Finite Group Databasebeta

← #11784153

Subgroups — #11784153

Order 1152.

490 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 87 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
1C2×#63803C211yesmaximal, characteristic
2C2×#63767C211yesmaximal, characteristic, complemented
3#10593349C211yesmaximal, characteristic
4C2×#63731C211yesmaximal, characteristic
5#10590703C211yesmaximal, characteristic, complemented
6#10590051C211yesmaximal, characteristic, complemented
7#10590047C211yesmaximal, characteristic, complemented
8C2×#3798C2211yescharacteristic
9C2×C4×#157C2211yescharacteristic
10C2×#3787C2211yescharacteristic
11C2×C8×C3⋊D3C2211yescharacteristic
12C2×C3×D3×C8—21no—
13#63874C2211yescharacteristic
14C2×#3712C2211yescharacteristic
15C2×#3712C2211yescharacteristic
16C2×#3711—21no—
17#63803—22no—
18#63803C414yescomplemented
19#63767—22no—
20#63740C412yescomplemented
21#63739C412yescomplemented
22#63731C414yescomplemented
23C3×#815—21no—
24Dic3×C3⋊C8—21no—
25C2×#901—61no—
26#4708—61no—
27C22×#157—21no—
28C2×C4×C3⋊D3C2311yescharacteristic
29C2×C3×C4×D3—21no—
30C2×#627C2×C411yescharacteristic
31C2×#626—21no—
32C2×#625C2×C411yescharacteristic
33#3798—21no—
34#3798—21no—
35#3798C2×C412yes—
36#3798C2×C412yes—
37C2×#622C2×C412yes—
38C4×#157—21no—
39C4×#157C2×C412yes—
40#3787—21no—
41#3787—21no—
42C2×C32×C8D411yescharacteristic
43C2×C3⋊(C3⋊C8)D411yescharacteristic
44C8×C3⋊D3C2×C412yes—
45C8×C3⋊D3D412yes—
46C3×C4×Dic3—21no—
47C2×C3×C3⋊C8—21no—
48C2×C3×C3⋊C8—21no—
49C3×D3×C8—24no—
50#3724C2×C412yes—
51#3722—21no—
52#3712—21no—
53#3712—21no—
54#3712C2×C412yes—
55#3712C2×C412yes—
56#3711—24no—
57#1765—91nomaximal, Sylow
58C2×#235—61no—
59C22×C3×C8—61no—
60C2×#208—61no—
61#901—64no—
62#901—64no—
63C2×ΓL(1,𝔽25)—61no—
64C2×ΓL(1,𝔽25)—61no—
65C2×ΓL(1,𝔽25)—61no—
66C2×D3×C8—21no—
67C2×D3×C8—61no—
68C2×D3×C8—61no—
69#872—61no—
70C3×#97—61no—
71#815—21no—
72C8×Dic3—61no—
73C4×C3⋊C8—61no—
74C22×C3⋊D3#4111yescharacteristic
75C22×C3×D3—21no—
76C2×#157—22no—
77C2×#157—42no—
78C2×C32×C4C2×D411yescharacteristic
79C2×C3⋊Dic3C22×C411yescharacteristic
80C4×C3⋊D3C22×C411yescharacteristic
81C4×C3⋊D3C22×C411yescharacteristic
82C4×C3⋊D3C2×D411yescharacteristic
83C4×C3⋊D3#4111yescharacteristic
84C2×C3×Dic3—21no—
85C2×C3×Dic3—22no—
86C3×C4×D3—22no—
87C3×C4×D3—22no—
88#627—21no—
89#627C4212yes—
90#626—22no—
91#626—22no—
92#625—21no—
93#625C4212yes—
94#622—22no—
95C32×C8C22⋊C412yes—
96C3⋊(C3⋊C8)C22⋊C412yes—
97C3×C3⋊C8—22no—
98C3×C3⋊C8—22no—
99C2×#131—91no—
100C2×#104—91no—
101#416—91no—
102#405—91no—
103C2×#97—91no—
104#341—91no—
105#339—91no—
106C22×C3×C4—61no—
107C2×#67—61no—
108C2×#67—61no—
109#235—62no—
110#235—62no—
111#235—62no—
112#235—62no—
113C2×D12—61no—
114C2×C4×D3—21no—
115C2×C4×D3—61no—
116C2×C4×D3—61no—
117C2×Dic6—61no—
118C2×C3×C8—21no—
119C2×C3×C8—21no—
120C2×C3×C8—64no—
121C2×C3×C8—61no—
122C2×C3×C8—61no—
123C3×C42—61no—
124(C2×D3)⋊C4—62no—
125Dic3⋊C4—62no—
126C4×Dic3—21no—
127#208—64no—
128C2×C3⋊C8—21no—
129C2×C3⋊C8—21no—
130C2×C3⋊C8—61no—
131C2×C3⋊C8—61no—
132ΓL(1,𝔽25)—62no—
133ΓL(1,𝔽25)—62no—
134ΓL(1,𝔽25)—62no—
135ΓL(1,𝔽25)—62no—
136ΓL(1,𝔽25)—64no—
137D3×C8—24no—
138D3×C8—62no—
139D3×C8—62no—
140D3×C8—62no—
141D3×C8—62no—
142C22×C32C4×D411yescharacteristic
143C2×C3⋊D3—22no—
144C2×C3⋊D3#11711yescharacteristic
145C2×C3⋊D3C4×D411yescharacteristic
146C2×C3×D3—22no—
147C2×C3×D3—42no—
148#157—42no—
149C32×C4C2×C22⋊C411yescharacteristic
150C32×C4C4×D411yescharacteristic
