Finite Group Databasebeta

← #11775763

Subgroups — #11775763

Order 1152.

523 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 523 conjugacy classes of subgroups — too many to draw. Only its 88 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#10593854C211yesmaximal, characteristic
2#10592406C211yesmaximal, characteristic
3#10590247C211yesmaximal, characteristic
4C3×#4465C212yesmaximal, complemented
5#10589088C212yesmaximal, complemented
6#68362—32nomaximal
7C2×#3743—21no—
8C42×C3⋊D3C2211yescharacteristic
9C3×#870C2212yes—
10#63919C411yescharacteristic
11#63919C411yescharacteristic
12#63865—21no—
13#63865—21no—
14#63849C412yes—
15#63838—21no—
16#63838—21no—
17C2×#3712—21no—
18C32×#97C2211yescharacteristic
19C8×C3⋊Dic3—21no—
20#63630C2211yescharacteristic
21C3×#803C2212yes—
22#63553—21no—
23#5688—32no—
24#4707—32no—
25#4707—32no—
26#4707—61no—
27C3×#330—32no—
28#4543—32no—
29#4465—32no—
30#4465D312yescomplemented
31C2×C4×C3⋊D3C2×C411yescharacteristic
32C2×C4×C3⋊D3D411yescharacteristic
33C2×C4×C3⋊D3D411yescharacteristic
34C2×#627—21no—
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×C4⋊Dic3C2×C412yes—
45C3×Dic3⋊C4—22no—
46C3×Dic3⋊C4—22no—
47C2×C3×C3⋊C8—22no—
48#3724—21no—
49#3724—21no—
50#3722—22no—
51Dic32—22no—
52#3712—24no—
53#1526—91noSylow
54C3×#125—32no—
55C2×ΓL(1,𝔽25)—62no—
56C2×ΓL(1,𝔽25)—62no—
57C2×ΓL(1,𝔽25)—62no—
58#896—62no—
59#896—62no—
60#892—32no—
61#892—32no—
62#888—32no—
63#888—32no—
64#887—62no—
65#887—62no—
66C42×D3—32no—
67C42×D3—61no—
68#870C2×D312yes—
69C3×#97—21no—
70C3×#97—32no—
71C3×#97C2×D312yes—
72C8×Dic3—62no—
73C8×Dic3—62no—
74C8×Dic3—62no—
75#803—32no—
76#803—61no—
77#803C2×D312yes—
78C22×C3⋊D3C22⋊C411yescharacteristic
79C2×C32×C4C22×C411yescharacteristic
80C2×C32×C4C2×D411yescharacteristic
81C2×C32×C4C2×D411yescharacteristic
82C2×C3⋊Dic3C22⋊C411yescharacteristic
83C2×C3⋊Dic3C22⋊C411yescharacteristic
84C2×C3⋊Dic3C22⋊C411yescharacteristic
85C4×C3⋊D3—22no—
86C4×C3⋊D3—22no—
87C4×C3⋊D3—22no—
88C2×C3×Dic3—22no—
89C2×C3×Dic3—22no—
90#627—42no—
91#627—42no—
92C32×C8—22no—
93C3⋊(C3⋊C8)—22no—
94C3×C3⋊C8—24no—
95#533—91no—
96C4×M16—91no—
97C4×M16—91no—
98#330—32no—
99#330—92no—
100C2×C4×D3—32no—
101C2×C4×D3—32no—
102C2×C4×D3—32no—
103C2×C4×D3—61no—
104C2×C4×D3—61no—
105C2×C4×D3—61no—
106C2×Dic6—62no—
107C2×Dic6—62no—
108C2×C3×C8—22no—
109C2×C3×C8—22no—
110C2×C3×C8—62no—
111C3×C4⋊C4—32no—
112C3×C4⋊C4—32no—
113C3×C4⋊C4—62no—
114C3×C4⋊C4—62no—
115C3×C42—21no—
116C3×C42C22×D312yes—
117(C2×D3)⋊C4—62no—
118(C2×D3)⋊C4—62no—
119C4⋊Dic3C4×D312yes—
120C4⋊Dic3C4×D312yes—
121Dic3⋊C4—22no—
122Dic3⋊C4—22no—
123Dic3⋊C4—62no—
124Dic3⋊C4—62no—
125C4×Dic3—32no—
126C4×Dic3—32no—
127C4×Dic3—32no—
128C4×Dic3—61no—
129C4×Dic3—61no—
130C4×Dic3—61no—
131C4×Dic3—62no—
132C4×Dic3—62no—
133C2×C3⋊C8—22no—
134C2×C3⋊C8—62no—
135C2×C3⋊C8—62no—
136ΓL(1,𝔽25)—68no—
137ΓL(1,𝔽25)—68no—
138ΓL(1,𝔽25)—68no—
139C22×C32C2×C22⋊C411yescharacteristic
140C2×C3⋊D3—21no—
141C2×C3⋊D3—21no—
142C2×C3⋊D3—21no—
143C32×C4—21no—
144C32×C4—21no—
145C32×C4—21no—
146C3⋊Dic3#10112yes—
147C3⋊Dic3#10412yes—
