Finite Group Databasebeta

← #11785210

Subgroups — #11785210

Order 1152.

606 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 606 conjugacy classes of subgroups — too many to draw. Only its 94 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×Q8×C3⋊D3C211yesmaximal, characteristic
2C2×#63784C212yesmaximal
3#10593735C211yesmaximal, characteristic
4#10593726C211yesmaximal, characteristic
5#10590163C212yesmaximal
6C2×Q8×C3⋊D3C2211yescharacteristic
7C2×C4⋊#157—21no—
8C2×C4⋊#157—21no—
9C2×C4⋊#157C2212yes—
10C2×#3787C2212yes—
11C32×C4×Q8C411yescharacteristic, complemented
12Q8×C3⋊Dic3C411yescharacteristic, complemented
13C4⋊C4×C3⋊D3—21no—
14C4⋊C4×C3⋊D3C2211yescharacteristic
15#64096—21no—
16#64096C411yescharacteristic, complemented
17C42×C3⋊D3—21no—
18C42×C3⋊D3C2211yescharacteristic
19C4×#634—21no—
20C4×#634C411yescharacteristic, complemented
21#63784—24no—
22#63779—21no—
23C4⋊#622—21no—
24C4×D3×Q8—62no—
25C22×#157—22no—
26C2×C32×Q8C2×C411yescharacteristic
27Q8×C3⋊D3—21no—
28Q8×C3⋊D3—21no—
29Q8×C3⋊D3D412yes—
30Q8×C3⋊D3Q812yes—
31C2×C4×C3⋊D3—21no—
32C2×C4×C3⋊D3—21no—
33C2×C4×C3⋊D3D411yescharacteristic
34C2×C4×C3⋊D3D411yescharacteristic
35C2×C4×C3⋊D3C2311yescharacteristic
36C2×#634—21no—
37C2×#634C2×C411yescharacteristic
38C2×#622—22no—
39C4⋊#157—22no—
40C4⋊#157—22no—
41C4⋊#157—42no—
42C4⋊#157—42no—
43#3787—22no—
44#3787—22no—
45C32×C4⋊C4—21no—
46C32×C4⋊C4C2×C411yescharacteristic
47C32×C42—21no—
48C32×C42C2×C411yescharacteristic
49C4⋊(C3⋊Dic3)—21no—
50C4⋊(C3⋊Dic3)C2×C411yescharacteristic
51#3750—21no—
52#3750—21no—
53#3750—21no—
54C4×C3⋊Dic3—21no—
55C4×C3⋊Dic3—21no—
56C4×C3⋊Dic3—21no—
57C4×C3⋊Dic3C2×C411yescharacteristic
58C4×C3⋊Dic3D411yescharacteristic
59C4×C3⋊Dic3D411yescharacteristic
60#1803—91nomaximal, Sylow
61C2×D3×Q8—62no—
62C3×C4×Q8—22no—
63Q8×Dic3—62no—
64D3×C4⋊C4—62no—
65D3×C4⋊C4—64no—
66#887—62no—
67#887—64no—
68C42×D3—62no—
69C42×D3—64no—
70C4×Dic6—62no—
71C4×Dic6—64no—
72C22×C3⋊D3C2×D411yescharacteristic
73C2×#157—42no—
74C2×#157—42no—
75C2×#157—42no—
76C32×Q8—21no—
77C32×Q8C4⋊C412yescomplemented
78C2×C32×C4—21no—
79C2×C32×C4—21no—
80C2×C32×C4C22⋊C411yescharacteristic
81C2×C32×C4C22⋊C411yescharacteristic
82C2×C32×C4C22×C411yescharacteristic
83C2×C3⋊Dic3—21no—
84C2×C3⋊Dic3—21no—
85C2×C3⋊Dic3C22⋊C411yescharacteristic
86C2×C3⋊Dic3C22⋊C411yescharacteristic
87C2×C3⋊Dic3C2×D411yescharacteristic
88C4×C3⋊D3—22no—
89C4×C3⋊D3—22no—
90C4×C3⋊D3—21no—
91C4×C3⋊D3—21no—
92C4×C3⋊D3—41no—
93C4×C3⋊D3—41no—
94C4×C3⋊D3SD1612yes—
95C4×C3⋊D3Q1612yes—
96C4×C3⋊D3C2×D411yescharacteristic
