Finite Group Databasebeta

← #11774684

Subgroups — #11774684

Order 1152.

742 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 742 conjugacy classes of subgroups — too many to draw. Only its 68 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
1C4×D4×C3⋊D3C211yesmaximal, characteristic
2#10593730C211yesmaximal, characteristic, complemented
3C4×#3788C211yesmaximal, characteristic, complemented
4D4⋊#622C212yesmaximal, complemented
5#10590160C212yesmaximal, complemented
6C2×D4×C3⋊D3C411yescharacteristic
7C22×C4×C3⋊D3—21no—
8C2×#3788—21no—
9C32×C4×D4C411yescharacteristic
10D4×C3⋊Dic3C2211yescharacteristic
11C4×#638—21no—
12#64102C2211yescharacteristic
13C4⋊C4×C3⋊D3C411yescharacteristic
14#64090—21no—
15C22⋊C4×C3⋊D3—21no—
16C4×C4⋊(C3⋊D3)C411yescharacteristic
17C42×C3⋊D3C2211yescharacteristic
18#63778—21no—
19#63777—21no—
20#63777—21no—
21C4⋊#622C2212yescomplemented
22C4×#622C2212yescomplemented
23C4×D3×D4—62no—
24C23×C3⋊D3—21no—
25C2×C32×D4C2×C411yescharacteristic
26C22×C32×C4—21no—
27C2×#638—21no—
28C22×C3⋊Dic3—21no—
29D4×C3⋊D3—22no—
30D4×C3⋊D3—22no—
31C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
32C2×C4×C3⋊D3—21no—
33C2×C4×C3⋊D3—21no—
34C2×C4×C3⋊D3—21no—
35C2×C4×C3⋊D3—44no—
36C2×C4×C3⋊D3C2×C411yescharacteristic
37C2×C4×C3⋊D3D411yescharacteristic
38C2×C4×C3⋊D3D411yescharacteristic
39C2×#622—22no—
40C2×#622—22no—
41#3788—24no—
42C32×C4⋊C4C2×C411yescharacteristic
43C32×C22⋊C4—21no—
44C32×C42C2×C411yescharacteristic
45#3757—21no—
46#3752—21no—
47#3752—21no—
48C4⋊(C3⋊Dic3)C2×C411yescharacteristic
49#3750—21no—
50C4×C3⋊Dic3D411yescharacteristic
51C4×C3⋊Dic3D411yescharacteristic
52C4×C3⋊Dic3C2311yescharacteristic
53#1490—91nomaximal, Sylow
54C2×D3×D4—62no—
55C22×C4×D3—64no—
56C3×C4×D4—22no—
57D4×Dic3—62no—
58C4×#67—64no—
59#893—62no—
60D3×C4⋊C4—62no—
61#67⋊C4—64no—
62D3×C22⋊C4—64no—
63C4×D12—62no—
64C42×D3—62no—
65C23×C32—21no—
66C22×C3⋊D3—24no—
67C22×C3⋊D3—21no—
68C22×C3⋊D3—42no—
69C22×C3⋊D3—42no—
70C22×C3⋊D3C22⋊C411yescharacteristic
71C32×D4—21no—
72C32×D4M1612yescomplemented
73C2×C32×C4—21no—
74C2×C32×C4—42no—
75C2×C32×C4C22⋊C411yescharacteristic
76C2×C32×C4C22⋊C411yescharacteristic
77C2×C32×C4C22×C411yescharacteristic
78#638—24no—
79C2×C3⋊Dic3—21no—
80C2×C3⋊Dic3—42no—
81C2×C3⋊Dic3C22⋊C411yescharacteristic
82C2×C3⋊Dic3C2×D411yescharacteristic
83C2×C3⋊Dic3C2×D411yescharacteristic
84C4⋊(C3⋊D3)—21no—
85C4⋊(C3⋊D3)M1612yescomplemented
86C4×C3⋊D3—21no—
87C4×C3⋊D3—21no—
88C4×C3⋊D3—22no—
89C4×C3⋊D3—22no—
90C4×C3⋊D3—42no—
91C4×C3⋊D3—42no—
92C4×C3⋊D3—42no—
93#622—24no—
94#622—42no—
95C2×C4×D4—91no—
96#432—91no—
97C4×M16—91no—
98D4⋊C8—92no—
99D4⋊C8—92no—
100C23×D3—64no—
101C2×C3×D4—22no—
102C22×C3×C4—24no—
103C2×#67—64no—
104C22×Dic3—64no—
105D3×D4—68no—
106D3×D4—68no—
107C2×D12—62no—
108C2×C4×D3—62no—
109C2×C4×D3—62no—
110C2×C4×D3—62no—
111C2×C4×D3—64no—
112C2×C4×D3—64no—
113C2×C4×D3—64no—
114C2×C4×D3—1216no—
115C3×C4⋊C4—22no—
116C3×C22⋊C4—24no—
117C3×C42—22no—
118#217—64no—
119(C2×D3)⋊C4—64no—
120(C2×D3)⋊C4—64no—
121C4⋊Dic3—62no—
122Dic3⋊C4—64no—
123C4×Dic3—62no—
124C4×Dic3—62no—
125C4×Dic3—62no—
126C22×C32—22no—
127C22×C32—41no—
128C22×C32—41no—
129C22×C32C2×C22⋊C411yescharacteristic
130C2×C3⋊D3—21no—
131C2×C3⋊D3—21no—
132C2×C3⋊D3—22no—
133C2×C3⋊D3—48no—
134C2×C3⋊D3—41no—
135C2×C3⋊D3—41no—
136C2×C3⋊D3#10412yes—
137C32×C4—21no—
138C32×C4—21no—
139C32×C4—41no—
140C32×C4C2×M1611yescharacteristic
141C32×C4C2×M1611yescharacteristic
142C3⋊Dic3—21no—
143C3⋊Dic3—21no—
144C3⋊Dic3—41no—
