×C4C2411yescharacteristic
468C23×C4C2412yes—
469C23×C4C2414yes—
470C23×C4C2411yescharacteristic
471C23×C4C2412yes—
472C23×C4C2412yes—
473C23×C4C2412yes—
474C23×C4C2412yes—
475C23×C4C2414yes—
476C23×C4C2414yes—
477C23×C4C2412yes—
478C23×C4C2411yescharacteristic
479C23×C4C2412yes—
480C23×C4C2411yescharacteristic
481C23×C4C2411yescharacteristic
482#125—48no—
483#123—216no—
484#123—232no—
485#123—216no—
486C22⋊Q8—28no—
487C22⋊Q8—28no—
488C22⋊Q8—28no—
489C22⋊Q8—28no—
490C22⋊Q8—48no—
491C4×Q8—48no—
492C4×D4—216no—
493C4×D4—216no—
494C4×D4—28no—
495C4×D4—28no—
496C4×D4—28no—
497C4×D4—28no—
498C4×D4—216no—
499C4×D4—216no—
500#117—28no—
501#117—232no—
502#117—232no—
503#117—28no—
504C2×C4⋊C4—28no—
505C2×C4⋊C4—28no—
506C2×C4⋊C4—24no—
507C2×C4⋊C4—24no—
508C2×C4⋊C4—28no—
509C2×C4⋊C4—28no—
510C2×C4⋊C4—28no—
511C2×C4⋊C4—216no—
512C2×C4⋊C4—24no—
513C2×C4⋊C4—24no—
514C2×C4⋊C4—28no—
515C2×C4⋊C4—216no—
516C2×C4⋊C4—44no—
517C2×C4⋊C4—44no—
518C2×C4⋊C4C2412yes—
519C2×C4⋊C4C2412yes—
520C2×C4⋊C4C2412yes—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2414yes—
523C2×C4⋊C4C2412yes—
524C2×C4⋊C4C2418yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2412yes—
527C2×C4⋊C4C2412yes—
528C2×C4⋊C4C2414yes—
529C2×C4⋊C4C2412yes—
530C2×C4⋊C4C2414yes—
531C2×C4⋊C4C2412yes—
532C2×C4⋊C4C2414yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2418yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2418yes—
543C2×C4⋊C4C2418yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2418yes—
548C2×C22⋊C4—28no—
549C2×C22⋊C4—24no—
550C2×C22⋊C4—28no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—24no—
554C2×C22⋊C4—28no—
555C2×C22⋊C4—216no—
556C2×C22⋊C4—28no—
557C2×C22⋊C4—24no—
558C2×C22⋊C4—28no—
559C2×C22⋊C4#4118yes—
560C2×C22⋊C4C2412yes—
561C2×C22⋊C4C2412yes—
562C2×C22⋊C4C2412yes—
563C2×C22⋊C4C2414yes—
564C2×C22⋊C4C2414yes—
565C2×C22⋊C4C2412yes—
566C2×C22⋊C4C2412yes—
567C2×C22⋊C4C2412yes—
568C2×C22⋊C4C2412yes—
569C2×C22⋊C4C2412yes—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2412yes—
572C2×C22⋊C4C2412yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2414yes—
576C2×C22⋊C4C2414yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2412yes—
583C2×C22⋊C4C2412yes—
584C2×C42—216no—
585C2×C42—24no—
586C2×C42—44no—
587C2×C42—48no—
588C2×C42—44no—
589C2×C42C2418yes—
590C2×C42C2418yes—
591C2×C42C2414yes—
592C2×C42C2414yes—
593C2×C42C2412yes—
594C2×C42C2412yes—
595C2×C42C2414yes—
596C2×C42C2414yes—
597C2×C42C2418yes—
598C2×C42C2414yes—
599C2×C42C2414yes—
600C2×C42C2414yes—
601C2×C42C2418yes—
602C2×C42C2414yes—
603C2×C42C2414yes—
604C2×C42C2414yes—
605#95C2414yes—
606#95C2414yes—
607#95C2418yes—
608#95C2418yes—
609#95C2418yes—
610#95C2418yes—
611#95C2414yes—
612#95C2414yes—
613#95C2414yes—
614#95C2414yes—
