Finite Group Databasebeta

← C2×#13080277 #15628936

Subgroups — C2×#13080277 #15628936

Order 2816.

2794 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66971C212yesmaximal, complemented
2C2×#10623108C211yesmaximal, characteristic
3C2×#10623258C211yesmaximal, characteristic, complemented
4#13080277C2116yesmaximal, direct product factor
5C2×#10622698C211yesmaximal, characteristic, complemented
6C2×#10622425C212yesmaximal, complemented
7C2×#10622461C211yesmaximal, characteristic, complemented
8C2×#10622800C212yesmaximal, complemented
9C2×#10622419C212yesmaximal, complemented
10C2×C4×#4326C211yesmaximal, characteristic, complemented
11C2×#10622451C211yesmaximal, characteristic, complemented
12C2×C11×#462C211yesmaximal, characteristic, complemented
13C22×#4343C2212yes—
14C22×Q8×D11C2212yes—
15C22×C11×Q16C2212yes—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×#66999C2212yes—
19C22×#4326C2211yescharacteristic
20C22×#4325C2212yes—
21C22×#4325C2212yes—
22C2×#66971—216no—
23C2×#66971C22116yescomplemented
24C22×#4314C2212yes—
25C22×#4313C2212yes—
26#10623258—24no—
27#10623258C2218yescomplemented
28#10623108—24no—
29#10623108C2218yes—
30C2×#66949—22no—
31C2×#66948—22no—
32C2×#66948C2212yes—
33C2×#66946—21no—
34C2×#66941—21no—
35C2×#66927—21no—
36C2×#66927C2211yescharacteristic
37C2×C4×D44—21no—
38C2×C4×D44C2211yescharacteristic
39C2×C4×Dic22C2211yescharacteristic
40C11×#462C2218yescomplemented
41C2×C11×C4⋊C8C2211yescharacteristic
42C2×C11×#103C2212yes—
43C2×#66899C2211yescharacteristic
44#10622800C22116yescomplemented
45C2×#66885C2212yes—
46C2×(C2×D11)⋊C8C2212yes—
47#10622698C2218yescomplemented
48C4×#4326C2218yescomplemented
49C2×#66874C2211yescharacteristic
50C2×#66871C2211yescharacteristic
51C2×C4×C11⋊C8C2211yescharacteristic
52#10622461C2218yescomplemented
53#10622451C2218yescomplemented
54#10622425C22116yescomplemented
55#10622419C22116yescomplemented
56C22×Q8×C11C2312yes—
57C22×Q8×C11C2311yescharacteristic
58C2×#4343—24no—
59C2×#4343—28no—
60C2×#4343—44no—
61C2×#4343C2318yes—
62C2×Q8×D11—24no—
63C2×Q8×D11—28no—
64C2×Q8×D11—44no—
65C2×Q8×D11C2318yes—
66C22×D44—22no—
67C22×D44—21no—
68C22×D44—22no—
69C22×D44—21no—
70C22×D44D411yescharacteristic
71C22×D44C2312yes—
72C22×C4×D11—22no—
73C22×C4×D11—22no—
74C22×C4×D11C2312yes—
75C22×Dic22—22no—
76C22×Dic22C2311yescharacteristic
77C2×C11×Q16—28no—
78C2×C11×Q16C2318yes—
79C22×C8×C11C2312yes—
80C11×C4⋊Q8—22no—
81C11×C4⋊Q8C2314yes—
82C4×Q8×C11—22no—
83C4×Q8×C11C2314yes—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C42×C11—21no—
89C2×C42×C11C2311yescharacteristic
90#66999—24no—
91#66999C2318yes—
92C2×#4326D418yescomplemented
93C2×#4326C2314yes—
94C2×#4325—28no—
