Finite Group Databasebeta

← C2×#38018 #7635216

Subgroups — C2×#38018 #7635216

Order 512.

4980 conjugacy classes of subgroups.

The subgroup lattice has 1302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2788C211yesmaximal, characteristic, complemented
2C2×#2786C211yesmaximal, characteristic
3C2×#2770C211yesmaximal, characteristic, complemented
4C2×#2744C211yesmaximal, characteristic, complemented
5C2×#2737C211yesmaximal, characteristic
6C2×#2698C211yesmaximal, characteristic, complemented
7C2×#2695C211yesmaximal, characteristic
8C2×#2687C211yesmaximal, characteristic
9#38018C2132yesmaximal, direct product factor
10C2×#2852C211yesmaximal, characteristic
11C2×#2606C211yesmaximal, characteristic, complemented
12C2×#2605C211yesmaximal, characteristic, complemented
13C2×#2585C211yesmaximal, characteristic, complemented
14C2×#2574C211yesmaximal, characteristic, complemented
15C2×#2532C211yesmaximal, characteristic, complemented
16C2×#2532C211yesmaximal, characteristic, complemented
17C2×#2530C211yesmaximal, characteristic, complemented
18C2×#2525C211yesmaximal, characteristic, complemented
19C2×#2495C211yesmaximal, characteristic, complemented
20C2×#2524C211yesmaximal, characteristic, complemented
21C2×#2524C211yesmaximal, characteristic, complemented
22C2×#2524C211yesmaximal, characteristic, complemented
23C2×#2523C211yesmaximal, characteristic, complemented
24C2×#2518C211yesmaximal, characteristic
25C2×#2637C211yesmaximal, characteristic, complemented
26C2×#2666C211yesmaximal, characteristic, complemented
27C2×#2374C211yesmaximal, characteristic
28C2×#2373C211yesmaximal, characteristic, complemented
29C2×#2334C211yesmaximal, characteristic, complemented
30C2×#2320C211yesmaximal, characteristic, complemented
31C2×C4×C22⋊Q8C211yesmaximal, characteristic, complemented
32C2×#2283C211yesmaximal, characteristic, complemented
33C22×#126C2211yescharacteristic
34C22×#126C2211yescharacteristic
35C22×#123C2211yescharacteristic
36C22×C22⋊Q8C2211yescharacteristic
37C22×C4×Q8C2211yescharacteristic
38C23×C42C2211yescharacteristic
39#2852C22116yes—
40#2788C22116yescomplemented
41#2786C22116yes—
42#2770C22116yescomplemented
43#2744C22116yescomplemented
44#2737C22116yes—
45#2698C22116yescomplemented
46#2695C22116yes—
47#2687C22116yes—
48#2666C22116yescomplemented
49#2637C22116yescomplemented
50#2606C22116yescomplemented
51#2605C22116yescomplemented
52#2585C22116yescomplemented
53#2574C22116yescomplemented
54#2532C22116yescomplemented
55#2532C22116yescomplemented
56#2530C22116yescomplemented
57#2525C22116yescomplemented
58#2524C22116yescomplemented
59#2524C22116yescomplemented
60#2524C22116yescomplemented
61#2523C22116yescomplemented
62#2518C22116yes—
63#2495C22116yescomplemented
64C2×#400C2211yescharacteristic
65C2×#400C2211yescharacteristic
66C2×#400C2211yescharacteristic
67C2×#400C2211yescharacteristic
68C2×#400C2211yescharacteristic
69C2×#400C2211yescharacteristic
70C2×#400C2211yescharacteristic
71C2×#400C2211yescharacteristic
72C2×#400C2211yescharacteristic
73C2×#398C2211yescharacteristic
74C2×#398C2211yescharacteristic
75C2×#398C2211yescharacteristic
76C2×#398C2211yescharacteristic
77C2×#398C2211yescharacteristic
78C2×#398C2211yescharacteristic
79C2×#398C2211yescharacteristic
80C2×#398C2211yescharacteristic
81C2×#398C2211yescharacteristic
82C2×#398C2211yescharacteristic
