Finite Group Databasebeta

← C2×#13077417 #15617827

Subgroups — C2×#13077417 #15617827

Order 2816.

2854 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×Dic11C212yesmaximal, complemented
2#13077417C2116yesmaximal, direct product factor
3C2×#10622765C212yesmaximal, complemented
4C2×#10622797C212yesmaximal, complemented
5C2×#10622777C214yesmaximal, complemented
6C2×#10622719C211yesmaximal, characteristic, complemented
7C2×#10622846C212yesmaximal, complemented
8C22×#66879C211yesmaximal, characteristic, complemented
9C22×C11×#135C211yesmaximal, characteristic
10C22×C11×#41C2212yes—
11C2×C11×#135C4116yescomplemented
12C2×C11×#135C2218yes—
13C22×C11×Q16C2211yescharacteristic
14C22×C11×SD16C2212yes—
15C22×C11×D8C2211yescharacteristic
16C23×C8×C11C2211yescharacteristic
17#41×Dic11—28no—
18#41×Dic11C22116yescomplemented
19C2×Q8×Dic11C2214yes—
20C2×D4×Dic11—24no—
21C2×D4×Dic11C2214yes—
22C2×#66979—22no—
23C2×#66979C2212yes—
24C22×C4×Dic11—22no—
25C22×C4×Dic11C2211yescharacteristic
26C23×C11⋊C8C2211yescharacteristic
27#10622846C22116yescomplemented
28C2×#66899C2214yes—
29C2×#66896C2214yes—
30#10622797C22116yescomplemented
31#10622777C22132yescomplemented
32#10622765C22116yescomplemented
33#10622719C2218yescomplemented
34C2×#66882C2212yes—
35C2×#66881C2212yes—
36C2×#66879C2212yes—
37C2×#66879C2212yes—
38C2×#66879C2218yescomplemented
39C2×C11×#41—24no—
40C2×C11×#41—28no—
41C2×C11×#41C2×C4116yescomplemented
42C2×C11×#41C2318yes—
43C22×Q8×C11C2312yes—
44C22×D4×C11—22no—
45C22×D4×C11C2312yes—
46C23×C4×C11—22no—
47C23×C4×C11C2311yescharacteristic
48C23×Dic11—24no—
49C23×Dic11D412yes—
50C11×#135C2×C4164yescomplemented
51C2×C11×Q16C2×C418yescomplemented
52C2×C11×Q16C2314yes—
53C2×C11×SD16C2×C4116yescomplemented
54C2×C11×SD16C2318yes—
55C2×C11×D8C2×C418yescomplemented
56C2×C11×D8C2314yes—
57C22×C8×C11C2×C418yescomplemented
58C22×C8×C11C2311yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C22×C8×C11C2314yes—
61C2×C22⋊Dic11—22no—
62C2×C22⋊Dic11—24no—
63Q8×Dic11—28no—
64Q8×Dic11C23116yes—
65D4×Dic11—232no—
66D4×Dic11—28no—
67D4×Dic11C23116yes—
68#66979—24no—
69#66979—216no—
70#66979C2318yes—
71C2×C4⋊Dic11—24no—
72C2×C4⋊Dic11C2314yes—
73C2×C4×Dic11—22no—
74C2×C4×Dic11—24no—
75C2×C4×Dic11—216no—
76C2×C4×Dic11D412yes—
77C2×C4×Dic11D414yes—
78C2×C4×Dic11C2312yes—
79C2×C4×Dic11C2314yes—
80C22×C11⋊C8—24no—
81C22×C11⋊C8C2312yes—
82C22×C11⋊C8C2314yes—
83#66899C23116yes—
84#66896C23116yes—
85#66882C2318yes—
86#66881C2318yes—
87#66879C2318yes—
88#66879C2318yes—
89C2×#2943—111nomaximal, Sylow
90C24×C11—22no—
91C24×C11C2×D411yescharacteristic
92C11×#41—232no—
93C11×#41—216no—
94C11×#41C22×C4132yescomplemented
95C2×Q8×C11—22no—
96C2×Q8×C11—24no—
97C2×Q8×C11C22×C418yes—
98C2×Q8×C11C2414yes—
99C2×D4×C11—216no—
100C2×D4×C11—28no—
101C2×D4×C11—22no—
102C2×D4×C11—24no—
103C2×D4×C11C22×C418yes—
104C2×D4×C11C2414yes—
105C22×C4×C11—22no—
106C22×C4×C11—216no—
107C22×C4×C11—28no—
108C22×C4×C11C22×C414yes—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11#4114yes—
112C22×C4×C11C2411yescharacteristic
113C22×C4×C11C2412yes—
114C22×Dic11—216no—
