Finite Group Databasebeta

← #11774535

Subgroups — #11774535

Order 1152.

507 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 507 conjugacy classes of subgroups — too many to draw. Only its 100 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#10593882C211yesmaximal, characteristic
2C4×#3743C211yesmaximal, characteristic
3#10590256C211yesmaximal, characteristic
4C3×#4456C212yesmaximal, complemented
5#10589083C212yesmaximal, complemented
6#68235—32nomaximal
7C2×#3743—21no—
8C42×C3⋊D3C2211yescharacteristic
9C3×C4×Dic6C2212yes—
10#63919C411yescharacteristic
11C4×#627—21no—
12#63874—21no—
13#63873C411yescharacteristic
14#63871C412yes—
15#63870—21no—
16#63865—21no—
17C32×C4×C8C2211yescharacteristic
18#63642—21no—
19C4×C3⋊(C3⋊C8)C2211yescharacteristic
20C3×C4⋊(C3⋊C8)C2212yes—
21#63557—21no—
22#63553—21no—
23#5578—32no—
24#4833—32no—
25C4×ΓL(1,𝔽25)—32no—
26C4×ΓL(1,𝔽25)—61no—
27C3×Q8⋊C8—32no—
28#4535—32no—
29#4484—32no—
30#4456D312yescomplemented
31C2×C4×C3⋊D3C2×C411yescharacteristic
32C2×C4×C3⋊D3D411yescharacteristic
33C2×C4×C3⋊D3D411yescharacteristic
34C2×C3×Dic6C2×C412yes—
35C2×#627—21no—
36C2×C32×C8—21no—
37C32×C42C2311yescharacteristic
38C4×C3⋊Dic3C2×C411yescharacteristic
39C4×C3⋊Dic3D411yescharacteristic
40C4×C3⋊Dic3D411yescharacteristic
41C2×C3⋊(C3⋊C8)—21no—
42#3743—24no—
43C3×C4⋊Dic3C2×C412yes—
44C3×Dic3⋊C4—22no—
45C3×C4×Dic3—22no—
46C2×C3×C3⋊C8—22no—
47#3724—21no—
48#3724—21no—
49#3724—21no—
50Dic3⋊Dic3—22no—
51#3722—22no—
52#1485—91noSylow
53C3×C4×Q8—32no—
54#946—32no—
55#944—32no—
56C2×ΓL(1,𝔽25)—62no—
57C2×ΓL(1,𝔽25)—62no—
58#897—32no—
59#896—62no—
60#889—62no—
61#888—32no—
62#872—62no—
63C42×D3—32no—
64C42×D3—61no—
65C4×Dic6—62no—
66C4×Dic6C2×D312yes—
67C3×C4⋊C8—32no—
68C3×C4×C8—21no—
69C3×C4×C8C2×D312yes—
70(C2×D3)⋊C8—62no—
71#815—62no—
72#815—62no—
73C8×Dic3—62no—
74C4⋊(C3⋊C8)C2×D312yes—
75C4×C3⋊C8—32no—
76C4×C3⋊C8—61no—
77C22×C3⋊D3C22⋊C411yescharacteristic
78C2×C32×C4C22×C411yescharacteristic
79C2×C32×C4C2×D411yescharacteristic
80C2×C32×C4C2×D411yescharacteristic
81C2×C3⋊Dic3C22⋊C411yescharacteristic
82C2×C3⋊Dic3C22⋊C411yescharacteristic
83C2×C3⋊Dic3C22⋊C411yescharacteristic
84C4×C3⋊D3—22no—
85C4×C3⋊D3—22no—
86C4×C3⋊D3—22no—
87C2×C3×Dic3—22no—
88C2×C3×Dic3—22no—
89C3×Dic6—22no—
90C3×Dic6—22no—
91#627—42no—
92C32×C8—22no—
93C3⋊(C3⋊C8)—22no—
94C3×C3⋊C8—42no—
95#533—91no—
96#431—91no—
97C4×M16—91no—
98Q8⋊C8—32no—
99Q8⋊C8—92no—
100C2×C3×Q8—32no—
101C2×C4×D3—32no—
102C2×C4×D3—32no—
103C2×C4×D3—32no—
104C2×C4×D3—61no—
105C2×C4×D3—61no—
106C2×C4×D3—61no—
107C2×Dic6—62no—
108C2×Dic6C4×D312yes—
109C2×C3×C8—22no—
110C2×C3×C8—22no—
111C2×C3×C8—62no—
112C3×C4⋊C4—32no—
113C3×C4⋊C4—62no—
114C3×C42—21no—
115C3×C42—62no—
116C3×C42C22×D312yes—
117(C2×D3)⋊C4—62no—
118(C2×D3)⋊C4—62no—
119C4⋊Dic3—62no—
120C4⋊Dic3C4×D312yes—
121Dic3⋊C4—22no—
122Dic3⋊C4—62no—
123Dic3⋊C4—62no—
124Dic3⋊C4—62no—
125Dic3⋊C4—62no—
126C4×Dic3—22no—
127C4×Dic3—32no—
128C4×Dic3—32no—
129C4×Dic3—32no—
130C4×Dic3—61no—
131C4×Dic3—61no—
132C4×Dic3—61no—
133C2×C3⋊C8—22no—
134C2×C3⋊C8—62no—
135C2×C3⋊C8—62no—
136ΓL(1,𝔽25)—68no—
137ΓL(1,𝔽25)—68no—
138C22×C32C2×C22⋊C411yescharacteristic
139C2×C3⋊D3—21no—
140C2×C3⋊D3—21no—
141C2×C3⋊D3—21no—
142C32×C4—21no—
