Finite Group Databasebeta

← #11788955

Subgroups — #11788955

Order 1152.

434 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 92 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×#63779C211yesmaximal, characteristic
2C2×C4×#622C211yesmaximal, characteristic
3C4⋊C4×C3⋊Dic3C211yesmaximal, characteristic
4#10590207C211yesmaximal, characteristic
5#10590207C211yesmaximal, characteristic
6#10590207C211yesmaximal, characteristic
7#10590207C211yesmaximal, characteristic
8C22×#622C2211yescharacteristic
9C22×#622C2211yescharacteristic
10C22×#622C2211yescharacteristic
11C22×#622C2211yescharacteristic
12C2×C32×C4⋊C4C411yescharacteristic
13C2×C4⋊(C3⋊Dic3)C411yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×C4×C3⋊Dic3C2211yescharacteristic
17#63779—22no—
18C4×#622—22no—
19#63658C411yescharacteristic
20#63658C411yescharacteristic
21Dic3×C4⋊C4—62no—
22C22×C32×C4C2×C411yescharacteristic
23C22×C32×C4C2×C411yescharacteristic
24C22×C32×C4C2×C411yescharacteristic
25C22×C3⋊Dic3C2×C411yescharacteristic
26C22×C3⋊Dic3C2×C411yescharacteristic
27C22×C3⋊Dic3C2×C411yescharacteristic
28C22×C3⋊Dic3C2311yescharacteristic
29C2×#622—21no—
30C2×#622—21no—
31C2×#622—21no—
32C2×#622—21no—
33C2×#622—21no—
34C2×#622—21no—
35C2×#622—21no—
36C2×#622—21no—
37C2×#622—21no—
38C2×#622—21no—
39C2×#622D412yes—
40C2×#622Q812yes—
41C32×C4⋊C4—22no—
42C4⋊(C3⋊Dic3)C814yescomplemented
43C4×C3⋊Dic3—21no—
44C4×C3⋊Dic3—21no—
45C4×C3⋊Dic3—21no—
46C4×C3⋊Dic3—21no—
47C4×C3⋊Dic3—21no—
48C4×C3⋊Dic3—21no—
49#1916—91nomaximal, Sylow
50C2×C3×C4⋊C4—22no—
51C2×C4⋊Dic3—62no—
52C2×C4×Dic3—62no—
53C2×C4×Dic3—62no—
54C2×C4×Dic3—62no—
55C3⋊#95—62no—
56C3⋊#95—62no—
57C23×C32C22×C411yescharacteristic
58C2×C32×C4—21no—
59C2×C32×C4—21no—
60C2×C32×C4—21no—
61C2×C32×C4—21no—
62C2×C32×C4—21no—
63C2×C32×C4—21no—
64C2×C32×C4—21no—
65C2×C32×C4C2×C812yes—
66C2×C32×C4M1612yes—
67C2×C3⋊Dic3—21no—
68C2×C3⋊Dic3—21no—
69C2×C3⋊Dic3—21no—
70C2×C3⋊Dic3—21no—
71C2×C3⋊Dic3—21no—
72C2×C3⋊Dic3—21no—
73C2×C3⋊Dic3—21no—
74C2×C3⋊Dic3C2×C812yes—
75C2×C3⋊Dic3C2×C812yes—
76C2×C3⋊Dic3C2×D411yescharacteristic
77C2×C3⋊Dic3C2×Q811yescharacteristic
78C2×C3⋊Dic3#4111yescharacteristic
79C2×C3⋊Dic3#4111yescharacteristic
80C2×C3⋊Dic3#4111yescharacteristic
81C2×C3⋊Dic3#4111yescharacteristic
82#622—22no—
83#622—22no—
84#622—41no—
85#622—41no—
86C2×C4⋊C8—91no—
87C2×C4×C8—91no—
88C4×C4⋊C4—91no—
89#336—91no—
90#336—91no—
91#336—91no—
92#336—91no—
93C22×C3×C4—22no—
94C22×C3×C4—22no—
95C22×C3×C4—22no—
96C22×Dic3—62no—
97C22×Dic3—62no—
98C22×Dic3—62no—
99C22×Dic3—62no—
100C3×C4⋊C4—28no—
101C4⋊Dic3—68no—
102C4×Dic3—64no—
103C4×Dic3—64no—
104C4×Dic3—122no—
105C4×Dic3—122no—
106C4×Dic3—122no—
107C4×Dic3—122no—
108C22×C32#11711yescharacteristic
109C22×C32C4×D411yescharacteristic
110C22×C32C4×Q811yescharacteristic
111C22×C32C22×C811yescharacteristic
112C22×C32C2×M1611yescharacteristic
113C22×C32#13111yescharacteristic
114C22×C32#13111yescharacteristic
115C32×C4—22no—
116C32×C4—22no—
117C32×C4—41no—
118C3⋊Dic3—22no—
119C3⋊Dic3—22no—
120C3⋊Dic3—41no—
121C3⋊Dic3C22⋊Q811yescharacteristic
122C3⋊Dic3#12311yescharacteristic
123C3⋊Dic3#12511yescharacteristic
124C3⋊Dic3#12611yescharacteristic
125C22×C8—91no—
126C22×C8—91no—
127C22×C8—91no—
