Finite Group Databasebeta

← C2×#13079152 #15623403

Subgroups — C2×#13079152 #15623403

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×#10623031C212yesmaximal
2#13079152C2116yesmaximal, direct product factor
3C2×#10622489C214yesmaximal, complemented
4C2×#10622487C212yesmaximal, complemented
5C2×#10622491C212yesmaximal, complemented
6C2×#10622577C212yesmaximal
7C2×#10622719C211yesmaximal, characteristic
8C2×#10622714C211yesmaximal, characteristic
9C22×C11×#107C211yesmaximal, characteristic
10C23×C8×C11C2211yescharacteristic
11C22×C11×C4⋊C4C2212yes—
12C2×#66979C2212yes—
13C2×#66979C2211yescharacteristic
14C2×#66977—24no—
15C22×#4318C2211yescharacteristic
16#10623031—28no—
17#10623031C22116yes—
18C2×#66943—22no—
19C2×#66943C2214yes—
20C2×#66941—22no—
21C2×#66941C2214yes—
22C2×C11×#107C2212yes—
23C2×C11×#107C2212yes—
24C2×C11×#107C2218yes—
25#10622719C2218yes—
26C2×#66882C2211yescharacteristic
27C2×#66882C2211yescharacteristic
28C2×#66881C2212yes—
29#10622714C2218yes—
30C2×#66879C2212yes—
31C2×C8×Dic11C2212yes—
32#10622577C22116yes—
33C2×#66872C2214yes—
34C2×#66871C2214yes—
35#10622491C22116yescomplemented
36#10622489C22132yescomplemented
37#10622487C22116yescomplemented
38C23×C4×C11—22no—
39C23×C4×C11C2311yescharacteristic
40C22×Dic22—24no—
41C22×C8×C11Q818yescomplemented
42C22×C8×C11C2311yescharacteristic
43C22×C8×C11C2311yescharacteristic
44C22×C8×C11C2314yes—
45C2×C11×C4⋊C4—22no—
46C2×C11×C4⋊C4—24no—
47C2×C11×C4⋊C4C2314yes—
48C2×C11×C4⋊C4C2318yes—
49C2×C22⋊Dic11—22no—
50C2×C22⋊Dic11D412yes—
51#66979—24no—
52#66979D414yes—
53#66979C2318yes—
54#66979C2314yes—
55C2×C4⋊Dic11—24no—
56C2×C4⋊Dic11D411yescharacteristic
57C2×C4⋊Dic11D411yescharacteristic
58C2×C4⋊Dic11C2312yes—
59C2×C4⋊Dic11C2312yes—
60#66977—232no—
61C2×Dic11⋊C4—24no—
62C2×Dic11⋊C4—24no—
63C2×C4×Dic11—22no—
64C2×C4×Dic11C2312yes—
65C2×#4318Q818yescomplemented
66C2×#4318C2314yes—
67C22×C11⋊C8C2312yes—
68#66943—216no—
69#66943—28no—
70#66943C23116yes—
71#66941—216no—
72#66941—28no—
73#66941C23116yes—
74C11×#107C2318yes—
75C11×#107C2318yes—
76#66882C2314yes—
77#66882C2314yes—
78#66881C2318yes—
79#66879C2318yes—
80C8×Dic11C2318yes—
81#66872C23116yes—
82#66871C23116yes—
83C2×#3164—111nomaximal, Sylow
84C24×C11C2×D411yescharacteristic
85C22×C4×C11—24no—
86C22×C4×C11—28no—
87C22×C4×C11—84no—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D412yes—
90C22×C4×C11C2×Q814yes—
91C22×C4×C11C2×Q814yes—
92C22×C4×C11C2411yescharacteristic
93C22×C4×C11C2412yes—
94C22×Dic11—22no—
95C22×Dic11—22no—
96C22×Dic11C2×D412yes—
97C22×Dic11C2×D412yes—
98C2×Dic22—216no—
99C2×Dic22—88no—
100C2×C8×C11C2×Q814yes—
101C2×C8×C11C2×Q814yes—
102C2×C8×C11C2×Q8116yescomplemented
103C2×C8×C11C2412yes—
104C2×C8×C11C2412yes—
105C11×C4⋊C4—28no—
106C11×C4⋊C4—24no—
107C11×C4⋊C4C2418yes—
108C22⋊Dic11—28no—
109C22⋊Dic11C2×D418yes—
110C4⋊Dic11—216no—
