Finite Group Databasebeta

← #11775069

Subgroups — #11775069

Order 1152.

498 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 65 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#10593971C211yesmaximal, characteristic
2C4×C4⋊#157C211yesmaximal, characteristic, complemented
3#10590256C211yesmaximal, characteristic, complemented
4#10590033C214yesmaximal, complemented
5C2×#3796—21no—
6C2×C4⋊#157—21no—
7C2×C4×#157—21no—
8C42×C3⋊D3C2211yescharacteristic
9C3×#875—21no—
10#63914C411yescharacteristic, complemented
11#63912—21no—
12#63912C2212yes—
13#63902—21no—
14#63902C412yescomplemented
15#63873C411yescharacteristic, complemented
16#63781C2212yes—
17C3×C4⋊(C3⋊C8)—21no—
18#63557C2212yes—
19#63553—21no—
20#5668—61no—
21#4833—61no—
22C22×#157—22no—
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C4×C3⋊D3C2311yescharacteristic
26C2×C3×D12—21no—
27C2×C3×Dic6—21no—
28C2×#626—22no—
29C2×#625—21no—
30C2×#625C2×C412yes—
31C2×D3×Dic3—22no—
32#3796—42no—
33#3796—42no—
34C4⋊#157—24no—
35C4×#157—42no—
36C32×C42D411yescharacteristic
37C4×C3⋊Dic3C2×C411yescharacteristic
38C4×C3⋊Dic3C2×C411yescharacteristic
39C4×C3⋊Dic3D411yescharacteristic
40C3×(C2×D3)⋊C4—22no—
41C3×(C2×D3)⋊C4—22no—
42C2×C3×C3⋊C8—22no—
43#3724—21no—
44#3724C2×C412yes—
45#1502—91nomaximal, Sylow
46C2×#239—61no—
47C2×#237—61no—
48C3×#124—61no—
49#944—61no—
50#940—61no—
51#884—62no—
52#884—62no—
53#67⋊C4—62no—
54#67⋊C4—62no—
55#875—21no—
56C42×D3—61no—
57C42×D3—61no—
58C3×C4⋊C8—61no—
59(C2×D3)⋊C8—62no—
60C8×Dic3—62no—
61C4⋊(C3⋊C8)—21no—
62C22×C3⋊D3C2×D411yescharacteristic
63C22×C3×D3—22no—
64C2×#157—24no—
65C2×#157—42no—
66C2×#157—42no—
67C2×C32×C4C22⋊C411yescharacteristic
68C2×C32×C4C22⋊C411yescharacteristic
69C2×C32×C4C2×D411yescharacteristic
70C2×C3⋊Dic3C22⋊C411yescharacteristic
71C2×C3⋊Dic3C22⋊C411yescharacteristic
72C2×C3⋊Dic3C22×C411yescharacteristic
73C4×C3⋊D3—22no—
74C4×C3⋊D3—41no—
75C4×C3⋊D3D812yes—
76C4×C3⋊D3SD1612yes—
77C2×C3×Dic3—22no—
78C3×D12—42no—
79C3×Dic6—42no—
80#626—42no—
81#626—42no—
82#625—42no—
83#625—42no—
84D3×Dic3—44no—
85C3×C3⋊C8—42no—
86#532—91no—
87#431—91no—
88C4×C4⋊C4—91no—
89#327—94no—
90C2×C3×Q8—61no—
91C2×C3×D4—61no—
92C2×#67—62no—
93C2×#67—62no—
94C2×#67—62no—
95C22×Dic3—62no—
96#239—122no—
97#239—122no—
98#237—122no—
99#237—122no—
100C2×D12—21no—
101C2×D12—62no—
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×C4×D3—62no—
109C2×Dic6—21no—
110C2×C3×C8—62no—
111C3×C22⋊C4—62no—
112C3×C22⋊C4—62no—
113C3×C42—21no—
114C3×C42—21no—
115(C2×D3)⋊C4—22no—
116(C2×D3)⋊C4—22no—
117Dic3⋊C4—62no—
118Dic3⋊C4—62no—
119C4×Dic3—61no—
120C4×Dic3—61no—
121C4×Dic3—61no—
122C4×Dic3—61no—
123C4×Dic3—61no—
124C4×Dic3—61no—
125C2×C3⋊C8—22no—
126C22×C32C2×C22⋊C411yescharacteristic
127C2×C3⋊D3—21no—
128C2×C3⋊D3—21no—
129C2×C3⋊D3C2×D811yescharacteristic
130C2×C3⋊D3C2×SD1611yescharacteristic
131C2×C3×D3—42no—
132C2×C3×D3—42no—
133C2×C3×D3—42no—
134#157—44no—
135C32×C4—21no—
136C32×C4—21no—
137C32×C4#10212yes—
138C3⋊Dic3—21no—
139C3⋊Dic3#10212yes—
140C3⋊Dic3#10412yes—
141C3×Dic3—42no—
142C2×#41—181no—
143C4⋊Q8—91no—
144#127—91no—
145#124—61no—
146#121—92no—
147#121—181no—
148C4×D4—92no—
149C4×D4—181no—
150C2×C4⋊C4—181no—
151C2×C42—91no—
152C2×C42—181no—
