Finite Group Databasebeta

← C2×#13079155 #15623406

Subgroups — C2×#13079155 #15623406

Order 2816.

1854 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623050C212yesmaximal
2#13079155C2116yesmaximal, direct product factor
3C2×#10622315C214yesmaximal, complemented
4C2×#10622295C212yesmaximal, complemented
5C2×#10622296C212yesmaximal, complemented
6C2×#10622734C212yesmaximal
7C2×#10622719C211yesmaximal, characteristic
8C22×#66882C211yesmaximal, characteristic
9C2×C11×#405C211yesmaximal, characteristic
10C22×C11×M16C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C2×#66979C2212yes—
14C22×C4⋊Dic11C2212yes—
15#10623050—28no—
16#10623050C22116yes—
17C2×#66943—22no—
18C2×#66941—22no—
19C2×#66931—24no—
20C2×#66923C2214yes—
21C2×#66922C2214yes—
22C11×#405C2218yes—
23C2×C11×#97C2212yes—
24C2×C4×C8×C11C2212yes—
25#10622734C22116yes—
26#10622719C2218yes—
27C2×#66882C2211yescharacteristic
28C2×#66882C2212yes—
29C2×#66882C2211yescharacteristic
30C2×#66882C2214yes—
31C2×#66882C2212yes—
32C2×#66882C2218yes—
33C2×#66881C2214yes—
34C2×#66881C2212yes—
35#10622315C22132yescomplemented
36#10622296C22116yescomplemented
37#10622295C22116yescomplemented
38C23×C4×C11C2311yescharacteristic
39C23×Dic11—22no—
40C22×Dic22—24no—
41C2×C11×M16Q818yescomplemented
42C2×C11×M16C2314yes—
43C22×C8×C11Q818yescomplemented
44C22×C8×C11C2311yescharacteristic
45C22×C8×C11C2312yes—
46C22×C8×C11C2311yescharacteristic
47C22×C8×C11C2314yes—
48C11×#117D414yes—
49C11×#117C2314yes—
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C11×C22⋊C4D412yes—
53C2×C42×C11C2312yes—
54C2×C22⋊Dic11—22no—
55#66979—24no—
56#66979C2318yes—
57C2×C4⋊Dic11—24no—
58C2×C4⋊Dic11—22no—
59C2×C4⋊Dic11—24no—
60C2×C4⋊Dic11C2318yes—
61C2×C4⋊Dic11C2312yes—
62C2×C4⋊Dic11C2314yes—
63C2×C4⋊Dic11C2312yes—
64C2×Dic11⋊C4—24no—
65C2×Dic11⋊C4—24no—
66C2×C4×Dic11—22no—
67#66943—216no—
68#66941—216no—
69#66931—232no—
70#66923—28no—
71#66923C23116yes—
72#66922—28no—
73#66922C23116yes—
74C11×#97C2318yes—
75C4×C8×C11C2318yes—
76#66882C23116yes—
77#66882C2314yes—
78#66882C2318yes—
79#66882C2314yes—
80#66882C2318yes—
81#66881C23116yes—
82#66881C2318yes—
83C2×#3164—111nomaximal, Sylow
84C24×C11C2×D411yescharacteristic
85C22×C4×C11C2×D412yes—
86C22×C4×C11C2×D412yes—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D412yes—
89C22×C4×C11C2×Q814yes—
90C22×C4×C11C2×Q814yes—
91C22×C4×C11C2411yescharacteristic
92C22×C4×C11C2412yes—
93C22×Dic11—22no—
94C22×Dic11—22no—
95C22×Dic11—24no—
96C22×Dic11—28no—
97C22×Dic11—84no—
98C2×Dic22—216no—
99C2×Dic22—88no—
100C11×M16C2×Q8116yescomplemented
101C2×C8×C11C2×Q814yes—
102C2×C8×C11C2×Q814yes—
103C2×C8×C11C2×Q818yes—
104C2×C8×C11C2×Q8116yescomplemented
105C2×C8×C11C2414yes—
106C2×C8×C11C2412yes—
107C2×C8×C11C2412yes—
108C11×C4⋊C4C2×D414yes—
109C11×C4⋊C4C2×D414yes—
110C11×C22⋊C4C2×D418yes—
111C42×C11C2×D414yes—
112C42×C11C2414yes—
113C22⋊Dic11—28no—
114C4⋊Dic11—22no—
115C4⋊Dic11—24no—
116C4⋊Dic11—216no—
117C4⋊Dic11—22no—
118C4⋊Dic11—28no—
