Finite Group Databasebeta

← #11791639

Subgroups — #11791639

Order 1152.

506 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 85 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#10593909C211yesmaximal, characteristic
2C4×C4⋊#157C211yesmaximal, characteristic
3#10590331C211yesmaximal, characteristic
4#10590049C214yesmaximal
5C2×#3797—21no—
6C2×C4⋊#157C2212yes—
7C2×C4×#157—21no—
8C42×C3⋊D3C2211yescharacteristic
9C3×#869—21no—
10#63919—21no—
11#63919C412yescomplemented
12#63900—21no—
13#63900C2212yes—
14#63873C412yescomplemented
15C2×#3710C2212yes—
16#63781—21no—
17C3×C4⋊(C3⋊C8)—21no—
18#63572—21no—
19D3×C4⋊Q8—61no—
20D3×C4⋊C8—61no—
21C22×#157—22no—
22C2×C4×C3⋊D3D411yescharacteristic
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C4×C3⋊D3C2311yescharacteristic
25C2×C3×Dic6—22no—
26C2×#627—22no—
27C2×#624—22no—
28#3797—42no—
29#3797—42no—
30C4⋊#157—22no—
31C4⋊#157Q814yescomplemented
32C4×#157—42no—
33C32×C42D411yescharacteristic
34C4×C3⋊Dic3C2×C411yescharacteristic
35C4×C3⋊Dic3C2×C411yescharacteristic
36C4×C3⋊Dic3D411yescharacteristic
37C3×C4⋊Dic3—22no—
38C3×C4⋊Dic3—22no—
39C2×C3×C3⋊C8—22no—
40#3724—22no—
41#3724C2×C414yes—
42#3710—24no—
43#1988—91nomaximal, Sylow
44C2×D3×Q8—62no—
45C3×C4⋊Q8—61no—
46#944—62no—
47C2×D3×C8—62no—
48D3×C4⋊C4—62no—
49D3×C4⋊C4—62no—
50#888—62no—
51#888—62no—
52C42×D3—61no—
53C42×D3—61no—
54#869—21no—
55C3×C4⋊C8—61no—
56Dic3⋊C8—62no—
57C4⋊(C3⋊C8)—21no—
58C22×C3⋊D3C2×D411yescharacteristic
59C2×#157—24no—
60C2×#157—42no—
61C2×#157—42no—
62C2×C32×C4C22⋊C411yescharacteristic
63C2×C32×C4C22⋊C411yescharacteristic
64C2×C32×C4C2×D411yescharacteristic
65C2×C3⋊Dic3C22⋊C411yescharacteristic
66C2×C3⋊Dic3C22⋊C411yescharacteristic
67C2×C3⋊Dic3C22×C411yescharacteristic
68C4×C3⋊D3—22no—
69C4×C3⋊D3D812yes—
70C4×C3⋊D3SD1612yes—
71C4×C3⋊D3C2×Q812yes—
72C4×C3⋊D3#4112yes—
73C2×C3×Dic3—24no—
74C3×Dic6—44no—
75#627—44no—
76#624—42no—
77#624—42no—
78C3×C3⋊C8—42no—
79C2×C4⋊Q8—91no—
80C2×C4⋊C8—91no—
81C4×C4⋊C4—91no—
82#340—94no—
83C2×C3×Q8—62no—
84D3×Q8—124no—
85D3×Q8—124no—
86C2×C4×D3—61no—
87C2×C4×D3—61no—
88C2×C4×D3—61no—
89C2×C4×D3—61no—
90C2×C4×D3—61no—
91C2×C4×D3—61no—
92C2×C4×D3—64no—
93C2×Dic6—22no—
94C2×Dic6—64no—
95C2×C3×C8—62no—
96C3×C4⋊C4—62no—
97C3×C4⋊C4—62no—
98C3×C42—21no—
99C3×C42—21no—
100C4⋊Dic3—22no—
101C4⋊Dic3—22no—
102Dic3⋊C4—64no—
103Dic3⋊C4—64no—
104C4×Dic3—61no—
105C4×Dic3—61no—
106C4×Dic3—61no—
107C4×Dic3—61no—
108C4×Dic3—61no—
109C4×Dic3—61no—
110C2×C3⋊C8—22no—
111D3×C8—124no—
112C22×C32C2×C22⋊C411yescharacteristic
113C2×C3⋊D3C22⋊Q812yes—
114C2×C3⋊D3C2×D811yescharacteristic
115C2×C3⋊D3C2×SD1611yescharacteristic
116C2×C3⋊D3#13712yes—
117#157—44no—
118C32×C4—21no—
119C32×C4#10212yes—
120C32×C4#12411yescharacteristic
121C32×C4C4⋊Q811yescharacteristic
122C3⋊Dic3—21no—
123C3⋊Dic3#10212yes—
124C3⋊Dic3C4×Q812yes—
125C3×Dic3—44no—
126C22×Q8—181no—
127C22×C8—92no—
128C4⋊Q8—61no—
129C4⋊Q8—92no—