115C22×Dic11—24no—
116C22×Dic11—44no—
117C22×Dic11—416no—
118C22×Dic11C2×D414yes—
119C22×Dic11C2×D418yes—
120C11×Q16C22×C4116yescomplemented
121C11×SD16C22×C4132yescomplemented
122C11×D8C22×C4116yescomplemented
123C2×C8×C11C22×C414yes—
124C2×C8×C11C22×C414yes—
125C2×C8×C11C22×C4116yescomplemented
126C2×C8×C11C2412yes—
127C2×C8×C11C2412yes—
128C22⋊Dic11—216no—
129C22⋊Dic11—28no—
130C4⋊Dic11—216no—
131C4⋊Dic11—24no—
132C4⋊Dic11C2418yes—
133C4×Dic11—216no—
134C4×Dic11—28no—
135C4×Dic11C2×D418yes—
136C4×Dic11C2×D414yes—
137C4×Dic11C2414yes—
138C2×C11⋊C8—24no—
139C2×C11⋊C8—28no—
140C2×C11⋊C8C2414yes—
141C22×#135D1111yescharacteristic
142C2×C4×#41—112no—
143#2943—1116no—
144C2×#442—112no—
145C2×#441—112no—
146C2×#440—114no—
147C2×#427—111no—
148C2×#416—112no—
149C22×#97—111no—
150C23×C11—24no—
151C23×C11—28no—
152C23×C11—24no—
153C23×C11—48no—
154C23×C11C4×D414yes—
155C23×C11C22×D412yes—
156C23×C11C22×D411yescharacteristic
157Q8×C11—28no—
158Q8×C11—24no—
159Q8×C11C23×C418yes—
160D4×C11—232no—
161D4×C11—28no—
162D4×C11—24no—
163D4×C11C23×C418yes—
164C2×C4×C11—28no—
165C2×C4×C11—24no—
166C2×C4×C11—232no—
167C2×C4×C11C4×D414yes—
168C2×C4×C11C4×D418yes—
169C2×C4×C11C23×C412yes—
170C2×C4×C11C23×C414yes—
171C2×C4×C11C22×D412yes—
172C2×C4×C11C22×D411yescharacteristic
173C2×C4×C11C2×#4112yes—
174C2×C4×C11C2×#4114yes—
175C2×C4×C11C2511yescharacteristic
176C2×Dic11—28no—
177C2×Dic11—28no—
178C2×Dic11—48no—
179C2×Dic11—432no—
180C2×Dic11—48no—
181C2×Dic11C22×D418yes—
182C8×C11C23×C414yes—
183C8×C11C23×C414yes—
184C11⋊C8—24no—
185C22×#41C2×D1112yes—
186C2×#135Dic11116yescomplemented
187C2×#135C2×D1118yes—
188C22×Q16C2×D1111yescharacteristic
189C22×SD16C2×D1112yes—
190C22×D8C2×D1111yescharacteristic
191C23×C8—111no—
192C23×C8C2×D1111yescharacteristic
193C4×#41—1116no—
194C4×#41—228no—
195C2×C4×Q8—114no—
196C2×C4×D4—114no—
197C2×C4×D4—224no—
198C2×#117—112no—
199C2×#117—222no—
200C22×C42—111no—
201C22×C42—222no—
202#442—1116no—
203#441—1116no—
204#440—1132no—
205#427—118no—
206C2×#107—112no—
207C2×#106—112no—
208#416—1116no—
209C2×#103—114no—
210C2×#102—114no—
211C2×#97—112no—
212C2×#97—112no—
213C2×#97—118no—
214C22×C11—28no—
215C22×C11—24no—
216C22×C11—28no—
217C22×C11—416no—
218C22×C11—48no—
219C22×C11C2×C4×D414yes—
220C22×C11C2×C4×D412yes—
221C22×C11#57514yes—
222C22×C11C23×D411yescharacteristic
223C4×C11—28no—
224C4×C11C2×C4×D414yes—
225C4×C11C2×C4×D412yes—
226C4×C11C24×C411yescharacteristic
227C4×C11C22×#4111yescharacteristic
228Dic11—28no—
229Dic11—48no—
230C2×#41—24no—
231C2×#41—28no—
232C2×#41C2×Dic11116yescomplemented
233C2×#41C22×D1118yes—
234C22×Q8C22×D1112yes—
235C22×D4—22no—
236C22×D4C22×D1112yes—
237C23×C4—22no—
238C23×C4—112no—
239C23×C4—224no—
240C23×C4C22×D1111yescharacteristic
241#135C2×Dic11164yescomplemented
242C2×Q16C2×Dic1118yescomplemented
243C2×Q16C22×D1114yes—
244C2×SD16C2×Dic11116yescomplemented
245C2×SD16C22×D1118yes—
246C2×D8C2×Dic1118yescomplemented
247C2×D8C22×D1114yes—
248C22×C8—112no—
249C22×C8—114no—
250C22×C8—224no—
251C22×C8C2×Dic1118yescomplemented
252C22×C8C22×D1111yescharacteristic
