Finite Group Databasebeta

← #11775282

Subgroups — #11775282

Order 1152.

414 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 57 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#10593980C211yesmaximal, characteristic
2C4×C4⋊#157C211yesmaximal, characteristic, complemented
3#10590260C211yesmaximal, characteristic, complemented
4#10590034C212yesmaximal, complemented
5#10590033C212yesmaximal
6C2×C4⋊#157—21no—
7C2×C4×#157—21no—
8C42×C3⋊D3C2211yescharacteristic
9C3×#872—21no—
10C4×#627C411yescharacteristic, complemented
11#63915C411yescharacteristic, complemented
12#63912C2211yescharacteristic
13C4×#626—21no—
14C4×#625C411yescharacteristic, complemented
15#63870C411yescharacteristic, complemented
16#63865C2211yescharacteristic
17#63862—21no—
18#63853—21no—
19#63781C2212yes—
20C3×C4⋊(C3⋊C8)—21no—
21#63557C2212yes—
22#63555—21no—
23#5528—61no—
24#4835—61no—
25C22×#157—22no—
26C2×C4×C3⋊D3D411yescharacteristic
27C2×C4×C3⋊D3D411yescharacteristic
28C2×C4×C3⋊D3C2311yescharacteristic
29C2×C3×C4×D3—21no—
30C2×#627C2×C411yescharacteristic
31C2×#626—21no—
32C2×#625C2×C411yescharacteristic
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×Dic3⋊C4—21no—
42C3×Dic3⋊C4—21no—
43C3×C4×Dic3—21no—
44C2×C3×C3⋊C8—22no—
45#3724C2×C411yescharacteristic
46#3724C2×C411yescharacteristic
47Dic3⋊Dic3—21no—
48Dic3⋊Dic3—21no—
49#3722—21no—
50(C2×D3)⋊Dic3—21no—
51(C2×D3)⋊Dic3—21no—
52#1509—91nomaximal, Sylow
53C3×#117—61no—
54C4×#67—61no—
55C4×#67—61no—
56#898—61no—
57#896—61no—
58#894—61no—
59#889—61no—
60#885—61no—
61#884—61no—
62#883—61no—
63#879—61no—
64C4×D12—61no—
65#872—21no—
66C42×D3—61no—
67C42×D3—61no—
68C4×Dic6—61no—
69C3×C4⋊C8—61no—
70(C2×D3)⋊C8—62no—
71#815—62no—
72C4⋊(C3⋊C8)—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—
91C3×C4×D3—42no—
92#627—41no—
93#626—41no—
94#626—41no—
95#625—41no—
96C3×C3⋊C8—42no—
97#529—91no—
98#432—91no—
99C4×C4⋊C4—91no—
100#328—92no—
101#327—92no—
102C22×C3×C4—61no—
103C2×#67—61no—
104C2×#67—61no—
105C2×D12—61no—
106C2×C4×D3—21no—
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×C22⋊C4—61no—
118C3×C22⋊C4—61no—
119C3×C42—21no—
120C3×C42—21no—
121C3×C42—61no—
122#217—61no—
123#217—61no—
124(C2×D3)⋊C4—21no—
125(C2×D3)⋊C4—21no—
126(C2×D3)⋊C4—61no—
127(C2×D3)⋊C4—61no—
128(C2×D3)⋊C4—61no—
129(C2×D3)⋊C4—61no—
130C4⋊Dic3—61no—
131C4⋊Dic3—61no—
132Dic3⋊C4—21no—
133Dic3⋊C4—21no—
134Dic3⋊C4—61no—
135Dic3⋊C4—61no—
136Dic3⋊C4—61no—
137Dic3⋊C4—61no—
138C4×Dic3—21no—
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#10412yes—
158C3⋊Dic3—21no—
159C3⋊Dic3—21no—
160C3⋊Dic3—21no—
161C3×Dic3—41no—
162C3×Dic3—41no—
163C3×Dic3—41no—
164#126—181no—
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—61no—
174C2×C4⋊C4—181no—
175C2×C42—91no—
176C2×C42—181no—
177C4⋊C8—61no—
178C22⋊C8—92no—
179#97—181no—
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—
194C2×C3×C4—122no—
195#67—121no—
196#67—121no—
197#67—122no—
198C2×Dic3—21no—
199C2×Dic3—21no—
