Finite Group Databasebeta

← C2×#13080333 #15629012

Subgroups — C2×#13080333 #15629012

Order 2816.

2806 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66969C212yesmaximal, complemented
2C2×#10623086C211yesmaximal, characteristic, complemented
3C2×#10623257C211yesmaximal, characteristic, complemented
4#13080333C2116yesmaximal, direct product factor
5C2×#10622705C211yesmaximal, characteristic, complemented
6C2×#10622426C212yesmaximal, complemented
7C2×#10622454C211yesmaximal, characteristic, complemented
8C2×#10622423C212yesmaximal, complemented
9C2×#10622786C212yesmaximal, complemented
10C2×C4×#4323C211yesmaximal, characteristic, complemented
11C2×#10622447C211yesmaximal, characteristic, complemented
12C2×C11×#461C211yesmaximal, characteristic, complemented
13C22×#4343C2212yes—
14C22×#4341C2212yes—
15C22×C11×SD16C2212yes—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×#66999C2212yes—
19C22×#4326C2212yes—
20C22×#4326C2212yes—
21C22×#4323C2211yescharacteristic
22C2×#66983—21no—
23C22×C4⋊Dic11—21no—
24C2×#66969—216no—
25C2×#66969C22116yescomplemented
26C22×#4314C2212yes—
27C22×C8×D11C2212yes—
28#10623257—24no—
29#10623257C2218yescomplemented
30#10623086—24no—
31#10623086C2218yescomplemented
32C2×#66950C2212yes—
33C2×#66948—21no—
34C2×#66947—22no—
35C2×C4⋊C4×D11—21no—
36C2×#66939—22no—
37C2×C4×D44C2211yescharacteristic
38C2×C4×D44C2211yescharacteristic
39C2×#66922C2211yescharacteristic
40C11×#461C2218yescomplemented
41C2×C11×C4⋊C8C2211yescharacteristic
42C2×C11×#103C2212yes—
43C2×#66896C2211yescharacteristic
44#10622786C22116yescomplemented
45C2×(C2×D11)⋊C8C2212yes—
46C2×#66880C2212yes—
47#10622705C2218yescomplemented
48C4×#4323C2218yescomplemented
49C2×#66873C2211yescharacteristic
50C2×#66871C2211yescharacteristic
51C2×C4×C11⋊C8C2211yescharacteristic
52#10622454C2218yescomplemented
53#10622447C2218yescomplemented
54#10622426C22116yescomplemented
55#10622423C22116yescomplemented
56C22×Q8×C11C2312yes—
57C22×D4×C11C2311yescharacteristic
58C23×C4×C11—21no—
59C22×C22⋊D11—22no—
60C23×Dic11—22no—
61C2×#4343—24no—
62C2×#4343—28no—
63C2×#4343—44no—
64C2×#4343C2318yes—
65C2×#4341—28no—
66C2×#4341—24no—
67C2×#4341—44no—
68C2×#4341C2318yes—
69C22×D44—22no—
70C22×D44D411yescharacteristic
71C22×D44C2311yescharacteristic
72C22×C4×D11—21no—
73C22×C4×D11—22no—
74C22×C4×D11C2312yes—
75C22×Dic22C2312yes—
76C2×C11×SD16—28no—
77C2×C11×SD16C2318yes—
78C22×C8×C11C2312yes—
79C11×C4⋊Q8—22no—
80C11×C4⋊Q8C2314yes—
81C4×D4×C11—22no—
82C4×D4×C11C2314yes—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C22⋊C4—21no—
87C2×C42×C11C2311yescharacteristic
88#66999—24no—
89#66999C2318yes—
90C2×#4326—28no—
91C2×#4326—44no—
92C2×#4326C2318yes—
93C2×#4326C2318yes—
94C2×#4323D418yescomplemented
95C2×#4323C2314yes—
96#66983—28no—
