Finite Group Databasebeta

← C2×#10590064 #11796835

Subgroups — C2×#10590064 #11796835

Order 1152.

430 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 71 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×#63822C211yesmaximal, characteristic
2C2×#63773C211yesmaximal, characteristic, complemented
3C2×#63574C211yesmaximal, characteristic, complemented
4#10590064C214yesmaximal, direct product factor
5C2×C3×#235—21no—
6C22×C3⋊(C3⋊C8)C2211yescharacteristic
7C2×C3×C4⋊Dic3—21no—
8C2×#3718C411yescharacteristic, complemented
9C2×#3715—21no—
10#63822—21no—
11#63822—21no—
12#63822C412yescomplemented
13#63822C2212yes—
14C2×#3713C411yescharacteristic, complemented
15#63773—21no—
16#63773C2212yescomplemented
17C2×#3708—21no—
18#63574—21no—
19#63574C2212yescomplemented
20C2×#950—61no—
21C2×#808—61no—
22C22×C32×C4D411yescharacteristic
23C2×C3×#67—41no—
24C22×C3×Dic3—41no—
25C3×#235—22no—
26C3×#235—22no—
27C3×#235—41no—
28C3×#235—41no—
29C2×C3×D12—21no—
30C2×C3×C4×D3—41no—
31C2×C3×Dic6—21no—
32C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
33C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
34C2×C3⋊(C3⋊C8)D411yescharacteristic
35C2×C3⋊(C3⋊C8)D411yescharacteristic
36C2×C3⋊(C3⋊C8)D411yescharacteristic
37C2×C3⋊(C3⋊C8)C2311yescharacteristic
38C3×C4⋊Dic3—22no—
39C3×C4⋊Dic3—41no—
40#3718—21no—
41#3718C2×C412yescomplemented
42#3715—22no—
43#3715—22no—
44#3713—21no—
45#3713C2×C412yescomplemented
46#3708—22no—
47C2×#360—91nomaximal, Sylow
48C2×C3×#41—61no—
49C2×#235—21no—
50C2×C3×C4⋊C4—61no—
51#950—62no—
52#950—62no—
53#950—62no—
54#950—62no—
55C2×#216—61no—
56C2×#215—61no—
57C2×#214—61no—
58C2×#213—61no—
59C2×C4⋊Dic3—21no—
60C22×C3⋊C8—61no—
61C22×C3⋊C8—61no—
62#808—62no—
63#808—62no—
64C23×C32D811yescharacteristic
65C22×C3×D3—41no—
66C2×C32×C4C22⋊C411yescharacteristic
67C2×C32×C4C22⋊C411yescharacteristic
68C2×C32×C4D811yescharacteristic
69C2×C32×C4SD1611yescharacteristic
70C2×C32×C4SD1611yescharacteristic
71C2×C32×C4C2×D411yescharacteristic
72C3×#67—42no—
73C3×#67—42no—
74C2×C3×Dic3—41no—
75C2×C3×Dic3—42no—
76C2×C3×Dic3—82no—
77C3×D12—22no—
78C3×D12—41no—
79C3×C4×D3—42no—
80C3×C4×D3—42no—
81C3×Dic6—22no—
82C3×Dic6—41no—
83C3⋊(C3⋊C8)C22⋊C411yescharacteristic
84C3⋊(C3⋊C8)C22⋊C411yescharacteristic
85C3⋊(C3⋊C8)C22×C411yescharacteristic
86C3⋊(C3⋊C8)C2×D411yescharacteristic
87C2×#135—91no—
88C2×M32—91no—
89C2×#106—91no—
90#360—94no—
91C3×#41—62no—
92C3×#41—62no—
93C3×#41—121no—
94C3×#41—121no—
95C2×C3×Q8—61no—
96C2×C3×D4—61no—
97C2×C3×D4—121no—
98C22×C3×C4—21no—
99C22×C3×C4—21no—
100C22×C3×C4—121no—
101C22×C3×C4—121no—
102C2×#67—41no—
103C22×Dic3—41no—
104#235—22no—
105#235—22no—
106#235—41no—
107#235—41no—
108C2×D12—21no—
109C2×C4×D3—41no—
110C2×Dic6—21no—
111C3×C4⋊C4—62no—
112C3×C4⋊C4—121no—
113#216—62no—
114#216—62no—
115#215—62no—
116#215—62no—
117#214—62no—
118#214—62no—
119#213—62no—
120#213—62no—
121C4⋊Dic3—22no—
122C4⋊Dic3—41no—
123C2×C3⋊C8—61no—
124C2×C3⋊C8—61no—
125C2×C3⋊C8—61no—
126C2×C3⋊C8—61no—
127C2×C3⋊C8—61no—
128C2×C3⋊C8—61no—
129C2×C3⋊C8—61no—
130C2×C3⋊C8—61no—
131C2×C3⋊C8—61no—
132C2×C3⋊C8—61no—
133C2×C3⋊C8—61no—
134C2×C3⋊C8—61no—
135C22×C32—22no—
136C22×C32#10211yescharacteristic
137C22×C32#10211yescharacteristic
138C22×C32C2×D811yescharacteristic
139C2×C3×D3—42no—
140C2×C3×D3—82no—
141C32×C4#10211yescharacteristic
142C32×C4#10211yescharacteristic
143C32×C4C2×C22⋊C411yescharacteristic
144C32×C4C2×SD1611yescharacteristic
145C3×Dic3—42no—
146C3×Dic3—82no—
147C2×#41—61no—
148#135—92no—
149#135—92no—
