Finite Group Databasebeta

← C2×#13072454 #14921811

Subgroups — C2×#13072454 #14921811

Order 2816.

2702 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66941C211yesmaximal, characteristic
2C22×C4×Dic22C211yesmaximal, characteristic
3#13072454C2116yesmaximal, direct product factor
4C2×#10622597C211yesmaximal, characteristic
5C2×#10622274C211yesmaximal, characteristic
6C2×#10622269C211yesmaximal, characteristic
7C2×#10622269C211yesmaximal, characteristic
8C2×#10622542C211yesmaximal, characteristic
9C2×#10622259C211yesmaximal, characteristic
10C2×#10622259C211yesmaximal, characteristic
11C2×#10622259C211yesmaximal, characteristic
12C2×#10622260C211yesmaximal, characteristic
13C2×#10622260C211yesmaximal, characteristic
14C2×#10622594C211yesmaximal, characteristic
15C2×C4⋊C4×Dic11C211yesmaximal, characteristic
16C2×C11×#387C211yesmaximal, characteristic
17C23×Dic22C2211yescharacteristic
18C23×Dic22C2211yescharacteristic
19C23×Dic22C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C42×C11C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37C22×C4×Dic11C2211yescharacteristic
38C2×#66941—28no—
39C2×#66941C2218yes—
40C2×C4×Dic22—28no—
41C2×C4×Dic22C2218yes—
42C11×#387C2218yes—
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
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57#10622597C2218yes—
58#10622594C2218yes—
59C4⋊C4×Dic11C2218yes—
60#10622542C2218yes—
61#10622274C2218yes—
62#10622269C2218yes—
63#10622269C2218yes—
64#10622260C2218yes—
65#10622260C2218yes—
66#10622259C2218yes—
67#10622259C2218yes—
68#10622259C2218yes—
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
84C22×Dic22—24no—
85C22×Dic22—24no—
86C22×Dic22—24no—
87C22×Dic22—24no—
88C22×Dic22—24no—
89C22×Dic22—24no—
90C22×Dic22—42no—
91C22×Dic22—42no—
92C22×Dic22Q818yescomplemented
93C22×Dic22C2314yes—
94C22×Dic22C2314yes—
95C22×Dic22C2314yes—
96C2×C11×C4⋊C4—24no—
97C2×C11×C4⋊C4Q818yescomplemented
98C2×C11×C4⋊C4C2314yes—
99C2×C11×C4⋊C4C2314yes—
100C2×C42×C11—24no—
101C2×C42×C11C2314yes—
102C2×C4⋊Dic11—24no—
103C2×C4⋊Dic11—24no—
104C2×C4⋊Dic11—24no—
105C2×C4⋊Dic11—42no—
106C2×C4⋊Dic11—42no—
107C2×C4⋊Dic11C2314yes—
108C2×C4⋊Dic11C2314yes—
109C2×C4⋊Dic11C2314yes—
110C2×C4⋊Dic11C2314yes—
111C2×C4⋊Dic11C2314yes—
112C2×Dic11⋊C4—24no—
113C2×Dic11⋊C4—24no—
114C2×Dic11⋊C4—24no—
115C2×Dic11⋊C4—42no—
116C2×Dic11⋊C4—42no—
117C2×Dic11⋊C4D418yes—
118C2×Dic11⋊C4C2314yes—
119C2×Dic11⋊C4C2314yes—
120C2×Dic11⋊C4C2314yes—
121C2×Dic11⋊C4C2314yes—
122C2×Dic11⋊C4C2314yes—
123C2×Dic11⋊C4C2314yes—
124C2×C4×Dic11—24no—
125C2×C4×Dic11—24no—
126C2×C4×Dic11—24no—
127C2×C4×Dic11—24no—
128C2×C4×Dic11C2314yes—
129C2×C4×Dic11C2314yes—
130C2×C4×Dic11C2314yes—
131C2×C4×Dic11C2314yes—
132#66941—232no—
133C4×Dic22—232no—
134C11×#95C2314yes—
135C11×#95C2314yes—
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×#2451—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×C11C2×D414yes—
