Finite Group Databasebeta

← #11774188

Subgroups — #11774188

Order 1152.

626 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 626 conjugacy classes of subgroups — too many to draw. Only its 89 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
2C4×#3787C211yesmaximal, characteristic, complemented
3#10590331C211yesmaximal, characteristic, complemented
4#10590029C214yesmaximal, complemented
5C2×#3802C411yescharacteristic
6C2×C4×D32—21no—
7C2×#3787—21no—
8C42×C3⋊D3C2211yescharacteristic
9C3×C4×D12—21no—
10#63921—21no—
11#63902C412yes—
12C4×#625C2212yes—
13#63900C411yescharacteristic
14#63898—21no—
15C2×#3710—21no—
16C4×#622—21no—
17C4×#622C2212yescomplemented
18C3×C4⋊(C3⋊C8)—21no—
19#63572C2212yescomplemented
20C4×D3×D4—61no—
21D3×C4⋊C8—61no—
22C22×D32—21no—
23C2×C4×C3⋊D3C2×C411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C4×C3⋊D3D411yescharacteristic
26C2×C3×D12—21no—
27C2×C3×C4×D3—22no—
28C2×#625C2×C412yes—
29C2×#624—21no—
30C2×D3×Dic3—22no—
31#3802—22no—
32#3802C814yescomplemented
33C4×D32—42no—
34C4×D32—42no—
35C2×#622—22no—
36#3787—24no—
37C32×C42D411yescharacteristic
38C4×C3⋊Dic3C2×C411yescharacteristic
39C4×C3⋊Dic3D411yescharacteristic
40C4×C3⋊Dic3C2311yescharacteristic
41C3×(C2×D3)⋊C4—22no—
42C3×C4⋊Dic3—21no—
43C2×C3×C3⋊C8—22no—
44#3724C2×C412yes—
45(C2×D3)⋊Dic3—22no—
46#3710—42no—
47C2×D4⋊C8—91nomaximal, Sylow
48C2×D3×D4—61no—
49C22×C4×D3—62no—
50C3×C4×D4—61no—
51D4×Dic3—61no—
52C4×#67—62no—
53C2×D3×C8—62no—
54#893—61no—
55D3×C4⋊C4—61no—
56#67⋊C4—62no—
57D3×C22⋊C4—62no—
58C4×D12—21no—
59C42×D3—61no—
60C42×D3—61no—
61C3×C4⋊C8—61no—
62Dic3⋊C8—62no—
63C4⋊(C3⋊C8)—21no—
64C22×C3⋊D3C22⋊C411yescharacteristic
65C22×C3×D3—22no—
66C2×D32—24no—
67C2×D32—42no—
68C2×D32—42no—
69C2×C32×C4C22⋊C411yescharacteristic
70C2×C32×C4C22⋊C411yescharacteristic
71C2×C32×C4C2×D411yescharacteristic
72C2×C3⋊Dic3C22⋊C411yescharacteristic
73C2×C3⋊Dic3C22×C411yescharacteristic
74C2×C3⋊Dic3C2×D411yescharacteristic
75C4×C3⋊D3—22no—
76C4×C3⋊D3C2×C812yes—
77C4×C3⋊D3M1612yes—
78C4×C3⋊D3D812yes—
79C4×C3⋊D3SD1612yes—
80C2×C3×Dic3—22no—
81C3×D12—24no—
82C3×C4×D3—42no—
83C3×C4×D3—42no—
84#625—22no—
85#625C2×C814yescomplemented
86#624—42no—
87D3×Dic3—44no—
88#622—24no—
89C3×C3⋊C8—42no—
90C2×C4×D4—91no—
91C2×C4⋊C8—91no—
92C2×C4×C8—91no—
93D4⋊C8—94no—
94C23×D3—62no—
95C2×C3×D4—61no—
96C22×C3×C4—62no—
97C2×#67—62no—
98C22×Dic3—62no—
99D3×D4—64no—
100D3×D4—64no—
101C2×D12—21no—
102C2×C4×D3—22no—
103C2×C4×D3—61no—
104C2×C4×D3—61no—
105C2×C4×D3—61no—
106C2×C4×D3—61no—
107C2×C4×D3—61no—
108C2×C4×D3—61no—
109C2×C4×D3—62no—
110C2×C4×D3—62no—
111C2×C4×D3—124no—
112C2×C4×D3—124no—
113C2×C3×C8—62no—
114C3×C4⋊C4—61no—
115C3×C22⋊C4—62no—
116C3×C42—21no—
117C3×C42—21no—
118#217—62no—
119(C2×D3)⋊C4—22no—
120(C2×D3)⋊C4—62no—
121C4⋊Dic3—21no—
122Dic3⋊C4—62no—
123C4×Dic3—61no—
124C4×Dic3—61no—
125C4×Dic3—61no—
126C4×Dic3—61no—
127C4×Dic3—61no—
128C4×Dic3—61no—
129C2×C3⋊C8—22no—
130D3×C8—124no—
131C22×C32C2×C22⋊C411yescharacteristic
132C2×C3⋊D3C22⋊C812yes—
133C2×C3⋊D3#10212yes—
134C2×C3⋊D3#10412yes—
135C2×C3×D3—24no—
136C2×C3×D3—42no—
137C2×C3×D3—42no—
138D32—48no—
139C32×C4—21no—
140C32×C4C22⋊C812yes—
141C32×C4C2×D811yescharacteristic
142C32×C4C2×SD1611yescharacteristic
143C3⋊Dic3—21no—
144C3⋊Dic3#10212yes—
145C3⋊Dic3C22×C811yescharacteristic
146C3⋊Dic3C2×M1611yescharacteristic
147C3×Dic3—42no—
148C22×D4—91no—
149C23×C4—181no—
150C22×C8—181no—
151C22×C8—181no—
152C4×D4—61no—
153C4×D4—92no—
154C4×D4—92no—
155C4×D4—181no—
156C2×C4⋊C4—91no—
157C2×C22⋊C4—181no—
158C2×C42—91no—
159C4⋊C8—61no—
