Finite Group Databasebeta

← C2×#13081003 #15632229

Subgroups — C2×#13081003 #15632229

Order 2816.

1942 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623166C211yesmaximal, characteristic
2C2×#10623042C211yesmaximal, characteristic
3#13081003C2116yesmaximal, direct product factor
4C2×#10622487C211yesmaximal, characteristic, complemented
5C2×#10622497C211yesmaximal, characteristic, complemented
6C2×#10622335C211yesmaximal, characteristic, complemented
7C2×#10622422C211yesmaximal, characteristic, complemented
8C2×#10622488C211yesmaximal, characteristic, complemented
9C2×#10622407C211yesmaximal, characteristic, complemented
10C2×#10622426C211yesmaximal, characteristic, complemented
11C2×#10622664C211yesmaximal, characteristic, complemented
12C2×#10622403C211yesmaximal, characteristic, complemented
13C2×(C22⋊D11)⋊C8C211yesmaximal, characteristic
14C22×#66871C211yesmaximal, characteristic, complemented
15C2×D11×#107C211yesmaximal, characteristic, complemented
16C2×C11×#484C211yesmaximal, characteristic, complemented
17C2×C11×C22⋊Q8C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C2×#66999C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C22×#4326C2211yescharacteristic
22C2×C4×C22⋊D11—21no—
23C2×C4×C22⋊D11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C2×#66977—21no—
26C2×#66977C2211yescharacteristic
27C23×C11⋊C8C2211yescharacteristic
28C22×C8×D11C2211yescharacteristic
29#10623166—24no—
30#10623166C2218yes—
31#10623042—24no—
32#10623042C2218yes—
33C2×#66950—21no—
34C2×#66950C2211yescharacteristic
35C2×#66949—21no—
36C2×C4⋊C4×D11C2211yescharacteristic
37C2×C4⋊C4×D11C2211yescharacteristic
38C2×#66942—21no—
39C2×#66942—21no—
40C2×#66941C2211yescharacteristic
41C2×#66941C2211yescharacteristic
42C2×#66940C2211yescharacteristic
43C2×(C22⋊D11)⋊C4—21no—
44C2×#66931—21no—
45C11×#484C2218yescomplemented
46C2×C11×#107C2211yescharacteristic
47C2×C11×#107C2211yescharacteristic
48C2×C11×#103C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×C11×C22⋊C8C2211yescharacteristic
51C2×#66899C2211yescharacteristic
52C2×(C2×D11)⋊C8C2211yescharacteristic
53C2×#66882C2211yescharacteristic
54C2×#66882C2211yescharacteristic
55C2×#66880C2211yescharacteristic
56C2×#66880C2211yescharacteristic
57C2×Dic11⋊C8C2211yescharacteristic
58C2×C8×Dic11C2211yescharacteristic
59#10622664C2218yescomplemented
60C2×#66874C2211yescharacteristic
61C2×#66871C2211yescharacteristic
62C2×#66871C2211yescharacteristic
63C2×#66871C2211yescharacteristic
64C2×#66871C2211yescharacteristic
65C2×#66871C2211yescharacteristic
66C2×#66871C2218yescomplemented
67#10622497C2218yescomplemented
68D11×#107C2218yescomplemented
69#10622488C2218yescomplemented
70#10622487C2218yescomplemented
71#10622426C2218yescomplemented
72#10622422C2218yescomplemented
