Finite Group Databasebeta

← #11790837

Subgroups — #11790837

Order 1152.

834 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 834 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C2×#64147C211yesmaximal, characteristic
2C2×#63786C214yesmaximal, complemented
3#10593812C211yesmaximal, characteristic, complemented
4C4×C22⋊#157C211yesmaximal, characteristic, complemented
5C22×C32×D4C411yescharacteristic, complemented
6C22×#638C2212yes—
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×C22⋊#157C2212yes—
9C2×C22⋊#157C2212yes—
10C2×C4⋊#157—21no—
11C2×C4×#157—21no—
12C2×#3757C412yescomplemented
13#64147—21no—
14#64147—21no—
15#64147—21no—
16#64147—21no—
17C2×C4⋊(C3⋊Dic3)C411yescharacteristic, complemented
18#63786—28no—
19#63781—21no—
20#63781—21no—
21C2×#938—62no—
22C24×C32C2×C412yes—
23C23×C3⋊D3C2311yescharacteristic
24C22×#157—22no—
25C22×#157—22no—
26C2×C32×D4—21no—
27C2×C32×D4—21no—
28C2×C32×D4—42no—
29C22×C32×C4C2×C411yescharacteristic
30C2×#638—22no—
31C2×#638—22no—
32C2×#638—24no—
33C2×#638—24no—
34C22×C3⋊Dic3C2×C412yes—
35C22×C3⋊Dic3C2×C411yescharacteristic
36C2×C4×C3⋊D3—42no—
37C2×C4×C3⋊D3D411yescharacteristic
38C2×C4×C3⋊D3D411yescharacteristic
39C2×C4×C3⋊D3D411yescharacteristic
40C2×C4×C3⋊D3D411yescharacteristic
41C22⋊#157—22no—
42C22⋊#157—24no—
43C22⋊#157D414yescomplemented
44C4⋊#157—42no—
45C4×#157—42no—
46#3757—22no—
47#3757—22no—
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)—21no—
50#1964—91nomaximal, Sylow
51C22×C3×D4—22no—
52C22×#67—64no—
53C22×C4×D3—62no—
54C2×#217—64no—
55#938—64no—
56#938—64no—
57#938—64no—
58#938—64no—
59C2×C4⋊Dic3—62no—
60C23×C32—22no—
61C23×C32—24no—
62C23×C32—42no—
63C23×C32—42no—
64C23×C32C22×C411yescharacteristic
65C22×C3⋊D3—41no—
66C22×C3⋊D3—41no—
67C22×C3⋊D3C2×D411yescharacteristic
68C22×C3⋊D3C2×D411yescharacteristic
69C22×C3⋊D3C2×D412yes—
70C22×C3⋊D3#4112yes—
71C2×#157—24no—
72C2×#157—42no—
73C2×#157—42no—
74C2×#157—42no—
75C2×#157—42no—
76C2×#157—42no—
77C32×D4—42no—
78C32×D4—42no—
79C2×C32×C4—22no—
80C2×C32×C4C22⋊C411yescharacteristic
81C2×C32×C4C22⋊C411yescharacteristic
82#638—44no—
83#638—42no—
84#638—42no—
85C2×C3⋊Dic3—22no—
86C2×C3⋊Dic3—24no—
87C2×C3⋊Dic3—41no—
88C2×C3⋊Dic3C22⋊C411yescharacteristic
89C2×C3⋊Dic3C22⋊C411yescharacteristic
90C4×C3⋊D3—22no—
91C4×C3⋊D3—22no—
92C4×C3⋊D3—41no—
93C4×C3⋊D3—41no—
94C2×#121—91no—
95C2×#99—94no—
96#380—91no—
97C4×C22⋊C4—91no—
98C24×C3—24no—
99C23×D3—62no—
100C2×C3×D4—24no—
101C2×C3×D4—24no—
102C2×C3×D4—48no—
103C22×C3×C4—22no—
104C2×#67—68no—
105C2×#67—68no—
106C2×#67—128no—
107C2×#67—128no—
108C22×Dic3—64no—
109C22×Dic3—62no—
110C2×C4×D3—62no—
111C2×C4×D3—62no—
112C2×C4×D3—62no—
113C2×C4×D3—62no—
114C2×C4×D3—128no—
115#217—68no—
116#217—68no—
117C4⋊Dic3—64no—
118C4⋊Dic3—64no—
119C22×C32—21no—
120C22×C32—21no—
121C22×C32—42no—
122C22×C32—42no—
123C22×C32—42no—
124C22×C32—84no—
125C22×C32C2×C22⋊C411yescharacteristic
126C22×C32C4×D412yes—
127C2×C3⋊D3—21no—
128C2×C3⋊D3—21no—
129C2×C3⋊D3—21no—
130C2×C3⋊D3—21no—
131C2×C3⋊D3—42no—
132C2×C3⋊D3—42no—
133C2×C3⋊D3#12112yes—
134C2×C3⋊D3#12411yescharacteristic
135C2×C3⋊D3#12711yescharacteristic
136#157—44no—
137#157—82no—
138C32×C4—21no—
139C32×C4#9912yescomplemented
140C3⋊Dic3—21no—
141C3⋊Dic3—21no—
142C3⋊Dic3—42no—
143C22×D4—92no—
144C22×D4#15711yescharacteristic, complemented
145C23×C4—91no—
146#121—181no—
147#121—181no—
148#121—181no—
149#121—181no—
150C2×C4⋊C4—91no—
151C2×C4⋊C4—181no—
152C2×C22⋊C4—92no—
153C2×C22⋊C4—92no—
154C2×C22⋊C4—92no—
