Finite Group Databasebeta

← #11796961

Subgroups — #11796961

Order 1152.

398 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 59 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
1#10594684C211yesmaximal, characteristic
2#10593771C211yesmaximal, characteristic, complemented
3C2×#63544C211yesmaximal, characteristic, complemented
4#10590021C212yesmaximal, complemented
5#10590020C212yesmaximal, complemented
6#64306—21no—
7#64283—21no—
8C2×C8×C3⋊D3C2211yescharacteristic
9C3×#904—21no—
10#63822C412yes—
11#63810—21no—
12#63809C412yes—
13#63802C2211yescharacteristic
14#63797C2211yescharacteristic
15#63796—21no—
16#63771C2212yes—
17#63770—21no—
18C2×C3×C3⋊C16—21no—
19#63544—21no—
20#63544C2212yes—
21D3×#135—61no—
22C2×#798—61no—
23C2×C4×C3⋊D3D411yescharacteristic
24C3×#235—22no—
25#3811—41no—
26#3805—41no—
27#3802—21no—
28C4×D32—41no—
29#3798—41no—
30#3797—21no—
31#3796—22no—
32#3792—41no—
33#3788—22no—
34#3787—41no—
35C2×C32×C8D411yescharacteristic
36C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
37C8×C3⋊D3C2×C411yescharacteristic
38C8×C3⋊D3D411yescharacteristic
39C8×C3⋊D3D411yescharacteristic
40C8×C3⋊D3C2311yescharacteristic
41C3×Dic12—21no—
42C3×D24—21no—
43C3×#204—22no—
44#3718C2×C412yes—
45#3715—22no—
46#3713C2×C412yes—
47C3×C3⋊C16—22no—
48#2148—91nomaximal, Sylow
49D3×#41—62no—
50C3×#135—61no—
51#950—62no—
52#919—61no—
53D3×Q16—61no—
54#916—62no—
55D3×SD16—62no—
56#912—61no—
57D3×D8—61no—
58#904—21no—
59C2×D3×C8—61no—
60C2×D3×C8—61no—
61C2×C3×C16—61no—
62C2×C3⋊C16—21no—
63#798—62no—
64#798—62no—
65C22×C3⋊D3SD1611yescharacteristic
66C2×D32—41no—
67C2×C32×C4C22⋊C411yescharacteristic
68C2×C3⋊Dic3D811yescharacteristic
69C4×C3⋊D3C22⋊C411yescharacteristic
70C4×C3⋊D3D811yescharacteristic
71C4×C3⋊D3SD1611yescharacteristic
72C4×C3⋊D3C2×D411yescharacteristic
73C3×#67—42no—
74C3×D12—22no—
75C3×C4×D3—42no—
76C3×Dic6—22no—
77#627—41no—
78#626—42no—
79#625—41no—
80#624—41no—
81D3×Dic3—42no—
82#622—42no—
83C32×C8C22⋊C411yescharacteristic
84C32×C8C2×D411yescharacteristic
85C3⋊(C3⋊C8)C22⋊C411yescharacteristic
86C3⋊(C3⋊C8)C22×C411yescharacteristic
87C2×#135—91no—
88C2×M32—91no—
89C2×#108—91no—
90#362—92no—
91#361—92no—
92C3×#41—62no—
93#239—62no—
94D3×Q8—62no—
95#237—62no—
96#237—122no—
97D3×D4—62no—
98D3×D4—122no—
99#235—22no—
100#235—122no—
101C2×C4×D3—61no—
102C2×C4×D3—61no—
103C2×C4×D3—122no—
104C3×Q16—61no—
105C3×SD16—62no—
106C3×D8—61no—
107C2×C3×C8—21no—
108C2×C3×C8—21no—
109#216—62no—
110#215—62no—
111#214—62no—
112#213—62no—
113C2×C3⋊C8—61no—
114C2×C3⋊C8—61no—
115Dic12—21no—
116D24—21no—
117#204—22no—
118D3×C8—61no—
119D3×C8—61no—
120D3×C8—61no—
121D3×C8—61no—
122D3×C8—61no—
123D3×C8—61no—
124D3×C8—61no—
125D3×C8—61no—
126C3×C16—62no—
127C3⋊C16—22no—
128C22×C32#10211yescharacteristic
129C2×C3⋊D3—41no—
130C2×C3⋊D3#10211yescharacteristic
131C2×C3⋊D3C2×SD1611yescharacteristic
132C2×C3×D3—42no—
133D32—82no—
134C32×C4#10211yescharacteristic
135C32×C4C2×C22⋊C411yescharacteristic
136C3⋊Dic3#10211yescharacteristic
137C3⋊Dic3C2×D811yescharacteristic
138C3×Dic3—42no—
