Finite Group Databasebeta

← C2×#13074382 #14920989

Subgroups — C2×#13074382 #14920989

Order 2816.

3046 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66922C211yesmaximal, characteristic, complemented
2C22×#66977C212yesmaximal
3#13074382C2116yesmaximal, direct product factor
4C2×#10622596C214yesmaximal, complemented
5C2×#10622566C214yesmaximal
6C2×#10622542C212yesmaximal, complemented
7C2×#10622549C211yesmaximal, characteristic, complemented
8C22×C11×#117C211yesmaximal, characteristic
9C24×C4×C11C2211yescharacteristic
10C23×Dic22C2212yes—
11C2×C11×#117—28no—
12C2×C11×#117C2218yes—
13C22×C11×C4⋊C4C2212yes—
14C22×C11×C22⋊C4C2212yes—
15C22×C42×C11C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C22×C22⋊Dic11C2214yes—
18C22×C4⋊Dic11C2214yes—
19C22×C4⋊Dic11C2212yes—
20C2×#66977—216no—
21C2×#66977C22116yes—
22C22×Dic11⋊C4C2214yes—
23C2×#66922—28no—
24C2×#66922C2218yescomplemented
25C2×C11⋊#95C2214yes—
26C2×C11⋊#95C2218yes—
27#10622596C22132yescomplemented
28#10622566C22132yes—
29#10622549C2218yescomplemented
30#10622542C22116yescomplemented
31C25×C11C2311yescharacteristic
32C23×C4×C11—24no—
33C23×C4×C11—24no—
34C23×C4×C11D418yes—
35C23×C4×C11C2312yes—
36C23×C4×C11C2311yescharacteristic
37C23×C4×C11C2314yes—
38C23×C4×C11C2312yes—
39C23×C4×C11C2311yescharacteristic
40C23×Dic11C2314yes—
41C23×Dic11C2314yes—
42C22×Dic22—28no—
43C22×Dic22—28no—
44C22×Dic22—28no—
45C22×Dic22C2318yes—
46C11×#117—232no—
47C2×C11×C4⋊C4—28no—
48C2×C11×C4⋊C4C2318yes—
49C2×C11×C22⋊C4—28no—
50C2×C11×C22⋊C4C2318yes—
51C2×C42×C11—24no—
52C2×C42×C11D418yes—
53C2×C42×C11C2314yes—
54C2×C42×C11C2314yes—
55C2×C22⋊Dic11—216no—
56C2×C22⋊Dic11C23116yes—
57C2×C4⋊Dic11—216no—
58C2×C4⋊Dic11—28no—
59C2×C4⋊Dic11C23116yes—
60C2×C4⋊Dic11C2318yes—
61#66977—264no—
62C2×Dic11⋊C4—216no—
63C2×Dic11⋊C4C23116yes—
64#66922—232no—
65C11⋊#95C23132yes—
66C11⋊#95C23116yes—
67C2×#2621—111nomaximal, Sylow
68C24×C11—22no—
69C24×C11—22no—
70C24×C11—28no—
71C24×C11C2×D414yes—
72C24×C11C2412yes—
73C24×C11C2411yescharacteristic
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—28no—
77C22×C4×C11—232no—
78C22×C4×C11—28no—
79C22×C4×C11—28no—
80C22×C4×C11—24no—
81C22×C4×C11—28no—
82C22×C4×C11C2×D414yes—
83C22×C4×C11C2×D4116yes—
84C22×C4×C11C2×D418yes—
85C22×C4×C11C2×D414yes—
86C22×C4×C11C2×D414yes—
87C22×C4×C11#4114yes—
88C22×C4×C11C2414yes—
89C22×C4×C11C2414yes—
90C22×C4×C11C2412yes—
91C22×C4×C11C2412yes—
92C22×Dic11—28no—
93C22×Dic11—28no—
94C22×Dic11—28no—
95C22×Dic11—28no—
96C22×Dic11—216no—
97C22×Dic11C2418yes—
98C22×Dic11C2418yes—
99C2×Dic22—216no—
100C2×Dic22—216no—
101C2×Dic22—216no—
102C2×Dic22—432no—
103C11×C4⋊C4—216no—
104C11×C22⋊C4—216no—
105C42×C11—28no—
106C42×C11C2×D4116yes—
107C22⋊Dic11—232no—
