Finite Group Databasebeta

← C2×#13080042 #15626699

Subgroups — C2×#13080042 #15626699

Order 2816.

1818 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623049C211yesmaximal, characteristic, complemented
2#13080042C2116yesmaximal, direct product factor
3C2×#10622635C211yesmaximal, characteristic, complemented
4C2×#10622704C211yesmaximal, characteristic, complemented
5C2×#10622707C211yesmaximal, characteristic, complemented
6C2×#10622622C211yesmaximal, characteristic, complemented
7C2×#10622665C211yesmaximal, characteristic, complemented
8C2×#10622655C211yesmaximal, characteristic
9C2×#10622664C211yesmaximal, characteristic, complemented
10C2×#10622654C211yesmaximal, characteristic
11C2×#10622667C211yesmaximal, characteristic, complemented
12C2×#10622667C211yesmaximal, characteristic, complemented
13C2×#10622644C211yesmaximal, characteristic, complemented
14C2×#10622632C211yesmaximal, characteristic, complemented
15C2×#10622612C211yesmaximal, characteristic, complemented
16C2×C11×#542C211yesmaximal, characteristic
17C11×#542—24no—
18C11×#542C2218yes—
19C2×C11×C4⋊Q8C2211yescharacteristic
20C2×C11×#126—21no—
21C2×C11×#124—21no—
22C2×C11×#124C2211yescharacteristic
23C2×C11×#123—21no—
24C2×C11×C22⋊Q8—21no—
25C2×C11×C22⋊Q8C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C2×C11×#117C2211yescharacteristic
30C22×#4326C2211yescharacteristic
31C22×#4326C2211yescharacteristic
32C22×#4324C2211yescharacteristic
33C22×#4324C2211yescharacteristic
34C2×#66977C2211yescharacteristic
35C2×#66977C2211yescharacteristic
36C22×#4318C2211yescharacteristic
37C23×C11⋊C8C2211yescharacteristic
38#10623049—24no—
39#10623049C2218yescomplemented
40C2×#66942—21no—
41C2×#66942—21no—
42C2×#66932—21no—
43C2×#66932—21no—
44C2×#66923C2211yescharacteristic
45C2×#66922C2211yescharacteristic
46C2×C4×Dic22C2211yescharacteristic
47C2×C4×Dic22C2211yescharacteristic
48C2×#66899C2211yescharacteristic
49C2×#66899C2211yescharacteristic
50C2×#66896C2211yescharacteristic
51C2×#66896C2211yescharacteristic
52#10622707C2218yescomplemented
53#10622704C2218yescomplemented
54#10622667C2218yescomplemented
55#10622667C2218yescomplemented
56#10622665C2218yescomplemented
57#10622664C2218yescomplemented
58#10622655C2218yes—
59#10622654C2218yes—
60#10622644C2218yescomplemented
61#10622635C2218yescomplemented
62#10622632C2218yescomplemented
63#10622622C2218yescomplemented
64#10622612C2218yescomplemented
65C2×#66874C2211yescharacteristic
66C2×#66874C2211yescharacteristic
67C2×#66874C2211yescharacteristic
68C2×#66874C2211yescharacteristic
69C2×#66872C2211yescharacteristic
70C2×#66872C2211yescharacteristic
71C2×#66871C2211yescharacteristic
72C2×#66871C2211yescharacteristic
