Finite Group Databasebeta

← #11774697

Subgroups — #11774697

Order 1152.

600 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 63 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
1C2×#63902C211yesmaximal, characteristic
2#10593804C211yesmaximal, characteristic, complemented
3#10591060C211yesmaximal, characteristic, complemented
4#10590030C214yesmaximal, complemented
5C22×#625C411yescharacteristic
6C22×D3×Dic3—21no—
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C2×C3×(C2×D3)⋊C4—21no—
9C2×C3×#208—21no—
10C2×#3724C411yescharacteristic
11#63902—21no—
12#63902—21no—
13#63902C412yes—
14#63902C2212yes—
15C22⋊#622—21no—
16#63779C2212yescomplemented
17#63777—21no—
18#63555—21no—
19#63553C2212yescomplemented
20C2×#67⋊C4—61no—
21Dic3×M16—61no—
22C23×C3×D3—21no—
23C22×C32×C4D411yescharacteristic
24C22×C3⋊Dic3C2×C411yescharacteristic
25C22×C3⋊Dic3D411yescharacteristic
26C22×C3×Dic3—21no—
27C2×#625—21no—
28C2×#625—24no—
29C2×#625C2×C412yes—
30C2×D3×Dic3—22no—
31C2×D3×Dic3—22no—
32C2×D3×Dic3—44no—
33C2×#622—22no—
34C4×C3⋊Dic3C2×C411yescharacteristic
35C4×C3⋊Dic3D411yescharacteristic
36C4×C3⋊Dic3D411yescharacteristic
37C4×C3⋊Dic3C2311yescharacteristic
38C3×(C2×D3)⋊C4—22no—
39C3×(C2×D3)⋊C4—22no—
40C3×#208—24no—
41C2×C3×C3⋊C8—22no—
42#3724—21no—
43#3724C2×C412yes—
44#1490—91nomaximal, Sylow
45C22×#67—61no—
46C23×Dic3—61no—
47C22×C4×D3—61no—
48C2×C3×M16—61no—
49C2×C3×C22⋊C4—61no—
50C2×(C2×D3)⋊C4—21no—
51C2×Dic3⋊C4—61no—
52C2×C4×Dic3—61no—
53C2×C4×Dic3—61no—
54C2×#208—21no—
55#67⋊C4—62no—
56#67⋊C4—62no—
57#67⋊C4—62no—
58#67⋊C4—62no—
59#815—62no—
60C8×Dic3—62no—
61C23×C32C22⋊C411yescharacteristic
62C22×C3×D3—24no—
63C22×C3×D3—22no—
64C22×C3×D3—42no—
65C22×C3×D3—42no—
66C2×C32×C4—22no—
67C2×C32×C4C22⋊C411yescharacteristic
68C2×C32×C4C2×D411yescharacteristic
69C2×C3⋊Dic3—22no—
70C2×C3⋊Dic3—22no—
71C2×C3⋊Dic3C22⋊C411yescharacteristic
72C2×C3⋊Dic3C22⋊C411yescharacteristic
73C2×C3⋊Dic3C22×C411yescharacteristic
74C2×C3⋊Dic3C2×D411yescharacteristic
75C2×C3×Dic3—22no—
76C2×C3×Dic3—42no—
77#625—24no—
78#625—22no—
79#625M1614yescomplemented
80D3×Dic3—44no—
81D3×Dic3—44no—
82#622—42no—
83C3×C3⋊C8—24no—
84C2×C4×D4—91no—
85#432—91no—
86C4×M16—91no—
87D4⋊C8—94no—
88C24×C3—61no—
89C23×D3—21no—
90C22×C3×C4—21no—
91C22×C3×C4—21no—
92C22×C3×C4—61no—
93C2×#67—62no—
94C2×#67—62no—
95C2×#67—68no—
96C22×Dic3—21no—
97C22×Dic3—61no—
98C22×Dic3—61no—
99C22×Dic3—61no—
100C22×Dic3—61no—
101C22×Dic3—62no—
102C22×Dic3—62no—
103C22×Dic3—124no—
104C2×C4×D3—62no—
105C2×C4×D3—62no—
106C2×C4×D3—124no—
107C3×M16—64no—
108C2×C3×C8—62no—
109C3×C22⋊C4—62no—
110C3×C22⋊C4—62no—
111(C2×D3)⋊C4—22no—
112(C2×D3)⋊C4—22no—
113Dic3⋊C4—62no—
114Dic3⋊C4—62no—
115C4×Dic3—61no—
116C4×Dic3—61no—
117C4×Dic3—61no—
118C4×Dic3—61no—
119C4×Dic3—61no—
120C4×Dic3—61no—
121C4×Dic3—61no—
122C4×Dic3—61no—
123#208—24no—
124C2×C3⋊C8—22no—
125C22×C32—21no—
126C22×C32—21no—
127C22×C32#10412yes—
128C22×C32C2×C22⋊C411yescharacteristic
129C2×C3×D3—24no—
130C2×C3×D3—48no—
131C2×C3×D3—42no—
132C2×C3×D3—42no—
133C32×C4—21no—
134C32×C4—21no—
135C3⋊Dic3—21no—
136C3⋊Dic3—21no—
137C3⋊Dic3C2×M1612yes—
138C3⋊Dic3AGL(1,ℤ/8)12yes—
139C3×Dic3—42no—
140C22×D4—91no—
141C23×C4—181no—
142C2×M16—61no—
143C4×D4—92no—
144C4×D4—92no—
145C4×D4—181no—
146C4×D4—181no—
