Finite Group Databasebeta

← #11784057

Subgroups — #11784057

Order 1152.

546 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C4×#3797C211yesmaximal, characteristic
2C4×C4⋊#157C211yesmaximal, characteristic
3C2×#63730C212yesmaximal
4#10590322C211yesmaximal, characteristic
5#10590049C212yesmaximal
6C2×#3797C2211yescharacteristic
7C2×C4⋊#157C2212yes—
8C2×C4×#157—21no—
9C42×C3⋊D3C2211yescharacteristic
10C3×C4×Dic6—21no—
11C4×#627C412yescomplemented
12#63900C2211yescharacteristic
13#63883—21no—
14C4×#624—21no—
15#63843—21no—
16#63838C412yescomplemented
17C2×#3710C2212yes—
18#63781—21no—
19#63730C418yescomplemented
20C3×#803—21no—
21#63555—21no—
22C4×D3×Q8—61no—
23D3×#97—61no—
24C22×#157—22no—
25C2×C4×C3⋊D3D411yescharacteristic
26C2×C4×C3⋊D3D411yescharacteristic
27C2×C4×C3⋊D3C2311yescharacteristic
28C2×C3×Dic6—21no—
29C2×#627C2×C412yes—
30C2×#624—21no—
31C2×#624—21no—
32#3797—22no—
33#3797C2×C414yes—
34C4⋊#157—22no—
35C4⋊#157C2×C414yes—
36C4×#157—42no—
37C32×C42D411yescharacteristic
38C4×C3⋊Dic3C2×C411yescharacteristic
39C4×C3⋊Dic3C2×C411yescharacteristic
40C4×C3⋊Dic3D411yescharacteristic
41C3×C4⋊Dic3—21no—
42C3×Dic3⋊C4—22no—
43C3×C4×Dic3—22no—
44C2×C3×C3⋊C8—22no—
45#3724C2×C412yes—
46Dic3⋊Dic3—22no—
47Dic32—22no—
48#3710—22no—
49#3710C2×C414yes—
50#1763—91nomaximal, Sylow
51C2×D3×Q8—61no—
52C3×C4×Q8—61no—
53Q8×Dic3—61no—
54C2×D3×C8—62no—
55D3×C4⋊C4—61no—
56D3×C4⋊C4—62no—
57#887—62no—
58#887—61no—
59C42×D3—61no—
60C42×D3—61no—
61C42×D3—62no—
62C4×Dic6—21no—
63C4×Dic6—62no—
64C3×#97—61no—
65#815—62no—
66#803—21no—
67C22×C3⋊D3C2×D411yescharacteristic
68C2×#157—24no—
69C2×#157—42no—
70C2×#157—42no—
71C2×C32×C4C22⋊C411yescharacteristic
72C2×C32×C4C22⋊C411yescharacteristic
73C2×C32×C4C2×D411yescharacteristic
74C2×C3⋊Dic3C22⋊C411yescharacteristic
75C2×C3⋊Dic3C22⋊C411yescharacteristic
76C2×C3⋊Dic3C22×C411yescharacteristic
77C4×C3⋊D3—22no—
78C4×C3⋊D3—21no—
79C4×C3⋊D3—21no—
80C4×C3⋊D3C22×C412yes—
81C4×C3⋊D3#4112yes—
82C2×C3×Dic3—22no—
83C2×C3×Dic3—22no—
84C3×Dic6—24no—
85#627—22no—
86#627C4214yescomplemented
87#624—24no—
88#624—41no—
89#624—41no—
90C3×C3⋊C8—24no—
91C2×C4×Q8—91no—
92C2×#103—92no—
93C2×#97—91no—
94C4×C4⋊C4—91no—
95#340—92no—
96C2×C3×Q8—61no—
97D3×Q8—64no—
98D3×Q8—64no—
99C2×C4×D3—61no—
100C2×C4×D3—61no—
101C2×C4×D3—61no—
102C2×C4×D3—61no—
103C2×C4×D3—61no—
104C2×C4×D3—61no—
105C2×C4×D3—62no—
106C2×C4×D3—62no—
107C2×Dic6—21no—
108C2×Dic6—62no—
109C2×C3×C8—62no—
110C3×C4⋊C4—62no—
111C3×C4⋊C4—61no—
112C3×C42—21no—
113C3×C42—21no—
114C3×C42—62no—
115C4⋊Dic3—21no—
116C4⋊Dic3—62no—
117Dic3⋊C4—22no—
118Dic3⋊C4—62no—
119Dic3⋊C4—62no—
120C4×Dic3—22no—
121C4×Dic3—61no—
122C4×Dic3—61no—
123C4×Dic3—61no—
124C4×Dic3—61no—
125C4×Dic3—61no—
126C4×Dic3—61no—
127C4×Dic3—62no—
128C4×Dic3—62no—
129C2×C3⋊C8—22no—
130D3×C8—64no—
131D3×C8—64no—
132C22×C32C2×C22⋊C411yescharacteristic
133C2×C3⋊D3C4×D412yes—
134C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
135C2×C3⋊D3#13712yes—
136C2×C3⋊D3#13711yescharacteristic
137#157—44no—
138C32×C4—21no—
139C32×C4—21no—
140C32×C4C4×D412yes—
141C3⋊Dic3—21no—
142C3⋊Dic3—21no—
143C3⋊Dic3C2×C4211yescharacteristic
144C3⋊Dic3#11711yescharacteristic
145C3×Dic3—24no—
146C3×Dic3—42no—
147C22×Q8—91no—
148C22×C8—92no—
