Finite Group Databasebeta

← C2×#13071482 #14913006

Subgroups — C2×#13071482 #14913006

Order 2816.

3526 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66945C211yesmaximal, characteristic
2C22×#66925C211yesmaximal, characteristic
3C22×C4⋊C4×D11C211yesmaximal, characteristic
4#13071482C2116yesmaximal, direct product factor
5C2×#10622260C211yesmaximal, characteristic, complemented
6C2×#10622585C211yesmaximal, characteristic, complemented
7C2×#10622594C211yesmaximal, characteristic, complemented
8C2×#10622266C211yesmaximal, characteristic, complemented
9C2×#10622267C211yesmaximal, characteristic, complemented
10C2×#10622277C211yesmaximal, characteristic
11C2×#10622277C211yesmaximal, characteristic
12C2×#10622280C211yesmaximal, characteristic
13C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
14C2×#10622262C211yesmaximal, characteristic, complemented
15C2×#10622279C211yesmaximal, characteristic
16C2×C11×#387C211yesmaximal, characteristic, complemented
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C42×C11C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C22×C4⋊Dic11C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37C22×C4×Dic11C2211yescharacteristic
38C22×C4×Dic11C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40C2×#66945—28no—
41C2×#66945C2218yes—
42C2×C4⋊C4×D11C4116yescomplemented
43C2×C4⋊C4×D11C2218yes—
44C2×#66925—28no—
45C2×#66925C2218yes—
46C11×#387C2218yescomplemented
47C2×C11×#95C2211yescharacteristic
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
58C2×C11⋊#95C2211yescharacteristic
59#10622594C2218yescomplemented
60#10622585C2218yescomplemented
61C4×Dic11⋊C4C2218yescomplemented
62#10622280C2218yes—
63#10622279C2218yes—
64#10622277C2218yes—
65#10622277C2218yes—
66#10622267C2218yescomplemented
67#10622266C2218yescomplemented
68#10622262C2218yescomplemented
69#10622260C2218yescomplemented
70C24×D11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C22×C4×D11—24no—
86C22×C4×D11—24no—
87C22×C4×D11—24no—
88C22×C4×D11—24no—
89C22×C4×D11—24no—
90C22×C4×D11—24no—
91C22×C4×D11C2×C418yes—
92C22×C4×D11C2×C418yes—
93C22×C4×D11C2×C418yes—
94C22×C4×D11C2314yes—
95C22×C4×D11C2314yes—
96C22×C4×D11C2314yes—
97C2×C11×C4⋊C4—24no—
98C2×C11×C4⋊C4C2×C418yes—
99C2×C11×C4⋊C4C2314yes—
100C2×C11×C4⋊C4C2314yes—
101C2×C42×C11—24no—
102C2×C42×C11C2314yes—
103C2×(C2×D11)⋊C4—24no—
104C2×(C2×D11)⋊C4—24no—
105C2×(C2×D11)⋊C4—24no—
106C2×(C2×D11)⋊C4D418yes—
107C2×(C2×D11)⋊C4C2314yes—
108C2×(C2×D11)⋊C4C2314yes—
109C2×(C2×D11)⋊C4C2314yes—
110C2×(C2×D11)⋊C4C2314yes—
111C2×C4⋊Dic11—24no—
112C2×C4⋊Dic11C2×C418yes—
113C2×C4⋊Dic11C2314yes—
114C2×C4⋊Dic11C2314yes—
115C2×Dic11⋊C4—24no—
116C2×Dic11⋊C4—24no—
117C2×Dic11⋊C4—24no—
118C2×Dic11⋊C4—24no—
119C2×Dic11⋊C4C2×C418yes—
120C2×Dic11⋊C4C2×C418yes—
121C2×Dic11⋊C4C2314yes—
122C2×Dic11⋊C4C2314yes—
123C2×Dic11⋊C4C2314yes—
124C2×Dic11⋊C4C2314yes—
125C2×Dic11⋊C4C2314yes—
126C2×Dic11⋊C4C2314yes—
127C2×C4×Dic11—24no—
128C2×C4×Dic11—24no—
129C2×C4×Dic11—24no—
130C2×C4×Dic11—24no—
