Finite Group Databasebeta

← C2×#13073646 #14925590

Subgroups — C2×#13073646 #14925590

Order 2816.

2446 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66942C211yesmaximal, characteristic
2C22×#66942C211yesmaximal, characteristic
3#13073646C2116yesmaximal, direct product factor
4C2×#10622270C211yesmaximal, characteristic
5C2×#10622597C211yesmaximal, characteristic
6C2×#10622274C211yesmaximal, characteristic
7C2×#10622260C211yesmaximal, characteristic
8C2×#10622260C211yesmaximal, characteristic
9C2×#10622585C211yesmaximal, characteristic
10C2×#10622585C211yesmaximal, characteristic
11C2×#10622589C211yesmaximal, characteristic
12C2×#10622589C211yesmaximal, characteristic
13C2×#10622589C211yesmaximal, characteristic
14C2×#10622262C211yesmaximal, characteristic
15C2×#10622262C211yesmaximal, characteristic
16C2×C11×#398C211yesmaximal, characteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
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
42C22×C4×Dic11C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C2×#66942—28no—
45C2×#66942—28no—
46C2×#66942C2218yes—
47C2×#66942C2218yes—
48C11×#398C2218yes—
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#10622597C2218yes—
58#10622589C2218yes—
59#10622589C2218yes—
60#10622589C2218yes—
61#10622585C2218yes—
62#10622585C2218yes—
63#10622274C2218yes—
64#10622270C2218yes—
65#10622262C2218yes—
66#10622262C2218yes—
67#10622260C2218yes—
68#10622260C2218yes—
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
83C23×Dic11C2311yescharacteristic
84C2×C11×C4⋊C4—24no—
85C2×C11×C4⋊C4—24no—
86C2×C11×C4⋊C4—42no—
87C2×C11×C4⋊C4—42no—
88C2×C11×C4⋊C4C2314yes—
89C2×C11×C4⋊C4C2314yes—
90C2×C11×C4⋊C4C2314yes—
91C2×C11×C4⋊C4C2314yes—
92C2×C4⋊Dic11—24no—
93C2×C4⋊Dic11—24no—
94C2×C4⋊Dic11—42no—
95C2×C4⋊Dic11—42no—
96C2×C4⋊Dic11C2314yes—
97C2×C4⋊Dic11C2314yes—
98C2×C4⋊Dic11C2314yes—
99C2×C4⋊Dic11C2314yes—
100C2×Dic11⋊C4—24no—
101C2×Dic11⋊C4—24no—
102C2×Dic11⋊C4—24no—
103C2×Dic11⋊C4—24no—
104C2×Dic11⋊C4—24no—
105C2×Dic11⋊C4—24no—
106C2×Dic11⋊C4—24no—
107C2×Dic11⋊C4—24no—
108C2×Dic11⋊C4—24no—
109C2×Dic11⋊C4—24no—
110C2×Dic11⋊C4—42no—
111C2×Dic11⋊C4—42no—
112C2×Dic11⋊C4D418yes—
113C2×Dic11⋊C4Q818yes—
114C2×Dic11⋊C4C2314yes—
115C2×Dic11⋊C4C2314yes—
116C2×Dic11⋊C4C2314yes—
117C2×Dic11⋊C4C2314yes—
118C2×Dic11⋊C4C2314yes—
119C2×Dic11⋊C4C2314yes—
120C2×Dic11⋊C4C2314yes—
121C2×Dic11⋊C4C2314yes—
122C2×Dic11⋊C4C2314yes—
123C2×Dic11⋊C4C2314yes—
124C2×Dic11⋊C4C2314yes—
125C2×Dic11⋊C4C2314yes—
126C2×Dic11⋊C4C2314yes—
127C2×Dic11⋊C4C2314yes—
128C2×C4×Dic11—24no—
129C2×C4×Dic11—24no—
130C2×C4×Dic11—24no—
