Finite Group Databasebeta

← C2×#55219 #8102453

Subgroups — C2×#55219 #8102453

Order 512.

4534 conjugacy classes of subgroups.

The subgroup lattice has 1296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#55219C2132yesmaximal, direct product factor
2C2×#2795C211yesmaximal, characteristic
3C2×#2792C211yesmaximal, characteristic, complemented
4C2×#2791C211yesmaximal, characteristic, complemented
5C2×#2788C211yesmaximal, characteristic, complemented
6C2×#2787C211yesmaximal, characteristic, complemented
7C2×#2787C211yesmaximal, characteristic, complemented
8C2×#2786C211yesmaximal, characteristic
9C2×#2783C211yesmaximal, characteristic, complemented
10C2×#2783C211yesmaximal, characteristic, complemented
11C2×#2779C211yesmaximal, characteristic
12C2×#2772C211yesmaximal, characteristic, complemented
13C2×#2772C211yesmaximal, characteristic, complemented
14C2×#2762C211yesmaximal, characteristic, complemented
15C2×#2719C211yesmaximal, characteristic, complemented
16C2×#2707C211yesmaximal, characteristic
17C2×#2690C211yesmaximal, characteristic, complemented
18C2×#2839C211yesmaximal, characteristic, complemented
19C2×#2836C211yesmaximal, characteristic, complemented
20C2×#2814C211yesmaximal, characteristic
21C2×#2590C211yesmaximal, characteristic, complemented
22C2×#2590C211yesmaximal, characteristic, complemented
23C2×#2556C211yesmaximal, characteristic, complemented
24C2×#2525C211yesmaximal, characteristic, complemented
25C2×#2525C211yesmaximal, characteristic, complemented
26C2×#2497C211yesmaximal, characteristic, complemented
27C2×#2506C211yesmaximal, characteristic, complemented
28C2×#2470C211yesmaximal, characteristic
29C2×#2475C211yesmaximal, characteristic, complemented
30C2×#2629C211yesmaximal, characteristic, complemented
31C2×#2650C211yesmaximal, characteristic, complemented
32C2×#2651C211yesmaximal, characteristic
33C22×#125C2211yescharacteristic
34C22×#125C2211yescharacteristic
35C22×#125C2211yescharacteristic
36C22×#123C2211yescharacteristic
37C22×C22⋊Q8C2211yescharacteristic
38C22×#117C2211yescharacteristic
39#2839C22116yescomplemented
40#2836C22116yescomplemented
41#2814C22116yes—
42#2795C22116yes—
43#2792C22116yescomplemented
44#2791C22116yescomplemented
45#2788C22116yescomplemented
46#2787C22116yescomplemented
47#2787C22116yescomplemented
48#2786C22116yes—
49#2783C22116yescomplemented
50#2783C22116yescomplemented
51#2779C22116yes—
52#2772C22116yescomplemented
53#2772C22116yescomplemented
54#2762C22116yescomplemented
55#2719C22116yescomplemented
56#2707C22116yes—
57#2690C22116yescomplemented
58#2651C22116yes—
59#2650C22116yescomplemented
60#2629C22116yescomplemented
61#2590C22116yescomplemented
62#2590C22116yescomplemented
63#2556C22116yescomplemented
64#2525C22116yescomplemented
65#2525C22116yescomplemented
66#2506C22116yescomplemented
67#2497C22116yescomplemented
68#2475C22116yescomplemented
69#2470C22116yes—
70C2×#401C2211yescharacteristic
