Finite Group Databasebeta

← #11775283

Subgroups — #11775283

Order 1152.

414 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 55 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#10593979C211yesmaximal, characteristic
2C4×C4⋊#157C211yesmaximal, characteristic, complemented
3#10590299C211yesmaximal, characteristic, complemented
4#10590034C212yesmaximal, complemented
5#10590033C212yesmaximal
6C2×C4⋊#157—21no—
7C2×C4×#157—21no—
8C42×C3⋊D3C2211yescharacteristic
9C3×#876—21no—
10#63915C411yescharacteristic, complemented
11#63912C2211yescharacteristic
12#63902C411yescharacteristic, complemented
13#63881—21no—
14#63878—21no—
15#63870C411yescharacteristic, complemented
16#63865C2211yescharacteristic
17#63853—21no—
18#63838C411yescharacteristic, complemented
19#63781C2212yes—
20C3×#803—21no—
21#63572—21no—
22#63557C2212yes—
23#5706—61no—
24#4705—61no—
25C22×#157—22no—
26C2×C4×C3⋊D3D411yescharacteristic
27C2×C4×C3⋊D3D411yescharacteristic
28C2×C4×C3⋊D3C2311yescharacteristic
29C2×#627C2×C411yescharacteristic
30C2×#626—21no—
31C2×#625C2×C411yescharacteristic
32C2×D3×Dic3—21no—
33C4⋊#157—24no—
34C4×#157—42no—
35C32×C42D411yescharacteristic
36C4×C3⋊Dic3C2×C411yescharacteristic
37C4×C3⋊Dic3C2×C411yescharacteristic
38C4×C3⋊Dic3D411yescharacteristic
39C3×(C2×D3)⋊C4—21no—
40C3×(C2×D3)⋊C4—21no—
41C3×(C2×D3)⋊C4—21no—
42C3×Dic3⋊C4—21no—
43C3×Dic3⋊C4—21no—
44C3×Dic3⋊C4—21no—
45C2×C3×C3⋊C8—22no—
46#3724C2×C411yescharacteristic
47#3724C2×C411yescharacteristic
48Dic3⋊Dic3—21no—
49#3722—21no—
50(C2×D3)⋊Dic3—21no—
51Dic32—21no—
52#1509—91nomaximal, Sylow
53C3×#126—61no—
54#896—61no—
55#894—61no—
56#893—61no—
57#892—61no—
58#889—61no—
59#887—61no—
60#885—61no—
61#884—61no—
62#883—61no—
63#67⋊C4—61no—
64#67⋊C4—61no—
65#877—61no—
66#876—21no—
67C42×D3—61no—
68C42×D3—61no—
69C3×#97—61no—
70(C2×D3)⋊C8—62no—
71Dic3⋊C8—62no—
72#803—21no—
73C22×C3⋊D3C2×D411yescharacteristic
74C22×C3×D3—21no—
75C2×#157—24no—
76C2×#157—42no—
77C2×#157—42no—
78C2×C32×C4C22⋊C411yescharacteristic
79C2×C32×C4C22⋊C411yescharacteristic
80C2×C32×C4C2×D411yescharacteristic
81C2×C3⋊Dic3C22⋊C411yescharacteristic
82C2×C3⋊Dic3C22⋊C411yescharacteristic
83C2×C3⋊Dic3C22×C411yescharacteristic
84C4×C3⋊D3—21no—
85C4×C3⋊D3—21no—
86C4×C3⋊D3—22no—
87C4×C3⋊D3—41no—
88C2×C3×Dic3—21no—
89C2×C3×Dic3—21no—
90C2×C3×Dic3—21no—
91#627—41no—
92#626—41no—
93#626—41no—
94#625—41no—
95D3×Dic3—42no—
96C3×C3⋊C8—42no—
97#529—91no—
98#432—91no—
99C4×C4⋊C4—91no—
100#328—92no—
101#327—92no—
102C2×#67—61no—
103C2×#67—61no—
104C22×Dic3—61no—
105C2×D12—61no—
106C2×C4×D3—61no—
107C2×C4×D3—61no—
108C2×C4×D3—61no—
109C2×C4×D3—61no—
110C2×C4×D3—61no—
111C2×C4×D3—61no—
112C2×C4×D3—61no—
113C2×Dic6—61no—
114C2×C3×C8—62no—
115C3×C4⋊C4—61no—
116C3×C4⋊C4—61no—
117C3×C4⋊C4—61no—
118C3×C22⋊C4—61no—
119C3×C22⋊C4—61no—
120C3×C22⋊C4—61no—
121C3×C42—21no—
122C3×C42—21no—
123#217—61no—
124(C2×D3)⋊C4—21no—
125(C2×D3)⋊C4—21no—
126(C2×D3)⋊C4—21no—
127(C2×D3)⋊C4—61no—
128(C2×D3)⋊C4—61no—
129(C2×D3)⋊C4—61no—
130C4⋊Dic3—61no—
131Dic3⋊C4—21no—
132Dic3⋊C4—21no—
133Dic3⋊C4—21no—
134Dic3⋊C4—61no—
135Dic3⋊C4—61no—
136Dic3⋊C4—61no—
137C4×Dic3—61no—
138C4×Dic3—61no—
139C4×Dic3—61no—
140C4×Dic3—61no—
141C4×Dic3—61no—
142C4×Dic3—61no—
143C4×Dic3—61no—
144C4×Dic3—61no—
145C2×C3⋊C8—22no—
146C22×C32C2×C22⋊C411yescharacteristic
147C2×C3⋊D3—21no—
148C2×C3⋊D3—21no—
149C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
150C2×C3⋊D3#13711yescharacteristic
151C2×C3×D3—41no—
152C2×C3×D3—41no—
153C2×C3×D3—41no—
154#157—44no—
155C32×C4—21no—
156C32×C4—21no—
157C32×C4—21no—
158C3⋊Dic3—21no—
159C3⋊Dic3—21no—
