Finite Group Databasebeta

← #11790823

Subgroups — #11790823

Order 1152.

538 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 67 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#10593972C211yesmaximal, characteristic
2#10593733C211yesmaximal, characteristic, complemented
3C2×#63731C214yesmaximal, complemented
4#10590340C211yesmaximal, characteristic, complemented
5C2×#3798C2212yes—
6C2×C4×#157C2212yes—
7C42×C3⋊D3C2211yescharacteristic
8C3×C4×D12—21no—
9#63919C411yescharacteristic, complemented
10#63916—21no—
11#63915C412yescomplemented
12#63914C411yescharacteristic, complemented
13#63912—21no—
14C4×#625—21no—
15C2×#3712C2212yes—
16#63781—21no—
17#63781—21no—
18#63731—28no—
19C3×C4⋊(C3⋊C8)—21no—
20#63572—21no—
21#5548—61no—
22#4837—61no—
23C22×#157—22no—
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C4×C3⋊D3D411yescharacteristic
26C2×C4×C3⋊D3C2311yescharacteristic
27C2×C3×D12—21no—
28C2×C3×C4×D3—22no—
29C2×#627C2×C412yes—
30C2×#626—22no—
31C2×#625—21no—
32C2×#625C2×C412yes—
33#3798—24no—
34#3798—24no—
35C4×#157—22no—
36C4×#157D414yescomplemented
37C32×C42D411yescharacteristic
38C4×C3⋊Dic3C2×C411yescharacteristic
39C4×C3⋊Dic3C2×C411yescharacteristic
40C4×C3⋊Dic3D411yescharacteristic
41C3×(C2×D3)⋊C4—22no—
42C3×C4⋊Dic3—21no—
43C2×C3×C3⋊C8—22no—
44#3724—21no—
45(C2×D3)⋊Dic3—22no—
46#3712—24no—
47#1963—91nomaximal, Sylow
48C2×#235—62no—
49C3×C4×D4—61no—
50#940—61no—
51#938—61no—
52C4×#67—62no—
53C2×ΓL(1,𝔽25)—62no—
54#895—61no—
55#888—61no—
56#885—62no—
57#884—62no—
58C4×D12—21no—
59C42×D3—61no—
60C42×D3—61no—
61C3×C4⋊C8—61no—
62Dic3⋊C8—62no—
63C4⋊(C3⋊C8)—21no—
64C22×C3⋊D3C2×D411yescharacteristic
65C22×C3×D3—22no—
66C2×#157—24no—
67C2×#157—42no—
68C2×#157—42no—
69C2×C32×C4C22⋊C411yescharacteristic
70C2×C32×C4C22⋊C411yescharacteristic
71C2×C32×C4C2×D411yescharacteristic
72C2×C3⋊Dic3C22⋊C411yescharacteristic
73C2×C3⋊Dic3C22⋊C411yescharacteristic
74C2×C3⋊Dic3C22×C411yescharacteristic
75C4×C3⋊D3—41no—
76C4×C3⋊D3—41no—
77C4×C3⋊D3C2×D412yes—
78C4×C3⋊D3#4112yes—
79C2×C3×Dic3—22no—
80C3×D12—42no—
81C3×C4×D3—42no—
82C3×C4×D3—42no—
83#627—24no—
84#626—44no—
85#625—24no—
86#625—42no—
87C3×C3⋊C8—42no—
88#532—91no—
89#423—91no—
90C2×#104—94no—
91#376—91no—
92C2×C3×D4—61no—
93C22×C3×C4—62no—
94C2×#67—62no—
95C2×#67—62no—
96C2×#67—62no—
97#235—124no—
98#235—124no—
99C2×D12—21no—
100C2×D12—62no—
101C2×C4×D3—22no—
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×Dic6—62no—
109C2×C3×C8—62no—
110C3×C4⋊C4—61no—
111C3×C22⋊C4—62no—
112C3×C42—21no—
113C3×C42—21no—
114#217—62no—
115(C2×D3)⋊C4—22no—
116(C2×D3)⋊C4—62no—
117C4⋊Dic3—21no—
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—
126ΓL(1,𝔽25)—124no—
127C22×C32C2×C22⋊C411yescharacteristic
128C2×C3⋊D3—21no—
129C2×C3⋊D3—21no—
130C2×C3⋊D3#12112yes—
131C2×C3×D3—42no—
132C2×C3×D3—42no—
133C2×C3×D3—42no—
134#157—44no—
135C32×C4—21no—
136C32×C4—21no—
137C32×C4#12411yescharacteristic
138C32×C4#12711yescharacteristic
139C3⋊Dic3—21no—
140C3⋊Dic3—21no—
141C3⋊Dic3C4×D412yes—
142C3×Dic3—42no—
143C2×#41—92no—
144C2×M16—92no—
145C4⋊Q8—91no—
146#127—91no—
147#124—92no—
148#121—181no—
149#121—181no—
150C4×D4—61no—
151C4×D4—181no—
