Finite Group Databasebeta

← C2×#13080652 #15630443

Subgroups — C2×#13080652 #15630443

Order 2816.

2254 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623073C211yesmaximal, characteristic, complemented
2#13080652C2116yesmaximal, direct product factor
3C2×#10622668C211yesmaximal, characteristic, complemented
4C2×#10622658C211yesmaximal, characteristic, complemented
5C2×#10622648C211yesmaximal, characteristic, complemented
6C2×#10622621C211yesmaximal, characteristic, complemented
7C2×#10622665C211yesmaximal, characteristic, complemented
8C2×#10622654C211yesmaximal, characteristic, complemented
9C2×#10622667C211yesmaximal, characteristic, complemented
10C2×#10622852C211yesmaximal, characteristic, complemented
11C2×#10622831C211yesmaximal, characteristic, complemented
12C2×#10622631C211yesmaximal, characteristic, complemented
13C2×#10622624C211yesmaximal, characteristic, complemented
14C2×#10622828C211yesmaximal, characteristic, complemented
15C2×#10622846C211yesmaximal, characteristic, complemented
16C2×C11×#546C211yesmaximal, characteristic
17C22×C11×#41C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C11×#546—24no—
20C11×#546C2218yes—
21C2×C11×#124C2211yescharacteristic
22C2×C11×#123—21no—
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C11×#121—21no—
25C2×C11×#121C2211yescharacteristic
26C2×C11×#120—21no—
27C2×C4×D4×C11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C22×C11×C22⋊C4—21no—
30C22×#4326C2211yescharacteristic, complemented
31C2×#66989—21no—
32C22×#4324C2211yescharacteristic
33C22×#4324C2211yescharacteristic
34C2×#66979C2211yescharacteristic
35C2×#66979C2211yescharacteristic, complemented
36C2×#66977C2211yescharacteristic
37C2×#66977C2211yescharacteristic, complemented
38C22×#4318C2211yescharacteristic
39C23×C11⋊C8C2211yescharacteristic, complemented
40#10623073—24no—
41#10623073C2218yescomplemented
42C2×#66940—21no—
43C2×#66932—21no—
44C2×#66932—21no—
45C2×#66922C2211yescharacteristic, complemented
46C2×C4×Dic22C2211yescharacteristic, complemented
47#10622852C2218yescomplemented
48#10622846C2218yescomplemented
49C2×#66899C2211yescharacteristic, complemented
50C2×#66899C2211yescharacteristic, complemented
51C2×#66899C2211yescharacteristic, complemented
52#10622831C2218yescomplemented
53#10622828C2218yescomplemented
54C2×#66896C2211yescharacteristic
55C2×#66896C2211yescharacteristic
56C2×#66896C2211yescharacteristic
57C2×#66896C2211yescharacteristic
58C2×#66896C2211yescharacteristic
59C2×#66896C2211yescharacteristic
60C2×C22⋊(C11⋊C8)C2211yescharacteristic
61C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
62#10622668C2218yescomplemented
63#10622667C2218yescomplemented
64#10622665C2218yescomplemented
65#10622658C2218yescomplemented
66#10622654C2218yescomplemented