131C2×C4×Dic11—24no—
132C2×C4×Dic11Q818yes—
133C2×C4×Dic11C2314yes—
134C2×C4×Dic11C2314yes—
135C2×C4×Dic11C2314yes—
136C2×C4×Dic11C2314yes—
137C2×C4×Dic11C2314yes—
138#66942—232no—
139#66942—232no—
140C11×#95C2314yes—
141C11×#95C2314yes—
142C11×#95C2314yes—
143C11⋊#95C2314yes—
144C11⋊#95C2314yes—
145C11⋊#95C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C2×#2552—111nomaximal, Sylow
149C24×C11C2411yescharacteristic
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
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×C11C2×D414yes—
169C22×C4×C11C2×Q814yes—
170C22×C4×C11C2×Q814yes—
171C22×C4×C11C2412yes—
172C22×C4×C11C2412yes—
173C22×C4×C11C2412yes—
174C22×C4×C11C2412yes—
175C22×C4×C11C2412yes—
176C22×C4×C11C2412yes—
177C22×C4×C11C2412yes—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—22no—
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×Dic11C2×D414yes—
195C22×Dic11C2×D414yes—
196C22×Dic11C2×Q814yes—
197C22×Dic11C2×Q814yes—
198C22×Dic11C2×Q814yes—
199C22×Dic11C2×Q814yes—
200C22×Dic11#4114yes—
201C22×Dic11#4114yes—
202C22×Dic11C2412yes—
203C22×Dic11C2412yes—
204C22×Dic11C2412yes—
205C22×Dic11C2412yes—
206C22×Dic11C2412yes—
207C22×Dic11C2412yes—
208C22×Dic11C2412yes—
209C22×Dic11C2412yes—
210C11×C4⋊C4—28no—
211C11×C4⋊C4—28no—
212C11×C4⋊C4—44no—
213C11×C4⋊C4—44no—
214C4⋊Dic11—28no—
215C4⋊Dic11—28no—
216C4⋊Dic11—44no—
217C4⋊Dic11—44no—
218Dic11⋊C4—28no—
219Dic11⋊C4—28no—
220Dic11⋊C4—28no—
221Dic11⋊C4—28no—
222Dic11⋊C4—28no—
223Dic11⋊C4—28no—
224Dic11⋊C4—28no—
225Dic11⋊C4—28no—
226Dic11⋊C4—28no—
227Dic11⋊C4—28no—
228Dic11⋊C4—44no—
229Dic11⋊C4—44no—
230Dic11⋊C4C2×D4116yes—
231Dic11⋊C4C2×Q8116yes—
232C4×Dic11—28no—
233C4×Dic11—28no—
234C4×Dic11—28no—
235C4×Dic11—28no—
236C4×Dic11C2×Q8116yes—
237C22×#125—111no—
238C22×#125—111no—
239#2552—1116no—
240C2×#398—111no—
241C2×#398—111no—
242C2×#398—111no—
243C2×#398D1111yescharacteristic
244C2×#389—111no—
245C2×#389—111no—
246C2×#389—111no—
247C2×#389—111no—
248C2×#384—111no—
249C2×#384—111no—
250C2×#384—111no—
251C2×C4×C4⋊C4—111no—
252C2×C4×C4⋊C4—111no—
253C23×C11C22×D412yes—
254C23×C11C22×Q812yes—
255C23×C11C22×Q812yes—
256C23×C11C2×#4112yes—
257C23×C11C2×#4112yes—
258C23×C11H(5,𝔽2)12yes—
259C23×C112−1+412yes—
260C23×C11C2511yescharacteristic
261C2×C4×C11—28no—
262C2×C4×C11—28no—
263C2×C4×C11—28no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—44no—
283C2×C4×C11—44no—
284C2×C4×C11—44no—
285C2×C4×C11—44no—
286C2×C4×C11C22×D414yes—
287C2×C4×C11C22×Q814yes—
288C2×C4×C11C22×Q814yes—
289C2×Dic11—28no—
290C2×Dic11—28no—
291C2×Dic11—22no—
292C2×Dic11—22no—
