Finite Group Databasebeta

← C2×#13067971 #14736002

Subgroups — C2×#13067971 #14736002

Order 2816.

958 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622308C211yesmaximal, characteristic, complemented
2C2×#10622628C212yesmaximal, complemented
3#13067971C218yesmaximal, direct product factor
4C2×#10622096C211yesmaximal, characteristic, complemented
5C2×#10622123C212yesmaximal, complemented
6C2×C8×D4×C11C211yesmaximal, characteristic, complemented
7C23×C8×C11—21no—
8C2×C4×D4×C11C2211yescharacteristic
9C22×#4323—22no—
10C22×D88—21no—
11C22×D88—21no—
12C2×#66927C2212yes—
13C8×D4×C11—22no—
14C8×D4×C11C2214yescomplemented
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C11×C22⋊C8—21no—
17C2×C4×C8×C11C2211yescharacteristic
18#10622628—24no—
19#10622628C2218yescomplemented
20C2×#66873—22no—
21C2×C4⋊(C11⋊C8)C2212yes—
22#10622308—22no—
23#10622308C2214yescomplemented
24#10622123C2218yescomplemented
25#10622096C2214yescomplemented
26C22×D4×C11D411yescharacteristic
27C23×C4×C11—21no—
28C22×D44—22no—
29C22×D44—22no—
30C22×D44—22no—
31C22×C8×C11—21no—
32C22×C8×C11—24no—
33C22×C8×C11—44no—
34C22×C8×C11D411yescharacteristic
35C22×C8×C11D411yescharacteristic
36C4×D4×C11—21no—
37C4×D4×C11—21no—
38C4×D4×C11D412yes—
39C4×D4×C11C2312yes—
40C2×C11×C4⋊C4D411yescharacteristic
41C2×C11×C22⋊C4—21no—
42C2×C42×C11C2311yescharacteristic
43C2×#4323—28no—
44C2×#4323—48no—
45C22×C11⋊C8—22no—
46C2×D88—24no—
47C2×D88—24no—
48C2×D88—44no—
49C2×D88—44no—
50#66927—22no—
51#66927—22no—
52#66927—22no—
53#66927C2314yes—
54C11×C4⋊C8—21no—
55C11×C4⋊C8C2312yes—
56C11×C22⋊C8—24no—
57C4×C8×C11D412yes—
58C4×C8×C11C2312yes—
59#66873—28no—
60C4⋊(C11⋊C8)—22no—
61C4⋊(C11⋊C8)C2314yes—
62C2×#1667—111nomaximal, Sylow
63C24×C11—21no—
64C23×D11—42no—
65C2×D4×C11—21no—
66C2×D4×C11—22no—
67C2×D4×C11D814yescomplemented
68C2×D4×C11C2×D412yes—
69C22×C4×C11—21no—
70C22×C4×C11—22no—
71C22×C4×C11—22no—
72C22×C4×C11—42no—
73C22×C4×C11—42no—
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11#4111yescharacteristic
77C2×D44—24no—
78C2×D44—24no—
79C2×D44—24no—
80C2×D44—42no—
81C2×D44—42no—
82C2×D44—42no—
83C2×D44—44no—
84C2×D44—44no—
85C2×D44—44no—
86C2×D44—44no—
87C2×D44—84no—
88C2×C8×C11—22no—
89C2×C8×C11—22no—
90C2×C8×C11—48no—
91C2×C8×C11—42no—
92C2×C8×C11D814yescomplemented
93C2×C8×C11C2×D412yes—
94C2×C8×C11C2×D412yes—
95C11×C4⋊C4—21no—
96C11×C4⋊C4C2×D412yes—
97C11×C22⋊C4—22no—
98C11×C22⋊C4—22no—
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11#4111yescharacteristic
102C42×C11C2411yescharacteristic
103#4323—416no—
104C2×C11⋊C8—24no—
105C2×C11⋊C8—44no—
106D88—48no—
107D88—48no—
108C2×#493—111no—
109C2×#459—112no—
110C2×C8×D4D1111yescharacteristic, complemented
111#1667—118no—
112C2×#335—111no—
113C2×#331—112no—
114C23×C11—22no—
115C23×C11—24no—
116C23×C11—42no—
117C23×C11—42no—
118C23×C11#12111yescharacteristic
119C22×D11—44no—
120C22×D11—84no—
