Finite Group Databasebeta

← #11773822

Subgroups — #11773822

Order 1152.

584 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C4×#3802C211yesmaximal, characteristic
2#10593725C211yesmaximal, characteristic, complemented
3#10590256C211yesmaximal, characteristic, complemented
4#10590027C214yesmaximal, complemented
5C2×#3802C411yescharacteristic
6C2×C4×D32C412yes—
7C42×C3⋊D3C2211yescharacteristic
8C3×C4×D12—21no—
9#63921C2212yes—
10#63902—21no—
11C4×#625—21no—
12#63900C411yescharacteristic
13#63898—21no—
14#63779—21no—
15#63778C2212yes—
16C4×#622—21no—
17C3×C4⋊(C3⋊C8)—21no—
18#63557C2212yes—
19#63553—21no—
20C4×D3×D4—61no—
21#4833—61no—
22C22×D32C2×C412yes—
23C2×C4×C3⋊D3C2×C411yescharacteristic
24C2×C4×C3⋊D3C2×C411yescharacteristic
25C2×C4×C3⋊D3C2311yescharacteristic
26C2×C3×D12—21no—
27C2×C3×C4×D3—22no—
28C2×#625—21no—
29C2×#624C2×C412yes—
30C2×D3×Dic3—22no—
31#3802—22no—
32#3802C814yescomplemented
33C4×D32—44no—
34C2×#622—22no—
35C32×C42D411yescharacteristic
36C4×C3⋊Dic3D411yescharacteristic
37C4×C3⋊Dic3D411yescharacteristic
38C4×C3⋊Dic3D411yescharacteristic
39C3×(C2×D3)⋊C4—22no—
40C3×C4⋊Dic3—21no—
41C2×C3×C3⋊C8—22no—
42#3724—21no—
43(C2×D3)⋊Dic3—22no—
44#1460—91nomaximal, Sylow
45C2×D3×D4—61no—
46C22×C4×D3—62no—
47C3×C4×D4—61no—
48D4×Dic3—61no—
49C4×#67—62no—
50#893—61no—
51D3×C4⋊C4—61no—
52#67⋊C4—62no—
53D3×C22⋊C4—62no—
54C4×D12—21no—
55C42×D3—61no—
56C42×D3—61no—
57C3×C4⋊C8—61no—
58(C2×D3)⋊C8—62no—
59C8×Dic3—62no—
60C4⋊(C3⋊C8)—21no—
61C22×C3⋊D3C22×C411yescharacteristic
62C22×C3×D3—22no—
63C2×D32—22no—
64C2×D32—42no—
65C2×D32—42no—
66C2×D32C2×C814yes—
67C2×C32×C4C22⋊C411yescharacteristic
68C2×C32×C4C22⋊C411yescharacteristic
69C2×C32×C4C2×D411yescharacteristic
70C2×C3⋊Dic3C22⋊C411yescharacteristic
71C2×C3⋊Dic3C22⋊C411yescharacteristic
72C2×C3⋊Dic3C2×D411yescharacteristic
73C4×C3⋊D3—22no—
74C4×C3⋊D3—41no—
75C4×C3⋊D3C2×C812yes—
76C4×C3⋊D3M1612yes—
77C2×C3×Dic3—22no—
78C3×D12—24no—
79C3×C4×D3—44no—
80#625—24no—
81#624—42no—
82D3×Dic3—44no—
83#622—42no—
84C3×C3⋊C8—42no—
85C2×C4×D4—91no—
86#431—91no—
87#431—91no—
88#323—94no—
89C23×D3—62no—
90C2×C3×D4—61no—
91C22×C3×C4—62no—
92C2×#67—62no—
93C22×Dic3—62no—
94D3×D4—64no—
95D3×D4—64no—
96C2×D12—21no—
97C2×C4×D3—22no—
98C2×C4×D3—61no—
99C2×C4×D3—61no—
100C2×C4×D3—61no—
101C2×C4×D3—62no—
102C2×C4×D3—61no—
103C2×C4×D3—61no—
104C2×C4×D3—61no—
105C2×C4×D3—62no—
106C2×C4×D3—128no—
107C2×C3×C8—62no—
108C3×C4⋊C4—61no—
109C3×C22⋊C4—62no—
110C3×C42—21no—
111C3×C42—21no—
112#217—62no—
113(C2×D3)⋊C4—22no—
114(C2×D3)⋊C4—62no—
115C4⋊Dic3—21no—
116Dic3⋊C4—62no—
117C4×Dic3—61no—
118C4×Dic3—61no—
119C4×Dic3—61no—
120C4×Dic3—61no—
121C4×Dic3—61no—
122C4×Dic3—61no—
123C2×C3⋊C8—22no—
124C22×C32C2×C22⋊C411yescharacteristic
125C2×C3⋊D3—21no—
126C2×C3⋊D3—21no—
127C2×C3⋊D3C22×C811yescharacteristic
128C2×C3⋊D3C2×M1611yescharacteristic
129C2×C3×D3—24no—
130C2×C3×D3—42no—
131C2×C3×D3—42no—
132D32—44no—
133D32—44no—
134C32×C4—21no—
135C32×C4—21no—
136C32×C4C22⋊C812yes—
137C3⋊Dic3—21no—
138C3⋊Dic3C22⋊C812yes—
139C3⋊Dic3#10012yes—
140C3×Dic3—42no—
141C22×D4—91no—
142C23×C4—92no—
143C4×D4—61no—
144C4×D4—181no—
145C4×D4—181no—
146C4×D4—181no—
147C2×C4⋊C4—91no—
148C2×C22⋊C4—92no—
149C2×C42—91no—
150C4⋊C8—61no—
151C4⋊C8—181no—