83C2×#398C2211yescharacteristic
84C2×#398C2211yescharacteristic
85C2×#397C2211yescharacteristic
86C2×#397C2211yescharacteristic
87C2×#397C2211yescharacteristic
88C2×#397C2211yescharacteristic
89C2×#397C2211yescharacteristic
90C2×#397C2211yescharacteristic
91C2×#397C2211yescharacteristic
92C2×#397C2211yescharacteristic
93C2×#396C2211yescharacteristic
94C2×#396C2211yescharacteristic
95C2×#396C2211yescharacteristic
96C2×#395C2211yescharacteristic
97C2×#395C2211yescharacteristic
98C2×#395C2211yescharacteristic
99C2×#394C2211yescharacteristic
100C2×#394C2211yescharacteristic
101C2×#393C2211yescharacteristic
102C2×#393C2211yescharacteristic
103C2×#393C2211yescharacteristic
104#2374C22116yes—
105#2373C22116yescomplemented
106#2334C22116yescomplemented
107#2320C22116yescomplemented
108C4×C22⋊Q8C22116yescomplemented
109C2×#391C2211yescharacteristic
110C2×#391C2211yescharacteristic
111C2×#391C2211yescharacteristic
112C2×#391C2211yescharacteristic
113C2×#391C2211yescharacteristic
114C2×#391C2211yescharacteristic
115C2×#390C2211yescharacteristic
116C2×#389C2211yescharacteristic
117C2×#389C2211yescharacteristic
118C2×#389C2211yescharacteristic
119C2×#389C2211yescharacteristic
120C2×#389C2211yescharacteristic
121C2×#389C2211yescharacteristic
122C2×#389C2211yescharacteristic
123C2×#389C2211yescharacteristic
124C2×#388C2211yescharacteristic
125C2×#388C2211yescharacteristic
126C2×#388C2211yescharacteristic
127C2×#388C2211yescharacteristic
128C2×#388C2211yescharacteristic
129C2×#388C2211yescharacteristic
130C2×#388C2211yescharacteristic
131C2×#388C2211yescharacteristic
132C2×#388C2211yescharacteristic
133C2×#388C2211yescharacteristic
134C2×#388C2211yescharacteristic
135C2×#388C2211yescharacteristic
136C2×#388C2211yescharacteristic
137C2×#388C2211yescharacteristic
138C2×#388C2211yescharacteristic
139C2×#388C2211yescharacteristic
140C2×#388C2211yescharacteristic
141C2×#388C2211yescharacteristic
142C2×#387C2211yescharacteristic
143C2×#387C2211yescharacteristic
144C2×#387C2211yescharacteristic
145C2×#387C2211yescharacteristic
146C2×#387C2211yescharacteristic
147C2×#387C2211yescharacteristic
148C2×#387C2211yescharacteristic
149C2×#387C2211yescharacteristic
150C2×#387C2211yescharacteristic
151C2×#387C2211yescharacteristic
152C2×#387C2211yescharacteristic
153C2×#387C2211yescharacteristic
154C2×#387C2211yescharacteristic
155C2×#387C2211yescharacteristic
156C2×#387C2211yescharacteristic
157C2×#387C2211yescharacteristic
158C2×#387C2211yescharacteristic
159C2×#387C2211yescharacteristic
160C2×#387C2211yescharacteristic
161C2×#387C2211yescharacteristic
162C2×#387C2211yescharacteristic
163C2×#387C2211yescharacteristic
164C2×#387C2211yescharacteristic
165C2×#387C2211yescharacteristic
166C2×#387C2211yescharacteristic
167C2×#387C2211yescharacteristic
168C2×#387C2211yescharacteristic
169C2×#386C2211yescharacteristic
170C2×#386C2211yescharacteristic
171C2×#386C2211yescharacteristic
172C2×#385C2211yescharacteristic
173C2×#385C2211yescharacteristic
174C2×#385C2211yescharacteristic
175C2×#385C2211yescharacteristic
176C2×#385C2211yescharacteristic
177C2×#385C2211yescharacteristic
178C2×#385C2211yescharacteristic
179#2283C22116yescomplemented
180C2×#383C2211yescharacteristic
181C2×#383C2211yescharacteristic
182C2×#383C2211yescharacteristic
183C2×#383C2211yescharacteristic
184C2×#383C2211yescharacteristic
185C2×#383C2211yescharacteristic