121C22×D11—84no—
122C22×D11—84no—
123D4×C11—22no—
124D4×C11—24no—
125D4×C11C2×D814yescomplemented
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—42no—
129C2×C4×C11—42no—
130C2×C4×C11—42no—
131C2×C4×C11—44no—
132C2×C4×C11#12111yescharacteristic
133C2×C4×C11#12111yescharacteristic
134C2×C4×C11#12111yescharacteristic
135C2×C4×C11C2×D812yes—
136C2×C4×C11C2×D812yes—
137C2×C4×C11#13512yes—
138C2×C4×C11AGL(1,ℤ/8)12yes—
139C2×C4×C11C22×D411yescharacteristic
140C2×C4×C11C22×D411yescharacteristic
141C2×C4×C11C2×#4111yescharacteristic
142D44—44no—
143D44—44no—
144D44—44no—
145D44—44no—
146D44—84no—
147D44—84no—
148D44—84no—
149D44—84no—
150C8×C11—22no—
151C8×C11—42no—
152C8×C11C2×D814yescomplemented
153C11⋊C8—44no—
154C22×D8—222no—
155C22×D8—221no—
156C22×D8—221no—
157C23×C8—21no—
158C2×#127—112no—
159C2×C4×D4C2×D1111yescharacteristic
160#493—114no—
161#493—222no—
162#459—118no—
163#459—224no—
164C8×D4—22no—
165C8×D4C2×D1114yescomplemented
166C2×C4⋊C8—112no—
167C2×C4⋊C8C2×D1111yescharacteristic
168C2×#102—222no—
169C2×C22⋊C8—21no—
170C2×C4×C8C2×D1111yescharacteristic
171#335—114no—
172#331—118no—
173C22×C11—24no—
174C22×C11—48no—
175C22×C11—42no—
176C22×C11—42no—
177C22×C11#45912yes—
178C22×C11#46612yes—
179C22×C11#47212yes—
180C22×C11C2×#12111yescharacteristic
181C2×D11—84no—
182C2×D11—84no—
183C2×D11—84no—
184C2×D11—168no—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—42no—
188C4×C11#45912yes—
189C4×C11#46612yes—
190C4×C11C22×D811yescharacteristic
191C4×C11C22×D811yescharacteristic
192C4×C11C2×#13511yescharacteristic
193C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
194C22×D4—222no—
195C22×D4—222no—
196C22×D4—222no—
197C22×D4D4411yescharacteristic
198C23×C4—21no—
199C2×D8—228no—
200C2×D8—224no—
201C2×D8—224no—
202C2×D8—444no—
203C2×D8—448no—
204C2×D8—444no—
205C22×C8—21no—
206C22×C8—24no—
207C22×C8—44no—
208C22×C8—222no—
209C22×C8C22⋊D1111yescharacteristic
210C22×C8C22⋊D1111yescharacteristic
211#127—114no—
212#127—222no—
213#127—222no—
214#127—222no—
215C4×D4—21no—
216C4×D4—21no—
217C4×D4D4412yes—
218C4×D4C22×D1112yes—
219C2×C4⋊C4D4411yescharacteristic
220C2×C22⋊C4—21no—
221C2×C42C22×D1111yescharacteristic
222C4⋊C8—21no—
223C4⋊C8—114no—
224C4⋊C8—222no—
225C4⋊C8C22×D1112yes—
226#102—228no—
227C22⋊C8—24no—
228C4×C8C22⋊D1112yes—
229C4×C8C22×D1112yes—
230C2×C11—44no—
231C2×C11#166714yescomplemented
232C2×C11C2×#45911yescharacteristic
233C2×C11C2×#46611yescharacteristic
234C2×C11C2×#47211yescharacteristic
235D11—164no—
236C24—21no—
237C24—442no—
238C2×D4—22no—
239C2×D4—21no—
240C2×D4—224no—
241C2×D4—224no—
242C2×D4—224no—
243C2×D4—444no—
244C2×D4—444no—
245C2×D4—442no—
246C2×D4—442no—
247C2×D4—442no—
248C2×D4—444no—
249C2×D4—444no—
250C2×D4—884no—
251C2×D4D8814yescomplemented
252C2×D4C2×D4412yes—
253C22×C4—21no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4C2×D4411yescharacteristic