97C2×(C2×D11)⋊C4—22no—
98C2×(C2×D11)⋊C4—22no—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4D412yes—
101C2×C4⋊Dic11—21no—
102C2×C4⋊Dic11—21no—
103C2×C4⋊Dic11—22no—
104C2×C4⋊Dic11—28no—
105C2×C4⋊Dic11D411yescharacteristic
106C2×C4⋊Dic11C2311yescharacteristic
107C2×Dic11⋊C4—22no—
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110#66969—264no—
111C2×#4314—28no—
112C2×#4314C2318yes—
113C2×C8×D11—28no—
114C2×C8×D11C2318yes—
115#66950—24no—
116#66950C2318yes—
117#66948—28no—
118#66947—216no—
119C4⋊C4×D11—28no—
120#66939—216no—
121C4×D44—22no—
122C4×D44D414yes—
123C4×D44C2314yes—
124C4×D44C2314yes—
125#66922—22no—
126#66922C2314yes—
127C11×C4⋊C8C2314yes—
128C11×#103C2318yes—
129#66896C2314yes—
130(C2×D11)⋊C8C2318yes—
131#66880C2318yes—
132#66873C2314yes—
133#66871C2314yes—
134C4×C11⋊C8C2314yes—
135C2×#3283—111nomaximal, Sylow
136C24×C11—21no—
137C23×D11—21no—
138C23×D11C2×D412yes—
139C2×Q8×C11—22no—
140C2×Q8×C11—24no—
141C2×Q8×C11—24no—
142C2×Q8×C11C2414yes—
143C2×D4×C11—21no—
144C2×D4×C11—22no—
145C2×D4×C11C2×D414yes—
146C2×D4×C11C2412yes—
147C22×C4×C11—22no—
148C22×C4×C11—21no—
149C22×C4×C11—24no—
150C22×C4×C11—44no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2411yescharacteristic
154C2×C22⋊D11—28no—
155C2×C22⋊D11—48no—
156C22×Dic11—28no—
157C22×Dic11—21no—
158C22×Dic11—22no—
159C22×Dic11—48no—
160C22×Dic11C2×D412yes—
161#4343—216no—
162#4343—48no—
163#4343—416no—
164#4341—216no—
165#4341—48no—
166#4341—416no—
167C2×D44—28no—
168C2×D44—24no—
169C2×D44—21no—
170C2×D44—22no—
171C2×D44—48no—
172C2×D44C2×D414yes—
173C2×D44C2×D414yes—
174C2×D44C2412yes—
175C2×C4×D11—28no—
176C2×C4×D11—24no—
177C2×C4×D11—24no—
178C2×C4×D11—24no—
179C2×C4×D11—48no—
180C2×C4×D11—44no—
181C2×C4×D11C2×D414yes—
182C2×C4×D11C2414yes—
183C2×Dic22—24no—
184C2×Dic22—22no—
185C2×Dic22—24no—
186C2×Dic22C2414yes—
187C11×SD16—216no—
188C2×C8×C11—24no—
189C2×C8×C11C2414yes—
190C11×C4⋊C4—24no—
191C11×C4⋊C4—24no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4C2412yes—
194C11×C22⋊C4—24no—
195C42×C11C2×D412yes—
196C42×C11C2412yes—
197#4326—216no—
198#4326—48no—
199#4323C2×D4116yescomplemented
200(C2×D11)⋊C4—28no—
201(C2×D11)⋊C4—28no—
202(C2×D11)⋊C4—24no—
203(C2×D11)⋊C4C2×D418yes—
204C4⋊Dic11—28no—
205C4⋊Dic11—24no—
206C4⋊Dic11—24no—
207C4⋊Dic11—21no—
208C4⋊Dic11C2×D414yes—
209C4⋊Dic11C2412yes—
210Dic11⋊C4—28no—
211C2×C11⋊C8—22no—
212C2×C11⋊C8C2×D414yes—
213C2×C11⋊C8C2412yes—
214C2×C11⋊C8C2412yes—
215#4314—216no—
216C8×D11—216no—
217C22×#135—112no—
218C2×#547—111no—
219C2×#547—111no—
220#3283—1116no—
221C2×#494—111no—
222C2×#467—112no—
223C2×#461—111no—
224C2×#461D1111yescharacteristic, complemented
225C2×#452—112no—
226C2×#452—112no—
227C2×C4×D8—111no—
228C2×C8×D4—111no—
229C23×C11—24no—
230C23×C11—22no—
231C23×C11—42no—
