Finite Group Databasebeta

← C2×#13067914 #14734913

Subgroups — C2×#13067914 #14734913

Order 2816.

1010 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 1010 conjugacy classes of subgroups — too many to draw. Only its 187 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622671C211yesmaximal, characteristic
2C2×#10622680C212yesmaximal, complemented
3#13067914C218yesmaximal, direct product factor
4C2×#10622181C212yesmaximal, complemented
5C2×#10622178C211yesmaximal, characteristic, complemented
6C2×C11×#563C211yesmaximal, characteristic, complemented
7C11×#563—24no—
8C11×#563—22no—
9C11×#563C2214yescomplemented
10C2×C11×C4⋊Q8—21no—
11C2×C11×#126—22no—
12C2×C11×#125C2212yes—
13C2×C11×#124C2211yescharacteristic
14C2×C11×#123—21no—
15C2×C11×C22⋊Q8—22no—
16C22×#4325—21no—
17C22×#4323—21no—
18C2×#66927C2211yescharacteristic
19#10622680—24no—
20#10622680C2218yescomplemented
21#10622671—22no—
22#10622671C2214yes—
23C2×#66873—22no—
24C2×#66873—22no—
25C2×#66867C2211yescharacteristic
26C2×#66867C2212yes—
27#10622181C2218yescomplemented
28#10622178C2214yescomplemented
29C22×Q8×C11—21no—
30C22×Q8×C11D411yescharacteristic
31C22×D4×C11D411yescharacteristic
32C23×C4×C11—21no—
33C22×D44—21no—
34C22×D44—22no—
35C11×C4⋊Q8—24no—
36C11×C4⋊Q8—24no—
37C11×#126—28no—
38C11×#126—28no—
39C11×#125—22no—
40C11×#125—22no—
41C11×#125D414yes—
42C11×#125C2314yes—
43C11×#124—22no—
44C11×#124D412yes—
45C11×#124C2312yes—
46C11×#123—24no—
47C11×#123—24no—
48C11×C22⋊Q8—28no—
49C11×C22⋊Q8—28no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4D412yes—
54C2×C11×C4⋊C4D412yes—
55C2×C11×C22⋊C4—22no—
56C2×C11×C22⋊C4—21no—
57C2×C11×C22⋊C4—22no—
58C2×C42×C11—21no—
59C2×C42×C11C2311yescharacteristic
60C2×#4325—24no—
61C2×#4325—44no—
62C2×#4323—24no—
63C2×#4323—44no—
64C22×C11⋊C8—21no—
65C22×C11⋊C8—22no—
66#66927—21no—
67#66927—22no—
68#66927C2312yes—
69#66873—28no—
70#66873—28no—
71#66867—21no—
72#66867—22no—
73#66867C2312yes—
74#66867C2314yes—
75C2×#1657—111nomaximal, Sylow
76C24×C11—21no—
77C23×D11—41no—
78C2×Q8×C11—24no—
79C2×Q8×C11—21no—
80C2×Q8×C11—42no—
81C2×Q8×C11—82no—
82C2×Q8×C11C2×D412yes—
83C2×D4×C11—21no—
84C2×D4×C11—42no—
85C2×D4×C11C2×D412yes—
86C22×C4×C11—22no—
87C22×C4×C11—21no—
88C22×C4×C11—22no—
89C22×C4×C11—24no—
90C22×C4×C11—82no—
91C22×C4×C11C2×D412yes—
92C22×C4×C11C2×D411yescharacteristic
93C2×D44—24no—
94C2×D44—22no—
95C2×D44—42no—
96C2×D44—42no—
97C2×D44—48no—
98C2×D44—42no—
99C2×D44—41no—
100C11×C4⋊C4—28no—
101C11×C4⋊C4—24no—
102C11×C4⋊C4—24no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—24no—
106C11×C4⋊C4—24no—
107C11×C4⋊C4C2×D414yes—
108C11×C4⋊C4C2×D414yes—
109C11×C22⋊C4—28no—
110C11×C22⋊C4—24no—