293C2×Dic11—22no—
294C2×Dic11—22no—
295C2×Dic11—22no—
296C2×Dic11—22no—
297C2×Dic11—22no—
298C2×Dic11—22no—
299C2×Dic11—22no—
300C2×Dic11—22no—
301C2×Dic11—22no—
302C2×Dic11—22no—
303C2×Dic11—22no—
304C2×Dic11—22no—
305C2×Dic11—22no—
306C2×Dic11—22no—
307C2×Dic11—44no—
308C2×Dic11—44no—
309C2×Dic11—44no—
310C2×Dic11—44no—
311C2×Dic11#125116yescomplemented
312C2×Dic11C4⋊Q8116yes—
313C2×Dic11C22×D414yes—
314C2×Dic11C22×D414yes—
315C2×Dic11C22×Q814yes—
316C2×Dic11C22×Q814yes—
317C2×Dic11C22×Q814yes—
318C2×Dic11C22×Q814yes—
319C2×Dic11C2×#4114yes—
320C2×Dic11C2×#4114yes—
321C2×#125—118no—
322C2×#125—118no—
323C2×#125—228no—
324C2×#125—228no—
325C22×C4⋊C4—111no—
326C22×C4⋊C4—111no—
327C22×C4⋊C4—111no—
328C22×C4⋊C4—111no—
329C22×C4⋊C4—111no—
330C22×C4⋊C4—111no—
331C22×C4⋊C4—111no—
332C22×C4⋊C4—111no—
333C22×C4⋊C4—111no—
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⋊C4—111no—
343C22×C4⋊C4C2×D1111yescharacteristic
344C22×C4⋊C4C2×D1111yescharacteristic
345C22×C4⋊C4C2×D1111yescharacteristic
346C22×C4⋊C4C2×D1111yescharacteristic
347C22×C42—111no—
348C22×C42—111no—
349C22×C42—111no—
350C22×C42—111no—
351C22×C42—111no—
352#398—118no—
353#398—118no—
354#398—118no—
355#398C2×D1118yes—
356#389—118no—
357#389—118no—
358#389—118no—
359#389—118no—
360#384—118no—
361#384—118no—
362#384—118no—
363C4×C4⋊C4—118no—
364C4×C4⋊C4—118no—
365C2×#95—111no—
366C2×#95—111no—
367C2×#95—111no—
368C2×#95—111no—
369C2×#95—111no—
370C2×#95C2×D1111yescharacteristic
371C2×#95C2×D1111yescharacteristic
372C2×#95C2×D1111yescharacteristic
373C22×C11C2×#12514yes—
374C22×C11C2×C4⋊Q814yes—
375C22×C11#54414yes—
376C22×C11#54714yes—
377C22×C11#55014yes—
378C22×C11#55414yes—
379C22×C11#55714yes—
380C22×C11C23×D411yescharacteristic
381C22×C11C23×Q811yescharacteristic
382C22×C11C23×Q811yescharacteristic
383C22×C11C22×#4111yescharacteristic
384C22×C11C22×#4111yescharacteristic
385C22×C11C2×H(5,𝔽2)11yescharacteristic
386C22×C11C2×2−1+411yescharacteristic
387C4×C11—24no—
388C4×C11—24no—
389C4×C11—24no—
390C4×C11—42no—
391C4×C11—42no—
392C4×C11—42no—
393C4×C11—42no—
394Dic11—24no—
395Dic11—24no—
396Dic11—42no—
397Dic11—42no—
398Dic11—42no—
399Dic11—42no—
400Dic11C2×#12518yescomplemented
401Dic11C2×C4⋊Q818yes—
402C23×C4—111no—
403C23×C4—111no—
404C23×C4—111no—
405C23×C4—111no—
406C23×C4—111no—
407C23×C4—111no—
408C23×C4—111no—
409C23×C4—111no—
410C23×C4C22×D1111yescharacteristic
411C23×C4C22×D1111yescharacteristic
412C23×C4C22×D1111yescharacteristic
413C23×C4C22×D1111yescharacteristic
414C23×C4C22×D1111yescharacteristic
415C23×C4C22×D1111yescharacteristic
416C23×C4C22×D1111yescharacteristic