186C2×#383C2211yescharacteristic
187C2×#383C2211yescharacteristic
188C2×#382C2211yescharacteristic
189C2×#382C2211yescharacteristic
190C2×#382C2211yescharacteristic
191C2×#382C2211yescharacteristic
192C2×#382C2211yescharacteristic
193C2×#381C2211yescharacteristic
194C2×#381C2211yescharacteristic
195C2×#380C2211yescharacteristic
196C2×#380C2211yescharacteristic
197C2×#380C2211yescharacteristic
198C2×#380C2211yescharacteristic
199C2×#380C2211yescharacteristic
200C2×C4×C4⋊C4C2211yescharacteristic
201C2×C4×C4⋊C4C2211yescharacteristic
202C2×C4×C4⋊C4C2211yescharacteristic
203C2×C4×C4⋊C4C2211yescharacteristic
204C2×C4×C4⋊C4C2211yescharacteristic
205C2×C4×C4⋊C4C2211yescharacteristic
206C2×C4×C4⋊C4C2211yescharacteristic
207C2×C4×C4⋊C4C2211yescharacteristic
208C2×C4×C4⋊C4C2211yescharacteristic
209C2×C4×C4⋊C4C2211yescharacteristic
210C2×C4×C22⋊C4C2211yescharacteristic
211C2×C4×C22⋊C4C2211yescharacteristic
212C2×C4×C22⋊C4C2211yescharacteristic
213C2×C4×C22⋊C4C2211yescharacteristic
214C2×C4×C22⋊C4C2211yescharacteristic
215C2×C4×C22⋊C4C2211yescharacteristic
216C2×#376C2211yescharacteristic
217C2×#376C2211yescharacteristic
218C2×#376C2211yescharacteristic
219C23×Q8C2311yescharacteristic
220C23×Q8C2311yescharacteristic
221C23×D4C2311yescharacteristic
222C24×C4C2311yescharacteristic
223C24×C4C2311yescharacteristic
224C24×C4C2311yescharacteristic
225C24×C4C2311yescharacteristic
226C2×#126—28no—
227C2×#126—28no—
228C2×#126C2318yes—
229C2×#126C2318yes—
230C2×#123—28no—
231C2×#123C2318yes—
232C2×C22⋊Q8—28no—
233C2×C22⋊Q8C2318yes—
234C2×C4×Q8—28no—
235C2×C4×Q8C2318yes—
236C22×C4⋊C4C2311yescharacteristic
237C22×C4⋊C4C2311yescharacteristic
238C22×C4⋊C4C2311yescharacteristic
239C22×C4⋊C4C2311yescharacteristic
240C22×C4⋊C4C2311yescharacteristic
241C22×C4⋊C4C2311yescharacteristic
242C22×C4⋊C4C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C4⋊C4C2311yescharacteristic
257C22×C4⋊C4C2311yescharacteristic
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C4⋊C4C2311yescharacteristic
267C22×C4⋊C4C2311yescharacteristic
268C22×C4⋊C4C2311yescharacteristic
269C22×C4⋊C4C2311yescharacteristic
270C22×C4⋊C4C2311yescharacteristic
271C22×C4⋊C4C2311yescharacteristic
272C22×C4⋊C4C2311yescharacteristic
273C22×C4⋊C4C2311yescharacteristic
274C22×C4⋊C4C2311yescharacteristic
275C22×C22⋊C4C2311yescharacteristic
276C22×C22⋊C4C2311yescharacteristic
277C22×C22⋊C4C2311yescharacteristic
278C22×C22⋊C4C2311yescharacteristic
279C22×C22⋊C4C2311yescharacteristic
280C22×C22⋊C4C2311yescharacteristic
281C22×C22⋊C4C2311yescharacteristic
282C22×C22⋊C4C2311yescharacteristic
283C22×C22⋊C4C2311yescharacteristic
284C22×C22⋊C4C2311yescharacteristic
285C22×C22⋊C4C2311yescharacteristic
286C22×C22⋊C4C2311yescharacteristic
287C22×C22⋊C4C2311yescharacteristic
288C22×C22⋊C4C2311yescharacteristic
289C22×C22⋊C4C2311yescharacteristic
290C22×C22⋊C4C2311yescharacteristic
291C22×C22⋊C4C2311yescharacteristic
292C22×C22⋊C4C2311yescharacteristic
293C22×C22⋊C4C2311yescharacteristic
294C22×C22⋊C4C2311yescharacteristic
295C22×C22⋊C4C2311yescharacteristic
296C22×C22⋊C4C2311yescharacteristic
297C22×C22⋊C4C2311yescharacteristic
298C22×C22⋊C4C2311yescharacteristic
299C22×C42—28no—
300C22×C42C2318yes—
301C22×C42C2311yescharacteristic
302C22×C42C2311yescharacteristic
303C22×C42C2311yescharacteristic
304C22×C42C2311yescharacteristic
