Finite Group Databasebeta

← #11774381

Subgroups — #11774381

Order 1152.

474 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 65 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#10593971C211yesmaximal, characteristic
2#10593726C211yesmaximal, characteristic, complemented
3#10590256C211yesmaximal, characteristic, complemented
4#10590030C214yesmaximal, complemented
5C2×#3796—21no—
6C2×#3787—21no—
7C42×C3⋊D3C2211yescharacteristic
8C3×#875—21no—
9#63914C411yescharacteristic
10#63912—21no—
11#63912C412yes—
12#63902—21no—
13#63902C2212yes—
14#63873C411yescharacteristic
15#63779C2212yes—
16C4⋊#622—21no—
17C3×C4⋊(C3⋊C8)—21no—
18#63557—21no—
19#63553C2212yes—
20#5668—61no—
21#4833—61no—
22C2×C4×C3⋊D3C2×C411yescharacteristic
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C3×D12—21no—
26C2×C3×Dic6—21no—
27C2×#626—22no—
28C2×#625—21no—
29C2×#625C2×C412yes—
30C2×D3×Dic3—22no—
31#3796—42no—
32#3796—42no—
33C2×#622—22no—
34#3787—42no—
35C32×C42D411yescharacteristic
36C4×C3⋊Dic3C2×C411yescharacteristic
37C4×C3⋊Dic3D411yescharacteristic
38C4×C3⋊Dic3C2311yescharacteristic
39C3×(C2×D3)⋊C4—22no—
40C3×(C2×D3)⋊C4—22no—
41C2×C3×C3⋊C8—22no—
42#3724—21no—
43#3724C2×C412yes—
44#1480—91nomaximal, Sylow
45C2×#239—61no—
46C2×#237—61no—
47C3×#124—61no—
48#944—61no—
49#940—61no—
50#884—62no—
51#884—62no—
52#67⋊C4—62no—
53#67⋊C4—62no—
54#875—21no—
55C42×D3—61no—
56C42×D3—61no—
57C3×C4⋊C8—61no—
58(C2×D3)⋊C8—62no—
59C8×Dic3—62no—
60C4⋊(C3⋊C8)—21no—
61C22×C3⋊D3C22⋊C411yescharacteristic
62C22×C3×D3—22no—
63C2×C32×C4C22⋊C411yescharacteristic
64C2×C32×C4C22⋊C411yescharacteristic
65C2×C32×C4C2×D411yescharacteristic
66C2×C3⋊Dic3C22⋊C411yescharacteristic
67C2×C3⋊Dic3C22×C411yescharacteristic
68C2×C3⋊Dic3C2×D411yescharacteristic
69C4×C3⋊D3—22no—
70C4×C3⋊D3—41no—
71C4×C3⋊D3D812yes—
72C4×C3⋊D3SD1612yes—
73C2×C3×Dic3—22no—
74C3×D12—42no—
75C3×Dic6—42no—
76#626—44no—
77#625—24no—
78#625—42no—
79D3×Dic3—42no—
80D3×Dic3—42no—
81#622—42no—
82C3×C3⋊C8—42no—
83#532—91no—
84#431—91no—
85C2×C4⋊C8—91no—
86D4⋊C8—94no—
87C2×C3×Q8—61no—
88C2×C3×D4—61no—
89C2×#67—62no—
90C2×#67—62no—
91C2×#67—62no—
92C22×Dic3—62no—
93#239—122no—
94#239—122no—
95#237—122no—
96#237—122no—
97C2×D12—21no—
98C2×D12—62no—
99C2×C4×D3—61no—
100C2×C4×D3—61no—
101C2×C4×D3—61no—
102C2×C4×D3—61no—
103C2×C4×D3—61no—
104C2×C4×D3—61no—
105C2×C4×D3—62no—
106C2×Dic6—21no—
107C2×C3×C8—62no—
108C3×C22⋊C4—62no—
109C3×C22⋊C4—62no—
110C3×C42—21no—
111C3×C42—21no—
112(C2×D3)⋊C4—22no—
113(C2×D3)⋊C4—22no—
114Dic3⋊C4—62no—
115Dic3⋊C4—62no—
116C4×Dic3—61no—
117C4×Dic3—61no—
118C4×Dic3—61no—
119C4×Dic3—61no—
120C4×Dic3—61no—
121C4×Dic3—61no—
122C2×C3⋊C8—22no—
123C22×C32C2×C22⋊C411yescharacteristic
124C2×C3⋊D3—21no—
125C2×C3⋊D3—21no—
126C2×C3⋊D3#10212yes—
127C2×C3×D3—42no—
128C2×C3×D3—42no—
129C2×C3×D3—42no—
130C32×C4—21no—
131C32×C4—21no—
132C32×C4#10212yes—
133C3⋊Dic3—21no—
134C3⋊Dic3#13112yes—
135C3⋊Dic3C2×D811yescharacteristic
136C3⋊Dic3C2×SD1611yescharacteristic
137C3×Dic3—42no—
138C2×#41—181no—
139C22×C8—181no—
140C4⋊Q8—91no—
141#127—91no—
142#124—61no—
143#121—92no—
144#121—181no—
145C4×D4—92no—
146C4×D4—181no—
