Finite Group Databasebeta

← #11789096

Subgroups — #11789096

Order 1152.

360 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 70 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
1#10593759C211yesmaximal, characteristic
2C4⋊C4×#157C211yesmaximal, characteristic
3C3⋊D3×#106C211yesmaximal, characteristic
4#10590182C211yesmaximal, characteristic
5#10590181C211yesmaximal, characteristic
6#10590163C211yesmaximal, characteristic
7#10590163C211yesmaximal, characteristic
8C2×C4⋊#157—21no—
9C2×C4⋊#157C2211yescharacteristic
10C2×C4⋊#157C2211yescharacteristic
11C2×C4×#157—21no—
12C2×C4×#157C2211yescharacteristic
13C2×#3787C2211yescharacteristic
14C2×C8×C3⋊D3C2211yescharacteristic
15C4⋊C4×C3⋊D3C2211yescharacteristic
16C4⋊C4×C3⋊D3C2211yescharacteristic
17#63781—21no—
18#63781—21no—
19C32×#106C411yescharacteristic, complemented
20#63644C411yescharacteristic, complemented
21#63635C411yescharacteristic, complemented
22#63635C411yescharacteristic, complemented
23D3×#106—62no—
24C22×#157—21no—
25C22×#157—21no—
26C22×#157D411yescharacteristic
27C22×#157D411yescharacteristic
28C2×C4×C3⋊D3—21no—
29C2×C4×C3⋊D3—21no—
30C2×C4×C3⋊D3C2311yescharacteristic
31C2×#622—21no—
32C4⋊#157—21no—
33C4⋊#157—21no—
34C4⋊#157—21no—
35C4⋊#157—42no—
36C4⋊#157Q812yes—
37C4×#157—21no—
38C4×#157—21no—
39C4×#157—42no—
40#3787—21no—
41#3787—21no—
42C2×C32×C8C2×C411yescharacteristic
43C32×C4⋊C4C2×C411yescharacteristic
44C32×C4⋊C4C2×C411yescharacteristic
45C4⋊(C3⋊Dic3)C2×C411yescharacteristic
46C4⋊(C3⋊Dic3)C2×C411yescharacteristic
47#3750—21no—
48#3750—21no—
49C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
50C8×C3⋊D3—21no—
51C8×C3⋊D3—21no—
52#1919—91nomaximal, Sylow
53C2×D3×C8—62no—
54D3×C4⋊C4—62no—
55D3×C4⋊C4—62no—
56C3×#106—22no—
57#817—62no—
58#808—62no—
59#808—62no—
60C22×C3⋊D3C2×D411yescharacteristic
61C2×#157—21no—
62C2×#157—21no—
63C2×#157—22no—
64C2×#157—21no—
65C2×#157—21no—
66C2×#157—21no—
67C2×#157—41no—
68C2×#157—41no—
69C2×#157—41no—
70C2×#157—41no—
71C2×#157—41no—
72C2×#157SD1612yes—
73C2×C32×C4—21no—
74C2×C32×C4—21no—
75C2×C32×C4C22×C411yescharacteristic
76C2×C3⋊Dic3—21no—
77C2×C3⋊Dic3—21no—
78C2×C3⋊Dic3#4111yescharacteristic
79C4×C3⋊D3—41no—
80C4×C3⋊D3—41no—
81C4×C3⋊D3—41no—
82C4×C3⋊D3—41no—
83C4×C3⋊D3C2×Q811yescharacteristic
84C4×C3⋊D3#4111yescharacteristic
85C4×C3⋊D3#4111yescharacteristic
86C4×C3⋊D3#4111yescharacteristic
87#622—41no—
88C32×C8—21no—
89C3⋊(C3⋊C8)—21no—
90C2×#106—91no—
91#389—91no—
92C4×C4⋊C4—91no—
93#340—91no—
94#340—91no—
95#340—91no—
96#336—91no—
97C2×C4×D3—62no—
98C2×C4×D3—122no—
99C2×C4×D3—122no—
100C2×C3×C8—22no—
101C3×C4⋊C4—22no—
102C3×C4⋊C4—22no—
103C4⋊Dic3—62no—
104C4⋊Dic3—62no—
105Dic3⋊C4—122no—
106Dic3⋊C4—122no—
107C2×C3⋊C8—62no—
108D3×C8—64no—
109D3×C8—64no—
110C22×C32C4×D411yescharacteristic
111C2×C3⋊D3C22⋊Q811yescharacteristic
112C2×C3⋊D3#12311yescharacteristic
113C2×C3⋊D3C2×SD1611yescharacteristic
114C2×C3⋊D3#13511yescharacteristic
115C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
116C2×C3⋊D3#13711yescharacteristic
117#157—22no—
118#157—42no—
119#157—41no—
120#157—81no—
121C32×C4—41no—
122C32×C4—41no—
123C32×C4#11711yescharacteristic
124C32×C4C4×Q811yescharacteristic
125C3⋊Dic3—41no—
126C3⋊Dic3—41no—
127C3⋊Dic3#12511yescharacteristic
