Finite Group Databasebeta

← C2×#10590063 #11796775

Subgroups — C2×#10590063 #11796775

Order 1152.

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

normal subgroups only

This group has 410 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
2C22×#3708C211yesmaximal, characteristic, complemented
3C2×#63578C211yesmaximal, characteristic, complemented
4#10590063C214yesmaximal, direct product factor
5C2×C3×#235—21no—
6C22×C3⋊(C3⋊C8)C2211yescharacteristic
7C2×C3×#208—21no—
8C2×#3718C411yescharacteristic
9C2×#3715—21no—
10#63822—21no—
11#63822—21no—
12#63822C412yes—
13#63822C2212yes—
14C2×#3713C411yescharacteristic
15C2×#3708—21no—
16C2×#3708—21no—
17C2×#3708C2212yescomplemented
18#63578—21no—
19#63578C2212yescomplemented
20C2×#950—61no—
21C2×#822—61no—
22C22×C32×C4D411yescharacteristic
23C2×C3×#67—41no—
24C3×#235—22no—
25C3×#235—22no—
26C3×#235—41no—
27C3×#235—41no—
28C2×C3×D12—21no—
29C2×C3×C4×D3—41no—
30C2×C3×Dic6—21no—
31C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
32C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
33C2×C3⋊(C3⋊C8)D411yescharacteristic
34C2×C3⋊(C3⋊C8)D411yescharacteristic
35C2×C3⋊(C3⋊C8)D411yescharacteristic
36C2×C3⋊(C3⋊C8)C2311yescharacteristic
37C3×#208—22no—
38C3×#208—41no—
39C2×C3×C3⋊C8—41no—
40#3718—21no—
41#3718C2×C412yes—
42#3715—22no—
43#3715—22no—
44#3713—21no—
45#3713C2×C412yes—
46#3708—22no—
47C2×#359—91nomaximal, Sylow
48C2×C3×#41—61no—
49C2×#235—21no—
50C2×C3×M16—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×#208—21no—
60C22×C3⋊C8—61no—
61C22×C3⋊C8—61no—
62#822—62no—
63#822—62no—
64C23×C32SD1611yescharacteristic
65C22×C3×D3—41no—
66C2×C32×C4C22⋊C411yescharacteristic
67C2×C32×C4C22⋊C411yescharacteristic
68C2×C32×C4D811yescharacteristic
69C2×C32×C4D811yescharacteristic
70C2×C32×C4SD1611yescharacteristic
71C2×C32×C4C2×D411yescharacteristic
72C3×#67—42no—
73C3×#67—42no—
74C2×C3×Dic3—41no—
75C3×D12—22no—
76C3×D12—41no—
77C3×C4×D3—42no—
78C3×C4×D3—42no—
79C3×Dic6—22no—
80C3×Dic6—41no—
81C3⋊(C3⋊C8)C22⋊C411yescharacteristic
82C3⋊(C3⋊C8)C22⋊C411yescharacteristic
83C3⋊(C3⋊C8)C22×C411yescharacteristic
84C3⋊(C3⋊C8)C2×D411yescharacteristic
85C3×C3⋊C8—42no—
86C2×#135—91no—
87C22×C16—91no—
88C2×#108—91no—
89#359—94no—
90C3×#41—62no—
91C3×#41—62no—
92C3×#41—121no—
93C3×#41—121no—
94C2×C3×Q8—61no—
95C2×C3×D4—61no—
96C2×C3×D4—121no—
97C22×C3×C4—21no—
98C22×C3×C4—21no—
99C22×C3×C4—121no—
100C2×#67—41no—
101#235—22no—
102#235—22no—
103#235—41no—
104#235—41no—
105C2×D12—21no—
106C2×C4×D3—41no—
107C2×Dic6—21no—
108C3×M16—62no—
109C3×M16—121no—
110C2×C3×C8—121no—
111#216—62no—
112#216—62no—
113#215—62no—
114#215—62no—
115#214—62no—
116#214—62no—
117#213—62no—
118#213—62no—
119#208—22no—
120#208—41no—
121C2×C3⋊C8—41no—
122C2×C3⋊C8—61no—
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—
134C22×C32—22no—
135C22×C32#10211yescharacteristic
136C22×C32#10211yescharacteristic
137C22×C32C2×SD1611yescharacteristic
138C2×C3×D3—42no—
139C2×C3×D3—82no—
140C32×C4#10211yescharacteristic
141C32×C4#10211yescharacteristic
142C32×C4C2×C22⋊C411yescharacteristic
143C32×C4C2×D811yescharacteristic
144C3×Dic3—42no—
145C2×#41—61no—
146#135—92no—