71C2×#400C2211yescharacteristic
72C2×#400C2211yescharacteristic
73C2×#400C2211yescharacteristic
74C2×#400C2211yescharacteristic
75C2×#400C2211yescharacteristic
76C2×#400C2211yescharacteristic
77C2×#400C2211yescharacteristic
78C2×#400C2211yescharacteristic
79C2×#400C2211yescharacteristic
80C2×#400C2211yescharacteristic
81C2×#400C2211yescharacteristic
82C2×#400C2211yescharacteristic
83C2×#400C2211yescharacteristic
84C2×#400C2211yescharacteristic
85C2×#399C2211yescharacteristic
86C2×#398C2211yescharacteristic
87C2×#398C2211yescharacteristic
88C2×#398C2211yescharacteristic
89C2×#398C2211yescharacteristic
90C2×#398C2211yescharacteristic
91C2×#398C2211yescharacteristic
92C2×#398C2211yescharacteristic
93C2×#398C2211yescharacteristic
94C2×#398C2211yescharacteristic
95C2×#398C2211yescharacteristic
96C2×#398C2211yescharacteristic
97C2×#398C2211yescharacteristic
98C2×#398C2211yescharacteristic
99C2×#398C2211yescharacteristic
100C2×#398C2211yescharacteristic
101C2×#398C2211yescharacteristic
102C2×#398C2211yescharacteristic
103C2×#398C2211yescharacteristic
104C2×#397C2211yescharacteristic
105C2×#397C2211yescharacteristic
106C2×#397C2211yescharacteristic
107C2×#397C2211yescharacteristic
108C2×#397C2211yescharacteristic
109C2×#397C2211yescharacteristic
110C2×#397C2211yescharacteristic
111C2×#397C2211yescharacteristic
112C2×#397C2211yescharacteristic
113C2×#397C2211yescharacteristic
114C2×#397C2211yescharacteristic
115C2×#396C2211yescharacteristic
116C2×#396C2211yescharacteristic
117C2×#396C2211yescharacteristic
118C2×#396C2211yescharacteristic
119C2×#396C2211yescharacteristic
120C2×#396C2211yescharacteristic
121C2×#396C2211yescharacteristic
122C2×#396C2211yescharacteristic
123C2×#396C2211yescharacteristic
124C2×#396C2211yescharacteristic
125C2×#396C2211yescharacteristic
126C2×#395C2211yescharacteristic
127C2×#395C2211yescharacteristic
128C2×#395C2211yescharacteristic
129C2×#394C2211yescharacteristic
130C2×#394C2211yescharacteristic
131C2×#394C2211yescharacteristic
132C2×#394C2211yescharacteristic
133C2×#393C2211yescharacteristic
134C2×#391C2211yescharacteristic
135C2×#391C2211yescharacteristic
136C2×#390C2211yescharacteristic
137C2×#389C2211yescharacteristic
138C2×#389C2211yescharacteristic
139C2×#389C2211yescharacteristic
140C2×#389C2211yescharacteristic
141C2×#389C2211yescharacteristic
142C2×#389C2211yescharacteristic
143C2×#389C2211yescharacteristic
144C2×#389C2211yescharacteristic
145C2×#389C2211yescharacteristic
146C2×#389C2211yescharacteristic
147C2×#389C2211yescharacteristic
148C2×#389C2211yescharacteristic
149C2×#389C2211yescharacteristic
150C2×#389C2211yescharacteristic
151C2×#389C2211yescharacteristic
152C2×#388C2211yescharacteristic
153C2×#388C2211yescharacteristic
154C2×#388C2211yescharacteristic
155C2×#388C2211yescharacteristic
156C2×#388C2211yescharacteristic
157C2×#388C2211yescharacteristic
158C2×#388C2211yescharacteristic
159C2×#388C2211yescharacteristic
160C2×#388C2211yescharacteristic