305C22×C42C2311yescharacteristic
306C22×C42C2311yescharacteristic
307C22×C42C2311yescharacteristic
308C22×C42C2311yescharacteristic
309C22×C42C2311yescharacteristic
310C22×C42C2311yescharacteristic
311C22×C42C2311yescharacteristic
312C22×C42C2311yescharacteristic
313C22×C42C2311yescharacteristic
314C22×C42C2311yescharacteristic
315C22×C42C2311yescharacteristic
316C22×C42C2311yescharacteristic
317C22×C42C2311yescharacteristic
318C22×C42C2311yescharacteristic
319C22×C42C2311yescharacteristic
320#400C2318yes—
321#400C2318yes—
322#400C2318yes—
323#400C2318yes—
324#400C2318yes—
325#400C2318yes—
326#400C2318yes—
327#400C2318yes—
328#400C2318yes—
329#398C2318yes—
330#398C2318yes—
331#398C2318yes—
332#398C2318yes—
333#398C2318yes—
334#398C2318yes—
335#398C2318yes—
336#398C2318yes—
337#398C2318yes—
338#398C2318yes—
339#398C2318yes—
340#398C2318yes—
341#397C2318yes—
342#397C2318yes—
343#397C2318yes—
344#397C2318yes—
345#397C2318yes—
346#397C2318yes—
347#397C2318yes—
348#397C2318yes—
349#396C2318yes—
350#396C2318yes—
351#396C2318yes—
352#395C2318yes—
353#395C2318yes—
354#395C2318yes—
355#394C2318yes—
356#394C2318yes—
357#393C2318yes—
358#393C2318yes—
359#393C2318yes—
360#391C2318yes—
361#391C2318yes—
362#391C2318yes—
363#391C2318yes—
364#391C2318yes—
365#391C2318yes—
366#390C2318yes—
367#389C2318yes—
368#389C2318yes—
369#389C2318yes—
370#389C2318yes—
371#389C2318yes—
372#389C2318yes—
373#389C2318yes—
374#389C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#386C2318yes—
421#386C2318yes—
422#386C2318yes—
423#385C2318yes—
424#385C2318yes—
425#385C2318yes—
426#385C2318yes—
427#385C2318yes—
428#385C2318yes—
429#385C2318yes—
430#383C2318yes—
431#383C2318yes—
432#383C2318yes—
433#383C2318yes—
434#383C2318yes—
435#383C2318yes—
436#383C2318yes—
437#383C2318yes—
438#382C2318yes—
439#382C2318yes—
440#382C2318yes—
441#382C2318yes—
442#382C2318yes—
443#381C2318yes—
444#381C2318yes—
445#380C2318yes—
446#380C2318yes—
447#380C2318yes—
448#380C2318yes—
449#380C2318yes—
450C4×C4⋊C4C2318yes—
451C4×C4⋊C4C2318yes—
452C4×C4⋊C4C2318yes—
453C4×C4⋊C4C2318yes—
454C4×C4⋊C4C2318yes—
455C4×C4⋊C4C2318yes—
456C4×C4⋊C4C2318yes—
457C4×C4⋊C4C2318yes—
458C4×C4⋊C4C2318yes—
459C4×C4⋊C4C2318yes—
460C4×C22⋊C4C2318yes—
461C4×C22⋊C4C2318yes—
462C4×C22⋊C4C2318yes—
463C4×C22⋊C4C2318yes—
464C4×C22⋊C4C2318yes—
465C4×C22⋊C4C2318yes—
466#376C2318yes—
467#376C2318yes—
468#376C2318yes—
469C2×#95C2311yescharacteristic
470C2×#95C2311yescharacteristic
471C2×#95C2311yescharacteristic
472C2×#95C2311yescharacteristic
473C2×#95C2311yescharacteristic
474C2×#95C2311yescharacteristic
475C2×#95C2311yescharacteristic
476C2×#95C2311yescharacteristic
477C2×#95C2311yescharacteristic
478C2×#95C2311yescharacteristic
479C2×#95C2311yescharacteristic
480C2×#95C2311yescharacteristic
481C2×#95C2311yescharacteristic
482C2×#95C2311yescharacteristic
483C2×#95C2311yescharacteristic
484C2×#95C2311yescharacteristic
485C2×#95C2311yescharacteristic
486C2×#95C2311yescharacteristic
487C2×#95C2311yescharacteristic
488C2×#95C2311yescharacteristic
489C2×#95C2311yescharacteristic
490C2×#95C2311yescharacteristic
491C2×#95C2311yescharacteristic
492C2×#95C2311yescharacteristic
493C2×#95C2311yescharacteristic
494C2×#95C2311yescharacteristic
495C2×#95C2311yescharacteristic
496C2×#95C2311yescharacteristic
497C2×#95C2311yescharacteristic
498C2×#95C2311yescharacteristic