73#10622407C2218yescomplemented
74#10622403C2218yescomplemented
75(C22⋊D11)⋊C8C2218yes—
76#10622335C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C23×C4×C11—21no—
79C23×C4×C11C2311yescharacteristic
80C22×C22⋊D11D411yescharacteristic
81C23×Dic11—21no—
82C22×C4×D11—21no—
83C22×C4×D11—21no—
84C22×C4×D11C2311yescharacteristic
85C22×Dic22—21no—
86C22×Dic22—21no—
87C22×Dic22C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C22×C8×C11C2311yescharacteristic
90C11×C22⋊Q8—22no—
91C11×C22⋊Q8C2314yes—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—22no—
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2314yes—
99C2×C11×C22⋊C4—21no—
100C2×C22⋊Dic11—21no—
101C2×C22⋊Dic11D411yescharacteristic
102#66999—22no—
103#66999C2314yes—
104Q8×Dic11—22no—
105Q8×Dic11C2314yes—
106C2×#4326—24no—
107C2×#4326C2314yes—
108C4×C22⋊D11—28no—
109C4×C22⋊D11D414yes—
110C4×C22⋊D11C2314yes—
111C2×(C2×D11)⋊C4—21no—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4D411yescharacteristic
114C2×C4⋊Dic11—21no—
115C2×C4⋊Dic11—22no—
116C2×C4⋊Dic11—21no—
117C2×C4⋊Dic11—21no—
118C2×C4⋊Dic11C2311yescharacteristic
119C2×C4⋊Dic11C2311yescharacteristic
120C2×C4⋊Dic11C2311yescharacteristic
121C2×C4⋊Dic11C2314yes—
122#66977—22no—
123#66977—28no—
124#66977C2314yes—
125C2×Dic11⋊C4—21no—
126C2×Dic11⋊C4—21no—
127C2×Dic11⋊C4—21no—
128C2×Dic11⋊C4—21no—
129C2×Dic11⋊C4—21no—
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4D411yescharacteristic
133C2×C4×Dic11—21no—
134C2×C4×Dic11—21no—
135C2×C4×Dic11C2311yescharacteristic
136C22×C11⋊C8—24no—
137C22×C11⋊C8C2311yescharacteristic
138C22×C11⋊C8C2314yes—
139C22×C11⋊C8C2311yescharacteristic
140C2×C8×D11—24no—
141C2×C8×D11C2314yes—
142#66950—22no—
143#66950—28no—
144#66950C2314yes—
145#66949—28no—
146C4⋊C4×D11—22no—
147C4⋊C4×D11—22no—
148C4⋊C4×D11C2314yes—
149C4⋊C4×D11C2314yes—
150#66942—28no—
151#66942—28no—
152#66941—22no—
153#66941—22no—
154#66941C2314yes—
155#66941C2314yes—
156#66940—22no—
157#66940C2314yes—
158(C22⋊D11)⋊C4—28no—
159#66931—28no—
160C11×#107C2314yes—
161C11×#107C2314yes—
162C11×#103C2314yes—
163C11×#103C2314yes—
164C11×C22⋊C8C2314yes—
165#66899C2314yes—
166(C2×D11)⋊C8C2314yes—
167#66882C2314yes—
168#66882C2314yes—
169#66880C2314yes—
170#66880C2314yes—
171Dic11⋊C8C2314yes—
172C8×Dic11C2314yes—
173#66874C2314yes—
174#66871C2314yes—
175#66871C2314yes—
176#66871C2314yes—
177#66871C2314yes—
178#66871C2314yes—
179C2×#3338—111nomaximal, Sylow
180C24×C11C2×D411yescharacteristic
181C23×D11C2×D411yescharacteristic
182C2×Q8×C11—21no—
183C2×Q8×C11—22no—
184C2×Q8×C11—22no—
185C2×Q8×C11C2412yes—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—24no—
193C22×C4×C11—82no—
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2×D412yes—
196C22×C4×C11C2412yes—
197C22×C4×C11C2411yescharacteristic