161C2×#388C2211yescharacteristic
162C2×#388C2211yescharacteristic
163C2×#388C2211yescharacteristic
164C2×#388C2211yescharacteristic
165C2×#388C2211yescharacteristic
166C2×#388C2211yescharacteristic
167C2×#388C2211yescharacteristic
168C2×#388C2211yescharacteristic
169C2×#388C2211yescharacteristic
170C2×#388C2211yescharacteristic
171C2×#388C2211yescharacteristic
172C2×#387C2211yescharacteristic
173C2×#387C2211yescharacteristic
174C2×#387C2211yescharacteristic
175C2×#387C2211yescharacteristic
176C2×#387C2211yescharacteristic
177C2×#387C2211yescharacteristic
178C2×#387C2211yescharacteristic
179C2×#387C2211yescharacteristic
180C2×#387C2211yescharacteristic
181C2×#387C2211yescharacteristic
182C2×#387C2211yescharacteristic
183C2×#387C2211yescharacteristic
184C2×#387C2211yescharacteristic
185C2×#387C2211yescharacteristic
186C2×#387C2211yescharacteristic
187C2×#387C2211yescharacteristic
188C2×#387C2211yescharacteristic
189C2×#387C2211yescharacteristic
190C2×#387C2211yescharacteristic
191C2×#387C2211yescharacteristic
192C2×#387C2211yescharacteristic
193C2×#387C2211yescharacteristic
194C2×#387C2211yescharacteristic
195C2×#387C2211yescharacteristic
196C2×#387C2211yescharacteristic
197C2×#387C2211yescharacteristic
198C2×#386C2211yescharacteristic
199C2×#385C2211yescharacteristic
200C2×#385C2211yescharacteristic
201C2×#385C2211yescharacteristic
202C2×#385C2211yescharacteristic
203C2×#385C2211yescharacteristic
204C2×#384C2211yescharacteristic
205C2×#384C2211yescharacteristic
206C2×#383C2211yescharacteristic
207C2×#382C2211yescharacteristic
208C2×#382C2211yescharacteristic
209C2×#380C2211yescharacteristic
210C2×#380C2211yescharacteristic
211C2×#380C2211yescharacteristic
212C2×#380C2211yescharacteristic
213C2×C4×C4⋊C4C2211yescharacteristic
214C2×C4×C4⋊C4C2211yescharacteristic
215C2×C4×C4⋊C4C2211yescharacteristic
216C2×C4×C4⋊C4C2211yescharacteristic
217C2×C4×C4⋊C4C2211yescharacteristic
218C2×C4×C22⋊C4C2211yescharacteristic
219C23×Q8C2311yescharacteristic
220C23×D4C2311yescharacteristic
221C24×C4C2311yescharacteristic
222C24×C4C2311yescharacteristic
223C2×#125—44no—
224C2×#125—44no—
225C2×#125—44no—
226C2×#125C2318yes—
227C2×#125C2318yes—
228C2×#125C2318yes—
229C2×#123—44no—
230C2×#123C2318yes—
231C2×C22⋊Q8—44no—
232C2×C22⋊Q8C2318yes—
233C2×#117—44no—
234C2×#117C2318yes—
235C22×C4⋊C4C2311yescharacteristic
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×C4⋊C4C2311yescharacteristic
276C22×C4⋊C4C2311yescharacteristic
277C22×C4⋊C4C2311yescharacteristic
278C22×C4⋊C4C2311yescharacteristic
279C22×C4⋊C4C2311yescharacteristic
280C22×C4⋊C4C2311yescharacteristic
281C22×C4⋊C4C2311yescharacteristic
282C22×C4⋊C4C2311yescharacteristic
283C22×C4⋊C4C2311yescharacteristic
284C22×C4⋊C4C2311yescharacteristic
285C22×C4⋊C4C2311yescharacteristic
286C22×C4⋊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×C22⋊C4C2311yescharacteristic
300C22×C22⋊C4C2311yescharacteristic