147#135—92no—
148#135—181no—
149#135—181no—
150C2×Q16—91no—
151C2×SD16—181no—
152C2×D8—91no—
153C2×M16—61no—
154C22×C8—91no—
155C2×C16—92no—
156C2×C16—181no—
157C2×C16—181no—
158#108—92no—
159#108—181no—
160C23×C3—21no—
161C23×C3—21no—
162C23×C3—121no—
163C22×D3—41no—
164C3×Q8—62no—
165C3×Q8—121no—
166C3×D4—62no—
167C3×D4—121no—
168C3×D4—122no—
169C3×D4—122no—
170C2×C3×C4—21no—
171C2×C3×C4—21no—
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—122no—
183C2×C3×C4—122no—
184C2×C3×C4—121no—
185#67—42no—
186#67—42no—
187C2×Dic3—41no—
188D12—22no—
189D12—41no—
190C4×D3—42no—
191C4×D3—42no—
192Dic6—22no—
193Dic6—41no—
194C3×C8—122no—
195C3⋊C8—42no—
196C3⋊C8—61no—
197C3⋊C8—61no—
198C3⋊C8—61no—
199C3⋊C8—61no—
200C3⋊C8—61no—
201C3⋊C8—61no—
202C3⋊C8—61no—
203C3⋊C8—61no—
204C2×C32—21no—
205C2×C32—21no—
206C2×C32#35912yescomplemented
207C2×C32C2×#10211yescharacteristic
208C3×D3—82no—
209#41—62no—
210#41—62no—
211#41—121no—
212#41—121no—
213C2×Q8—61no—
214C2×D4—61no—
215C2×D4—121no—
216C22×C4—121no—
217C22×C4GO+(4,𝔽2)11yescharacteristic
218Q16—92no—
219Q16—181no—
220SD16—182no—
221SD16—182no—
222D8—92no—
223D8—181no—
224M16—62no—
225M16—121no—
226C2×C8—91no—
227C2×C8—91no—
228C2×C8—91no—
229C2×C8—91no—
230C2×C8—91no—
231C2×C8—91no—
232C2×C8—121no—
233C16—182no—
234C22×C3—21no—
235C22×C3—21no—
236C22×C3—21no—
237C22×C3—21no—
238C22×C3—21no—
239C22×C3—21no—
240C22×C3—42no—
241C22×C3—42no—
242C22×C3—122no—
243C22×C3—242no—
244C2×D3—42no—
245C2×D3—82no—
246C3×C4—21no—
247C3×C4—21no—
248C3×C4—21no—
249C3×C4—21no—
250C3×C4—21no—
251C3×C4—21no—
252C3×C4—21no—
253C3×C4—21no—
254C3×C4—122no—
255Dic3—42no—
256C32C2×#35911yescharacteristic, complemented, Sylow
257C23—121no—
258C23#377511yescharacteristic
259Q8—62no—
260Q8—121no—
261D4—62no—
262D4—122no—
263D4—122no—
264D4—121no—
265C2×C4—121no—
266C2×C4—122no—
267C2×C4—122no—
268C2×C4D32⋊C411yescharacteristic
269C2×C4D32⋊C411yescharacteristic
270C2×C4#377411yescharacteristic
271C2×C4#377411yescharacteristic
272C2×C4#377511yescharacteristic
273C2×C4C2×GO+(4,𝔽2)11yescharacteristic
274C8—91no—
275C8—91no—
276C8—91no—
277C8—91no—
278C8—122no—
279C2×C3—22no—
280C2×C3—22no—
281C2×C3—21no—
282C2×C3—21no—
283C2×C3—41no—
284C2×C3—41no—
285C2×C3—41no—
286C2×C3—41no—
287C2×C3—242no—
288D3—82no—
289C22—22no—
290C22—122no—
291C22—242no—
292C22#6373911yescharacteristic
293C22#6373911yescharacteristic
294C22C2×#377511yescharacteristic
295C4—122no—
296C4#6373911yescharacteristic
297C4#6373911yescharacteristic
298C4C2×D32⋊C411yescharacteristic
299C4C2×#377411yescharacteristic
300C3—21no—
301C3—21no—
302C2—21no—
303C2—21no—
304C2—242no—
305C2#1059006312yesdirect product factor
306C2C2×#6373911yescharacteristic
subgroupG/H
centerC2×C4#3774
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×#359
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C22×#3708C2semidirect
3. C2×#63578C2semidirect
4. #10590063C2direct (N × H)
17. C2×#3708C22semidirect
19. #63578C22semidirect
206. C2×C32#359semidirect
256. C32C2×#359semidirect
305. C2#10590063direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#638222
C22×#37082
C2×#635782
#105900632
C2×#3599