73C2×C4⋊(C11⋊C8)C2211yescharacteristic
74C2×C4⋊(C11⋊C8)C2211yescharacteristic
75C2×C4⋊(C11⋊C8)C2211yescharacteristic
76C2×C4⋊(C11⋊C8)C2211yescharacteristic
77C22×Q8×C11—21no—
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11—21no—
80C22×D4×C11C2311yescharacteristic
81C23×C4×C11—21no—
82C23×C4×C11C2311yescharacteristic
83C22×Dic22C2311yescharacteristic
84C22×Dic22C2311yescharacteristic
85C11×C4⋊Q8—22no—
86C11×C4⋊Q8C2314yes—
87C11×#126—28no—
88C11×#124—28no—
89C11×#124—22no—
90C11×#124C2314yes—
91C11×#123—28no—
92C11×C22⋊Q8—22no—
93C11×C22⋊Q8—28no—
94C11×C22⋊Q8C2314yes—
95C11×#121—22no—
96C11×#121C2314yes—
97C4×Q8×C11—22no—
98C4×Q8×C11C2314yes—
99C4×D4×C11—22no—
100C4×D4×C11C2314yes—
101C11×#117D414yes—
102C11×#117C2314yes—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4D411yescharacteristic
107C2×C11×C4⋊C4D411yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4D411yescharacteristic
116C2×C11×C22⋊C4D411yescharacteristic
117C2×C42×C11—21no—
118C2×C42×C11C2311yescharacteristic
119C2×C42×C11C2311yescharacteristic
120C2×C22⋊Dic11—21no—
121C2×C22⋊Dic11—21no—
122C2×#4326—42no—
123C2×#4326—42no—
124C2×#4326C2314yes—
125C2×#4326C2314yes—
126C2×#4324—42no—
127C2×#4324—42no—
128C2×#4324C2314yes—
129C2×#4324C2314yes—
130C2×C4⋊Dic11—21no—
131C2×C4⋊Dic11—21no—
132C2×C4⋊Dic11C2311yescharacteristic
133C2×C4⋊Dic11C2311yescharacteristic
134#66977—22no—
135#66977—22no—
136#66977C2314yes—
137#66977C2314yes—
138C2×Dic11⋊C4—21no—
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4—21no—
141C2×Dic11⋊C4—21no—
142C2×Dic11⋊C4—21no—
143C2×Dic11⋊C4—21no—
144C2×C4×Dic11—21no—
145C2×C4×Dic11—21no—
146C2×#4318—42no—
147C2×#4318C2314yes—
148C22×C11⋊C8—42no—
149C22×C11⋊C8C2311yescharacteristic
150C22×C11⋊C8C2311yescharacteristic
151C22×C11⋊C8C2311yescharacteristic
152C22×C11⋊C8C2311yescharacteristic
153C22×C11⋊C8C2314yes—
154#66942—28no—
155#66942—28no—
156#66932—28no—
157#66932—28no—
158#66923—22no—
159#66923C2314yes—
160#66922—22no—
161#66922C2314yes—
162C4×Dic22—22no—
163C4×Dic22—22no—
164C4×Dic22C2314yes—
165C4×Dic22C2314yes—
166#66899C2314yes—
167#66899C2314yes—
168#66896C2314yes—
169#66896C2314yes—
170#66874C2314yes—
171#66874C2314yes—
172#66874C2314yes—
173#66874C2314yes—
174#66872C2314yes—
175#66872C2314yes—
176#66871C2314yes—
177#66871C2314yes—
178C4⋊(C11⋊C8)C2314yes—
179C4⋊(C11⋊C8)C2314yes—
180C4⋊(C11⋊C8)C2314yes—
181C4⋊(C11⋊C8)C2314yes—
182C2×#3258—111nomaximal, Sylow
183C24×C11—21no—
184C24×C11C2×D411yescharacteristic
185C2×Q8×C11—21no—
186C2×Q8×C11—24no—
187C2×Q8×C11—22no—
188C2×Q8×C11—22no—
189C2×Q8×C11—82no—
190C2×Q8×C11C2412yes—
191C2×D4×C11—24no—
192C2×D4×C11—21no—
193C2×D4×C11—22no—
194C2×D4×C11—22no—
195C2×D4×C11—82no—