131C2×C4×Dic11—24no—
132C2×C4×Dic11C2314yes—
133C2×C4×Dic11C2314yes—
134C2×C4×Dic11C2314yes—
135C2×C4×Dic11C2314yes—
136C2×C4×Dic11C2314yes—
137#66945—232no—
138C4⋊C4×D11C2×C4164yescomplemented
139#66925—232no—
140C11×#95C2314yes—
141C11×#95C2314yes—
142C11×#95C2314yes—
143C11×#95C2314yes—
144C11⋊#95C2314yes—
145C11⋊#95C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C2×#2344—111nomaximal, Sylow
153C24×C11C2411yescharacteristic
154C23×D11—22no—
155C23×D11—22no—
156C23×D11—22no—
157C23×D11—22no—
158C23×D11C22×C414yes—
159C23×D11C2×D414yes—
160C23×D11#4114yes—
161C23×D11C2412yes—
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—22no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11C22×C414yes—
180C22×C4×C11C22×C414yes—
181C22×C4×C11C22×C414yes—
182C22×C4×C11C2×D414yes—
183C22×C4×C11C2412yes—
184C22×C4×C11C2412yes—
185C22×C4×C11C2412yes—
186C22×C4×C11C2412yes—
187C22×C4×C11C2412yes—
188C22×C4×C11C2412yes—
189C22×C4×C11C2412yes—
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×Dic11C22×C414yes—
206C22×Dic11C22×C414yes—
207C22×Dic11C22×C414yes—
208C22×Dic11C2×D414yes—
209C22×Dic11#4114yes—
210C22×Dic11#4114yes—
211C22×Dic11C2412yes—
212C22×Dic11C2412yes—
213C22×Dic11C2412yes—
214C22×Dic11C2412yes—
215C22×Dic11C2412yes—
216C22×Dic11C2412yes—
217C22×Dic11C2412yes—
218C2×C4×D11—232no—
219C2×C4×D11—28no—
220C2×C4×D11—28no—
221C2×C4×D11—232no—
222C2×C4×D11—232no—
223C2×C4×D11—28no—
224C2×C4×D11—28no—
225C2×C4×D11—28no—
226C2×C4×D11—28no—
227C2×C4×D11C22×C4116yes—
228C2×C4×D11C22×C4116yes—
229C2×C4×D11C22×C4116yes—
230C11×C4⋊C4—28no—
231C11×C4⋊C4C22×C4116yes—
232C42×C11—28no—
233(C2×D11)⋊C4—28no—
234(C2×D11)⋊C4—28no—
235(C2×D11)⋊C4—28no—
236(C2×D11)⋊C4C2×D4116yes—
237C4⋊Dic11—28no—
238C4⋊Dic11C22×C4116yes—
239Dic11⋊C4—28no—
240Dic11⋊C4—28no—
241Dic11⋊C4—28no—
242Dic11⋊C4—28no—
243Dic11⋊C4C22×C4116yes—
244Dic11⋊C4C22×C4116yes—
245C4×Dic11—28no—
246C4×Dic11—28no—
247C4×Dic11—28no—
248C4×Dic11—28no—
249C4×Dic11—28no—
250C22×#117—111no—
251C22×#117—111no—
252C23×C4⋊C4—111no—
253#2344—1116no—
254C2×#389—111no—
255C2×#389—111no—
256C2×#387—111no—
257C2×#387—111no—
258C2×#387—111no—
259C2×#387D1111yescharacteristic, complemented
260C2×#381—111no—
261C2×#381—111no—
262C2×#380—111no—
263C2×C4×C4⋊C4—111no—
264C2×C4×C4⋊C4—111no—
265C2×C4×C22⋊C4—111no—
266C23×C11C23×C412yes—
267C23×C11C22×D412yes—
268C23×C11C2×#4112yes—
269C23×C11C2×#4112yes—
270C23×C11C2×#4112yes—
271C23×C112−1+412yes—
272C23×C112−1+412yes—
273C23×C11C2511yescharacteristic
274C22×D11—28no—
275C22×D11—28no—
276C22×D11—28no—
277C22×D11—28no—
278C22×D11—28no—
279C22×D11—28no—
280C22×D11—22no—
281C22×D11—22no—
282C22×D11—22no—
283C22×D11—22no—
284C22×D11C4×D4116yes—
285C22×D11C23×C414yes—
286C22×D11C22×D414yes—
287C22×D11C2×#4114yes—
288C2×C4×C11—28no—
289C2×C4×C11—28no—
290C2×C4×C11—28no—
291C2×C4×C11—28no—
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—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—44no—
310C2×C4×C11—44no—
311C2×C4×C11—44no—
312C2×C4×C11C23×C414yes—
