Finite Group Databasebeta

← #11783283

Subgroups — #11783283

Order 1152.

778 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 778 conjugacy classes of subgroups — too many to draw. Only its 138 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
1C22×C4⋊#157C211yesmaximal, characteristic
2C2×#64283C211yesmaximal, characteristic
3C3⋊D3×#117C211yesmaximal, characteristic
4#10590163C214yesmaximal, complemented
5C23×#157—21no—
6C22×C4×C3⋊D3C2211yescharacteristic
7C2×#3792—21no—
8C2×C4⋊#157—22no—
9C2×C4⋊#157—21no—
10C2×C4⋊#157C414yescomplemented
11C2×C4⋊#157C2212yes—
12#64283—22no—
13#64283C414yescomplemented
14C2×#3788—21no—
15C2×#3787C2212yes—
16C32×#117C411yescharacteristic, complemented
17#64135C411yescharacteristic, complemented
18#64101C412yescomplemented
19C4⋊C4×C3⋊D3C2212yes—
20C22⋊C4×C3⋊D3—21no—
21#64086—21no—
22#64081—21no—
23C42×C3⋊D3—21no—
24D3×#117—62no—
25C23×C3⋊D3D411yescharacteristic
26C22×#157—24no—
27C22×#157—22no—
28C22×#157—44no—
29C22×C32×C4C2×C411yescharacteristic
30C22×C3⋊Dic3D411yescharacteristic
31C2×C4×C3⋊D3—22no—
32C2×C4×C3⋊D3C2×C411yescharacteristic
33C2×C4×C3⋊D3C2×C412yes—
34C2×C4×C3⋊D3C2×C412yes—
35C2×C4×C3⋊D3D411yescharacteristic
36C2×C4×C3⋊D3D411yescharacteristic
37C2×C4×C3⋊D3D412yes—
38C2×C4×C3⋊D3Q812yes—
39C2×C4×C3⋊D3C2311yescharacteristic
40#3792—24no—
41C2×#622—22no—
42C4⋊#157—24no—
43C4⋊#157—22no—
44C4⋊#157C2×C414yes—
45#3788—24no—
46#3787—22no—
47#3787C2×C414yescomplemented
48C32×C4⋊C4C2×C412yescomplemented
49C32×C22⋊C4—21no—
50C32×C42—21no—
51#3757—21no—
52#3752—22no—
53C4⋊(C3⋊Dic3)C2×C412yescomplemented
54#3750—22no—
55C4×C3⋊Dic3—21no—
56C4×C3⋊Dic3—22no—
57#1736—91nomaximal, Sylow
58C22×C4×D3—62no—
59C3×#117—22no—
60#926—62no—
61#892—64no—
62D3×C4⋊C4—64no—
63D3×C22⋊C4—64no—
64#877—64no—
65#872—64no—
66C42×D3—64no—
67C23×C32C22⋊C411yescharacteristic
68C22×C3⋊D3—22no—
69C22×C3⋊D3—22no—
70C22×C3⋊D3C22⋊C411yescharacteristic
71C22×C3⋊D3C22⋊C412yes—
72C22×C3⋊D3C4⋊C412yes—
73C22×C3⋊D3C2×D411yescharacteristic
74C2×#157—24no—
75C2×#157—48no—
76C2×#157—44no—
77C2×C32×C4—22no—
78C2×C32×C4C4212yes—
79C2×C32×C4C22⋊C411yescharacteristic
80C2×C32×C4C4⋊C412yes—
81C2×C32×C4C22×C411yescharacteristic
82C2×C3⋊Dic3—22no—
83C2×C3⋊Dic3C22⋊C411yescharacteristic
84C2×C3⋊Dic3C22⋊C412yes—
85C2×C3⋊Dic3C4⋊C412yes—
86C2×C3⋊Dic3C2×D411yescharacteristic
87C4×C3⋊D3—42no—
88C4×C3⋊D3—42no—
89C4×C3⋊D3C4212yes—
90C4×C3⋊D3C22⋊C412yes—
91C4×C3⋊D3C22⋊C412yes—