196C2×D4×C11C2412yes—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—24no—
203C22×C4×C11—82no—
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D412yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2411yescharacteristic
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C2×Dic22—21no—
217C2×Dic22—21no—
218C2×Dic22—22no—
219C2×Dic22—22no—
220C2×Dic22—22no—
221C2×Dic22—22no—
222C2×Dic22C2412yes—
223C2×Dic22C2412yes—
224C11×C4⋊C4—24no—
225C11×C4⋊C4—24no—
226C11×C4⋊C4—24no—
227C11×C4⋊C4—21no—
228C11×C4⋊C4—21no—
229C11×C4⋊C4C2×D414yes—
230C11×C4⋊C4C2×D414yes—
231C11×C4⋊C4C2412yes—
232C11×C4⋊C4C2412yes—
233C11×C22⋊C4—24no—
234C11×C22⋊C4—24no—
235C11×C22⋊C4—24no—
236C11×C22⋊C4—24no—
237C11×C22⋊C4—24no—
238C11×C22⋊C4C2×D414yes—
239C11×C22⋊C4C2×D414yes—
240C42×C11—24no—
241C42×C11C2×D412yes—
242C42×C11C2×D412yes—
243C42×C11C2412yes—
244C42×C11C2412yes—
245C22⋊Dic11—24no—
246C22⋊Dic11—24no—
247#4326—44no—
248#4326—44no—
249#4324—44no—
250#4324—44no—
251C4⋊Dic11—21no—
252C4⋊Dic11—21no—
253C4⋊Dic11—24no—
254C4⋊Dic11—24no—
255C4⋊Dic11C2412yes—
256C4⋊Dic11C2412yes—
257Dic11⋊C4—24no—
258Dic11⋊C4—24no—
259Dic11⋊C4—24no—
260Dic11⋊C4—24no—
261Dic11⋊C4—24no—
262Dic11⋊C4—24no—
263C4×Dic11—24no—
264C4×Dic11—24no—
265#4318—44no—
266C2×C11⋊C8—22no—
267C2×C11⋊C8—22no—
268C2×C11⋊C8—22no—
269C2×C11⋊C8—22no—
270C2×C11⋊C8—44no—
271C2×C11⋊C8C2412yes—
272C2×C11⋊C8C2412yes—
273C2×C11⋊C8C2412yes—
274C2×C11⋊C8C2412yes—
275C2×#542D1111yescharacteristic
276C2×#541—111no—
277#3258—1116no—
278C2×#479—111no—
279C2×#477—111no—
280C2×#475—111no—
281C2×#478—111no—
282C2×#470—111no—
283C2×#468—111no—
284C2×#467—111no—
285C2×#465—111no—
286C2×#464—111no—
287C2×#464—111no—
288C2×#462—111no—
289C2×#461—111no—
290C2×#424—111no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—42no—
296C23×C11—42no—
297C23×C11—42no—
298C23×C11C22×D412yes—
299C23×C11C22×D411yescharacteristic
300Q8×C11—22no—
301Q8×C11—22no—
302Q8×C11—42no—
303Q8×C11—84no—
304D4×C11—22no—
305D4×C11—22no—
306D4×C11—42no—
307D4×C11—84no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—24no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—42no—
320C2×C4×C11—42no—
321C2×C4×C11—42no—
322C2×C4×C11—84no—
323C2×C4×C11C22×D412yes—
324C2×C4×C11C22×D412yes—
325C2×C4×C11C22×D412yes—
326C2×C4×C11C22×D412yes—
327C2×C4×C11C22×D412yes—
328C2×C4×C11C22×D411yescharacteristic
329C2×C4×C11H(5,𝔽2)12yes—
330C2×C4×C112−1+412yes—
331C2×C4×C11C2511yescharacteristic
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—42no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340Dic22—22no—
341Dic22—22no—
342Dic22—22no—
343Dic22—22no—
344Dic22—42no—
345Dic22—42no—
346C11⋊C8—22no—
347C11⋊C8—22no—
348C11⋊C8—22no—
349C11⋊C8—22no—