108C4⋊Dic11—232no—
109C4⋊Dic11—216no—
110Dic11⋊C4—232no—
111C22×C4⋊Q8—111no—
112C22×C22⋊Q8—112no—
113C22×#117D1111yescharacteristic
114#2621—1116no—
115C2×#398—114no—
116C2×#397—114no—
117C2×#391—112no—
118C2×#382—111no—
119C23×C11—28no—
120C23×C11—216no—
121C23×C11—22no—
122C23×C11—22no—
123C23×C11—28no—
124C23×C11—48no—
125C23×C11—48no—
126C23×C11C22×D414yes—
127C23×C11C22×D412yes—
128C23×C11C22×D412yes—
129C23×C11C2×#4112yes—
130C23×C112−1+418yes—
131C23×C11C2511yescharacteristic
132C2×C4×C11—28no—
133C2×C4×C11—216no—
134C2×C4×C11—22no—
135C2×C4×C11—22no—
136C2×C4×C11—28no—
137C2×C4×C11—232no—
138C2×C4×C11—24no—
139C2×C4×C11—28no—
140C2×C4×C11—48no—
141C2×C4×C11#121116yes—
142C2×C4×C11C22×D414yes—
143C2×C4×C11C22×D414yes—
144C2×C4×C11C22×D418yes—
145C2×C4×C11C22×D414yes—
146C2×C4×C11C2×#4114yes—
147C2×Dic11—28no—
148C2×Dic11—28no—
149C2×Dic11—28no—
150C2×Dic11—28no—
151C2×Dic11—216no—
152C2×Dic11—416no—
153C2×Dic11—416no—
154Dic22—432no—
155C23×Q8—112no—
156C24×C4C2×D1111yescharacteristic
157C2×C4⋊Q8—118no—
158C2×C4⋊Q8—228no—
159C2×C22⋊Q8—1116no—
160C2×C22⋊Q8—2216no—
161C2×#117—28no—
162C2×#117C2×D1118yes—
163C22×C4⋊C4—114no—
164C22×C4⋊C4—114no—
165C22×C4⋊C4—112no—
166C22×C4⋊C4C2×D1112yes—
167C22×C22⋊C4—114no—
168C22×C22⋊C4C2×D1112yes—
169C22×C42C2×D1111yescharacteristic
170C22×C42C2×D1111yescharacteristic
171#398—1132no—
172#397—1132no—
173#391—1116no—
174#382—118no—
175C2×#95—114no—
176C2×#95—118no—
177C22×C11—24no—
178C22×C11—28no—
179C22×C11—416no—
180C22×C11—44no—
181C22×C11—44no—
182C22×C11C2×#12114yes—
183C22×C11#53618yes—
184C22×C11#53618yes—
185C22×C11#54118yes—
186C22×C11C23×D411yescharacteristic
187C22×C11C23×D411yescharacteristic
188C22×C11C22×#4111yescharacteristic
189C22×C11C2×2−1+414yes—
190C4×C11—24no—
191C4×C11—28no—
192C4×C11—44no—
193C4×C11C2×#12118yes—
194Dic11—48no—
195Dic11—48no—
196C25C22×D1111yescharacteristic
197C22×Q8—118no—
198C22×Q8—228no—
199C22×Q8—228no—
200C22×Q8—228no—
201C23×C4—24no—
202C23×C4—24no—
203C23×C4—114no—
204C23×C4—114no—
205C23×C4D4418yes—
206C23×C4C22×D1112yes—
207C23×C4C22×D1114yes—
208C23×C4C22×D1111yescharacteristic
209C23×C4C22×D1112yes—
210C23×C4C22×D1111yescharacteristic
211C4⋊Q8—2232no—
212C22⋊Q8—2264no—
213#117—232no—
214C2×C4⋊C4—28no—
215C2×C4⋊C4—118no—
216C2×C4⋊C4—1116no—
217C2×C4⋊C4—1116no—
218C2×C4⋊C4—2216no—
219C2×C4⋊C4—228no—
220C2×C4⋊C4—2216no—
221C2×C4⋊C4C22×D1118yes—
222C2×C22⋊C4—28no—
223C2×C22⋊C4—1116no—
224C2×C22⋊C4—2216no—
225C2×C22⋊C4C22×D1118yes—
226C2×C42—24no—
227C2×C42C22⋊D1118yes—
228C2×C42C22×D1114yes—
229C2×C42C22×D1114yes—
230#95—1116no—
231#95—1132no—
232C2×C11—44no—
233C2×C11#262118yescomplemented
234C2×C11C22×#12111yescharacteristic
235C2×C11C2×#53612yes—
236C2×C11C2×#53612yes—