119C4⋊Dic11C2414yes—
120C4⋊Dic11C2414yes—
121C4⋊Dic11C2418yes—
122Dic11⋊C4—216no—
123Dic11⋊C4—216no—
124C4×Dic11—28no—
125C2×#544—112no—
126#3164—1116no—
127C2×#501—114no—
128C2×#500—112no—
129C2×#499—112no—
130C2×#428—112no—
131C2×#427—111no—
132C22×#107—111no—
133C2×#405D1111yescharacteristic
134C23×C11—22no—
135C23×C11—22no—
136C23×C11C4⋊Q814yes—
137C23×C11C22×D412yes—
138C23×C11C22×D411yescharacteristic
139C2×C4×C11—24no—
140C2×C4×C11—24no—
141C2×C4×C11C4⋊Q818yes—
142C2×C4×C11C4⋊Q814yes—
143C2×C4×C11C22×D414yes—
144C2×C4×C11C22×D414yes—
145C2×C4×C11C22×D412yes—
146C2×C4×C11C22×D411yescharacteristic
147C2×C4×C11C22×Q812yes—
148C2×C4×C11C22×Q812yes—
149C2×C4×C11C22×Q814yes—
150C2×C4×C11C22×Q814yes—
151C2×C4×C11C2511yescharacteristic
152C2×Dic11—24no—
153C2×Dic11—24no—
154C2×Dic11—28no—
155C2×Dic11—44no—
156C2×Dic11—48no—
157C2×Dic11—44no—
158C2×Dic11—88no—
159Dic22—816no—
160C8×C11C22×Q814yes—
161C8×C11C22×Q814yes—
162C8×C11C22×Q818yes—
163C22×M16C2×D1111yescharacteristic
164C23×C8C2×D1111yescharacteristic
165#544—1116no—
166#544—228no—
167C2×C4⋊Q8—114no—
168C2×C4⋊Q8—222no—
169C2×#125—114no—
170C2×#125—222no—
171C2×C22⋊Q8—224no—
172C2×#117—112no—
173C2×#117C2×D1111yescharacteristic
174C22×C4⋊C4—112no—
175#501—1132no—
176#500—1116no—
177#499—1116no—
178#428—1116no—
179#427—118no—
180C2×#107—111no—
181C2×#107—112no—
182C2×#107—111no—
183C2×#107—114no—
184C2×#107—112no—
185C2×#107—118no—
186C2×#106—114no—
187C2×#106—112no—
188#405C2×D1118yes—
189C2×#97C2×D1112yes—
190C2×C4×C8C2×D1112yes—
191C22×C11—28no—
192C22×C11—22no—
193C22×C11—22no—
194C22×C11C2×C4⋊Q814yes—
195C22×C11C2×C4⋊Q812yes—
196C22×C11#57612yes—
197C22×C11#57812yes—
198C22×C11C23×D411yescharacteristic
199C4×C11—24no—
200C4×C11—24no—
201C4×C11C2×C4⋊Q814yes—
202C4×C11C2×C4⋊Q812yes—
203C4×C11C23×Q811yescharacteristic
204C4×C11C23×Q811yescharacteristic
205Dic11—44no—
206Dic11—48no—
207Dic11—44no—
208C22×Q8—224no—
209C23×C4—222no—
210C23×C4C22×D1111yescharacteristic
211C2×M16Dic2218yescomplemented
212C2×M16C22×D1114yes—
213C22×C8Dic2218yescomplemented
214C22×C8C22×D1111yescharacteristic
215C22×C8C22×D1111yescharacteristic
216C22×C8C22×D1112yes—
217C22×C8C22×D1114yes—
218C4⋊Q8—1116no—
219C4⋊Q8—2216no—
220C4⋊Q8—228no—
221#125—1116no—
222#125—2216no—
223#125—228no—
224C22⋊Q8—2232no—
225#117—118no—
226#117—224no—
227#117D4414yes—
228#117C22×D1114yes—
229C2×C4⋊C4—114no—
230C2×C4⋊C4—118no—
231C2×C4⋊C4—112no—
232C2×C4⋊C4—112no—
233C2×C4⋊C4—222no—
234C2×C4⋊C4—224no—
235C2×C4⋊C4—224no—
236C2×C4⋊C4—224no—
237C2×C4⋊C4—224no—
238C2×C4⋊C4D4411yescharacteristic
239C2×C4⋊C4D4411yescharacteristic
240C2×C22⋊C4—222no—
241C2×C22⋊C4D4412yes—
242C2×C42—222no—
243C2×C42C22×D1112yes—
244#107—118no—
245#107—118no—
246#107—114no—
247#107—114no—
248#107—1116no—
249#106—118no—
250#106—1116no—
251#97C22×D1118yes—
252C4×C8C22×D1118yes—
253C2×C11—24no—
254C2×C11#316414yescomplemented
255C2×C11C22×C4⋊Q811yescharacteristic
256C2×C11C2×#57611yescharacteristic
257C2×C11C2×#57811yescharacteristic