95C2×#4325—44no—
96C2×#4325C2318yes—
97C2×#4325C2318yes—
98C2×(C2×D11)⋊C4—22no—
99C2×(C2×D11)⋊C4—22no—
100C2×(C2×D11)⋊C4D412yes—
101C2×C4⋊Dic11D411yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—22no—
105C2×C4×Dic11—21no—
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108#66971—264no—
109C2×#4314—28no—
110C2×#4314C2318yes—
111C2×#4313—28no—
112C2×#4313C2318yes—
113#66949—216no—
114#66948—24no—
115#66948—216no—
116#66948C2318yes—
117#66946—28no—
118#66941—28no—
119#66927—28no—
120#66927—22no—
121#66927C2314yes—
122C4×D44—28no—
123C4×D44D414yes—
124C4×D44C2314yes—
125C4×Dic22—22no—
126C4×Dic22C2314yes—
127C11×C4⋊C8C2314yes—
128C11×#103C2318yes—
129#66899C2314yes—
130#66885C2318yes—
131(C2×D11)⋊C8C2318yes—
132#66874C2314yes—
133#66871C2314yes—
134C4×C11⋊C8C2314yes—
135C2×#3278—111nomaximal, Sylow
136C23×D11—22no—
137C23×D11C2×D412yes—
138C2×Q8×C11—21no—
139C2×Q8×C11—22no—
140C2×Q8×C11—22no—
141C2×Q8×C11—24no—
142C2×Q8×C11—24no—
143C2×Q8×C11C2×D414yes—
144C2×Q8×C11C2414yes—
145C2×Q8×C11C2412yes—
146C22×C4×C11—21no—
147C22×C4×C11—22no—
148C22×C4×C11—21no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11C2×D412yes—
155#4343—216no—
156#4343—48no—
157#4343—416no—
158Q8×D11—216no—
159Q8×D11—48no—
160Q8×D11—416no—
161C2×D44—28no—
162C2×D44—28no—
163C2×D44—24no—
164C2×D44—24no—
165C2×D44—22no—
166C2×D44—24no—
167C2×D44—24no—
168C2×D44—24no—
169C2×D44—48no—
170C2×D44—44no—
171C2×D44—82no—
172C2×D44—84no—
173C2×D44C2×D414yes—
174C2×D44C2414yes—
175C2×C4×D11—28no—
176C2×C4×D11—28no—
177C2×C4×D11—24no—
178C2×C4×D11—24no—
179C2×C4×D11—48no—
180C2×C4×D11—48no—
181C2×C4×D11C2×D414yes—
182C2×C4×D11C2414yes—
183C2×Dic22—28no—
184C2×Dic22—21no—
185C2×Dic22—22no—
186C2×Dic22—48no—
187C2×Dic22C2×D414yes—
188C2×Dic22C2412yes—
189C11×Q16—216no—
190C2×C8×C11—24no—
191C2×C8×C11C2414yes—
192C11×C4⋊C4—24no—
193C11×C4⋊C4—24no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—24no—
196C11×C4⋊C4C2412yes—
197C42×C11—24no—
198C42×C11C2×D412yes—
199C42×C11C2412yes—
200#4326C2×D4116yescomplemented
201#4325—216no—
202#4325—48no—
203(C2×D11)⋊C4—28no—
204(C2×D11)⋊C4—28no—
205(C2×D11)⋊C4C2×D418yes—
206C4⋊Dic11—21no—
207C4⋊Dic11C2×D414yes—
208C4⋊Dic11C2412yes—
209Dic11⋊C4—28no—
210Dic11⋊C4—24no—
211C4×Dic11—24no—
212C2×C11⋊C8—22no—
213C2×C11⋊C8C2×D414yes—
214C2×C11⋊C8C2412yes—
215C2×C11⋊C8C2412yes—
216#4314—216no—
217#4313—216no—
218C22×#137—112no—
219C2×#550—111no—
220C2×D4×Q8—111no—
221#3278—1116no—
222C2×#492—111no—
223C2×#468—112no—
224C2×#462D1111yescharacteristic, complemented
225C2×#460—111no—
226C2×#452—112no—
227C2×#448—112no—
228C2×C4×Q16—111no—
229C2×#436—111no—
230C23×C11C22×D411yescharacteristic
231C22×D11—24no—
232C22×D11—24no—