143C32×C4#13112yes—
144C32×C4#13712yes—
145C3⋊Dic3—21no—
146C3⋊Dic3—21no—
147C3⋊Dic3#10412yes—
148C3×Dic3—42no—
149C3×Dic3—42no—
150C2×M16—181no—
151C4⋊Q8—91no—
152C4⋊Q8—91no—
153#125—181no—
154C22⋊Q8—92no—
155C22⋊Q8—181no—
156C4×Q8—32no—
157C4×Q8—181no—
158#117—181no—
159C2×C42—91no—
160C4⋊C8—32no—
161C22⋊C8—181no—
162#97—181no—
163C4×C8—91no—
164C4×C8—181no—
165C4×C8D3211yescharacteristic
166C22×D3—32no—
167C22×D3—61no—
168C3×Q8—62no—
169C3×Q8—62no—
170C2×C3×C4—21no—
171C2×C3×C4—21no—
172C2×C3×C4—21no—
173C2×C3×C4—62no—
174C2×C3×C4—62no—
175C2×C3×C4C2×C4×D312yes—
176C2×C3×C4D3×D412yes—
177C2×C3×C4D3×D412yes—
178C2×Dic3—22no—
179C2×Dic3—22no—
180C2×Dic3—32no—
181C2×Dic3—32no—
182C2×Dic3—32no—
183C2×Dic3—61no—
184C2×Dic3—61no—
185C2×Dic3—61no—
186C4×D3—64no—
187C4×D3—64no—
188C4×D3—62no—
189C4×D3—62no—
190C4×D3—62no—
191C4×D3—62no—
192C4×D3—122no—
193C4×D3—122no—
194Dic6—22no—
195Dic6—22no—
196Dic6—124no—
197C3×C8—24no—
198C3×C8—24no—
199C3×C8—122no—
200C3⋊C8—42no—
201C3⋊C8—64no—
202C3⋊C8—64no—
203C2×C32#40811yescharacteristic
204C2×C32#41911yescharacteristic
205C2×C32C2×#10411yescharacteristic
206C3⋊D3—41no—
207C2×Q8—32no—
208C2×Q8—181no—
209C22×C4—91no—
210C22×C4—91no—
211C22×C4—91no—
212M16—184no—
213C2×C8—21no—
214C2×C8—62no—
215C2×C8—181no—
216C4⋊C4—32no—
217C4⋊C4—62no—
218C4⋊C4—181no—
219C4⋊C4—181no—
220C4⋊C4—182no—
221C4⋊C4—181no—
222C22⋊C4—182no—
223C42—62no—
224C42—91no—
225C42—91no—
226C42—91no—
227C42C2×D3211yescharacteristic
228C22×C3—21no—
229C22×C3D3×C22⋊C412yes—
230C2×D3—62no—
231C2×D3—62no—
232C2×D3—62no—
233C2×D3—62no—
234C2×D3—121no—
235C2×D3—121no—
236C3×C4—22no—
237C3×C4—22no—
238C3×C4—22no—
239C3×C4—22no—
240C3×C4—122no—
241C3×C4—122no—
242C3×C4#90112yes—
243C3×C4#90712yes—
244C3×C4#91512yes—
245C3×C4#91812yes—
246Dic3—34no—
247Dic3—42no—
248Dic3—42no—
249Dic3—62no—
250Dic3—62no—
251Dic3—62no—
252Dic3—121no—
253Dic3—121no—
254C32#148511yescharacteristic, complemented, Sylow
255C23—91no—
256Q8—62no—
257Q8—62no—
258Q8—362no—
259C2×C4—62no—
260C2×C4—62no—
261C2×C4—91no—
262C2×C4—91no—
263C2×C4—91no—
264C2×C4—182no—
265C2×C4—182no—
266C2×C4—182no—
267C2×C4C4×D3211yescharacteristic
268C2×C4#380211yescharacteristic
269C2×C4#381111yescharacteristic
270C8—22no—
271C8—122no—
272C8—182no—
273C2×C3—21no—
274C2×C3—21no—
275C2×C3—21no—
276C2×C3#472712yes—
277C2×C3#480212yes—
278C2×C3D3×#10412yes—
279D3—122no—
280D3—122no—
281C22—181no—
282C22—181no—
283C22—181no—
284C22#6392111yescharacteristic
285C4—21no—
286C4—92no—
287C4—122no—
288C4—122no—
289C4—181no—
290C4—181no—
291C4#6380412yes—
292C4#6381112yes—
293C3—21no—
294C3#6823512yescomplemented
295C2—361no—
296C2#1059039311yescharacteristic
297C2#1059069111yescharacteristic
298C2#1059095911yescharacteristic
subgroupG/H
centerC2×C4#3802
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C22⋊C4
cosocleC32×C42C23
hypercenterC4×C8D32
hypocenterC32#1485
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
4. C3×#4456C2semidirect
5. #10589083C2semidirect
30. #4456D3semidirect
254. C32#1485semidirect
294. C3#68235semidirect

Maximal subgroups

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

subgroupindex
#105938822
C4×#37432
#105902562
C3×#44562
#105890832
#682353