151C3⋊Dic3C2×C4211yescharacteristic
152C3⋊Dic3C4×D411yescharacteristic
153C3×Dic3—22no—
154C3×Dic3—42no—
155C2×#41—91no—
156#131—94no—
157#131—182no—
158C2×M16—91no—
159C2×M16—91no—
160C2×M16—181no—
161C22×C8—61no—
162C22×C8—91no—
163C22×C8—91no—
164#117—91no—
165C2×C42—91no—
166#104—94no—
167#103—92no—
168#102—92no—
169#97—61no—
170#97—182no—
171C4×C8—181no—
172C23×C3—61no—
173C22×D3—21no—
174C22×D3—61no—
175C22×D3—61no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—62no—
179C2×C3×C4—62no—
180C2×C3×C4—61no—
181C2×C3×C4—62no—
182#67—62no—
183#67—62no—
184#67—62no—
185#67—62no—
186C2×Dic3—21no—
187C2×Dic3—22no—
188C2×Dic3—61no—
189C2×Dic3—61no—
190D12—62no—
191D12—62no—
192C4×D3—22no—
193C4×D3—22no—
194C4×D3—61no—
195C4×D3—61no—
196C4×D3—61no—
197C4×D3—61no—
198C4×D3—61no—
199C4×D3—61no—
200C4×D3—61no—
201C4×D3—61no—
202Dic6—62no—
203Dic6—62no—
204C3×C8—22no—
205C3×C8—22no—
206C3×C8—62no—
207C3×C8—62no—
208C3⋊C8—22no—
209C3⋊C8—22no—
210C3⋊C8—62no—
211C3⋊C8—62no—
212C2×C32C4×C22⋊C411yescharacteristic
213C2×C32#44412yes—
214C3⋊D3—21no—
215C3⋊D3—21no—
216C3×D3—42no—
217#41—92no—
218#41—92no—
219#41—181no—
220#41—181no—
221C2×Q8—91no—
222C2×D4—91no—
223C2×D4—181no—
224C22×C4—61no—
225C22×C4—91no—
226C22×C4—181no—
227M16—92no—
228M16—92no—
229M16—181no—
230M16—181no—
231M16—184no—
232C2×C8—61no—
233C2×C8—61no—
234C2×C8—64no—
235C2×C8—91no—
236C2×C8—92no—
237C2×C8—92no—
238C2×C8—92no—
239C2×C8—181no—
240C2×C8—181no—
241C2×C8GO+(4,𝔽2)11yescharacteristic
242C4⋊C4—92no—
243C22⋊C4—181no—
244C42—61no—
245C42—92no—
246C42—181no—
247C22×C3—21no—
248C22×C3—21no—
249C22×C3—62no—
250C22×C3—122no—
251C2×D3—22no—
252C2×D3—42no—
253C2×D3—61no—
254C2×D3—61no—
255C2×D3—61no—
256C2×D3—61no—
257C2×D3—122no—
258C2×D3—122no—
259C3×C4—21no—
260C3×C4—21no—
261C3×C4—21no—
262C3×C4—21no—
263C3×C4—62no—
264C3×C4—122no—
265Dic3—22no—
266Dic3—42no—
267Dic3—61no—
268Dic3—61no—
269Dic3—61no—
270Dic3—61no—
271C32#176511yescharacteristic, complemented, Sylow
272C23—61no—
273C23—91no—
274Q8—92no—
275Q8—181no—
276D4—92no—
277D4—182no—
278D4—182no—
279D4—181no—
280C2×C4—61no—
281C2×C4—62no—
282C2×C4—62no—
283C2×C4—62no—
284C2×C4—91no—
285C2×C4—91no—
286C2×C4—91no—
287C2×C4—91no—
288C2×C4—91no—
289C2×C4—182no—
290C2×C4—362no—
291C2×C4C2×GO+(4,𝔽2)11yescharacteristic
292C8—62no—
293C8—62no—
294C8—92no—
295C8—182no—
296C8D32⋊C412yes—
297C2×C3—22no—
298C2×C3—22no—
299C2×C3—21no—
300C2×C3—21no—
301C2×C3—122no—
302D3—42no—
303D3—121no—
304D3—121no—
305D3—121no—
306D3—121no—
307C22—62no—
308C22—91no—
309C22—91no—
310C22—122no—
311C22—182no—
312C22C4×GO+(4,𝔽2)11yescharacteristic
313C4—62no—
314C4—91no—
315C4—91no—
316C4—122no—
317C4—362no—
318C4C4×GO+(4,𝔽2)11yescharacteristic
319C4C2×D32⋊C411yescharacteristic
320C3—21no—
321C3—21no—
322C2—122no—
323C2—181no—
324C2—181no—
325C2#1059329812yes—
326C2C4×D32⋊C411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C2×C42
FittingC2×C32×C8D4
socleC22×C32C4×D4
prime radicalC2×#3798C22
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1765
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. C2×#63767C2semidirect
5. #10590703C2semidirect
6. #10590051C2semidirect
7. #10590047C2semidirect
18. #63803C4semidirect
20. #63740C4semidirect
21. #63739C4semidirect
22. #63731C4semidirect
271. C32#1765semidirect

Maximal subgroups

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

subgroupindex
C2×#638032
C2×#637672
#105933492
C2×#637312
#105907032
#105900512
#105900472
#17659