Finite Group Databasebeta

← C2×#13073634 #14924951

Subgroups — C2×#13073634 #14924951

Order 2816.

2574 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66997C211yesmaximal, characteristic
2C22×#66942C211yesmaximal, characteristic
3#13073634C2116yesmaximal, direct product factor
4C2×#10622270C211yesmaximal, characteristic
5C2×#10622593C211yesmaximal, characteristic
6C2×#10622269C211yesmaximal, characteristic
7C2×#10622842C211yesmaximal, characteristic
8C2×#10622259C211yesmaximal, characteristic
9C2×#10622541C211yesmaximal, characteristic
10C2×#10622260C211yesmaximal, characteristic
11C2×#10622260C211yesmaximal, characteristic
12C2×#10622260C211yesmaximal, characteristic
13C2×#10622263C211yesmaximal, characteristic
14C2×C4×Dic11⋊C4C211yesmaximal, characteristic
15C2×#10622262C211yesmaximal, characteristic
16C2×C11×#391C211yesmaximal, characteristic
17C23×Q8×C11C2211yescharacteristic
18C23×Dic22C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C2×#66997—28no—
22C2×#66997C2218yes—
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
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×C4×Dic11C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40C22×C4×Dic11C2211yescharacteristic
41C22×C4×Dic11C2211yescharacteristic
42C2×#66942—28no—
43C2×#66942C2218yes—
44C11×#391C2218yes—
45C2×C11×#95C2211yescharacteristic
46C2×C11×#95C2211yescharacteristic
47C2×C11×#95C2211yescharacteristic
48C2×C11×#95C2211yescharacteristic
49#10622842C2218yes—
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#10622593C2218yes—
59C4×Dic11⋊C4C2218yes—
60#10622541C2218yes—
61#10622270C2218yes—
62#10622269C2218yes—
63#10622263C2218yes—
64#10622262C2218yes—
65#10622260C2218yes—
66#10622260C2218yes—
67#10622260C2218yes—
68#10622259C2218yes—
69C22×Q8×C11—24no—
70C22×Q8×C11—24no—
71C22×Q8×C11—42no—
72C22×Q8×C11C2314yes—
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
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—42no—
91C22×Dic22C2314yes—
92C2×C11×C4⋊C4—24no—
93C2×C11×C4⋊C4C2314yes—
94C2×C42×C11—42no—
95C2×C42×C11C2314yes—
96#66997—232no—
97C2×C4⋊Dic11—24no—
98C2×C4⋊Dic11—24no—
99C2×C4⋊Dic11—42no—
100C2×C4⋊Dic11C2314yes—
101C2×C4⋊Dic11C2314yes—
102C2×C4⋊Dic11C2314yes—
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—24no—
111C2×Dic11⋊C4—24no—
112C2×Dic11⋊C4—42no—
113C2×Dic11⋊C4D418yes—
114C2×Dic11⋊C4Q818yescomplemented
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×C4×Dic11—24no—
128C2×C4×Dic11—24no—
129C2×C4×Dic11—42no—
130C2×C4×Dic11Q818yescomplemented
131C2×C4×Dic11C2314yes—
132C2×C4×Dic11C2314yes—
133C2×C4×Dic11C2314yes—
134C2×C4×Dic11C2314yes—
135#66942—232no—
136C11×#95C2314yes—
137C11×#95C2314yes—
138C11×#95C2314yes—
139C11×#95C2314yes—
140C11⋊#95C2314yes—
141C11⋊#95C2314yes—
142C11⋊#95C2314yes—
143C11⋊#95C2314yes—
144C11⋊#95C2314yes—
145C11⋊#95C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C2×#2550—111nomaximal, Sylow
149C24×C11C2411yescharacteristic
150C2×Q8×C11—28no—
151C2×Q8×C11—28no—
152C2×Q8×C11—44no—
