Finite Group Databasebeta

← #11796959

Subgroups — #11796959

Order 1152.

406 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 67 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×#63578C211yesmaximal, characteristic, complemented
4#10590066C212yesmaximal, complemented
5#10590065C212yesmaximal, complemented
6C2×C3×#235—21no—
7C22×C3⋊(C3⋊C8)C2211yescharacteristic
8C2×C3×#208—21no—
9C2×#3718C2211yescharacteristic
10C2×#3715—21no—
11#63822—21no—
12#63822—21no—
13#63822C412yes—
14#63822C412yes—
15C2×#3713C2211yescharacteristic
16#63773—21no—
17#63773C2212yes—
18C2×#3708—21no—
19#63578—21no—
20#63578C2212yes—
21C2×#950—61no—
22C2×#822—61no—
23C22×C32×C4D411yescharacteristic
24C2×C3×#67—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×#208—22no—
39C3×#208—41no—
40C2×C3×C3⋊C8—41no—
41#3718—21no—
42#3718C2×C412yes—
43#3715—22no—
44#3715—22no—
45#3713—21no—
46#3713C2×C412yes—
47#3708—22no—
48#2148—91nomaximal, Sylow
49C2×C3×#41—61no—
50C2×#235—21no—
51C2×C3×M16—61no—
52#950—62no—
53#950—62no—
54#950—62no—
55#950—62no—
56C2×#216—61no—
57C2×#215—61no—
58C2×#214—61no—
59C2×#213—61no—
60C2×#208—21no—
61C22×C3⋊C8—61no—
62C22×C3⋊C8—61no—
63#822—62no—
64#822—62no—
65C23×C32SD1611yescharacteristic
66C22×C3×D3—41no—
67C2×C32×C4C22⋊C411yescharacteristic
68C2×C32×C4C22⋊C411yescharacteristic
69C2×C32×C4D811yescharacteristic
70C2×C32×C4D811yescharacteristic
71C2×C32×C4SD1611yescharacteristic
72C2×C32×C4C2×D411yescharacteristic
73C3×#67—42no—
74C3×#67—42no—
75C2×C3×Dic3—41no—
76C3×D12—22no—
77C3×D12—41no—
78C3×C4×D3—42no—
79C3×C4×D3—42no—
80C3×Dic6—22no—
81C3×Dic6—41no—
82C3⋊(C3⋊C8)C22⋊C411yescharacteristic
83C3⋊(C3⋊C8)C22⋊C411yescharacteristic
84C3⋊(C3⋊C8)C22×C411yescharacteristic
85C3⋊(C3⋊C8)C2×D411yescharacteristic
86C3×C3⋊C8—42no—
87C2×#135—91no—
88C2×M32—91no—
89C2×#108—91no—
90#362—92no—
91#361—92no—
92C3×#41—62no—
93C3×#41—62no—
94C3×#41—121no—
95C3×#41—121no—
96C2×C3×Q8—61no—
97C2×C3×D4—61no—
98C2×C3×D4—121no—
99C22×C3×C4—21no—
100C22×C3×C4—21no—
101C22×C3×C4—121no—
102C2×#67—41no—
103#235—22no—
104#235—22no—
105#235—41no—
106#235—41no—
107C2×D12—21no—
108C2×C4×D3—41no—
109C2×Dic6—21no—
110C3×M16—62no—
111C3×M16—121no—
112C2×C3×C8—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—
121#208—22no—
122#208—41no—
123C2×C3⋊C8—41no—
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—
135C2×C3⋊C8—61no—
136C22×C32—41no—
137C22×C32#10211yescharacteristic
138C22×C32#10211yescharacteristic
139C22×C32C2×SD1611yescharacteristic
140C2×C3×D3—42no—
141C2×C3×D3—82no—
142C32×C4#10211yescharacteristic
143C32×C4#10211yescharacteristic
144C32×C4C2×C22⋊C411yescharacteristic
145C32×C4C2×D811yescharacteristic
146C3×Dic3—42no—
147C2×#41—61no—
148#135—92no—
149#135—92no—
150#135—181no—
151#135—181no—
152C2×Q16—91no—
153C2×SD16—181no—