301C22×C22⋊C4C2311yescharacteristic
302C22×C22⋊C4C2311yescharacteristic
303C22×C22⋊C4C2311yescharacteristic
304C22×C22⋊C4C2311yescharacteristic
305C22×C22⋊C4C2311yescharacteristic
306C22×C22⋊C4C2311yescharacteristic
307C22×C22⋊C4C2311yescharacteristic
308C22×C22⋊C4C2311yescharacteristic
309C22×C22⋊C4C2311yescharacteristic
310C22×C22⋊C4C2311yescharacteristic
311C22×C22⋊C4C2311yescharacteristic
312C22×C22⋊C4C2311yescharacteristic
313C22×C42C2311yescharacteristic
314C22×C42C2311yescharacteristic
315C22×C42C2311yescharacteristic
316C22×C42C2311yescharacteristic
317C22×C42C2311yescharacteristic
318C22×C42C2311yescharacteristic
319C22×C42C2311yescharacteristic
320C22×C42C2311yescharacteristic
321C22×C42C2311yescharacteristic
322C22×C42C2311yescharacteristic
323C22×C42C2311yescharacteristic
324C22×C42C2311yescharacteristic
325C22×C42C2311yescharacteristic
326#401C2318yes—
327#400C2318yes—
328#400C2318yes—
329#400C2318yes—
330#400C2318yes—
331#400C2318yes—
332#400C2318yes—
333#400C2318yes—
334#400C2318yes—
335#400C2318yes—
336#400C2318yes—
337#400C2318yes—
338#400C2318yes—
339#400C2318yes—
340#400C2318yes—
341#399C2318yes—
342#398C2318yes—
343#398C2318yes—
344#398C2318yes—
345#398C2318yes—
346#398C2318yes—
347#398C2318yes—
348#398C2318yes—
349#398C2318yes—
350#398C2318yes—
351#398C2318yes—
352#398C2318yes—
353#398C2318yes—
354#398C2318yes—
355#398C2318yes—
356#398C2318yes—
357#398C2318yes—
358#398C2318yes—
359#398C2318yes—
360#397C2318yes—
361#397C2318yes—
362#397C2318yes—
363#397C2318yes—
364#397C2318yes—
365#397C2318yes—
366#397C2318yes—
367#397C2318yes—
368#397C2318yes—
369#397C2318yes—
370#397C2318yes—
371#396C2318yes—
372#396C2318yes—
373#396C2318yes—
374#396C2318yes—
375#396C2318yes—
376#396C2318yes—
377#396C2318yes—
378#396C2318yes—
379#396C2318yes—
380#396C2318yes—
381#396C2318yes—
382#395C2318yes—
383#395C2318yes—
384#395C2318yes—
385#394C2318yes—
386#394C2318yes—
387#394C2318yes—
388#394C2318yes—
389#393C2318yes—
390#391C2318yes—
391#391C2318yes—
392#390C2318yes—
393#389C2318yes—
394#389C2318yes—
395#389C2318yes—
396#389C2318yes—
397#389C2318yes—
398#389C2318yes—
399#389C2318yes—
400#389C2318yes—
401#389C2318yes—
402#389C2318yes—
403#389C2318yes—
404#389C2318yes—
405#389C2318yes—
406#389C2318yes—
407#389C2318yes—
408#388C2318yes—
409#388C2318yes—
410#388C2318yes—
411#388C2318yes—
412#388C2318yes—
413#388C2318yes—
414#388C2318yes—
415#388C2318yes—
416#388C2318yes—
417#388C2318yes—
418#388C2318yes—
419#388C2318yes—
420#388C2318yes—
421#388C2318yes—
422#388C2318yes—
423#388C2318yes—
424#388C2318yes—
425#388C2318yes—
426#388C2318yes—
427#388C2318yes—
428#387C2318yes—
429#387C2318yes—
430#387C2318yes—
431#387C2318yes—
432#387C2318yes—
433#387C2318yes—
434#387C2318yes—
435#387C2318yes—
436#387C2318yes—
437#387C2318yes—
438#387C2318yes—
439#387C2318yes—
440#387C2318yes—
441#387C2318yes—
442#387C2318yes—
443#387C2318yes—
444#387C2318yes—
445#387C2318yes—
446#387C2318yes—
447#387C2318yes—
