Finite Group Databasebeta

← C2×#13070061 #14782669

Subgroups — C2×#13070061 #14782669

Order 2816.

950 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66881C211yesmaximal, characteristic, complemented
2C2×#10622845C212yesmaximal
3#13070061C218yesmaximal, direct product factor
4C2×#10622192C212yesmaximal, complemented
5C2×#10622190C211yesmaximal, characteristic, complemented
6C2×C11×#408C211yesmaximal, characteristic
7C22×C11×#41C2211yescharacteristic
8C22×C11×M16C2211yescharacteristic
9C23×C8×C11C2211yescharacteristic
10C22×C4⋊Dic11C2212yes—
11C22×#4318C2212yes—
12C11×#408—22no—
13C11×#408C2214yes—
14C2×C11×C22⋊C8—22no—
15#10622845—24no—
16#10622845C2218yes—
17C2×#66899—22no—
18C2×#66896—22no—
19C2×#66881—22no—
20C2×#66881—22no—
21C2×#66881C2214yescomplemented
22#10622192C2218yescomplemented
23#10622190C2214yescomplemented
24C2×C11×#41—21no—
25C2×C11×#41—21no—
26C2×C11×#41—24no—
27C2×C11×#41—24no—
28C2×C11×#41D412yes—
29C2×C11×#41C2312yes—
30C22×Q8×C11D411yescharacteristic
31C22×D4×C11—21no—
32C22×D4×C11D411yescharacteristic
33C23×C4×C11—21no—
34C23×C4×C11C2311yescharacteristic
35C23×Dic11—22no—
36C2×C11×M16—21no—
37C2×C11×M16—24no—
38C2×C11×M16C2312yes—
39C22×C8×C11—24no—
40C22×C8×C11—21no—
41C22×C8×C11D412yes—
42C22×C8×C11D412yes—
43C22×C8×C11C2312yes—
44C2×C4⋊Dic11—22no—
45C2×C4⋊Dic11—22no—
46C2×C4⋊Dic11—22no—
47C2×C4⋊Dic11—22no—
48C2×C4⋊Dic11—22no—
49C2×C4⋊Dic11C2314yes—
50C2×#4318—22no—
51C2×#4318—24no—
52C2×#4318—24no—
53C2×#4318C2314yes—
54C22×C11⋊C8—22no—
55C11×C22⋊C8—28no—
56#66899—28no—
57#66896—28no—
58#66881—28no—
59C2×#2079—111nomaximal, Sylow
60C24×C11—21no—
61C24×C11#4111yescharacteristic
62C11×#41—28no—
63C11×#41—24no—
64C11×#41—24no—
65C11×#41—42no—
66C11×#41—42no—
67C11×#41—44no—
68C2×Q8×C11—21no—
69C2×Q8×C11—24no—
70C2×Q8×C11C2×D412yes—
71C2×D4×C11—22no—
72C2×D4×C11—22no—
73C2×D4×C11—21no—
74C2×D4×C11—24no—
75C2×D4×C11—44no—
76C2×D4×C11C2×D412yes—
77C22×C4×C11—21no—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—42no—
81C22×C4×C11—42no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11#4111yescharacteristic
87C22×C4×C11#4114yes—
88C22×C4×C11#4114yes—
89C22×C4×C11C2411yescharacteristic
90C22×Dic11—24no—
91C22×Dic11—42no—
92C22×Dic11—42no—
93C22×Dic11—84no—
94C11×M16—24no—
95C11×M16—42no—
96C2×C8×C11—24no—
97C2×C8×C11—24no—
98C2×C8×C11—22no—
99C2×C8×C11—24no—
100C2×C8×C11—42no—
101C2×C8×C11C2×D414yes—
102C4⋊Dic11—24no—
103C4⋊Dic11—24no—
104C4⋊Dic11—42no—
105C4⋊Dic11—42no—
106#4318—24no—
107#4318—24no—
108#4318—44no—
109C2×C11⋊C8—24no—
110C2×C11⋊C8—44no—
111C22×#106—111no—
112C2×#417—112no—
113C2×#408D1111yescharacteristic
114#2079—118no—
115C2×#343—112no—
