Finite Group Databasebeta

← #11791415

Subgroups — #11791415

Order 1152.

588 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 71 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#10594929C211yesmaximal, characteristic
2C4×#3792C211yesmaximal, characteristic, complemented
3C2×#63741C214yesmaximal, complemented
4#10591274C211yesmaximal, characteristic, complemented
5C2×#3805C2212yes—
6C2×#3792C2212yes—
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C3×#930—21no—
9C2×C3×C4⋊Dic3—21no—
10#63980—21no—
11C2×Dic32C2212yes—
12#63919C411yescharacteristic, complemented
13#63915C412yescomplemented
14#63914C411yescharacteristic, complemented
15#63902—21no—
16#63898—21no—
17#63777—21no—
18C4×#622—21no—
19#63741—28no—
20#63579—21no—
21#5596—61no—
22Dic3×C4⋊C4—61no—
23C22×C32×C4D411yescharacteristic
24C22×C3⋊Dic3D411yescharacteristic
25C22×C3⋊Dic3C2311yescharacteristic
26C2×C3×#67—22no—
27C22×C3×Dic3—22no—
28C2×C3×D12—21no—
29C2×#627C2×C412yes—
30C2×#625—21no—
31C2×#625C2×C412yes—
32#3805—24no—
33#3805—24no—
34C2×D3×Dic3—22no—
35#3792—22no—
36#3792D414yescomplemented
37C2×#622—22no—
38C4×C3⋊Dic3C2×C411yescharacteristic
39C4×C3⋊Dic3C2×C411yescharacteristic
40C4×C3⋊Dic3D411yescharacteristic
41C4×C3⋊Dic3D411yescharacteristic
42C3×(C2×D3)⋊C4—22no—
43C3×C4⋊Dic3—24no—
44C3×C4⋊Dic3—21no—
45#3724—21no—
46(C2×D3)⋊Dic3—22no—
47Dic32—24no—
48#1980—91nomaximal, Sylow
49C2×#237—62no—
50C3×#121—61no—
51C2×C3×C4⋊C4—61no—
52#940—61no—
53#939—62no—
54D4×Dic3—61no—
55#930—21no—
56C2×C4⋊Dic3—21no—
57C2×C4×Dic3—61no—
58C2×C4×Dic3—61no—
59C2×C4×Dic3—62no—
60#893—61no—
61#888—61no—
62#885—62no—
63#67⋊C4—62no—
64C3⋊#95—62no—
65C23×C32C2×D411yescharacteristic
66C22×C3×D3—22no—
67C2×C32×C4—22no—
68C2×C32×C4C22⋊C411yescharacteristic
69C2×C32×C4C22⋊C411yescharacteristic
70C2×C3⋊Dic3—41no—
71C2×C3⋊Dic3C22⋊C411yescharacteristic
72C2×C3⋊Dic3C22⋊C411yescharacteristic
73C2×C3⋊Dic3C22×C411yescharacteristic
74C2×C3⋊Dic3C2×D412yes—
75C2×C3⋊Dic3C2×D411yescharacteristic
76C2×C3⋊Dic3#4112yes—
77C3×#67—42no—
78C3×#67—42no—
79C2×C3×Dic3—24no—
80C2×C3×Dic3—22no—
81C2×C3×Dic3—42no—
82C2×C3×Dic3—42no—
83C3×D12—42no—
84#627—24no—
85#625—24no—
86#625—42no—
87D3×Dic3—44no—
88#622—24no—
89#532—91no—
90C2×#104—94no—
91C4×M16—91no—
92C4×C4⋊C4—91no—
93C2×C3×D4—61no—
94C2×C3×D4—62no—
95C22×C3×C4—21no—
96C22×C3×C4—21no—
97C22×C3×C4—62no—
98C2×#67—22no—
99C2×#67—62no—
100C2×#67—62no—
101C22×Dic3—22no—
102C22×Dic3—61no—
103C22×Dic3—61no—
104C22×Dic3—61no—
105C22×Dic3—61no—
106C22×Dic3—62no—
107#237—124no—
108#237—124no—
109C2×D12—21no—
110C2×C4×D3—62no—
111C2×Dic6—62no—
112C3×C4⋊C4—61no—
113C3×C4⋊C4—64no—
114C3×C22⋊C4—62no—
115#217—62no—
116(C2×D3)⋊C4—22no—
117(C2×D3)⋊C4—62no—
118C4⋊Dic3—21no—
119C4⋊Dic3—24no—
120Dic3⋊C4—62no—
121C4×Dic3—61no—
122C4×Dic3—61no—
123C4×Dic3—61no—
124C4×Dic3—61no—
125C4×Dic3—61no—
126C4×Dic3—61no—
127C4×Dic3—61no—
128C4×Dic3—61no—
129C4×Dic3—124no—
130C22×C32—21no—
131C22×C32—21no—
132C22×C32C2×C22⋊C411yescharacteristic
133C22×C32#12411yescharacteristic
134C22×C32#12711yescharacteristic
135C2×C3×D3—42no—
136C2×C3×D3—42no—
137C2×C3×D3—42no—
138C32×C4—21no—
139C32×C4#10412yescomplemented
140C3⋊Dic3—21no—
141C3⋊Dic3—21no—
142C3⋊Dic3C4×D412yes—
143C3⋊Dic3#12112yes—
144C3×Dic3—44no—
145C3×Dic3—42no—
146C2×#41—92no—
147C2×M16—92no—
148C4⋊Q8—91no—
149#127—91no—
150#124—92no—
151#121—61no—
152#121—181no—
153C4×D4—181no—
154C4×D4—181no—
155C2×C4⋊C4—61no—
156C2×C42—91no—
157C2×C42—92no—
158#104—188no—
159#97—181no—
160C4×C8—181no—
161#95—181no—
162C23×C3—21no—
163C23×C3—21no—
