Finite Group Databasebeta

← C2×#13067696 #14729645

Subgroups — C2×#13067696 #14729645

Order 2816.

1126 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×Dic22C211yesmaximal, characteristic, complemented
2C2×#10622306C211yesmaximal, characteristic
3C2×#10622461C211yesmaximal, characteristic
4C2×#10622640C211yesmaximal, characteristic
5#13067696C218yesmaximal, direct product factor
6C2×#10622119C211yesmaximal, characteristic, complemented
7C2×#10622094C211yesmaximal, characteristic, complemented
8C2×C11×Q8⋊C8C211yesmaximal, characteristic, complemented
9C2×C4×Q8×C11C2211yescharacteristic
10C2×Q8×Dic11—21no—
11C22×#4325—21no—
12C22×#4314—21no—
13C22×#4314—22no—
14Q8×Dic22—22no—
15Q8×Dic22—22no—
16Q8×Dic22—22no—
17Q8×Dic22C2214yescomplemented
18C2×#66941—22no—
19C2×#66941—21no—
20C2×#66927C2211yescharacteristic
21C2×#66922—21no—
22C2×#66922C2211yescharacteristic
23C2×C4×Dic22—21no—
24C2×C4×Dic22C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C4×C8×C11C2211yescharacteristic
27C2×#66885—21no—
28#10622640—22no—
29#10622640C2214yes—
30C2×#66873—21no—
31C2×C4⋊(C11⋊C8)C2211yescharacteristic
32#10622461—22no—
33#10622461C2214yes—
34#10622306—22no—
35#10622306C2214yes—
36C11×Q8⋊C8C2214yescomplemented
37#10622119C2214yescomplemented
38#10622094C2214yescomplemented
39C22×Q8×C11D411yescharacteristic
40C22×D44—21no—
41C22×D44—21no—
42C22×D44—21no—
43C22×Dic22—22no—
44C22×Dic22D411yescharacteristic
45C22×Dic22D412yes—
46C22×C8×C11—21no—
47C22×C8×C11—21no—
48C4×Q8×C11—21no—
49C4×Q8×C11—21no—
50C4×Q8×C11D412yes—
51C4×Q8×C11C2312yes—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4D411yescharacteristic
54C2×C42×C11—21no—
55C2×C42×C11C2311yescharacteristic
56Q8×Dic11—24no—
57Q8×Dic11—24no—
58C2×#4325—24no—
59C2×#4325—44no—
60C2×C4⋊Dic11—22no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11D411yescharacteristic
64C2×Dic11⋊C4—22no—
65C2×Dic11⋊C4—21no—
66C2×C4×Dic11—22no—
67C2×C4×Dic11—21no—
68C22×C11⋊C8—21no—
69C2×#4314—28no—
70C2×#4314—24no—
71C2×#4314—48no—
72C2×#4314—44no—
73#66941—28no—
74#66941—24no—
75#66941—28no—
76#66941—24no—
77#66927—21no—
78#66927—21no—
79#66927—21no—
80#66927C2312yes—
81#66922—24no—
82#66922—21no—
83#66922—21no—
84#66922—24no—
85#66922D412yes—
86#66922C2312yes—
87C4×Dic22—24no—
88C4×Dic22—24no—
89C4×Dic22—21no—
90C4×Dic22—21no—
91C4×Dic22D412yes—
92C4×Dic22C2312yes—
93C11×C4⋊C8—21no—
94C11×C4⋊C8C2312yes—
95C4×C8×C11—21no—
96C4×C8×C11C2312yes—
97#66885—24no—
98#66873—24no—
99C4⋊(C11⋊C8)—21no—
100C4⋊(C11⋊C8)C2312yes—
101C2×#1623—111nomaximal, Sylow
102C23×D11—41no—
103C2×Q8×C11—21no—
104C2×Q8×C11—22no—
105C2×Q8×C11SD1614yescomplemented
106C2×Q8×C11C2×D412yes—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×Dic11—21no—