97C4×C3⋊D3C2×Q811yescharacteristic
98C4×C3⋊D3#4111yescharacteristic
99C4×C3⋊D3#4111yescharacteristic
100#634—21no—
101#634—22no—
102#634—22no—
103#634C4⋊C412yescomplemented
104#622—42no—
105C2×C4×Q8—91no—
106C2×C4⋊C8—91no—
107C2×#103—92no—
108#384—91no—
109#340—92no—
110C2×C3×Q8—22no—
111D3×Q8—64no—
112D3×Q8—64no—
113D3×Q8—64no—
114D3×Q8—64no—
115C2×C4×D3—62no—
116C2×C4×D3—62no—
117C2×C4×D3—62no—
118C2×C4×D3—64no—
119C2×C4×D3—64no—
120C2×Dic6—62no—
121C2×Dic6—64no—
122C3×C4⋊C4—24no—
123C3×C4⋊C4—22no—
124C3×C42—24no—
125C3×C42—22no—
126C4⋊Dic3—62no—
127C4⋊Dic3—64no—
128Dic3⋊C4—64no—
129Dic3⋊C4—64no—
130Dic3⋊C4—64no—
131C4×Dic3—62no—
132C4×Dic3—62no—
133C4×Dic3—62no—
134C4×Dic3—64no—
135C4×Dic3—64no—
136C4×Dic3—64no—
137C22×C32C2×C22⋊C411yescharacteristic
138C2×C3⋊D3#12111yescharacteristic
139C2×C3⋊D3C22⋊Q811yescharacteristic
140C2×C3⋊D3C2×SD1611yescharacteristic
141C2×C3⋊D3C2×Q1611yescharacteristic
142C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
143C2×C3⋊D3#13711yescharacteristic
144#157—82no—
145C32×C4—22no—
146C32×C4—21no—
147C32×C4—41no—
148C32×C4#10312yescomplemented
149C32×C4C2×C4⋊C411yescharacteristic
150C32×C4#11711yescharacteristic
151C3⋊Dic3—22no—
152C3⋊Dic3—21no—
153C3⋊Dic3—41no—
154C3⋊Dic3#10312yescomplemented
155C3⋊Dic3#12111yescharacteristic
156C3⋊Dic3C22⋊Q811yescharacteristic
157C22×Q8—91no—
158C22×C8—92no—
159C4×Q8—91no—
160C4×Q8—91no—
161C4×Q8—91no—
162C4×Q8—181no—
163C4×Q8—181no—
164C4×Q8#15711yescharacteristic, complemented
165C2×C4⋊C4—91no—
166C2×C4⋊C4—92no—
167C2×C4⋊C4—181no—
168C2×C4⋊C4—181no—
169C2×C4⋊C4—181no—
170C2×C42—91no—
171C2×C42—181no—
172C4⋊C8—181no—
173C4⋊C8—181no—
174#103—184no—
175C22×D3—62no—
176C3×Q8—24no—
177C3×Q8—24no—
178C2×C3×C4—24no—
179C2×C3×C4—24no—
180C2×C3×C4—22no—
181C2×C3×C4—22no—
182C2×C3×C4—22no—
183C2×Dic3—62no—
184C2×Dic3—62no—
185C2×Dic3—62no—
186C2×Dic3—64no—
187C2×Dic3—64no—
188C4×D3—64no—
189C4×D3—64no—
190C4×D3—62no—
191C4×D3—62no—
192C4×D3—62no—
193C4×D3—62no—
194C4×D3—68no—
195C4×D3—68no—
196C4×D3—122no—
197C4×D3—122no—
198C4×D3—124no—
199C4×D3—124no—
200Dic6—64no—
201Dic6—68no—
202Dic6—68no—
203Dic6—64no—
204C2×C32#38011yescharacteristic
205C2×C32C2×#10311yescharacteristic
206C2×C32#41711yescharacteristic
207C3⋊D3#46011yescharacteristic
208C3⋊D3#46211yescharacteristic
209C3⋊D3#47511yescharacteristic
210C3⋊D3#47711yescharacteristic
211C2×Q8—92no—
212C2×Q8—92no—
213C2×Q8—91no—
214C2×Q8—181no—
215C2×Q8—181no—
216C2×Q8—181no—
217C2×Q8C2×#15711yescharacteristic
218C22×C4—91no—
219C22×C4—91no—
220C22×C4—91no—