167C22×C4×C11C2×Q814yes—
168C22×C4×C11C2×Q814yes—
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×Dic11—22no—
195C22×Dic11—22no—
196C22×Dic11C2×D414yes—
197C22×Dic11C2×D414yes—
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—
210C2×Dic22—232no—
211C2×Dic22—28no—
212C2×Dic22—28no—
213C2×Dic22—28no—
214C2×Dic22—28no—
215C2×Dic22—28no—
216C2×Dic22—28no—
217C2×Dic22—44no—
218C2×Dic22—44no—
219C2×Dic22—416no—
220C2×Dic22—416no—
221C2×Dic22C2×Q8116yescomplemented
222C11×C4⋊C4—28no—
223C11×C4⋊C4C2×Q8116yescomplemented
224C42×C11—28no—
225C4⋊Dic11—28no—
226C4⋊Dic11—28no—
227C4⋊Dic11—28no—
228C4⋊Dic11—44no—
229C4⋊Dic11—44no—
230Dic11⋊C4—28no—
231Dic11⋊C4—28no—
232Dic11⋊C4—28no—
233Dic11⋊C4—44no—
234Dic11⋊C4—44no—
235Dic11⋊C4C2×D4116yes—
236C4×Dic11—28no—
237C4×Dic11—28no—
238C4×Dic11—28no—
239C4×Dic11—28no—
240C22×C4⋊Q8—111no—
241C22×C4×Q8—111no—
242#2451—1116no—
243C2×#398—111no—
244C2×#398—111no—
245C2×#395—111no—
246C2×#395—111no—
247C2×#391—111no—
248C2×#391—111no—
249C2×#391—111no—
250C2×#391—111no—
251C2×#389—111no—
252C2×#389—111no—
253C2×#387—111no—
254C2×#387D1111yescharacteristic
255C2×C4×C4⋊C4—111no—
256C23×C11C22×D412yes—
257C23×C11C22×Q812yes—
258C23×C11C22×Q812yes—
259C23×C11C2×#4112yes—
260C23×C11C2×#4112yes—
261C23×C11H(5,𝔽2)12yes—
262C23×C112−1+412yes—
263C23×C11C2511yescharacteristic
264C2×C4×C11—28no—
265C2×C4×C11—28no—
266C2×C4×C11—28no—
267C2×C4×C11—28no—
268C2×C4×C11—28no—
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×C11C22×D414yes—
288C2×C4×C11C22×Q814yes—
289C2×C4×C11C22×Q814yes—
290C2×C4×C11C22×Q814yes—
291C2×C4×C11C22×Q814yes—
292C2×Dic11—28no—
293C2×Dic11—28no—
294C2×Dic11—28no—
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—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×Dic11—44no—
317C2×Dic11C22⋊Q8116yes—
318C2×Dic11C22×D414yes—
319C2×Dic11C22×D414yes—
320C2×Dic11C22×Q814yes—
321C2×Dic11C22×Q814yes—
322C2×Dic11C2×#4114yes—
323C2×Dic11C2×#4114yes—
324Dic22—232no—
325Dic22—416no—
326Dic22—416no—
327C23×Q8—111no—
328C23×Q8—111no—
329C23×Q8—111no—
330C2×C4⋊Q8—118no—
331C2×C4⋊Q8—228no—
332C2×C4×Q8—118no—
333C2×C4×Q8—228no—
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⋊C4C2×D1111yescharacteristic
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#391—118no—
358#391—118no—
359#391—118no—
360#389—118no—
361#389—118no—
362#387—118no—
363#387C2×D1118yes—
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×#95—111no—
374C2×#95—111no—
375C2×#95C2×D1111yescharacteristic
376C2×#95C2×D1111yescharacteristic
377C2×#95C2×D1111yescharacteristic
378C2×#95C2×D1111yescharacteristic
379C22×C11C2×C22⋊Q814yes—
380C22×C11#53314yes—
381C22×C11#54214yes—
382C22×C11#54614yes—
383C22×C11D4×Q814yes—
384C22×C11#55714yes—
385C22×C11Q8214yes—
386C22×C11C23×D411yescharacteristic
387C22×C11C23×Q811yescharacteristic
388C22×C11C23×Q811yescharacteristic
389C22×C11C22×#4111yescharacteristic