232C23×C11—42no—
233C23×C11C22×D411yescharacteristic
234C22×D11—24no—
235C22×D11—24no—
236C22×D11—24no—
237C22×D11—24no—
238C22×D11—22no—
239C22×D11—42no—
240C22×D11—42no—
241C22×D11C22×D414yes—
242Q8×C11—24no—
243Q8×C11—24no—
244Q8×C11—44no—
245D4×C11—24no—
246D4×C11—22no—
247D4×C11C22×D414yes—
248C2×C4×C11—22no—
249C2×C4×C11—24no—
250C2×C4×C11—22no—
251C2×C4×C11—44no—
252C2×C4×C11—42no—
253C2×C4×C11—48no—
254C2×C4×C11#13514yescomplemented
255C2×C4×C11C22×D412yes—
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×D412yes—
258C2×C4×C11C22×D412yes—
259C2×C4×C11H(5,𝔽2)12yes—
260C2×C4×C11C2511yescharacteristic
261C22⋊D11—416no—
262C2×Dic11—24no—
263C2×Dic11—22no—
264C2×Dic11—24no—
265C2×Dic11—416no—
266C2×Dic11—44no—
267C2×Dic11—42no—
268C2×Dic11C22×D414yes—
269D44—24no—
270D44—28no—
271D44—22no—
272D44—416no—
273D44C22×D414yes—
274C4×D11—28no—
275C4×D11—24no—
276C4×D11—24no—
277C4×D11—416no—
278C4×D11—48no—
279Dic22—24no—
280Dic22—24no—
281Dic22—44no—
282C8×C11—24no—
283C11⋊C8—22no—
284C11⋊C8C22×D414yes—
285C22×#41—112no—
286C22×#41—112no—
287C2×#135—1116no—
288C2×#135—2216no—
289C22×Q16—112no—
290C22×Q16—112no—
291C22×SD16—112no—
292C22×SD16C2×D1112yes—
293C22×D8—111no—
294C23×C8—112no—
295#547—118no—
296#547—118no—
297#547—224no—
298#547—224no—
299C2×C4⋊Q8—111no—
300C2×C4⋊Q8C2×D1111yescharacteristic
301C2×#123—222no—
302C2×#123—222no—
303C2×C22⋊Q8—112no—
304C2×C22⋊Q8—112no—
305C2×#121—221no—
306C2×#121—221no—
307C2×C4×D4—111no—
308C2×C4×D4—111no—
309C2×C4×D4C2×D1111yescharacteristic
310C22×C4⋊C4—221no—
311C22×C4⋊C4—221no—
312#494—118no—
313#467—1116no—
314#461—118no—
315#461C2×D1118yescomplemented
316#452—1116no—
317#452—1116no—
318C4×D8—118no—
319C8×D4—118no—
320C2×#107—111no—
321C2×C4⋊C8C2×D1111yescharacteristic
322C2×#103—112no—
323C2×#103C2×D1112yes—
324C2×#102—111no—
325C2×#102—111no—
326C2×C22⋊C8—112no—
327C2×C4×C8—111no—
328C22×C11—24no—
329C22×C11—48no—
330C22×C11—42no—
331C22×C11—42no—
332C22×C11D4212yes—
333C22×C11C2×#13512yes—
334C22×C11#57812yes—
335C22×C11C23×D411yescharacteristic
336C2×D11—24no—
337C2×D11—24no—
338C2×D11—24no—
339C2×D11—24no—
340C2×D11—48no—
341C2×D11—48no—
342C2×D11—42no—
343C2×D11—42no—
344C4×C11—22no—
345C4×C11—44no—
346C4×C11—42no—
347C4×C11D4212yes—
348C4×C11C2×#13514yescomplemented
349C4×C11C23×D411yescharacteristic
350C4×C11C2×H(5,𝔽2)11yescharacteristic
351Dic11—24no—
352Dic11—44no—
353Dic11—42no—
354C2×#41—118no—
355C2×#41—118no—
356C2×#41—224no—
357C2×#41—224no—
358C2×#41—228no—
359C2×#41—228no—
360C2×#41—444no—
361C2×#41—444no—
362C22×Q8—112no—
363C22×Q8C22×D1112yes—
364C22×D4—111no—
365C22×D4—111no—
366C22×D4—222no—
367C22×D4—222no—
368C22×D4C22×D1111yescharacteristic
369C23×C4—21no—
370C23×C4—112no—
371C23×C4—222no—
372C23×C4—222no—
373C23×C4—221no—
374#135—2264no—