67#10622648C2218yescomplemented
68#10622631C2218yescomplemented
69#10622624C2218yescomplemented
70#10622621C2218yescomplemented
71C2×#66874C2211yescharacteristic, complemented
72C2×#66872C2211yescharacteristic, complemented
73C2×#66872C2211yescharacteristic, complemented
74C2×#66871C2211yescharacteristic, complemented
75C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
76C2×#66867C2211yescharacteristic, complemented
77C25×C11—21no—
78C2×C11×#41—22no—
79C2×C11×#41—24no—
80C2×C11×#41—42no—
81C2×C11×#41C2314yes—
82C22×Q8×C11C2311yescharacteristic
83C22×D4×C11—24no—
84C22×D4×C11—21no—
85C22×D4×C11—21no—
86C22×D4×C11—21no—
87C22×D4×C11—22no—
88C22×D4×C11—42no—
89C22×D4×C11D411yescharacteristic
90C22×D4×C11C2311yescharacteristic
91C22×D4×C11C2314yes—
92C22×D4×C11C2311yescharacteristic
93C23×C4×C11—21no—
94C23×C4×C11—21no—
95C23×C4×C11C2311yescharacteristic
96C23×C4×C11C2311yescharacteristic
97C22×Dic22—21no—
98C22×Dic22C2311yescharacteristic
99C11×#124—22no—
100C11×#124C2314yes—
101C11×#123—28no—
102C11×C22⋊Q8—22no—
103C11×C22⋊Q8C2314yes—
104C11×#121—22no—
105C11×#121—28no—
106C11×#121C2314yes—
107C11×#120—28no—
108C4×D4×C11—22no—
109C4×D4×C11D414yes—
110C4×D4×C11C2314yes—
111C4×D4×C11C2314yes—
112C2×C11×C4⋊C4—21no—
113C2×C11×C4⋊C4D411yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4—28no—
121C2×C11×C22⋊C4D411yescharacteristic
122C2×C11×C22⋊C4D411yescharacteristic
123C2×C42×C11C2311yescharacteristic
124C2×C22⋊Dic11—21no—
125C2×C22⋊Dic11—21no—
126C2×C22⋊Dic11—21no—
127C2×C22⋊Dic11—21no—
128C2×#4326—42no—
129C2×#4326C2314yescomplemented
130#66989—28no—
131C2×#4324—24no—
132C2×#4324—42no—
133C2×#4324C2314yes—
134C2×#4324C2314yes—
135#66979—22no—
136#66979—22no—
137#66979C2314yes—
138#66979C2314yescomplemented
139C2×C4⋊Dic11—21no—
140C2×C4⋊Dic11C2311yescharacteristic
141C2×C4⋊Dic11C2311yescharacteristic
142C2×C4⋊Dic11C2311yescharacteristic
143#66977—22no—
144#66977—22no—
145#66977C2314yes—
146#66977C2314yescomplemented
147C2×Dic11⋊C4—21no—
148C2×Dic11⋊C4—21no—
149C2×Dic11⋊C4—21no—
150C2×C4×Dic11—21no—
151C2×C4×Dic11—21no—
152C2×C4×Dic11—21no—
153C2×#4318—42no—
154C2×#4318C2314yes—
155C22×C11⋊C8—42no—
156C22×C11⋊C8C2311yescharacteristic
157C22×C11⋊C8C2311yescharacteristic
158C22×C11⋊C8C2311yescharacteristic
159C22×C11⋊C8C2311yescharacteristic
160C22×C11⋊C8C2314yescomplemented
161#66940—28no—
162#66932—28no—
163#66932—28no—
164#66922—22no—
165#66922C2314yescomplemented
166C4×Dic22—22no—
167C4×Dic22C2314yescomplemented
168#66899C2314yescomplemented
169#66899C2314yescomplemented
170#66899C2314yescomplemented
171#66896C2314yes—
172#66896C2314yes—
173#66896C2314yes—
174#66896C2314yes—
175#66896C2314yes—
176#66896C2314yes—
177C22⋊(C11⋊C8)C2314yes—
178C22⋊(C11⋊C8)C2314yescomplemented