153C2×Q8×C11—416no—
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×C11C2×D414yes—
172C22×C4×C11C2×Q814yes—
173C22×C4×C11C2×Q814yes—
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×Dic11C2×D414yes—
200C22×Dic11C2×D414yes—
201C22×Dic11C2×Q814yes—
202C22×Dic11C2×Q814yes—
203C22×Dic11C2×Q814yes—
204C22×Dic11C2×Q814yes—
205C22×Dic11#4114yes—
206C22×Dic11C2412yes—
207C22×Dic11C2412yes—
208C22×Dic11C2412yes—
209C22×Dic11C2412yes—
210C22×Dic11C2412yes—
211C22×Dic11C2412yes—
212C22×Dic11C2412yes—
213C22×Dic11C2412yes—
214C2×Dic22—28no—
215C2×Dic22—28no—
216C2×Dic22—44no—
217C2×Dic22—416no—
218C11×C4⋊C4—28no—
219C42×C11—44no—
220C4⋊Dic11—28no—
221C4⋊Dic11—28no—
222C4⋊Dic11—44no—
223Dic11⋊C4—28no—
224Dic11⋊C4—28no—
225Dic11⋊C4—28no—
226Dic11⋊C4—28no—
227Dic11⋊C4—28no—
228Dic11⋊C4—28no—
229Dic11⋊C4—28no—
230Dic11⋊C4—28no—
231Dic11⋊C4—28no—
232Dic11⋊C4—44no—
233Dic11⋊C4C2×D4116yes—
234Dic11⋊C4C2×Q8116yescomplemented
235C4×Dic11—28no—
236C4×Dic11—28no—
237C4×Dic11—44no—
238C4×Dic11C2×Q8116yescomplemented
239C22×C4⋊Q8—111no—
240C22×#125—111no—
241#2550—1116no—
242C2×#398—111no—
243C2×#398—111no—
244C2×#395—111no—
245C2×#395—111no—
246C2×#391—111no—
247C2×#391D1111yescharacteristic
248C2×#389—111no—
249C2×#389—111no—
250C2×#389—111no—
251C2×#389—111no—
252C2×#382—111no—
253C2×C4×C4⋊C4—111no—
254C2×C4×C4⋊C4—111no—
255C23×C11C22×D412yes—
256C23×C11C22×Q812yes—
257C23×C11C22×Q812yes—
258C23×C11C2×#4112yes—
259C23×C11C2×#4112yes—
260C23×C11H(5,𝔽2)12yes—
261C23×C112−1+412yes—
262C23×C11C2511yescharacteristic
263Q8×C11—416no—
264C2×C4×C11—28no—
265C2×C4×C11—28no—
266C2×C4×C11—28no—
267C2×C4×C11—28no—
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—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—44no—
286C2×C4×C11—44no—
287C2×C4×C11—44no—
288C2×C4×C11C22×D414yes—
289C2×C4×C11C22×Q814yes—
290C2×C4×C11C22×Q814yes—
291C2×C4×C11C2×#4114yes—
292C2×Dic11—28no—
293C2×Dic11—28no—
294C2×Dic11—28no—
295C2×Dic11—28no—
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—22no—
308C2×Dic11—22no—
309C2×Dic11—22no—
310C2×Dic11—22no—
311C2×Dic11—22no—
312C2×Dic11—22no—
313C2×Dic11—44no—
314C2×Dic11—44no—
315C2×Dic11—44no—
316C2×Dic11C4⋊Q8116yes—
317C2×Dic11C22×D414yes—
318C2×Dic11C22×D414yes—
319C2×Dic11C22×Q814yes—
320C2×Dic11C22×Q814yes—
321C2×Dic11C22×Q814yes—
322C2×Dic11C22×Q814yes—
323C2×Dic11C2×#4114yes—
324Dic22—416no—
325C23×Q8—111no—
326C23×Q8C2×D1111yescharacteristic
327C2×C4⋊Q8—118no—
328C2×C4⋊Q8—228no—
329C2×#125—118no—
330C2×#125—228no—
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⋊C4—111no—
344C22×C4⋊C4—111no—
345C22×C4⋊C4—111no—
346C22×C4⋊C4C2×D1111yescharacteristic
347C22×C42—111no—
348C22×C42—111no—
349C22×C42—111no—
350C22×C42—111no—
351C22×C42C2×D1111yescharacteristic
352#398—118no—
353#398—118no—
354#395—118no—
355#395—118no—
356#391—118no—
357#391C2×D1118yes—
358#389—118no—
359#389—118no—
360#389—118no—
361#389—118no—
362#382—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×#95—111no—
371C2×#95—111no—