154C2×D8—91no—
155C2×M16—61no—
156C22×C8—91no—
157M32—92no—
158M32—181no—
159C2×C16—181no—
160#108—92no—
161#108—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—
187#67—42no—
188#67—42no—
189C2×Dic3—41no—
190D12—22no—
191D12—41no—
192C4×D3—42no—
193C4×D3—42no—
194Dic6—22no—
195Dic6—41no—
196C3×C8—122no—
197C3⋊C8—42no—
198C3⋊C8—61no—
199C3⋊C8—61no—
200C3⋊C8—61no—
201C3⋊C8—61no—
202C3⋊C8—61no—
203C3⋊C8—61no—
204C3⋊C8—61no—
205C3⋊C8—61no—
206C2×C32—21no—
207C2×C32—21no—
208C2×C32—21no—
209C2×C32C2×#10211yescharacteristic
210C3×D3—82no—
211#41—62no—
212#41—62no—
213#41—121no—
214#41—121no—
215C2×Q8—61no—
216C2×D4—61no—
217C2×D4—121no—
218C22×C4—121no—
219C22×C4GO+(4,𝔽2)11yescharacteristic
220Q16—92no—
221Q16—181no—
222SD16—182no—
223SD16—182no—
224D8—92no—
225D8—181no—
226M16—62no—
227M16—121no—
228C2×C8—91no—
229C2×C8—91no—
230C2×C8—91no—
231C2×C8—91no—
232C2×C8—91no—
233C2×C8—91no—
234C2×C8—121no—
235C16—182no—
236C22×C3—21no—
237C22×C3—21no—
238C22×C3—21no—
239C22×C3—21no—
240C22×C3—21no—
241C22×C3—21no—
242C22×C3—42no—
243C22×C3—42no—
244C22×C3—122no—
245C22×C3—242no—
246C2×D3—42no—
247C2×D3—82no—
248C3×C4—21no—
249C3×C4—21no—
250C3×C4—21no—
251C3×C4—21no—
252C3×C4—21no—
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—21no—
256C3×C4—122no—
257Dic3—42no—
258C32#214811yescharacteristic, complemented, Sylow
259C23—121no—
260C23#377511yescharacteristic
261Q8—62no—
262Q8—121no—
263D4—62no—
264D4—122no—
265D4—122no—
266D4—121no—
267C2×C4—121no—
268C2×C4—122no—
269C2×C4—122no—
270C2×C4D32⋊C411yescharacteristic
271C2×C4D32⋊C411yescharacteristic
272C2×C4#377411yescharacteristic
273C2×C4#377411yescharacteristic
274C2×C4#377511yescharacteristic
275C2×C4C2×GO+(4,𝔽2)11yescharacteristic
276C8—91no—
277C8—91no—
278C8—91no—
279C8—91no—
280C8—122no—
281C2×C3—22no—
282C2×C3—22no—
283C2×C3—21no—
284C2×C3—21no—
285C2×C3—41no—
286C2×C3—41no—
287C2×C3—41no—
288C2×C3—41no—
289C2×C3—242no—
290D3—82no—
291C22—41no—
292C22—122no—
293C22—242no—
294C22#6373911yescharacteristic
295C22#6373911yescharacteristic
296C22C2×#377511yescharacteristic
297C4—122no—
298C4#6373911yescharacteristic
299C4#6373911yescharacteristic
300C4C2×D32⋊C411yescharacteristic
301C4C2×#377411yescharacteristic
302C3—21no—
303C3—21no—
304C2—21no—
305C2—21no—
306C2—21no—
307C2—242no—
308C2C2×#6373911yescharacteristic
subgroupG/H
centerC4#63739
commutatorC3⋊(C3⋊C8)C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC2×C32C2×#102
prime radicalC2×#63822C2
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#2148
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#63773C2semidirect
3. C2×#63578C2semidirect
4. #10590066C2semidirect
5. #10590065C2semidirect
258. C32#2148semidirect

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×#635782
#105900662
#105900652
#21489