350C22×Q16—111no—
351C22×Q16—111no—
352C22×SD16—111no—
353C22×SD16—111no—
354C22×M16—111no—
355C23×C8—111no—
356#542—24no—
357#542C2×D1118yes—
358#541—118no—
359#541—224no—
360C2×C4⋊Q8—111no—
361C2×C4⋊Q8C2×D1111yescharacteristic
362C2×#126—21no—
363C2×#126—221no—
364C2×#126—221no—
365C2×#125—111no—
366C2×#125—221no—
367C2×#125—221no—
368C2×#124—21no—
369C2×#124C2×D1111yescharacteristic
370C2×#123—21no—
371C2×C22⋊Q8—21no—
372C2×C22⋊Q8—111no—
373C2×C22⋊Q8—111no—
374C2×C22⋊Q8C2×D1111yescharacteristic
375C2×#121C2×D1111yescharacteristic
376C2×C4×Q8—111no—
377C2×C4×Q8—111no—
378C2×C4×Q8C2×D1111yescharacteristic
379C2×C4×D4C2×D1111yescharacteristic
380C2×#117C2×D1111yescharacteristic
381#479—118no—
382#478—118no—
383#477—118no—
384#475—118no—
385#470—118no—
386#468—118no—
387#467—118no—
388#465—118no—
389#464—118no—
390#464—118no—
391#462—118no—
392#461—118no—
393C2×#107—111no—
394C2×#107—111no—
395C2×#106—111no—
396C2×#106—111no—
397#424—118no—
398C2×C4⋊C8—111no—
399C2×C4⋊C8—111no—
400C2×C4⋊C8—111no—
401C2×C4⋊C8—111no—
402C2×#103—111no—
403C2×#103—111no—
404C2×#103—111no—
405C2×#103—111no—
406C2×#103—111no—
407C2×#103—111no—
408C2×#102—111no—
409C2×#102—111no—
410C22×C11—22no—
411C22×C11—22no—
412C22×C11—22no—
413C22×C11—44no—
414C22×C11—42no—
415C22×C11—42no—
416C22×C11—42no—
417C22×C11—84no—
418C22×C11#53712yes—
419C22×C11#57712yes—
420C22×C11#57812yes—
421C22×C11C23×D411yescharacteristic
422C4×C11—22no—
423C4×C11—22no—
424C4×C11—22no—
425C4×C11—22no—
426C4×C11—22no—
427C4×C11—42no—
428C4×C11—42no—
429C4×C11—42no—
430C4×C11#53712yes—
431C4×C11C2×H(5,𝔽2)11yescharacteristic
432C4×C11C2×2−1+411yescharacteristic
433Dic11—42no—
434Dic11—42no—
435Dic11—42no—
436Dic11—42no—
437C22×Q8—21no—
438C22×Q8—111no—
439C22×Q8—111no—
440C22×Q8C22×D1111yescharacteristic
441C22×D4—21no—
442C22×D4C22×D1111yescharacteristic
443C23×C4—21no—
444C23×C4C22×D1111yescharacteristic
445C2×Q16—114no—
446C2×Q16—114no—
447C2×Q16—442no—
448C2×Q16—442no—
449C2×SD16—114no—
450C2×SD16—114no—
451C2×SD16—442no—
452C2×SD16—442no—
453C2×M16—114no—
454C2×M16—442no—
455C22×C8—111no—
456C22×C8—111no—
457C22×C8—111no—
458C22×C8—111no—
459C22×C8—114no—
460C22×C8—442no—
461C4⋊Q8—22no—
462C4⋊Q8—114no—
463C4⋊Q8—222no—
464C4⋊Q8C22×D1114yes—
465#126—28no—
466#126—228no—
467#126—228no—
468#125—114no—
469#125—228no—
470#125—228no—
471#125—222no—
472#124—28no—
473#124—22no—
474#124C22×D1114yes—
475#123—28no—
476C22⋊Q8—22no—
477C22⋊Q8—28no—
478C22⋊Q8—114no—
479C22⋊Q8—114no—
480C22⋊Q8—222no—
481C22⋊Q8—222no—
482C22⋊Q8C22×D1114yes—
483#121—22no—
484#121C22×D1114yes—
485C4×Q8—22no—
486C4×Q8—114no—
487C4×Q8—114no—
488C4×Q8—222no—
489C4×Q8—222no—
490C4×Q8C22×D1114yes—
491C4×D4—22no—