198C2×C22⋊D11Q1618yescomplemented
199C2×C22⋊D11C2×D414yes—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—24no—
205C22×Dic11—82no—
206C22×Dic11C2×D411yescharacteristic
207C22×Dic11C2×D411yescharacteristic
208C22×Dic11C2×D411yescharacteristic
209C2×C4×D11—24no—
210C2×C4×D11—24no—
211C2×C4×D11—22no—
212C2×C4×D11—22no—
213C2×C4×D11—82no—
214C2×C4×D11—82no—
215C2×C4×D11C2×D412yes—
216C2×C4×D11C2412yes—
217C2×Dic22—24no—
218C2×Dic22—24no—
219C2×Dic22—21no—
220C2×Dic22—22no—
221C2×Dic22—22no—
222C2×Dic22—82no—
223C2×Dic22—82no—
224C2×Dic22C2412yes—
225C2×C8×C11—22no—
226C2×C8×C11—22no—
227C2×C8×C11C2412yes—
228C2×C8×C11C2412yes—
229C11×C4⋊C4—21no—
230C11×C4⋊C4—21no—
231C11×C4⋊C4—21no—
232C11×C4⋊C4—24no—
233C11×C4⋊C4—24no—
234C11×C4⋊C4C2412yes—
235C11×C4⋊C4C2412yes—
236C11×C4⋊C4C2412yes—
237C11×C22⋊C4—24no—
238C22⋊Dic11—24no—
239C22⋊Dic11C2×D414yes—
240#4326—28no—
241(C2×D11)⋊C4—24no—
242(C2×D11)⋊C4—24no—
243(C2×D11)⋊C4C2×D414yes—
244C4⋊Dic11—24no—
245C4⋊Dic11—24no—
246C4⋊Dic11—21no—
247C4⋊Dic11—21no—
248C4⋊Dic11—24no—
249C4⋊Dic11—21no—
250C4⋊Dic11C2412yes—
251C4⋊Dic11C2412yes—
252C4⋊Dic11C2412yes—
253Dic11⋊C4—24no—
254Dic11⋊C4—24no—
255Dic11⋊C4—24no—
256Dic11⋊C4—24no—
257Dic11⋊C4—24no—
258Dic11⋊C4—24no—
259Dic11⋊C4—24no—
260Dic11⋊C4C2×D414yes—
261C4×Dic11—24no—
262C4×Dic11—24no—
263C4×Dic11C2×D412yes—
264C4×Dic11C2412yes—
265C2×C11⋊C8—28no—
266C2×C11⋊C8—22no—
267C2×C11⋊C8#4114yes—
268C2×C11⋊C8C2412yes—
269C2×C11⋊C8C2412yes—
270C8×D11—28no—
271C2×#554—111no—
272C2×#554—111no—
273#3338—1116no—
274C2×#500—111no—
275C2×#484—111no—
276C2×#484—111no—
277C2×#484—111no—
278C2×#484D1111yescharacteristic, complemented
279C2×#477—111no—
280C2×#477—111no—
281C2×#467—111no—
282C2×#467—111no—
283C2×C4×Q16—111no—
284C2×C8×D4—111no—
285C22×#107—111no—
286C22×#107—111no—
287C23×C11—22no—
288C23×C11—22no—
289C23×C11C2×Q1614yes—
290C23×C11C22×D412yes—
291C23×C11C22×D411yescharacteristic
292C22×D11—22no—
293C22×D11—22no—
294C22×D11C2×Q1614yes—
295C22×D11C22×D412yes—
296Q8×C11—22no—
297Q8×C11—22no—
298Q8×C11—42no—
299C2×C4×C11—22no—
300C2×C4×C11—24no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—42no—
308C2×C4×C11—42no—
309C2×C4×C11—42no—
310C2×C4×C11—42no—
311C2×C4×C11—84no—
312C2×C4×C11C22×D412yes—
313C2×C4×C11C22×D411yescharacteristic
314C2×C4×C11C2×#4112yes—
315C2×C4×C112−1+412yes—
316C2×C4×C11C2511yescharacteristic
317C22⋊D11C2×Q16116yescomplemented
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—42no—
325C2×Dic11—42no—
326C2×Dic11—42no—
327C2×Dic11—42no—
328C2×Dic11—84no—
329C2×Dic11C2×Q1614yes—
330C2×Dic11C22×D412yes—
331C2×Dic11C22×D412yes—
332C2×Dic11C22×D412yes—
333C4×D11—24no—
334C4×D11—22no—
335C4×D11—22no—
336C4×D11—84no—
337C4×D11—84no—
338Dic22—22no—
339Dic22—22no—
340Dic22—42no—
341Dic22—84no—
342Dic22—84no—
343C8×C11—22no—