259C22×C4#433911yescharacteristic
260C22×C4C2×C22⋊D1111yescharacteristic
261D8—448no—
262D8—4416no—
263D8—448no—
264C2×C8—22no—
265C2×C8—22no—
266C2×C8—42no—
267C2×C8—48no—
268C2×C8—224no—
269C2×C8—444no—
270C2×C8#432314yescomplemented
271C2×C8C2×C22⋊D1112yes—
272C2×C8C2×C22⋊D1112yes—
273C4⋊C4—21no—
274C4⋊C4C2×D4412yes—
275C22⋊C4—22no—
276C22⋊C4—22no—
277C42C2×D4411yescharacteristic
278C42#433911yescharacteristic
279C42C2×C22⋊D1111yescharacteristic
280C42C23×D1111yescharacteristic
281C11C2×#166711yescharacteristic, complemented, Sylow
282C23—24no—
283C23—22no—
284C23—42no—
285C23—42no—
286C23—444no—
287C23—884no—
288C23—884no—
289C23—884no—
290C23#6698311yescharacteristic
291D4—24no—
292D4—22no—
293D4—444no—
294D4—444no—
295D4—444no—
296D4—444no—
297D4—884no—
298D4—884no—
299D4—884no—
300D4—884no—
301D4C2×D8814yescomplemented
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—44no—
308C2×C4C2×D8812yes—
309C2×C4#6695712yes—
310C2×C4#6698311yescharacteristic
311C2×C4#6698311yescharacteristic
312C2×C4#6698311yescharacteristic
313C2×C4C2×#432312yes—
314C2×C4#6700212yes—
315C2×C4C22×D4411yescharacteristic
316C2×C4C2×#433911yescharacteristic
317C2×C4C22×C22⋊D1111yescharacteristic
318C8—22no—
319C8—42no—
320C8—444no—
321C8C2×#432314yescomplemented
322C22—24no—
323C22—42no—
324C22—42no—
325C22—48no—
326C22—884no—
327C22—884no—
328C22—884no—
329C22—1768no—
330C22#1062262812yes—
331C22#1062272812yes—
332C22#1062275512yes—
333C22C2×#6698311yescharacteristic
334C4—21no—
335C4—21no—
336C4—42no—
337C4#1062262812yes—
338C4#1062272812yes—
339C4C22×D8811yescharacteristic
340C4C2×#6695711yescharacteristic
341C4C22×#432311yescharacteristic
342C4C2×#6700211yescharacteristic
343C2—44no—
344C2—1764no—
345C2#1306797114yesdirect product factor
346C2C2×#1062262811yescharacteristic
347C2C2×#1062272811yescharacteristic
348C2C2×#1062275511yescharacteristic
subgroupG/H
centerC23#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C8×D4×C11C2
socleC23×C11#121
hypercenterC2×C8×D4D11
hypocenterC11C2×#1667
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
1. C2×#10622308C2semidirect
2. C2×#10622628C2semidirect
3. #13067971C2direct (N × H)
4. C2×#10622096C2semidirect
5. C2×#10622123C2semidirect
6. C2×C8×D4×C11C2semidirect
14. C8×D4×C11C22semidirect
19. #10622628C22semidirect
23. #10622308C22semidirect
24. #10622123C22semidirect
25. #10622096C22semidirect
67. C2×D4×C11D8semidirect
92. C2×C8×C11D8semidirect
110. C2×C8×D4D11semidirect
125. D4×C11C2×D8semidirect
152. C8×C11C2×D8semidirect
165. C8×D4C2×D11semidirect
231. C2×C11#1667semidirect
251. C2×D4D88semidirect
270. C2×C8#4323semidirect
281. C11C2×#1667semidirect
301. D4C2×D88semidirect
321. C8C2×#4323semidirect
345. C2#13067971direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106223082
C2×#106226282
#130679712
C2×#106220962
C2×#106221232
C2×C8×D4×C112
C2×#166711