492C4×D4C22×D1114yes—
493#117C22⋊D1114yes—
494#117C22×D1114yes—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—111no—
499C2×C4⋊C4—111no—
500C2×C4⋊C4—221no—
501C2×C4⋊C4—221no—
502C2×C4⋊C4—221no—
503C2×C4⋊C4—221no—
504C2×C4⋊C4—221no—
505C2×C4⋊C4—221no—
506C2×C4⋊C4—221no—
507C2×C4⋊C4—221no—
508C2×C4⋊C4C22⋊D1111yescharacteristic
509C2×C4⋊C4C22⋊D1111yescharacteristic
510C2×C4⋊C4C22×D1111yescharacteristic
511C2×C4⋊C4C22×D1111yescharacteristic
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—221no—
518C2×C22⋊C4—221no—
519C2×C22⋊C4C22⋊D1111yescharacteristic
520C2×C22⋊C4C22⋊D1111yescharacteristic
521C2×C42—21no—
522C2×C42—221no—
523C2×C42—221no—
524C2×C42C22×D1111yescharacteristic
525C2×C42C22×D1111yescharacteristic
526#107—114no—
527#107—114no—
528#106—114no—
529#106—114no—
530C4⋊C8—114no—
531C4⋊C8—114no—
532C4⋊C8—114no—
533C4⋊C8—114no—
534#103—114no—
535#103—114no—
536#103—114no—
537#103—114no—
538#103—114no—
539#103—114no—
540#102—114no—
541#102—114no—
542C2×C11—42no—
543C2×C11—82no—
544C2×C11#325814yescomplemented
545C2×C11C2×#53711yescharacteristic
546C2×C11C2×#57711yescharacteristic
547C2×C11C2×#57811yescharacteristic
548C24—21no—
549C24C2×C22⋊D1111yescharacteristic
550C2×Q8—21no—
551C2×Q8—24no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—82no—
555C2×Q8—112no—
556C2×Q8—112no—
557C2×Q8—221no—
558C2×Q8—221no—
559C2×Q8—222no—
560C2×Q8—222no—
561C2×Q8—222no—
562C2×Q8—222no—
563C2×Q8C23×D1112yes—
564C2×D4—24no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—21no—
568C2×D4—82no—
569C2×D4C23×D1112yes—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—24no—
576C22×C4—82no—
577C22×C4—221no—
578C22×C4—221no—
579C22×C4—221no—
580C22×C4—221no—
581C22×C4C2×C22⋊D1112yes—
582C22×C4C2×C22⋊D1111yescharacteristic
583C22×C4C2×C22⋊D1111yescharacteristic
584C22×C4C2×C22⋊D1111yescharacteristic
585C22×C4C2×C22⋊D1111yescharacteristic
586C22×C4C2×C22⋊D1111yescharacteristic
587C22×C4C23×D1112yes—
588C22×C4C23×D1111yescharacteristic
589Q16—444no—
590Q16—444no—
591SD16—444no—
592SD16—444no—
593M16—444no—
594C2×C8—112no—
595C2×C8—112no—
596C2×C8—112no—
597C2×C8—112no—
598C2×C8—222no—
599C2×C8—222no—
600C2×C8—222no—
601C2×C8—222no—
602C2×C8—444no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—112no—
609C4⋊C4—112no—
610C4⋊C4—221no—
611C4⋊C4—221no—
612C4⋊C4—224no—
613C4⋊C4—224no—
614C4⋊C4—224no—
615C4⋊C4—224no—
616C4⋊C4—224no—
617C4⋊C4—224no—
618C4⋊C4—224no—
619C4⋊C4—224no—
620C4⋊C4C2×C22⋊D1114yes—
621C4⋊C4C2×C22⋊D1114yes—
622C4⋊C4C23×D1112yes—
623C4⋊C4C23×D1112yes—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—224no—
630C22⋊C4—224no—
631C22⋊C4C2×C22⋊D1114yes—
632C22⋊C4C2×C22⋊D1114yes—
633C42—24no—
634C42—224no—
635C42—224no—