313C2×C4×C11C23×C414yes—
314C2×C4×C11C23×C414yes—
315C2×C4×C11C22×D414yes—
316C2×Dic11—28no—
317C2×Dic11—28no—
318C2×Dic11—28no—
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—44no—
335C2×Dic11—44no—
336C2×Dic11—44no—
337C2×Dic11#117116yescomplemented
338C2×Dic11C23×C414yes—
339C2×Dic11C23×C414yes—
340C2×Dic11C23×C414yes—
341C2×Dic11C22×D414yes—
342C2×Dic11C2×#4114yes—
343C2×Dic11C2×#4114yes—
344C4×D11—232no—
345C4×D11—232no—
346C4×D11—232no—
347C24×C4—111no—
348C24×C4—111no—
349C24×C4—111no—
350C2×#117—118no—
351C2×#117—118no—
352C2×#117—228no—
353C2×#117—228no—
354C22×C4⋊C4—111no—
355C22×C4⋊C4—111no—
356C22×C4⋊C4—111no—
357C22×C4⋊C4—118no—
358C22×C4⋊C4—1116no—
359C22×C4⋊C4—111no—
360C22×C4⋊C4—111no—
361C22×C4⋊C4—111no—
362C22×C4⋊C4—111no—
363C22×C4⋊C4—111no—
364C22×C4⋊C4C2×D1111yescharacteristic
365C22×C4⋊C4C2×D1111yescharacteristic
366C22×C22⋊C4—111no—
367C22×C22⋊C4—111no—
368C22×C22⋊C4—111no—
369C22×C22⋊C4—111no—
370C22×C42—111no—
371C22×C42—111no—
372C22×C42—111no—
373C22×C42—111no—
374C22×C42—111no—
375C22×C42C2×D1111yescharacteristic
376#389—118no—
377#389—118no—
378#387—118no—
379#387—118no—
380#387—118no—
381#387C2×D1118yescomplemented
382#381—118no—
383#381—118no—
384#380—118no—
385C4×C4⋊C4—118no—
386C4×C4⋊C4—118no—
387C4×C22⋊C4—118no—
388C2×#95—111no—
389C2×#95—111no—
390C2×#95—111no—
391C2×#95—111no—
392C2×#95—111no—
393C2×#95—111no—
394C2×#95—111no—
395C2×#95—111no—
396C2×#95C2×D1111yescharacteristic
397C2×#95C2×D1111yescharacteristic
398C2×#95C2×D1111yescharacteristic
399C2×#95C2×D1111yescharacteristic
400C22×C11C2×#11714yes—
401C22×C11C2×C4×D414yes—
402C22×C11#51914yes—
403C22×C11#54714yes—
404C22×C11#54714yes—
405C22×C11#55214yes—
406C22×C11#55214yes—
407C22×C11C24×C411yescharacteristic
408C22×C11C23×D411yescharacteristic
409C22×C11C22×#4111yescharacteristic
410C22×C11C22×#4111yescharacteristic
411C22×C11C22×#4111yescharacteristic
412C22×C11C2×2−1+411yescharacteristic
413C22×C11C2×2−1+411yescharacteristic
414C2×D11—232no—
415C2×D11—24no—
416C2×D11—24no—
417C2×D11—24no—
418C2×D11—24no—
419C2×D11—24no—
420C2×D11—24no—
421C2×D11C2×C4×D418yes—
422C4×C11—24no—
423C4×C11—24no—
424C4×C11—24no—
425C4×C11—24no—
426C4×C11—42no—
427C4×C11—42no—
428C4×C11—42no—
429Dic11—24no—
430Dic11—24no—
431Dic11—24no—
432Dic11—42no—
433Dic11—42no—
434Dic11—42no—
435Dic11C2×#11718yescomplemented
436C25—111no—
437C23×C4—111no—
438C23×C4—111no—
439C23×C4—111no—
440C23×C4—111no—
441C23×C4—118no—
442C23×C4—118no—
443C23×C4—118no—
444C23×C4—114no—
445C23×C4—114no—
446C23×C4—114no—
447C23×C4—111no—
448C23×C4—111no—
449C23×C4—111no—
450C23×C4—224no—
451C23×C4—224no—
452C23×C4—224no—
453C23×C4—224no—
454C23×C4—224no—
455C23×C4—224no—
456C23×C4C22×D1111yescharacteristic
457C23×C4C22×D1111yescharacteristic
458C23×C4C22×D1111yescharacteristic
459C23×C4C22×D1111yescharacteristic
460C23×C4C22×D1111yescharacteristic
461C23×C4C22×D1111yescharacteristic
462C23×C4C22×D1111yescharacteristic
463#117—2232no—
464#117—2232no—
465C2×C4⋊C4—24no—