148C3⋊Dic3#10412yes—
149C3×Dic3—42no—
150C3×Dic3—42no—
151C2×M16—181no—
152C2×M16—181no—
153C4⋊Q8—91no—
154C4⋊Q8—91no—
155#125—32no—
156C22⋊Q8—181no—
157C22⋊Q8—181no—
158C4×Q8—181no—
159C4×Q8—181no—
160#117—92no—
161C2×C42—91no—
162#97—32no—
163#97—91no—
164#97D3211yescharacteristic
165C4×C8—181no—
166C4×C8—181no—
167C22×D3—32no—
168C22×D3—61no—
169C2×C3×C4—21no—
170C2×C3×C4—21no—
171C2×C3×C4—21no—
172C2×C3×C4—62no—
173C2×C3×C4—62no—
174C2×C3×C4C2×C4×D312yes—
175C2×C3×C4D3×D412yes—
176C2×C3×C4D3×D412yes—
177C2×Dic3—22no—
178C2×Dic3—22no—
179C2×Dic3—32no—
180C2×Dic3—32no—
181C2×Dic3—32no—
182C2×Dic3—61no—
183C2×Dic3—61no—
184C2×Dic3—61no—
185C4×D3—64no—
186C4×D3—64no—
187C4×D3—64no—
188C4×D3—64no—
189C4×D3—122no—
190C4×D3—122no—
191Dic6—124no—
192Dic6—124no—
193C3×C8—24no—
194C3×C8—24no—
195C3×C8—64no—
196C3⋊C8—24no—
197C3⋊C8—64no—
198C3⋊C8—64no—
199C2×C32C2×#10111yescharacteristic
200C2×C32C2×#10411yescharacteristic
201C2×C32C2×#10411yescharacteristic
202C3⋊D3—41no—
203C2×Q8—181no—
204C2×Q8—181no—
205C22×C4—91no—
206C22×C4—91no—
207C22×C4—91no—
208M16—184no—
209M16—184no—
210C2×C8—21no—
211C2×C8—62no—
212C2×C8—181no—
213C4⋊C4—32no—
214C4⋊C4—32no—
215C4⋊C4—62no—
216C4⋊C4—62no—
217C4⋊C4—181no—
218C4⋊C4—181no—
219C22⋊C4—182no—
220C42—91no—
221C42—91no—
222C42—91no—
223C42—182no—
224C42C2×D3211yescharacteristic
225C22×C3—21no—
226C22×C3D3×C22⋊C412yes—
227C2×D3—62no—
228C2×D3—62no—
229C2×D3—62no—
230C2×D3—62no—
231C2×D3—121no—
232C2×D3—121no—
233C3×C4—22no—
234C3×C4—22no—
235C3×C4—22no—
236C3×C4—22no—
237C3×C4—41no—
238C3×C4—41no—
239C3×C4—122no—
240C3×C4—122no—
241Dic3—34no—
242Dic3—34no—
243Dic3—34no—
244Dic3—42no—
245Dic3—42no—
246Dic3—62no—
247Dic3—62no—
248Dic3—62no—
249C32#152611yescharacteristic, complemented, Sylow
250C23—91no—
251Q8—362no—
252Q8—362no—
253C2×C4—62no—
254C2×C4—62no—
255C2×C4—91no—
256C2×C4—91no—
257C2×C4—91no—
258C2×C4—182no—
259C2×C4—182no—
260C2×C4—182no—
261C2×C4C4×D3211yescharacteristic
262C2×C4#380211yescharacteristic
263C2×C4#381111yescharacteristic
264C8—22no—
265C8—64no—
266C8—182no—
267C2×C3—21no—
268C2×C3—21no—
269C2×C3—21no—
270C2×C3D3×#10112yes—
271C2×C3D3×#10412yes—
272C2×C3D3×#10412yes—
273D3—122no—
274D3—122no—
275C22—181no—
276C22—181no—
277C22—181no—
278C22#6392111yescharacteristic
279C4—21no—
280C4—21no—
281C4—21no—
282C4—92no—
283C4—92no—
284C4—92no—
285C4—122no—
286C4—122no—
287C3—21no—
288C3#6836212yescomplemented
289C2—361no—
290C2#1059039311yescharacteristic
291C2#1059100311yescharacteristic
292C2#1059100811yescharacteristic
subgroupG/H
centerC22#63921
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×#97C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C22⋊C4
cosocleC32×C42C23
hypercenter#97D32
hypocenterC32#1526
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
4. C3×#4465C2semidirect
5. #10589088C2semidirect
30. #4465D3semidirect
249. C32#1526semidirect
288. C3#68362semidirect

Maximal subgroups

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

subgroupindex
#105938542
#105924062
#105902472
C3×#44652
#105890882
#683623