Finite Group Databasebeta

← C2×#13074774 #14920575

Subgroups — C2×#13074774 #14920575

Order 2816.

2354 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
2C22×#66942C211yesmaximal, characteristic, complemented
3#13074774C2116yesmaximal, direct product factor
4C2×#10622271C211yesmaximal, characteristic, complemented
5C2×#10622605C211yesmaximal, characteristic
6C2×#10622270C211yesmaximal, characteristic, complemented
7C2×#10622597C211yesmaximal, characteristic, complemented
8C2×#10622288C211yesmaximal, characteristic
9C2×#10622607C211yesmaximal, characteristic
10C2×#10622607C211yesmaximal, characteristic
11C2×#10622598C211yesmaximal, characteristic, complemented
12C2×#10622260C211yesmaximal, characteristic, complemented
13C2×#10622283C211yesmaximal, characteristic
14C2×#10622282C211yesmaximal, characteristic
15C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
16C2×C11×#398C211yesmaximal, characteristic, complemented
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
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×(C2×D11)⋊C4C2211yescharacteristic
28C22×C4⋊Dic11C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40C22×C4×Dic11C2211yescharacteristic
41C22×C4×Dic11C2211yescharacteristic
42C2×#66951—28no—
43C2×#66951C2218yes—
44C2×#66942—28no—
45C2×#66942C2218yescomplemented
46C11×#398C2218yescomplemented
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
57#10622607C2218yes—
58#10622607C2218yes—
59#10622605C2218yes—
60#10622598C2218yescomplemented
61#10622597C2218yescomplemented
62C4⋊C4×Dic11C2218yescomplemented
63#10622288C2218yes—
64#10622283C2218yes—
65#10622282C2218yes—
66#10622271C2218yescomplemented
67#10622270C2218yescomplemented
68#10622260C2218yescomplemented
69C24×D11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C2×C11×C4⋊C4—24no—
85C2×C11×C4⋊C4—24no—
86C2×C11×C4⋊C4—24no—
87C2×C11×C4⋊C4—24no—
88C2×C11×C4⋊C4C2314yes—
89C2×C11×C4⋊C4C2314yes—
90C2×C11×C4⋊C4C2314yes—
91C2×C11×C4⋊C4C2314yes—
92C2×(C2×D11)⋊C4—24no—
93C2×(C2×D11)⋊C4—24no—
94C2×(C2×D11)⋊C4—24no—
95C2×(C2×D11)⋊C4—24no—
96C2×(C2×D11)⋊C4—24no—
97C2×(C2×D11)⋊C4—42no—
98C2×(C2×D11)⋊C4—42no—
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×(C2×D11)⋊C4C2314yes—
106C2×C4⋊Dic11—24no—
107C2×C4⋊Dic11—24no—
108C2×C4⋊Dic11—24no—
109C2×C4⋊Dic11—42no—
110C2×C4⋊Dic11C2314yes—
111C2×C4⋊Dic11C2314yes—
112C2×C4⋊Dic11C2314yes—
113C2×C4⋊Dic11C2314yes—
114C2×Dic11⋊C4—24no—
115C2×Dic11⋊C4—24no—
116C2×Dic11⋊C4—24no—
117C2×Dic11⋊C4—24no—
118C2×Dic11⋊C4—24no—
119C2×Dic11⋊C4—24no—
120C2×Dic11⋊C4—42no—
121C2×Dic11⋊C4C2314yes—
122C2×Dic11⋊C4C2314yes—
123C2×Dic11⋊C4C2314yes—
124C2×Dic11⋊C4C2314yes—
125C2×Dic11⋊C4C2314yes—
126C2×Dic11⋊C4C2314yes—
127C2×Dic11⋊C4C2314yes—
128C2×C4×Dic11—42no—
129C2×C4×Dic11—42no—
130C2×C4×Dic11D418yes—
131C2×C4×Dic11C2314yes—
132C2×C4×Dic11C2314yes—
133C2×C4×Dic11C2314yes—
134#66951—232no—
135#66942—232no—
136C11×#95C2314yes—
137C11×#95C2314yes—
138C11×#95C2314yes—
139C11⋊#95C2314yes—
140C11⋊#95C2314yes—
141C11⋊#95C2314yes—
142C11⋊#95C2314yes—
143C11⋊#95C2314yes—
144C11⋊#95C2314yes—
145C11⋊#95C2314yes—
146C2×#2664—111nomaximal, Sylow
147C24×C11C2411yescharacteristic
148C23×D11—22no—
149C23×D11—22no—
150C23×D11—22no—
151C23×D11—22no—
152C23×D11—22no—
153C23×D11—22no—
154C23×D11—22no—
155C23×D11C2412yes—