636C42C2×C22⋊D1112yes—
637C42C2×C22⋊D1112yes—
638C42C23×D1112yes—
639C42C23×D1112yes—
640C11C2×#325811yescharacteristic, complemented, Sylow
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23C22×C22⋊D1112yes—
649C23C22×C22⋊D1111yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653Q8—84no—
654Q8—222no—
655Q8—222no—
656Q8—222no—
657Q8—222no—
658Q8—442no—
659Q8—442no—
660D4—22no—
661D4—22no—
662D4—42no—
663D4—84no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—84no—
679C2×C4—222no—
680C2×C4—222no—
681C2×C4—222no—
682C2×C4—222no—
683C2×C4—442no—
684C2×C4—442no—
685C2×C4—442no—
686C2×C4—442no—
687C2×C4#6704212yes—
688C2×C4#6704312yes—
689C2×C4C22×C22⋊D1112yes—
690C2×C4C22×C22⋊D1112yes—
691C2×C4C22×C22⋊D1112yes—
692C2×C4C22×C22⋊D1112yes—
693C2×C4C22×C22⋊D1112yes—
694C2×C4C22×C22⋊D1111yescharacteristic
695C2×C4C24×D1111yescharacteristic
696C8—222no—
697C8—222no—
698C8—222no—
699C8—222no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—84no—
708C22#1062336412yes—
709C22#1062336712yes—
710C22#1062336912yes—
711C22C23×C22⋊D1111yescharacteristic
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—22no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—442no—
721C4—442no—
722C4—442no—
723C4—442no—
724C4#1062336412yes—
725C4C2×#6704211yescharacteristic
726C4C2×#6704311yescharacteristic
727C2—42no—
728C2—82no—
729C2#1308004214yesdirect product factor
730C2C2×#1062336411yescharacteristic
731C2C2×#1062336711yescharacteristic
732C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#542C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenterC2×#542D11
hypocenterC11C2×#3258
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#10623049C2semidirect
2. #13080042C2direct (N × H)
3. C2×#10622635C2semidirect
4. C2×#10622704C2semidirect
5. C2×#10622707C2semidirect
6. C2×#10622622C2semidirect
7. C2×#10622665C2semidirect
9. C2×#10622664C2semidirect
11. C2×#10622667C2semidirect
12. C2×#10622667C2semidirect
13. C2×#10622644C2semidirect
14. C2×#10622632C2semidirect
15. C2×#10622612C2semidirect
39. #10623049C22semidirect
52. #10622707C22semidirect
53. #10622704C22semidirect
54. #10622667C22semidirect
55. #10622667C22semidirect
56. #10622665C22semidirect
57. #10622664C22semidirect
60. #10622644C22semidirect
61. #10622635C22semidirect
62. #10622632C22semidirect
63. #10622622C22semidirect
64. #10622612C22semidirect
544. C2×C11#3258semidirect
640. C11C2×#3258semidirect
729. C2#13080042direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230492
#130800422
C2×#106226352
C2×#106227042
C2×#106227072
C2×#106226222
C2×#106226652
C2×#106226552
C2×#106226642
C2×#106226542
C2×#106226672
C2×#106226442
C2×#106226322
C2×#106226122
C2×C11×#5422
C2×#325811