147C2×C42—91no—
148C4⋊C8—61no—
149C4⋊C8—92no—
150C4⋊C8—181no—
151C22⋊C8—181no—
152C4×C8—92no—
153C23×C3—62no—
154C22×D3—22no—
155C22×D3—61no—
156C22×D3—61no—
157C3×Q8—122no—
158C3×D4—122no—
159C2×C3×C4—21no—
160C2×C3×C4—21no—
161C2×C3×C4—21no—
162C2×C3×C4—21no—
163C2×C3×C4—21no—
164C2×C3×C4—21no—
165C2×C3×C4—62no—
166#67—124no—
167#67—124no—
168#67—124no—
169C2×Dic3—22no—
170C2×Dic3—61no—
171C2×Dic3—61no—
172C2×Dic3—61no—
173C2×Dic3—61no—
174C2×Dic3—61no—
175C2×Dic3—61no—
176C2×Dic3—122no—
177C2×Dic3—122no—
178D12—42no—
179D12—124no—
180C4×D3—62no—
181C4×D3—62no—
182C4×D3—62no—
183C4×D3—62no—
184C4×D3—122no—
185C4×D3—122no—
186C4×D3—122no—
187C4×D3—122no—
188C4×D3—122no—
189C4×D3—121no—
190C4×D3—121no—
191Dic6—42no—
192C3×C8—122no—
193C3⋊C8—42no—
194C2×C32#40811yescharacteristic
195C2×C32C2×#10211yescharacteristic
196C2×C32#42111yescharacteristic
197C3⋊D3—22no—
198C3×D3—82no—
199#41—362no—
200#41—362no—
201C2×Q8—61no—
202C2×D4—61no—
203C2×D4—92no—
204C2×D4—182no—
205C2×D4—181no—
206C22×C4—91no—
207C22×C4—91no—
208C22×C4—91no—
209C22×C4—182no—
210C2×C8—62no—
211C2×C8—182no—
212C2×C8—362no—
213C4⋊C4—92no—
214C4⋊C4—181no—
215C22⋊C4—62no—
216C22⋊C4—62no—
217C42—91no—
218C42—91no—
219C42—91no—
220C42GO+(4,𝔽2)11yescharacteristic
221C22×C3—21no—
222C22×C3—21no—
223C22×C3—122no—
224C22×C3—122no—
225C22×C3—122no—
226C2×D3—42no—
227C2×D3—42no—
228C2×D3—42no—
229C2×D3—62no—
230C2×D3—62no—
231C2×D3—121no—
232C2×D3—121no—
233C2×D3—121no—
234C2×D3—121no—
235C3×C4—21no—
236C3×C4—21no—
237C3×C4—22no—
238C3×C4—22no—
239C3×C4—41no—
240C3×C4—41no—
241C3×C4—41no—
242C3×C4—122no—
243Dic3—42no—
244Dic3—61no—
245Dic3—61no—
246Dic3—61no—
247Dic3—61no—
248Dic3—62no—
249Dic3—62no—
250Dic3—62no—
251Dic3—121no—
252C32#148011yescharacteristic, complemented, Sylow
253C23—62no—
254C23—91no—
255Q8—122no—
256D4—122no—
257D4—184no—
258D4—364no—
259D4—362no—
260C2×C4—62no—
261C2×C4—91no—
262C2×C4—91no—
263C2×C4—92no—
264C2×C4—92no—
265C2×C4—91no—
266C2×C4—182no—
267C2×C4—361no—
268C2×C4—362no—
269C2×C4—362no—
270C2×C4D32⋊C411yescharacteristic
271C2×C4D32⋊C411yescharacteristic
272C2×C4C2×GO+(4,𝔽2)11yescharacteristic
273C8—122no—
274C8—362no—
275C2×C3—21no—
276C2×C3—21no—
277C2×C3—21no—
278C2×C3—21no—
279C2×C3—21no—
280C2×C3—21no—
281C2×C3—242no—
282D3—82no—
283D3—122no—
284D3—122no—
285C22—92no—
286C22—122no—
287C22—122no—
288C22—122no—
289C22—181no—
290C22—181no—
291C22C2×D32⋊C411yescharacteristic
292C4—21no—
293C4—21no—
294C4—92no—
295C4—91no—
296C4—91no—
297C4—122no—
298C4—181no—
299C4#6372912yes—
300C3—21no—
301C3—21no—
302C2—182no—
303C2—242no—
304C2#1059330911yescharacteristic
305C2C2×#6372911yescharacteristic
306C2#1059338111yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radical#10593971C2
cosocleC4×C3⋊Dic3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1480
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #10593726C2semidirect
3. #10590256C2semidirect
4. #10590030C2semidirect
252. C32#1480semidirect

Maximal subgroups

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

subgroupindex
#105939712
#105937262
#105902562
#105900302
#14809