111C11×C22⋊C4—24no—
112C11×C22⋊C4—24no—
113C42×C11—24no—
114C42×C11C2×D412yes—
115C42×C11C2×D411yescharacteristic
116C42×C11C2411yescharacteristic
117#4325—48no—
118#4323—48no—
119C2×C11⋊C8—24no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—24no—
122C2×C11⋊C8—44no—
123C2×#563D1111yescharacteristic, complemented
124C2×#496—111no—
125C2×#490—112no—
126#1657—118no—
127C2×#330—112no—
128C2×#329—111no—
129C23×C11—22no—
130C23×C11—42no—
131C23×C11—44no—
132C23×C11#12011yescharacteristic
133C22×D11—42no—
134C22×D11—82no—
135C22×D11—84no—
136Q8×C11—42no—
137Q8×C11—81no—
138Q8×C11—84no—
139D4×C11—42no—
140D4×C11—81no—
141C2×C4×C11—22no—
142C2×C4×C11—24no—
143C2×C4×C11—24no—
144C2×C4×C11—22no—
145C2×C4×C11—24no—
146C2×C4×C11—44no—
147C2×C4×C11—42no—
148C2×C4×C11—44no—
149C2×C4×C11—84no—
150C2×C4×C11#12012yes—
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11C22×D412yes—
153C2×C4×C11C22×D411yescharacteristic
154D44—42no—
155D44—42no—
156D44—48no—
157D44—82no—
158D44—84no—
159C11⋊C8—24no—
160C11⋊C8—44no—
161C22×SD16—221no—
162C22×D8—221no—
163#563—24no—
164#563—22no—
165#563C2×D1114yescomplemented
166C2×C4⋊Q8—21no—
167C2×#127—111no—
168C2×#126—22no—
169C2×#125C2×D1112yes—
170C2×#124C2×D1111yescharacteristic
171C2×#123—21no—
172C2×C22⋊Q8—22no—
173#496—114no—
174#496—222no—
175#490—118no—
176#490—224no—
177C2×#102—222no—
178C2×#102—222no—
179C2×#97—112no—
180C2×#97—111no—
181#330—118no—
182#329—114no—
183C22×C11—42no—
184C22×C11—44no—
185C22×C11—84no—
186C22×C11#45312yes—
187C22×C11#45414yes—
188C22×C11C2×#12011yescharacteristic
189C2×D11—82no—
190C2×D11—84no—
191C2×D11—164no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—22no—
195C4×C11—22no—
196C4×C11—44no—
197C4×C11—42no—
198C4×C11—44no—
199C22×Q8—21no—
200C22×Q8C22⋊D1111yescharacteristic
201C22×D4—221no—
202C22×D4—222no—
203C22×D4C22⋊D1111yescharacteristic
204C23×C4—21no—
205C2×SD16—224no—
206C2×SD16—444no—
207C2×D8—224no—
208C2×D8—444no—
209C22×C8—221no—
210C22×C8—222no—
211C4⋊Q8—24no—
212C4⋊Q8—24no—
213#127—112no—
214#127—222no—
215#127—221no—
216#126—28no—
217#126—28no—
218#125—22no—
219#125—22no—
220#125C22⋊D1114yes—
221#125C22×D1114yes—
222#124—22no—
223#124C22⋊D1112yes—
224#124C22×D1112yes—
225#123—24no—
226#123—24no—
227C22⋊Q8—28no—
228C22⋊Q8—28no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4C22⋊D1112yes—
233C2×C4⋊C4C22⋊D1112yes—
234C2×C22⋊C4—22no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—22no—
237C2×C42—21no—
238C2×C42C22×D1111yescharacteristic
239#102—228no—
240#102—228no—
241#97—114no—
242#97—112no—
243#97—222no—
244#97—221no—
245C2×C11—82no—
246C2×C11#165714yescomplemented
247C2×C11C2×#45311yescharacteristic
