Finite Group Databasebeta

← C2×#13072637 #14921749

Subgroups — C2×#13072637 #14921749

Order 2816.

2854 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66977C211yesmaximal, characteristic
2C22×C4×Dic22C211yesmaximal, characteristic, complemented
3#13072637C2116yesmaximal, direct product factor
4C2×#10622561C211yesmaximal, characteristic
5C2×#10622269C211yesmaximal, characteristic, complemented
6C2×#10622269C211yesmaximal, characteristic, complemented
7C2×#10622560C211yesmaximal, characteristic
8C2×#10622259C211yesmaximal, characteristic, complemented
9C2×#10622541C211yesmaximal, characteristic, complemented
10C2×#10622564C211yesmaximal, characteristic
11C2×#10622564C211yesmaximal, characteristic
12C2×#10622268C211yesmaximal, characteristic, complemented
13C2×#10622546C211yesmaximal, characteristic, complemented
14C2×#10622546C211yesmaximal, characteristic, complemented
15C2×#10622823C211yesmaximal, characteristic
16C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
17C24×C4×C11C2211yescharacteristic
18C23×Dic22C2211yescharacteristic
19C23×Dic22C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C42×C11C2211yescharacteristic
23C22×C42×C11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C4⋊Dic11C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic
32C2×#66977—28no—
33C2×#66977C2218yes—
34C22×Dic11⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×C4×Dic11C2211yescharacteristic
41C22×C4×Dic11C2211yescharacteristic
42C2×C4×Dic22—28no—
43C2×C4×Dic22C2218yescomplemented
44C4×C11×C22⋊C4C2218yes—
45C2×C11×#95C2211yescharacteristic
46C2×C11×#95C2211yescharacteristic
47#10622823C2218yes—
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58#10622564C2218yes—
59#10622564C2218yes—
60#10622561C2218yes—
61#10622560C2218yes—
62#10622546C2218yescomplemented
63#10622546C2218yescomplemented
64#10622541C2218yescomplemented
65#10622269C2218yescomplemented
66#10622269C2218yescomplemented
67#10622268C2218yescomplemented
68#10622259C2218yescomplemented
69C25×C11C2311yescharacteristic
70C23×C4×C11—24no—
71C23×C4×C11—24no—
72C23×C4×C11—42no—
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2314yes—
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C22×Dic22—24no—
89C22×Dic22—24no—
90C22×Dic22—24no—
91C22×Dic22—24no—
92C22×Dic22—24no—
93C22×Dic22—42no—
94C22×Dic22C2314yes—
95C22×Dic22C2314yes—
96C2×C11×C22⋊C4—24no—
97C2×C11×C22⋊C4Q818yescomplemented
98C2×C11×C22⋊C4C2314yes—
99C2×C11×C22⋊C4C2314yes—
100C2×C42×C11—24no—
101C2×C42×C11—42no—
102C2×C42×C11C2314yes—
103C2×C42×C11C2314yes—
104C2×C22⋊Dic11—24no—
105C2×C22⋊Dic11—24no—
106C2×C22⋊Dic11—24no—
107C2×C22⋊Dic11—42no—
108C2×C22⋊Dic11C2314yes—
109C2×C22⋊Dic11C2314yes—
110C2×C22⋊Dic11C2314yes—
111C2×C22⋊Dic11C2314yes—
112C2×C4⋊Dic11—24no—
113C2×C4⋊Dic11—24no—
114C2×C4⋊Dic11—24no—
115C2×C4⋊Dic11—42no—
116C2×C4⋊Dic11C2314yes—
117C2×C4⋊Dic11C2314yes—
118C2×C4⋊Dic11C2314yes—
119C2×C4⋊Dic11C2314yes—
120#66977—232no—
121C2×Dic11⋊C4—24no—
122C2×Dic11⋊C4—24no—
123C2×Dic11⋊C4—24no—
124C2×Dic11⋊C4—24no—
125C2×Dic11⋊C4—42no—