200C2×Dic3—21no—
201C2×Dic3—61no—
202C2×Dic3—61no—
203C2×Dic3—61no—
204C2×Dic3—61no—
205C2×Dic3—61no—
206C2×Dic3—61no—
207D12—121no—
208D12—121no—
209C4×D3—42no—
210C4×D3—122no—
211C4×D3—122no—
212C4×D3—121no—
213C4×D3—121no—
214C4×D3—121no—
215C4×D3—121no—
216C4×D3—122no—
217C4×D3—121no—
218C4×D3—121no—
219Dic6—122no—
220C3×C8—122no—
221C3⋊C8—42no—
222C2×C32#41011yescharacteristic
223C2×C32#41711yescharacteristic
224C2×C32C2×#10411yescharacteristic
225C3⋊D3—21no—
226C3⋊D3—21no—
227C3×D3—81no—
228C2×Q8—91no—
229C2×D4—91no—
230C2×D4—181no—
231C22×C4—61no—
232C22×C4—91no—
233C22×C4—91no—
234C22×C4—91no—
235C22×C4—182no—
236C2×C8—62no—
237C4⋊C4—61no—
238C4⋊C4—61no—
239C4⋊C4—91no—
240C4⋊C4—91no—
241C4⋊C4—181no—
242C4⋊C4—181no—
243C4⋊C4—184no—
244C22⋊C4—61no—
245C22⋊C4—61no—
246C22⋊C4—181no—
247C22⋊C4—181no—
248C22⋊C4—181no—
249C42—61no—
250C42—91no—
251C42—91no—
252C42—91no—
253C42—362no—
254C42GO+(4,𝔽2)11yescharacteristic
255C22×C3—21no—
256C22×C3—21no—
257C22×C3—121no—
258C22×C3—121no—
259C22×C3—121no—
260C2×D3—41no—
261C2×D3—41no—
262C2×D3—41no—
263C2×D3—61no—
264C2×D3—61no—
265C2×D3—61no—
266C2×D3—61no—
267C2×D3—121no—
268C2×D3—121no—
269C2×D3—121no—
270C2×D3—121no—
271C3×C4—21no—
272C3×C4—21no—
273C3×C4—22no—
274C3×C4—22no—
275C3×C4—41no—
276C3×C4—41no—
277C3×C4—41no—
278C3×C4—121no—
279C3×C4—121no—
280C3×C4—121no—
281Dic3—41no—
282Dic3—41no—
283Dic3—41no—
284Dic3—62no—
285Dic3—121no—
286Dic3—121no—
287Dic3—121no—
288Dic3—121no—
289Dic3—121no—
290C32#150911yescharacteristic, complemented, Sylow
291C23—61no—
292C23—91no—
293Q8—361no—
294D4—361no—
295D4—361no—
296D4—361no—
297C2×C4—61no—
298C2×C4—61no—
299C2×C4—61no—
300C2×C4—91no—
301C2×C4—91no—
302C2×C4—91no—
303C2×C4—122no—
304C2×C4—181no—
305C2×C4—181no—
306C2×C4—182no—
307C2×C4—184no—
308C2×C4—361no—
309C2×C4—362no—
310C2×C4—362no—
311C2×C4D32⋊C411yescharacteristic
312C2×C4D32⋊C411yescharacteristic
313C2×C4C2×GO+(4,𝔽2)11yescharacteristic
314C8—122no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—21no—
318C2×C3—21no—
319C2×C3—21no—
320C2×C3—21no—
321C2×C3—241no—
322D3—81no—
323D3—121no—
324D3—121no—
325D3—121no—
326D3—121no—
327C22—91no—
328C22—91no—
329C22—121no—
330C22—121no—
331C22—121no—
332C22—181no—
333C22—181no—
334C22C2×D32⋊C411yescharacteristic
335C4—21no—
336C4—21no—
337C4—121no—
338C4—121no—
339C4—121no—
340C4—181no—
341C4—181no—
342C4—181no—
343C4—364no—
344C4#6373112yes—
345C3—21no—
346C3—21no—
347C2—181no—
348C2—181no—
349C2—241no—
350C2#1059331911yescharacteristic
351C2C2×#6373111yescharacteristic
352C2#1059334611yescharacteristic
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. #10590260C2semidirect
4. #10590034C2semidirect
10. C4×#627C4semidirect
11. #63915C4semidirect
14. C4×#625C4semidirect
15. #63870C4semidirect
290. C32#1509semidirect

Maximal subgroups

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

subgroupindex
#105939802
C4×C4⋊#1572
#105902602
#105900342
#105900332
#15099