233C22×D11—24no—
234C22×D11—24no—
235C22×D11—44no—
236C22×D11—44no—
237C22×D11—44no—
238C22×D11C22×D414yes—
239Q8×C11—24no—
240Q8×C11—22no—
241Q8×C11—24no—
242Q8×C11—24no—
243Q8×C11—44no—
244Q8×C11C22×D414yes—
245C2×C4×C11—24no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—24no—
249C2×C4×C11—22no—
250C2×C4×C11—44no—
251C2×C4×C11—42no—
252C2×C4×C11#13714yescomplemented
253C2×C4×C11C22×D412yes—
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C22×D412yes—
256C2×C4×C11C22×D412yes—
257C2×C4×C11H(5,𝔽2)12yes—
258C2×C4×C11C2511yescharacteristic
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—42no—
264C2×Dic11C22×D414yes—
265D44—28no—
266D44—24no—
267D44—24no—
268D44—416no—
269D44—44no—
270D44—48no—
271D44—84no—
272D44—88no—
273C4×D11—28no—
274C4×D11—24no—
275C4×D11—24no—
276C4×D11—416no—
277C4×D11—416no—
278Dic22—24no—
279Dic22—22no—
280Dic22—416no—
281Dic22C22×D414yes—
282C8×C11—24no—
283C11⋊C8—22no—
284C11⋊C8C22×D414yes—
285C22×#41—112no—
286C23×Q8—112no—
287C2×#137—1116no—
288C2×#137—2216no—
289C22×Q16—111no—
290C22×Q16C2×D1112yes—
291C22×SD16—112no—
292C22×SD16—112no—
293C22×SD16—112no—
294C22×M16—112no—
295#550—118no—
296#550—224no—
297D4×Q8—118no—
298D4×Q8—224no—
299C2×C4⋊Q8—221no—
300C2×C4⋊Q8C2×D1111yescharacteristic
301C2×#127—111no—
302C2×#127—221no—
303C2×C22⋊Q8—112no—
304C2×C22⋊Q8—222no—
305C2×#121—112no—
306C2×#121—222no—
307C2×C4×Q8—111no—
308C2×C4×Q8C2×D1111yescharacteristic
309C2×C4×D4—111no—
310C2×C4×D4—221no—
311C2×C4×D4—221no—
312#492—118no—
313#468—1116no—
314#462C2×D1118yescomplemented
315#460—118no—
316#452—1116no—
317#448—1116no—
318C4×Q16—118no—
319#436—118no—
320C2×#107—111no—
321C2×C4⋊C8C2×D1111yescharacteristic
322C2×#103—111no—
323C2×#103—111no—
324C2×#103C2×D1112yes—
325C2×#102—112no—
326C2×C22⋊C8—112no—
327C2×C4×C8—111no—
328C22×C11D4212yes—
329C22×C11C2×#13712yes—
330C22×C11#57712yes—
331C22×C11C23×D411yescharacteristic
332C2×D11—24no—
333C2×D11—24no—
334C2×D11—24no—
335C2×D11—48no—
336C2×D11—44no—
337C2×D11—44no—
338C2×D11—44no—
339C2×D11—88no—
340C4×C11—24no—
341C4×C11—22no—
342C4×C11—44no—
343C4×C11—42no—
344C4×C11D4212yes—
345C4×C11C2×#13714yescomplemented
346C4×C11C23×D411yescharacteristic
347C4×C11C2×H(5,𝔽2)11yescharacteristic
348Dic11—24no—
349Dic11—24no—
350Dic11—42no—
351C2×#41—118no—
352C2×#41—224no—
353C2×#41—228no—
354C2×#41—444no—
355C22×Q8—118no—
356C22×Q8—111no—
357C22×Q8—222no—
358C22×Q8—224no—
359C22×Q8—228no—
360C22×Q8—444no—
361C22×Q8C22×D1112yes—
362C22×Q8C22×D1111yescharacteristic
363C22×D4—111no—
364C22×D4—112no—
365C22×D4—222no—
366C22×D4—222no—
367C22×D4—221no—
368C22×D4—221no—
369C23×C4—112no—
370C23×C4—222no—
371C23×C4—222no—
372#137—2264no—
373C2×Q16—28no—