111C4⋊Dic11—22no—
112C4⋊Dic11—22no—
113C4⋊Dic11C2×D414yes—
114C4⋊Dic11C2×D414yes—
115C4⋊Dic11C2414yes—
116C4⋊Dic11C2414yes—
117Dic11⋊C4—216no—
118Dic11⋊C4—216no—
119C4×Dic11—28no—
120C4×Dic11C2×D414yes—
121C4×Dic11C2414yes—
122#4318C2×Q8116yescomplemented
123C2×C11⋊C8C2×Q818yes—
124C2×C11⋊C8C2414yes—
125C2×#544—112no—
126#3164—1116no—
127C2×#501—114no—
128C2×#500—112no—
129C2×#499—112no—
130C2×#428—112no—
131C2×#427—111no—
132C22×#107D1111yescharacteristic
133C2×#405—111no—
134C23×C11—22no—
135C23×C11—22no—
136C23×C11C4⋊Q814yes—
137C23×C11C22×D412yes—
138C23×C11C22×D411yescharacteristic
139C2×C4×C11—28no—
140C2×C4×C11—48no—
141C2×C4×C11—88no—
142C2×C4×C11C4⋊Q818yes—
143C2×C4×C11C4⋊Q814yes—
144C2×C4×C11C22×D412yes—
145C2×C4×C11C22×D411yescharacteristic
146C2×C4×C11C22×Q812yes—
147C2×C4×C11C22×Q814yes—
148C2×C4×C11C22×Q812yes—
149C2×C4×C11C22×Q814yes—
150C2×C4×C11C2511yescharacteristic
151C2×Dic11—24no—
152C2×Dic11—24no—
153C2×Dic11—24no—
154C2×Dic11—24no—
155C2×Dic11—44no—
156C2×Dic11—44no—
157C2×Dic11C22×D414yes—
158C2×Dic11C22×D414yes—
159Dic22—816no—
160C8×C11C22×Q814yes—
161C8×C11C22×Q814yes—
162C11⋊C8C22×Q818yes—
163C22×M16—111no—
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—111no—
173C2×#117—112no—
174C22×C4⋊C4C2×D1112yes—
175#501—1132no—
176#500—1116no—
177#499—1116no—
178#428—1116no—
179#427—118no—
180C2×#107—111no—
181C2×#107—111no—
182C2×#107—114no—
183C2×#107C2×D1112yes—
184C2×#107C2×D1112yes—
185C2×#107C2×D1118yes—
186C2×#106—112no—
187C2×#106—114no—
188#405—118no—
189C2×#97—112no—
190C2×C4×C8—112no—
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—48no—
200C4×C11C2×C4⋊Q814yes—
201C4×C11C2×C4⋊Q812yes—
202C4×C11C23×Q811yescharacteristic
203C4×C11C23×Q811yescharacteristic
204Dic11—24no—
205Dic11—24no—
206Dic11—44no—
207Dic11—44no—
208C22×Q8—224no—
209C23×C4—22no—
210C23×C4C22×D1111yescharacteristic
211C2×M16—118no—
212C2×M16—114no—
213C22×C8—112no—
214C22×C8Dic2218yescomplemented
215C22×C8C22×D1111yescharacteristic
216C22×C8C22×D1111yescharacteristic
217C22×C8C22×D1114yes—
218C4⋊Q8—1116no—
219C4⋊Q8—228no—
220C4⋊Q8—2216no—
221#125—1116no—
222#125—228no—
223#125—2216no—
224C22⋊Q8—2232no—
225#117—114no—
226#117—114no—
227#117—118no—
228#117—224no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—24no—
231C2×C4⋊C4—111no—
232C2×C4⋊C4—111no—
233C2×C4⋊C4—112no—
234C2×C4⋊C4—112no—
235C2×C4⋊C4—224no—
236C2×C4⋊C4—224no—
237C2×C4⋊C4—224no—
238C2×C4⋊C4C22×D1114yes—
239C2×C4⋊C4C22×D1118yes—
240C2×C22⋊C4—112no—
241C2×C22⋊C4—222no—
242C2×C42—112no—
243C2×C42—222no—
244#107—114no—
245#107—114no—
246#107—1116no—
247#107C22×D1118yes—
248#107C22×D1118yes—
249#106—118no—
250#106—1116no—
251#97—118no—
252C4×C8—118no—
253C2×C11—24no—
254C2×C11#316414yescomplemented
255C2×C11C22×C4⋊Q811yescharacteristic
256C2×C11C2×#57611yescharacteristic
257C2×C11C2×#57811yescharacteristic