448#387C2318yes—
449#387C2318yes—
450#387C2318yes—
451#387C2318yes—
452#387C2318yes—
453#387C2318yes—
454#386C2318yes—
455#385C2318yes—
456#385C2318yes—
457#385C2318yes—
458#385C2318yes—
459#385C2318yes—
460#384C2318yes—
461#384C2318yes—
462#383C2318yes—
463#382C2318yes—
464#382C2318yes—
465#380C2318yes—
466#380C2318yes—
467#380C2318yes—
468#380C2318yes—
469C4×C4⋊C4C2318yes—
470C4×C4⋊C4C2318yes—
471C4×C4⋊C4C2318yes—
472C4×C4⋊C4C2318yes—
473C4×C4⋊C4C2318yes—
474C4×C22⋊C4C2318yes—
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—42no—
538C22×Q8—42no—
539C22×Q8—42no—
540C22×Q8C2414yes—
541C22×D4—42no—
542C22×D4—42no—
543C22×D4—42no—
544C22×D4C2414yes—
545C23×C4—24no—
546C23×C4—24no—
547C23×C4—42no—
548C23×C4—42no—
549C23×C4—42no—
550C23×C4—42no—
551C23×C4C2411yescharacteristic
552C23×C4C2411yescharacteristic
553C23×C4C2411yescharacteristic
554C23×C4C2411yescharacteristic
555C23×C4C2411yescharacteristic
556C23×C4C2411yescharacteristic
557C23×C4C2411yescharacteristic
558C23×C4C2411yescharacteristic
559C23×C4C2411yescharacteristic
560C23×C4C2411yescharacteristic
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×C4C2414yes—
581C23×C4C2414yes—
582#125—416no—
583#125—416no—
584#125—416no—
585#123—416no—
586C22⋊Q8—416no—
587#117—416no—
588C2×C4⋊C4—24no—
589C2×C4⋊C4—24no—
590C2×C4⋊C4—24no—
591C2×C4⋊C4—24no—
592C2×C4⋊C4—24no—
593C2×C4⋊C4—24no—
594C2×C4⋊C4—24no—
595C2×C4⋊C4—24no—
596C2×C4⋊C4—24no—
597C2×C4⋊C4—24no—
598C2×C4⋊C4—24no—
599C2×C4⋊C4—24no—
600C2×C4⋊C4—42no—
601C2×C4⋊C4—42no—
602C2×C4⋊C4—42no—
603C2×C4⋊C4—42no—
604C2×C4⋊C4—42no—
605C2×C4⋊C4—42no—
606C2×C4⋊C4—42no—
607C2×C4⋊C4—42no—
608C2×C4⋊C4—42no—
609C2×C4⋊C4—42no—
610C2×C4⋊C4—42no—
611C2×C4⋊C4—42no—
612C2×C4⋊C4—42no—
613C2×C4⋊C4—42no—
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⋊C4—42no—
639C2×C4⋊C4—42no—
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×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2414yes—
692C2×C22⋊C4—24no—
693C2×C22⋊C4—24no—
694C2×C22⋊C4—24no—
695C2×C22⋊C4—24no—
696C2×C22⋊C4—42no—
697C2×C22⋊C4—42no—
698C2×C22⋊C4—42no—
699C2×C22⋊C4—42no—
700C2×C22⋊C4—42no—
701C2×C22⋊C4—42no—
702C2×C22⋊C4—42no—
703C2×C22⋊C4—42no—
704C2×C22⋊C4—42no—
705C2×C22⋊C4—42no—
706C2×C22⋊C4—42no—
707C2×C22⋊C4—42no—
708C2×C22⋊C4—42no—
709C2×C22⋊C4—42no—
710C2×C22⋊C4—42no—
711C2×C22⋊C4—42no—
712C2×C22⋊C4—42no—
713C2×C22⋊C4—42no—
714C2×C22⋊C4—42no—
715C2×C22⋊C4—42no—
716C2×C22⋊C4—42no—
717C2×C22⋊C4—42no—
718C2×C22⋊C4C2414yes—
719C2×C22⋊C4C2414yes—
720C2×C22⋊C4C2414yes—
721C2×C22⋊C4C2414yes—
722C2×C22⋊C4C2414yes—
723C2×C22⋊C4C2414yes—
724C2×C22⋊C4C2414yes—
725C2×C22⋊C4C2414yes—
726C2×C22⋊C4C2414yes—
727C2×C22⋊C4C2414yes—
728C2×C22⋊C4C2414yes—
729C2×C22⋊C4C2414yes—
730C2×C22⋊C4C2414yes—
731C2×C22⋊C4C2414yes—
732C2×C22⋊C4C2414yes—
733C2×C22⋊C4C2414yes—
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2414yes—
736C2×C22⋊C4C2414yes—
737C2×C22⋊C4C2414yes—
738C2×C22⋊C4C2414yes—
739C2×C22⋊C4C2414yes—