153C4⋊C8—61no—
154C22⋊C8—92no—
155C4×C8—181no—
156#95—92no—
157C23×C3—62no—
158C22×D3—22no—
159C22×D3—61no—
160C22×D3—61no—
161C3×Q8—122no—
162C3×D4—122no—
163C2×C3×C4—21no—
164C2×C3×C4—21no—
165C2×C3×C4—21no—
166C2×C3×C4—21no—
167C2×C3×C4—21no—
168C2×C3×C4—21no—
169C2×C3×C4—62no—
170#67—122no—
171#67—122no—
172#67—124no—
173#67—124no—
174C2×Dic3—22no—
175C2×Dic3—61no—
176C2×Dic3—61no—
177C2×Dic3—61no—
178C2×Dic3—61no—
179C2×Dic3—61no—
180C2×Dic3—61no—
181C2×Dic3—124no—
182D12—42no—
183D12—122no—
184D12—122no—
185C4×D3—62no—
186C4×D3—62no—
187C4×D3—62no—
188C4×D3—62no—
189C4×D3—122no—
190C4×D3—122no—
191C4×D3—122no—
192C4×D3—124no—
193C4×D3—121no—
194C4×D3—121no—
195Dic6—42no—
196C3×C8—122no—
197C3⋊C8—42no—
198C2×C32#41011yescharacteristic
199C2×C32C2×#10211yescharacteristic
200C2×C32C2×#10411yescharacteristic
201C3⋊D3—21no—
202C3⋊D3—21no—
203C3×D3—82no—
204#41—362no—
205#41—362no—
206C2×Q8—61no—
207C2×D4—61no—
208C2×D4—92no—
209C2×D4—182no—
210C2×D4—181no—
211C22×C4—91no—
212C22×C4—91no—
213C22×C4—91no—
214C22×C4—182no—
215C22×C4—182no—
216C2×C8—62no—
217C4⋊C4—92no—
218C4⋊C4—181no—
219C4⋊C4—184no—
220C22⋊C4—62no—
221C22⋊C4—62no—
222C42—91no—
223C42—91no—
224C42—91no—
225C42—362no—
226C42GO+(4,𝔽2)11yescharacteristic
227C22×C3—21no—
228C22×C3—21no—
229C22×C3—122no—
230C22×C3—122no—
231C22×C3—122no—
232C2×D3—42no—
233C2×D3—42no—
234C2×D3—42no—
235C2×D3—61no—
236C2×D3—61no—
237C2×D3—61no—
238C2×D3—61no—
239C2×D3—121no—
240C2×D3—121no—
241C2×D3—121no—
242C2×D3—121no—
243C3×C4—21no—
244C3×C4—21no—
245C3×C4—22no—
246C3×C4—22no—
247C3×C4—41no—
248C3×C4—41no—
249C3×C4—41no—
250C3×C4—122no—
251Dic3—42no—
252Dic3—62no—
253Dic3—62no—
254Dic3—62no—
255Dic3—62no—
256Dic3—62no—
257Dic3—121no—
258C32#150211yescharacteristic, complemented, Sylow
259C23—62no—
260C23—91no—
261Q8—122no—
262D4—122no—
263D4—362no—
264D4—362no—
265D4—362no—
266D4—362no—
267C2×C4—62no—
268C2×C4—91no—
269C2×C4—91no—
270C2×C4—92no—
271C2×C4—92no—
272C2×C4—91no—
273C2×C4—182no—
274C2×C4—184no—
275C2×C4—361no—
276C2×C4—364no—
277C2×C4—362no—
278C2×C4—362no—
279C2×C4D32⋊C411yescharacteristic
280C2×C4D32⋊C411yescharacteristic
281C2×C4C2×GO+(4,𝔽2)11yescharacteristic
282C8—122no—
283C2×C3—21no—
284C2×C3—21no—
285C2×C3—21no—
286C2×C3—21no—
287C2×C3—21no—
288C2×C3—21no—
289C2×C3—242no—
290D3—82no—
291D3—121no—
292D3—121no—
293D3—121no—
294D3—121no—
295C22—91no—
296C22—91no—
297C22—122no—
298C22—122no—
299C22—122no—
300C22—181no—
301C22—181no—
302C22C2×D32⋊C411yescharacteristic
303C4—21no—
304C4—21no—
305C4—92no—
306C4—92no—
307C4—122no—
308C4—181no—
309C4—364no—
310C4#6372912yes—
311C3—21no—
312C3—21no—
313C2—181no—
314C2—181no—
315C2—242no—
316C2C2×#6372911yescharacteristic
317C2#1059332511yescharacteristic
318C2#1059334611yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radical#10593971C2
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1502
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. #10590256C2semidirect
4. #10590033C2semidirect
10. #63914C4semidirect
14. #63902C4semidirect
15. #63873C4semidirect
258. C32#1502semidirect

Maximal subgroups

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

subgroupindex
#105939712
C4×C4⋊#1572
#105902562
#105900332
#15029