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×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—22no—
175C22×C4×C11C2×D414yes—
176C22×C4×C11#4114yes—
177C22×C4×C11C2412yes—
178C22×C4×C11C2412yes—
179C22×C4×C11C2412yes—
180C22×C4×C11C2412yes—
181C22×C4×C11C2412yes—
182C22×C4×C11C2412yes—
183C22×C4×C11C2412yes—
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×Dic11—22no—
200C22×Dic11—22no—
201C22×Dic11—22no—
202C22×Dic11C2×D414yes—
203C22×Dic11C2×D414yes—
204C22×Dic11#4114yes—
205C22×Dic11C2412yes—
206C22×Dic11C2412yes—
207C22×Dic11C2412yes—
208C22×Dic11C2412yes—
209C22×Dic11C2412yes—
210C22×Dic11C2412yes—
211C22×Dic11C2412yes—
212C11×C4⋊C4—28no—
213C11×C4⋊C4—28no—
214C11×C4⋊C4—28no—
215C11×C4⋊C4—28no—
216(C2×D11)⋊C4—28no—
217(C2×D11)⋊C4—28no—
218(C2×D11)⋊C4—28no—
219(C2×D11)⋊C4—28no—
220(C2×D11)⋊C4—28no—
221(C2×D11)⋊C4—44no—
222(C2×D11)⋊C4—44no—
223C4⋊Dic11—28no—
224C4⋊Dic11—28no—
225C4⋊Dic11—28no—
226C4⋊Dic11—44no—
227Dic11⋊C4—28no—
228Dic11⋊C4—28no—
229Dic11⋊C4—28no—
230Dic11⋊C4—28no—
231Dic11⋊C4—28no—
232Dic11⋊C4—28no—
233Dic11⋊C4—44no—
234C4×Dic11—44no—
235C4×Dic11—44no—
236C4×Dic11C2×D4116yes—
237C22×#126—111no—
238C22×#125—111no—
239#2664—1116no—
240C2×#400—111no—
241C2×#399—111no—
242C2×#398—111no—
243C2×#398—111no—
244C2×#398D1111yescharacteristic, complemented
245C2×#397—111no—
246C2×#396—111no—
247C2×#396—111no—
248C2×#389—111no—
249C2×#389—111no—
250C2×#388—111no—
251C2×#388—111no—
252C2×C4×C4⋊C4—111no—
253C23×C11C22×D412yes—
254C23×C11C2×#4112yes—
255C23×C11C2×#4112yes—
256C23×C11H(5,𝔽2)12yes—
257C23×C112−1+412yes—
258C23×C112−1+412yes—
259C23×C112−1+412yes—
260C23×C11C2511yescharacteristic
261C22×D11—22no—
262C22×D11—22no—
263C22×D11—22no—
264C22×D11—22no—
265C22×D11—22no—
266C22×D11—22no—
267C22×D11—22no—
268C22×D11—44no—
269C22×D11—44no—
270C22×D11—44no—
271C22×D11—44no—
272C22×D11—44no—
273C22×D11—44no—
274C22×D11—44no—
275C2×C4×C11—28no—
276C2×C4×C11—28no—
277C2×C4×C11—22no—
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—22no—
296C2×C4×C11—44no—
297C2×C4×C11—44no—
298C2×C4×C11—44no—
299C2×C4×C11—44no—
300C2×C4×C11—44no—
301C2×C4×C11C22×D414yes—
302C2×C4×C11C2×#4114yes—
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—22no—
324C2×Dic11—44no—
325C2×Dic11—44no—
326C2×Dic11—44no—
327C2×Dic11—44no—
328C2×Dic11C22×D414yes—
329C2×Dic11C22×D414yes—
330C2×Dic11C2×#4114yes—
331C2×#126—118no—
332C2×#126—228no—
333C2×#125—118no—
334C2×#125—228no—
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⋊C4—111no—
343C22×C4⋊C4—111no—
344C22×C4⋊C4—111no—
345C22×C4⋊C4—111no—
346C22×C4⋊C4C2×D1111yescharacteristic
347C22×C4⋊C4C2×D1111yescharacteristic
348C22×C4⋊C4C2×D1111yescharacteristic
349C22×C4⋊C4C2×D1111yescharacteristic
350C22×C22⋊C4—111no—
351C22×C22⋊C4—111no—
352C22×C22⋊C4—111no—
353C22×C22⋊C4—111no—
354C22×C22⋊C4—111no—
355C22×C22⋊C4—111no—
356C22×C22⋊C4—111no—
357C22×C42—111no—
358C22×C42—111no—
359C22×C42—111no—
360#400—118no—
361#399—118no—
362#398—118no—
363#398—118no—
364#398C2×D1118yescomplemented
365#397—118no—
366#396—118no—
367#396—118no—
368#389—118no—
369#389—118no—
370#388—118no—
371#388—118no—
372C4×C4⋊C4—118no—
373C2×#95—111no—
374C2×#95—111no—
375C2×#95—111no—
376C2×#95—111no—
377C2×#95—111no—
378C2×#95—111no—
379C2×#95—111no—
380C2×#95C2×D1111yescharacteristic
381C2×#95C2×D1111yescharacteristic