126C2×Dic11⋊C4D418yes—
127C2×Dic11⋊C4C2314yes—
128C2×Dic11⋊C4C2314yes—
129C2×Dic11⋊C4C2314yes—
130C2×Dic11⋊C4C2314yes—
131C2×Dic11⋊C4C2314yes—
132C2×Dic11⋊C4C2314yes—
133C2×C4×Dic11—24no—
134C2×C4×Dic11—24no—
135C2×C4×Dic11C2314yes—
136C2×C4×Dic11C2314yes—
137C4×Dic22—232no—
138C11×#95C2314yes—
139C11×#95C2314yes—
140C11⋊#95C2314yes—
141C11⋊#95C2314yes—
142C11⋊#95C2314yes—
143C11⋊#95C2314yes—
144C11⋊#95C2314yes—
145C11⋊#95C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C2×#2465—111nomaximal, Sylow
151C24×C11—22no—
152C24×C11—22no—
153C24×C11—22no—
154C24×C11—22no—
155C24×C11—22no—
156C24×C11—22no—
157C24×C11C2×Q814yes—
158C24×C11C2412yes—
159C24×C11C2411yescharacteristic
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—28no—
174C22×C4×C11—28no—
175C22×C4×C11—44no—
176C22×C4×C11—416no—
177C22×C4×C11C2×D414yes—
178C22×C4×C11C2×Q814yes—
179C22×C4×C11C2×Q814yes—
180C22×C4×C11#4114yes—
181C22×C4×C11#4114yes—
182C22×C4×C11C2412yes—
183C22×C4×C11C2412yes—
184C22×C4×C11C2412yes—
185C22×C4×C11C2412yes—
186C22×C4×C11C2412yes—
187C22×C4×C11C2412yes—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—22no—
195C22×Dic11—22no—
196C22×Dic11—22no—
197C22×Dic11—22no—
198C22×Dic11—22no—
199C22×Dic11—22no—
200C22×Dic11—22no—
201C22×Dic11—22no—
202C22×Dic11—22no—
203C22×Dic11—22no—
204C22×Dic11—22no—
205C22×Dic11—22no—
206C22×Dic11—22no—
207C22×Dic11—22no—
208C22×Dic11—22no—
209C22×Dic11C2×D414yes—
210C22×Dic11C2×D414yes—
211C22×Dic11#4114yes—
212C22×Dic11C2412yes—
213C22×Dic11C2412yes—
214C22×Dic11C2412yes—
215C22×Dic11C2412yes—
216C22×Dic11C2412yes—
217C22×Dic11C2412yes—
218C22×Dic11C2412yes—
219C22×Dic11C2412yes—
220C2×Dic22—232no—
221C2×Dic22—28no—
222C2×Dic22—28no—
223C2×Dic22—28no—
224C2×Dic22—28no—
225C2×Dic22—28no—
226C2×Dic22—44no—
227C2×Dic22—416no—
228C11×C22⋊C4—28no—
229C11×C22⋊C4C2×Q8116yescomplemented
230C42×C11—28no—
231C42×C11—44no—
232C22⋊Dic11—28no—
233C22⋊Dic11—28no—
234C22⋊Dic11—28no—
235C22⋊Dic11—44no—
236C4⋊Dic11—28no—
237C4⋊Dic11—28no—
238C4⋊Dic11—28no—
239C4⋊Dic11—44no—
240Dic11⋊C4—28no—
241Dic11⋊C4—28no—
242Dic11⋊C4—28no—
243Dic11⋊C4—28no—
244Dic11⋊C4—44no—
245Dic11⋊C4C2×D4116yes—
246C4×Dic11—28no—
247C4×Dic11—28no—
248C22×C22⋊Q8—111no—
249C22×C4×Q8—111no—
250#2465—1116no—
251C2×#396—111no—
252C2×#395—111no—
253C2×#395—111no—
254C2×#393—111no—
255C2×#391—111no—
256C2×#389—111no—
257C2×#388—111no—
258C2×#388—111no—
259C2×#387—111no—
260C2×#387—111no—
261C2×#387—111no—
262C2×#385—111no—
263C2×C4×C22⋊C4D1111yescharacteristic
264C23×C11—28no—
265C23×C11—28no—
266C23×C11—28no—
267C23×C11—22no—
268C23×C11—22no—
269C23×C11—22no—
270C23×C11—22no—
271C23×C11—22no—
272C23×C11—22no—
273C23×C11—44no—
274C23×C11—44no—
275C23×C11—44no—
276C23×C11—44no—
277C23×C11C22×D412yes—
278C23×C11C22×Q814yes—
279C23×C11C22×Q812yes—
280C23×C11C2×#4112yes—
281C23×C11C2×#4112yes—
282C23×C11C2×#4112yes—
283C23×C11H(5,𝔽2)12yes—
284C23×C112−1+412yes—
285C23×C11C2511yescharacteristic
286C2×C4×C11—28no—
287C2×C4×C11—28no—
288C2×C4×C11—28no—
289C2×C4×C11—28no—