344C8×C11—22no—
345C11⋊C8—22no—
346C11⋊C8C2×#4114yes—
347C22×Q16—111no—
348C23×C8—111no—
349C23×C8—111no—
350#554—118no—
351#554—118no—
352#554—224no—
353#554—224no—
354C2×C4⋊Q8—111no—
355C2×C4⋊Q8—111no—
356C2×#125—221no—
357C2×#125—221no—
358C2×C22⋊Q8—111no—
359C2×C22⋊Q8—111no—
360C2×C22⋊Q8—111no—
361C2×C22⋊Q8—221no—
362C2×C22⋊Q8—221no—
363C2×C22⋊Q8—221no—
364C2×C22⋊Q8—221no—
365C2×C22⋊Q8C2×D1111yescharacteristic
366C2×C4×Q8—111no—
367C2×C4×Q8—111no—
368C2×C4×D4—111no—
369C2×C4×D4—221no—
370C2×C4×D4—221no—
371C22×C4⋊C4—111no—
372C22×C4⋊C4—111no—
373C22×C4⋊C4—111no—
374C22×C4⋊C4C2×D1111yescharacteristic
375#500—118no—
376#484—118no—
377#484—118no—
378#484—118no—
379#484C2×D1118yescomplemented
380#477—118no—
381#477—118no—
382#467—118no—
383#467—118no—
384C4×Q16—118no—
385C8×D4—118no—
386C2×#107—111no—
387C2×#107—111no—
388C2×#107—111no—
389C2×#107—111no—
390C2×#107—118no—
391C2×#107—111no—
392C2×#107—111no—
393C2×#107—111no—
394C2×#107—118no—
395C2×#107C2×D1111yescharacteristic
396C2×#107C2×D1111yescharacteristic
397C2×C4⋊C8—111no—
398C2×#103—111no—
399C2×#103—111no—
400C2×#103—111no—
401C2×#103—111no—
402C2×#103C2×D1111yescharacteristic
403C2×#103C2×D1111yescharacteristic
404C2×C22⋊C8—111no—
405C2×C22⋊C8C2×D1111yescharacteristic
406C2×C4×C8—111no—
407C22×C11—28no—
408C22×C11—22no—
409C22×C11—22no—
410C22×C11#54712yes—
411C22×C11C22×Q1614yes—
412C22×C11C22×Q1612yes—
413C22×C11#57612yes—
414C22×C11C23×D411yescharacteristic
415C2×D11—28no—
416C2×D11—22no—
417C2×D11—22no—
418C2×D11C22×Q1614yes—
419C4×C11—22no—
420C4×C11—42no—
421C4×C11—42no—
422C4×C11—42no—
423C4×C11—42no—
424C4×C11#54712yes—
425C4×C11C22×#4111yescharacteristic
426C4×C11C2×2−1+411yescharacteristic
427Dic11—22no—
428Dic11—22no—
429Dic11—42no—
430Dic11—42no—
431Dic11—42no—
432Dic11—42no—
433Dic11C22×Q1614yes—
434C22×Q8—111no—
435C22×Q8—221no—
436C22×Q8—221no—
437C22×Q8C22×D1111yescharacteristic
438C22×D4—111no—
439C23×C4—21no—
440C23×C4—111no—
441C23×C4—221no—
442C23×C4—221no—
443C23×C4—221no—
444C23×C4C22×D1111yescharacteristic
445C2×Q16—114no—
446C2×Q16—224no—
447C22×C8—111no—
448C22×C8—111no—
449C22×C8—114no—
450C22×C8—114no—
451C22×C8—224no—
452C22×C8—224no—
453C22×C8C22×D1111yescharacteristic
454C22×C8C22×D1111yescharacteristic
455C4⋊Q8—114no—
456C4⋊Q8—114no—
457C4⋊Q8—222no—
458C4⋊Q8—222no—
459#125—228no—
460#125—228no—
461C22⋊Q8—22no—
462C22⋊Q8—114no—
463C22⋊Q8—114no—
464C22⋊Q8—114no—
465C22⋊Q8—228no—
466C22⋊Q8—228no—
467C22⋊Q8—228no—
468C22⋊Q8—228no—
469C22⋊Q8—222no—
470C22⋊Q8—222no—
471C22⋊Q8—222no—
472C22⋊Q8C22×D1114yes—
473C4×Q8—114no—
474C4×Q8—114no—
475C4×Q8—222no—
476C4×Q8—222no—
477C4×D4—114no—
478C4×D4—114no—
479C4×D4—228no—
480C4×D4—228no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—111no—
485C2×C4⋊C4—111no—
486C2×C4⋊C4—111no—