116C2×#341—111no—
117C23×C11—24no—
118C23×C11—22no—
119C23×C11—42no—
120C23×C11—44no—
121C23×C11#12111yescharacteristic
122C23×C11#12111yescharacteristic
123C23×C11#12614yes—
124C23×C11C2×#4111yescharacteristic
125Q8×C11—24no—
126Q8×C11—42no—
127D4×C11—24no—
128D4×C11—44no—
129D4×C11—44no—
130D4×C11—42no—
131C2×C4×C11—22no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11—44no—
136C2×C4×C11#12111yescharacteristic
137C2×C4×C11#12111yescharacteristic
138C2×C4×C11#12314yes—
139C2×C4×C11#12314yes—
140C2×C4×C11#12312yes—
141C2×C4×C11#12312yes—
142C2×C4×C11#12412yes—
143C2×C4×C11#12412yes—
144C2×C4×C11#12614yes—
145C2×C4×C11C22×D411yescharacteristic
146C2×C4×C11C22×D411yescharacteristic
147C2×C4×C11C2×#4112yes—
148C2×C4×C11C2×#4112yes—
149C2×Dic11—44no—
150C2×Dic11—84no—
151C2×Dic11—84no—
152C2×Dic11—84no—
153C8×C11—24no—
154C8×C11—42no—
155C11⋊C8—44no—
156C22×#41C2×D1111yescharacteristic
157C22×M16—112no—
158C22×M16C2×D1111yescharacteristic
159C23×C8C2×D1111yescharacteristic
160C22×C4⋊C4—112no—
161C2×#106—114no—
162C2×#106—222no—
163C2×#106—222no—
164#417—118no—
165#417—224no—
166C2×#103—222no—
167C2×#102—222no—
168#408—22no—
169#408C2×D1114yes—
170C2×C22⋊C8—22no—
171#343—118no—
172#341—114no—
173C22×C11—28no—
174C22×C11—22no—
175C22×C11—22no—
176C22×C11—42no—
177C22×C11—44no—
178C22×C11—84no—
179C22×C11#39712yes—
180C22×C11#39712yes—
181C22×C11#47114yes—
182C22×C11C2×#12111yescharacteristic
183C22×C11C2×#12612yes—
184C4×C11—42no—
185C4×C11#39712yes—
186C4×C11#39712yes—
187C4×C11C2×#12312yes—
188C4×C11C2×#12311yescharacteristic
189C4×C11C2×#12411yescharacteristic
190Dic11—84no—
191C2×#41—21no—
192C2×#41—21no—
193C2×#41—24no—
194C2×#41—24no—
195C2×#41D4412yes—
196C2×#41C22×D1112yes—
197C22×Q8D4411yescharacteristic
198C22×D4—21no—
199C22×D4D4411yescharacteristic
200C23×C4—21no—
201C23×C4—222no—
202C23×C4C22×D1111yescharacteristic
203C2×M16—21no—
204C2×M16—24no—
205C2×M16—114no—
206C2×M16—222no—
207C2×M16—224no—
208C2×M16—224no—
209C2×M16C22×D1112yes—
210C22×C8—24no—
211C22×C8—21no—
212C22×C8—222no—
213C22×C8C22⋊D1112yes—
214C22×C8C22⋊D1112yes—
215C22×C8C22×D1112yes—
216C2×C4⋊C4—114no—
217C2×C4⋊C4—222no—
218C2×C4⋊C4—222no—
219C2×C4⋊C4—222no—
220C2×C4⋊C4—222no—
221C2×C4⋊C4—222no—
222#106—228no—
223#103—228no—
224#102—228no—
225C22⋊C8—28no—
226C2×C11—22no—
227C2×C11—22no—
228C2×C11—82no—
229C2×C11#207914yescomplemented
230C2×C11C2×#39711yescharacteristic
231C2×C11C2×#47112yes—
232C24—21no—
233C24#433911yescharacteristic
234#41—28no—
235#41—24no—
236#41—24no—
237#41—44no—
238#41—42no—
239#41—42no—
240C2×Q8—21no—
241C2×Q8—24no—
242C2×Q8C2×D4412yes—
243C2×D4—22no—
244C2×D4—22no—
245C2×D4—24no—
246C2×D4—21no—