372C2×#95—111no—
373C2×#95C2×D1111yescharacteristic
374C2×#95C2×D1111yescharacteristic
375C2×#95C2×D1111yescharacteristic
376C2×#95C2×D1111yescharacteristic
377C22×C11C2×C4⋊Q814yes—
378C22×C11#53314yes—
379C22×C11#54414yes—
380C22×C11#54614yes—
381C22×C11#54814yes—
382C22×C11#55414yes—
383C22×C11#55714yes—
384C22×C11C23×D411yescharacteristic
385C22×C11C23×Q811yescharacteristic
386C22×C11C23×Q811yescharacteristic
387C22×C11C22×#4111yescharacteristic
388C22×C11C22×#4111yescharacteristic
389C22×C11C2×H(5,𝔽2)11yescharacteristic
390C22×C11C2×2−1+411yescharacteristic
391C4×C11—24no—
392C4×C11—24no—
393C4×C11—24no—
394C4×C11—24no—
395C4×C11—42no—
396C4×C11—42no—
397C4×C11—42no—
398Dic11—24no—
399Dic11—24no—
400Dic11—24no—
401Dic11—24no—
402Dic11—42no—
403Dic11—42no—
404Dic11—42no—
405Dic11C2×C4⋊Q818yes—
406C22×Q8—24no—
407C22×Q8—24no—
408C22×Q8—42no—
409C22×Q8—114no—
410C22×Q8—224no—
411C22×Q8—224no—
412C22×Q8—442no—
413C22×Q8C22×D1114yes—
414C23×C4—111no—
415C23×C4—111no—
416C23×C4—111no—
417C23×C4—111no—
418C23×C4—111no—
419C23×C4—111no—
420C23×C4—111no—
421C23×C4—111no—
422C23×C4C22×D1111yescharacteristic
423C23×C4C22×D1111yescharacteristic
424C23×C4C22×D1111yescharacteristic
425C23×C4C22×D1111yescharacteristic
426C23×C4C22×D1111yescharacteristic
427C23×C4C22×D1111yescharacteristic
428C23×C4C22×D1111yescharacteristic
429C4⋊Q8—2232no—
430#125—2232no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—118no—
433C2×C4⋊C4—118no—
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—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—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×C42—42no—
464C2×C42—118no—
465C2×C42—114no—
466C2×C42—114no—
467C2×C42—114no—
468C2×C42—114no—
469C2×C42—224no—
470C2×C42—224no—
471C2×C42—442no—
472C2×C42C22×D1114yes—
473#95—114no—
474#95—114no—
475#95—114no—
476#95—114no—
477#95—114no—
478#95—114no—
479#95—114no—
480#95—114no—
481#95C22×D1114yes—
482#95C22×D1114yes—
483#95C22×D1114yes—
484#95C22×D1114yes—
485C2×C11#255018yescomplemented
486C2×C11C22×C4⋊Q811yescharacteristic
487C2×C11C2×#53311yescharacteristic
488C2×C11C2×#54411yescharacteristic
489C2×C11C2×#54611yescharacteristic
490C2×C11C2×#54811yescharacteristic
491C2×C11C2×#55411yescharacteristic
492C2×C11C2×#55711yescharacteristic
493C24C23×D1111yescharacteristic
494C2×Q8—28no—
495C2×Q8—28no—
496C2×Q8—44no—
497C2×Q8—416no—
498C2×Q8—228no—
499C2×Q8—228no—
500C2×Q8—444no—
501C2×Q8—4416no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—114no—
520C22×C4—114no—
521C22×C4—114no—
522C22×C4—112no—
523C22×C4—114no—
524C22×C4—114no—
525C22×C4—114no—
526C22×C4—114no—
527C22×C4—112no—
528C22×C4—112no—
529C22×C4—112no—
530C22×C4—112no—
531C22×C4—112no—
532C22×C4—112no—
533C22×C4—112no—
534C22×C4—222no—
535C22×C4—222no—
536C22×C4—222no—
537C22×C4—222no—
538C22×C4—222no—
539C22×C4—222no—
540C22×C4—222no—
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#433914yes—
552C22×C4D4×D1114yes—
553C22×C4Q8×D1114yes—
554C22×C4Q8×D1114yes—
555C22×C4C23×D1112yes—
