Finite Group Databasebeta

← C2×#13071396 #14912656

Subgroups — C2×#13071396 #14912656

Order 2816.

2614 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66951C211yesmaximal, characteristic
2#13071396C2116yesmaximal, direct product factor
3C2×#10622598C211yesmaximal, characteristic, complemented
4C2×#10622260C211yesmaximal, characteristic, complemented
5C2×#10622283C211yesmaximal, characteristic
6C2×#10622553C211yesmaximal, characteristic
7C2×#10622603C211yesmaximal, characteristic
8C2×#10622267C211yesmaximal, characteristic, complemented
9C2×#10622265C211yesmaximal, characteristic, complemented
10C2×#10622281C211yesmaximal, characteristic
11C2×#10622281C211yesmaximal, characteristic
12C2×#10622263C211yesmaximal, characteristic, complemented
13C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
14C2×C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
15C2×#10622279C211yesmaximal, characteristic
16C2×C11×#387C211yesmaximal, characteristic, complemented
17C23×C4×D11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C22×C4⋊Dic11C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
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×#66951C4116yescomplemented
41C2×#66951C2218yes—
42C11×#387C2218yescomplemented
43C2×C11×#95C2211yescharacteristic
44C2×C11×#95C2211yescharacteristic
45C2×C11×#95C2211yescharacteristic
46C2×C11×#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55#10622603C2218yes—
56#10622598C2218yescomplemented
57C4⋊C4×Dic11C2218yescomplemented
58#10622553C2218yes—
59C4×C4⋊Dic11C2218yescomplemented
60#10622283C2218yes—
61#10622281C2218yes—
62#10622281C2218yes—
63#10622279C2218yes—
64#10622267C2218yescomplemented
65#10622265C2218yescomplemented
66#10622263C2218yescomplemented
67#10622260C2218yescomplemented
68C24×D11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C22×C4×D11—24no—
84C22×C4×D11—42no—
85C22×C4×D11—42no—
86C22×C4×D11C2314yes—
87C2×C11×C4⋊C4—24no—
88C2×C11×C4⋊C4C2×C418yescomplemented
89C2×C11×C4⋊C4C2314yes—
90C2×C11×C4⋊C4C2314yes—
91C2×C42×C11—24no—
92C2×C42×C11C2314yes—
93C2×(C2×D11)⋊C4—24no—
94C2×(C2×D11)⋊C4—42no—
95C2×(C2×D11)⋊C4—42no—
96C2×(C2×D11)⋊C4C2×C418yes—
97C2×(C2×D11)⋊C4C2×C418yes—
98C2×(C2×D11)⋊C4C2×C418yes—
99C2×(C2×D11)⋊C4C2314yes—
100C2×(C2×D11)⋊C4C2314yes—
101C2×(C2×D11)⋊C4C2314yes—
102C2×(C2×D11)⋊C4C2314yes—
103C2×(C2×D11)⋊C4C2314yes—
104C2×(C2×D11)⋊C4C2314yes—
105C2×C4⋊Dic11—24no—
106C2×C4⋊Dic11—24no—
107C2×C4⋊Dic11—42no—
108C2×C4⋊Dic11C2×C418yescomplemented
109C2×C4⋊Dic11C2314yes—
110C2×C4⋊Dic11C2314yes—
111C2×C4⋊Dic11C2314yes—
112C2×C4⋊Dic11C2314yes—
113C2×Dic11⋊C4—42no—
114C2×Dic11⋊C4—42no—
115C2×Dic11⋊C4—42no—
116C2×Dic11⋊C4C2×C418yescomplemented
117C2×Dic11⋊C4C2314yes—
118C2×Dic11⋊C4C2314yes—
119C2×Dic11⋊C4C2314yes—
120C2×Dic11⋊C4C2314yes—
121C2×C4×Dic11—42no—
122C2×C4×Dic11—42no—
123C2×C4×Dic11—42no—
124C2×C4×Dic11—42no—
125C2×C4×Dic11C2×C418yescomplemented
126C2×C4×Dic11C2314yes—
127C2×C4×Dic11C2314yes—
128C2×C4×Dic11C2314yes—
129C2×C4×Dic11C2314yes—