179#66874C2314yescomplemented
180#66872C2314yescomplemented
181#66872C2314yescomplemented
182#66871C2314yescomplemented
183C4⋊(C11⋊C8)C2314yescomplemented
184#66867C2314yescomplemented
185C2×#3311—111nomaximal, Sylow
186C24×C11—21no—
187C24×C11—21no—
188C24×C11—24no—
189C24×C11—44no—
190C24×C11—44no—
191C24×C11—82no—
192C24×C11C2×D411yescharacteristic
193C24×C11C2×D411yescharacteristic
194C11×#41—28no—
195C11×#41—44no—
196C11×#41—48no—
197C2×Q8×C11—21no—
198C2×Q8×C11—22no—
199C2×Q8×C11—22no—
200C2×Q8×C11C2412yes—
201C2×D4×C11—28no—
202C2×D4×C11—24no—
203C2×D4×C11—24no—
204C2×D4×C11—21no—
205C2×D4×C11—24no—
206C2×D4×C11—21no—
207C2×D4×C11—22no—
208C2×D4×C11—22no—
209C2×D4×C11—22no—
210C2×D4×C11—44no—
211C2×D4×C11—48no—
212C2×D4×C11—42no—
213C2×D4×C11—44no—
214C2×D4×C11—44no—
215C2×D4×C11—82no—
216C2×D4×C11C2×D414yes—
217C2×D4×C11#4114yes—
218C2×D4×C11C2412yes—
219C2×D4×C11C2412yes—
220C22×C4×C11—22no—
221C22×C4×C11—22no—
222C22×C4×C11—22no—
223C22×C4×C11—22no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—24no—
227C22×C4×C11—24no—
228C22×C4×C11—44no—
229C22×C4×C11—82no—
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2×D411yescharacteristic
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11C2×D411yescharacteristic
234C22×C4×C11C2×D412yes—
235C22×C4×C11C2×D412yes—
236C22×C4×C11C2412yes—
237C22×C4×C11C2412yes—
238C22×C4×C11C2411yescharacteristic
239C22×Dic11—21no—
240C22×Dic11—21no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C2×Dic22—21no—
244C2×Dic22—24no—
245C2×Dic22—22no—
246C2×Dic22—22no—
247C2×Dic22—44no—
248C2×Dic22C2412yes—
249C11×C4⋊C4—24no—
250C11×C4⋊C4—21no—
251C11×C4⋊C4C2×D414yes—
252C11×C4⋊C4C2412yes—
253C11×C22⋊C4—24no—
254C11×C22⋊C4—24no—
255C11×C22⋊C4—24no—
256C11×C22⋊C4—24no—
257C11×C22⋊C4—24no—
258C11×C22⋊C4C2×D414yes—
259C11×C22⋊C4C2×D414yes—
260C42×C11C2×D412yes—
261C42×C11C2412yes—
262C22⋊Dic11—24no—
263C22⋊Dic11—24no—
264C22⋊Dic11—24no—
265C22⋊Dic11—24no—
266#4326—44no—
267#4324—28no—
268#4324—44no—
269C4⋊Dic11—21no—
270C4⋊Dic11—21no—
271C4⋊Dic11—21no—
272C4⋊Dic11—24no—
273C4⋊Dic11C2412yes—
274C4⋊Dic11C2412yes—
275C4⋊Dic11C2412yes—
276Dic11⋊C4—24no—
277Dic11⋊C4—24no—
278Dic11⋊C4—24no—
279C4×Dic11—24no—
280C4×Dic11—24no—
281C4×Dic11—24no—
282#4318—44no—
283C2×C11⋊C8—22no—
284C2×C11⋊C8—22no—
285C2×C11⋊C8—22no—
286C2×C11⋊C8—22no—
287C2×C11⋊C8—44no—
288C2×C11⋊C8C2412yes—
289C2×C11⋊C8C2412yes—
290C2×C11⋊C8C2412yes—
291C2×C11⋊C8C2412yes—
292C2×#556—111no—
293C2×#546D1111yescharacteristic
294#3311—1116no—
295C2×#489—111no—
296C2×#485—111no—
297C2×#482—111no—
298C2×#476—111no—
299C2×#470—111no—
300C2×#465—111no—
301C2×#464—111no—
302C2×#452—111no—
303C2×#450—111no—
304C2×#440—111no—
305C2×#435—111no—
306C2×#418—111no—
