Finite Group Databasebeta

← #11776148

Subgroups — #11776148

Order 1152.

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

normal subgroups only

This group has 470 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
1#10594929C211yesmaximal, characteristic
2C2×C4⋊#622C211yesmaximal, characteristic, complemented
3#10591061C211yesmaximal, characteristic, complemented
4#10590039C212yesmaximal, complemented
5#10590037C212yesmaximal, complemented
6C2×#3805—21no—
7C22×#622—21no—
8C2×C4×C3⋊Dic3C2211yescharacteristic
9C3×#930—21no—
10#63980C412yes—
11#63919C2211yescharacteristic
12#63915—21no—
13#63914C2211yescharacteristic
14#63902C412yes—
15#63898—21no—
16C4⋊#622—21no—
17C4⋊#622C2212yes—
18C3×#830—21no—
19#63572C2212yes—
20#63553—21no—
21#5596—61no—
22#4718—61no—
23C22×C32×C4D411yescharacteristic
24C22×C3⋊Dic3C2×C411yescharacteristic
25C22×C3⋊Dic3D411yescharacteristic
26C2×C3×#67—22no—
27C2×C3×D12—21no—
28C2×#627—21no—
29C2×#625—21no—
30C2×#625C2×C412yes—
31#3805—42no—
32#3805—42no—
33C2×D3×Dic3—22no—
34C2×#622—22no—
35C2×#622—42no—
36C4×C3⋊Dic3C2×C411yescharacteristic
37C4×C3⋊Dic3D411yescharacteristic
38C4×C3⋊Dic3D411yescharacteristic
39C4×C3⋊Dic3C2311yescharacteristic
40C3×(C2×D3)⋊C4—22no—
41C3×C4⋊Dic3—21no—
42C2×C3×C3⋊C8—22no—
43#3724C2×C412yes—
44(C2×D3)⋊Dic3—22no—
45#1540—91nomaximal, Sylow
46C2×#237—62no—
47C3×#121—61no—
48#940—61no—
49#939—62no—
50D4×Dic3—61no—
51#930—21no—
52C2×C4×Dic3—61no—
53C2×C4×Dic3—61no—
54#893—61no—
55#888—61no—
56#885—62no—
57#67⋊C4—62no—
58C3×C22⋊C8—61no—
59#830—21no—
60Dic3⋊C8—62no—
61C8×Dic3—62no—
62C23×C32C22⋊C411yescharacteristic
63C22×C3×D3—22no—
64C2×C32×C4—22no—
65C2×C32×C4C22⋊C411yescharacteristic
66C2×C32×C4C2×D411yescharacteristic
67C2×C3⋊Dic3—41no—
68C2×C3⋊Dic3C22⋊C411yescharacteristic
69C2×C3⋊Dic3C22⋊C411yescharacteristic
70C2×C3⋊Dic3D812yes—
71C2×C3⋊Dic3SD1612yes—
72C2×C3⋊Dic3C22×C411yescharacteristic
73C2×C3⋊Dic3C2×D411yescharacteristic
74C3×#67—44no—
75C2×C3×Dic3—22no—
76C3×D12—42no—
77#627—41no—
78#627—41no—
79#625—42no—
80#625—41no—
81#625—41no—
82D3×Dic3—44no—
83#622—42no—
84C3×C3⋊C8—42no—
85#532—91no—
86#431—91no—
87C2×C4⋊C8—91no—
88#332—92no—
89#331—92no—
90C2×C3×D4—61no—
91C2×C3×D4—62no—
92C22×C3×C4—21no—
93C22×C3×C4—21no—
94C2×#67—22no—
95C2×#67—62no—
96C2×#67—62no—
97C22×Dic3—61no—
98C22×Dic3—61no—
99C22×Dic3—61no—
100C22×Dic3—61no—
101C22×Dic3—62no—
102#237—124no—
103#237—124no—
104C2×D12—21no—
105C2×C4×D3—62no—
106C2×Dic6—62no—
107C2×C3×C8—62no—
108C3×C4⋊C4—61no—
109C3×C22⋊C4—62no—
110#217—62no—
111(C2×D3)⋊C4—22no—
112(C2×D3)⋊C4—62no—
113C4⋊Dic3—21no—
114Dic3⋊C4—62no—
115C4×Dic3—61no—
116C4×Dic3—61no—
117C4×Dic3—61no—
118C4×Dic3—61no—
119C4×Dic3—61no—
120C4×Dic3—61no—
121C4×Dic3—61no—
122C4×Dic3—61no—
123C2×C3⋊C8—22no—
124C22×C32—21no—
125C22×C32—21no—
126C22×C32#10212yes—
127C22×C32C2×C22⋊C411yescharacteristic
128C2×C3×D3—42no—
129C2×C3×D3—42no—
130C2×C3×D3—42no—
131C32×C4—21no—
132C32×C4#13512yes—
133C3⋊Dic3—21no—
134C3⋊Dic3—21no—
135C3⋊Dic3#10212yes—
136C3⋊Dic3C2×D811yescharacteristic
137C3⋊Dic3C2×SD1611yescharacteristic
138C3×Dic3—42no—
139C2×#41—181no—
140C22×C8—181no—
141C4⋊Q8—91no—
142#127—91no—
143#124—181no—