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2414yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2414yes—
744C2×C42—24no—
745C2×C42—42no—
746C2×C42—42no—
747C2×C42—42no—
748C2×C42—42no—
749C2×C42—42no—
750C2×C42—42no—
751C2×C42—42no—
752C2×C42—42no—
753C2×C42—42no—
754C2×C42—42no—
755C2×C42—42no—
756C2×C42—42no—
757C2×C42C2414yes—
758C2×C42C2414yes—
759C2×C42C2414yes—
760C2×C42C2414yes—
761C2×C42C2414yes—
762C2×C42C2414yes—
763C2×C42C2414yes—
764C2×C42C2414yes—
765C2×C42C2414yes—
766C2×C42C2414yes—
767C2×C42C2414yes—
768C2×C42C2414yes—
769C2×C42C2414yes—
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—
843C24—22no—
844C24C2512yes—
845C24C2512yes—
846C24C2511yescharacteristic
847C2×Q8—44no—
848C2×Q8—44no—
849C2×Q8—44no—
850C2×Q8—88no—
851C2×D4—44no—
852C2×D4—44no—
853C2×D4—44no—
854C2×D4—88no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—22no—
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—22no—
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—28no—
940C22×C4—28no—
941C22×C4—44no—
942C22×C4—44no—
943C22×C4—44no—
944C22×C4—44no—
945C22×C4—416no—
946C22×C4—88no—
947C22×C4H(5,𝔽2)14yes—
948C22×C42−1+414yes—
949C22×C42−1+414yes—
950C22×C4C2512yes—
951C22×C4C2512yes—
952C22×C4C2512yes—
953C22×C4C2512yes—
954C22×C4C2512yes—
955C22×C4C2512yes—
956C22×C4C2512yes—
957C22×C4C2512yes—
958C22×C4C2512yes—
959C22×C4C2512yes—
960C22×C4C2512yes—
961C22×C4C2512yes—
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—
979C4⋊C4—28no—
980C4⋊C4—28no—
981C4⋊C4—28no—
982C4⋊C4—28no—
983C4⋊C4—28no—
984C4⋊C4—28no—
985C4⋊C4—28no—
986C4⋊C4—28no—
987C4⋊C4—28no—
988C4⋊C4—28no—
989C4⋊C4—28no—
990C4⋊C4—28no—
991C4⋊C4—44no—
992C4⋊C4—44no—
993C4⋊C4—44no—
994C4⋊C4—44no—
995C4⋊C4—44no—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C4⋊C4—44no—
999C4⋊C4—44no—
1000C4⋊C4—44no—
1001C4⋊C4—44no—
1002C4⋊C4—44no—
1003C4⋊C4—44no—
1004C4⋊C4—44no—
1005C4⋊C4—44no—
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—
1030C4⋊C4—44no—
1031C22⋊C4—28no—
1032C22⋊C4—28no—
1033C22⋊C4—28no—
1034C22⋊C4—28no—
1035C22⋊C4—44no—
1036C22⋊C4—44no—
1037C22⋊C4—44no—
1038C22⋊C4—44no—
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⋊C4—44no—
1054C22⋊C4—44no—
1055C22⋊C4—44no—
1056C22⋊C4—44no—
1057C42—28no—
1058C42—44no—
1059C42—44no—
1060C42—44no—
1061C42—44no—
1062C42—44no—
1063C42—44no—
1064C42—44no—
1065C42—44no—
1066C42—44no—
1067C42—44no—
1068C42—44no—
1069C42—44no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—44no—
1085C23—44no—
1086C23—44no—
1087C23—44no—
1088C23—44no—
1089C23—44no—
1090C23—44no—
1091C23—44no—
1092C23—44no—
1093C23—44no—
1094C23—44no—
1095C23—44no—
1096C23—44no—
1097C23—44no—
1098C23C2×H(5,𝔽2)12yes—
1099C23C2×2−1+412yes—
1100C23C2×2−1+412yes—
1101C23#58512yes—
1102C23#58512yes—
1103C23#58512yes—
1104C23#58512yes—
1105C23C2611yescharacteristic
1106Q8—88no—
1107D4—88no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—28no—
1115C2×C4—28no—