615#95C2418yes—
616#95C2418yes—
617#95C2414yes—
618#95C2418yes—
619#95C2418yes—
620#95C2418yes—
621#95C2414yes—
622#95C2414yes—
623#95C2414yes—
624#95C2418yes—
625#95C2418yes—
626#95C2418yes—
627#95C2418yes—
628#95C2418yes—
629#95C2418yes—
630#95C2418yes—
631#95C2414yes—
632#95C2414yes—
633#95C2418yes—
634#95C2418yes—
635#95C2418yes—
636#95C2418yes—
637#95C2418yes—
638#95C2418yes—
639#95C2418yes—
640#95C2418yes—
641#95C2418yes—
642#95C2418yes—
643#95C2418yes—
644#95C2418yes—
645C24—22no—
646C24—22no—
647C24—42no—
648C24—42no—
649C24—42no—
650C24—42no—
651C24C2×#4114yes—
652C24C2×#4114yes—
653C24C2×#4114yes—
654C24C2×#4114yes—
655C24C2512yes—
656C24C2511yescharacteristic
657C24C2511yescharacteristic
658C24C2511yescharacteristic
659C2×Q8—24no—
660C2×Q8—24no—
661C2×Q8—28no—
662C2×Q8—44no—
663C2×Q8—88no—
664C2×D4—232no—
665C2×D4—24no—
666C2×D4—24no—
667C2×D4—24no—
668C2×D4—24no—
669C2×D4C2×#4118yes—
670C2×D4C2×#4118yes—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—24no—
674C22×C4—24no—
675C22×C4—24no—
676C22×C4—24no—
677C22×C4—28no—
678C22×C4—24no—
679C22×C4—24no—
680C22×C4—28no—
681C22×C4—28no—
682C22×C4—24no—
683C22×C4—28no—
684C22×C4—28no—
685C22×C4—24no—
686C22×C4—28no—
687C22×C4—24no—
688C22×C4—22no—
689C22×C4—28no—
690C22×C4—28no—
691C22×C4—24no—
692C22×C4—22no—
693C22×C4—24no—
694C22×C4—28no—
695C22×C4—24no—
696C22×C4—24no—
697C22×C4—24no—
698C22×C4—24no—
699C22×C4—28no—
700C22×C4—28no—
701C22×C4—24no—
702C22×C4—416no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—42no—
706C22×C4—42no—
707C22×C4—42no—
708C22×C4—44no—
709C22×C4—42no—
710C22×C4—42no—
711C22×C4—42no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—44no—
715C22×C4—44no—
716C22×C4—42no—
717C22×C4—44no—
718C22×C4—42no—
719C22×C4—44no—
720C22×C4—44no—
721C22×C4—42no—
722C22×C4—42no—
723C22×C4—42no—
724C22×C4—44no—
725C22×C4—44no—
726C22×C4—44no—
727C22×C4—432no—
728C22×C4—88no—
729C22×C4C2×#4114yes—
730C22×C4C2×#4114yes—
731C22×C4C2×#4114yes—
732C22×C4C2×#4114yes—
733C22×C4C2×#4118yes—
734C22×C4C2×#4114yes—
735C22×C4C2×#4114yes—
736C22×C4C2×#4114yes—
737C22×C4C2512yes—
738C22×C4C2514yes—
739C22×C4C2514yes—
740C22×C4C2514yes—
741C22×C4C2514yes—
742C22×C4C2512yes—
743C22×C4C2514yes—
744C22×C4C2514yes—
745C22×C4C2514yes—
746C22×C4C2518yes—
747C22×C4C2518yes—
748C22×C4C2511yescharacteristic
749C22×C4C2511yescharacteristic
750C22×C4C2514yes—
751C22×C4C2512yes—
752C22×C4C2511yescharacteristic
753C22×C4C2511yescharacteristic
754C4⋊C4—28no—
755C4⋊C4—24no—
756C4⋊C4—24no—
757C4⋊C4—28no—
758C4⋊C4—24no—
759C4⋊C4—24no—
760C4⋊C4—216no—
761C4⋊C4—216no—
762C4⋊C4—24no—
763C4⋊C4—24no—
764C4⋊C4—24no—
765C4⋊C4—24no—
766C4⋊C4—28no—
767C4⋊C4—28no—
768C4⋊C4—216no—
769C4⋊C4—216no—
770C4⋊C4—28no—
771C4⋊C4—28no—