113C22×Dic11—22no—
114C22×Dic11—21no—
115C2×D44—22no—
116C2×D44—22no—
117C2×D44—22no—
118C2×D44—44no—
119C2×D44—41no—
120C2×D44—41no—
121C2×D44—41no—
122C2×D44—42no—
123C2×D44—42no—
124C2×D44—42no—
125C2×D44—42no—
126C2×Dic22—28no—
127C2×Dic22—21no—
128C2×Dic22—22no—
129C2×Dic22—22no—
130C2×Dic22—44no—
131C2×Dic22—84no—
132C2×Dic22SD1614yescomplemented
133C2×Dic22C2×D412yes—
134C2×Dic22C2×D414yes—
135C2×C8×C11—24no—
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C2×C8×C11—42no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4C2×D412yes—
143C42×C11—22no—
144C42×C11—22no—
145C42×C11C2×D411yescharacteristic
146C42×C11C2×D411yescharacteristic
147C42×C11C2×D411yescharacteristic
148C42×C11C2411yescharacteristic
149#4325—48no—
150C4⋊Dic11—28no—
151C4⋊Dic11—21no—
152C4⋊Dic11—22no—
153C4⋊Dic11—22no—
154C4⋊Dic11—22no—
155C4⋊Dic11—22no—
156C4⋊Dic11C2×D412yes—
157Dic11⋊C4—28no—
158Dic11⋊C4—22no—
159Dic11⋊C4—22no—
160C4×Dic11—28no—
161C4×Dic11—22no—
162C4×Dic11—22no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—42no—
165#4314—416no—
166#4314—48no—
167C2×Q82—111no—
168C2×#492—111no—
169C2×#460—111no—
170C2×#460—111no—
171#1623—118no—
172C2×#333—111no—
173C2×Q8⋊C8—111no—
174C2×Q8⋊C8D1111yescharacteristic, complemented
175C23×C11#12011yescharacteristic
176C22×D11—42no—
177C22×D11—82no—
178C22×D11—82no—
179C22×D11—82no—
180Q8×C11—22no—
181Q8×C11—24no—
182Q8×C11C2×SD1614yescomplemented
183C2×C4×C11—22no—
184C2×C4×C11—24no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—42no—
188C2×C4×C11#12011yescharacteristic
189C2×C4×C11#12011yescharacteristic
190C2×C4×C11#12011yescharacteristic
191C2×C4×C11C2×SD1612yes—
192C2×C4×C11C2×SD1612yes—
193C2×C4×C11#13712yes—
194C2×C4×C11#13712yes—
195C2×C4×C11C22×D411yescharacteristic
196C2×C4×C11C22×D411yescharacteristic
197C2×C4×C11C22×D411yescharacteristic
198C2×Dic11—22no—
199C2×Dic11—24no—
200C2×Dic11—24no—
201C2×Dic11—22no—
202C2×Dic11—44no—
203C2×Dic11—42no—
204D44—44no—
205D44—42no—
206D44—42no—
207D44—42no—
208D44—42no—
209D44—82no—
210D44—82no—
211D44—82no—
212Dic22—22no—
213Dic22—24no—
214Dic22—44no—
215Dic22—82no—
216Dic22—88no—
217Dic22C2×SD1614yescomplemented
218C8×C11—24no—
219C8×C11—42no—
220C11⋊C8—42no—
221C22×SD16—222no—
222C22×SD16—221no—
223C22×SD16—221no—
224Q82—114no—
225Q82—222no—
226Q82—222no—
227Q82—222no—
228C2×C4⋊Q8—111no—
229C2×C4⋊Q8—221no—
230C2×C4⋊Q8—222no—
231C2×C4⋊Q8—221no—
232C2×#127—111no—
233C2×C4×Q8—111no—
234C2×C4×Q8—221no—
235C2×C4×Q8—221no—
236C2×C4×Q8C2×D1111yescharacteristic
237#492—114no—
238#492—222no—
239#460—114no—
240#460—114no—
241#460—222no—
242#460—222no—
243C2×C4⋊C8—111no—
244C2×C4⋊C8C2×D1111yescharacteristic
245C2×#102—221no—
246C2×#102—221no—
