Finite Group Databasebeta

← #11787175

Subgroups — #11787175

Order 1152.

834 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 834 conjugacy classes of subgroups — too many to draw. Only its 94 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×#3792C211yesmaximal, characteristic, complemented
2C2×D4×C3⋊Dic3C211yesmaximal, characteristic
3C2×C22⋊#622C211yesmaximal, characteristic, complemented
4C2×C22⋊#622C212yesmaximal, complemented
5#10590207C212yesmaximal, complemented
6C22×C32×D4C411yescharacteristic
7C23×C3⋊Dic3C2211yescharacteristic
8C23×C3⋊Dic3C2211yescharacteristic
9C2×#3792—22no—
10C2×#3792—24no—
11C22×#622C2212yes—
12C22×#622C2212yes—
13C2×#3757C411yescharacteristic
14C2×#3757C411yescharacteristic
15D4×C3⋊Dic3—22no—
16D4×C3⋊Dic3—22no—
17C2×C4⋊(C3⋊Dic3)C411yescharacteristic
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C22⋊#622—22no—
20C22⋊#622—24no—
21C2×D4×Dic3—62no—
22C24×C32C2×C411yescharacteristic
23C24×C32C2×C411yescharacteristic
24C2×C32×D4—22no—
25C2×C32×D4—22no—
26C2×C32×D4—22no—
27C22×C32×C4C2×C411yescharacteristic
28C22×C3⋊Dic3—22no—
29C22×C3⋊Dic3—22no—
30C22×C3⋊Dic3—21no—
31C22×C3⋊Dic3—21no—
32C22×C3⋊Dic3—22no—
33C22×C3⋊Dic3—22no—
34C22×C3⋊Dic3C2×C411yescharacteristic
35C22×C3⋊Dic3C2×C411yescharacteristic
36C22×C3⋊Dic3C2×C411yescharacteristic
37C22×C3⋊Dic3D412yes—
38C22×C3⋊Dic3D412yes—
39C22×C3⋊Dic3C2311yescharacteristic
40#3792—28no—
41C2×#622—22no—
42C2×#622—22no—
43C2×#622—22no—
44C2×#622—22no—
45C2×#622—22no—
46C2×#622D414yescomplemented
47#3757—22no—
48#3757—22no—
49C4⋊(C3⋊Dic3)—22no—
50C4×C3⋊Dic3—21no—
51C4×C3⋊Dic3—21no—
52#1870—91nomaximal, Sylow
53C22×C3×D4—22no—
54C23×Dic3—62no—
55C23×Dic3—62no—
56C2×#217—62no—
57C2×#217—62no—
58D4×Dic3—68no—
59D4×Dic3—68no—
60C2×C4⋊Dic3—62no—
61C2×C4×Dic3—62no—
62C23×C32—21no—
63C23×C32—21no—
64C23×C32—21no—
65C23×C32—21no—
66C23×C32—22no—
67C23×C32—22no—
68C23×C32—22no—
69C23×C32—22no—
70C23×C32C22⋊C412yes—
71C23×C32M1612yescomplemented
72C23×C32C22×C411yescharacteristic
73C32×D4—28no—
74C2×C32×C4—21no—
75C2×C32×C4—21no—
76C2×C32×C4M1612yescomplemented
77C2×C3⋊Dic3—21no—
78C2×C3⋊Dic3—21no—
79C2×C3⋊Dic3—22no—
80C2×C3⋊Dic3—22no—
81C2×C3⋊Dic3—24no—
82C2×C3⋊Dic3—22no—
83C2×C3⋊Dic3—22no—
84C2×C3⋊Dic3—22no—
85C2×C3⋊Dic3—41no—
86C2×C3⋊Dic3—42no—
87C2×C3⋊Dic3—41no—
88C2×C3⋊Dic3C22⋊C412yes—
89C2×C3⋊Dic3C2×D412yes—
90C2×C3⋊Dic3C2×D411yescharacteristic
91C2×C3⋊Dic3C2×D411yescharacteristic
92C2×C3⋊Dic3#4112yes—
93#622—24no—
94#622—42no—
95C22×M16—91no—
96C2×C4×D4—91no—
97C2×C22⋊C8—92no—
98C2×C22⋊C8—91no—
99#336—92no—
100C24×C3—22no—
101C24×C3—22no—
102C2×C3×D4—28no—
103C2×C3×D4—28no—
104C2×C3×D4—28no—
105C22×C3×C4—22no—
106C22×Dic3—62no—
107C22×Dic3—62no—
108C22×Dic3—62no—
109C22×Dic3—62no—
110C22×Dic3—64no—
111C22×Dic3—64no—
112C22×Dic3—64no—
113C22×Dic3—64no—
114C22×Dic3—124no—
115C22×Dic3—124no—
116C22×Dic3—124no—
117C22×Dic3—124no—
118#217—68no—
119#217—68no—
120C4⋊Dic3—68no—
121C4×Dic3—64no—
122C4×Dic3—64no—
123C22×C32—22no—
124C22×C32—22no—
125C22×C32—22no—
126C22×C32—22no—
127C22×C32—24no—
128C22×C32—41no—
129C22×C32—41no—
130C22×C32—42no—
131C22×C32—42no—
132C22×C32—42no—
133C22×C32C2×C22⋊C411yescharacteristic
134C22×C32C4×D412yes—
135C22×C32C2×M1611yescharacteristic
136C22×C32C2×M1611yescharacteristic
137C22×C32#13112yes—
138C32×C4—22no—
139C3⋊Dic3—22no—
140C3⋊Dic3—41no—
141C3⋊Dic3—41no—
142C3⋊Dic3#12011yescharacteristic
143C3⋊Dic3#12112yes—
144C3⋊Dic3#12311yescharacteristic
145C22×D4#15711yescharacteristic
146C23×C4—91no—
147C23×C4—91no—
148C2×M16—184no—
149C2×M16—182no—
150C22×C8—92no—
151C22×C8—92no—
152C4×D4—182no—