160C3⋊Dic3#10412yes—
161C3×Dic3—41no—
162C3×Dic3—41no—
163C3×Dic3—41no—
164#126—61no—
165#125—91no—
166#124—91no—
167#123—181no—
168C22⋊Q8—91no—
169#121—91no—
170C4×Q8—91no—
171C4×D4—91no—
172C4×D4—181no—
173#117—181no—
174C2×C4⋊C4—181no—
175C2×C42—91no—
176C2×C42—181no—
177C4⋊C8—181no—
178C22⋊C8—92no—
179#97—61no—
180#95—92no—
181C23×C3—61no—
182C22×D3—21no—
183C22×D3—61no—
184C22×D3—61no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—61no—
192C2×C3×C4—61no—
193C2×C3×C4—61no—
194#67—121no—
195#67—121no—
196#67—122no—
197C2×Dic3—21no—
198C2×Dic3—21no—
199C2×Dic3—21no—
200C2×Dic3—61no—
201C2×Dic3—61no—
202C2×Dic3—61no—
203C2×Dic3—61no—
204C2×Dic3—61no—
205C2×Dic3—61no—
206C2×Dic3—122no—
207D12—121no—
208D12—121no—
209C4×D3—122no—
210C4×D3—122no—
211C4×D3—121no—
212C4×D3—121no—
213C4×D3—121no—
214C4×D3—121no—
215C4×D3—122no—
216C4×D3—122no—
217C4×D3—122no—
218Dic6—122no—
219C3×C8—122no—
220C3⋊C8—42no—
221C2×C32#41011yescharacteristic
222C2×C32#41711yescharacteristic
223C2×C32C2×#10411yescharacteristic
224C3⋊D3—21no—
225C3⋊D3—21no—
226C3×D3—81no—
227C2×Q8—91no—
228C2×D4—91no—
229C2×D4—181no—
230C22×C4—91no—
231C22×C4—91no—
232C22×C4—91no—
233C22×C4—181no—
234C22×C4—182no—
235C2×C8—62no—
236C4⋊C4—61no—
237C4⋊C4—61no—
238C4⋊C4—61no—
239C4⋊C4—91no—
240C4⋊C4—91no—
241C4⋊C4—181no—
242C4⋊C4—184no—
243C22⋊C4—61no—
244C22⋊C4—61no—
245C22⋊C4—61no—
246C22⋊C4—181no—
247C22⋊C4—181no—
248C42—91no—
249C42—91no—
250C42—91no—
251C42—181no—
252C42—362no—
253C42GO+(4,𝔽2)11yescharacteristic
254C22×C3—21no—
255C22×C3—21no—
256C22×C3—121no—
257C22×C3—121no—
258C22×C3—121no—
259C2×D3—41no—
260C2×D3—41no—
261C2×D3—41no—
262C2×D3—61no—
263C2×D3—61no—
264C2×D3—61no—
265C2×D3—61no—
266C2×D3—121no—
267C2×D3—121no—
268C2×D3—121no—
269C2×D3—121no—
270C3×C4—22no—
271C3×C4—41no—
272C3×C4—41no—
273C3×C4—41no—
274C3×C4—41no—
275C3×C4—41no—
276C3×C4—121no—
277C3×C4—121no—
278C3×C4—121no—
279Dic3—41no—
280Dic3—41no—
281Dic3—41no—
282Dic3—62no—
283Dic3—62no—
284Dic3—62no—
285Dic3—121no—
286Dic3—121no—
287Dic3—121no—
288C32#150911yescharacteristic, complemented, Sylow
289C23—61no—
290C23—91no—
291Q8—361no—
292D4—361no—
293D4—361no—
294D4—361no—
295C2×C4—61no—
296C2×C4—61no—
297C2×C4—61no—
298C2×C4—91no—
299C2×C4—91no—
300C2×C4—91no—
301C2×C4—182no—
302C2×C4—181no—
303C2×C4—181no—
304C2×C4—184no—
305C2×C4—361no—
306C2×C4—362no—
307C2×C4—362no—
308C2×C4—362no—
309C2×C4D32⋊C411yescharacteristic
310C2×C4D32⋊C411yescharacteristic
311C2×C4C2×GO+(4,𝔽2)11yescharacteristic
312C8—122no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—21no—
318C2×C3—21no—
319C2×C3—241no—
320D3—81no—
321D3—121no—
322D3—121no—
323D3—121no—
324D3—121no—
325C22—91no—
326C22—91no—
327C22—121no—
328C22—121no—
329C22—121no—
330C22—181no—
331C22—181no—
332C22C2×D32⋊C411yescharacteristic
333C4—21no—
334C4—21no—
335C4—21no—
336C4—92no—
337C4—121no—
338C4—121no—
339C4—121no—
340C4—181no—
341C4—181no—
342C4—364no—
343C3—21no—
344C3—21no—
345C2—181no—
346C2—181no—
347C2—241no—
348C2#1059331911yescharacteristic
349C2#1059332511yescharacteristic
350C2#1059334511yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radical#63912C22
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1509
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C4×C4⋊#157C2semidirect
3. #10590299C2semidirect
4. #10590034C2semidirect
10. #63915C4semidirect
12. #63902C4semidirect
15. #63870C4semidirect
18. #63838C4semidirect
288. C32#1509semidirect

Maximal subgroups

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

subgroupindex
#105939792
C4×C4⋊#1572
#105902992
#105900342
#105900332
#15099