Finite Group Databasebeta

← #11774310

Subgroups — #11774310

Order 1152.

738 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 78 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#10593727C211yesmaximal, characteristic, complemented
3#10593725C211yesmaximal, characteristic, complemented
4D4⋊#622C212yesmaximal, complemented
5#10590160C212yesmaximal, complemented
6C2×D4×C3⋊D3C411yescharacteristic
7C22×C4×C3⋊D3—21no—
8C32×C4×D4C411yescharacteristic
9D4×C3⋊Dic3C2211yescharacteristic
10C4×#638—21no—
11#64102C2211yescharacteristic
12C4⋊C4×C3⋊D3C411yescharacteristic
13#64090—21no—
14C22⋊C4×C3⋊D3—21no—
15C4×C4⋊(C3⋊D3)C411yescharacteristic
16C42×C3⋊D3C2211yescharacteristic
17#63779—21no—
18#63778—21no—
19#63778—21no—
20C4⋊#622C2212yescomplemented
21C4×#622—21no—
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⋊D3C814yescomplemented
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—
41C32×C4⋊C4C2×C411yescharacteristic
42C32×C22⋊C4—21no—
43C32×C42C2×C411yescharacteristic
44#3757—21no—
45#3752—21no—
46#3752—21no—
47C4⋊(C3⋊Dic3)C2×C411yescharacteristic
48#3750—21no—
49C4×C3⋊Dic3D411yescharacteristic
50C4×C3⋊Dic3D411yescharacteristic
51C4×C3⋊Dic3C2311yescharacteristic
52#1478—91nomaximal, Sylow
53C2×D3×D4—62no—
54C22×C4×D3—64no—
55C3×C4×D4—22no—
56D4×Dic3—62no—
57C4×#67—64no—
58#893—62no—
59D3×C4⋊C4—62no—
60#67⋊C4—64no—
61D3×C22⋊C4—64no—
62C4×D12—62no—
63C42×D3—62no—
64C23×C32—21no—
65C22×C3⋊D3—21no—
66C22×C3⋊D3—24no—
67C22×C3⋊D3—42no—
68C22×C3⋊D3—42no—
69C22×C3⋊D3C22⋊C411yescharacteristic
70C32×D4—21no—
71C32×D4C2×C812yes—
72C2×C32×C4—21no—
73C2×C32×C4—42no—
74C2×C32×C4C22⋊C411yescharacteristic
75C2×C32×C4C22⋊C411yescharacteristic
76C2×C32×C4C22×C411yescharacteristic
77#638—24no—
78C2×C3⋊Dic3—21no—
79C2×C3⋊Dic3—42no—
80C2×C3⋊Dic3C22⋊C411yescharacteristic
81C2×C3⋊Dic3C2×D411yescharacteristic
82C2×C3⋊Dic3C2×D411yescharacteristic
83C4⋊(C3⋊D3)—21no—
84C4⋊(C3⋊D3)C2×C812yes—
85C4×C3⋊D3—22no—
86C4×C3⋊D3—41no—
87C4×C3⋊D3—42no—
88C4×C3⋊D3—42no—
89C4×C3⋊D3—42no—
90C4×C3⋊D3C2×C812yes—
91C4×C3⋊D3M1612yes—
92#622—42no—
93#622—42no—
94C2×C4×D4—91no—
95#431—91no—
96#431—91no—
97D4⋊C8—92no—
98D4⋊C8—92no—
99C23×D3—64no—
100C2×C3×D4—22no—
101C22×C3×C4—24no—
102C2×#67—64no—
103C22×Dic3—64no—
104D3×D4—68no—
105D3×D4—68no—
106C2×D12—62no—
107C2×C4×D3—62no—
108C2×C4×D3—62no—
109C2×C4×D3—62no—
110C2×C4×D3—64no—
111C2×C4×D3—64no—
112C2×C4×D3—64no—
113C2×C4×D3—1216no—
114C3×C4⋊C4—22no—
115C3×C22⋊C4—24no—
116C3×C42—22no—
117#217—64no—
118(C2×D3)⋊C4—64no—
119(C2×D3)⋊C4—64no—
120C4⋊Dic3—62no—
121Dic3⋊C4—64no—
122C4×Dic3—62no—
123C4×Dic3—62no—
124C4×Dic3—62no—
125C22×C32—22no—
126C22×C32—41no—
127C22×C32—41no—
128C22×C32C2×C22⋊C411yescharacteristic
129C2×C3⋊D3—21no—
130C2×C3⋊D3—21no—
131C2×C3⋊D3—22no—
132C2×C3⋊D3—48no—
133C2×C3⋊D3—41no—
134C2×C3⋊D3—41no—
135C2×C3⋊D3C22⋊C812yes—
136C32×C4—21no—
137C32×C4—21no—
138C32×C4—41no—
139C32×C4C22×C811yescharacteristic
140C32×C4C2×M1611yescharacteristic
141C3⋊Dic3—21no—
142C3⋊Dic3—41no—
143C3⋊Dic3C22⋊C812yes—
144C3⋊Dic3AGL(1,ℤ/8)12yes—
145C22×D4—91no—
146C23×C4—181no—
147C4×D4—91no—
148C4×D4—91no—
149C4×D4—91no—
150C4×D4—181no—
151C4×D4—181no—
152C4×D4#15711yescharacteristic
153C2×C4⋊C4—91no—
154C2×C22⋊C4—181no—
155C2×C42—91no—