164C23×C3—62no—
165C22×D3—22no—
166C3×D4—122no—
167C3×D4—122no—
168C3×D4—122no—
169C2×C3×C4—22no—
170C2×C3×C4—22no—
171C2×C3×C4—21no—
172C2×C3×C4—21no—
173C2×C3×C4—21no—
174C2×C3×C4—21no—
175C2×C3×C4—42no—
176C2×C3×C4—62no—
177C2×C3×C4—64no—
178C2×C3×C4—122no—
179C2×C3×C4—122no—
180#67—42no—
181#67—42no—
182#67—124no—
183#67—124no—
184C2×Dic3—22no—
185C2×Dic3—24no—
186C2×Dic3—42no—
187C2×Dic3—42no—
188C2×Dic3—61no—
189C2×Dic3—61no—
190C2×Dic3—61no—
191C2×Dic3—61no—
192C2×Dic3—61no—
193C2×Dic3—62no—
194C2×Dic3—62no—
195C2×Dic3—62no—
196C2×Dic3—62no—
197C2×Dic3—61no—
198C2×Dic3—61no—
199C2×Dic3—61no—
200C2×Dic3—124no—
201C2×Dic3—122no—
202C2×Dic3—121no—
203C2×Dic3—121no—
204D12—42no—
205C4×D3—124no—
206Dic6—124no—
207C2×C32—21no—
208C2×C32—21no—
209C2×C32#39011yescharacteristic
210C2×C32C2×#10411yescharacteristic
211C2×C32#42111yescharacteristic
212C3×D3—82no—
213#41—184no—
214#41—184no—
215C2×Q8—92no—
216C2×D4—62no—
217C2×D4—61no—
218C2×D4—92no—
219C2×D4—181no—
220C22×C4—62no—
221C22×C4—91no—
222C22×C4—91no—
223C22×C4—182no—
224C22×C4GO+(4,𝔽2)11yescharacteristic
225M16—94no—
226M16—182no—
227C2×C8—182no—
228C4⋊C4—64no—
229C4⋊C4—61no—
230C4⋊C4—181no—
231C22⋊C4—62no—
232C22⋊C4—182no—
233C42—91no—
234C42—91no—
235C42—91no—
236C42—91no—
237C42—184no—
238C22×C3—21no—
239C22×C3—21no—
240C22×C3—21no—
241C22×C3—21no—
242C22×C3—21no—
243C22×C3—21no—
244C22×C3—21no—
245C22×C3—21no—
246C22×C3—21no—
247C22×C3—21no—
248C22×C3—41no—
249C22×C3—41no—
250C22×C3—122no—
251C22×C3—122no—
252C22×C3—122no—
253C2×D3—42no—
254C2×D3—42no—
255C2×D3—42no—
256C3×C4—22no—
257C3×C4—22no—
258C3×C4—22no—
259C3×C4—41no—
260C3×C4—122no—
261C3×C4—124no—
262Dic3—42no—
263Dic3—44no—
264Dic3—62no—
265Dic3—62no—
266Dic3—62no—
267Dic3—62no—
268Dic3—62no—
269Dic3—121no—
270Dic3—121no—
271Dic3—121no—
272C32#198011yescharacteristic, complemented, Sylow
273C23—62no—
274C23C2×GO+(4,𝔽2)11yescharacteristic
275Q8—184no—
276D4—122no—
277D4—122no—
278D4—122no—
279D4—184no—
280D4—362no—
281C2×C4—22no—
282C2×C4—64no—
283C2×C4—62no—
284C2×C4—92no—
285C2×C4—92no—
286C2×C4—91no—
287C2×C4—91no—
288C2×C4—91no—
289C2×C4—91no—
290C2×C4—122no—
291C2×C4—122no—
292C2×C4—364no—
293C2×C4—361no—
294C2×C4D32⋊C411yescharacteristic
295C2×C4D32⋊C411yescharacteristic
296C8—184no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3—21no—
300C2×C3—21no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3—21no—
305C2×C3—21no—
306C2×C3—21no—
307C2×C3—41no—
308C2×C3—41no—
309C2×C3—242no—
310D3—82no—
311C22—21no—
312C22—21no—
313C22—122no—
314C22—122no—
315C22—122no—
316C22#6422111yescharacteristic
317C22#6423111yescharacteristic
318C22C2×D32⋊C411yescharacteristic
319C4—21no—
320C4—92no—
321C4—92no—
322C4—124no—
323C4—122no—
324C4—181no—
325C4—181no—
326C4#6374112yescomplemented
327C3—21no—
328C3—21no—
329C2—21no—
330C2—21no—
331C2—242no—
332C2#1059338111yescharacteristic
333C2#1059340711yescharacteristic
334C2C2×#6374111yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC23C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radical#10594929C2
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1980
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. C4×#3792C2semidirect
3. C2×#63741C2semidirect
4. #10591274C2semidirect
12. #63919C4semidirect
13. #63915C4semidirect
14. #63914C4semidirect
36. #3792D4semidirect
139. C32×C4#104semidirect
272. C32#1980semidirect
326. C4#63741semidirect

Maximal subgroups

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

subgroupindex
#105949292
C4×#37922
C2×#637412
#105912742
#19809