247C2×C4×C8C2×D1111yescharacteristic
248#333—114no—
249Q8⋊C8—114no—
250Q8⋊C8C2×D1114yescomplemented
251C22×C11#44812yes—
252C22×C11#44812yes—
253C22×C11#45312yes—
254C22×C11C2×#12011yescharacteristic
255C2×D11—82no—
256C2×D11—82no—
257C2×D11—82no—
258C2×D11—164no—
259C4×C11—24no—
260C4×C11—21no—
261C4×C11—21no—
262C4×C11—42no—
263C4×C11#44812yes—
264C4×C11#44812yes—
265C4×C11C22×SD1611yescharacteristic
266C4×C11C22×SD1611yescharacteristic
267C4×C11C2×#13711yescharacteristic
268C4×C11C2×#13711yescharacteristic
269Dic11—24no—
270Dic11—44no—
271Dic11—42no—
272C22×Q8—111no—
273C22×Q8—112no—
274C22×Q8—222no—
275C22×Q8D4411yescharacteristic
276C22×D4—221no—
277C22×D4—221no—
278C22×D4—221no—
279C2×SD16—224no—
280C2×SD16—228no—
281C2×SD16—224no—
282C2×SD16—448no—
283C2×SD16—444no—
284C2×SD16—444no—
285C22×C8—21no—
286C22×C8—21no—
287C22×C8—221no—
288C4⋊Q8—112no—
289C4⋊Q8—112no—
290C4⋊Q8—224no—
291C4⋊Q8—224no—
292C4⋊Q8—228no—
293C4⋊Q8—228no—
294C4⋊Q8—224no—
295C4⋊Q8—224no—
296C4⋊Q8—221no—
297C4⋊Q8—221no—
298#127—112no—
299#127—221no—
300#127—221no—
301#127—221no—
302C4×Q8—21no—
303C4×Q8—21no—
304C4×Q8—112no—
305C4×Q8—112no—
306C4×Q8—224no—
307C4×Q8—224no—
308C4×Q8—224no—
309C4×Q8—224no—
310C4×Q8—221no—
311C4×Q8—221no—
312C4×Q8D4412yes—
313C4×Q8C22×D1112yes—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—111no—
316C2×C4⋊C4—222no—
317C2×C4⋊C4—222no—
318C2×C4⋊C4—221no—
319C2×C4⋊C4—221no—
320C2×C4⋊C4—221no—
321C2×C4⋊C4D4411yescharacteristic
322C2×C42—21no—
323C2×C42—222no—
324C2×C42—221no—
325C2×C42C22×D1111yescharacteristic
326C4⋊C8—21no—
327C4⋊C8—112no—
328C4⋊C8—221no—
329C4⋊C8C22×D1112yes—
330#102—224no—
331#102—224no—
332C4×C8—21no—
333C4×C8C22×D1112yes—
334C2×C11#162314yescomplemented
335C2×C11C2×#44811yescharacteristic
336C2×C11C2×#44811yescharacteristic
337C2×C11C2×#45311yescharacteristic
338D11—162no—
339C24—441no—
340C2×Q8—21no—
341C2×Q8—22no—
342C2×Q8—114no—
343C2×Q8—112no—
344C2×Q8—114no—
345C2×Q8—228no—
346C2×Q8—221no—
347C2×Q8—222no—
348C2×Q8—222no—
349C2×Q8—444no—
350C2×Q8—884no—
351C2×Q8#431414yescomplemented
352C2×Q8C2×D4412yes—
353C2×D4—222no—
354C2×D4—222no—
355C2×D4—222no—
356C2×D4—444no—
357C2×D4—441no—
358C2×D4—441no—
359C2×D4—441no—
360C2×D4—442no—
361C2×D4—442no—
362C2×D4—442no—
363C2×D4—442no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—221no—
367C22×C4—221no—
368C22×C4—222no—
369C22×C4C2×D4411yescharacteristic
370C22×C4D4×D1111yescharacteristic
371C22×C4D4×D1111yescharacteristic
372SD16—4416no—
373SD16—448no—
374SD16—448no—
375C2×C8—24no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—42no—
379C2×C8—222no—
380C2×C8—442no—
381C4⋊C4—22no—
382C4⋊C4—21no—
383C4⋊C4—22no—
384C4⋊C4—112no—
385C4⋊C4—228no—
386C4⋊C4—228no—
387C4⋊C4—221no—