247C2×D4—44no—
248C2×D4C2×D4412yes—
249C22×C4—21no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—42no—
253C22×C4—42no—
254C22×C4—224no—
255C22×C4—442no—
256C22×C4—442no—
257C22×C4—884no—
258C22×C4C2×D4411yescharacteristic
259C22×C4C2×D4411yescharacteristic
260C22×C4#433911yescharacteristic
261C22×C4#434114yes—
262C22×C4#434114yes—
263C22×C4C2×C22⋊D1111yescharacteristic
264C22×C4C2×C22⋊D1111yescharacteristic
265C22×C4C23×D1111yescharacteristic
266M16—24no—
267M16—42no—
268M16—224no—
269M16—224no—
270M16—444no—
271C2×C8—24no—
272C2×C8—24no—
273C2×C8—24no—
274C2×C8—22no—
275C2×C8—42no—
276C2×C8—224no—
277C2×C8—444no—
278C2×C8C2×C22⋊D1114yes—
279C4⋊C4—224no—
280C4⋊C4—224no—
281C4⋊C4—442no—
282C4⋊C4—442no—
283C11C2×#207911yescharacteristic, complemented, Sylow
284C23—24no—
285C23—22no—
286C23—44no—
287C23—42no—
288C23#6693214yes—
289C23#6698311yescharacteristic
290C23#6698311yescharacteristic
291C23C2×#433911yescharacteristic
292Q8—24no—
293Q8—42no—
294D4—24no—
295D4—44no—
296D4—44no—
297D4—42no—
298C2×C4—22no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—44no—
303C2×C4—444no—
304C2×C4—884no—
305C2×C4—884no—
306C2×C4—884no—
307C2×C4#6693214yes—
308C2×C4#6693914yes—
309C2×C4#6693914yes—
310C2×C4#6698311yescharacteristic
311C2×C4#6698311yescharacteristic
312C2×C4#6698812yes—
313C2×C4#6698812yes—
314C2×C4#6698912yes—
315C2×C4#6698912yes—
316C2×C4C22×D4411yescharacteristic
317C2×C4C2×#434112yes—
318C2×C4C2×#434112yes—
319C2×C4C22×C22⋊D1111yescharacteristic
320C8—24no—
321C8—42no—
322C8—444no—
323C22—22no—
324C22—22no—
325C22—28no—
326C22—44no—
327C22—42no—
328C22—84no—
329C22#1062256612yes—
330C22#1062256612yes—
331C22#1062275414yes—
332C22C2×#6693212yes—
333C22C2×#6698311yescharacteristic
334C4—42no—
335C4—884no—
336C4#1062256612yes—
337C4#1062256612yes—
338C4C2×#6693912yes—
339C4C2×#6698811yescharacteristic
340C4C2×#6698911yescharacteristic
341C2—22no—
342C2—22no—
343C2—82no—
344C2#1307006114yesdirect product factor
345C2C2×#1062256611yescharacteristic
346C2C2×#1062275412yes—
subgroupG/H
centerC23#66983
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#408C2
socleC23×C11#121
prime radicalC22×C11×#41C22
hypercenterC2×#408D11
hypocenterC11C2×#2079
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
1. C22×#66881C2semidirect
3. #13070061C2direct (N × H)
4. C2×#10622192C2semidirect
5. C2×#10622190C2semidirect
21. C2×#66881C22semidirect
22. #10622192C22semidirect
23. #10622190C22semidirect
229. C2×C11#2079semidirect
283. C11C2×#2079semidirect
344. C2#13070061direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#668812
C2×#106228452
#130700612
C2×#106221922
C2×#106221902
C2×C11×#4082
C2×#207911