152C2×C42—91no—
153C2×C42—92no—
154C4⋊C8—61no—
155C4⋊C8—181no—
156#104—188no—
157#95—181no—
158#95—181no—
159C23×C3—62no—
160C22×D3—22no—
161C22×D3—61no—
162C22×D3—61no—
163C3×D4—122no—
164C2×C3×C4—21no—
165C2×C3×C4—21no—
166C2×C3×C4—21no—
167C2×C3×C4—21no—
168C2×C3×C4—21no—
169C2×C3×C4—21no—
170C2×C3×C4—62no—
171C2×C3×C4—122no—
172C2×C3×C4—122no—
173#67—124no—
174#67—124no—
175#67—124no—
176C2×Dic3—22no—
177C2×Dic3—61no—
178C2×Dic3—61no—
179C2×Dic3—61no—
180C2×Dic3—61no—
181C2×Dic3—61no—
182C2×Dic3—61no—
183D12—42no—
184D12—124no—
185C4×D3—42no—
186C4×D3—42no—
187C4×D3—62no—
188C4×D3—62no—
189C4×D3—62no—
190C4×D3—62no—
191C4×D3—122no—
192C4×D3—122no—
193C4×D3—122no—
194C4×D3—122no—
195Dic6—124no—
196C3×C8—122no—
197C3⋊C8—42no—
198C2×C32#39011yescharacteristic
199C2×C32#42111yescharacteristic
200C2×C32#42111yescharacteristic
201C3⋊D3—22no—
202C3×D3—82no—
203#41—184no—
204#41—184no—
205C2×Q8—92no—
206C2×D4—61no—
207C2×D4—92no—
208C2×D4—182no—
209C2×D4—181no—
210C22×C4—62no—
211C22×C4—91no—
212C22×C4—91no—
213C22×C4—91no—
214C22×C4—182no—
215M16—184no—
216C2×C8—62no—
217C4⋊C4—61no—
218C4⋊C4—181no—
219C22⋊C4—62no—
220C22⋊C4—182no—
221C42—91no—
222C42—91no—
223C42—91no—
224C42—94no—
225C42—182no—
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—62no—
236C2×D3—62no—
237C2×D3—121no—
238C2×D3—121no—
239C2×D3—121no—
240C2×D3—121no—
241C3×C4—22no—
242C3×C4—22no—
243C3×C4—21no—
244C3×C4—21no—
245C3×C4—21no—
246C3×C4—21no—
247C3×C4—41no—
248C3×C4—41no—
249C3×C4—122no—
250Dic3—42no—
251Dic3—62no—
252Dic3—62no—
253Dic3—62no—
254Dic3—62no—
255Dic3—121no—
256Dic3—121no—
257C32#196311yescharacteristic, complemented, Sylow
258C23—62no—
259C23—91no—
260Q8—184no—
261D4—122no—
262D4—184no—
263D4—364no—
264D4—362no—
265C2×C4—62no—
266C2×C4—91no—
267C2×C4—92no—
268C2×C4—92no—
269C2×C4—91no—
270C2×C4—91no—
271C2×C4—122no—
272C2×C4—122no—
273C2×C4—184no—
274C2×C4—361no—
275C2×C4—361no—
276C2×C4—362no—
277C2×C4—362no—
278C2×C4D32⋊C411yescharacteristic
279C2×C4D32⋊C411yescharacteristic
280C2×C4C2×GO+(4,𝔽2)11yescharacteristic
281C8—122no—
282C2×C3—21no—
283C2×C3—21no—
284C2×C3—21no—
285C2×C3—21no—
286C2×C3—21no—
287C2×C3—21no—
288C2×C3—242no—
289D3—82no—
290D3—122no—
291D3—122no—
292C22—92no—
293C22—122no—
294C22—122no—
295C22—122no—
296C22—181no—
297C22—181no—
298C22C2×D32⋊C411yescharacteristic
299C4—21no—
300C4—21no—
301C4—92no—
302C4—122no—
303C4—181no—
304C4—181no—
305C4—364no—
306C4#6422111yescharacteristic
307C4#6423111yescharacteristic
308C3—21no—
309C3—21no—
310C2—182no—
311C2—242no—
312C2#1059332311yescharacteristic
313C2#1059332411yescharacteristic
314C2#1059340711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radical#10593972C2
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1963
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #10593733C2semidirect
3. C2×#63731C2semidirect
4. #10590340C2semidirect
9. #63919C4semidirect
11. #63915C4semidirect
12. #63914C4semidirect
36. C4×#157D4semidirect
257. C32#1963semidirect

Maximal subgroups

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

subgroupindex
#105939722
#105937332
C2×#637312
#105903402
#19639