Finite Group Databasebeta

← #11775311

Subgroups — #11775311

Order 1152.

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

normal subgroups only

This group has 634 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#10595081C211yesmaximal, characteristic
2#10593811C211yesmaximal, characteristic, complemented
3#10591159C211yesmaximal, characteristic, complemented
4#10590033C214yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C2×#3811—21no—
7C2×#3802C411yescharacteristic, complemented
8C2×C22⋊#157—21no—
9C3×#930—21no—
10#63980C412yescomplemented
11#63921—21no—
12#63916—21no—
13#63912C2212yes—
14#63900C411yescharacteristic, complemented
15C2×#3712—21no—
16#63781—21no—
17#63781C2212yescomplemented
18C3×#830—21no—
19#63557C2212yescomplemented
20D3×#121—61no—
21#4726—61no—
22C23×C3⋊D3D411yescharacteristic
23C22×D32—21no—
24C22×#157—22no—
25C22×C32×C4D411yescharacteristic
26C22×C3⋊Dic3C2×C411yescharacteristic
27C2×C4×C3⋊D3—42no—
28C2×C4×C3⋊D3C2×C411yescharacteristic
29C2×C4×C3⋊D3D411yescharacteristic
30C2×C4×C3⋊D3D411yescharacteristic
31C2×C4×C3⋊D3C2311yescharacteristic
32C2×C3×#67—22no—
33C2×C3×D12—21no—
34#3811—44no—
35C2×#626—22no—
36C2×#625C2×C412yes—
37C2×#624—21no—
38#3802—42no—
39C22⋊#157—42no—
40C3×(C2×D3)⋊C4—22no—
41C3×C4⋊Dic3—21no—
42C2×C3×C3⋊C8—22no—
43#3724C2×C412yes—
44(C2×D3)⋊Dic3—22no—
45#3712—42no—
46#1510—91nomaximal, Sylow
47C2×D3×D4—61no—
48C2×D3×D4—62no—
49C22×C4×D3—61no—
50C22×C4×D3—61no—
51C3×#121—61no—
52#939—62no—
53#938—61no—
54#930—21no—
55C2×ΓL(1,𝔽25)—62no—
56#895—61no—
57D3×C4⋊C4—61no—
58#884—62no—
59D3×C22⋊C4—62no—
60C3×C22⋊C8—61no—
61#830—21no—
62(C2×D3)⋊C8—62no—
63C23×C32C22⋊C411yescharacteristic
64C22×C3⋊D3—22no—
65C22×C3⋊D3—22no—
66C22×C3⋊D3—41no—
67C22×C3⋊D3C22⋊C411yescharacteristic
68C22×C3⋊D3C2×D411yescharacteristic
69C22×C3×D3—22no—
70C2×D32—42no—
71C2×D32—42no—
72C2×D32—42no—
73C2×#157—42no—
74C2×#157—42no—
75C2×#157—42no—
76C2×C32×C4—41no—
77C2×C32×C4C22⋊C411yescharacteristic
78C2×C32×C4C2×D411yescharacteristic
79C2×C3⋊Dic3—41no—
80C2×C3⋊Dic3C22⋊C411yescharacteristic
81C2×C3⋊Dic3C22×C411yescharacteristic
82C4×C3⋊D3—22no—
83C4×C3⋊D3—22no—
84C4×C3⋊D3—41no—
85C4×C3⋊D3—41no—
86C3×#67—44no—
87C2×C3×Dic3—22no—
88C3×D12—42no—
89#626—44no—
90#625—42no—
91#624—42no—
92C3×C3⋊C8—42no—
93C2×#121—91no—
94#407—91no—
95#381—91no—
96#327—94no—
97C23×D3—61no—
98C23×D3—61no—
99C23×D3—62no—
100C2×C3×D4—61no—
101C2×C3×D4—62no—
102C22×C3×C4—21no—
103C22×C3×C4—21no—