487C2×C4⋊C4—111no—
488C2×C4⋊C4—114no—
489C2×C4⋊C4—114no—
490C2×C4⋊C4—114no—
491C2×C4⋊C4—222no—
492C2×C4⋊C4—222no—
493C2×C4⋊C4—221no—
494C2×C4⋊C4—221no—
495C2×C4⋊C4—221no—
496C2×C4⋊C4—221no—
497C2×C4⋊C4—221no—
498C2×C4⋊C4—221no—
499C2×C4⋊C4—221no—
500C2×C4⋊C4—221no—
501C2×C4⋊C4—221no—
502C2×C4⋊C4—222no—
503C2×C4⋊C4—221no—
504C2×C4⋊C4C22×D1111yescharacteristic
505C2×C4⋊C4C22×D1111yescharacteristic
506C2×C4⋊C4C22×D1111yescharacteristic
507C2×C4⋊C4C22×D1114yes—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—111no—
510C2×C22⋊C4—111no—
511C2×C22⋊C4—221no—
512C2×C22⋊C4—221no—
513C2×C22⋊C4—221no—
514C2×C42—111no—
515C2×C42—221no—
516C2×C42—221no—
517#107—114no—
518#107—114no—
519#107—114no—
520#107—114no—
521#107—114no—
522#107—114no—
523#107—114no—
524#107C22×D1114yes—
525#107C22×D1114yes—
526C4⋊C8—114no—
527#103—114no—
528#103—114no—
529#103—114no—
530#103—114no—
531#103C22×D1114yes—
532#103C22×D1114yes—
533C22⋊C8—114no—
534C22⋊C8C22×D1114yes—
535C4×C8—114no—
536C2×C11—24no—
537C2×C11#333814yescomplemented
538C2×C11C2×#54711yescharacteristic
539C2×C11C23×Q1611yescharacteristic
540C2×C11C2×#57611yescharacteristic
541D11—24no—
542C24—111no—
543C24D4×D1111yescharacteristic
544C2×Q8—21no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—112no—
548C2×Q8—224no—
549C2×Q8—224no—
550C2×Q8—221no—
551C2×Q8—222no—
552C2×Q8—222no—
553C2×Q8—882no—
554C2×Q8—882no—
555C2×Q8C23×D1112yes—
556C2×D4—118no—
557C2×D4—114no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—24no—
565C22×C4—82no—
566C22×C4—111no—
567C22×C4—111no—
568C22×C4—111no—
569C22×C4—112no—
570C22×C4—112no—
571C22×C4—224no—
572C22×C4—224no—
573C22×C4—222no—
574C22×C4—222no—
575C22×C4—221no—
576C22×C4—221no—
577C22×C4—221no—
578C22×C4—221no—
579C22×C4—224no—
580C22×C4—882no—
581C22×C4—882no—
582C22×C4—882no—
583C22×C4D4×D1112yes—
584C22×C4D4×D1111yescharacteristic
585C22×C4C23×D1112yes—
586C22×C4C23×D1111yescharacteristic
587Q16—228no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—114no—
591C2×C8—112no—
592C2×C8—112no—
593C2×C8—228no—
594C2×C8—228no—
595C2×C8—222no—
596C2×C8C23×D1112yes—
597C2×C8C23×D1112yes—
598C4⋊C4—21no—
599C4⋊C4—24no—
600C4⋊C4—21no—
601C4⋊C4—24no—
602C4⋊C4—21no—
603C4⋊C4—114no—
604C4⋊C4—112no—
605C4⋊C4—112no—
606C4⋊C4—112no—
607C4⋊C4—224no—
608C4⋊C4—224no—
609C4⋊C4—224no—
610C4⋊C4—224no—
611C4⋊C4—224no—
612C4⋊C4—224no—
613C4⋊C4—224no—
614C4⋊C4—224no—
615C4⋊C4—221no—
616C4⋊C4—224no—
617C4⋊C4—221no—
618C4⋊C4—221no—
619C4⋊C4—224no—
620C4⋊C4C23×D1112yes—
621C4⋊C4C23×D1112yes—
622C4⋊C4C23×D1112yes—
623C22⋊C4—24no—
624C22⋊C4—114no—
625C22⋊C4—114no—
626C22⋊C4—224no—
627C22⋊C4—224no—
628C22⋊C4—224no—
629C42—112no—
630C42—112no—
631C42—224no—
632C42—224no—
633C11C2×#333811yescharacteristic, complemented, Sylow
634C23—22no—
635C23—22no—
636C23—114no—