130C2×C4×Dic11C2314yes—
131#66951C2×C4164yescomplemented
132C11×#95C2314yes—
133C11×#95C2314yes—
134C11×#95C2314yes—
135C11×#95C2314yes—
136C11⋊#95C2314yes—
137C11⋊#95C2314yes—
138C11⋊#95C2314yes—
139C11⋊#95C2314yes—
140C11⋊#95C2314yes—
141C11⋊#95C2314yes—
142C11⋊#95C2314yes—
143C11⋊#95C2314yes—
144C2×#2334—111nomaximal, Sylow
145C24×C11C2411yescharacteristic
146C23×D11—22no—
147C23×D11—22no—
148C23×D11—22no—
149C23×D11—22no—
150C23×D11—22no—
151C23×D11—22no—
152C23×D11C22×C414yes—
153C23×D11C2412yes—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
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×C11C22×C414yes—
172C22×C4×C11C22×C414yes—
173C22×C4×C11C22×C414yes—
174C22×C4×C11#4114yes—
175C22×C4×C11C2412yes—
176C22×C4×C11C2412yes—
177C22×C4×C11C2412yes—
178C22×C4×C11C2412yes—
179C22×C4×C11C2412yes—
180C22×C4×C11C2412yes—
181C22×C4×C11C2412yes—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—22no—
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×Dic11C22×C414yes—
200C22×Dic11C22×C414yes—
201C22×Dic11C22×C414yes—
202C22×Dic11#4114yes—
203C22×Dic11C2412yes—
204C22×Dic11C2412yes—
205C22×Dic11C2412yes—
206C22×Dic11C2412yes—
207C22×Dic11C2412yes—
208C22×Dic11C2412yes—
209C22×Dic11C2412yes—
210C2×C4×D11—28no—
211C2×C4×D11—44no—
212C2×C4×D11—44no—
213C2×C4×D11—416no—
214C11×C4⋊C4—28no—
215C11×C4⋊C4C22×C4116yescomplemented
216C42×C11—28no—
217(C2×D11)⋊C4—28no—
218(C2×D11)⋊C4—44no—
219(C2×D11)⋊C4—44no—
220(C2×D11)⋊C4C22×C4116yes—
221(C2×D11)⋊C4C22×C4116yes—
222(C2×D11)⋊C4C22×C4116yes—
223C4⋊Dic11—28no—
224C4⋊Dic11—28no—
225C4⋊Dic11—44no—
226C4⋊Dic11C22×C4116yescomplemented
227Dic11⋊C4—44no—
228Dic11⋊C4—44no—
229Dic11⋊C4—44no—
230Dic11⋊C4C22×C4116yescomplemented
231C4×Dic11—44no—
232C4×Dic11—44no—
233C4×Dic11—44no—
234C4×Dic11—44no—
235C4×Dic11C22×C4116yescomplemented
236C22×#126—111no—
237#2334—1116no—
238C2×#389—111no—
239C2×#389—111no—
240C2×#388—111no—
241C2×#388—111no—
242C2×#388—111no—
243C2×#387—111no—
244C2×#387—111no—
245C2×#387D1111yescharacteristic, complemented
246C2×#385—111no—
247C2×#385—111no—
248C2×#382—111no—
249C2×C4×C4⋊C4—111no—
250C2×C4×C4⋊C4—111no—
251C2×C4×C22⋊C4—111no—
252C23×C11C23×C412yes—
253C23×C11C2×#4112yes—
254C23×C11C2×#4112yes—
255C23×C11H(5,𝔽2)12yes—
256C23×C11H(5,𝔽2)12yes—
257C23×C112−1+412yes—
258C23×C112−1+412yes—
259C23×C11C2511yescharacteristic
260C22×D11—28no—
261C22×D11—28no—
262C22×D11—28no—
263C22×D11—22no—
264C22×D11—22no—
265C22×D11—22no—
266C22×D11—22no—
267C22×D11—22no—
268C22×D11—22no—
269C22×D11—44no—
270C22×D11—44no—
271C22×D11—44no—
272C22×D11—44no—
273C22×D11C23×C414yes—
274C2×C4×C11—28no—
275C2×C4×C11—28no—
276C2×C4×C11—28no—
277C2×C4×C11—28no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—44no—
296C2×C4×C11—44no—
297C2×C4×C11—44no—
298C2×C4×C11C23×C414yes—
299C2×C4×C11C23×C414yes—
300C2×C4×C11C23×C414yes—
301C2×C4×C11C2×#4114yes—
302C2×Dic11—28no—
303C2×Dic11—28no—
304C2×Dic11—28no—
305C2×Dic11—28no—
306C2×Dic11—22no—
307C2×Dic11—22no—
308C2×Dic11—22no—
309C2×Dic11—22no—