92C4×C3⋊D3C4⋊C412yes—
93C4×C3⋊D3C4⋊C412yes—
94C4×C3⋊D3C4⋊C412yes—
95C4×C3⋊D3C22×C411yescharacteristic
96C4×C3⋊D3C22×C411yescharacteristic
97C4×C3⋊D3C2×D411yescharacteristic
98C4×C3⋊D3C2×Q811yescharacteristic
99#622—24no—
100C22×M16—91no—
101C2×#117—91no—
102C22×C4⋊C4—91no—
103#340—94no—
104C23×D3—62no—
105C22×C3×C4—22no—
106C22×Dic3—62no—
107C2×C4×D3—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—64no—
115C2×C4×D3—68no—
116C3×C4⋊C4—24no—
117C3×C22⋊C4—24no—
118C3×C42—24no—
119#217—64no—
120(C2×D3)⋊C4—68no—
121C4⋊Dic3—64no—
122Dic3⋊C4—68no—
123C4×Dic3—64no—
124C4×Dic3—68no—
125C22×C32—22no—
126C22×C32#9512yes—
127C22×C32C2×C22⋊C411yescharacteristic
128C2×C3⋊D3—22no—
129C2×C3⋊D3—22no—
130C2×C3⋊D3—22no—
131C2×C3⋊D3—24no—
132C2×C3⋊D3#9512yes—
133C2×C3⋊D3C2×C22⋊C411yescharacteristic
134C2×C3⋊D3C2×C4⋊C411yescharacteristic
135C2×C3⋊D3AGL(1,ℤ/8)12yes—
136C2×C3⋊D3#13712yes—
137#157—44no—
138C32×C4—42no—
139C32×C4#9512yes—
140C32×C4C2×C4211yescharacteristic
141C32×C4C2×C4⋊C411yescharacteristic
142C3⋊Dic3—42no—
143C3⋊Dic3#9512yes—
144C3⋊Dic3C2×C22⋊C411yescharacteristic
145C3⋊Dic3C2×C4⋊C411yescharacteristic
146C23×C4—91no—
147C23×C4—181no—
148C2×M16—94no—
149C2×M16—181no—
150C2×M16—182no—
151C2×M16—181no—
152C22×C8—92no—
153#117—91no—
154#117—92no—
155#117—181no—
156#117—181no—
157#117#15711yescharacteristic, complemented
158C2×C4⋊C4—94no—
159C2×C4⋊C4—92no—
160C2×C4⋊C4—92no—
161C2×C4⋊C4—182no—
162C2×C4⋊C4—181no—
163C2×C22⋊C4—181no—
164C2×C42—181no—
165C23×C3—22no—
166C22×D3—62no—
167C22×D3—62no—
168C22×D3—64no—
169C22×D3—64no—
170C22×D3—124no—
171C22×D3—124no—
172C2×C3×C4—28no—
173C2×C3×C4—22no—
174C2×C3×C4—24no—
175C2×C3×C4—24no—
176C2×C3×C4—22no—
177C2×Dic3—62no—
178C2×Dic3—64no—
179C2×Dic3—64no—
180C2×Dic3—62no—
181C2×Dic3—68no—
182C4×D3—64no—
183C4×D3—64no—
184C4×D3—64no—
185C4×D3—64no—
186C4×D3—64no—
187C4×D3—64no—
188C4×D3—62no—
189C4×D3—62no—
190C4×D3—62no—
191C4×D3—62no—
192C4×D3—128no—
193C4×D3—128no—
194C2×C32—22no—
195C2×C32C2×#9511yescharacteristic
196C2×C32#41712yes—
197C3⋊D3—22no—
198C3⋊D3#41811yescharacteristic
199C3⋊D3#41911yescharacteristic
200C3⋊D3#42812yes—
201C24—91no—
202C22×C4—91no—
203C22×C4—91no—
204C22×C4—91no—
205C22×C4—92no—
206C22×C4—92no—
207C22×C4—92no—
208C22×C4—92no—
209C22×C4—91no—
210C22×C4—91no—
211C22×C4—182no—
212C22×C4—182no—
213C22×C4—184no—
214C22×C4—364no—
215C22×C4C2×#15711yescharacteristic
216M16—184no—
217M16—184no—