153C4×D4—182no—
154C2×C4⋊C4—91no—
155C2×C22⋊C4—91no—
156C2×C22⋊C4—91no—
157C2×C42—91no—
158C22⋊C8—184no—
159C22⋊C8—182no—
160C23×C3—24no—
161C23×C3—24no—
162C23×C3—24no—
163C23×C3—24no—
164C23×C3—22no—
165C23×C3—24no—
166C23×C3—24no—
167C23×C3—44no—
168C23×C3—44no—
169C23×C3—44no—
170C23×C3—44no—
171C3×D4—232no—
172C2×C3×C4—24no—
173C2×C3×C4—24no—
174C2×C3×C4—24no—
175C2×Dic3—62no—
176C2×Dic3—62no—
177C2×Dic3—64no—
178C2×Dic3—64no—
179C2×Dic3—64no—
180C2×Dic3—64no—
181C2×Dic3—64no—
182C2×Dic3—124no—
183C2×Dic3—128no—
184C2×Dic3—124no—
185C2×Dic3—124no—
186C2×Dic3—124no—
187C2×Dic3—124no—
188C2×Dic3—124no—
189C2×Dic3—128no—
190C2×Dic3—124no—
191C2×C32—42no—
192C2×C32—42no—
193C2×C32#38611yescharacteristic
194C2×C32#40711yescharacteristic
195C2×C32#40811yescharacteristic
196C2×C32#43512yes—
197C2×C32#43612yes—
198C24C2×#15711yescharacteristic
199C24C2×#15711yescharacteristic
200C2×D4—22no—
201C2×D4—22no—
202C2×D4—22no—
203C22×C4—91no—
204C22×C4—91no—
205C22×C4—92no—
206C22×C4—92no—
207C22×C4—91no—
208C22×C4—91no—
209C22×C4—182no—
210C22×C4—182no—
211C22×C4—182no—
212C22×C4—181no—
213C22×C4—181no—
214C22×C4—182no—
215C22×C4C2×#15711yescharacteristic
216M16—188no—
217C2×C8—94no—
218C2×C8—182no—
219C2×C8—182no—
220C2×C8—182no—
221C2×C8—182no—
222C2×C8—182no—
223C4⋊C4—182no—
224C22⋊C4—182no—
225C22⋊C4—182no—
226C42—181no—
227C42—181no—
228C22×C3—28no—
229C22×C3—28no—
230C22×C3—24no—
231C22×C3—24no—
232C22×C3—22no—
233C22×C3—22no—
234C22×C3—22no—
235C22×C3—44no—
236C22×C3—48no—
237C22×C3—44no—
238C22×C3—44no—
239C22×C3—48no—
240C22×C3—48no—
241C22×C3—48no—
242C22×C3—44no—
243C3×C4—28no—
244Dic3—62no—
245Dic3—64no—
246Dic3—62no—
247Dic3—124no—
248Dic3—124no—
249Dic3—124no—
250C32#187011yescharacteristic, complemented, Sylow
251C23—22no—
252C23—22no—
253C23—22no—
254C23—22no—
255C23—21no—
256C23—21no—
257C23—21no—
258C23—21no—
259C23#379212yescomplemented
260C23C22⋊#15712yes—
261C23C22×#15711yescharacteristic
262D4—28no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—92no—
266C2×C4—92no—
267C2×C4—91no—
268C2×C4—91no—
269C2×C4—92no—
270C2×C4—182no—
271C2×C4—184no—
272C2×C4—182no—
273C2×C4—182no—
274C2×C4—182no—
275C2×C4—182no—
276C2×C4—181no—
277C2×C4—181no—
278C2×C4—361no—
279C2×C4—362no—
280C2×C4—361no—
281C2×C4#379212yescomplemented
282C8—184no—
283C8—362no—
284C2×C3—24no—
285C2×C3—24no—
286C2×C3—22no—
287C2×C3—22no—
288C2×C3—22no—
289C2×C3—48no—
290C2×C3—48no—
291C22—24no—
292C22—22no—
293C22—22no—
294C22—22no—
295C22—22no—
296C22—42no—
297C22—42no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22#6428712yes—
302C22D4×#15712yes—
303C22C2×#379211yescharacteristic
304C22C2×#379211yescharacteristic
305C22C2×C22⋊#15711yescharacteristic
306C4—22no—
307C4—91no—
308C4—92no—
309C4—91no—
310C4—182no—
311C4—361no—
312C4—361no—
313C3—22no—
314C2—42no—
315C2—42no—
316C2#1059382012yes—
317C2#1059382112yes—
318C2#1059382211yescharacteristic
319C2#1059382611yescharacteristic
320C2#1059384511yescharacteristic
subgroupG/H
center, FrattiniC23C22×#157
commutator, socleC23×C32C22×C4
Fitting, prime radicalC22×C32×D4C4
cosocleC22×C3⋊Dic3C23
hypercenterC22×D4#157
hypocenterC32#1870
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#3792C2semidirect
3. C2×C22⋊#622C2semidirect
4. C2×C22⋊#622C2semidirect
5. #10590207C2semidirect
46. C2×#622D4semidirect
71. C23×C32M16semidirect
76. C2×C32×C4M16semidirect
250. C32#1870semidirect
259. C23#3792semidirect
281. C2×C4#3792semidirect

Maximal subgroups

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

subgroupindex
C22×#37922
C2×D4×C3⋊Dic32
C2×C22⋊#6222
#105902072
#18709