Finite Group Databasebeta

← #11775860

Subgroups — #11775860

Order 1152.

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

normal subgroups only

This group has 388 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#10593980C211yesmaximal, characteristic
2C4×#3788C211yesmaximal, characteristic, complemented
3#10590260C211yesmaximal, characteristic, complemented
4#10590036C212yesmaximal, complemented
5#10590035C212yesmaximal, complemented
6C2×#3788—21no—
7C42×C3⋊D3C2211yescharacteristic
8C3×#872—21no—
9C4×#627C411yescharacteristic
10#63915C2211yescharacteristic
11#63912C411yescharacteristic
12C4×#626—21no—
13C4×#625C411yescharacteristic
14#63870C2211yescharacteristic
15#63865C411yescharacteristic
16#63862—21no—
17#63853—21no—
18#63777C2212yes—
19C4×#622—21no—
20C3×C4⋊(C3⋊C8)—21no—
21#63557—21no—
22#63555C2212yes—
23#5528—61no—
24#4835—61no—
25C2×C4×C3⋊D3C2×C411yescharacteristic
26C2×C4×C3⋊D3D411yescharacteristic
27C2×C4×C3⋊D3D411yescharacteristic
28C2×C3×C4×D3—21no—
29C2×#627C2×C411yescharacteristic
30C2×#626—21no—
31C2×#625C2×C411yescharacteristic
32C2×#622—22no—
33#3788—24no—
34C32×C42D411yescharacteristic
35C4×C3⋊Dic3C2×C411yescharacteristic
36C4×C3⋊Dic3D411yescharacteristic
37C4×C3⋊Dic3C2311yescharacteristic
38C3×(C2×D3)⋊C4—21no—
39C3×(C2×D3)⋊C4—21no—
40C3×Dic3⋊C4—21no—
41C3×Dic3⋊C4—21no—
42C3×C4×Dic3—21no—
43C2×C3×C3⋊C8—22no—
44#3724C2×C411yescharacteristic
45#3724C2×C411yescharacteristic
46Dic3⋊Dic3—21no—
47Dic3⋊Dic3—21no—
48#3722—21no—
49(C2×D3)⋊Dic3—21no—
50(C2×D3)⋊Dic3—21no—
51#1529—91nomaximal, Sylow
52C3×#117—61no—
53C4×#67—61no—
54C4×#67—61no—
55#898—61no—
56#896—61no—
57#894—61no—
58#889—61no—
59#885—61no—
60#884—61no—
61#883—61no—
62#879—61no—
63C4×D12—61no—
64#872—21no—
65C42×D3—61no—
66C42×D3—61no—
67C4×Dic6—61no—
68C3×C4⋊C8—61no—
69(C2×D3)⋊C8—62no—
70#815—62no—
71C4⋊(C3⋊C8)—21no—
72C22×C3⋊D3C22⋊C411yescharacteristic
73C22×C3×D3—21no—
74C2×C32×C4C22⋊C411yescharacteristic
75C2×C32×C4C22⋊C411yescharacteristic
76C2×C32×C4C2×D411yescharacteristic
77C2×C3⋊Dic3C22⋊C411yescharacteristic
78C2×C3⋊Dic3C22×C411yescharacteristic
79C2×C3⋊Dic3C2×D411yescharacteristic
80C4×C3⋊D3—22no—
81C4×C3⋊D3—41no—
82C4×C3⋊D3—41no—
83C2×C3×Dic3—21no—
84C2×C3×Dic3—21no—
85C2×C3×Dic3—21no—
86C3×C4×D3—42no—
87#627—41no—
88#626—42no—
89#625—41no—
90#622—24no—
91C3×C3⋊C8—42no—
92#529—91no—
93#432—91no—
94C4×M16—91no—
95#330—92no—
96#329—92no—
97C22×C3×C4—61no—
98C2×#67—61no—
99C2×#67—61no—
100C2×D12—61no—
101C2×C4×D3—21no—
102C2×C4×D3—61no—
103C2×C4×D3—61no—
104C2×C4×D3—61no—
105C2×C4×D3—61no—
106C2×C4×D3—61no—
107C2×C4×D3—61no—
108C2×Dic6—61no—
109C2×C3×C8—62no—
110C3×C4⋊C4—61no—
111C3×C4⋊C4—61no—
112C3×C22⋊C4—61no—
113C3×C22⋊C4—61no—
114C3×C42—21no—
115C3×C42—21no—
116C3×C42—61no—
117#217—61no—
118#217—61no—
119(C2×D3)⋊C4—21no—
120(C2×D3)⋊C4—21no—
121(C2×D3)⋊C4—61no—
122(C2×D3)⋊C4—61no—
123(C2×D3)⋊C4—61no—
124(C2×D3)⋊C4—61no—
125C4⋊Dic3—61no—
126C4⋊Dic3—61no—
127Dic3⋊C4—21no—
128Dic3⋊C4—21no—
129Dic3⋊C4—61no—
130Dic3⋊C4—61no—
131Dic3⋊C4—61no—
132Dic3⋊C4—61no—
133C4×Dic3—21no—
134C4×Dic3—61no—
135C4×Dic3—61no—
136C4×Dic3—61no—
137C4×Dic3—61no—
138C4×Dic3—61no—
139C4×Dic3—61no—
140C2×C3⋊C8—22no—
141C22×C32C2×C22⋊C411yescharacteristic
142C2×C3⋊D3—21no—
143C2×C3⋊D3—21no—
144C2×C3⋊D3—21no—
145C2×C3×D3—41no—
146C2×C3×D3—41no—
147C2×C3×D3—41no—
148C32×C4—21no—
149C32×C4—21no—
150C32×C4#10412yes—