139C2×#41—181no—
140#135—61no—
141#135—92no—
142#135—92no—
143#135—181no—
144C2×Q16—91no—
145C2×SD16—181no—
146C2×D8—91no—
147C2×M16—181no—
148C22×C8—91no—
149M32—92no—
150M32—181no—
151C2×C16—61no—
152#108—92no—
153#108—181no—
154C22×D3—61no—
155C22×D3—61no—
156C22×D3—122no—
157C3×Q8—62no—
158C3×D4—62no—
159C3×D4—122no—
160C2×C3×C4—21no—
161C2×C3×C4—21no—
162C2×C3×C4—122no—
163#67—42no—
164#67—122no—
165#67—122no—
166C2×Dic3—61no—
167C2×Dic3—61no—
168C2×Dic3—122no—
169D12—22no—
170D12—122no—
171C4×D3—42no—
172C4×D3—61no—
173C4×D3—61no—
174C4×D3—61no—
175C4×D3—61no—
176C4×D3—61no—
177C4×D3—61no—
178C4×D3—61no—
179C4×D3—61no—
180C4×D3—122no—
181C4×D3—122no—
182Dic6—22no—
183Dic6—122no—
184C3×C8—21no—
185C3×C8—21no—
186C3×C8—21no—
187C3×C8—21no—
188C3⋊C8—61no—
189C3⋊C8—61no—
190C3⋊C8—61no—
191C3⋊C8—61no—
192C2×C32—21no—
193C2×C32C2×#10211yescharacteristic
194C3⋊D3—21no—
195C3⋊D3—21no—
196C3×D3—82no—
197#41—62no—
198#41—182no—
199#41—361no—
200#41—361no—
201C2×Q8—181no—
202C2×D4—181no—
203C2×D4—361no—
204C22×C4—91no—
205C22×C4—361no—
206Q16—61no—
207Q16—92no—
208SD16—62no—
209SD16—182no—
210D8—61no—
211D8—92no—
212M16—182no—
213M16—361no—
214C2×C8—91no—
215C2×C8—91no—
216C2×C8—91no—
217C2×C8—91no—
218C2×C8—91no—
219C2×C8—361no—
220C2×C8GO+(4,𝔽2)11yescharacteristic
221C16—62no—
222C22×C3—21no—
223C22×C3—21no—
224C22×C3—122no—
225C2×D3—42no—
226C2×D3—61no—
227C2×D3—61no—
228C2×D3—61no—
229C2×D3—61no—
230C2×D3—122no—
231C2×D3—122no—
232C2×D3—244no—
233C3×C4—21no—
234C3×C4—21no—
235C3×C4—21no—
236C3×C4—21no—
237C3×C4—122no—
238Dic3—42no—
239Dic3—61no—
240Dic3—61no—
241Dic3—61no—
242Dic3—61no—
243C32#214811yescharacteristic, complemented, Sylow
244C23—91no—
245C23—361no—
246Q8—62no—
247Q8—361no—
248D4—62no—
249D4—122no—
250D4—361no—
251D4—362no—
252C2×C4—91no—
253C2×C4—91no—
254C2×C4—91no—
255C2×C4—91no—
256C2×C4—91no—
257C2×C4—122no—
258C2×C4—362no—
259C2×C4—361no—
260C2×C4D32⋊C411yescharacteristic
261C8—91no—
262C8—91no—
263C8—362no—
264C8D32⋊C411yescharacteristic
265C8C2×GO+(4,𝔽2)11yescharacteristic
266C2×C3—22no—
267C2×C3—21no—
268C2×C3—21no—
269C2×C3—41no—
270C2×C3—242no—
271D3—62no—
272D3—82no—
273D3—121no—
274D3—121no—
275D3—121no—
276C22—91no—
277C22—91no—
278C22—122no—
279C22—361no—
280C22—722no—
281C22#6372911yescharacteristic
282C4—91no—
283C4—91no—
284C4—122no—
285C4#6372911yescharacteristic
286C4C2×D32⋊C411yescharacteristic
287C3—21no—
288C3—21no—
289C2—21no—
290C2—181no—
291C2—181no—
292C2—242no—
293C2C2×#6372911yescharacteristic
subgroupG/H
centerC4#63729
commutatorC3⋊(C3⋊C8)C22×C4
FrattiniC8C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32C2×#102
prime radical#10594684C2
cosocleC8×C3⋊D3C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#2148
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. #10593771C2semidirect
3. C2×#63544C2semidirect
4. #10590021C2semidirect
5. #10590020C2semidirect
243. C32#2148semidirect

Maximal subgroups

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

subgroupindex
#105946842
#105937712
C2×#635442
#105900212
#105900202
#21489