104C2×#67—22no—
105C2×#67—62no—
106C2×#67—62no—
107C22×Dic3—61no—
108C22×Dic3—61no—
109D3×D4—124no—
110D3×D4—128no—
111C2×D12—21no—
112C2×D12—62no—
113C2×C4×D3—61no—
114C2×C4×D3—61no—
115C2×C4×D3—61no—
116C2×C4×D3—61no—
117C2×C4×D3—61no—
118C2×C4×D3—61no—
119C2×C4×D3—61no—
120C2×C4×D3—61no—
121C2×C4×D3—62no—
122C2×C4×D3—124no—
123C2×C4×D3—124no—
124C2×C3×C8—62no—
125C3×C4⋊C4—61no—
126C3×C22⋊C4—62no—
127#217—62no—
128(C2×D3)⋊C4—22no—
129(C2×D3)⋊C4—62no—
130C4⋊Dic3—21no—
131Dic3⋊C4—62no—
132C2×C3⋊C8—22no—
133ΓL(1,𝔽25)—124no—
134C22×C32—21no—
135C22×C32—21no—
136C22×C32—21no—
137C22×C32C2×C22⋊C411yescharacteristic
138C2×C3⋊D3—21no—
139C2×C3⋊D3—21no—
140C2×C3⋊D3—21no—
141C2×C3⋊D3—21no—
142C2×C3⋊D3—44no—
143C2×C3⋊D3#9912yes—
144C2×C3⋊D3AGL(1,ℤ/8)12yes—
145C2×C3×D3—42no—
146C2×C3×D3—42no—
147C2×C3×D3—42no—
148D32—84no—
149#157—82no—
150C32×C4—21no—
151C32×C4—21no—
152C3⋊Dic3—21no—
153C3⋊Dic3—21no—
154C3×Dic3—42no—
155C22×D4—91no—
156C22×D4—181no—
157C23×C4—91no—
158C2×M16—181no—
159#121—61no—
160#121—92no—
161#121—92no—
162#121—181no—
163C2×C4⋊C4—91no—
164C2×C22⋊C4—181no—
165C2×C22⋊C4—181no—
166C22⋊C8—61no—
167C22⋊C8—92no—
168#95—92no—
169#95—181no—
170C23×C3—21no—
171C23×C3—21no—
172C23×C3—62no—
173C22×D3—22no—
174C22×D3—61no—
175C22×D3—61no—
176C22×D3—61no—
177C22×D3—61no—
178C22×D3—64no—
179C22×D3—122no—
180C22×D3—122no—
181C22×D3—122no—
182C22×D3—124no—
183C22×D3—124no—
184C22×D3—124no—
185C22×D3—122no—
186C22×D3—122no—
187C3×D4—122no—
188C3×D4—124no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—42no—
194C2×C3×C4—42no—
195C2×C3×C4—62no—
196#67—44no—
197#67—124no—
198#67—124no—
199C2×Dic3—22no—
200C2×Dic3—61no—
201C2×Dic3—61no—
202C2×Dic3—61no—
203C2×Dic3—61no—
204C2×Dic3—122no—
205C2×Dic3—122no—
206D12—42no—
207D12—124no—
208C4×D3—64no—
209C4×D3—64no—
210C4×D3—122no—
211C4×D3—122no—
212C4×D3—124no—
213C4×D3—122no—
214C4×D3—122no—
215C4×D3—122no—
216C4×D3—122no—
217C3×C8—122no—
218C3⋊C8—42no—
219C2×C32—41no—
220C2×C32C2×#9911yescharacteristic
221C2×C32#41811yescharacteristic
222C2×C32#42111yescharacteristic
223C3⋊D3—22no—
224C3⋊D3—22no—
225C3×D3—82no—
226C24—91no—
227C24—181no—
228C2×D4—62no—
229C2×D4—61no—
230C2×D4—92no—
231C2×D4—182no—
232C2×D4—362no—
233C2×D4—364no—
234C22×C4—91no—
235C22×C4—91no—
236C22×C4—91no—
237C22×C4—91no—
238C22×C4—91no—
239C22×C4—181no—
240C22×C4—182no—
241C22×C4—362no—
242C22×C4GO+(4,𝔽2)11yescharacteristic
243M16—362no—
244C2×C8—62no—
245C4⋊C4—61no—