466C2×C4⋊C4—118no—
467C2×C4⋊C4—118no—
468C2×C4⋊C4—118no—
469C2×C4⋊C4—114no—
470C2×C4⋊C4—114no—
471C2×C4⋊C4—114no—
472C2×C4⋊C4—1164no—
473C2×C4⋊C4—114no—
474C2×C4⋊C4—114no—
475C2×C4⋊C4—114no—
476C2×C4⋊C4—114no—
477C2×C4⋊C4—114no—
478C2×C4⋊C4—224no—
479C2×C4⋊C4—224no—
480C2×C4⋊C4—224no—
481C2×C4⋊C4—224no—
482C2×C4⋊C4—224no—
483C2×C4⋊C4C4×D1118yes—
484C2×C4⋊C4C22×D1114yes—
485C2×C4⋊C4C22×D1114yes—
486C2×C22⋊C4—118no—
487C2×C22⋊C4—114no—
488C2×C22⋊C4—114no—
489C2×C22⋊C4—114no—
490C2×C22⋊C4—114no—
491C2×C22⋊C4—224no—
492C2×C22⋊C4—224no—
493C2×C22⋊C4—224no—
494C2×C42—24no—
495C2×C42—114no—
496C2×C42—114no—
497C2×C42—114no—
498C2×C42—114no—
499C2×C42—114no—
500C2×C42—224no—
501C2×C42—224no—
502C2×C42—224no—
503C2×C42—224no—
504C2×C42—224no—
505C2×C42C22×D1114yes—
506#95—114no—
507#95—114no—
508#95—114no—
509#95—114no—
510#95—114no—
511#95—114no—
512#95—114no—
513#95—114no—
514#95C22×D1114yes—
515#95C22×D1114yes—
516#95C22×D1114yes—
517#95C22×D1114yes—
518C2×C11#234418yescomplemented
519C2×C11C22×#11711yescharacteristic
520C2×C11C22×C4×D411yescharacteristic
521C2×C11C2×#51911yescharacteristic
522C2×C11C2×#54711yescharacteristic
523C2×C11C2×#54711yescharacteristic
524C2×C11C2×#55211yescharacteristic
525C2×C11C2×#55211yescharacteristic
526D11—28no—
527C24—114no—
528C24—114no—
529C24—114no—
530C24—112no—
531C24—222no—
532C24—222no—
533C24—222no—
534C24—222no—
535C24C23×D1111yescharacteristic
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
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—114no—
554C22×C4—114no—
555C22×C4—114no—
556C22×C4—112no—
557C22×C4—114no—
558C22×C4—114no—
559C22×C4—114no—
560C22×C4—112no—
561C22×C4—112no—
562C22×C4—112no—
563C22×C4—1116no—
564C22×C4—1116no—
565C22×C4—1116no—
566C22×C4—112no—
567C22×C4—112no—
568C22×C4—112no—
569C22×C4—2232no—
570C22×C4—228no—
571C22×C4—228no—
572C22×C4—228no—
573C22×C4—228no—
574C22×C4—2232no—
575C22×C4—2232no—
576C22×C4—228no—
577C22×C4—228no—
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×C4—222no—
590C22×C4—222no—
591C22×C4—222no—
592C22×C4—222no—
593C22×C4C2×C4×D1114yes—
594C22×C4C2×C4×D1114yes—
595C22×C4C2×C4×D1114yes—
596C22×C4D4×D1114yes—
597C22×C4C23×D1112yes—
598C22×C4C23×D1112yes—
599C22×C4C23×D1112yes—
600C22×C4C23×D1112yes—
601C22×C4C23×D1112yes—
602C22×C4C23×D1112yes—
603C22×C4C23×D1112yes—
604C4⋊C4—28no—
605C4⋊C4—1116no—
606C4⋊C4—1116no—
607C4⋊C4—1116no—
608C4⋊C4—228no—
609C4⋊C4—228no—
610C4⋊C4—228no—
611C4⋊C4—228no—
612C4⋊C4—228no—
613C4⋊C4C2×C4×D11116yes—
614C22⋊C4—1116no—
615C22⋊C4—228no—
616C22⋊C4—228no—
617C22⋊C4—228no—
618C42—28no—
619C42—228no—
620C42—228no—
621C42—228no—
622C42—228no—
623C42—228no—
624C11C2×#234411yescharacteristic, complemented, Sylow
625C23—1116no—
626C23—114no—
627C23—114no—
628C23—114no—
629C23—228no—
630C23—228no—
631C23—228no—
632C23—228no—
633C23—228no—
634C23—222no—
635C23—222no—
636C23—222no—
637C23—222no—
638C23—228no—
639C23C22×C4×D1112yes—
640C23C2×D4×D1112yes—
641C23#6704012yes—
642C23#41×D1112yes—
643C23#41×D1112yes—