499C2×#95C2311yescharacteristic
500C2×#95C2311yescharacteristic
501C2×#95C2311yescharacteristic
502C2×#95C2311yescharacteristic
503C2×#95C2311yescharacteristic
504C2×#95C2311yescharacteristic
505C2×#95C2311yescharacteristic
506C2×#95C2311yescharacteristic
507C2×#95C2311yescharacteristic
508C2×#95C2311yescharacteristic
509C2×#95C2311yescharacteristic
510C2×#95C2311yescharacteristic
511C2×#95C2311yescharacteristic
512C2×#95C2311yescharacteristic
513C2×#95C2311yescharacteristic
514C2×#95C2311yescharacteristic
515C2×#95C2311yescharacteristic
516C2×#95C2311yescharacteristic
517C2×#95C2311yescharacteristic
518C2×#95C2311yescharacteristic
519C2×#95C2311yescharacteristic
520C2×#95C2311yescharacteristic
521C2×#95C2311yescharacteristic
522C2×#95C2311yescharacteristic
523C2×#95C2311yescharacteristic
524C2×#95C2311yescharacteristic
525C2×#95C2311yescharacteristic
526C2×#95C2311yescharacteristic
527C2×#95C2311yescharacteristic
528C2×#95C2311yescharacteristic
529C2×#95C2311yescharacteristic
530C2×#95C2311yescharacteristic
531C2×#95C2311yescharacteristic
532C2×#95C2311yescharacteristic
533C2×#95C2311yescharacteristic
534C2×#95C2311yescharacteristic
535C25C2411yescharacteristic
536C25C2411yescharacteristic
537C22×Q8—24no—
538C22×Q8—24no—
539C22×Q8—42no—
540C22×Q8—42no—
541C22×Q8—42no—
542C22×Q8—42no—
543C22×Q8C2414yes—
544C22×Q8C2414yes—
545C22×D4—24no—
546C22×D4—42no—
547C22×D4—42no—
548C22×D4C2414yes—
549C23×C4—24no—
550C23×C4—24no—
551C23×C4—24no—
552C23×C4—24no—
553C23×C4—24no—
554C23×C4—24no—
555C23×C4—42no—
556C23×C4—42no—
557C23×C4—42no—
558C23×C4—42no—
559C23×C4—42no—
560C23×C4—42no—
561C23×C4C2411yescharacteristic
562C23×C4C2411yescharacteristic
563C23×C4C2411yescharacteristic
564C23×C4C2411yescharacteristic
565C23×C4C2411yescharacteristic
566C23×C4C2411yescharacteristic
567C23×C4C2411yescharacteristic
568C23×C4C2411yescharacteristic
569C23×C4C2411yescharacteristic
570C23×C4C2411yescharacteristic
571C23×C4C2411yescharacteristic
572C23×C4C2411yescharacteristic
573C23×C4C2411yescharacteristic
574C23×C4C2411yescharacteristic
575C23×C4C2411yescharacteristic
576C23×C4C2411yescharacteristic
577C23×C4C2411yescharacteristic
578C23×C4C2411yescharacteristic
579C23×C4C2411yescharacteristic
580C23×C4C2411yescharacteristic
581C23×C4C2411yescharacteristic
582C23×C4C2411yescharacteristic
583C23×C4C2411yescharacteristic
584C23×C4C2414yes—
585C23×C4C2414yes—
586C23×C4C2411yescharacteristic
587C23×C4C2411yescharacteristic
588C23×C4C2411yescharacteristic
589C23×C4C2411yescharacteristic
590C23×C4C2411yescharacteristic
591C23×C4C2411yescharacteristic
592C23×C4C2414yes—
593C23×C4C2414yes—
594#126—232no—
595#126—232no—
596#123—232no—
597C22⋊Q8—232no—
598C4×Q8—232no—
599C2×C4⋊C4—24no—
600C2×C4⋊C4—24no—
601C2×C4⋊C4—24no—
602C2×C4⋊C4—24no—
603C2×C4⋊C4—24no—
604C2×C4⋊C4—24no—
605C2×C4⋊C4—24no—
606C2×C4⋊C4—24no—
607C2×C4⋊C4—24no—
608C2×C4⋊C4—24no—
609C2×C4⋊C4—24no—
610C2×C4⋊C4—24no—
611C2×C4⋊C4—24no—
612C2×C4⋊C4—24no—
613C2×C4⋊C4—24no—
614C2×C4⋊C4—42no—
615C2×C4⋊C4—42no—
616C2×C4⋊C4—42no—
617C2×C4⋊C4—42no—
618C2×C4⋊C4—42no—
619C2×C4⋊C4—42no—
620C2×C4⋊C4—42no—
621C2×C4⋊C4—42no—
622C2×C4⋊C4—42no—
623C2×C4⋊C4—42no—
624C2×C4⋊C4—42no—
625C2×C4⋊C4—42no—
626C2×C4⋊C4—42no—
627C2×C4⋊C4—42no—
628C2×C4⋊C4—42no—
629C2×C4⋊C4—42no—
630C2×C4⋊C4—42no—
631C2×C4⋊C4—42no—
632C2×C4⋊C4—42no—
633C2×C4⋊C4—42no—
634C2×C4⋊C4—42no—