772C4⋊C4—28no—
773C4⋊C4—28no—
774C4⋊C4—44no—
775C4⋊C4—44no—
776C4⋊C4—48no—
777C4⋊C4—48no—
778C4⋊C4—48no—
779C4⋊C4—48no—
780C4⋊C4—48no—
781C4⋊C4—48no—
782C4⋊C4—48no—
783C4⋊C4—48no—
784C22⋊C4—24no—
785C22⋊C4—24no—
786C22⋊C4—24no—
787C22⋊C4—28no—
788C22⋊C4—28no—
789C22⋊C4—24no—
790C22⋊C4—24no—
791C22⋊C4—28no—
792C22⋊C4—24no—
793C22⋊C4—24no—
794C22⋊C4—24no—
795C22⋊C4—28no—
796C22⋊C4—28no—
797C22⋊C4—28no—
798C22⋊C4—28no—
799C22⋊C4—216no—
800C22⋊C4—216no—
801C22⋊C4—24no—
802C22⋊C4—24no—
803C22⋊C4—28no—
804C22⋊C4—48no—
805C22⋊C4—48no—
806C22⋊C4C2×#4118yes—
807C22⋊C4C2×#4118yes—
808C42—216no—
809C42—216no—
810C42—24no—
811C42—24no—
812C42—28no—
813C42—28no—
814C42—28no—
815C42—28no—
816C42—44no—
817C42—44no—
818C42—44no—
819C42—44no—
820C42—44no—
821C42—48no—
822C42—44no—
823C42—48no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—24no—
833C23—24no—
834C23—28no—
835C23—44no—
836C23—48no—
837C23—48no—
838C23—44no—
839C23—48no—
840C23—82no—
841C23—84no—
842C23—82no—
843C23#529116yes—
844C23C22×#4114yes—
845C23C22×#4112yes—
846C23C22×#4112yes—
847C23C22×#4112yes—
848C23C22×#4112yes—
849C23C22×#4112yes—
850C23C22×#4112yes—
851C23C22×#4112yes—
852C23C22×#4112yes—
853C23C22×#4112yes—
854C23C2611yescharacteristic
855Q8—48no—
856Q8—84no—
857D4—216no—
858D4—216no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—24no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—24no—
866C2×C4—28no—
867C2×C4—28no—
868C2×C4—28no—
869C2×C4—28no—
870C2×C4—24no—
871C2×C4—22no—
872C2×C4—28no—
873C2×C4—24no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—28no—
877C2×C4—24no—
878C2×C4—22no—
879C2×C4—24no—
880C2×C4—24no—
881C2×C4—24no—
882C2×C4—24no—
883C2×C4—24no—
884C2×C4—24no—
885C2×C4—24no—
886C2×C4—24no—
887C2×C4—24no—
888C2×C4—24no—
889C2×C4—28no—
890C2×C4—28no—
891C2×C4—28no—
892C2×C4—24no—
893C2×C4—28no—
894C2×C4—28no—
895C2×C4—24no—
896C2×C4—24no—
897C2×C4—24no—
898C2×C4—28no—
899C2×C4—44no—
900C2×C4—44no—
901C2×C4—44no—
902C2×C4—48no—
903C2×C4—416no—
904C2×C4—48no—
905C2×C4—48no—
906C2×C4—416no—
907C2×C4—48no—
908C2×C4—88no—
909C2×C4—84no—
910C2×C4—88no—
911C2×C4—88no—
912C2×C4—84no—
913C2×C4—84no—
914C2×C4—84no—
915C2×C4—88no—
916C2×C4—84no—
917C2×C4—82no—
918C2×C4—82no—
919C2×C4—84no—
920C2×C4C22×#4118yes—
921C2×C4C22×#4114yes—
922C2×C4C22×#4112yes—
923C2×C4C22×#4112yes—
924C2×C4C22×#4112yes—
925C2×C4C22×#4112yes—
926C2×C4#58514yes—
927C22—24no—
928C22—24no—
929C22—24no—
930C22—24no—
931C22—24no—
932C22—24no—
933C22—22no—
934C22—22no—
935C22—22no—
936C22—22no—
937C22—22no—
938C22—22no—
939C22—28no—
940C22—24no—
941C22—416no—
942C22—44no—
943C22—42no—
944C22—42no—
945C22—88no—
946C22C2×#52914yes—
947C22C2×#52914yes—
948C22C2×#52914yes—
949C22C23×#4111yescharacteristic