253C22×C8C22×D1111yescharacteristic
254C22×C8C22×D1114yes—
255C4×Q8—1116no—
256C4×Q8—228no—
257C4×D4—1116no—
258C4×D4—228no—
259C4×D4—2232no—
260#117—118no—
261#117—2216no—
262#117—224no—
263C2×C4⋊C4—114no—
264C2×C4⋊C4—224no—
265C2×C22⋊C4—224no—
266C2×C22⋊C4—222no—
267C2×C42—114no—
268C2×C42—112no—
269C2×C42—112no—
270C2×C42—114no—
271C2×C42—2216no—
272C2×C42—224no—
273C2×C42—222no—
274#107—118no—
275#106—118no—
276#103—1116no—
277#102—1116no—
278#97—118no—
279#97—118no—
280C2×C11—24no—
281C2×C11—48no—
282C2×C11#294314yescomplemented
283C2×C11C22×C4×D411yescharacteristic
284C2×C11C2×#57512yes—
285C24—22no—
286C24D4×D1111yescharacteristic
287#41—232no—
288#41—216no—
289#41C22×Dic11132yescomplemented
290C2×Q8—22no—
291C2×Q8—24no—
292C2×Q8C22×Dic1118yes—
293C2×Q8C23×D1114yes—
294C2×D4—216no—
295C2×D4—28no—
296C2×D4—22no—
297C2×D4—24no—
298C2×D4C22×Dic1118yes—
299C2×D4C23×D1114yes—
300C22×C4—22no—
301C22×C4—216no—
302C22×C4—28no—
303C22×C4—114no—
304C22×C4—118no—
305C22×C4—2216no—
306C22×C4—224no—
307C22×C4—444no—
308C22×C4—4416no—
309C22×C4D4×D1112yes—
310C22×C4D4×D1111yescharacteristic
311C22×C4#434114yes—
312C22×C4C22×Dic1114yes—
313C22×C4C23×D1111yescharacteristic
314C22×C4C23×D1112yes—
315Q16C22×Dic11116yescomplemented
316SD16C22×Dic11132yescomplemented
317D8C22×Dic11116yescomplemented
318C2×C8—114no—
319C2×C8—224no—
320C2×C8—228no—
321C2×C8C22×Dic1114yes—
322C2×C8C22×Dic1114yes—
323C2×C8C22×Dic11116yescomplemented
324C2×C8C23×D1112yes—
325C2×C8C23×D1112yes—
326C4⋊C4—118no—
327C4⋊C4—2216no—
328C4⋊C4—224no—
329C22⋊C4—2216no—
330C22⋊C4—228no—
331C42—118no—
332C42—114no—
333C42—114no—
334C42—2216no—
335C42—228no—
336C11C2×#294311yescharacteristic, complemented, Sylow
337C23—24no—
338C23—28no—
339C23—24no—
340C23—48no—
341C23D4×Dic1114yes—
342C23C2×D4×D1112yes—
343C23C2×D4×D1111yescharacteristic
344Q8—28no—
345Q8—24no—
346Q8C23×Dic1118yes—
347D4—232no—
348D4—28no—
349D4—24no—
350D4C23×Dic1118yes—
351C2×C4—28no—
352C2×C4—24no—
353C2×C4—232no—
354C2×C4—118no—
355C2×C4—228no—
356C2×C4—228no—
357C2×C4—448no—
358C2×C4—4432no—
359C2×C4—448no—
360C2×C4D4×Dic1114yes—
361C2×C4D4×Dic1118yes—
362C2×C4C2×D4×D1112yes—
363C2×C4C2×D4×D1111yescharacteristic
364C2×C4C2×#434112yes—
365C2×C4C2×#434114yes—
366C2×C4C23×Dic1112yes—
367C2×C4C23×Dic1114yes—
368C2×C4C24×D1111yescharacteristic
369C8—224no—
370C8C23×Dic1114yes—
371C8C23×Dic1114yes—
372C22—28no—
373C22—24no—
374C22—28no—
375C22—416no—
376C22—48no—
377C22#1062329914yes—
378C22C2×D4×Dic1114yes—
379C22C2×D4×Dic1112yes—
380C22C22×D4×D1111yescharacteristic
381C4—28no—
382C4—228no—
383C4—448no—
384C4C2×D4×Dic1114yes—
385C4C2×D4×Dic1112yes—
386C4C22×#434111yescharacteristic
387C4C24×Dic1111yescharacteristic
388C2—24no—
389C2—48no—
390C2#1307741714yesdirect product factor
391C2C22×D4×Dic1111yescharacteristic
392C2C2×#1062329912yes—
subgroupG/H
centerC22×C4D4×D11
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
Fitting, prime radicalC22×C11×#135C2
socleC23×C11C22×D4
cosocleC2×C4×C11C25
hypercenterC22×#135D11
hypocenterC11C2×#2943
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#135