388C4⋊C4—222no—
389C4⋊C4—222no—
390C4⋊C4—222no—
391C4⋊C4—222no—
392C4⋊C4—222no—
393C4⋊C4—222no—
394C4⋊C4C2×D4412yes—
395C42—22no—
396C42—22no—
397C42—228no—
398C42—222no—
399C42—222no—
400C42C2×D4411yescharacteristic
401C42D4×D1111yescharacteristic
402C42D4×D1111yescharacteristic
403C42C23×D1111yescharacteristic
404C11C2×#162311yescharacteristic, complemented, Sylow
405C23—442no—
406C23—882no—
407C23—882no—
408C23—882no—
409C23#6693511yescharacteristic
410Q8—22no—
411Q8—24no—
412Q8—114no—
413Q8—222no—
414Q8—224no—
415Q8—444no—
416Q8—882no—
417Q8—888no—
418Q8C2×#431414yescomplemented
419D4—444no—
420D4—442no—
421D4—442no—
422D4—442no—
423D4—442no—
424D4—882no—
425D4—882no—
426D4—882no—
427C2×C4—22no—
428C2×C4—24no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—42no—
432C2×C4—222no—
433C2×C4—224no—
434C2×C4—222no—
435C2×C4—224no—
436C2×C4—444no—
437C2×C4—442no—
438C2×C4#6693511yescharacteristic
439C2×C4#6693511yescharacteristic
440C2×C4#6693511yescharacteristic
441C2×C4C2×#431412yes—
442C2×C4#6696212yes—
443C2×C4SD16×D1112yes—
444C2×C4#6697112yes—
445C2×C4C22×D4411yescharacteristic
446C2×C4C2×D4×D1111yescharacteristic
447C2×C4C2×D4×D1111yescharacteristic
448C8—24no—
449C8—42no—
450C8—442no—
451C22—882no—
452C22—882no—
453C22—882no—
454C22—1764no—
455C22#1062235112yes—
456C22#1062241912yes—
457C22#1062243512yes—
458C22C2×#6693511yescharacteristic
459C4—24no—
460C4—21no—
461C4—21no—
462C4—42no—
463C4—224no—
464C4—444no—
465C4—442no—
466C4#1062235112yes—
467C4#1062241912yes—
468C4C22×#431411yescharacteristic
469C4C2×#6696211yescharacteristic
470C4C2×SD16×D1111yescharacteristic
471C4C2×#6697111yescharacteristic
472C2—1762no—
473C2#1306769614yesdirect product factor
474C2C2×#1062241911yescharacteristic
475C2C2×#1062235111yescharacteristic
476C2C2×#1062243511yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×Q8⋊C8C2
socleC23×C11#120
prime radicalC2×#66927C22
hypercenterC2×Q8⋊C8D11
hypocenterC11C2×#1623
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic22C2semidirect
5. #13067696C2direct (N × H)
6. C2×#10622119C2semidirect
7. C2×#10622094C2semidirect
8. C2×C11×Q8⋊C8C2semidirect
17. Q8×Dic22C22semidirect
36. C11×Q8⋊C8C22semidirect
37. #10622119C22semidirect
38. #10622094C22semidirect
105. C2×Q8×C11SD16semidirect
132. C2×Dic22SD16semidirect
174. C2×Q8⋊C8D11semidirect
182. Q8×C11C2×SD16semidirect
217. Dic22C2×SD16semidirect
250. Q8⋊C8C2×D11semidirect
334. C2×C11#1623semidirect
351. C2×Q8#4314semidirect
404. C11C2×#1623semidirect
418. Q8C2×#4314semidirect
473. C2#13067696direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×Dic222
C2×#106223062
C2×#106224612
C2×#106226402
#130676962
C2×#106221192
C2×#106220942
C2×C11×Q8⋊C82
C2×#162311