382C2×#95C2×D1111yescharacteristic
383C22×C11#53214yes—
384C22×C11#53614yes—
385C22×C11#53714yes—
386C22×C11#53914yes—
387C22×C11#53914yes—
388C22×C11#54114yes—
389C22×C11#54114yes—
390C22×C11C23×D411yescharacteristic
391C22×C11C22×#4111yescharacteristic
392C22×C11C22×#4111yescharacteristic
393C22×C11C2×H(5,𝔽2)11yescharacteristic
394C22×C11C2×2−1+411yescharacteristic
395C22×C11C2×2−1+411yescharacteristic
396C22×C11C2×2−1+411yescharacteristic
397C2×D11—42no—
398C2×D11—42no—
399C2×D11—42no—
400C2×D11—42no—
401C2×D11—42no—
402C2×D11—42no—
403C2×D11—42no—
404C2×D11—88no—
405C4×C11—24no—
406C4×C11—24no—
407C4×C11—42no—
408C4×C11—42no—
409C4×C11—42no—
410C4×C11—42no—
411C4×C11—42no—
412Dic11—24no—
413Dic11—24no—
414Dic11—24no—
415Dic11—42no—
416Dic11—42no—
417Dic11—42no—
418Dic11—42no—
419C25—111no—
420C23×C4—111no—
421C23×C4—111no—
422C23×C4—111no—
423C23×C4—111no—
424C23×C4—111no—
425C23×C4—111no—
426C23×C4—111no—
427C23×C4C22×D1111yescharacteristic
428C23×C4C22×D1111yescharacteristic
429C23×C4C22×D1111yescharacteristic
430C23×C4C22×D1111yescharacteristic
431C23×C4C22×D1111yescharacteristic
432C23×C4C22×D1111yescharacteristic
433C23×C4C22×D1111yescharacteristic
434#126—2232no—
435#125—2232no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—114no—
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—114no—
450C2×C4⋊C4—114no—
451C2×C4⋊C4—224no—
452C2×C4⋊C4—224no—
453C2×C4⋊C4—224no—
454C2×C4⋊C4—224no—
455C2×C4⋊C4—224no—
456C2×C4⋊C4—224no—
457C2×C4⋊C4—224no—
458C2×C4⋊C4—224no—
459C2×C4⋊C4—224no—
460C2×C4⋊C4—442no—
461C2×C4⋊C4—442no—
462C2×C4⋊C4C22×D1114yes—
463C2×C4⋊C4C22×D1114yes—
464C2×C4⋊C4C22×D1114yes—
465C2×C4⋊C4C22×D1114yes—
466C2×C22⋊C4—114no—
467C2×C22⋊C4—114no—
468C2×C22⋊C4—114no—
469C2×C22⋊C4—114no—
470C2×C22⋊C4—114no—
471C2×C22⋊C4—114no—
472C2×C22⋊C4—114no—
473C2×C22⋊C4—224no—
474C2×C22⋊C4—224no—
475C2×C22⋊C4—224no—
476C2×C22⋊C4—224no—
477C2×C22⋊C4—224no—
478C2×C22⋊C4—442no—
479C2×C22⋊C4—442no—
480C2×C42—118no—
481C2×C42—114no—
482C2×C42—114no—
483C2×C42—114no—
484C2×C42—442no—
485C2×C42—442no—
486#95—114no—
487#95—114no—
488#95—114no—
489#95—114no—
490#95—114no—
491#95—114no—
492#95—114no—
493#95C22×D1114yes—
494#95C22×D1114yes—
495#95C22×D1114yes—
496C2×C11#266418yescomplemented
497C2×C11C2×#53211yescharacteristic
498C2×C11C2×#53611yescharacteristic
499C2×C11C2×#53711yescharacteristic
500C2×C11C2×#53911yescharacteristic
501C2×C11C2×#53911yescharacteristic
502C2×C11C2×#54111yescharacteristic
503C2×C11C2×#54111yescharacteristic
504D11—82no—
505C24—112no—
506C24—222no—
507C24—222no—
508C24—222no—
509C24—222no—
510C24—222no—
511C24—222no—
512C24—222no—
513C24C23×D1111yescharacteristic
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—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—114no—
534C22×C4—114no—
535C22×C4—114no—
536C22×C4—112no—
537C22×C4—112no—
538C22×C4—112no—
539C22×C4—112no—
540C22×C4—112no—
541C22×C4—112no—
542C22×C4—112no—
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—222no—
559C22×C4—222no—
560C22×C4—222no—
561C22×C4D4×D1114yes—
562C22×C4#434114yes—
563C22×C4C23×D1112yes—
564C22×C4C23×D1112yes—
565C22×C4C23×D1112yes—
566C22×C4C23×D1112yes—
567C22×C4C23×D1112yes—
568C22×C4C23×D1112yes—
569C22×C4C23×D1112yes—
570C4⋊C4—28no—
571C4⋊C4—28no—
572C4⋊C4—28no—
573C4⋊C4—28no—
574C4⋊C4—228no—
575C4⋊C4—228no—
576C4⋊C4—228no—