390C22×C11C22×#4111yescharacteristic
391C22×C11C2×H(5,𝔽2)11yescharacteristic
392C22×C11C2×2−1+411yescharacteristic
393C4×C11—24no—
394C4×C11—24no—
395C4×C11—24no—
396C4×C11—24no—
397C4×C11—24no—
398C4×C11—42no—
399C4×C11—42no—
400Dic11—24no—
401Dic11—24no—
402Dic11—24no—
403Dic11—42no—
404Dic11—42no—
405Dic11—42no—
406Dic11—42no—
407Dic11C2×C22⋊Q818yes—
408C22×Q8—118no—
409C22×Q8—114no—
410C22×Q8—114no—
411C22×Q8—114no—
412C22×Q8—224no—
413C22×Q8—224no—
414C22×Q8—224no—
415C22×Q8—224no—
416C22×Q8—224no—
417C22×Q8—224no—
418C22×Q8—442no—
419C22×Q8—442no—
420C23×C4—111no—
421C23×C4—111no—
422C23×C4—111no—
423C23×C4—111no—
424C23×C4—111no—
425C23×C4—111no—
426C23×C4—111no—
427C23×C4—111no—
428C23×C4C22×D1111yescharacteristic
429C23×C4C22×D1111yescharacteristic
430C23×C4C22×D1111yescharacteristic
431C23×C4C22×D1111yescharacteristic
432C23×C4C22×D1111yescharacteristic
433C23×C4C22×D1111yescharacteristic
434C23×C4C22×D1111yescharacteristic
435C4⋊Q8—2232no—
436C4×Q8—2232no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—118no—
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—114no—
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—442no—
457C2×C4⋊C4—442no—
458C2×C4⋊C4—442no—
459C2×C4⋊C4—442no—
460C2×C4⋊C4Dic2218yescomplemented
461C2×C4⋊C4C22×D1114yes—
462C2×C4⋊C4C22×D1114yes—
463C2×C42—24no—
464C2×C42—114no—
465C2×C42—114no—
466C2×C42—114no—
467C2×C42—114no—
468C2×C42—224no—
469C2×C42—224no—
470C2×C42—224no—
471C2×C42—224no—
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#95—114no—
482#95—114no—
483#95C22×D1114yes—
484#95C22×D1114yes—
485#95C22×D1114yes—
486#95C22×D1114yes—
487C2×C11#245118yescomplemented
488C2×C11C22×C22⋊Q811yescharacteristic
489C2×C11C2×#53311yescharacteristic
490C2×C11C2×#54211yescharacteristic
491C2×C11C2×#54611yescharacteristic
492C2×C11C2×D4×Q811yescharacteristic
493C2×C11C2×#55711yescharacteristic
494C2×C11C2×Q8211yescharacteristic
495C24C23×D1111yescharacteristic
496C2×Q8—1116no—
497C2×Q8—228no—
498C2×Q8—2232no—
499C2×Q8—228no—
500C2×Q8—228no—
501C2×Q8—228no—
502C2×Q8—228no—
503C2×Q8—228no—
504C2×Q8—444no—
505C2×Q8—444no—
506C2×Q8—4416no—
507C2×Q8—4416no—
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—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—114no—
525C22×C4—114no—
526C22×C4—114no—
527C22×C4—112no—
528C22×C4—114no—
529C22×C4—114no—
530C22×C4—114no—
531C22×C4—112no—
532C22×C4—112no—
533C22×C4—112no—
534C22×C4—112no—
535C22×C4—112no—
536C22×C4—112no—
537C22×C4—112no—
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—222no—
552C22×C4—222no—
553C22×C4—222no—
554C22×C4—222no—
555C22×C4—222no—
556C22×C4C2×Dic2214yes—
557C22×C4C2×Dic2214yes—
558C22×C4C2×Dic2214yes—
559C22×C4D4×D1114yes—
560C22×C4Q8×D1114yes—
561C22×C4C23×D1112yes—
562C22×C4C23×D1112yes—
563C22×C4C23×D1112yes—
564C22×C4C23×D1112yes—
565C22×C4C23×D1112yes—
566C22×C4C23×D1112yes—
567C22×C4C23×D1112yes—
