Finite Group Databasebeta

← C2×#13070849 #14909068

Subgroups — C2×#13070849 #14909068

Order 2816.

610 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622491C211yesmaximal, characteristic, complemented
2C2×#10622804C211yesmaximal, characteristic
3#13070849C218yesmaximal, direct product factor
4C2×#10622202C211yesmaximal, characteristic, complemented
5C2×#10622147C211yesmaximal, characteristic
6C2×#10622129C211yesmaximal, characteristic
7C2×C16×Dic11C211yesmaximal, characteristic, complemented
8C2×C11×#358C211yesmaximal, characteristic, complemented
9C22×C11×Q16C2211yescharacteristic
10C2×#67000—21no—
11C22×#4325—21no—
12C22×D88C2211yescharacteristic
13C2×#66943—21no—
14C22×C11×C16C2211yescharacteristic
15C2×C11×#107C2211yescharacteristic
16#10622804—22no—
17#10622804C2214yes—
18C2×#66882C2211yescharacteristic
19C2×C8×Dic11C2211yescharacteristic
20C22×C11⋊C16C2211yescharacteristic
21C2×#66872—21no—
22#10622491—22no—
23#10622491C2214yescomplemented
24C11×#358C2214yescomplemented
25#10622202C2214yescomplemented
26#10622147C2214yes—
27C16×Dic11C2214yescomplemented
28#10622129C2214yes—
29C22×Q8×C11—21no—
30C22×D44—21no—
31C2×C11×Q16—21no—
32C2×C11×Q16—22no—
33C2×C11×Q16—22no—
34C2×C11×Q16C2312yes—
35C22×C8×C11C2311yescharacteristic
36C2×C11×C4⋊C4—21no—
37#67000—24no—
38#67000—42no—
39C2×#4325—24no—
40C2×#4325—44no—
41C2×(C2×D11)⋊C4—41no—
42C2×(C2×D11)⋊C4—41no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11—41no—
45C2×Dic11⋊C4—41no—
46C2×C4×Dic11D411yescharacteristic
47C22×C11⋊C8D411yescharacteristic
48C2×D88—22no—
49C2×D88—22no—
50C2×D88—21no—
51C2×D88C2312yes—
52#66943—24no—
53#66943—42no—
54C2×C11×C16—22no—
55C2×C11×C16C2312yes—
56C11×#107—21no—
57C11×#107C2312yes—
58#66882—21no—
59#66882C2312yes—
60C8×Dic11D412yes—
61C8×Dic11C2312yes—
62C2×C11⋊C16—22no—
63C2×C11⋊C16C2312yes—
64#66872—24no—
65C2×#2242—111nomaximal, Sylow
66C23×D11—41no—
67C2×Q8×C11—22no—
68C2×Q8×C11—41no—
69C2×Q8×C11—42no—
70C2×Q8×C11—42no—
71C22×C4×C11—41no—
72C22×C4×C11—41no—
73C22×C4×C11C2×D411yescharacteristic
74C22×Dic11—41no—
75C22×Dic11D811yescharacteristic
76C22×Dic11D811yescharacteristic
77C2×D44—22no—
78C2×D44—42no—
79C2×D44—41no—
80C2×D44—42no—
81C11×Q16—22no—
82C11×Q16—22no—
83C11×Q16—42no—
84C2×C8×C11C2×D411yescharacteristic
85C2×C8×C11#4112yes—
86C2×C8×C11#4112yes—
87C2×C8×C11C2411yescharacteristic
88C11×C4⋊C4—22no—
89C11×C4⋊C4—41no—
90#4325—48no—
91(C2×D11)⋊C4—44no—
92(C2×D11)⋊C4—44no—
93C4⋊Dic11—22no—
94C4⋊Dic11—44no—
95C4⋊Dic11—41no—
96Dic11⋊C4—44no—
97C4×Dic11D812yes—
98C4×Dic11C2×D412yes—
99C2×C11⋊C8SD1614yes—
100C2×C11⋊C8C2×D412yes—
101D88—22no—
102D88—22no—
103D88—42no—
104C11×C16—22no—
105C11⋊C16—22no—
106C2×#499—111no—
107C2×#495—111no—
108#2242—118no—
109C2×#358—111no—
110C2×#358D1111yescharacteristic, complemented
111C2×#357—111no—
112C2×#357—111no—
113C2×C4×C16—111no—
114C23×C11C2×D811yescharacteristic
115C22×D11—42no—
116C22×D11—82no—
117C22×D11—82no—
118C22×D11—82no—
119Q8×C11—42no—
120Q8×C11—42no—
121Q8×C11—82no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C2×C4×C11—82no—
125C2×C4×C11—82no—
126C2×C4×C11#12412yes—
127C2×C4×C11C2×D811yescharacteristic
128C2×C4×C11C2×SD1612yes—
129C2×C4×C11C22×D411yescharacteristic
130C2×Dic11—22no—
131C2×Dic11—22no—
132C2×Dic11—42no—
133C2×Dic11—82no—
134C2×Dic11C2×D812yes—
135C2×Dic11C2×D812yes—
136D44—42no—
137D44—42no—
138D44—82no—
139C8×C11#12412yes—
140C8×C11C2×#4111yescharacteristic
141C8×C11C2×#4111yescharacteristic
142C11⋊C8C2×SD1614yes—
143C22×Q16C2×D1111yescharacteristic
144C22×SD16—221no—
145C22×D8—111no—
146C2×#125—221no—
147C2×#124—221no—
148C22×C16—111no—
149C22×C16C2×D1111yescharacteristic
150#499—114no—
151#499—222no—
152#495—114no—
153#495—222no—
154C2×#107—111no—
155C2×#107C2×D1111yescharacteristic
156C2×#106—221no—