149C4×Q8—61no—
150C4×Q8—92no—
151C4×Q8—92no—
152C4×Q8—181no—
153C2×C4⋊C4—91no—
154C2×C4⋊C4—92no—
155C2×C4⋊C4—181no—
156C2×C42—91no—
157C2×C42—181no—
158C2×C42—181no—
159#103—98no—
160#97—61no—
161#97—181no—
162#95—181no—
163C22×D3—61no—
164C22×D3—61no—
165C3×Q8—64no—
166C2×C3×C4—21no—
167C2×C3×C4—21no—
168C2×C3×C4—21no—
169C2×C3×C4—21no—
170C2×C3×C4—21no—
171C2×C3×C4—21no—
172C2×C3×C4—62no—
173C2×C3×C4—62no—
174C2×Dic3—22no—
175C2×Dic3—22no—
176C2×Dic3—61no—
177C2×Dic3—61no—
178C2×Dic3—61no—
179C2×Dic3—61no—
180C2×Dic3—61no—
181C2×Dic3—61no—
182C4×D3—62no—
183C4×D3—62no—
184C4×D3—62no—
185C4×D3—62no—
186C4×D3—68no—
187C4×D3—64no—
188C4×D3—121no—
189C4×D3—121no—
190C4×D3—122no—
191C4×D3—121no—
192C4×D3—121no—
193C4×D3—122no—
194C4×D3—122no—
195Dic6—24no—
196Dic6—64no—
197Dic6—64no—
198C3×C8—64no—
199C3⋊C8—24no—
200C2×C32C4×C22⋊C411yescharacteristic
201C2×C32#41711yescharacteristic
202C2×C32#41911yescharacteristic
203C3⋊D3#44012yes—
204C3⋊D3#44112yes—
205C2×Q8—61no—
206C2×Q8—92no—
207C2×Q8—94no—
208C2×Q8—182no—
209C22×C4—91no—
210C22×C4—91no—
211C22×C4—91no—
212C22×C4—181no—
213C22×C4—181no—
214C22×C4—182no—
215C2×C8—62no—
216C2×C8—94no—
217C2×C8—182no—
218C4⋊C4—61no—
219C4⋊C4—62no—
220C4⋊C4—92no—
221C4⋊C4—94no—
222C4⋊C4—182no—
223C4⋊C4—182no—
224C42—62no—
225C42—91no—
226C42—91no—
227C42—91no—
228C42—182no—
229C42—362no—
230C42GO+(4,𝔽2)11yescharacteristic
231C22×C3—21no—
232C22×C3—21no—
233C2×D3—62no—
234C2×D3—62no—
235C2×D3—62no—
236C2×D3—61no—
237C2×D3—61no—
238C2×D3—61no—
239C2×D3—61no—
240C2×D3—62no—
241C3×C4—22no—
242C3×C4—22no—
243C3×C4—22no—
244C3×C4—41no—
245C3×C4—41no—
246C3×C4—41no—
247C3×C4—64no—
248C3×C4—122no—
249Dic3—24no—
250Dic3—42no—
251Dic3—61no—
252Dic3—61no—
253Dic3—61no—
254Dic3—61no—
255Dic3—62no—
256Dic3—121no—
257Dic3—121no—
258Dic3—121no—
259C32#176311yescharacteristic, complemented, Sylow
260C23—91no—
261Q8—64no—
262Q8—94no—
263Q8—182no—
264C2×C4—62no—
265C2×C4—62no—
266C2×C4—91no—
267C2×C4—92no—
268C2×C4—92no—
269C2×C4—91no—
270C2×C4—91no—
271C2×C4—181no—
272C2×C4—182no—
273C2×C4—181no—
274C2×C4—184no—
275C2×C4—184no—
276C2×C4—361no—
277C2×C4—361no—
278C2×C4—362no—
279C2×C4—362no—
280C2×C4D32⋊C411yescharacteristic
281C2×C4D32⋊C411yescharacteristic
282C2×C4C2×GO+(4,𝔽2)11yescharacteristic
283C8—64no—
284C2×C3—21no—
285C2×C3—21no—
286C2×C3—21no—
287C2×C3—21no—
288C2×C3—21no—
289C2×C3—21no—
290D3—62no—
291D3—62no—
292D3—62no—
293D3—62no—
294C22—91no—
295C22—91no—
296C22—92no—
297C22—92no—
298C22C2×D32⋊C411yescharacteristic
299C4—21no—
300C4—21no—
301C4—64no—
302C4—91no—
303C4—91no—
304C4—122no—
305C4—181no—
306C4—181no—
307C4—364no—
308C4C4×GO+(4,𝔽2)12yes—
309C3—21no—
310C3—21no—
311C2—92no—
312C2—92no—
313C2#1059331911yescharacteristic
314C2#1059332111yescharacteristic
315C2C4×D32⋊C411yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC3⋊Dic3C2×C42
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1763
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
11. C4×#627C4semidirect
16. #63838C4semidirect
19. #63730C4semidirect
86. #627C42semidirect
259. C32#1763semidirect

Maximal subgroups

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

subgroupindex
C4×#37972
C4×C4⋊#1572
C2×#637302
#105903222
#105900492
#17639