258C24C2×D4411yescharacteristic
259C2×Q8—2216no—
260C2×Q8—888no—
261C22×C4—222no—
262C22×C4—222no—
263C22×C4—224no—
264C22×C4—228no—
265C22×C4—884no—
266C22×C4C2×Dic2214yes—
267C22×C4C2×Dic2214yes—
268C22×C4C2×D4412yes—
269C22×C4C2×D4412yes—
270C22×C4C2×D4412yes—
271C22×C4C2×D4411yescharacteristic
272C22×C4C23×D1112yes—
273C22×C4C23×D1111yescharacteristic
274M16C2×Dic22116yescomplemented
275C2×C8C2×Dic2214yes—
276C2×C8C2×Dic2214yes—
277C2×C8C2×Dic2218yes—
278C2×C8C2×Dic22116yescomplemented
279C2×C8C23×D1112yes—
280C2×C8C23×D1114yes—
281C2×C8C23×D1112yes—
282C4⋊C4—114no—
283C4⋊C4—118no—
284C4⋊C4—114no—
285C4⋊C4—228no—
286C4⋊C4—224no—
287C4⋊C4—222no—
288C4⋊C4—222no—
289C4⋊C4—2216no—
290C4⋊C4—2216no—
291C4⋊C4—2216no—
292C4⋊C4C2×D4414yes—
293C4⋊C4C2×D4414yes—
294C22⋊C4—228no—
295C22⋊C4C2×D4418yes—
296C42—228no—
297C42C2×D4414yes—
298C42C23×D1114yes—
299C11C2×#316411yescharacteristic, complemented, Sylow
300C23—22no—
301C23—22no—
302C23#6692214yes—
303C23C22×D4412yes—
304C23C22×D4411yescharacteristic
305Q8—8816no—
306C2×C4—24no—
307C2×C4—24no—
308C2×C4—224no—
309C2×C4—224no—
310C2×C4—228no—
311C2×C4—448no—
312C2×C4—444no—
313C2×C4—444no—
314C2×C4—888no—
315C2×C4#6692218yes—
316C2×C4#6692214yes—
317C2×C4C22×Dic2212yes—
318C2×C4C22×Dic2212yes—
319C2×C4C22×Dic2214yes—
320C2×C4C22×Dic2214yes—
321C2×C4C22×D4414yes—
322C2×C4C22×D4414yes—
323C2×C4C22×D4412yes—
324C2×C4C22×D4411yescharacteristic
325C2×C4C24×D1111yescharacteristic
326C8C22×Dic2214yes—
327C8C22×Dic2214yes—
328C8C22×Dic2218yes—
329C22—28no—
330C22—22no—
331C22—22no—
332C22C2×#6692214yes—
333C22C2×#6692212yes—
334C22#1062328312yes—
335C22#1062328412yes—
336C22C23×D4411yescharacteristic
337C4—24no—
338C4—24no—
339C4—448no—
340C4—444no—
341C4—444no—
342C4C2×#6692212yes—
343C4C2×#6692214yes—
344C4C23×Dic2211yescharacteristic
345C4C23×Dic2211yescharacteristic
346C2—24no—
347C2#1307915514yesdirect product factor
348C2C22×#6692211yescharacteristic
349C2C2×#1062328311yescharacteristic
350C2C2×#1062328411yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#405C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenterC2×#405D11
hypocenterC11C2×#3164
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#405

Complements

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

NH ≅ G/Ntype
2. #13079155C2direct (N × H)
3. C2×#10622315C2semidirect
4. C2×#10622295C2semidirect
5. C2×#10622296C2semidirect
35. #10622315C22semidirect
36. #10622296C22semidirect
37. #10622295C22semidirect
41. C2×C11×M16Q8semidirect
43. C22×C8×C11Q8semidirect
100. C11×M16C2×Q8semidirect
104. C2×C8×C11C2×Q8semidirect
211. C2×M16Dic22semidirect
213. C22×C8Dic22semidirect
254. C2×C11#3164semidirect
274. M16C2×Dic22semidirect
278. C2×C8C2×Dic22semidirect
299. C11C2×#3164semidirect
347. C2#13079155direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230502
#130791552
C2×#106223152
C2×#106222952
C2×#106222962
C2×#106227342
C2×#106227192
C22×#668822
C2×C11×#4052
C2×#316411