375C2×Q16—118no—
376C2×Q16—118no—
377C2×Q16—228no—
378C2×Q16—444no—
379C2×SD16—28no—
380C2×SD16—118no—
381C2×SD16—228no—
382C2×SD16C22×D1118yes—
383C2×D8—118no—
384C2×D8—114no—
385C22×C8—111no—
386C22×C8—111no—
387C22×C8—118no—
388C22×C8—228no—
389C22×C8C22×D1112yes—
390C4⋊Q8—22no—
391C4⋊Q8—114no—
392C4⋊Q8—222no—
393C4⋊Q8C22×D1114yes—
394#123—2216no—
395#123—2216no—
396C22⋊Q8—118no—
397C22⋊Q8—118no—
398C22⋊Q8—224no—
399C22⋊Q8—224no—
400#121—228no—
401#121—228no—
402C4×D4—22no—
403C4×D4—114no—
404C4×D4—114no—
405C4×D4—114no—
406C4×D4—222no—
407C4×D4C22×D1114yes—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—228no—
413C2×C4⋊C4—228no—
414C2×C4⋊C4—222no—
415C2×C4⋊C4—222no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4C22×D1111yescharacteristic
419C2×C22⋊C4—21no—
420C2×C22⋊C4—112no—
421C2×C22⋊C4—222no—
422C2×C22⋊C4—222no—
423C2×C22⋊C4—221no—
424C2×C42C22×D1111yescharacteristic
425#107—114no—
426C4⋊C8C22×D1114yes—
427#103—118no—
428#103C22×D1118yes—
429#102—114no—
430#102—114no—
431C22⋊C8—118no—
432C4×C8—114no—
433C2×C11—44no—
434C2×C11#328314yescomplemented
435C2×C11C2×D4211yescharacteristic
436C2×C11C22×#13511yescharacteristic
437C2×C11C2×#57811yescharacteristic
438D11—44no—
439D11—44no—
440C24—21no—
441C24—112no—
442C24—221no—
443#41—2216no—
444#41—2216no—
445#41—448no—
446#41—4416no—
447#41—448no—
448#41—4416no—
449C2×Q8—22no—
450C2×Q8—24no—
451C2×Q8—24no—
452C2×Q8—114no—
453C2×Q8—222no—
454C2×Q8—224no—
455C2×Q8—224no—
456C2×Q8C23×D1114yes—
457C2×D4—21no—
458C2×D4—22no—
459C2×D4—114no—
460C2×D4—114no—
461C2×D4—112no—
462C2×D4—228no—
463C2×D4—228no—
464C2×D4—224no—
465C2×D4—221no—
466C2×D4—222no—
467C2×D4—448no—
468C2×D4—448no—
469C2×D4D4×D1114yes—
470C2×D4C23×D1112yes—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—24no—
474C22×C4—44no—
475C22×C4—112no—
476C22×C4—114no—
477C22×C4—114no—
478C22×C4—228no—
479C22×C4—228no—
480C22×C4—224no—
481C22×C4—224no—
482C22×C4—221no—
483C22×C4—222no—
484C22×C4—224no—
485C22×C4—448no—
486C22×C4—448no—
487C22×C4—444no—
488C22×C4D4×D1111yescharacteristic
489C22×C4D4×D1111yescharacteristic
490C22×C4C23×D1111yescharacteristic
491Q16—2216no—
492Q16—448no—
493SD16—216no—
494SD16—2216no—
495D8—1116no—
496C2×C8—24no—
497C2×C8—114no—
498C2×C8—112no—
499C2×C8—112no—
500C2×C8—2216no—
501C2×C8—222no—
502C2×C8C23×D1114yes—
503C4⋊C4—24no—
504C4⋊C4—24no—
505C4⋊C4—21no—
506C4⋊C4—114no—
507C4⋊C4—112no—
508C4⋊C4—228no—
509C4⋊C4—228no—
510C4⋊C4—221no—
511C4⋊C4—224no—
512C4⋊C4—224no—
513C4⋊C4C23×D1112yes—
514C22⋊C4—24no—
515C22⋊C4—118no—
516C22⋊C4—228no—
517C22⋊C4—228no—
518C22⋊C4—224no—
519C42D4×D1112yes—
520C42C23×D1112yes—
521C11C2×#328311yescharacteristic, complemented, Sylow
522C23—24no—
523C23—22no—
524C23—42no—
525C23—42no—
526C23—114no—
527C23—224no—
528C23—224no—