374C2×Q16—118no—
375C2×Q16—114no—
376C2×Q16C22×D1118yes—
377C2×SD16—118no—
378C2×SD16—118no—
379C2×SD16—118no—
380C2×SD16—228no—
381C2×SD16—228no—
382C2×SD16—444no—
383C2×M16—118no—
384C2×M16—228no—
385C22×C8—111no—
386C22×C8—111no—
387C22×C8C22×D1112yes—
388C4⋊Q8—22no—
389C4⋊Q8—228no—
390C4⋊Q8C22×D1114yes—
391#127—114no—
392#127—228no—
393#127—222no—
394C22⋊Q8—118no—
395C22⋊Q8—2216no—
396C22⋊Q8—224no—
397#121—118no—
398#121—2216no—
399#121—224no—
400C4×Q8—22no—
401C4×Q8—114no—
402C4×Q8—222no—
403C4×Q8C22×D1114yes—
404C4×D4—114no—
405C4×D4—114no—
406C4×D4—228no—
407C4×D4—228no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—222no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4C22×D1111yescharacteristic
416C2×C22⋊C4—112no—
417C2×C22⋊C4—222no—
418C2×C22⋊C4—222no—
419C2×C42—21no—
420C2×C42—221no—
421C2×C42C22×D1111yescharacteristic
422#107—114no—
423C4⋊C8C22×D1114yes—
424#103—114no—
425#103—114no—
426#103C22×D1118yes—
427#102—118no—
428C22⋊C8—118no—
429C4×C8—114no—
430C2×C11#327814yescomplemented
431C2×C11C2×D4211yescharacteristic
432C2×C11C22×#13711yescharacteristic
433C2×C11C2×#57711yescharacteristic
434D11—44no—
435D11—84no—
436C24—112no—
437C24—222no—
438#41—2216no—
439#41—448no—
440#41—4416no—
441C2×Q8—21no—
442C2×Q8—22no—
443C2×Q8—22no—
444C2×Q8—24no—
445C2×Q8—24no—
446C2×Q8—114no—
447C2×Q8—112no—
448C2×Q8—228no—
449C2×Q8—221no—
450C2×Q8—222no—
451C2×Q8—2216no—
452C2×Q8—448no—
453C2×Q8—448no—
454C2×Q8—4416no—
455C2×Q8D4×D1114yes—
456C2×Q8C23×D1114yes—
457C2×Q8C23×D1112yes—
458C2×D4—114no—
459C2×D4—114no—
460C2×D4—228no—
461C2×D4—228no—
462C2×D4—224no—
463C2×D4—224no—
464C2×D4—224no—
465C2×D4—222no—
466C2×D4—224no—
467C2×D4—224no—
468C2×D4—448no—
469C2×D4—444no—
470C2×D4—882no—
471C2×D4—884no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—112no—
476C22×C4—114no—
477C22×C4—114no—
478C22×C4—228no—
479C22×C4—228no—
480C22×C4—221no—
481C22×C4—224no—
482C22×C4—224no—
483C22×C4—221no—
484C22×C4—448no—
485C22×C4—448no—
486C22×C4D4×D1111yescharacteristic
487C22×C4D4×D1111yescharacteristic
488C22×C4C23×D1111yescharacteristic
489Q16—216no—
490Q16—1116no—
491SD16—2216no—
492SD16—2216no—
493SD16—448no—
494M16—2216no—
495C2×C8—24no—
496C2×C8—114no—
497C2×C8—112no—
498C2×C8—112no—
499C2×C8—222no—
500C2×C8C23×D1114yes—
501C4⋊C4—24no—
502C4⋊C4—24no—
503C4⋊C4—24no—
504C4⋊C4—21no—
505C4⋊C4—114no—
506C4⋊C4—112no—
507C4⋊C4—228no—
508C4⋊C4—221no—
509C4⋊C4—224no—
510C4⋊C4C23×D1112yes—
511C22⋊C4—118no—
512C22⋊C4—228no—
513C22⋊C4—228no—
514C42—24no—
515C42—224no—
516C42D4×D1112yes—
517C42C23×D1112yes—
518C11C2×#327811yescharacteristic, complemented, Sylow
519C23—114no—
520C23—224no—
521C23—224no—
522C23—224no—