147C2×C4⋊C4—91no—
148C2×C22⋊C4—61no—
149C2×C42—91no—
150C4⋊C8—92no—
151C22⋊C8—181no—
152#97—181no—
153#97—181no—
154C4×C8—92no—
155C23×C3—21no—
156C23×C3—21no—
157C23×C3—62no—
158C23×C3—64no—
159C23×C3—122no—
160C23×C3—122no—
161C22×D3—22no—
162C22×D3—24no—
163C22×D3—42no—
164C22×D3—42no—
165C2×C3×C4—22no—
166C2×C3×C4—22no—
167C2×C3×C4—21no—
168C2×C3×C4—21no—
169C2×C3×C4—21no—
170C2×C3×C4—21no—
171C2×C3×C4—42no—
172C2×C3×C4—62no—
173C2×C3×C4—122no—
174#67—64no—
175#67—64no—
176#67—68no—
177C2×Dic3—22no—
178C2×Dic3—42no—
179C2×Dic3—61no—
180C2×Dic3—61no—
181C2×Dic3—61no—
182C2×Dic3—61no—
183C2×Dic3—61no—
184C2×Dic3—61no—
185C2×Dic3—61no—
186C2×Dic3—61no—
187C2×Dic3—64no—
188C2×Dic3—64no—
189C2×Dic3—122no—
190C2×Dic3—122no—
191C2×Dic3—124no—
192C2×Dic3—124no—
193C4×D3—124no—
194C4×D3—124no—
195C3×C8—64no—
196C3⋊C8—24no—
197C2×C32—22no—
198C2×C32#40711yescharacteristic
199C2×C32#41811yescharacteristic
200C2×C32C2×#10411yescharacteristic
201C3×D3—44no—
202C24—61no—
203C2×D4—92no—
204C2×D4—181no—
205C2×D4—184no—
206C22×C4—61no—
207C22×C4—91no—
208C22×C4—91no—
209C22×C4—182no—
210C22×C4—182no—
211C22×C4—364no—
212C22×C4GO+(4,𝔽2)11yescharacteristic
213M16—64no—
214C2×C8—62no—
215C2×C8—182no—
216C4⋊C4—92no—
217C4⋊C4—181no—
218C22⋊C4—62no—
219C22⋊C4—62no—
220C42—91no—
221C42—91no—
222C42—91no—
223C42—91no—
224C22×C3—22no—
225C22×C3—22no—
226C22×C3—21no—
227C22×C3—21no—
228C22×C3—22no—
229C22×C3—22no—
230C22×C3—41no—
231C22×C3—41no—
232C22×C3—64no—
233C22×C3—122no—
234C22×C3—128no—
235C22×C3—122no—
236C2×D3—24no—
237C2×D3—42no—
238C2×D3—48no—
239C2×D3—42no—
240C3×C4—21no—
241C3×C4—21no—
242C3×C4—22no—
243C3×C4—41no—
244C3×C4—41no—
245C3×C4—122no—
246Dic3—42no—
247Dic3—62no—
248Dic3—62no—
249Dic3—62no—
250Dic3—62no—
251Dic3—62no—
252Dic3—62no—
253Dic3—121no—
254Dic3—121no—
255C32#149011yescharacteristic, complemented, Sylow
256C23—64no—
257C23—62no—
258C23—122no—
259C23—122no—
260C23D32⋊C411yescharacteristic
261D4—94no—
262D4—182no—
263D4—184no—
264C2×C4—22no—
265C2×C4—62no—
266C2×C4—91no—
267C2×C4—91no—
268C2×C4—91no—
269C2×C4—91no—
270C2×C4—122no—
271C2×C4—182no—
272C2×C4—182no—
273C2×C4—364no—
274C2×C4—364no—
275C2×C4D32⋊C411yescharacteristic
276C2×C4C2×GO+(4,𝔽2)11yescharacteristic
277C8—64no—
278C8—362no—
279C2×C3—24no—
280C2×C3—21no—
281C2×C3—21no—
282C2×C3—21no—
283C2×C3—21no—
284C2×C3—21no—
285C2×C3—21no—
286C2×C3—42no—
287C2×C3—124no—
288D3—44no—
289C22—21no—
290C22—21no—
291C22—64no—
292C22—128no—
293C22—122no—
294C22—122no—
295C22#6374112yes—
296C22C2×D32⋊C411yescharacteristic
297C4—21no—
298C4—21no—
299C4—92no—
300C4—92no—
301C4—122no—
302C4—181no—
303C4—181no—
304C3—21no—
305C3—21no—
306C2—22no—
307C2—124no—
308C2#1059330711yescharacteristic
309C2#1059331811yescharacteristic
310C2C2×#6374111yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC22×#625C4
cosocleC4×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1490
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #10593804C2semidirect
3. #10591060C2semidirect
4. #10590030C2semidirect
16. #63779C22semidirect
19. #63553C22semidirect
79. #625M16semidirect
255. C32#1490semidirect

Maximal subgroups

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

subgroupindex
C2×#639022
#105938042
#105910602
#105900302
#14909