310C2×Dic11—22no—
311C2×Dic11—22no—
312C2×Dic11—22no—
313C2×Dic11—22no—
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—44no—
324C2×Dic11—44no—
325C2×Dic11—44no—
326C2×Dic11C23×C414yes—
327C2×Dic11C23×C414yes—
328C2×Dic11C23×C414yes—
329C2×Dic11C2×#4114yes—
330C4×D11—416no—
331C24×C4—111no—
332C2×#126—118no—
333C2×#126—1116no—
334C22×C4⋊C4—111no—
335C22×C4⋊C4—111no—
336C22×C4⋊C4—111no—
337C22×C4⋊C4—111no—
338C22×C4⋊C4—111no—
339C22×C4⋊C4—111no—
340C22×C4⋊C4—111no—
341C22×C4⋊C4—111no—
342C22×C4⋊C4C2×D1111yescharacteristic
343C22×C4⋊C4C2×D1111yescharacteristic
344C22×C22⋊C4—111no—
345C22×C22⋊C4—111no—
346C22×C22⋊C4—111no—
347C22×C22⋊C4—111no—
348C22×C22⋊C4—111no—
349C22×C22⋊C4—111no—
350C22×C42—111no—
351C22×C42—111no—
352C22×C42—111no—
353C22×C42—111no—
354C22×C42—111no—
355C22×C42C2×D1111yescharacteristic
356#389—118no—
357#389—118no—
358#388—118no—
359#388—118no—
360#388—118no—
361#387—118no—
362#387—118no—
363#387C2×D1118yescomplemented
364#385—118no—
365#385—118no—
366#382—118no—
367C4×C4⋊C4—118no—
368C4×C4⋊C4—118no—
369C4×C22⋊C4—118no—
370C2×#95—111no—
371C2×#95—111no—
372C2×#95—111no—
373C2×#95—111no—
374C2×#95—111no—
375C2×#95—111no—
376C2×#95—111no—
377C2×#95—111no—
378C2×#95C2×D1111yescharacteristic
379C2×#95C2×D1111yescharacteristic
380C2×#95C2×D1111yescharacteristic
381C2×#95C2×D1111yescharacteristic
382C22×C11C4×#4114yes—
383C22×C11#52014yes—
384C22×C11#52014yes—
385C22×C11#53814yes—
386C22×C11#53914yes—
387C22×C11#54114yes—
388C22×C11#54214yes—
389C22×C11C24×C411yescharacteristic
390C22×C11C22×#4111yescharacteristic
391C22×C11C22×#4111yescharacteristic
392C22×C11C2×H(5,𝔽2)11yescharacteristic
393C22×C11C2×H(5,𝔽2)11yescharacteristic
394C22×C11C2×2−1+411yescharacteristic
395C22×C11C2×2−1+411yescharacteristic
396C2×D11—24no—
397C2×D11—24no—
398C2×D11—24no—
399C2×D11—416no—
400C2×D11—42no—
401C2×D11—42no—
402C2×D11—42no—
403C2×D11—42no—
404C4×C11—24no—
405C4×C11—24no—
406C4×C11—24no—
407C4×C11—24no—
408C4×C11—42no—
409C4×C11—42no—
410C4×C11—42no—
411Dic11—24no—
412Dic11—24no—
413Dic11—24no—
414Dic11—24no—
415Dic11—42no—
416Dic11—42no—
417Dic11—42no—
418C25—111no—
419C23×C4—111no—
420C23×C4—111no—
421C23×C4—111no—
422C23×C4—111no—
423C23×C4—111no—
424C23×C4—111no—
425C23×C4—111no—
426C23×C4—114no—
427C23×C4—224no—
428C23×C4—442no—
429C23×C4—442no—
430C23×C4C22×D1111yescharacteristic
431C23×C4C22×D1111yescharacteristic
432C23×C4C22×D1111yescharacteristic
433C23×C4C22×D1111yescharacteristic
434C23×C4C22×D1111yescharacteristic
435C23×C4C22×D1111yescharacteristic
436C23×C4C22×D1111yescharacteristic
437#126—1164no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—118no—
440C2×C4⋊C4—118no—
441C2×C4⋊C4—114no—
442C2×C4⋊C4—114no—
443C2×C4⋊C4—114no—
444C2×C4⋊C4—114no—
445C2×C4⋊C4—114no—
446C2×C4⋊C4—114no—
447C2×C4⋊C4—114no—
448C2×C4⋊C4—114no—
449C2×C4⋊C4—224no—
450C2×C4⋊C4—224no—
451C2×C4⋊C4—442no—
452C2×C4⋊C4—442no—
453C2×C4⋊C4—442no—
454C2×C4⋊C4—442no—
455C2×C4⋊C4C4×D1118yescomplemented
456C2×C4⋊C4C22×D1114yes—