130C4⋊Q8—92no—
131C4⋊Q8—181no—
132C2×C4⋊C4—92no—
133C2×C4⋊C4—92no—
134C2×C4⋊C4—181no—
135C2×C42—91no—
136C2×C42—181no—
137C4⋊C8—61no—
138C4⋊C8—181no—
139#95—181no—
140C22×D3—61no—
141C22×D3—61no—
142C3×Q8—124no—
143C2×C3×C4—21no—
144C2×C3×C4—21no—
145C2×C3×C4—21no—
146C2×C3×C4—21no—
147C2×C3×C4—21no—
148C2×C3×C4—21no—
149C2×C3×C4—64no—
150C2×Dic3—24no—
151C2×Dic3—61no—
152C2×Dic3—61no—
153C2×Dic3—61no—
154C2×Dic3—61no—
155C2×Dic3—61no—
156C2×Dic3—61no—
157C4×D3—62no—
158C4×D3—62no—
159C4×D3—62no—
160C4×D3—62no—
161C4×D3—62no—
162C4×D3—62no—
163C4×D3—62no—
164C4×D3—62no—
165C4×D3—64no—
166C4×D3—122no—
167C4×D3—124no—
168C4×D3—124no—
169Dic6—44no—
170Dic6—128no—
171C3×C8—122no—
172C3⋊C8—42no—
173C2×C32#39111yescharacteristic
174C2×C32C2×#10211yescharacteristic
175C2×C32#41911yescharacteristic
176C3⋊D3#47412yes—
177C3⋊D3#47512yes—
178C2×Q8—62no—
179C2×Q8—182no—
180C2×Q8—362no—
181C2×Q8—362no—
182C22×C4—91no—
183C22×C4—91no—
184C22×C4—91no—
185C22×C4—182no—
186C22×C4—182no—
187C2×C8—62no—
188C2×C8—184no—
189C4⋊C4—62no—
190C4⋊C4—62no—
191C4⋊C4—94no—
192C4⋊C4—94no—
193C4⋊C4—182no—
194C4⋊C4—182no—
195C42—91no—
196C42—91no—
197C42—91no—
198C42—362no—
199C42GO+(4,𝔽2)11yescharacteristic
200C22×C3—21no—
201C22×C3—21no—
202C2×D3—61no—
203C2×D3—61no—
204C2×D3—62no—
205C2×D3—62no—
206C2×D3—61no—
207C2×D3—61no—
208C2×D3—62no—
209C2×D3—62no—
210C3×C4—22no—
211C3×C4—21no—
212C3×C4—21no—
213C3×C4—21no—
214C3×C4—21no—
215C3×C4—22no—
216C3×C4—22no—
217C3×C4—41no—
218C3×C4—124no—
219Dic3—44no—
220Dic3—62no—
221Dic3—62no—
222Dic3—62no—
223Dic3—62no—
224Dic3—62no—
225Dic3—121no—
226C32#198811yescharacteristic, complemented, Sylow
227C23—91no—
228Q8—124no—
229Q8—364no—
230C2×C4—64no—
231C2×C4—91no—
232C2×C4—91no—
233C2×C4—92no—
234C2×C4—92no—
235C2×C4—92no—
236C2×C4—92no—
237C2×C4—91no—
238C2×C4—182no—
239C2×C4—184no—
240C2×C4—362no—
241C2×C4—362no—
242C2×C4—362no—
243C2×C4—362no—
244C2×C4D32⋊C411yescharacteristic
245C2×C4D32⋊C411yescharacteristic
246C2×C4C2×GO+(4,𝔽2)11yescharacteristic
247C8—122no—
248C2×C3—21no—
249C2×C3—21no—
250C2×C3—21no—
251C2×C3—21no—
252C2×C3—21no—
253C2×C3—21no—
254D3—62no—
255D3—62no—
256D3—62no—
257D3—62no—
258C22—91no—
259C22—91no—
260C22—92no—
261C22—92no—
262C22C2×D32⋊C411yescharacteristic
263C4—21no—
264C4—92no—
265C4—92no—
266C4—124no—
267C4—181no—
268C4—364no—
269C4#6372912yes—
270C4#6422111yescharacteristic
271C4#6422211yescharacteristic
272C3—21no—
273C3—21no—
274C2—92no—
275C2—92no—
276C2C2×#6372911yescharacteristic
277C2#1059332111yescharacteristic
278C2#1059334211yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1988
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
11. #63919C4semidirect
14. #63873C4semidirect
31. C4⋊#157Q8semidirect
226. C32#1988semidirect

Maximal subgroups

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

subgroupindex
#105939092
C4×C4⋊#1572
#105903312
#105900492
#19889