221C22×C4—181no—
222C22×C4—181no—
223C22×C4—182no—
224C2×C8—182no—
225C2×C8—182no—
226C2×C8—182no—
227C4⋊C4—21no—
228C4⋊C4—91no—
229C4⋊C4—181no—
230C4⋊C4—181no—
231C4⋊C4—181no—
232C4⋊C4—182no—
233C4⋊C4—182no—
234C4⋊C4—181no—
235C4⋊C4—362no—
236C4⋊C4—362no—
237C4⋊C4C2×#15711yescharacteristic
238C42—21no—
239C42—91no—
240C42—91no—
241C42—91no—
242C42—181no—
243C42—181no—
244C42—181no—
245C42C2×#15711yescharacteristic
246C22×C3—22no—
247C2×D3—62no—
248C2×D3—62no—
249C2×D3—62no—
250C2×D3—62no—
251C2×D3—62no—
252C2×D3—62no—
253C3×C4—28no—
254C3×C4—22no—
255C3×C4—22no—
256C3×C4—24no—
257C3×C4—42no—
258C3×C4—44no—
259Dic3—62no—
260Dic3—62no—
261Dic3—64no—
262Dic3—68no—
263Dic3—122no—
264Dic3—124no—
265C32#180311yescharacteristic, complemented, Sylow
266C23—91no—
267Q8—21no—
268Q8—92no—
269Q8—182no—
270Q8—182no—
271Q8—181no—
272Q8C4⋊#15712yescomplemented
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—91no—
276C2×C4—91no—
277C2×C4—91no—
278C2×C4—91no—
279C2×C4—91no—
280C2×C4—91no—
281C2×C4—92no—
282C2×C4—92no—
283C2×C4—91no—
284C2×C4—181no—
285C2×C4—181no—
286C2×C4—182no—
287C2×C4—182no—
288C2×C4—181no—
289C2×C4—181no—
290C2×C4—361no—
291C2×C4—361no—
292C2×C4—362no—
293C2×C4—362no—
294C2×C4—362no—
295C2×C4C22⋊#15711yescharacteristic
296C2×C4C22⋊#15711yescharacteristic
297C2×C4C22×#15711yescharacteristic
298C8—362no—
299C2×C3—22no—
300C2×C3—22no—
301C2×C3—22no—
302D3—62no—
303D3—62no—
304D3—62no—
305D3—62no—
306C22—91no—
307C22—91no—
308C22—91no—
309C22—91no—
310C22—91no—
311C22—91no—
312C22C2×C22⋊#15711yescharacteristic
313C4—22no—
314C4—21no—
315C4—41no—
316C4—91no—
317C4—91no—
318C4—92no—
319C4—182no—
320C4—181no—
321C4—361no—
322C4—722no—
323C4#6378412yescomplemented
324C4C2×C4⋊#15711yescharacteristic
325C4#6428611yescharacteristic
326C3—22no—
327C2—91no—
328C2—91no—
329C2—91no—
330C2—91no—
331C2#1059381211yescharacteristic
332C2C2×#6378411yescharacteristic
333C2#1059384011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C4×Q8C4
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C4×C3⋊D3C23
hypercenterC4×Q8#157
hypocenterC32#1803
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
11. C32×C4×Q8C4semidirect
12. Q8×C3⋊Dic3C4semidirect
16. #64096C4semidirect
20. C4×#634C4semidirect
77. C32×Q8C4⋊C4semidirect
103. #634C4⋊C4semidirect
148. C32×C4#103semidirect
154. C3⋊Dic3#103semidirect
164. C4×Q8#157semidirect
265. C32#1803semidirect
272. Q8C4⋊#157semidirect
323. C4#63784semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×C3⋊D32
C2×#637842
#105937352
#105937262
#105901632
#18039