290C2×C4×C11—28no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—416no—
305C2×C4×C11—44no—
306C2×C4×C11C22×D414yes—
307C2×C4×C11C22×Q814yes—
308C2×C4×C11C22×Q814yes—
309C2×C4×C11C2×#4114yes—
310C2×C4×C11C2×#4114yes—
311C2×Dic11—28no—
312C2×Dic11—28no—
313C2×Dic11—28no—
314C2×Dic11—22no—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—44no—
336C2×Dic11—44no—
337C2×Dic11—44no—
338C2×Dic11—44no—
339C2×Dic11—44no—
340C2×Dic11C22×D414yes—
341C2×Dic11C22×D414yes—
342C2×Dic11C2×#4114yes—
343Dic22—232no—
344Dic22—416no—
345C23×Q8—111no—
346C23×Q8—111no—
347C24×C4C2×D1111yescharacteristic
348C2×C22⋊Q8—118no—
349C2×C22⋊Q8—228no—
350C2×C4×Q8—118no—
351C2×C4×Q8—228no—
352C22×C4⋊C4—111no—
353C22×C4⋊C4—111no—
354C22×C4⋊C4—111no—
355C22×C4⋊C4—111no—
356C22×C4⋊C4—111no—
357C22×C4⋊C4—111no—
358C22×C4⋊C4—111no—
359C22×C4⋊C4—111no—
360C22×C4⋊C4—111no—
361C22×C4⋊C4—111no—
362C22×C22⋊C4—111no—
363C22×C22⋊C4—111no—
364C22×C22⋊C4—111no—
365C22×C22⋊C4—111no—
366C22×C22⋊C4C2×D1111yescharacteristic
367C22×C22⋊C4C2×D1111yescharacteristic
368C22×C42—111no—
369C22×C42—111no—
370C22×C42C2×D1111yescharacteristic
371C22×C42C2×D1111yescharacteristic
372#396—118no—
373#395—118no—
374#395—118no—
375#393—118no—
376#391—118no—
377#389—118no—
378#388—118no—
379#388—118no—
380#387—118no—
381#387—118no—
382#387—118no—
383#385—118no—
384C4×C22⋊C4C2×D1118yes—
385C2×#95—111no—
386C2×#95—111no—
387C2×#95—111no—
388C2×#95—111no—
389C2×#95—111no—
390C2×#95—111no—
391C2×#95—111no—
392C2×#95—111no—
393C2×#95—111no—
394C2×#95—111no—
395C2×#95C2×D1111yescharacteristic
396C2×#95C2×D1111yescharacteristic
397C22×C11—24no—
398C22×C11—24no—
399C22×C11—24no—
400C22×C11—42no—
401C22×C11—42no—
402C22×C11—42no—
403C22×C11—42no—
404C22×C11—416no—
405C22×C11#52514yes—
406C22×C11#53314yes—
407C22×C11#54214yes—
408C22×C11#54614yes—
409C22×C11D4×Q814yes—
410C22×C11#55414yes—
411C22×C11#55614yes—
412C22×C11C23×D411yescharacteristic
413C22×C11C23×Q811yescharacteristic
414C22×C11C22×#4111yescharacteristic
415C22×C11C22×#4111yescharacteristic
416C22×C11C22×#4111yescharacteristic
417C22×C11C2×H(5,𝔽2)11yescharacteristic
418C22×C11C2×2−1+411yescharacteristic
419C4×C11—24no—
420C4×C11—24no—
421C4×C11—24no—
422C4×C11—24no—
423C4×C11—24no—
424C4×C11—42no—
425Dic11—24no—
426Dic11—24no—
427Dic11—24no—
428Dic11—42no—
429Dic11—42no—
430Dic11—42no—
431Dic11—42no—
432Dic11—42no—
433C25C22×D1111yescharacteristic
434C22×Q8—114no—
435C22×Q8—114no—
436C22×Q8—224no—
437C22×Q8—224no—
438C22×Q8—224no—
439C22×Q8—224no—
440C22×Q8—224no—
441C22×Q8—442no—
442C23×C4—24no—
443C23×C4—24no—
444C23×C4—42no—
445C23×C4—111no—
446C23×C4—111no—
447C23×C4—111no—
448C23×C4—111no—
449C23×C4—111no—
450C23×C4—111no—
451C23×C4—111no—
452C23×C4—111no—
453C23×C4C22×D1111yescharacteristic
454C23×C4C22×D1114yes—
455C23×C4C22×D1111yescharacteristic
456C23×C4C22×D1111yescharacteristic
457C23×C4C22×D1111yescharacteristic
458C23×C4C22×D1111yescharacteristic
459C23×C4C22×D1111yescharacteristic
460C22⋊Q8—2232no—
461C4×Q8—2232no—
462C2×C4⋊C4—118no—
463C2×C4⋊C4—114no—