1116C2×C4—28no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
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—416no—
1196C2×C4—44no—
1197C2×C4—44no—
1198C2×C4—44no—
1199C2×C4—44no—
1200C2×C4—44no—
1201C2×C4—44no—
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—88no—
1223C2×C4C2×H(5,𝔽2)14yes—
1224C2×C4C2×2−1+414yes—
1225C2×C4C2×2−1+414yes—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—88no—
1241C22—88no—
1242C22#354114yes—
1243C22#354714yes—
1244C22#355314yes—
1245C22#355514yes—
1246C22#356014yes—
1247C22#356514yes—
1248C22#356714yes—
1249C22C22×H(5,𝔽2)11yescharacteristic
1250C22C22×2−1+411yescharacteristic
1251C22C22×2−1+411yescharacteristic
1252C22C2×#58511yescharacteristic
1253C22C2×#58511yescharacteristic
1254C22C2×#58511yescharacteristic
1255C22C2×#58511yescharacteristic
1256C4—24no—
1257C4—24no—
1258C4—24no—
1259C4—42no—
1260C4—42no—
1261C4—42no—
1262C4—42no—
1263C4—42no—
1264C4—42no—
1265C4—42no—
1266C4—42no—
1267C4—42no—
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—
1285C2—82no—
1286C2—82no—
1287C2#5521918yesdirect product factor
1288C2C2×#354111yescharacteristic
1289C2C2×#356011yescharacteristic
1290C2C2×#356711yescharacteristic
1291C2C2×#356511yescharacteristic
1292C2C2×#354711yescharacteristic
1293C2C2×#355511yescharacteristic
1294C2C2×#355311yescharacteristic
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. #55219C2direct (N × H)
3. C2×#2792C2semidirect
4. C2×#2791C2semidirect
5. C2×#2788C2semidirect
6. C2×#2787C2semidirect
7. C2×#2787C2semidirect
9. C2×#2783C2semidirect
10. C2×#2783C2semidirect
12. C2×#2772C2semidirect
13. C2×#2772C2semidirect
14. C2×#2762C2semidirect
15. C2×#2719C2semidirect
17. C2×#2690C2semidirect
18. C2×#2839C2semidirect
19. C2×#2836C2semidirect
21. C2×#2590C2semidirect
22. C2×#2590C2semidirect
23. C2×#2556C2semidirect
24. C2×#2525C2semidirect
25. C2×#2525C2semidirect
26. C2×#2497C2semidirect
27. C2×#2506C2semidirect
29. C2×#2475C2semidirect
30. C2×#2629C2semidirect
31. C2×#2650C2semidirect
39. #2839C22semidirect
40. #2836C22semidirect
43. #2792C22semidirect
44. #2791C22semidirect
45. #2788C22semidirect
46. #2787C22semidirect
47. #2787C22semidirect
49. #2783C22semidirect
50. #2783C22semidirect
52. #2772C22semidirect
53. #2772C22semidirect
54. #2762C22semidirect
55. #2719C22semidirect
57. #2690C22semidirect
59. #2650C22semidirect
60. #2629C22semidirect
61. #2590C22semidirect
62. #2590C22semidirect
63. #2556C22semidirect
64. #2525C22semidirect
65. #2525C22semidirect
66. #2506C22semidirect
67. #2497C22semidirect
68. #2475C22semidirect
1287. C2#55219direct (N × H)

Maximal subgroups

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

subgroupindex
#552192
C2×#27952
C2×#27922
C2×#27912
C2×#27882
C2×#27872
C2×#27862
C2×#27832
C2×#27792
C2×#27722
C2×#27622
C2×#27192
C2×#27072
C2×#26902
C2×#28392
C2×#28362
C2×#28142
C2×#25902
C2×#25562
C2×#25252
C2×#24972
C2×#25062
C2×#24702
C2×#24752
C2×#26292
C2×#26502
C2×#26512