248C2×C11C2×#45412yes—
249D11—162no—
250C24—21no—
251C24—441no—
252C2×Q8—24no—
253C2×Q8—21no—
254C2×Q8—42no—
255C2×Q8—82no—
256C2×Q8C2×C22⋊D1112yes—
257C2×D4—21no—
258C2×D4—42no—
259C2×D4—224no—
260C2×D4—222no—
261C2×D4—442no—
262C2×D4—442no—
263C2×D4—448no—
264C2×D4—442no—
265C2×D4—441no—
266C2×D4C2×C22⋊D1112yes—
267C22×C4—22no—
268C22×C4—21no—
269C22×C4—22no—
270C22×C4—24no—
271C22×C4—82no—
272C22×C4C2×C22⋊D1112yes—
273C22×C4C2×C22⋊D1111yescharacteristic
274SD16—448no—
275D8—448no—
276C2×C8—224no—
277C2×C8—222no—
278C2×C8—224no—
279C2×C8—444no—
280C4⋊C4—28no—
281C4⋊C4—24no—
282C4⋊C4—24no—
283C4⋊C4—22no—
284C4⋊C4—22no—
285C4⋊C4—24no—
286C4⋊C4—24no—
287C4⋊C4C2×C22⋊D1114yes—
288C4⋊C4C2×C22⋊D1114yes—
289C22⋊C4—28no—
290C22⋊C4—24no—
291C22⋊C4—24no—
292C22⋊C4—24no—
293C42—24no—
294C42C2×C22⋊D1112yes—
295C42C2×C22⋊D1111yescharacteristic
296C42C23×D1111yescharacteristic
297C11C2×#165711yescharacteristic, complemented, Sylow
298C23—22no—
299C23—42no—
300C23—44no—
301C23—442no—
302C23—882no—
303C23—884no—
304C23#6700611yescharacteristic
305Q8—42no—
306Q8—81no—
307Q8—84no—
308D4—42no—
309D4—81no—
310D4—442no—
311D4—442no—
312D4—448no—
313D4—882no—
314D4—884no—
315C2×C4—22no—
316C2×C4—24no—
317C2×C4—24no—
318C2×C4—22no—
319C2×C4—24no—
320C2×C4—44no—
321C2×C4—42no—
322C2×C4—44no—
323C2×C4—84no—
324C2×C4#6700612yes—
325C2×C4#6700611yescharacteristic
326C2×C4C22×C22⋊D1112yes—
327C2×C4C22×C22⋊D1111yescharacteristic
328C8—224no—
329C8—444no—
330C22—42no—
331C22—44no—
332C22—84no—
333C22—882no—
334C22—884no—
335C22—1764no—
336C22#1062285412yes—
337C22#1062285814yes—
338C22C2×#6700611yescharacteristic
339C4—21no—
340C4—21no—
341C4—22no—
342C4—22no—
343C4—44no—
344C4—42no—
345C4—44no—
346C2—82no—
347C2—1762no—
348C2#1306791414yesdirect product factor
349C2C2×#1062285411yescharacteristic
350C2C2×#1062285812yes—
subgroupG/H
centerC23#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#563C2
socleC23×C11#120
prime radicalC2×#10622671C2
hypercenterC2×#563D11
hypocenterC11C2×#1657
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#563

Complements

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

NH ≅ G/Ntype
2. C2×#10622680C2semidirect
3. #13067914C2direct (N × H)
4. C2×#10622181C2semidirect
5. C2×#10622178C2semidirect
6. C2×C11×#563C2semidirect
9. C11×#563C22semidirect
20. #10622680C22semidirect
27. #10622181C22semidirect
28. #10622178C22semidirect
123. C2×#563D11semidirect
165. #563C2×D11semidirect
246. C2×C11#1657semidirect
297. C11C2×#1657semidirect
348. C2#13067914direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226712
C2×#106226802
#130679142
C2×#106221812
C2×#106221782
C2×C11×#5632
C2×#165711