523C23—224no—
524C23—444no—
525C23—444no—
526C23—444no—
527C23C2×D4×D1111yescharacteristic
528Q8—24no—
529Q8—22no—
530Q8—24no—
531Q8—24no—
532Q8—44no—
533Q8—114no—
534Q8—224no—
535Q8—222no—
536Q8—4416no—
537Q8C2×D4×D1114yes—
538D4—228no—
539D4—224no—
540D4—224no—
541D4—4416no—
542D4—448no—
543D4—444no—
544D4—884no—
545D4—888no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—42no—
552C2×C4—44no—
553C2×C4—114no—
554C2×C4—224no—
555C2×C4—224no—
556C2×C4—222no—
557C2×C4—228no—
558C2×C4—224no—
559C2×C4—224no—
560C2×C4—222no—
561C2×C4—4416no—
562C2×C4—4416no—
563C2×C4—442no—
564C2×C4#6697114yescomplemented
565C2×C4C2×D4×D1112yes—
566C2×C4C2×D4×D1112yes—
567C2×C4C2×D4×D1111yescharacteristic
568C2×C4C2×D4×D1112yes—
569C2×C4#6704212yes—
570C2×C4C24×D1111yescharacteristic
571C8—24no—
572C8—114no—
573C8—222no—
574C22—224no—
575C22—224no—
576C22—224no—
577C22—448no—
578C22—444no—
579C22—444no—
580C22—444no—
581C22—888no—
582C22#1062314012yes—
583C22C2×#6697112yes—
584C22#1062330912yes—
585C22C22×D4×D1111yescharacteristic
586C4—24no—
587C4—22no—
588C4—44no—
589C4—42no—
590C4—224no—
591C4—224no—
592C4—442no—
593C4#1062314012yes—
594C4C2×#6697114yescomplemented
595C4C22×D4×D1111yescharacteristic
596C4C2×#6704211yescharacteristic
597C2—444no—
598C2—884no—
599C2#1308027714yesdirect product factor
600C2C2×#1062314011yescharacteristic
601C2C22×#6697111yescharacteristic
602C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#462C2
socleC23×C11C22×D4
prime radicalC2×#10623108C2
hypercenterC2×#462D11
hypocenterC11C2×#3278
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
1. C22×#66971C2semidirect
3. C2×#10623258C2semidirect
4. #13080277C2direct (N × H)
5. C2×#10622698C2semidirect
6. C2×#10622425C2semidirect
7. C2×#10622461C2semidirect
8. C2×#10622800C2semidirect
9. C2×#10622419C2semidirect
10. C2×C4×#4326C2semidirect
11. C2×#10622451C2semidirect
12. C2×C11×#462C2semidirect
23. C2×#66971C22semidirect
27. #10623258C22semidirect
40. C11×#462C22semidirect
44. #10622800C22semidirect
47. #10622698C22semidirect
48. C4×#4326C22semidirect
52. #10622461C22semidirect
53. #10622451C22semidirect
54. #10622425C22semidirect
55. #10622419C22semidirect
92. C2×#4326D4semidirect
200. #4326C2×D4semidirect
224. C2×#462D11semidirect
252. C2×C4×C11#137semidirect
314. #462C2×D11semidirect
345. C4×C11C2×#137semidirect
430. C2×C11#3278semidirect
518. C11C2×#3278semidirect
564. C2×C4#66971semidirect
594. C4C2×#66971semidirect
599. C2#13080277direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669712
C2×#106231082
C2×#106232582
#130802772
C2×#106226982
C2×#106224252
C2×#106224612
C2×#106228002
C2×#106224192
C2×C4×#43262
C2×#106224512
C2×C11×#4622
C2×#327811