644C23#41×D1112yes—
645C23#6704312yes—
646C23C24×D1111yescharacteristic
647C2×C4—28no—
648C2×C4—28no—
649C2×C4—28no—
650C2×C4—28no—
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—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—44no—
669C2×C4—44no—
670C2×C4—44no—
671C2×C4—1116no—
672C2×C4—114no—
673C2×C4—114no—
674C2×C4—114no—
675C2×C4—114no—
676C2×C4—114no—
677C2×C4—114no—
678C2×C4—2232no—
679C2×C4—2232no—
680C2×C4—2232no—
681C2×C4—228no—
682C2×C4—228no—
683C2×C4—228no—
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—222no—
693C2×C4—222no—
694C2×C4—222no—
695C2×C4—222no—
696C2×C4—222no—
697C2×C4—222no—
698C2×C4—222no—
699C2×C4—444no—
700C2×C4—444no—
701C2×C4—444no—
702C2×C4C22×C4×D1114yes—
703C2×C4C22×C4×D1114yes—
704C2×C4C22×C4×D1114yes—
705C2×C4C2×D4×D1114yes—
706C22—118no—
707C22—224no—
708C22—224no—
709C22—2232no—
710C22—224no—
711C22—224no—
712C22—224no—
713C22—224no—
714C22D11×#11714yes—
715C22C4×D4×D1114yes—
716C22#1062310314yes—
717C22#1062316214yes—
718C22#1062318614yes—
719C22#1062322414yes—
720C22#1062323914yes—
721C22C23×C4×D1111yescharacteristic
722C22C22×D4×D1111yescharacteristic
723C22C2×#6704011yescharacteristic
724C22C2×#41×D1111yescharacteristic
725C22C2×#41×D1111yescharacteristic
726C22C2×#41×D1111yescharacteristic
727C22C2×#6704311yescharacteristic
728C4—24no—
729C4—24no—
730C4—24no—
731C4—24no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—118no—
736C4—224no—
737C4—224no—
738C4—224no—
739C4—442no—
740C4—442no—
741C4—442no—
742C2—228no—
743C2#1307148218yesdirect product factor
744C2C2×D11×#11711yescharacteristic
745C2C2×C4×D4×D1111yescharacteristic
746C2C2×#1062310311yescharacteristic
747C2C2×#1062318611yescharacteristic
748C2C2×#1062316211yescharacteristic
749C2C2×#1062322411yescharacteristic
750C2C2×#1062323911yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#387C2
socleC24×C11C24
prime radicalC24×D11C23
cosocleC23×C11C25
hypercenterC2×#387D11
hypocenterC11C2×#2344
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
4. #13071482C2direct (N × H)
5. C2×#10622260C2semidirect
6. C2×#10622585C2semidirect
7. C2×#10622594C2semidirect
8. C2×#10622266C2semidirect
9. C2×#10622267C2semidirect
13. C2×C4×Dic11⋊C4C2semidirect
14. C2×#10622262C2semidirect
16. C2×C11×#387C2semidirect
42. C2×C4⋊C4×D11C4semidirect
46. C11×#387C22semidirect
59. #10622594C22semidirect
60. #10622585C22semidirect
61. C4×Dic11⋊C4C22semidirect
66. #10622267C22semidirect
67. #10622266C22semidirect
68. #10622262C22semidirect
69. #10622260C22semidirect
138. C4⋊C4×D11C2×C4semidirect
259. C2×#387D11semidirect
337. C2×Dic11#117semidirect
381. #387C2×D11semidirect
435. Dic11C2×#117semidirect
518. C2×C11#2344semidirect
624. C11C2×#2344semidirect
743. C2#13071482direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669452
C22×#669252
C22×C4⋊C4×D112
#130714822
C2×#106222602
C2×#106225852
C2×#106225942
C2×#106222662
C2×#106222672
C2×#106222772
C2×#106222802
C2×C4×Dic11⋊C42
C2×#106222622
C2×#106222792
C2×C11×#3872
C2×#234411