457C2×C4⋊C4C22×D1114yes—
458C2×C22⋊C4—118no—
459C2×C22⋊C4—118no—
460C2×C22⋊C4—118no—
461C2×C22⋊C4—114no—
462C2×C22⋊C4—114no—
463C2×C22⋊C4—114no—
464C2×C22⋊C4—114no—
465C2×C22⋊C4—114no—
466C2×C22⋊C4—114no—
467C2×C22⋊C4—224no—
468C2×C22⋊C4—442no—
469C2×C22⋊C4—442no—
470C2×C42—24no—
471C2×C42—118no—
472C2×C42—114no—
473C2×C42—114no—
474C2×C42—114no—
475C2×C42—114no—
476C2×C42—114no—
477C2×C42—442no—
478C2×C42—442no—
479C2×C42—442no—
480C2×C42—442no—
481C2×C42C22×D1114yes—
482#95—114no—
483#95—114no—
484#95—114no—
485#95—114no—
486#95—114no—
487#95—114no—
488#95—114no—
489#95—114no—
490#95C22×D1114yes—
491#95C22×D1114yes—
492#95C22×D1114yes—
493#95C22×D1114yes—
494C2×C11#233418yescomplemented
495C2×C11C2×C4×#4111yescharacteristic
496C2×C11C2×#52011yescharacteristic
497C2×C11C2×#52011yescharacteristic
498C2×C11C2×#53811yescharacteristic
499C2×C11C2×#53911yescharacteristic
500C2×C11C2×#54111yescharacteristic
501C2×C11C2×#54211yescharacteristic
502D11—44no—
503C24—114no—
504C24—112no—
505C24—222no—
506C24—222no—
507C24—222no—
508C24—222no—
509C24—222no—
510C24—222no—
511C24C23×D1111yescharacteristic
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—114no—
530C22×C4—114no—
531C22×C4—114no—
532C22×C4—114no—
533C22×C4—112no—
534C22×C4—112no—
535C22×C4—112no—
536C22×C4—112no—
537C22×C4—112no—
538C22×C4—112no—
539C22×C4—112no—
540C22×C4—228no—
541C22×C4—222no—
542C22×C4—222no—
543C22×C4—222no—
544C22×C4—222no—
545C22×C4—222no—
546C22×C4—222no—
547C22×C4—222no—
548C22×C4—222no—
549C22×C4—222no—
550C22×C4—222no—
551C22×C4—222no—
552C22×C4—222no—
553C22×C4—222no—
554C22×C4—222no—
555C22×C4—222no—
556C22×C4—222no—
557C22×C4—222no—
558C22×C4—444no—
559C22×C4—444no—
560C22×C4—4416no—
561C22×C4C2×C4×D1114yes—
562C22×C4C2×C4×D1114yes—
563C22×C4C2×C4×D1114yes—
564C22×C4#434114yes—
565C22×C4C23×D1112yes—
566C22×C4C23×D1112yes—
567C22×C4C23×D1112yes—
568C22×C4C23×D1112yes—
569C22×C4C23×D1112yes—
570C22×C4C23×D1112yes—
571C22×C4C23×D1112yes—
572C4⋊C4—28no—
573C4⋊C4—1116no—
574C4⋊C4—1116no—
575C4⋊C4—228no—
576C4⋊C4—228no—
577C4⋊C4—444no—
578C4⋊C4—444no—
579C4⋊C4—444no—
580C4⋊C4—444no—
581C4⋊C4C2×C4×D11116yescomplemented
582C22⋊C4—1116no—
583C22⋊C4—1116no—
584C22⋊C4—1116no—
585C22⋊C4—228no—
586C22⋊C4—444no—
587C22⋊C4—444no—
588C42—28no—
589C42—1116no—
590C42—444no—
591C42—444no—
592C42—444no—
593C42—444no—
594C11C2×#233411yescharacteristic, complemented, Sylow
595C23—114no—
596C23—228no—
597C23—228no—
598C23—228no—
599C23—222no—
600C23—222no—
601C23—222no—
602C23—222no—
603C23—222no—
604C23—222no—
605C23—444no—
606C23—444no—
607C23—444no—
608C23—444no—
609C23C22×C4×D1112yes—
610C23C2×#434112yes—
611C23#6704012yes—
612C23#41×D1112yes—
613C23#6704212yes—
614C23#6704212yes—
615C23#6704312yes—
616C23C24×D1111yescharacteristic
617C2×C4—28no—
618C2×C4—28no—
619C2×C4—28no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—28no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—44no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—114no—