128C3⋊Dic3#12611yescharacteristic
129C22×C8—91no—
130C22×C8—91no—
131C2×C4⋊C4—91no—
132C2×C4⋊C4—91no—
133C2×C4⋊C4—91no—
134C2×C4⋊C4—91no—
135C2×C4⋊C4—181no—
136C2×C42—91no—
137C2×C42—181no—
138#106—91no—
139#106—91no—
140#106—91no—
141#106#15711yescharacteristic, complemented
142#95—181no—
143#95—181no—
144C22×D3—62no—
145C2×C3×C4—22no—
146C2×C3×C4—42no—
147C2×C3×C4—42no—
148C2×Dic3—62no—
149C2×Dic3—122no—
150C2×Dic3—122no—
151C4×D3—62no—
152C4×D3—62no—
153C4×D3—62no—
154C4×D3—62no—
155C4×D3—242no—
156C4×D3—242no—
157C4×D3—242no—
158C4×D3—242no—
159C3×C8—24no—
160C3⋊C8—64no—
161C2×C32#38711yescharacteristic
162C2×C32C4×SD1611yescharacteristic
163C2×C32#44011yescharacteristic
164C3⋊D3#47511yescharacteristic
165C3⋊D3#47811yescharacteristic
166C3⋊D3#48111yescharacteristic
167C3⋊D3#48511yescharacteristic
168C22×C4—91no—
169C22×C4—91no—
170C22×C4—91no—
171C22×C4—181no—
172C22×C4—181no—
173C22×C4—181no—
174C22×C4—181no—
175C2×C8—91no—
176C2×C8—181no—
177C2×C8—181no—
178C2×C8—181no—
179C2×C8—181no—
180C2×C8—181no—
181C2×C8C2×#15711yescharacteristic
182C4⋊C4—92no—
183C4⋊C4—91no—
184C4⋊C4—91no—
185C4⋊C4—181no—
186C4⋊C4—181no—
187C4⋊C4—181no—
188C4⋊C4—181no—
189C4⋊C4—181no—
190C4⋊C4—362no—
191C4⋊C4C2×#15711yescharacteristic
192C4⋊C4C2×#15711yescharacteristic
193C42—181no—
194C42—181no—
195C42—362no—
196C22×C3—22no—
197C2×D3—62no—
198C2×D3—62no—
199C2×D3—62no—
200C2×D3—62no—
201C2×D3—62no—
202C2×D3—62no—
203C3×C4—22no—
204C3×C4—22no—
205C3×C4—82no—
206C3×C4—82no—
207Dic3—62no—
208Dic3—62no—
209Dic3—242no—
210Dic3—242no—
211C32#191911yescharacteristic, complemented, Sylow
212C23—91no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—91no—
216C2×C4—91no—
217C2×C4—91no—
218C2×C4—91no—
219C2×C4—91no—
220C2×C4—92no—
221C2×C4—181no—
222C2×C4—181no—
223C2×C4—181no—
224C2×C4—182no—
225C2×C4—181no—
226C2×C4—181no—
227C2×C4—181no—
228C2×C4—181no—
229C2×C4—361no—
230C2×C4—361no—
231C2×C4—361no—
232C2×C4—361no—
233C2×C4—361no—
234C2×C4—361no—
235C2×C4—361no—
236C2×C4—361no—
237C2×C4—361no—
238C2×C4C22×#15711yescharacteristic
239C8—21no—
240C8—181no—
241C8—361no—
242C2×C3—22no—
243C2×C3—22no—
244C2×C3—22no—
245D3—62no—
246D3—62no—
247D3—62no—
248D3—62no—
249C22—91no—
250C22—91no—
251C22—91no—
252C22—91no—
253C22—91no—
254C22—91no—
255C22D4×#15711yescharacteristic
256C4—41no—
257C4—41no—
258C4—91no—
259C4—91no—
260C4—182no—
261C4—361no—
262C4—362no—
263C4—361no—
264C4—361no—
265C4—721no—
266C4#6428611yescharacteristic
267C4Q8×#15711yescharacteristic
268C3—22no—
269C2—91no—
270C2—91no—
271C2—91no—
272C2—91no—
273C2#1059375811yescharacteristic
274C2SD16×#15711yescharacteristic
275C2#1059378211yescharacteristic
subgroupG/H
centerC22D4×#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#106C4
socleC22×C32C4×D4
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C4×C3⋊D3C23
hypercenter#106#157
hypocenterC32#1919
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
19. C32×#106C4semidirect
20. #63644C4semidirect
21. #63635C4semidirect
22. #63635C4semidirect
141. #106#157semidirect
211. C32#1919semidirect

Maximal subgroups

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

subgroupindex
#105937592
C4⋊C4×#1572
C3⋊D3×#1062
#105901822
#105901812
#105901632
#19199