950C22C23×#4111yescharacteristic
951C22C23×#4111yescharacteristic
952C22C2×#58512yes—
953C222−1+612yes—
954C4—28no—
955C4—22no—
956C4—22no—
957C4—22no—
958C4—24no—
959C4—48no—
960C4—48no—
961C4—44no—
962C4—44no—
963C4—44no—
964C4—42no—
965C4—44no—
966C4—42no—
967C4—44no—
968C4—44no—
969C4—44no—
970C4#349114yes—
971C2—24no—
972C2—24no—
973C2—24no—
974C2—44no—
975C2C22×#52911yescharacteristic
976C2C2×#349111yescharacteristic
977C2#6286011yescharacteristic
978C2#6299112yes—
979C2#6299112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36307C2semidirect
2. #36304C2semidirect
3. #36171C2semidirect
4. #36167C2semidirect
5. #36043C2semidirect
6. #36023C2semidirect
7. #36013C2semidirect
8. #35461C2semidirect
9. #35456C2semidirect
11. #35026C2semidirect
12. #35020C2semidirect
14. #34780C2semidirect
15. C2×#2503C2semidirect
17. #34212C2semidirect
19. #34177C2semidirect
20. C2×#2344C2semidirect
29. #2864C22semidirect
30. #2863C22semidirect
32. #2855C22semidirect
33. #2851C22semidirect
34. #2851C22semidirect
36. #2655C22semidirect
37. #2652C22semidirect
38. #2646C22semidirect
41. #2590C22semidirect
42. #2588C22semidirect
43. #2585C22semidirect
45. #2577C22semidirect
46. #2575C22semidirect
47. #2573C22semidirect
49. #2569C22semidirect
51. #2533C22semidirect
52. #2533C22semidirect
53. #2530C22semidirect
54. #2528C22semidirect
55. #2528C22semidirect
56. #2527C22semidirect
57. #2524C22semidirect
58. #2524C22semidirect
59. #2523C22semidirect
60. #2520C22semidirect
61. #2517C22semidirect
62. #2515C22semidirect
63. #2514C22semidirect
64. #2509C22semidirect
65. #2508C22semidirect
66. #2505C22semidirect
69. #2503C22semidirect
70. #2503C22semidirect
71. #2503C22semidirect
72. #2495C22semidirect
73. #2494C22semidirect
76. #2493C22semidirect
77. #2493C22semidirect
78. #2493C22semidirect
79. #2493C22semidirect
80. #2493C22semidirect
81. #2489C22semidirect
90. #2453C22semidirect
92. #2442C22semidirect
93. #2421C22semidirect
100. #2402C22semidirect
101. #2401C22semidirect
102. C2×#400C22semidirect
109. #2345C22semidirect
110. #2345C22semidirect
114. #2344C22semidirect
115. #2344C22semidirect
118. #2343C22semidirect
119. #2343C22semidirect
121. Q8×C22⋊C4C22semidirect
122. #2329C22semidirect
128. #2313C22semidirect
130. C4×#125C22semidirect
131. C4×C22⋊Q8C22semidirect
132. C4×C22⋊Q8C22semidirect
134. #2295C22semidirect
135. C2×#391C22semidirect
137. C2×#389C22semidirect
138. C2×#387C22semidirect
139. #2283C22semidirect
140. #2283C22semidirect
141. C2×#382C22semidirect
159. C2×C4×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#363072
#363042
#361712
#361672
#360432
#360232
#360132
#354612
#354562
#354482
#350262
#350202
#350102
#347802
C2×#25032
C2×#24862
#342122
#341992
#341772
C2×#23442
C4×#5182