307C2×#416—111no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—24no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—48no—
318C23×C11—48no—
319C23×C11—42no—
320C23×C11—42no—
321C23×C11—42no—
322C23×C11—42no—
323C23×C11—42no—
324C23×C11—84no—
325C23×C11—816no—
326C23×C11C22×D412yes—
327C23×C11C22×D412yes—
328C23×C11C22×D411yescharacteristic
329Q8×C11—22no—
330Q8×C11—22no—
331Q8×C11—42no—
332D4×C11—24no—
333D4×C11—22no—
334D4×C11—22no—
335D4×C11—22no—
336D4×C11—44no—
337D4×C11—48no—
338D4×C11—48no—
339D4×C11—42no—
340D4×C11—84no—
341D4×C11C2×#4114yes—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—24no—
347C2×C4×C11—24no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—48no—
355C2×C4×C11—42no—
356C2×C4×C11—42no—
357C2×C4×C11—84no—
358C2×C4×C11C22×D412yes—
359C2×C4×C11C22×D412yes—
360C2×C4×C11C22×D412yes—
361C2×C4×C11C22×D412yes—
362C2×C4×C11C22×D411yescharacteristic
363C2×C4×C11C2×#4112yes—
364C2×C4×C11H(5,𝔽2)12yes—
365C2×C4×C11C2511yescharacteristic
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—42no—
371C2×Dic11—42no—
372C2×Dic11—42no—
373C2×Dic11—42no—
374Dic22—22no—
375Dic22—22no—
376Dic22—48no—
377Dic22—42no—
378C11⋊C8—22no—
379C11⋊C8—22no—
380C11⋊C8—22no—
381C11⋊C8—22no—
382C22×#41C2×D1111yescharacteristic
383C23×D4C2×D1111yescharacteristic
384C22×Q16—111no—
385C22×SD16—111no—
386C22×SD16—111no—
387C22×M16—111no—
388C23×C8—111no—
389#556—118no—
390#556—224no—
391#546—24no—
392#546C2×D1118yes—
393C2×C4⋊Q8—111no—
394C2×#126—221no—
395C2×#126—221no—
396C2×#124—221no—
397C2×#124C2×D1111yescharacteristic
398C2×#123—21no—
399C2×C22⋊Q8—111no—
400C2×C22⋊Q8—111no—
401C2×C22⋊Q8C2×D1111yescharacteristic
402C2×#121—21no—
403C2×#121C2×D1111yescharacteristic
404C2×#120—21no—
405C2×C4×Q8—111no—
406C2×C4×Q8—221no—
407C2×C4×D4C2×D1111yescharacteristic
408C2×C4×D4C2×D1111yescharacteristic
409C2×#117—111no—
410C2×#117—111no—
411C22×C22⋊C4—21no—
412#489—118no—
413#485—118no—
414#482—118no—
415#476—118no—
416#470—118no—
417#465—118no—
418#464—118no—
419#452—118no—
420#450—118no—
421#440—118no—
422#435—118no—
423C2×#107—111no—
424C2×#106—111no—
425C2×#106—111no—
426C2×C4⋊C8—111no—
427#418—118no—
428#416—118no—
429C2×#103—111no—
430C2×#103—111no—
431C2×#103—111no—
432C2×#103—111no—
433C2×#102—111no—
434C2×#102—111no—
435C2×#102—111no—
436C2×#102—111no—
437C2×#102—111no—
438C2×#102—111no—
439C2×C22⋊C8—111no—
440C2×C22⋊C8—111no—
441C2×#97—111no—
442C22×C11—22no—
443C22×C11—22no—
444C22×C11—24no—
445C22×C11—22no—
446C22×C11—22no—
447C22×C11—22no—
448C22×C11—22no—
449C22×C11—44no—
450C22×C11—44no—
451C22×C11—48no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—816no—
458C22×C11—84no—
459C22×C11#54612yes—
460C22×C11#57512yes—
461C22×C11#57712yes—
462C22×C11C23×D411yescharacteristic
463C4×C11—22no—
464C4×C11—22no—