568C4⋊C4—28no—
569C4⋊C4—1116no—
570C4⋊C4—228no—
571C4⋊C4—228no—
572C4⋊C4—228no—
573C4⋊C4—228no—
574C4⋊C4—228no—
575C4⋊C4—228no—
576C4⋊C4—444no—
577C4⋊C4—444no—
578C4⋊C4—444no—
579C4⋊C4—444no—
580C4⋊C4C2×Dic22116yescomplemented
581C42—28no—
582C42—228no—
583C42—228no—
584C42—228no—
585C42—228no—
586C11C2×#245111yescharacteristic, complemented, Sylow
587C23C22×Dic2212yes—
588C23C2×D4×D1112yes—
589C23C2×Q8×D1112yes—
590C23#41×D1112yes—
591C23#41×D1112yes—
592C23#6704212yes—
593C23#6704312yes—
594C23C24×D1111yescharacteristic
595Q8—2232no—
596Q8—4416no—
597Q8—4416no—
598C2×C4—28no—
599C2×C4—28no—
600C2×C4—28no—
601C2×C4—28no—
602C2×C4—28no—
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—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—44no—
620C2×C4—44no—
621C2×C4—1116no—
622C2×C4—114no—
623C2×C4—114no—
624C2×C4—114no—
625C2×C4—114no—
626C2×C4—114no—
627C2×C4—114no—
628C2×C4—228no—
629C2×C4—228no—
630C2×C4—228no—
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—222no—
640C2×C4—222no—
641C2×C4—222no—
642C2×C4—222no—
643C2×C4—222no—
644C2×C4—222no—
645C2×C4—222no—
646C2×C4—222no—
647C2×C4—222no—
648C2×C4—222no—
649C2×C4—444no—
650C2×C4—444no—
651C2×C4—444no—
652C2×C4—444no—
653C2×C4C22×Dic2214yes—
654C2×C4C22×Dic2214yes—
655C2×C4C22×Dic2214yes—
656C2×C4C2×D4×D1114yes—
657C2×C4C2×Q8×D1114yes—
658C22#1062304814yes—
659C22D4×Dic2214yes—
660C22Q8×Dic2214yes—
661C22D11×C22⋊Q814yes—
662C22#1062318514yes—
663C22#1062321614yes—
664C22#1062324114yes—
665C22C23×Dic2211yescharacteristic
666C22C22×D4×D1111yescharacteristic
667C22C22×Q8×D1111yescharacteristic
668C22C2×#41×D1111yescharacteristic
669C22C2×#41×D1111yescharacteristic
670C22C2×#6704211yescharacteristic
671C22C2×#6704311yescharacteristic
672C4—24no—
673C4—24no—
674C4—24no—
675C4—24no—
676C4—24no—
677C4—42no—
678C4—42no—
679C4—118no—
680C4—224no—
681C4—224no—
682C4—224no—
683C4—442no—
684C4—442no—
685C4—442no—
686C4—442no—
687C2#1307245418yesdirect product factor
688C2C2×D11×C22⋊Q811yescharacteristic
689C2C2×#1062304811yescharacteristic
690C2C2×#1062324111yescharacteristic
691C2C2×#1062318511yescharacteristic
692C2C2×D4×Dic2211yescharacteristic
693C2C2×#1062321611yescharacteristic
694C2C2×Q8×Dic2211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#387C2
socle, prime radicalC24×C11C24
hypercenterC2×#387D11
hypocenterC11C2×#2451
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
3. #13072454C2direct (N × H)
92. C22×Dic22Q8semidirect
97. C2×C11×C4⋊C4Q8semidirect
221. C2×Dic22C2×Q8semidirect
223. C11×C4⋊C4C2×Q8semidirect
460. C2×C4⋊C4Dic22semidirect
487. C2×C11#2451semidirect
580. C4⋊C4C2×Dic22semidirect
586. C11C2×#2451semidirect
687. C2#13072454direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669412
C22×C4×Dic222
#130724542
C2×#106225972
C2×#106222742
C2×#106222692
C2×#106225422
C2×#106222592
C2×#106222602
C2×#106225942
C2×C4⋊C4×Dic112
C2×C11×#3872
C2×#245111