635C2×C4⋊C4—42no—
636C2×C4⋊C4—42no—
637C2×C4⋊C4—42no—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C22⋊C4—24no—
678C2×C22⋊C4—24no—
679C2×C22⋊C4—24no—
680C2×C22⋊C4—24no—
681C2×C22⋊C4—24no—
682C2×C22⋊C4—24no—
683C2×C22⋊C4—24no—
684C2×C22⋊C4—24no—
685C2×C22⋊C4—24no—
686C2×C22⋊C4—42no—
687C2×C22⋊C4—42no—
688C2×C22⋊C4—42no—
689C2×C22⋊C4—42no—
690C2×C22⋊C4—42no—
691C2×C22⋊C4—42no—
692C2×C22⋊C4—42no—
693C2×C22⋊C4—42no—
694C2×C22⋊C4—42no—
695C2×C22⋊C4—42no—
696C2×C22⋊C4—42no—
697C2×C22⋊C4—42no—
698C2×C22⋊C4—42no—
699C2×C22⋊C4—42no—
700C2×C22⋊C4#4118yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2414yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2414yes—
719C2×C22⋊C4C2414yes—
720C2×C22⋊C4C2414yes—
721C2×C22⋊C4C2414yes—
722C2×C22⋊C4C2414yes—
723C2×C22⋊C4C2414yes—
724C2×C22⋊C4C2414yes—
725C2×C42—24no—
726C2×C42—24no—
727C2×C42—24no—
728C2×C42—24no—
729C2×C42—24no—
730C2×C42—24no—
731C2×C42—24no—
732C2×C42—24no—
733C2×C42—232no—
734C2×C42—42no—
735C2×C42—42no—
736C2×C42—42no—
737C2×C42—42no—
738C2×C42—42no—
739C2×C42—42no—
740C2×C42—42no—
741C2×C42—42no—
742C2×C42—42no—
743C2×C42—42no—
744C2×C42#4118yes—
745C2×C42C2414yes—
746C2×C42C2414yes—
747C2×C42C2414yes—
748C2×C42C2414yes—
749C2×C42C2414yes—
750C2×C42C2414yes—
751C2×C42C2414yes—
752C2×C42C2414yes—
753C2×C42C2414yes—
754C2×C42C2414yes—
755C2×C42C2414yes—
756C2×C42C2414yes—
757C2×C42C2414yes—
758C2×C42C2414yes—
759C2×C42C2414yes—
760C2×C42C2414yes—
761C2×C42C2414yes—
762C2×C42C2414yes—
763C2×C42C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2414yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2414yes—
780#95C2414yes—
781#95C2414yes—
782#95C2414yes—
783#95C2414yes—
784#95C2414yes—
785#95C2414yes—
786#95C2414yes—
787#95C2414yes—
788#95C2414yes—
789#95C2414yes—
790#95C2414yes—
791#95C2414yes—
792#95C2414yes—
793#95C2414yes—
794#95C2414yes—
795#95C2414yes—
796#95C2414yes—
797#95C2414yes—
798#95C2414yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2414yes—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808#95C2414yes—
809#95C2414yes—
810#95C2414yes—
811#95C2414yes—
812#95C2414yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2414yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821#95C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830C24—22no—
831C24—22no—
832C24—22no—
833C24—22no—
834C24—22no—
835C24—22no—
836C24—22no—
837C24—22no—
838C24—22no—
839C24—22no—
840C24—22no—
841C24—22no—
842C24—22no—
843C24C2×#4114yes—
844C24C2512yes—
845C24C2512yes—
846C24C2511yescharacteristic
847C2×Q8—28no—
848C2×Q8—28no—
849C2×Q8—44no—
850C2×Q8—44no—
851C2×Q8—44no—
852C2×Q8—44no—
853C2×Q8—416no—
854C2×Q8—88no—
855C2×D4—28no—
856C2×D4—44no—
857C2×D4—44no—
858C2×D4—88no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—22no—
873C22×C4—22no—
874C22×C4—22no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—22no—
889C22×C4—28no—
890C22×C4—22no—
891C22×C4—22no—
892C22×C4—22no—
893C22×C4—22no—
894C22×C4—22no—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—22no—
898C22×C4—22no—
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—22no—
902C22×C4—22no—
903C22×C4—22no—
904C22×C4—22no—
905C22×C4—22no—
906C22×C4—22no—
907C22×C4—22no—
908C22×C4—22no—
909C22×C4—22no—
910C22×C4—22no—
911C22×C4—22no—
912C22×C4—22no—
913C22×C4—22no—
914C22×C4—22no—
915C22×C4—22no—
916C22×C4—22no—
917C22×C4—22no—
918C22×C4—22no—