465C4×C11—22no—
466C4×C11—22no—
467C4×C11—42no—
468C4×C11—42no—
469C4×C11#54612yes—
470C4×C11C22×#4111yescharacteristic
471C4×C11C2×H(5,𝔽2)11yescharacteristic
472Dic11—42no—
473Dic11—42no—
474Dic11—42no—
475Dic11—42no—
476C25—21no—
477C2×#41—22no—
478C2×#41—24no—
479C2×#41—42no—
480C2×#41C22×D1114yes—
481C22×Q8—111no—
482C22×Q8—221no—
483C22×Q8C22×D1111yescharacteristic
484C22×D4—24no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4—22no—
489C22×D4—42no—
490C22×D4C22⋊D1111yescharacteristic
491C22×D4C22×D1111yescharacteristic
492C22×D4C22×D1114yes—
493C22×D4C22×D1111yescharacteristic
494C23×C4—21no—
495C23×C4—21no—
496C23×C4C22×D1111yescharacteristic
497C23×C4C22×D1111yescharacteristic
498C2×Q16—114no—
499C2×Q16—442no—
500C2×SD16—114no—
501C2×SD16—114no—
502C2×SD16—224no—
503C2×SD16—442no—
504C2×M16—114no—
505C2×M16—442no—
506C22×C8—111no—
507C22×C8—111no—
508C22×C8—111no—
509C22×C8—111no—
510C22×C8—114no—
511C22×C8—442no—
512C4⋊Q8—114no—
513C4⋊Q8—222no—
514#126—228no—
515#126—228no—
516#124—22no—
517#124—228no—
518#124C22×D1114yes—
519#123—28no—
520C22⋊Q8—22no—
521C22⋊Q8—114no—
522C22⋊Q8—114no—
523C22⋊Q8—222no—
524C22⋊Q8—222no—
525C22⋊Q8C22×D1114yes—
526#121—22no—
527#121—28no—
528#121C22×D1114yes—
529#120—28no—
530C4×Q8—114no—
531C4×Q8—228no—
532C4×Q8—222no—
533C4×D4—22no—
534C4×D4C22⋊D1114yes—
535C4×D4C22×D1114yes—
536C4×D4C22×D1114yes—
537#117—114no—
538#117—114no—
539#117—222no—
540#117—222no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—111no—
543C2×C4⋊C4—111no—
544C2×C4⋊C4—111no—
545C2×C4⋊C4—221no—
546C2×C4⋊C4—221no—
547C2×C4⋊C4—221no—
548C2×C4⋊C4—221no—
549C2×C4⋊C4C22⋊D1111yescharacteristic
550C2×C4⋊C4C22×D1111yescharacteristic
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—28no—
557C2×C22⋊C4—221no—
558C2×C22⋊C4—221no—
559C2×C22⋊C4—221no—
560C2×C22⋊C4—221no—
561C2×C22⋊C4C22⋊D1111yescharacteristic
562C2×C22⋊C4C22⋊D1111yescharacteristic
563C2×C42—221no—
564C2×C42—221no—
565C2×C42—221no—
566C2×C42C22×D1111yescharacteristic
567#107—114no—
568#106—114no—
569#106—114no—
570C4⋊C8—114no—
571#103—114no—
572#103—114no—
573#103—114no—
574#103—114no—
575#102—114no—
576#102—114no—
577#102—114no—
578#102—114no—
579#102—114no—
580#102—114no—
581C22⋊C8—114no—
582C22⋊C8—114no—
583#97—114no—
584C2×C11—42no—
585C2×C11—42no—
586C2×C11—44no—
587C2×C11—82no—
588C2×C11#331114yescomplemented
589C2×C11C2×#54611yescharacteristic
590C2×C11C2×#57511yescharacteristic
591C2×C11C2×#57711yescharacteristic
592C24—21no—
593C24—21no—
594C24—24no—
595C24—44no—
596C24—44no—
597C24—82no—
598C24C2×C22⋊D1111yescharacteristic
599C24C2×C22⋊D1111yescharacteristic
600#41—28no—
601#41—44no—
602#41—48no—
603C2×Q8—21no—
604C2×Q8—22no—
605C2×Q8—22no—
606C2×Q8—112no—
607C2×Q8—221no—
608C2×Q8—224no—
609C2×Q8—222no—