258C24D4×D1111yescharacteristic
259C2×Q8—2216no—
260C2×Q8—888no—
261C22×C4—24no—
262C22×C4—28no—
263C22×C4—84no—
264C22×C4—112no—
265C22×C4—112no—
266C22×C4—222no—
267C22×C4—222no—
268C22×C4C2×Dic2214yes—
269C22×C4D4×D1112yes—
270C22×C4D4×D1111yescharacteristic
271C22×C4Q8×D1114yes—
272C22×C4C23×D1112yes—
273C22×C4C23×D1111yescharacteristic
274M16—1116no—
275C2×C8—118no—
276C2×C8—114no—
277C2×C8C2×Dic2214yes—
278C2×C8C2×Dic2214yes—
279C2×C8C2×Dic22116yescomplemented
280C2×C8C23×D1112yes—
281C2×C8C23×D1112yes—
282C4⋊C4—24no—
283C4⋊C4—28no—
284C4⋊C4—114no—
285C4⋊C4—114no—
286C4⋊C4—114no—
287C4⋊C4—114no—
288C4⋊C4—2216no—
289C4⋊C4—2216no—
290C4⋊C4—2216no—
291C4⋊C4—222no—
292C4⋊C4—222no—
293C4⋊C4C23×D1118yes—
294C22⋊C4—118no—
295C22⋊C4—228no—
296C42—114no—
297C42—114no—
298C42—228no—
299C11C2×#316411yescharacteristic, complemented, Sylow
300C23—22no—
301C23—22no—
302C23#6694114yes—
303C23C2×D4×D1112yes—
304C23C2×D4×D1111yescharacteristic
305Q8—8816no—
306C2×C4—28no—
307C2×C4—48no—
308C2×C4—88no—
309C2×C4—114no—
310C2×C4—114no—
311C2×C4—224no—
312C2×C4—224no—
313C2×C4—224no—
314C2×C4—224no—
315C2×C4—444no—
316C2×C4—444no—
317C2×C4#6694118yes—
318C2×C4#6694114yes—
319C2×C4C22×Dic2212yes—
320C2×C4C22×Dic2214yes—
321C2×C4C2×D4×D1111yescharacteristic
322C2×C4C2×D4×D1112yes—
323C2×C4C2×Q8×D1112yes—
324C2×C4C2×Q8×D1114yes—
325C2×C4C24×D1111yescharacteristic
326C8—118no—
327C8C22×Dic2214yes—
328C8C22×Dic2214yes—
329C22—28no—
330C22—22no—
331C22—22no—
332C22C2×#6694114yes—
333C22C2×#6694112yes—
334C22#1062328812yes—
335C22#1062329712yes—
336C22C22×D4×D1111yescharacteristic
337C4—48no—
338C4—224no—
339C4—224no—
340C4—444no—
341C4—444no—
342C4C2×#6694112yes—
343C4C2×#6694114yes—
344C4C23×Dic2211yescharacteristic
345C4C22×Q8×D1111yescharacteristic
346C2—24no—
347C2#1307915214yesdirect product factor
348C2C22×#6694111yescharacteristic
349C2C2×#1062328811yescharacteristic
350C2C2×#1062329711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×#107C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenterC22×#107D11
hypocenterC11C2×#3164
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#107

Complements

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

NH ≅ G/Ntype
2. #13079152C2direct (N × H)
3. C2×#10622489C2semidirect
4. C2×#10622487C2semidirect
5. C2×#10622491C2semidirect
35. #10622491C22semidirect
36. #10622489C22semidirect
37. #10622487C22semidirect
41. C22×C8×C11Q8semidirect
65. C2×#4318Q8semidirect
102. C2×C8×C11C2×Q8semidirect
122. #4318C2×Q8semidirect
214. C22×C8Dic22semidirect
254. C2×C11#3164semidirect
279. C2×C8C2×Dic22semidirect
299. C11C2×#3164semidirect
347. C2#13079152direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230312
#130791522
C2×#106224892
C2×#106224872
C2×#106224912
C2×#106225772
C2×#106227192
C2×#106227142
C22×C11×#1072
C2×#316411