919C22×C4—22no—
920C22×C4—22no—
921C22×C4—22no—
922C22×C4—22no—
923C22×C4—22no—
924C22×C4—22no—
925C22×C4—22no—
926C22×C4—22no—
927C22×C4—22no—
928C22×C4—22no—
929C22×C4—22no—
930C22×C4—22no—
931C22×C4—22no—
932C22×C4—22no—
933C22×C4—22no—
934C22×C4—22no—
935C22×C4—22no—
936C22×C4—22no—
937C22×C4—22no—
938C22×C4—22no—
939C22×C4—22no—
940C22×C4—22no—
941C22×C4—28no—
942C22×C4—28no—
943C22×C4—28no—
944C22×C4—28no—
945C22×C4—28no—
946C22×C4—44no—
947C22×C4—44no—
948C22×C4—44no—
949C22×C4—44no—
950C22×C4—416no—
951C22×C4—44no—
952C22×C4—44no—
953C22×C4—416no—
954C22×C4—416no—
955C22×C4—88no—
956C22×C4C2×#4114yes—
957C22×C4C2×#4114yes—
958C22×C4C2×#4114yes—
959C22×C4C2×#4114yes—
960C22×C4C2×#4114yes—
961C22×C42−1+414yes—
962C22×C4C2512yes—
963C22×C4C2512yes—
964C22×C4C2512yes—
965C22×C4C2512yes—
966C22×C4C2512yes—
967C22×C4C2512yes—
968C22×C4C2512yes—
969C22×C4C2512yes—
970C22×C4C2512yes—
971C22×C4C2512yes—
972C22×C4C2512yes—
973C22×C4C2512yes—
974C22×C4C2512yes—
975C22×C4C2512yes—
976C22×C4C2512yes—
977C22×C4C2512yes—
978C22×C4C2512yes—
979C22×C4C2512yes—
980C22×C4C2512yes—
981C22×C4C2512yes—
982C22×C4C2512yes—
983C22×C4C2512yes—
984C22×C4C2512yes—
985C22×C4C2512yes—
986C22×C4C2512yes—
987C22×C4C2512yes—
988C22×C4C2512yes—
989C22×C4C2512yes—
990C22×C4C2512yes—
991C4⋊C4—28no—
992C4⋊C4—28no—
993C4⋊C4—28no—
994C4⋊C4—28no—
995C4⋊C4—28no—
996C4⋊C4—28no—
997C4⋊C4—28no—
998C4⋊C4—28no—
999C4⋊C4—28no—
1000C4⋊C4—28no—
1001C4⋊C4—28no—
1002C4⋊C4—28no—
1003C4⋊C4—28no—
1004C4⋊C4—28no—
1005C4⋊C4—28no—
1006C4⋊C4—44no—
1007C4⋊C4—44no—
1008C4⋊C4—44no—
1009C4⋊C4—44no—
1010C4⋊C4—44no—
1011C4⋊C4—44no—
1012C4⋊C4—44no—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—44no—
1017C4⋊C4—44no—
1018C4⋊C4—44no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4—44no—
1022C4⋊C4—44no—
1023C4⋊C4—44no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C22⋊C4—28no—
1031C22⋊C4—28no—
1032C22⋊C4—28no—
1033C22⋊C4—28no—
1034C22⋊C4—28no—
1035C22⋊C4—28no—
1036C22⋊C4—28no—
1037C22⋊C4—28no—
1038C22⋊C4—28no—
1039C22⋊C4—44no—
1040C22⋊C4—44no—
1041C22⋊C4—44no—
1042C22⋊C4—44no—
1043C22⋊C4—44no—
1044C22⋊C4—44no—
1045C22⋊C4—44no—
1046C22⋊C4—44no—
1047C22⋊C4—44no—
1048C22⋊C4—44no—
1049C22⋊C4—44no—
1050C22⋊C4—44no—
1051C22⋊C4—44no—
1052C22⋊C4—44no—
1053C22⋊C4C2×#41116yes—
1054C42—28no—
1055C42—28no—
1056C42—28no—
1057C42—28no—
1058C42—28no—
1059C42—28no—
1060C42—28no—
1061C42—28no—
1062C42—44no—
1063C42—44no—
1064C42—44no—
1065C42—44no—
1066C42—44no—
1067C42—44no—
1068C42—44no—
1069C42—44no—
1070C42—44no—
1071C42—44no—
1072C42C2×#41116yes—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—28no—
1080C23—28no—
1081C23—28no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—44no—
1090C23—44no—
1091C23—44no—
1092C23—44no—
1093C23—44no—
1094C23—44no—
1095C23—44no—
1096C23—44no—
1097C23—44no—
1098C23—44no—
1099C23—44no—
1100C23C22×#4114yes—
1101C23C22×#4112yes—
1102C23C22×#4112yes—
1103C23C2×2−1+412yes—
1104C23#58512yes—
1105C23#58512yes—
1106C23#58512yes—
1107C23#58512yes—
1108C23C2611yescharacteristic
1109Q8—416no—
1110Q8—88no—
1111D4—88no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—28no—
1125C2×C4—28no—
1126C2×C4—28no—
1127C2×C4—28no—
1128C2×C4—28no—
1129C2×C4—28no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—416no—
1200C2×C4—416no—
1201C2×C4—416no—
1202C2×C4—44no—
1203C2×C4—44no—
1204C2×C4—44no—