610C2×Q8—222no—
611C2×Q8—444no—
612C2×Q8C23×D1112yes—
613C2×D4—28no—
614C2×D4—24no—
615C2×D4—24no—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—21no—
620C2×D4—24no—
621C2×D4—21no—
622C2×D4—44no—
623C2×D4—48no—
624C2×D4—42no—
625C2×D4—44no—
626C2×D4—44no—
627C2×D4—82no—
628C2×D4#434114yes—
629C2×D4C2×C22⋊D1114yes—
630C2×D4C23×D1112yes—
631C2×D4C23×D1112yes—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—24no—
639C22×C4—24no—
640C22×C4—44no—
641C22×C4—82no—
642C22×C4—221no—
643C22×C4—221no—
644C22×C4—221no—
645C22×C4—221no—
646C22×C4C2×C22⋊D1112yes—
647C22×C4C2×C22⋊D1112yes—
648C22×C4C2×C22⋊D1111yescharacteristic
649C22×C4C2×C22⋊D1111yescharacteristic
650C22×C4C2×C22⋊D1111yescharacteristic
651C22×C4C2×C22⋊D1111yescharacteristic
652C22×C4C23×D1112yes—
653C22×C4C23×D1112yes—
654C22×C4C23×D1111yescharacteristic
655Q16—444no—
656SD16—228no—
657SD16—444no—
658M16—444no—
659C2×C8—112no—
660C2×C8—112no—
661C2×C8—112no—
662C2×C8—112no—
663C2×C8—222no—
664C2×C8—222no—
665C2×C8—222no—
666C2×C8—222no—
667C2×C8—444no—
668C4⋊C4—24no—
669C4⋊C4—21no—
670C4⋊C4—112no—
671C4⋊C4—112no—
672C4⋊C4—112no—
673C4⋊C4—221no—
674C4⋊C4—221no—
675C4⋊C4—221no—
676C4⋊C4—224no—
677C4⋊C4—224no—
678C4⋊C4—224no—
679C4⋊C4—224no—
680C4⋊C4C2×C22⋊D1114yes—
681C4⋊C4C23×D1112yes—
682C22⋊C4—24no—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—224no—
688C22⋊C4—224no—
689C22⋊C4—224no—
690C22⋊C4—224no—
691C22⋊C4C2×C22⋊D1114yes—
692C22⋊C4C2×C22⋊D1114yes—
693C42—224no—
694C42—224no—
695C42—224no—
696C42C2×C22⋊D1112yes—
697C42C23×D1112yes—
698C11C2×#331111yescharacteristic, complemented, Sylow
699C23—22no—
700C23—22no—
701C23—24no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—48no—
709C23—48no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—84no—
716C23—816no—
717C23C22×C22⋊D1112yes—
718C23C22×C22⋊D1112yes—
719C23C22×C22⋊D1111yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—42no—
723Q8—222no—
724Q8—222no—
725Q8—448no—
726Q8—442no—
727D4—24no—
728D4—22no—
729D4—22no—
730D4—22no—
731D4—44no—
732D4—48no—
733D4—48no—
734D4—42no—
735D4—84no—
736D4C2×#434114yes—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—48no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—84no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—222no—
757C2×C4—442no—
758C2×C4—442no—
759C2×C4—442no—
760C2×C4—442no—
761C2×C4C2×#434112yes—
762C2×C4#6703712yes—
763C2×C4C22×C22⋊D1112yes—
764C2×C4C22×C22⋊D1112yes—
765C2×C4C22×C22⋊D1112yes—
766C2×C4C22×C22⋊D1112yes—
767C2×C4C22×C22⋊D1111yescharacteristic
768C2×C4C24×D1111yescharacteristic
769C8—222no—
770C8—222no—
771C8—222no—
772C8—222no—
773C22—22no—
774C22—22no—
775C22—24no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—44no—
781C22—44no—
782C22—48no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—816no—