156C4⋊C8—92no—
157C4⋊C8—181no—
158C22⋊C8—181no—
159C22⋊C8—181no—
160C4×C8—92no—
161C4×C8—181no—
162C23×C3—24no—
163C22×D3—62no—
164C22×D3—64no—
165C22×D3—616no—
166C22×D3—128no—
167C22×D3—128no—
168C3×D4—24no—
169C3×D4—24no—
170C2×C3×C4—24no—
171C2×C3×C4—22no—
172C2×C3×C4—22no—
173C2×C3×C4—22no—
174C2×C3×C4—48no—
175#67—616no—
176C2×Dic3—62no—
177C2×Dic3—62no—
178C2×Dic3—62no—
179C2×Dic3—64no—
180C2×Dic3—128no—
181D12—64no—
182D12—64no—
183C4×D3—64no—
184C4×D3—64no—
185C4×D3—68no—
186C4×D3—128no—
187C4×D3—128no—
188C4×D3—124no—
189C4×D3—128no—
190C2×C32—42no—
191C2×C32C2×C22⋊C811yescharacteristic
192C2×C32#41811yescharacteristic
193C2×C32#42111yescharacteristic
194C3⋊D3—22no—
195C3⋊D3—42no—
196C24—181no—
197C2×D4—94no—
198C2×D4—91no—
199C2×D4—182no—
200C2×D4—181no—
201C2×D4C2×#15711yescharacteristic
202C22×C4—21no—
203C22×C4—91no—
204C22×C4—91no—
205C22×C4—91no—
206C22×C4—181no—
207C22×C4—181no—
208C22×C4—181no—
209C22×C4—181no—
210C22×C4—364no—
211C2×C8—182no—
212C2×C8—182no—
213C4⋊C4—91no—
214C4⋊C4—181no—
215C4⋊C4C2×#15711yescharacteristic
216C22⋊C4—21no—
217C22⋊C4—181no—
218C22⋊C4—181no—
219C22⋊C4—181no—
220C42—91no—
221C42—91no—
222C42—91no—
223C42C2×#15711yescharacteristic
224C22×C3—28no—
225C22×C3—22no—
226C22×C3—44no—
227C22×C3—44no—
228C2×D3—64no—
229C2×D3—64no—
230C2×D3—64no—
231C2×D3—68no—
232C2×D3—1232no—
233C2×D3—124no—
234C2×D3—124no—
235C3×C4—24no—
236C3×C4—22no—
237C3×C4—22no—
238C3×C4—42no—
239C3×C4—44no—
240Dic3—64no—
241Dic3—64no—
242Dic3—122no—
243Dic3—124no—
244C32#147811yescharacteristic, complemented, Sylow
245C23—21no—
246C23—91no—
247C23—184no—
248C23—181no—
249C23—362no—
250C23—362no—
251D4—21no—
252D4—92no—
253D4—184no—
254D4—181no—
255D4#378712yes—
256C2×C4—21no—
257C2×C4—42no—
258C2×C4—91no—
259C2×C4—91no—
260C2×C4—92no—
261C2×C4—92no—
262C2×C4—91no—
263C2×C4—182no—
264C2×C4—181no—
265C2×C4—361no—
266C2×C4—362no—
267C2×C4—362no—
268C2×C4—362no—
269C2×C4—362no—
270C2×C4C22⋊#15711yescharacteristic
271C2×C4C22⋊#15711yescharacteristic
272C2×C4C22×#15711yescharacteristic
273C8—362no—
274C8—362no—
275C2×C3—22no—
276C2×C3—22no—
277C2×C3—22no—
278C2×C3—48no—
279D3—68no—
280D3—128no—
281C22—22no—
282C22—41no—
283C22—41no—
284C22—92no—
285C22—181no—
286C22—181no—
287C22—182no—
288C22—368no—
289C22—361no—
290C22—361no—
291C22C2×C22⋊#15711yescharacteristic
292C4—21no—
293C4—21no—
294C4—41no—
295C4—92no—
296C4—92no—
297C4—181no—
298C4—361no—
299C4C2×#378711yescharacteristic
300C4#6428311yescharacteristic
301C3—22no—
302C2—42no—
303C2—182no—
304C2—362no—
305C2#1059380011yescharacteristic
306C2#1059381411yescharacteristic
307C2#1059384211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC32×C4C22×C8
FrattiniC2×C4C22×#157
FittingC32×C4×D4C4
socleC22×C32C2×C22⋊C4
prime radicalC2×D4×C3⋊D3C4
cosocleC4×C3⋊Dic3C23
hypercenterC4×D4#157
hypocenterC32#1478
LCSG ▷ 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. #10593727C2semidirect
3. #10593725C2semidirect
4. D4⋊#622C2semidirect
5. #10590160C2semidirect
20. C4⋊#622C22semidirect
22. C4×#622C22semidirect
30. D4×C3⋊D3C8semidirect
244. C32#1478semidirect

Maximal subgroups

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

subgroupindex
C4×D4×C3⋊D32
#105937272
#105937252
D4⋊#6222
#105901602
#14789