Complements

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

NH ≅ G/Ntype
1. C2×#41×Dic11C2semidirect
2. #13077417C2direct (N × H)
3. C2×#10622765C2semidirect
4. C2×#10622797C2semidirect
5. C2×#10622777C2semidirect
6. C2×#10622719C2semidirect
7. C2×#10622846C2semidirect
8. C22×#66879C2semidirect
11. C2×C11×#135C4semidirect
18. #41×Dic11C22semidirect
27. #10622846C22semidirect
30. #10622797C22semidirect
31. #10622777C22semidirect
32. #10622765C22semidirect
33. #10622719C22semidirect
38. C2×#66879C22semidirect
41. C2×C11×#41C2×C4semidirect
50. C11×#135C2×C4semidirect
51. C2×C11×Q16C2×C4semidirect
53. C2×C11×SD16C2×C4semidirect
55. C2×C11×D8C2×C4semidirect
57. C22×C8×C11C2×C4semidirect
94. C11×#41C22×C4semidirect
120. C11×Q16C22×C4semidirect
121. C11×SD16C22×C4semidirect
122. C11×D8C22×C4semidirect
125. C2×C8×C11C22×C4semidirect
186. C2×#135Dic11semidirect
232. C2×#41C2×Dic11semidirect
241. #135C2×Dic11semidirect
242. C2×Q16C2×Dic11semidirect
244. C2×SD16C2×Dic11semidirect
246. C2×D8C2×Dic11semidirect
251. C22×C8C2×Dic11semidirect
282. C2×C11#2943semidirect
289. #41C22×Dic11semidirect
315. Q16C22×Dic11semidirect
316. SD16C22×Dic11semidirect
317. D8C22×Dic11semidirect
323. C2×C8C22×Dic11semidirect
336. C11C2×#2943semidirect
390. C2#13077417direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#41×Dic112
#130774172
C2×#106227652
C2×#106227972
C2×#106227772
C2×#106227192
C2×#106228462
C22×#668792
C22×C11×#1352
C2×#294311