789C22—84no—
790C22#1062333712yes—
791C22#1062335312yes—
792C22#1062336712yes—
793C22C23×C22⋊D1111yescharacteristic
794C4—22no—
795C4—22no—
796C4—22no—
797C4—22no—
798C4—42no—
799C4—42no—
800C4—442no—
801C4—442no—
802C4—442no—
803C4—442no—
804C4#1062333712yes—
805C4C22×#434111yescharacteristic
806C4C2×#6703711yescharacteristic
807C2—42no—
808C2—42no—
809C2—44no—
810C2—82no—
811C2#1308065214yesdirect product factor
812C2C2×#1062333711yescharacteristic
813C2C2×#1062335311yescharacteristic
814C2C2×#1062336711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×C11×#546C2
socleC23×C11C22×D4
hypercenterC2×#546D11
hypocenterC11C2×#3311
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#10623073C2semidirect
2. #13080652C2direct (N × H)
3. C2×#10622668C2semidirect
4. C2×#10622658C2semidirect
5. C2×#10622648C2semidirect
6. C2×#10622621C2semidirect
7. C2×#10622665C2semidirect
8. C2×#10622654C2semidirect
9. C2×#10622667C2semidirect
10. C2×#10622852C2semidirect
11. C2×#10622831C2semidirect
12. C2×#10622631C2semidirect
13. C2×#10622624C2semidirect
14. C2×#10622828C2semidirect
15. C2×#10622846C2semidirect
30. C22×#4326C22semidirect
35. C2×#66979C22semidirect
37. C2×#66977C22semidirect
39. C23×C11⋊C8C22semidirect
41. #10623073C22semidirect
45. C2×#66922C22semidirect
46. C2×C4×Dic22C22semidirect
47. #10622852C22semidirect
48. #10622846C22semidirect
49. C2×#66899C22semidirect
50. C2×#66899C22semidirect
51. C2×#66899C22semidirect
52. #10622831C22semidirect
53. #10622828C22semidirect
61. C2×C22⋊(C11⋊C8)C22semidirect
62. #10622668C22semidirect
63. #10622667C22semidirect
64. #10622665C22semidirect
65. #10622658C22semidirect
66. #10622654C22semidirect
67. #10622648C22semidirect
68. #10622631C22semidirect
69. #10622624C22semidirect
70. #10622621C22semidirect
71. C2×#66874C22semidirect
72. C2×#66872C22semidirect
73. C2×#66872C22semidirect
74. C2×#66871C22semidirect
75. C2×C4⋊(C11⋊C8)C22semidirect
76. C2×#66867C22semidirect
129. C2×#4326C23semidirect
138. #66979C23semidirect
146. #66977C23semidirect
160. C22×C11⋊C8C23semidirect
165. #66922C23semidirect
167. C4×Dic22C23semidirect
168. #66899C23semidirect
169. #66899C23semidirect
170. #66899C23semidirect
178. C22⋊(C11⋊C8)C23semidirect
179. #66874C23semidirect
180. #66872C23semidirect
181. #66872C23semidirect
182. #66871C23semidirect
183. C4⋊(C11⋊C8)C23semidirect
184. #66867C23semidirect
588. C2×C11#3311semidirect
698. C11C2×#3311semidirect
811. C2#13080652direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230732
#130806522
C2×#106226682
C2×#106226582
C2×#106226482
C2×#106226212
C2×#106226652
C2×#106226542
C2×#106226672
C2×#106228522
C2×#106228312
C2×#106226312
C2×#106226242
C2×#106228282
C2×#106228462
C2×C11×#5462
C2×#331111