464C2×C4⋊C4—114no—
465C2×C4⋊C4—114no—
466C2×C4⋊C4—114no—
467C2×C4⋊C4—114no—
468C2×C4⋊C4—114no—
469C2×C4⋊C4—114no—
470C2×C4⋊C4—114no—
471C2×C4⋊C4—114no—
472C2×C4⋊C4—114no—
473C2×C4⋊C4—224no—
474C2×C4⋊C4—224no—
475C2×C4⋊C4—224no—
476C2×C4⋊C4—224no—
477C2×C4⋊C4—224no—
478C2×C4⋊C4—224no—
479C2×C4⋊C4—224no—
480C2×C4⋊C4—442no—
481C2×C4⋊C4—442no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—114no—
484C2×C22⋊C4—114no—
485C2×C22⋊C4—114no—
486C2×C22⋊C4—114no—
487C2×C22⋊C4—224no—
488C2×C22⋊C4—224no—
489C2×C22⋊C4—224no—
490C2×C22⋊C4—442no—
491C2×C22⋊C4Dic2218yescomplemented
492C2×C22⋊C4C22×D1114yes—
493C2×C22⋊C4C22×D1114yes—
494C2×C42—24no—
495C2×C42—42no—
496C2×C42—114no—
497C2×C42—114no—
498C2×C42—224no—
499C2×C42—224no—
500C2×C42C22×D1114yes—
501C2×C42C22×D1114yes—
502#95—114no—
503#95—114no—
504#95—114no—
505#95—114no—
506#95—114no—
507#95—114no—
508#95—114no—
509#95—114no—
510#95—114no—
511#95—114no—
512#95C22×D1114yes—
513#95C22×D1114yes—
514C2×C11—44no—
515C2×C11#246518yescomplemented
516C2×C11C2×#52511yescharacteristic
517C2×C11C2×#53311yescharacteristic
518C2×C11C2×#54211yescharacteristic
519C2×C11C2×#54611yescharacteristic
520C2×C11C2×D4×Q811yescharacteristic
521C2×C11C2×#55411yescharacteristic
522C2×C11C2×#55611yescharacteristic
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24C2×Dic2214yes—
530C24C23×D1112yes—
531C24C23×D1111yescharacteristic
532C2×Q8—228no—
533C2×Q8—228no—
534C2×Q8—228no—
535C2×Q8—2232no—
536C2×Q8—228no—
537C2×Q8—228no—
538C2×Q8—444no—
539C2×Q8—4416no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—28no—
554C22×C4—28no—
555C22×C4—44no—
556C22×C4—416no—
557C22×C4—114no—
558C22×C4—114no—
559C22×C4—114no—
560C22×C4—112no—
561C22×C4—112no—
562C22×C4—112no—
563C22×C4—112no—
564C22×C4—112no—
565C22×C4—112no—
566C22×C4—112no—
567C22×C4—112no—
568C22×C4—222no—
569C22×C4—222no—
570C22×C4—222no—
571C22×C4—222no—
572C22×C4—222no—
573C22×C4—222no—
574C22×C4—222no—
575C22×C4—222no—
576C22×C4—222no—
577C22×C4—222no—
578C22×C4—222no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—222no—
582C22×C4—222no—
583C22×C4—222no—
584C22×C4—222no—
585C22×C4—222no—
586C22×C4—222no—
587C22×C4—222no—
588C22×C4—222no—
589C22×C4C2×Dic2214yes—
590C22×C4C2×Dic2214yes—
591C22×C4#433914yes—
592C22×C4#433914yes—
593C22×C4D4×D1114yes—
594C22×C4C23×D1112yes—
595C22×C4C23×D1112yes—
596C22×C4C23×D1112yes—
597C22×C4C23×D1112yes—
598C22×C4C23×D1112yes—
599C22×C4C23×D1112yes—
600C4⋊C4—1116no—
601C4⋊C4—228no—
602C4⋊C4—228no—
603C4⋊C4—228no—
604C4⋊C4—228no—
605C4⋊C4—228no—
606C4⋊C4—228no—
607C4⋊C4—228no—
608C4⋊C4—444no—
609C4⋊C4—444no—
610C22⋊C4—28no—
611C22⋊C4—228no—
612C22⋊C4—228no—
613C22⋊C4—228no—
614C22⋊C4—444no—
615C22⋊C4C2×Dic22116yescomplemented
616C42—28no—
617C42—44no—
618C42—228no—
619C42—228no—
620C11C2×#246511yescharacteristic, complemented, Sylow
621C23—28no—
622C23—28no—
623C23—28no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—44no—
631C23—44no—
632C23—44no—
633C23—44no—
634C23C22×Dic2214yes—
635C23C22×Dic2212yes—
636C23C2×#433912yes—
637C23C2×#433912yes—