157C2×C4×C8—111no—
158#358—114no—
159#358C2×D1114yescomplemented
160#357—114no—
161#357—114no—
162C4×C16—114no—
163C22×C11#48612yes—
164C22×C11#50812yes—
165C22×C11#50812yes—
166C22×C11C22×D811yescharacteristic
167C2×D11—82no—
168C2×D11—82no—
169C2×D11—82no—
170C2×D11—164no—
171C4×C11—82no—
172C4×C11—82no—
173C4×C11#48612yes—
174C4×C11C2×#12411yescharacteristic
175C4×C11C22×SD1611yescharacteristic
176Dic11—22no—
177Dic11—22no—
178Dic11—82no—
179C22×Q8—21no—
180C22×D4—221no—
181C2×Q16—22no—
182C2×Q16—21no—
183C2×Q16—22no—
184C2×Q16C22×D1112yes—
185C2×SD16—224no—
186C2×SD16—444no—
187C2×D8—112no—
188C2×D8—222no—
189C2×D8—221no—
190C2×D8—222no—
191C22×C8—111no—
192C22×C8C22×D1111yescharacteristic
193#125—224no—
194#125—442no—
195#124—224no—
196#124—442no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4—441no—
200C2×C4⋊C4—441no—
201C2×C22⋊C4—441no—
202C2×C22⋊C4—441no—
203C2×C42—111no—
204C2×C16—22no—
205C2×C16—112no—
206C2×C16—222no—
207C2×C16C22×D1112yes—
208#107—21no—
209#107—112no—
210#107—221no—
211#107C22×D1112yes—
212#106—224no—
213C4×C8—112no—
214C4×C8—112no—
215C2×C11#224214yescomplemented
216C2×C11C2×#48611yescharacteristic
217C2×C11C2×#50811yescharacteristic
218C2×C11C2×#50811yescharacteristic
219D11—162no—
220C24—441no—
221C2×Q8—22no—
222C2×Q8—41no—
223C2×Q8—42no—
224C2×Q8—42no—
225C2×D4—222no—
226C2×D4—442no—
227C2×D4—441no—
228C2×D4—442no—
229C22×C4—41no—
230C22×C4—41no—
231C22×C4—111no—
232C22×C4—111no—
233C22×C4—441no—
234C22×C4D4×D1111yescharacteristic
235Q16—22no—
236Q16—22no—
237Q16—42no—
238SD16—448no—
239D8—222no—
240D8—222no—
241D8—442no—
242C2×C8—114no—
243C2×C8—112no—
244C2×C8#433912yes—
245C2×C8D4×D1111yescharacteristic
246C2×C8#434112yes—
247C2×C8C23×D1111yescharacteristic
248C4⋊C4—22no—
249C4⋊C4—41no—
250C4⋊C4—222no—
251C4⋊C4—444no—
252C4⋊C4—444no—
253C4⋊C4—441no—
254C22⋊C4—444no—
255C22⋊C4—444no—
256C42—112no—
257C42—112no—
258C16—22no—
259C16—222no—
260C11C2×#224211yescharacteristic, complemented, Sylow
261C23—442no—
262C23—882no—
263C23—882no—
264C23—882no—
265C23D8×D1111yescharacteristic
266Q8—42no—
267Q8—42no—
268Q8—82no—
269D4—442no—
270D4—442no—
271D4—882no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—82no—
275C2×C4—82no—
276C2×C4—112no—
277C2×C4—112no—
278C2×C4—222no—
279C2×C4—222no—
280C2×C4—442no—
281C2×C4—882no—
282C2×C4#6693812yes—
283C2×C4D8×D1111yescharacteristic
284C2×C4SD16×D1112yes—
285C2×C4C2×D4×D1111yescharacteristic
286C8—114no—
287C8#6693812yes—
288C8C2×#433911yescharacteristic
289C8C2×#434111yescharacteristic
290C22—882no—
291C22—882no—
292C22—882no—
293C22—1764no—
294C22#1062237312yes—
295C22#1062252912yes—
296C22#1062253212yes—
297C22C2×D8×D1111yescharacteristic
298C4—82no—
299C4—82no—
300C4—222no—
301C4—222no—
302C4—882no—
303C4#1062237312yes—
304C4C2×#6693811yescharacteristic
305C4C2×SD16×D1111yescharacteristic
306C2—1762no—
307C2#1307084914yesdirect product factor
308C2C2×#1062237311yescharacteristic
309C2C2×#1062252911yescharacteristic
310C2C2×#1062253211yescharacteristic
subgroupG/H
centerC23D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#358C2
socleC23×C11C2×D8
prime radicalC22×D88C22
hypercenterC2×#358D11
hypocenterC11C2×#2242
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
1. C2×#10622491C2semidirect
3. #13070849C2direct (N × H)
4. C2×#10622202C2semidirect
7. C2×C16×Dic11C2semidirect
8. C2×C11×#358C2semidirect
23. #10622491C22semidirect
24. C11×#358C22semidirect
25. #10622202C22semidirect
27. C16×Dic11C22semidirect
110. C2×#358D11semidirect
159. #358C2×D11semidirect
215. C2×C11#2242semidirect
260. C11C2×#2242semidirect
307. C2#13070849direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106224912
C2×#106228042
#130708492
C2×#106222022
C2×#106221472
C2×#106221292
C2×C16×Dic112
C2×C11×#3582
C2×#224211