160C4⋊C8—92no—
161C4×C8—92no—
162C4×C8—181no—
163C23×C3—62no—
164C22×D3—22no—
165C22×D3—61no—
166C22×D3—61no—
167C22×D3—68no—
168C22×D3—124no—
169C22×D3—124no—
170C3×D4—64no—
171C2×C3×C4—21no—
172C2×C3×C4—21no—
173C2×C3×C4—21no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—62no—
178C2×C3×C4—122no—
179C2×C3×C4—122no—
180#67—64no—
181#67—64no—
182C2×Dic3—22no—
183C2×Dic3—61no—
184C2×Dic3—61no—
185C2×Dic3—61no—
186C2×Dic3—61no—
187C2×Dic3—61no—
188C2×Dic3—61no—
189C2×Dic3—124no—
190D12—24no—
191C4×D3—42no—
192C4×D3—42no—
193C4×D3—62no—
194C4×D3—62no—
195C4×D3—62no—
196C4×D3—62no—
197C4×D3—62no—
198C4×D3—62no—
199C4×D3—62no—
200C4×D3—62no—
201C4×D3—122no—
202C4×D3—122no—
203C4×D3—124no—
204C4×D3—124no—
205C3×C8—122no—
206C3⋊C8—42no—
207C2×C32C2×C22⋊C811yescharacteristic
208C2×C32C2×#10211yescharacteristic
209C2×C32C2×#10411yescharacteristic
210C3⋊D3D4⋊C814yescomplemented
211C3×D3—44no—
212C24—181no—
213C2×D4—61no—
214C2×D4—94no—
215C2×D4—92no—
216C2×D4—182no—
217C22×C4—62no—
218C22×C4—91no—
219C22×C4—91no—
220C22×C4—91no—
221C22×C4—181no—
222C22×C4—182no—
223C22×C4—362no—
224C22×C4—362no—
225C2×C8—62no—
226C2×C8—182no—
227C2×C8—184no—
228C2×C8—362no—
229C4⋊C4—61no—
230C4⋊C4—92no—
231C22⋊C4—62no—
232C22⋊C4—182no—
233C42—91no—
234C42—91no—
235C42—91no—
236C42GO+(4,𝔽2)11yescharacteristic
237C22×C3—21no—
238C22×C3—21no—
239C22×C3—64no—
240C22×C3—122no—
241C22×C3—122no—
242C2×D3—24no—
243C2×D3—42no—
244C2×D3—42no—
245C2×D3—62no—
246C2×D3—62no—
247C2×D3—62no—
248C2×D3—62no—
249C2×D3—62no—
250C2×D3—62no—
251C2×D3—1216no—
252C3×C4—21no—
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—21no—
256C3×C4—22no—
257C3×C4—22no—
258C3×C4—41no—
259C3×C4—41no—
260C3×C4—122no—
261Dic3—42no—
262Dic3—62no—
263Dic3—61no—
264Dic3—61no—
265Dic3—62no—
266Dic3—61no—
267Dic3—61no—
268Dic3—121no—
269Dic3—121no—
270C32C2×D4⋊C811yescharacteristic, complemented, Sylow
271C23—62no—
272C23—91no—
273C23—184no—
274C23—362no—
275C23—362no—
276D4—64no—
277D4—94no—
278D4—182no—
279C2×C4—62no—
280C2×C4—91no—
281C2×C4—91no—
282C2×C4—92no—
283C2×C4—92no—
284C2×C4—92no—
285C2×C4—92no—
286C2×C4—91no—
287C2×C4—122no—
288C2×C4—122no—
289C2×C4—182no—
290C2×C4—364no—
291C2×C4—362no—
292C2×C4D32⋊C411yescharacteristic
293C2×C4D32⋊C411yescharacteristic
294C2×C4C2×GO+(4,𝔽2)11yescharacteristic
295C8—122no—
296C8—184no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3—21no—
300C2×C3—21no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3—124no—
304D3—44no—
305D3—64no—
306D3—64no—
307C22—64no—
308C22—92no—
309C22—92no—
310C22—92no—
311C22—122no—
312C22—122no—
313C22—368no—
314C22C2×D32⋊C411yescharacteristic
315C4—21no—
316C4—91no—
317C4—91no—
318C4—92no—
319C4—122no—
320C4—181no—
321C4D32⋊C812yes—
322C4#6422511yescharacteristic
323C4#6422711yescharacteristic
324C3—21no—
325C3—21no—
326C2—94no—
327C2—124no—
328C2C2×D32⋊C811yescharacteristic
329C2#1059332511yescharacteristic
330C2#1059336511yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C22×C8
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radicalC2×#3802C4
cosocleC4×C3⋊Dic3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32C2×D4⋊C8
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C4×#3787C2semidirect
3. #10590331C2semidirect
4. #10590029C2semidirect
17. C4×#622C22semidirect
19. #63572C22semidirect
32. #3802C8semidirect
85. #625C2×C8semidirect
210. C3⋊D3D4⋊C8semidirect
270. C32C2×D4⋊C8semidirect

Maximal subgroups

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

subgroupindex
C4×#38022
C4×#37872
#105903312
#105900292
C2×D4⋊C89