638C23C2×D4×D1112yes—
639C23#6703712yes—
640C23#41×D1112yes—
641C23#6704312yes—
642C23C24×D1111yescharacteristic
643Q8—2232no—
644Q8—4416no—
645C2×C4—28no—
646C2×C4—28no—
647C2×C4—28no—
648C2×C4—28no—
649C2×C4—28no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—416no—
664C2×C4—44no—
665C2×C4—114no—
666C2×C4—114no—
667C2×C4—114no—
668C2×C4—228no—
669C2×C4—228no—
670C2×C4—228no—
671C2×C4—222no—
672C2×C4—222no—
673C2×C4—222no—
674C2×C4—222no—
675C2×C4—222no—
676C2×C4—222no—
677C2×C4—222no—
678C2×C4—222no—
679C2×C4—222no—
680C2×C4—222no—
681C2×C4—222no—
682C2×C4—222no—
683C2×C4—222no—
684C2×C4—222no—
685C2×C4—222no—
686C2×C4—222no—
687C2×C4—222no—
688C2×C4—222no—
689C2×C4—222no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—444no—
693C2×C4—444no—
694C2×C4—444no—
695C2×C4—444no—
696C2×C4—444no—
697C2×C4C22×Dic2214yes—
698C2×C4C22×Dic2214yes—
699C2×C4C2×#433914yes—
700C2×C4C2×#433914yes—
701C2×C4C2×D4×D1114yes—
702C22—24no—
703C22—24no—
704C22—24no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—416no—
710C22#1062300114yes—
711C22#1062302114yes—
712C22#1062306414yes—
713C22D4×Dic2214yes—
714C22#1062307014yes—
715C22#1062307814yes—
716C22#1062309214yes—
717C22C23×Dic2211yescharacteristic
718C22C22×#433911yescharacteristic
719C22C22×#433911yescharacteristic
720C22C22×D4×D1111yescharacteristic
721C22C2×#6703711yescharacteristic
722C22C2×#41×D1111yescharacteristic
723C22C2×#6704311yescharacteristic
724C4—24no—
725C4—24no—
726C4—24no—
727C4—24no—
728C4—24no—
729C4—42no—
730C4—224no—
731C4—224no—
732C4—224no—
733C4—442no—
734C4—442no—
735C4—442no—
736C4—442no—
737C4—442no—
738C2—44no—
739C2#1307263718yesdirect product factor
740C2C2×#1062307811yescharacteristic
741C2C2×#1062300111yescharacteristic
742C2C2×#1062309211yescharacteristic
743C2C2×#1062302111yescharacteristic
744C2C2×D4×Dic2211yescharacteristic
745C2C2×#1062307011yescharacteristic
746C2C2×#1062306411yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C4×C11×C22⋊C4C2
socleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×C4×C22⋊C4D11
hypocenterC11C2×#2465
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic22C2semidirect
3. #13072637C2direct (N × H)
5. C2×#10622269C2semidirect
6. C2×#10622269C2semidirect
8. C2×#10622259C2semidirect
9. C2×#10622541C2semidirect
12. C2×#10622268C2semidirect
13. C2×#10622546C2semidirect
14. C2×#10622546C2semidirect
43. C2×C4×Dic22C22semidirect
62. #10622546C22semidirect
63. #10622546C22semidirect
64. #10622541C22semidirect
65. #10622269C22semidirect
66. #10622269C22semidirect
67. #10622268C22semidirect
68. #10622259C22semidirect
97. C2×C11×C22⋊C4Q8semidirect
229. C11×C22⋊C4C2×Q8semidirect
491. C2×C22⋊C4Dic22semidirect
515. C2×C11#2465semidirect
615. C22⋊C4C2×Dic22semidirect
620. C11C2×#2465semidirect
739. C2#13072637direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669772
C22×C4×Dic222
#130726372
C2×#106225612
C2×#106222692
C2×#106225602
C2×#106222592
C2×#106225412
C2×#106225642
C2×#106222682
C2×#106225462
C2×#106228232
C2×C4×C11×C22⋊C42
C2×#246511