556C22×C4C23×D1112yes—
557C22×C4C23×D1112yes—
558C22×C4C23×D1112yes—
559C22×C4C23×D1112yes—
560C22×C4C23×D1112yes—
561C22×C4C23×D1112yes—
562C4⋊C4—28no—
563C4⋊C4—1116no—
564C4⋊C4—1116no—
565C4⋊C4—228no—
566C4⋊C4—228no—
567C4⋊C4—228no—
568C4⋊C4—228no—
569C4⋊C4—228no—
570C4⋊C4—228no—
571C4⋊C4—228no—
572C4⋊C4—228no—
573C4⋊C4—228no—
574C4⋊C4—228no—
575C4⋊C4—228no—
576C4⋊C4—444no—
577C4⋊C4—444no—
578C42—44no—
579C42—1116no—
580C42—228no—
581C42—228no—
582C42—444no—
583C11C2×#255011yescharacteristic, complemented, Sylow
584C23C2×#433912yes—
585C23C2×D4×D1112yes—
586C23#6703712yes—
587C23C2×Q8×D1112yes—
588C23C2×Q8×D1112yes—
589C23#41×D1112yes—
590C23#6704312yes—
591C23C24×D1111yescharacteristic
592Q8—416no—
593Q8—4416no—
594C2×C4—28no—
595C2×C4—28no—
596C2×C4—28no—
597C2×C4—28no—
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—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—44no—
616C2×C4—44no—
617C2×C4—44no—
618C2×C4—1116no—
619C2×C4—114no—
620C2×C4—114no—
621C2×C4—114no—
622C2×C4—114no—
623C2×C4—114no—
624C2×C4—114no—
625C2×C4—114no—
626C2×C4—228no—
627C2×C4—228no—
628C2×C4—228no—
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—228no—
638C2×C4—222no—
639C2×C4—222no—
640C2×C4—222no—
641C2×C4—222no—
642C2×C4—222no—
643C2×C4—222no—
644C2×C4—222no—
645C2×C4—222no—
646C2×C4—222no—
647C2×C4—444no—
648C2×C4—444no—
649C2×C4—444no—
650C2×C4C2×#433914yes—
651C2×C4C2×D4×D1114yes—
652C2×C4C2×Q8×D1114yes—
653C2×C4C2×Q8×D1114yes—
654C22#1062302114yes—
655C22#1062309814yes—
656C22#1062310914yes—
657C22#1062315414yes—
658C22#1062316714yes—
659C22#1062320814yes—
660C22D11×C4⋊Q814yes—
661C22C22×#433911yescharacteristic
662C22C22×D4×D1111yescharacteristic
663C22C2×#6703711yescharacteristic
664C22C22×Q8×D1111yescharacteristic
665C22C22×Q8×D1111yescharacteristic
666C22C2×#41×D1111yescharacteristic
667C22C2×#6704311yescharacteristic
668C4—24no—
669C4—24no—
670C4—24no—
671C4—24no—
672C4—42no—
673C4—42no—
674C4—42no—
675C4—118no—
676C4—224no—
677C4—224no—
678C4—224no—
679C4—224no—
680C4—442no—
681C4—442no—
682C4—442no—
683C2#1307363418yesdirect product factor
684C2C2×D11×C4⋊Q811yescharacteristic
685C2C2×#1062310911yescharacteristic
686C2C2×#1062315411yescharacteristic
687C2C2×#1062302111yescharacteristic
688C2C2×#1062320811yescharacteristic
689C2C2×#1062316711yescharacteristic
690C2C2×#1062309811yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#391C2
socle, prime radicalC24×C11C24
hypercenterC2×#391D11
hypocenterC11C2×#2550
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
3. #13073634C2direct (N × H)
114. C2×Dic11⋊C4Q8semidirect
130. C2×C4×Dic11Q8semidirect
234. Dic11⋊C4C2×Q8semidirect
238. C4×Dic11C2×Q8semidirect
485. C2×C11#2550semidirect
583. C11C2×#2550semidirect
683. C2#13073634direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669972
C22×#669422
#130736342
C2×#106222702
C2×#106225932
C2×#106222692
C2×#106228422
C2×#106222592
C2×#106225412
C2×#106222602
C2×#106222632
C2×C4×Dic11⋊C42
C2×#106222622
C2×C11×#3912
C2×#255011