417#125—2232no—
418#125—2232no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—42no—
422C2×C4⋊C4—42no—
423C2×C4⋊C4—118no—
424C2×C4⋊C4—118no—
425C2×C4⋊C4—114no—
426C2×C4⋊C4—114no—
427C2×C4⋊C4—114no—
428C2×C4⋊C4—114no—
429C2×C4⋊C4—114no—
430C2×C4⋊C4—114no—
431C2×C4⋊C4—114no—
432C2×C4⋊C4—114no—
433C2×C4⋊C4—114no—
434C2×C4⋊C4—114no—
435C2×C4⋊C4—114no—
436C2×C4⋊C4—114no—
437C2×C4⋊C4—114no—
438C2×C4⋊C4—114no—
439C2×C4⋊C4—114no—
440C2×C4⋊C4—114no—
441C2×C4⋊C4—114no—
442C2×C4⋊C4—114no—
443C2×C4⋊C4—224no—
444C2×C4⋊C4—224no—
445C2×C4⋊C4—224no—
446C2×C4⋊C4—224no—
447C2×C4⋊C4—224no—
448C2×C4⋊C4—224no—
449C2×C4⋊C4—224no—
450C2×C4⋊C4—224no—
451C2×C4⋊C4—224no—
452C2×C4⋊C4—224no—
453C2×C4⋊C4—224no—
454C2×C4⋊C4—224no—
455C2×C4⋊C4—442no—
456C2×C4⋊C4—442no—
457C2×C4⋊C4—442no—
458C2×C4⋊C4—442no—
459C2×C4⋊C4C22×D1114yes—
460C2×C4⋊C4C22×D1114yes—
461C2×C4⋊C4C22×D1114yes—
462C2×C4⋊C4C22×D1114yes—
463C2×C42—118no—
464C2×C42—114no—
465C2×C42—114no—
466C2×C42—114no—
467C2×C42—114no—
468C2×C42—114no—
469C2×C42—224no—
470C2×C42—224no—
471C2×C42—224no—
472C2×C42—224no—
473#95—114no—
474#95—114no—
475#95—114no—
476#95—114no—
477#95—114no—
478#95C22×D1114yes—
479#95C22×D1114yes—
480#95C22×D1114yes—
481C2×C11#255218yescomplemented
482C2×C11C22×#12511yescharacteristic
483C2×C11C22×C4⋊Q811yescharacteristic
484C2×C11C2×#54411yescharacteristic
485C2×C11C2×#54711yescharacteristic
486C2×C11C2×#55011yescharacteristic
487C2×C11C2×#55411yescharacteristic
488C2×C11C2×#55711yescharacteristic
489C24C23×D1111yescharacteristic
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—114no—
509C22×C4—114no—
510C22×C4—114no—
511C22×C4—114no—
512C22×C4—114no—
513C22×C4—114no—
514C22×C4—112no—
515C22×C4—112no—
516C22×C4—114no—
517C22×C4—114no—
518C22×C4—112no—
519C22×C4—112no—
520C22×C4—112no—
521C22×C4—112no—
522C22×C4—112no—
523C22×C4—112no—
524C22×C4—222no—
525C22×C4—222no—
526C22×C4—222no—
527C22×C4—222no—
528C22×C4—222no—
529C22×C4—222no—
530C22×C4—222no—
531C22×C4—222no—
532C22×C4—222no—
533C22×C4—222no—
534C22×C4—222no—
535C22×C4—222no—
536C22×C4—222no—
537C22×C4—222no—
538C22×C4—222no—
539C22×C4—222no—
540C22×C4D4×D1114yes—
541C22×C4Q8×D1114yes—
542C22×C4Q8×D1114yes—
543C22×C4C23×D1112yes—
544C22×C4C23×D1112yes—
545C22×C4C23×D1112yes—
546C22×C4C23×D1112yes—
547C22×C4C23×D1112yes—
548C22×C4C23×D1112yes—
549C22×C4C23×D1112yes—
550C4⋊C4—28no—
551C4⋊C4—28no—
552C4⋊C4—44no—
553C4⋊C4—44no—
554C4⋊C4—1116no—
555C4⋊C4—1116no—
556C4⋊C4—228no—
557C4⋊C4—228no—
558C4⋊C4—228no—
559C4⋊C4—228no—
560C4⋊C4—228no—
561C4⋊C4—228no—
562C4⋊C4—228no—
563C4⋊C4—228no—
564C4⋊C4—228no—