150#135—181no—
151#135—181no—
152C2×Q16—91no—
153C2×SD16—181no—
154C2×D8—91no—
155C22×C8—91no—
156C2×C4⋊C4—61no—
157M32—92no—
158M32—181no—
159C2×C16—181no—
160#106—92no—
161#106—181no—
162C23×C3—21no—
163C23×C3—21no—
164C23×C3—121no—
165C22×D3—41no—
166C3×Q8—62no—
167C3×Q8—121no—
168C3×D4—62no—
169C3×D4—121no—
170C3×D4—122no—
171C3×D4—122no—
172C2×C3×C4—21no—
173C2×C3×C4—21no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4—122no—
185C2×C3×C4—122no—
186C2×C3×C4—121no—
187C2×C3×C4—122no—
188C2×C3×C4—242no—
189#67—42no—
190#67—42no—
191C2×Dic3—41no—
192C2×Dic3—42no—
193C2×Dic3—82no—
194D12—22no—
195D12—41no—
196C4×D3—42no—
197C4×D3—42no—
198Dic6—22no—
199Dic6—41no—
200C3⋊C8—61no—
201C3⋊C8—61no—
202C3⋊C8—61no—
203C3⋊C8—61no—
204C3⋊C8—61no—
205C3⋊C8—61no—
206C3⋊C8—61no—
207C3⋊C8—61no—
208C2×C32—21no—
209C2×C32—21no—
210C2×C32#36012yescomplemented
211C2×C32C2×#10211yescharacteristic
212C3×D3—82no—
213#41—62no—
214#41—62no—
215#41—121no—
216#41—121no—
217C2×Q8—61no—
218C2×D4—61no—
219C2×D4—121no—
220C22×C4—121no—
221C22×C4—121no—
222C22×C4GO+(4,𝔽2)11yescharacteristic
223Q16—92no—
224Q16—181no—
225SD16—182no—
226SD16—182no—
227D8—92no—
228D8—181no—
229C2×C8—91no—
230C2×C8—91no—
231C2×C8—91no—
232C2×C8—91no—
233C2×C8—91no—
234C2×C8—91no—
235C4⋊C4—62no—
236C4⋊C4—121no—
237C16—182no—
238C22×C3—22no—
239C22×C3—22no—
240C22×C3—21no—
241C22×C3—21no—
242C22×C3—21no—
243C22×C3—21no—
244C22×C3—21no—
245C22×C3—21no—
246C22×C3—42no—
247C22×C3—122no—
248C22×C3—242no—
249C2×D3—42no—
250C2×D3—82no—
251C3×C4—21no—
252C3×C4—21no—
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—21no—
256C3×C4—21no—
257C3×C4—21no—
258C3×C4—21no—
259C3×C4—122no—
260C3×C4—242no—
261Dic3—42no—
262Dic3—82no—
263C32C2×#36011yescharacteristic, complemented, Sylow
264C23—121no—
265C23#377411yescharacteristic
266Q8—62no—
267Q8—121no—
268D4—62no—
269D4—122no—
270D4—122no—
271D4—121no—
272C2×C4—121no—
273C2×C4—122no—
274C2×C4—122no—
275C2×C4—122no—
276C2×C4—242no—
277C2×C4D32⋊C411yescharacteristic
278C2×C4D32⋊C411yescharacteristic
279C2×C4#377411yescharacteristic
280C2×C4#377511yescharacteristic
281C2×C4#377511yescharacteristic
282C2×C4C2×GO+(4,𝔽2)11yescharacteristic
283C8—91no—
284C8—91no—
285C8—91no—
286C8—91no—
287C2×C3—21no—
288C2×C3—21no—
289C2×C3—22no—
290C2×C3—22no—
291C2×C3—22no—
292C2×C3—21no—
293C2×C3—21no—
294C2×C3—41no—
295C2×C3—41no—
296C2×C3—242no—
297D3—82no—
298C22—22no—
299C22—122no—
300C22—242no—
301C22#6373911yescharacteristic
302C22#6373911yescharacteristic
303C22C2×#377411yescharacteristic
304C4—122no—
305C4—242no—
306C4#6373911yescharacteristic
307C4#6373911yescharacteristic
308C4C2×D32⋊C411yescharacteristic
309C4C2×#377511yescharacteristic
310C3—21no—
311C3—21no—
312C2—21no—
313C2—21no—
314C2—242no—
315C2#1059006412yesdirect product factor
316C2C2×#6373911yescharacteristic
subgroupG/H
centerC22#63739
commutatorC3⋊(C3⋊C8)C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32#102
prime radicalC2×#63822C2
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#360
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#63773C2semidirect
3. C2×#63574C2semidirect
4. #10590064C2direct (N × H)
8. C2×#3718C4semidirect
12. #63822C4semidirect
14. C2×#3713C4semidirect
16. #63773C22semidirect
19. #63574C22semidirect
41. #3718C2×C4semidirect
45. #3713C2×C4semidirect
210. C2×C32#360semidirect
263. C32C2×#360semidirect
315. C2#10590064direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#638222
C2×#637732
C2×#635742
#105900642
C2×#3609