577C4⋊C4—228no—
578C4⋊C4—228no—
579C4⋊C4—228no—
580C4⋊C4—228no—
581C4⋊C4—228no—
582C4⋊C4—228no—
583C4⋊C4—444no—
584C4⋊C4—444no—
585C22⋊C4—228no—
586C22⋊C4—228no—
587C22⋊C4—228no—
588C22⋊C4—228no—
589C22⋊C4—228no—
590C22⋊C4—444no—
591C22⋊C4—444no—
592C42—1116no—
593C42—444no—
594C42—444no—
595C11C2×#266411yescharacteristic, complemented, Sylow
596C23—222no—
597C23—222no—
598C23—222no—
599C23—222no—
600C23—222no—
601C23—222no—
602C23—222no—
603C23—444no—
604C23—444no—
605C23—444no—
606C23—444no—
607C23—444no—
608C23—444no—
609C23—444no—
610C23C2×D4×D1112yes—
611C23C2×#434112yes—
612C23#6704012yes—
613C23#6704012yes—
614C23#41×D1112yes—
615C23#6704212yes—
616C23#6704312yes—
617C23C24×D1111yescharacteristic
618C2×C4—28no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—28no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
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—22no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—114no—
645C2×C4—114no—
646C2×C4—114no—
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—228no—
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—222no—
667C2×C4—222no—
668C2×C4—444no—
669C2×C4—444no—
670C2×C4—444no—
671C2×C4—444no—
672C2×C4C2×D4×D1114yes—
673C2×C4C2×#434114yes—
674C22—442no—
675C22—442no—
676C22—442no—
677C22—442no—
678C22—442no—
679C22—442no—
680C22—442no—
681C22—888no—
682C22#1062312714yes—
683C22#1062315914yes—
684C22#1062316014yes—
685C22#1062319614yes—
686C22#1062322314yes—
687C22#1062322714yes—
688C22#1062326214yes—
689C22C22×D4×D1111yescharacteristic
690C22C22×#434111yescharacteristic
691C22C2×#6704011yescharacteristic
692C22C2×#6704011yescharacteristic
693C22C2×#41×D1111yescharacteristic
694C22C2×#6704211yescharacteristic
695C22C2×#6704311yescharacteristic
696C4—24no—
697C4—24no—
698C4—42no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—224no—
704C4—224no—
705C4—224no—
706C4—442no—
707C4—442no—
708C4—442no—
709C4—442no—
710C2—882no—
711C2#1307477418yesdirect product factor
712C2C2×#1062312711yescharacteristic
713C2C2×#1062315911yescharacteristic
714C2C2×#1062316011yescharacteristic
715C2C2×#1062319611yescharacteristic
716C2C2×#1062322311yescharacteristic
717C2C2×#1062322711yescharacteristic
718C2C2×#1062326211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#398C2
socleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×#398D11
hypocenterC11C2×#2664
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
2. C22×#66942C2semidirect
3. #13074774C2direct (N × H)
4. C2×#10622271C2semidirect
6. C2×#10622270C2semidirect
7. C2×#10622597C2semidirect
11. C2×#10622598C2semidirect
12. C2×#10622260C2semidirect
15. C2×C4⋊C4×Dic11C2semidirect
16. C2×C11×#398C2semidirect
45. C2×#66942C22semidirect
46. C11×#398C22semidirect
60. #10622598C22semidirect
61. #10622597C22semidirect
62. C4⋊C4×Dic11C22semidirect
66. #10622271C22semidirect
67. #10622270C22semidirect
68. #10622260C22semidirect
244. C2×#398D11semidirect
364. #398C2×D11semidirect
496. C2×C11#2664semidirect
595. C11C2×#2664semidirect
711. C2#13074774direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669512
C22×#669422
#130747742
C2×#106222712
C2×#106226052
C2×#106222702
C2×#106225972
C2×#106222882
C2×#106226072
C2×#106225982
C2×#106222602
C2×#106222832
C2×#106222822
C2×C4⋊C4×Dic112
C2×C11×#3982
C2×#266411