565C4⋊C4—228no—
566C4⋊C4—228no—
567C4⋊C4—228no—
568C4⋊C4—444no—
569C4⋊C4—444no—
570C4⋊C4—444no—
571C4⋊C4—444no—
572C42—1116no—
573C42—228no—
574C42—228no—
575C42—228no—
576C42—228no—
577C11C2×#255211yescharacteristic, complemented, Sylow
578C23C2×D4×D1112yes—
579C23#6703712yes—
580C23C2×Q8×D1112yes—
581C23C2×Q8×D1112yes—
582C23#41×D1112yes—
583C23#41×D1112yes—
584C23#6704312yes—
585C23C24×D1111yescharacteristic
586C2×C4—28no—
587C2×C4—28no—
588C2×C4—28no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—44no—
608C2×C4—44no—
609C2×C4—44no—
610C2×C4—44no—
611C2×C4—1116no—
612C2×C4—114no—
613C2×C4—114no—
614C2×C4—114no—
615C2×C4—114no—
616C2×C4—114no—
617C2×C4—114no—
618C2×C4—1116no—
619C2×C4—114no—
620C2×C4—114no—
621C2×C4—228no—
622C2×C4—228no—
623C2×C4—222no—
624C2×C4—222no—
625C2×C4—222no—
626C2×C4—222no—
627C2×C4—222no—
628C2×C4—222no—
629C2×C4—222no—
630C2×C4—222no—
631C2×C4—222no—
632C2×C4—222no—
633C2×C4—222no—
634C2×C4—222no—
635C2×C4—222no—
636C2×C4—222no—
637C2×C4—222no—
638C2×C4—222no—
639C2×C4—444no—
640C2×C4—444no—
641C2×C4—444no—
642C2×C4—444no—
643C2×C4C2×D4×D1114yes—
644C2×C4C2×Q8×D1114yes—
645C2×C4C2×Q8×D1114yes—
646C22#1062313014yes—
647C22#1062315414yes—
648C22#1062316714yes—
649C22#1062318614yes—
650C22#1062321614yes—
651C22D11×#12514yes—
652C22D11×C4⋊Q814yes—
653C22C22×D4×D1111yescharacteristic
654C22C2×#6703711yescharacteristic
655C22C22×Q8×D1111yescharacteristic
656C22C22×Q8×D1111yescharacteristic
657C22C2×#41×D1111yescharacteristic
658C22C2×#41×D1111yescharacteristic
659C22C2×#6704311yescharacteristic
660C4—24no—
661C4—24no—
662C4—24no—
663C4—42no—
664C4—42no—
665C4—42no—
666C4—42no—
667C4—118no—
668C4—118no—
669C4—224no—
670C4—224no—
671C4—442no—
672C4—442no—
673C4—442no—
674C4—442no—
675C2#1307364618yesdirect product factor
676C2C2×D11×#12511yescharacteristic
677C2C2×D11×C4⋊Q811yescharacteristic
678C2C2×#1062315411yescharacteristic
679C2C2×#1062318611yescharacteristic
680C2C2×#1062313011yescharacteristic
681C2C2×#1062316711yescharacteristic
682C2C2×#1062321611yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#398C2
socle, prime radicalC24×C11C24
hypercenterC2×#398D11
hypocenterC11C2×#2552
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
3. #13073646C2direct (N × H)
311. C2×Dic11#125semidirect
400. Dic11C2×#125semidirect
481. C2×C11#2552semidirect
577. C11C2×#2552semidirect
675. C2#13073646direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669422
#130736462
C2×#106222702
C2×#106225972
C2×#106222742
C2×#106222602
C2×#106225852
C2×#106225892
C2×#106222622
C2×C11×#3982
C2×#255211