145C3⋊Dic3AGL(1,ℤ/8)12yes—
146C22×D4—91no—
147C23×C4—181no—
148C2×M16—181no—
149C4×D4—91no—
150C4×D4—91no—
151C4×D4—91no—
152C4×D4—181no—
153C4×D4—181no—
154C4×D4#15711yescharacteristic
155C2×C4⋊C4—91no—
156C2×C22⋊C4—181no—
157C2×C42—91no—
158C4⋊C8—92no—
159C22⋊C8—181no—
160#97—181no—
161#97—181no—
162C4×C8—92no—
163C23×C3—24no—
164C22×D3—62no—
165C22×D3—64no—
166C22×D3—616no—
167C22×D3—128no—
168C22×D3—128no—
169C3×D4—24no—
170C3×D4—24no—
171C2×C3×C4—24no—
172C2×C3×C4—22no—
173C2×C3×C4—22no—
174C2×C3×C4—22no—
175C2×C3×C4—48no—
176#67—616no—
177C2×Dic3—62no—
178C2×Dic3—62no—
179C2×Dic3—62no—
180C2×Dic3—64no—
181C2×Dic3—128no—
182D12—64no—
183D12—64no—
184C4×D3—68no—
185C4×D3—64no—
186C4×D3—64no—
187C4×D3—124no—
188C4×D3—128no—
189C4×D3—128no—
190C4×D3—128no—
191C2×C32—42no—
192C2×C32#40711yescharacteristic
193C2×C32#41811yescharacteristic
194C2×C32C2×#10411yescharacteristic
195C3⋊D3—22no—
196C3⋊D3—42no—
197C24—181no—
198C2×D4—91no—
199C2×D4—181no—
200C2×D4—182no—
201C2×D4—182no—
202C2×D4C2×#15711yescharacteristic
203C22×C4—21no—
204C22×C4—91no—
205C22×C4—91no—
206C22×C4—91no—
207C22×C4—181no—
208C22×C4—181no—
209C22×C4—181no—
210C22×C4—181no—
211C22×C4—364no—
212M16—184no—
213C2×C8—182no—
214C2×C8—182no—
215C4⋊C4—91no—
216C4⋊C4—181no—
217C4⋊C4C2×#15711yescharacteristic
218C22⋊C4—21no—
219C22⋊C4—181no—
220C22⋊C4—181no—
221C22⋊C4—181no—
222C42—91no—
223C42—91no—
224C42—91no—
225C42C2×#15711yescharacteristic
226C22×C3—28no—
227C22×C3—22no—
228C22×C3—44no—
229C22×C3—44no—
230C2×D3—64no—
231C2×D3—64no—
232C2×D3—64no—
233C2×D3—68no—
234C2×D3—1232no—
235C2×D3—124no—
236C2×D3—124no—
237C3×C4—24no—
238C3×C4—22no—
239C3×C4—22no—
240C3×C4—42no—
241C3×C4—44no—
242Dic3—64no—
243Dic3—64no—
244Dic3—122no—
245Dic3—124no—
246C32#149011yescharacteristic, complemented, Sylow
247C23—21no—
248C23—91no—
249C23—184no—
250C23—181no—
251C23—362no—
252C23—362no—
253D4—21no—
254D4—92no—
255D4—184no—
256D4—181no—
257D4#378812yescomplemented
258C2×C4—21no—
259C2×C4—42no—
260C2×C4—91no—
261C2×C4—91no—
262C2×C4—91no—
263C2×C4—182no—
264C2×C4—182no—
265C2×C4—181no—
266C2×C4—181no—
267C2×C4—181no—
268C2×C4—362no—
269C2×C4—362no—
270C2×C4—362no—
271C2×C4—362no—
272C2×C4C22⋊#15711yescharacteristic
273C2×C4C22⋊#15711yescharacteristic
274C2×C4C22×#15711yescharacteristic
275C8—184no—
276C8—362no—
277C2×C3—22no—
278C2×C3—22no—
279C2×C3—22no—
280C2×C3—48no—
281D3—68no—
282D3—128no—
283C22—22no—
284C22—41no—
285C22—41no—
286C22—92no—
287C22—181no—
288C22—181no—
289C22—182no—
290C22—368no—
291C22—361no—
292C22—361no—
293C22C2×C22⋊#15711yescharacteristic
294C4—21no—
295C4—21no—
296C4—41no—
297C4—92no—
298C4—181no—
299C4—181no—
300C4—361no—
301C4C2×#378811yescharacteristic
302C4#6428311yescharacteristic
303C3—22no—
304C2—42no—
305C2—182no—
306C2—362no—
307C2#1059380311yescharacteristic
308C2#1059381411yescharacteristic
309C2#1059383911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C4×D4C4
socleC22×C32C2×C22⋊C4
prime radicalC2×D4×C3⋊D3C4
cosocleC4×C3⋊Dic3C23
hypercenterC4×D4#157
hypocenterC32#1490
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #10593730C2semidirect
3. C4×#3788C2semidirect
4. D4⋊#622C2semidirect
5. #10590160C2semidirect
21. C4⋊#622C22semidirect
22. C4×#622C22semidirect
72. C32×D4M16semidirect
85. C4⋊(C3⋊D3)M16semidirect
246. C32#1490semidirect
257. D4#3788semidirect

Maximal subgroups

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

subgroupindex
C4×D4×C3⋊D32
#105937302
C4×#37882
D4⋊#6222
#105901602
#14909