151C3⋊Dic3—21no—
152C3⋊Dic3—21no—
153C3⋊Dic3—21no—
154C3×Dic3—41no—
155C3×Dic3—41no—
156C3×Dic3—41no—
157C2×M16—181no—
158#126—181no—
159#125—91no—
160#124—91no—
161#123—181no—
162C22⋊Q8—91no—
163#121—91no—
164C4×Q8—91no—
165C4×D4—91no—
166C4×D4—181no—
167#117—61no—
168C2×C42—91no—
169C4⋊C8—61no—
170C22⋊C8—181no—
171#97—92no—
172#97—92no—
173C4×C8—181no—
174C23×C3—61no—
175C22×D3—21no—
176C22×D3—61no—
177C22×D3—61no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4—61no—
185C2×C3×C4—61no—
186C2×C3×C4—61no—
187C2×C3×C4—122no—
188#67—122no—
189#67—122no—
190C2×Dic3—21no—
191C2×Dic3—21no—
192C2×Dic3—21no—
193C2×Dic3—61no—
194C2×Dic3—61no—
195C2×Dic3—61no—
196C2×Dic3—61no—
197C2×Dic3—61no—
198C2×Dic3—61no—
199D12—122no—
200C4×D3—42no—
201C4×D3—122no—
202C4×D3—122no—
203C4×D3—122no—
204C4×D3—121no—
205C4×D3—121no—
206C4×D3—122no—
207C4×D3—122no—
208Dic6—122no—
209C3×C8—122no—
210C3⋊C8—42no—
211C2×C32#41311yescharacteristic
212C2×C32C2×#10411yescharacteristic
213C2×C32#42111yescharacteristic
214C3⋊D3—41no—
215C3×D3—81no—
216C2×Q8—91no—
217C2×D4—91no—
218C2×D4—181no—
219C22×C4—61no—
220C22×C4—91no—
221C22×C4—91no—
222C22×C4—91no—
223M16—184no—
224C2×C8—62no—
225C2×C8—182no—
226C4⋊C4—61no—
227C4⋊C4—61no—
228C4⋊C4—91no—
229C4⋊C4—91no—
230C4⋊C4—181no—
231C4⋊C4—181no—
232C22⋊C4—61no—
233C22⋊C4—61no—
234C22⋊C4—181no—
235C22⋊C4—181no—
236C22⋊C4—181no—
237C42—61no—
238C42—91no—
239C42—91no—
240C42—91no—
241C42GO+(4,𝔽2)11yescharacteristic
242C22×C3—21no—
243C22×C3—21no—
244C22×C3—121no—
245C22×C3—121no—
246C22×C3—121no—
247C2×D3—41no—
248C2×D3—41no—
249C2×D3—41no—
250C2×D3—62no—
251C2×D3—62no—
252C2×D3—121no—
253C2×D3—121no—
254C2×D3—121no—
255C2×D3—121no—
256C3×C4—21no—
257C3×C4—21no—
258C3×C4—22no—
259C3×C4—22no—
260C3×C4—41no—
261C3×C4—41no—
262C3×C4—41no—
263C3×C4—121no—
264C3×C4—121no—
265C3×C4—121no—
266Dic3—41no—
267Dic3—41no—
268Dic3—41no—
269Dic3—62no—
270Dic3—121no—
271Dic3—121no—
272Dic3—121no—
273Dic3—121no—
274Dic3—121no—
275C32#152911yescharacteristic, complemented, Sylow
276C23—61no—
277C23—91no—
278Q8—361no—
279D4—362no—
280D4—361no—
281C2×C4—61no—
282C2×C4—61no—
283C2×C4—61no—
284C2×C4—91no—
285C2×C4—91no—
286C2×C4—91no—
287C2×C4—122no—
288C2×C4—182no—
289C2×C4—361no—
290C2×C4—361no—
291C2×C4D32⋊C411yescharacteristic
292C2×C4D32⋊C411yescharacteristic
293C2×C4C2×GO+(4,𝔽2)11yescharacteristic
294C8—122no—
295C8—184no—
296C2×C3—21no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3—21no—
300C2×C3—21no—
301C2×C3—21no—
302C2×C3—241no—
303D3—81no—
304D3—122no—
305D3—122no—
306C22—121no—
307C22—121no—
308C22—121no—
309C22—181no—
310C22—181no—
311C22—181no—
312C22C2×D32⋊C411yescharacteristic
313C4—21no—
314C4—21no—
315C4—121no—
316C4—121no—
317C4—121no—
318C4—181no—
319C4—181no—
320C4—181no—
321C4#6373112yes—
322C3—21no—
323C3—21no—
324C2—241no—
325C2—361no—
326C2#1059331311yescharacteristic
327C2C2×#6373111yescharacteristic
328C2#1059338111yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radical#63912C4
cosocleC4×C3⋊Dic3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1529
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×#3788C2semidirect
3. #10590260C2semidirect
4. #10590036C2semidirect
5. #10590035C2semidirect
275. C32#1529semidirect

Maximal subgroups

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

subgroupindex
#105939802
C4×#37882
#105902602
#105900362
#105900352
#15299