218C2×C8—94no—
219C2×C8—182no—
220C2×C8—182no—
221C4⋊C4—94no—
222C4⋊C4—92no—
223C4⋊C4—182no—
224C4⋊C4—182no—
225C4⋊C4—184no—
226C4⋊C4C2×#15712yescomplemented
227C22⋊C4—21no—
228C22⋊C4—182no—
229C22⋊C4—181no—
230C42—21no—
231C42—182no—
232C42—181no—
233C22×C3—24no—
234C22×C3—22no—
235C22×C3—44no—
236C2×D3—62no—
237C2×D3—62no—
238C2×D3—64no—
239C2×D3—64no—
240C2×D3—64no—
241C2×D3—124no—
242C2×D3—124no—
243C2×D3—128no—
244C2×D3—124no—
245C3×C4—22no—
246C3×C4—22no—
247C3×C4—24no—
248C3×C4—48no—
249Dic3—64no—
250Dic3—62no—
251Dic3—62no—
252Dic3—128no—
253C32#173611yescharacteristic, complemented, Sylow
254C23—91no—
255C23—92no—
256C23—92no—
257C23—91no—
258C23—182no—
259C23—182no—
260C23C22⋊#15711yescharacteristic
261C2×C4—22no—
262C2×C4—92no—
263C2×C4—92no—
264C2×C4—91no—
265C2×C4—91no—
266C2×C4—91no—
267C2×C4—91no—
268C2×C4—92no—
269C2×C4—91no—
270C2×C4—91no—
271C2×C4—92no—
272C2×C4—92no—
273C2×C4—92no—
274C2×C4—92no—
275C2×C4—92no—
276C2×C4—184no—
277C2×C4—182no—
278C2×C4—362no—
279C2×C4—362no—
280C2×C4—364no—
281C2×C4—368no—
282C2×C4C4×#15712yes—
283C2×C4C4⋊#15712yes—
284C2×C4C22⋊#15711yescharacteristic
285C2×C4C22×#15711yescharacteristic
286C8—184no—
287C2×C3—22no—
288C2×C3—24no—
289C2×C3—44no—
290D3—62no—
291D3—62no—
292D3—64no—
293D3—124no—
294C22—22no—
295C22—91no—
296C22—91no—
297C22—92no—
298C22—92no—
299C22—92no—
300C22—182no—
301C22—182no—
302C22—184no—
303C22—182no—
304C22#6378112yes—
305C22C2×C22⋊#15711yescharacteristic
306C4—42no—
307C4—91no—
308C4—92no—
309C4—91no—
310C4—364no—
311C4—362no—
312C4#6378112yes—
313C4C2×C4×#15711yescharacteristic
314C4C2×C4⋊#15711yescharacteristic
315C3—22no—
316C2—22no—
317C2—91no—
318C2—91no—
319C2—92no—
320C2—182no—
321C2C2×#6378111yescharacteristic
322C2#1059384012yes—
subgroupG/H
centerC22C2×C22⋊#157
commutatorC32×C4C2×C42
FrattiniC2×C4C22×#157
FittingC32×#117C4
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC2×C4×C3⋊D3C23
hypercenter#117#157
hypocenterC32#1736
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
4. #10590163C2semidirect
10. C2×C4⋊#157C4semidirect
13. #64283C4semidirect
16. C32×#117C4semidirect
17. #64135C4semidirect
18. #64101C4semidirect
47. #3787C2×C4semidirect
48. C32×C4⋊C4C2×C4semidirect
53. C4⋊(C3⋊Dic3)C2×C4semidirect
157. #117#157semidirect
226. C4⋊C4C2×#157semidirect
253. C32#1736semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊#1572
C2×#642832
C3⋊D3×#1172
#105901632
#17369