155C2×C42—181no—
156#99—188no—
157#95—181no—
158#95—181no—
159C23×C3—28no—
160C23×C3—22no—
161C23×C3—48no—
162C23×C3—48no—
163C23×C3—48no—
164C22×D3—62no—
165C22×D3—62no—
166C22×D3—64no—
167C22×D3—64no—
168C22×D3—124no—
169C22×D3—124no—
170C3×D4—48no—
171C3×D4—48no—
172C2×C3×C4—28no—
173C2×C3×C4—22no—
174C2×C3×C4—22no—
175#67—1216no—
176#67—128no—
177#67—128no—
178C2×Dic3—62no—
179C2×Dic3—62no—
180C2×Dic3—68no—
181C2×Dic3—128no—
182C2×Dic3—124no—
183C4×D3—124no—
184C4×D3—124no—
185C4×D3—124no—
186C4×D3—124no—
187C2×C32—22no—
188C2×C32—82no—
189C2×C32#39011yescharacteristic
190C2×C32C2×#9911yescharacteristic
191C2×C32#41011yescharacteristic
192C3⋊D3—22no—
193C3⋊D3—21no—
194C3⋊D3—21no—
195C24—91no—
196C24C2×#15712yes—
197C2×D4—21no—
198C2×D4—21no—
199C2×D4—42no—
200C2×D4—184no—
201C2×D4—182no—
202C2×D4—182no—
203C2×D4—184no—
204C22×C4—91no—
205C22×C4—91no—
206C22×C4—91no—
207C22×C4—91no—
208C22×C4—91no—
209C22×C4—92no—
210C22×C4—182no—
211C22×C4—182no—
212C22×C4—362no—
213C22×C4C2×#15711yescharacteristic
214C4⋊C4—181no—
215C4⋊C4—181no—
216C4⋊C4—362no—
217C22⋊C4—94no—
218C22⋊C4—182no—
219C22⋊C4—182no—
220C22⋊C4—182no—
221C22⋊C4—184no—
222C42—362no—
223C22×C3—24no—
224C22×C3—24no—
225C22×C3—24no—
226C22×C3—22no—
227C22×C3—48no—
228C22×C3—48no—
229C22×C3—48no—
230C22×C3—816no—
231C2×D3—64no—
232C2×D3—62no—
233C2×D3—62no—
234C2×D3—122no—
235C2×D3—122no—
236C2×D3—122no—
237C2×D3—122no—
238C2×D3—128no—
239C2×D3—128no—
240C3×C4—24no—
241C3×C4—24no—
242Dic3—122no—
243Dic3—122no—
244Dic3—128no—
245C32#196411yescharacteristic, complemented, Sylow
246C23—22no—
247C23—24no—
248C23—42no—
249C23—42no—
250C23—91no—
251C23—91no—
252C23—92no—
253C23—92no—
254C23—361no—
255C23—361no—
256C23C22×#15711yescharacteristic
257D4—42no—
258D4—42no—
259D4—364no—
260D4—362no—
261D4—362no—
262C2×C4—22no—
263C2×C4—91no—
264C2×C4—91no—
265C2×C4—182no—
266C2×C4—182no—
267C2×C4—184no—
268C2×C4—184no—
269C2×C4—182no—
270C2×C4—361no—
271C2×C4—361no—
272C2×C4—361no—
273C2×C4—362no—
274C2×C4—362no—
275C2×C4—362no—
276C2×C4—362no—
277C2×C4—362no—
278C2×C4C22⋊#15711yescharacteristic
279C2×C4C22⋊#15711yescharacteristic
280C2×C3—28no—
281C2×C3—22no—
282C2×C3—22no—
283C2×C3—22no—
284C2×C3—88no—
285D3—124no—
286D3—122no—
287D3—122no—
288C22—21no—
289C22—21no—
290C22—42no—
291C22—42no—
292C22—42no—
293C22—84no—
294C22—92no—
295C22—91no—
296C22—91no—
297C22—181no—
298C22—181no—
299C22—181no—
300C22—181no—
301C22—362no—
302C22—362no—
303C22D4×#15712yes—
304C22C2×C22⋊#15711yescharacteristic
305C4—21no—
306C4—181no—
307C4—181no—
308C4—364no—
309C4—362no—
310C4—722no—
311C4#6378612yescomplemented
312C3—22no—
313C2—22no—
314C2—82no—
315C2—182no—
316C2—181no—
317C2—181no—
318C2#1059381811yescharacteristic
319C2#1059382711yescharacteristic
320C2C2×#6378611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC23×C32C22×C4
FrattiniC23C22×#157
FittingC22×C32×D4C4
socleC22×C32C2×C22⋊C4
prime radicalC2×#64147C2
cosocleC23×C3⋊D3C23
hypercenterC22×D4#157
hypocenterC32#1964
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63786C2semidirect
3. #10593812C2semidirect
4. C4×C22⋊#157C2semidirect
5. C22×C32×D4C4semidirect
12. C2×#3757C4semidirect
17. C2×C4⋊(C3⋊Dic3)C4semidirect
43. C22⋊#157D4semidirect
139. C32×C4#99semidirect
144. C22×D4#157semidirect
245. C32#1964semidirect
311. C4#63786semidirect

Maximal subgroups

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

subgroupindex
C2×#641472
C2×#637862
#105938122
C4×C22⋊#1572
#19649