529C23—224no—
530C23—224no—
531C23—222no—
532C23—442no—
533C23—442no—
534C23C2×D4×D1111yescharacteristic
535Q8—24no—
536Q8—24no—
537Q8—44no—
538Q8—224no—
539Q8—224no—
540Q8—444no—
541D4—24no—
542D4—22no—
543D4—114no—
544D4—228no—
545D4—224no—
546D4—222no—
547D4—4416no—
548D4—4416no—
549D4C2×D4×D1114yes—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—42no—
554C2×C4—44no—
555C2×C4—48no—
556C2×C4—114no—
557C2×C4—224no—
558C2×C4—228no—
559C2×C4—224no—
560C2×C4—224no—
561C2×C4—222no—
562C2×C4—224no—
563C2×C4—4416no—
564C2×C4—4416no—
565C2×C4—442no—
566C2×C4—444no—
567C2×C4—448no—
568C2×C4#6696914yescomplemented
569C2×C4C2×D4×D1112yes—
570C2×C4C2×D4×D1112yes—
571C2×C4C2×D4×D1111yescharacteristic
572C2×C4C2×D4×D1112yes—
573C2×C4#6704212yes—
574C2×C4C24×D1111yescharacteristic
575C8—24no—
576C8—114no—
577C8—222no—
578C22—24no—
579C22—48no—
580C22—42no—
581C22—42no—
582C22—224no—
583C22—224no—
584C22—224no—
585C22—224no—
586C22—448no—
587C22—448no—
588C22—442no—
589C22—442no—
590C22#1062314012yes—
591C22C2×#6696912yes—
592C22#1062331012yes—
593C22C22×D4×D1111yescharacteristic
594C4—22no—
595C4—44no—
596C4—42no—
597C4—224no—
598C4—444no—
599C4—442no—
600C4#1062314012yes—
601C4C2×#6696914yescomplemented
602C4C22×D4×D1111yescharacteristic
603C4C2×#6704211yescharacteristic
604C2—44no—
605C2—444no—
606C2—444no—
607C2#1308033314yesdirect product factor
608C2C2×#1062314011yescharacteristic
609C2C22×#6696911yescharacteristic
610C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#461C2
socleC23×C11C22×D4
hypercenterC2×#461D11
hypocenterC11C2×#3283
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C22×#66969C2semidirect
2. C2×#10623086C2semidirect
3. C2×#10623257C2semidirect
4. #13080333C2direct (N × H)
5. C2×#10622705C2semidirect
6. C2×#10622426C2semidirect
7. C2×#10622454C2semidirect
8. C2×#10622423C2semidirect
9. C2×#10622786C2semidirect
10. C2×C4×#4323C2semidirect
11. C2×#10622447C2semidirect
12. C2×C11×#461C2semidirect
25. C2×#66969C22semidirect
29. #10623257C22semidirect
31. #10623086C22semidirect
40. C11×#461C22semidirect
44. #10622786C22semidirect
47. #10622705C22semidirect
48. C4×#4323C22semidirect
52. #10622454C22semidirect
53. #10622447C22semidirect
54. #10622426C22semidirect
55. #10622423C22semidirect
94. C2×#4323D4semidirect
199. #4323C2×D4semidirect
224. C2×#461D11semidirect
254. C2×C4×C11#135semidirect
315. #461C2×D11semidirect
348. C4×C11C2×#135semidirect
434. C2×C11#3283semidirect
521. C11C2×#3283semidirect
568. C2×C4#66969semidirect
601. C4C2×#66969semidirect
607. C2#13080333direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669692
C2×#106230862
C2×#106232572
#130803332
C2×#106227052
C2×#106224262
C2×#106224542
C2×#106224232
C2×#106227862
C2×C4×#43232
C2×#106224472
C2×C11×#4612
C2×#328311