1205C2×C4—44no—
1206C2×C4—44no—
1207C2×C4—44no—
1208C2×C4—44no—
1209C2×C4—44no—
1210C2×C4—44no—
1211C2×C4—44no—
1212C2×C4—44no—
1213C2×C4—44no—
1214C2×C4—44no—
1215C2×C4—44no—
1216C2×C4—44no—
1217C2×C4—44no—
1218C2×C4—44no—
1219C2×C4—44no—
1220C2×C4—44no—
1221C2×C4—44no—
1222C2×C4—44no—
1223C2×C4—44no—
1224C2×C4—44no—
1225C2×C4—88no—
1226C2×C4C22×#4114yes—
1227C2×C4C22×#4114yes—
1228C2×C4C22×#4114yes—
1229C2×C4C22×#4114yes—
1230C2×C4C22×#4114yes—
1231C2×C4C2×2−1+414yes—
1232C22—24no—
1233C22—24no—
1234C22—24no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—416no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—88no—
1248C22#346114yes—
1249C22#347514yes—
1250C22#349314yes—
1251C22#349514yes—
1252C22#352114yes—
1253C22#356514yes—
1254C22#356614yes—
1255C22C23×#4111yescharacteristic
1256C22C23×#4111yescharacteristic
1257C22C22×2−1+411yescharacteristic
1258C22C2×#58511yescharacteristic
1259C22C2×#58511yescharacteristic
1260C22C2×#58511yescharacteristic
1261C22C2×#58511yescharacteristic
1262C4—24no—
1263C4—24no—
1264C4—24no—
1265C4—24no—
1266C4—24no—
1267C4—24no—
1268C4—42no—
1269C4—42no—
1270C4—42no—
1271C4—42no—
1272C4—42no—
1273C4—42no—
1274C4—42no—
1275C4—42no—
1276C4—42no—
1277C4—42no—
1278C4—42no—
1279C4—42no—
1280C4—42no—
1281C4—42no—
1282C4—42no—
1283C4—42no—
1284C4—42no—
1285C4—42no—
1286C4—42no—
1287C4—42no—
1288C4—42no—
1289C4—42no—
1290C4—42no—
1291C2—44no—
1292C2—82no—
1293C2#3801818yesdirect product factor
1294C2C2×#346111yescharacteristic
1295C2C2×#347511yescharacteristic
1296C2C2×#356511yescharacteristic
1297C2C2×#356611yescharacteristic
1298C2C2×#349311yescharacteristic
1299C2C2×#352111yescharacteristic
1300C2C2×#349511yescharacteristic
subgroupG/H
center, socleC24C25
commutator, Frattini, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2788C2semidirect
3. C2×#2770C2semidirect
4. C2×#2744C2semidirect
6. C2×#2698C2semidirect
9. #38018C2direct (N × H)
11. C2×#2606C2semidirect
12. C2×#2605C2semidirect
13. C2×#2585C2semidirect
14. C2×#2574C2semidirect
15. C2×#2532C2semidirect
16. C2×#2532C2semidirect
17. C2×#2530C2semidirect
18. C2×#2525C2semidirect
19. C2×#2495C2semidirect
20. C2×#2524C2semidirect
21. C2×#2524C2semidirect
22. C2×#2524C2semidirect
23. C2×#2523C2semidirect
25. C2×#2637C2semidirect
26. C2×#2666C2semidirect
28. C2×#2373C2semidirect
29. C2×#2334C2semidirect
30. C2×#2320C2semidirect
31. C2×C4×C22⋊Q8C2semidirect
32. C2×#2283C2semidirect
40. #2788C22semidirect
42. #2770C22semidirect
43. #2744C22semidirect
45. #2698C22semidirect
48. #2666C22semidirect
49. #2637C22semidirect
50. #2606C22semidirect
51. #2605C22semidirect
52. #2585C22semidirect
53. #2574C22semidirect
54. #2532C22semidirect
55. #2532C22semidirect
56. #2530C22semidirect
57. #2525C22semidirect
58. #2524C22semidirect
59. #2524C22semidirect
60. #2524C22semidirect
61. #2523C22semidirect
63. #2495C22semidirect
105. #2373C22semidirect
106. #2334C22semidirect
107. #2320C22semidirect
108. C4×C22⋊Q8C22semidirect
179. #2283C22semidirect
1293. C2#38018direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#27882
C2×#27862
C2×#27702
C2×#27442
C2×#27372
C2×#26982
C2×#26952
C2×#26872
#380182
C2×#28522
C2×#26062
C2×#26052
C2×#25852
C2×#25742
C2×#25322
C2×#25302
C2×#25252
C2×#24952
C2×#25242
C2×#25232
C2×#25182
C2×#26372
C2×#26662
C2×#23742
C2×#23732
C2×#23342
C2×#23202
C2×C4×C22⋊Q82
C2×#22832