246C4⋊C4—92no—
247C22⋊C4—62no—
248C22⋊C4—182no—
249C22⋊C4—362no—
250C22×C3—22no—
251C22×C3—22no—
252C22×C3—21no—
253C22×C3—21no—
254C22×C3—41no—
255C22×C3—41no—
256C22×C3—41no—
257C22×C3—41no—
258C22×C3—122no—
259C22×C3—122no—
260C22×C3—122no—
261C2×D3—42no—
262C2×D3—42no—
263C2×D3—42no—
264C2×D3—62no—
265C2×D3—62no—
266C2×D3—62no—
267C2×D3—62no—
268C2×D3—62no—
269C2×D3—62no—
270C2×D3—121no—
271C2×D3—121no—
272C2×D3—121no—
273C2×D3—121no—
274C2×D3—121no—
275C2×D3—121no—
276C2×D3—128no—
277C2×D3—128no—
278C2×D3—248no—
279C3×C4—22no—
280C3×C4—22no—
281C3×C4—41no—
282C3×C4—41no—
283C3×C4—122no—
284Dic3—42no—
285Dic3—62no—
286Dic3—62no—
287Dic3—121no—
288Dic3—121no—
289C32#151011yescharacteristic, complemented, Sylow
290C23—62no—
291C23—91no—
292C23—91no—
293C23—182no—
294C23—182no—
295C23—361no—
296C23—362no—
297C23—362no—
298C23—362no—
299C23D32⋊C411yescharacteristic
300D4—122no—
301D4—124no—
302D4—364no—
303D4—362no—
304C2×C4—41no—
305C2×C4—62no—
306C2×C4—91no—
307C2×C4—91no—
308C2×C4—182no—
309C2×C4—182no—
310C2×C4—361no—
311C2×C4—361no—
312C2×C4—362no—
313C2×C4—361no—
314C2×C4—362no—
315C2×C4—362no—
316C2×C4—362no—
317C2×C4D32⋊C411yescharacteristic
318C2×C4C2×GO+(4,𝔽2)11yescharacteristic
319C8—122no—
320C2×C3—21no—
321C2×C3—21no—
322C2×C3—21no—
323C2×C3—21no—
324C2×C3—21no—
325C2×C3—21no—
326C2×C3—42no—
327C2×C3—42no—
328C2×C3—242no—
329D3—64no—
330D3—82no—
331D3—122no—
332D3—122no—
333D3—122no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—92no—
338C22—92no—
339C22—122no—
340C22—122no—
341C22—122no—
342C22—181no—
343C22—181no—
344C22—181no—
345C22—181no—
346C22—364no—
347C22—724no—
348C22C2×D32⋊C411yescharacteristic
349C4—21no—
350C4—21no—
351C4—122no—
352C4—181no—
353C4—181no—
354C4—722no—
355C3—21no—
356C3—21no—
357C2—41no—
358C2—182no—
359C2—182no—
360C2—242no—
361C2#1059331811yescharacteristic
362C2#1059332411yescharacteristic
363C2#1059349011yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radical#10595081C2
cosocleC2×C4×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1510
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #10593811C2semidirect
3. #10591159C2semidirect
4. #10590033C2semidirect
7. C2×#3802C4semidirect
10. #63980C4semidirect
14. #63900C4semidirect
17. #63781C22semidirect
19. #63557C22semidirect
289. C32#1510semidirect

Maximal subgroups

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

subgroupindex
#105950812
#105938112
#105911592
#105900332
#15109