642C2×C4—114no—
643C2×C4—114no—
644C2×C4—114no—
645C2×C4—228no—
646C2×C4—228no—
647C2×C4—228no—
648C2×C4—228no—
649C2×C4—222no—
650C2×C4—222no—
651C2×C4—222no—
652C2×C4—222no—
653C2×C4—222no—
654C2×C4—222no—
655C2×C4—222no—
656C2×C4—222no—
657C2×C4—222no—
658C2×C4—222no—
659C2×C4—222no—
660C2×C4—222no—
661C2×C4—222no—
662C2×C4—222no—
663C2×C4—222no—
664C2×C4—222no—
665C2×C4—222no—
666C2×C4—4416no—
667C2×C4—444no—
668C2×C4—444no—
669C2×C4—444no—
670C2×C4C22×C4×D1114yes—
671C2×C4C22×C4×D1114yes—
672C2×C4C22×C4×D1114yes—
673C2×C4C2×#434114yes—
674C22—224no—
675C22—224no—
676C22—224no—
677C22—4416no—
678C22—442no—
679C22—442no—
680C22—442no—
681C22—442no—
682C22#1062305414yes—
683C22C4×#434114yes—
684C22#1062310514yes—
685C22#1062317414yes—
686C22#1062319614yes—
687C22#1062322714yes—
688C22#1062323514yes—
689C22C23×C4×D1111yescharacteristic
690C22C22×#434111yescharacteristic
691C22C2×#6704011yescharacteristic
692C22C2×#41×D1111yescharacteristic
693C22C2×#6704211yescharacteristic
694C22C2×#6704211yescharacteristic
695C22C2×#6704311yescharacteristic
696C4—24no—
697C4—24no—
698C4—24no—
699C4—24no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—224no—
704C4—224no—
705C4—224no—
706C4—224no—
707C4—442no—
708C4—442no—
709C4—442no—
710C2—444no—
711C2#1307139618yesdirect product factor
712C2C2×C4×#434111yescharacteristic
713C2C2×#1062305411yescharacteristic
714C2C2×#1062310511yescharacteristic
715C2C2×#1062323511yescharacteristic
716C2C2×#1062319611yescharacteristic
717C2C2×#1062322711yescharacteristic
718C2C2×#1062317411yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#387C2
socleC24×C11C24
prime radicalC24×D11C23
cosocleC23×C11C25
hypercenterC2×#387D11
hypocenterC11C2×#2334
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #13071396C2direct (N × H)
3. C2×#10622598C2semidirect
4. C2×#10622260C2semidirect
8. C2×#10622267C2semidirect
9. C2×#10622265C2semidirect
12. C2×#10622263C2semidirect
13. C2×C4⋊C4×Dic11C2semidirect
14. C2×C4×C4⋊Dic11C2semidirect
16. C2×C11×#387C2semidirect
40. C2×#66951C4semidirect
42. C11×#387C22semidirect
56. #10622598C22semidirect
57. C4⋊C4×Dic11C22semidirect
59. C4×C4⋊Dic11C22semidirect
64. #10622267C22semidirect
65. #10622265C22semidirect
66. #10622263C22semidirect
67. #10622260C22semidirect
88. C2×C11×C4⋊C4C2×C4semidirect
108. C2×C4⋊Dic11C2×C4semidirect
116. C2×Dic11⋊C4C2×C4semidirect
125. C2×C4×Dic11C2×C4semidirect
131. #66951C2×C4semidirect
215. C11×C4⋊C4C22×C4semidirect
226. C4⋊Dic11C22×C4semidirect
230. Dic11⋊C4C22×C4semidirect
235. C4×Dic11C22×C4semidirect
245. C2×#387D11semidirect
363. #387C2×D11semidirect
455. C2×C4⋊C4C4×D11semidirect
494. C2×C11#2334semidirect
581. C4⋊C4C2×C4×D11semidirect
594. C11C2×#2334semidirect
711. C2#13071396direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669512
#130713962
C2×#106225982
C2×#106222602
C2×#106222832
C2×#106225532
C2×#106226032
C2×#106222672
C2×#106222652
C2×#106222812
C2×#106222632
C2×C4⋊C4×Dic112
C2×C4×C4⋊Dic112
C2×#106222792
C2×C11×#3872
C2×#233411