152C22⋊C8—92no—
153C22⋊C8—92no—
154C4×C8—181no—
155C4×C8—181no—
156C23×C3—62no—
157C22×D3—22no—
158C22×D3—64no—
159C22×D3—61no—
160C22×D3—61no—
161C22×D3—64no—
162C22×D3—124no—
163C22×D3—124no—
164C3×D4—64no—
165C2×C3×C4—21no—
166C2×C3×C4—21no—
167C2×C3×C4—21no—
168C2×C3×C4—21no—
169C2×C3×C4—21no—
170C2×C3×C4—21no—
171C2×C3×C4—62no—
172C2×C3×C4—124no—
173#67—68no—
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—24no—
183C4×D3—44no—
184C4×D3—62no—
185C4×D3—62no—
186C4×D3—62no—
187C4×D3—62no—
188C4×D3—64no—
189C4×D3—122no—
190C4×D3—124no—
191C4×D3—124no—
192C4×D3—121no—
193C4×D3—121no—
194C4×D3—122no—
195C3×C8—122no—
196C3⋊C8—42no—
197C2×C32C2×C22⋊C811yescharacteristic
198C2×C32#41011yescharacteristic
199C2×C32C2×#10011yescharacteristic
200C3⋊D3—21no—
201C3⋊D3—21no—
202C3×D3—44no—
203C24—92no—
204C2×D4—61no—
205C2×D4—94no—
206C2×D4—182no—
207C2×D4—181no—
208C22×C4—62no—
209C22×C4—92no—
210C22×C4—91no—
211C22×C4—91no—
212C22×C4—91no—
213C22×C4—182no—
214C22×C4—364no—
215C2×C8—62no—
216C2×C8—182no—
217C4⋊C4—61no—
218C4⋊C4—181no—
219C22⋊C4—62no—
220C22⋊C4—182no—
221C42—91no—
222C42—91no—
223C42—91no—
224C42GO+(4,𝔽2)11yescharacteristic
225C22×C3—21no—
226C22×C3—21no—
227C22×C3—64no—
228C22×C3—122no—
229C22×C3—122no—
230C2×D3—24no—
231C2×D3—42no—
232C2×D3—42no—
233C2×D3—61no—
234C2×D3—61no—
235C2×D3—61no—
236C2×D3—61no—
237C2×D3—62no—
238C2×D3—62no—
239C2×D3—121no—
240C2×D3—121no—
241C2×D3—128no—
242C2×D3—128no—
243C3×C4—21no—
244C3×C4—21no—
245C3×C4—22no—
246C3×C4—22no—
247C3×C4—22no—
248C3×C4—41no—
249C3×C4—41no—
250C3×C4—122no—
251Dic3—42no—
252Dic3—62no—
253Dic3—62no—
254Dic3—62no—
255Dic3—62no—
256Dic3—121no—
257Dic3—121no—
258C32#146011yescharacteristic, complemented, Sylow
259C23—62no—
260C23—94no—
261C23—91no—
262C23—182no—
263C23—362no—
264C23—362no—
265D4—64no—
266D4—184no—
267C2×C4—62no—
268C2×C4—91no—
269C2×C4—91no—
270C2×C4—92no—
271C2×C4—92no—
272C2×C4—91no—
273C2×C4—124no—
274C2×C4—182no—
275C2×C4—361no—
276C2×C4—364no—
277C2×C4—362no—
278C2×C4D32⋊C411yescharacteristic
279C2×C4D32⋊C411yescharacteristic
280C2×C4C2×GO+(4,𝔽2)11yescharacteristic
281C8—122no—
282C8—362no—
283C2×C3—21no—
284C2×C3—21no—
285C2×C3—21no—
286C2×C3—21no—
287C2×C3—21no—
288C2×C3—21no—
289C2×C3—124no—
290D3—44no—
291D3—62no—
292D3—62no—
293D3—121no—
294D3—121no—
295C22—64no—
296C22—91no—
297C22—91no—
298C22—122no—
299C22—122no—
300C22—181no—
301C22—181no—
302C22—364no—
303C22—364no—
304C22C2×D32⋊C411yescharacteristic
305C4—21no—
306C4—21no—
307C4—92no—
308C4—92no—
309C4—122no—
310C4—181no—
311C4D32⋊C812yes—
312C3—21no—
313C3—21no—
314C2—124no—
315C2—181no—
316C2—181no—
317C2C2×D32⋊C811yescharacteristic
318C2#1059331211yescharacteristic
319C2#1059334611yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊D3C22×C8
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radicalC2×#3802C4
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1460
LCSG ▷ C2×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #10593725C2semidirect
3. #10590256C2semidirect
4. #10590027C2semidirect
32. #3802C8semidirect
258. C32#1460semidirect

Maximal subgroups

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

subgroupindex
C4×#38022
#105937252
#105902562
#105900272
#14609