128C22×C8—91no—
129C2×C4⋊C4—91no—
130C2×C4⋊C4#15711yescharacteristic
131C2×C42—91no—
132C2×C42—91no—
133C2×C42—91no—
134C4⋊C8—182no—
135C4×C8—182no—
136#95—91no—
137#95—91no—
138C23×C3—22no—
139C2×C3×C4—24no—
140C2×C3×C4—24no—
141C2×C3×C4—24no—
142C2×C3×C4—24no—
143C2×C3×C4—24no—
144C2×C3×C4—42no—
145C2×C3×C4—42no—
146C2×C3×C4—42no—
147C2×C3×C4—42no—
148C2×Dic3—62no—
149C2×Dic3—62no—
150C2×Dic3—62no—
151C2×Dic3—62no—
152C2×Dic3—62no—
153C2×Dic3—62no—
154C2×Dic3—64no—
155C2×Dic3—64no—
156C2×Dic3—64no—
157C2×Dic3—122no—
158C2×Dic3—122no—
159C2×Dic3—122no—
160C2×Dic3—122no—
161C2×Dic3—122no—
162C2×Dic3—122no—
163C2×C32#38711yescharacteristic
164C2×C32#43111yescharacteristic
165C2×C32#43311yescharacteristic
166C2×C32C8×D411yescharacteristic
167C2×C32#43511yescharacteristic
168C2×C32C8×Q811yescharacteristic
169C2×C32#44611yescharacteristic
170C22×C4—91no—
171C22×C4—91no—
172C22×C4—91no—
173C22×C4—91no—
174C22×C4C2×#15711yescharacteristic
175C22×C4C2×#15711yescharacteristic
176C22×C4C2×#15711yescharacteristic
177C2×C8—92no—
178C2×C8—92no—
179C2×C8—181no—
180C2×C8—181no—
181C2×C8—181no—
182C2×C8—181no—
183C2×C8—181no—
184C2×C8—181no—
185C2×C8—181no—
186C2×C8—181no—
187C2×C8—181no—
188C2×C8—181no—
189C4⋊C4—22no—
190C4⋊C4—94no—
191C42—181no—
192C42—181no—
193C42—181no—
194C42—181no—
195C42—181no—
196C42—181no—
197C22×C3—22no—
198C22×C3—22no—
199C22×C3—22no—
200C22×C3—22no—
201C22×C3—22no—
202C22×C3—22no—
203C22×C3—22no—
204C3×C4—28no—
205C3×C4—44no—
206C3×C4—44no—
207Dic3—62no—
208Dic3—62no—
209Dic3—62no—
210Dic3—62no—
211Dic3—124no—
212Dic3—124no—
213Dic3—124no—
214C32#191611yescharacteristic, complemented, Sylow
215C23C22×#15711yescharacteristic
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—91no—
224C2×C4—91no—
225C2×C4—91no—
226C2×C4—91no—
227C2×C4—91no—
228C2×C4—91no—
229C2×C4—92no—
230C2×C4—92no—
231C2×C4—181no—
232C2×C4—181no—
233C2×C4—181no—
234C2×C4—181no—
235C2×C4—181no—
236C2×C4—181no—
237C2×C4—181no—
238C2×C4#378712yes—
239C2×C4#379212yes—
240C8—182no—
241C8—182no—
242C8—361no—
243C8—361no—
244C2×C3—22no—
245C2×C3—22no—
246C2×C3—22no—
247C2×C3—22no—
248C2×C3—22no—
249C2×C3—22no—
250C2×C3—22no—
251C22C2×#378711yescharacteristic
252C22#6428611yescharacteristic
253C22#6428711yescharacteristic
254C22D4×#15711yescharacteristic
255C22#6428911yescharacteristic
256C22Q8×#15711yescharacteristic
257C22C2×#379211yescharacteristic
258C4—22no—
259C4—22no—
260C4—41no—
261C4—91no—
262C4—91no—
263C4—91no—
264C4—91no—
265C4—182no—
266C4—182no—
267C4—361no—
268C3—22no—
269C2#1059374911yescharacteristic
270C2#1059375011yescharacteristic
271C2#1059375311yescharacteristic
272C2#1059375811yescharacteristic
273C2#1059380111yescharacteristic
274C2#1059382011yescharacteristic
275C2#1059383511yescharacteristic
subgroupG/H
center, FrattiniC23C22×#157
commutatorC22×C32C22×C8
FittingC2×C32×C4⋊C4C4
socle, prime radicalC23×C32C22×C4
cosocleC22×C3⋊Dic3C23
hypercenterC2×C4⋊C4#157
hypocenterC32#1916
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
42. C4⋊(C3⋊Dic3)C8semidirect
214. C32#1916semidirect

Maximal subgroups

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

subgroupindex
C2×#637792
C2×C4×#6222
C4⋊C4×C3⋊Dic32
#105902072
#19169