237C2×C11C2×#54112yes—
238C24—22no—
239C24—28no—
240C24—22no—
241C24C2×D4414yes—
242C24C23×D1112yes—
243C24C23×D1111yescharacteristic
244C2×Q8—2216no—
245C2×Q8—2216no—
246C2×Q8—2216no—
247C2×Q8—4432no—
248C22×C4—22no—
249C22×C4—28no—
250C22×C4—22no—
251C22×C4—232no—
252C22×C4—28no—
253C22×C4—28no—
254C22×C4—28no—
255C22×C4—24no—
256C22×C4—118no—
257C22×C4—118no—
258C22×C4—228no—
259C22×C4—228no—
260C22×C4—228no—
261C22×C4—2216no—
262C22×C4—228no—
263C22×C4C2×D4414yes—
264C22×C4C2×D44116yes—
265C22×C4C2×D4414yes—
266C22×C4#433914yes—
267C22×C4C2×C22⋊D1118yes—
268C22×C4C2×C22⋊D1114yes—
269C22×C4C23×D1114yes—
270C22×C4C23×D1112yes—
271C22×C4C23×D1114yes—
272C22×C4C23×D1112yes—
273C4⋊C4—216no—
274C4⋊C4—2232no—
275C4⋊C4—2216no—
276C4⋊C4—2232no—
277C22⋊C4—216no—
278C22⋊C4—2232no—
279C42—28no—
280C42C2×C22⋊D11116yes—
281C11C2×#262111yescharacteristic, complemented, Sylow
282C23—216no—
283C23—28no—
284C23—22no—
285C23—28no—
286C23—22no—
287C23—48no—
288C23—48no—
289C23C22×D4414yes—
290C23C22×D4412yes—
291C23C2×#433912yes—
292C23#6704318yes—
293C23C22×C22⋊D1112yes—
294C23C24×D1111yescharacteristic
295Q8—4432no—
296C2×C4—28no—
297C2×C4—216no—
298C2×C4—22no—
299C2×C4—28no—
300C2×C4—22no—
301C2×C4—232no—
302C2×C4—28no—
303C2×C4—24no—
304C2×C4—48no—
305C2×C4—228no—
306C2×C4—228no—
307C2×C4—228no—
308C2×C4—2216no—
309C2×C4—228no—
310C2×C4—4416no—
311C2×C4—4416no—
312C2×C4#66983116yes—
313C2×C4C22×D4414yes—
314C2×C4C22×D4414yes—
315C2×C4C2×#433914yes—
316C2×C4C22×C22⋊D1118yes—
317C2×C4C22×C22⋊D1114yes—
318C22—28no—
319C22—24no—
320C22—44no—
321C22—44no—
322C22—416no—
323C22#1062304918yes—
324C22#1062305718yes—
325C22C2×#6698314yes—
326C22#1062335618yes—
327C22C23×D4411yescharacteristic
328C22C22×#433911yescharacteristic
329C22C2×#6704314yes—
330C22C23×C22⋊D1111yescharacteristic
331C4—28no—
332C4—24no—
333C4—44no—
334C4—448no—
335C4—448no—
336C4C2×#6698318yes—
337C2—44no—
338C2#1307438218yesdirect product factor
339C2C22×#6698311yescharacteristic
340C2C2×#1062335612yes—
341C2C2×#1062305712yes—
342C2C2×#1062304912yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#117C2
socleC24×C11C24
prime radicalC25×C11C23
hypercenterC22×#117D11
hypocenterC11C2×#2621
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
1. C22×#66922C2semidirect
3. #13074382C2direct (N × H)
4. C2×#10622596C2semidirect
6. C2×#10622542C2semidirect
7. C2×#10622549C2semidirect
24. C2×#66922C22semidirect
27. #10622596C22semidirect
29. #10622549C22semidirect
30. #10622542C22semidirect
233. C2×C11#2621semidirect
281. C11C2×#2621semidirect
338. C2#13074382direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669222
C22×#669772
#130743822
C2×#106225962
C2×#106225662
C2×#106225422
C2×#106225492
C22×C11×#1172
C2×#262111