637C23—112no—
638C23—222no—
639C23—222no—
640C23Q16×D1114yes—
641C23C2×D4×D1112yes—
642C23C2×D4×D1111yescharacteristic
643Q8—22no—
644Q8—22no—
645Q8—42no—
646Q8—222no—
647Q8—222no—
648Q8—442no—
649Q8—884no—
650Q8—884no—
651D4—1116no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—84no—
665C2×C4—114no—
666C2×C4—112no—
667C2×C4—112no—
668C2×C4—112no—
669C2×C4—222no—
670C2×C4—222no—
671C2×C4—224no—
672C2×C4—222no—
673C2×C4—222no—
674C2×C4—222no—
675C2×C4—222no—
676C2×C4—222no—
677C2×C4—222no—
678C2×C4—442no—
679C2×C4—442no—
680C2×C4—442no—
681C2×C4—442no—
682C2×C4—884no—
683C2×C4—884no—
684C2×C4—884no—
685C2×C4C2×D4×D1112yes—
686C2×C4C2×D4×D1111yescharacteristic
687C2×C4#41×D1112yes—
688C2×C4#6704312yes—
689C2×C4C24×D1111yescharacteristic
690C8—22no—
691C8—22no—
692C8—114no—
693C8—222no—
694C22—28no—
695C22—22no—
696C22—22no—
697C22—114no—
698C22—228no—
699C22—222no—
700C22—222no—
701C22#1062318612yes—
702C22C2×Q16×D1114yes—
703C22C2×Q16×D1112yes—
704C22#1062330512yes—
705C22C22×D4×D1111yescharacteristic
706C4—22no—
707C4—42no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—114no—
712C4—222no—
713C4—222no—
714C4—442no—
715C4—442no—
716C4—442no—
717C4—442no—
718C4#1062318612yes—
719C4C2×#41×D1111yescharacteristic
720C4C2×#6704311yescharacteristic
721C2—24no—
722C2—224no—
723C2#1308100314yesdirect product factor
724C2C2×#1062318611yescharacteristic
725C2C22×Q16×D1111yescharacteristic
726C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#484C2
socleC23×C11C22×D4
prime radicalC22×C22⋊D11D4
hypercenterC2×#484D11
hypocenterC11C2×#3338
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
3. #13081003C2direct (N × H)
4. C2×#10622487C2semidirect
5. C2×#10622497C2semidirect
6. C2×#10622335C2semidirect
7. C2×#10622422C2semidirect
8. C2×#10622488C2semidirect
9. C2×#10622407C2semidirect
10. C2×#10622426C2semidirect
11. C2×#10622664C2semidirect
12. C2×#10622403C2semidirect
14. C22×#66871C2semidirect
15. C2×D11×#107C2semidirect
16. C2×C11×#484C2semidirect
45. C11×#484C22semidirect
59. #10622664C22semidirect
66. C2×#66871C22semidirect
67. #10622497C22semidirect
68. D11×#107C22semidirect
69. #10622488C22semidirect
70. #10622487C22semidirect
71. #10622426C22semidirect
72. #10622422C22semidirect
73. #10622407C22semidirect
74. #10622403C22semidirect
76. #10622335C22semidirect
198. C2×C22⋊D11Q16semidirect
278. C2×#484D11semidirect
317. C22⋊D11C2×Q16semidirect
379. #484C2×D11semidirect
537. C2×C11#3338semidirect
633. C11C2×#3338semidirect
723. C2#13081003direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231662
C2×#106230422
#130810032
C2×#106224872
C2×#106224972
C2×#106223352
C2×#106224222
C2×#106224882
C2×#106224072
C2×#106224262
C2×#106226642
C2×#106224032
C2×(C22⋊D11)⋊C82
C22×#668712
C2×D11×#1072
C2×C11×#4842
C2×#333811