144#121—61no—
145#121—92no—
146C4×D4—92no—
147C4×D4—181no—
148C2×C42—91no—
149C4⋊C8—92no—
150C4⋊C8—92no—
151C4⋊C8—181no—
152C22⋊C8—61no—
153C4×C8—181no—
154C23×C3—21no—
155C23×C3—21no—
156C23×C3—62no—
157C22×D3—22no—
158C3×D4—122no—
159C3×D4—124no—
160C2×C3×C4—21no—
161C2×C3×C4—21no—
162C2×C3×C4—21no—
163C2×C3×C4—21no—
164C2×C3×C4—42no—
165C2×C3×C4—42no—
166C2×C3×C4—62no—
167#67—44no—
168#67—122no—
169#67—122no—
170#67—124no—
171C2×Dic3—22no—
172C2×Dic3—61no—
173C2×Dic3—61no—
174C2×Dic3—61no—
175C2×Dic3—62no—
176C2×Dic3—62no—
177C2×Dic3—62no—
178C2×Dic3—62no—
179C2×Dic3—61no—
180C2×Dic3—61no—
181C2×Dic3—61no—
182C2×Dic3—61no—
183C2×Dic3—61no—
184C2×Dic3—124no—
185C2×Dic3—122no—
186C2×Dic3—122no—
187D12—42no—
188C4×D3—124no—
189Dic6—122no—
190Dic6—122no—
191C3×C8—122no—
192C3⋊C8—42no—
193C2×C32—22no—
194C2×C32#41311yescharacteristic
195C2×C32C2×#10211yescharacteristic
196C2×C32#41611yescharacteristic
197C3×D3—82no—
198#41—362no—
199#41—362no—
200C2×Q8—181no—
201C2×D4—62no—
202C2×D4—61no—
203C2×D4—92no—
204C2×D4—181no—
205C22×C4—91no—
206C22×C4—91no—
207C22×C4—182no—
208C22×C4GO+(4,𝔽2)11yescharacteristic
209C2×C8—62no—
210C2×C8—182no—
211C2×C8—362no—
212C4⋊C4—61no—
213C4⋊C4—92no—
214C22⋊C4—62no—
215C22⋊C4—182no—
216C42—91no—
217C42—91no—
218C42—91no—
219C42—91no—
220C22×C3—21no—
221C22×C3—21no—
222C22×C3—22no—
223C22×C3—22no—
224C22×C3—41no—
225C22×C3—41no—
226C22×C3—41no—
227C22×C3—41no—
228C22×C3—122no—
229C22×C3—122no—
230C22×C3—122no—
231C2×D3—42no—
232C2×D3—42no—
233C2×D3—42no—
234C3×C4—22no—
235C3×C4—22no—
236C3×C4—41no—
237C3×C4—41no—
238C3×C4—122no—
239Dic3—42no—
240Dic3—61no—
241Dic3—61no—
242Dic3—62no—
243Dic3—62no—
244Dic3—61no—
245Dic3—61no—
246Dic3—62no—
247Dic3—62no—
248Dic3—121no—
249Dic3—121no—
250C32#154011yescharacteristic, complemented, Sylow
251C23—62no—
252C23D32⋊C411yescharacteristic
253Q8—361no—
254Q8—361no—
255D4—124no—
256D4—122no—
257D4—361no—
258D4—361no—
259D4—362no—
260C2×C4—22no—
261C2×C4—62no—
262C2×C4—91no—
263C2×C4—91no—
264C2×C4—92no—
265C2×C4—92no—
266C2×C4—91no—
267C2×C4—91no—
268C2×C4—364no—
269C2×C4—361no—
270C2×C4D32⋊C411yescharacteristic
271C2×C4C2×GO+(4,𝔽2)11yescharacteristic
272C8—122no—
273C8—362no—
274C2×C3—21no—
275C2×C3—21no—
276C2×C3—21no—
277C2×C3—21no—
278C2×C3—21no—
279C2×C3—21no—
280C2×C3—42no—
281C2×C3—42no—
282C2×C3—242no—
283D3—82no—
284C22—21no—
285C22—21no—
286C22—122no—
287C22—122no—
288C22—122no—
289C22#6372912yes—
290C22C2×D32⋊C411yescharacteristic
291C4—21no—
292C4—91no—
293C4—92no—
294C4—91no—
295C4—122no—
296C4—181no—
297C4—181no—
298C4#6423712yes—
299C3—21no—
300C3—21no—
301C2—22no—
302C2—242no—
303C2#1059331311yescharacteristic
304C2C2×#6372911yescharacteristic
305C2#1059349811yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radical#10594929C2
cosocleC4×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1540
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊#622C2semidirect
3. #10591061C2semidirect
4. #10590039C2semidirect
5. #10590037C2semidirect
250. C32#1540semidirect

Maximal subgroups

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

subgroupindex
#105949292
C2×C4⋊#6222
#105910612
#105900392
#105900372
#15409