Finite Group Databasebeta

← #11785279

Subgroups — #11785279

Order 1152.

590 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 590 conjugacy classes of subgroups — too many to draw. Only its 84 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#10593736C211yesmaximal, characteristic
4#10593726C211yesmaximal, characteristic
5#10590163C212yesmaximal
6C2×Q8×C3⋊D3C2211yescharacteristic
7C2×C4⋊#157C2212yes—
8C2×#3787C2212yes—
9C32×C4×Q8C411yescharacteristic, complemented
10Q8×C3⋊Dic3C411yescharacteristic, complemented
11C4⋊C4×C3⋊D3—21no—
12C4⋊C4×C3⋊D3C2211yescharacteristic
13#64096—21no—
14#64096C411yescharacteristic, complemented
15C42×C3⋊D3—21no—
16C42×C3⋊D3C2211yescharacteristic
17C4×#634—21no—
18C4×#634C411yescharacteristic, complemented
19#63784—24no—
20#63781—21no—
21#63781—21no—
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—
41#3787—22no—
42#3787—22no—
43C32×C4⋊C4—21no—
44C32×C4⋊C4C2×C411yescharacteristic
45C32×C42—21no—
46C32×C42C2×C411yescharacteristic
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)C2×C411yescharacteristic
49#3750—21no—
50#3750—21no—
51#3750—21no—
52C4×C3⋊Dic3—21no—
53C4×C3⋊Dic3—21no—
54C4×C3⋊Dic3—21no—
55C4×C3⋊Dic3C2×C411yescharacteristic
56C4×C3⋊Dic3D411yescharacteristic
57C4×C3⋊Dic3D411yescharacteristic
58#1805—91nomaximal, Sylow
59C2×D3×Q8—62no—
60C3×C4×Q8—22no—
61Q8×Dic3—62no—
62D3×C4⋊C4—62no—
63D3×C4⋊C4—64no—
64#887—62no—
65#887—64no—
66C42×D3—62no—
67C42×D3—64no—
68C4×Dic6—62no—
69C4×Dic6—64no—
70C22×C3⋊D3C2×D411yescharacteristic
71C2×#157—42no—
72C2×#157—42no—
73C2×#157—42no—
74C32×Q8—21no—
75C32×Q8C4⋊C412yes—
76C2×C32×C4—21no—
77C2×C32×C4—21no—
78C2×C32×C4C22⋊C411yescharacteristic
79C2×C32×C4C22⋊C411yescharacteristic
80C2×C32×C4C22×C411yescharacteristic
81C2×C3⋊Dic3—21no—
82C2×C3⋊Dic3—21no—
83C2×C3⋊Dic3C22⋊C411yescharacteristic
84C2×C3⋊Dic3C22⋊C411yescharacteristic
85C2×C3⋊Dic3C2×D411yescharacteristic
86C4×C3⋊D3—22no—
87C4×C3⋊D3—22no—
88C4×C3⋊D3—22no—
89C4×C3⋊D3—22no—
90C4×C3⋊D3—42no—
91C4×C3⋊D3C2×D411yescharacteristic
92C4×C3⋊D3C2×Q811yescharacteristic
93C4×C3⋊D3#4111yescharacteristic
94C4×C3⋊D3#4111yescharacteristic
95#634—21no—
96#634—22no—
97#634—22no—
98#634C4⋊C412yes—
99#622—42no—
100C2×C4×Q8—91no—
101C2×C4⋊C8—91no—
102C2×#103—92no—
103#382—91no—
104#340—92no—
105C2×C3×Q8—22no—
106D3×Q8—64no—
107D3×Q8—64no—
108D3×Q8—64no—
109D3×Q8—64no—
110C2×C4×D3—62no—
111C2×C4×D3—62no—
112C2×C4×D3—62no—
113C2×C4×D3—64no—
114C2×C4×D3—64no—
115C2×Dic6—62no—
116C2×Dic6—64no—
117C3×C4⋊C4—24no—
118C3×C4⋊C4—22no—
119C3×C42—24no—
120C3×C42—22no—
121C4⋊Dic3—62no—
122C4⋊Dic3—64no—
123Dic3⋊C4—64no—
124Dic3⋊C4—64no—
125Dic3⋊C4—64no—
126C4×Dic3—62no—
127C4×Dic3—62no—
128C4×Dic3—62no—
129C4×Dic3—64no—
130C4×Dic3—64no—
131C4×Dic3—64no—
132C22×C32C2×C22⋊C411yescharacteristic
133C2×C3⋊D3#12111yescharacteristic
134C2×C3⋊D3C22⋊Q811yescharacteristic
135C2×C3⋊D3#13512yes—
136C2×C3⋊D3#13712yes—
137#157—82no—
138C32×C4—22no—
139C32×C4—21no—
140C32×C4—21no—
141C32×C4—41no—
142C32×C4C2×C4⋊C411yescharacteristic
143C32×C4#11711yescharacteristic
144C3⋊Dic3—22no—
145C3⋊Dic3—21no—
146C3⋊Dic3—21no—
147C3⋊Dic3—41no—
148C3⋊Dic3#12111yescharacteristic
149C3⋊Dic3C22⋊Q811yescharacteristic
150C22×Q8—91no—
151C22×C8—92no—
152C4×Q8—91no—
153C4×Q8—91no—
154C4×Q8—91no—
155C4×Q8—181no—
156C4×Q8—181no—
157C4×Q8#15711yescharacteristic, complemented
158C2×C4⋊C4—91no—
159C2×C4⋊C4—92no—
160C2×C4⋊C4—181no—
161C2×C42—91no—
162C2×C42—181no—
163C4⋊C8—181no—
164C4⋊C8—181no—
165#103—184no—
166#95—181no—
167#95—181no—
168C22×D3—62no—
169C3×Q8—24no—
170C3×Q8—24no—
171C2×C3×C4—24no—
172C2×C3×C4—24no—
173C2×C3×C4—22no—
174C2×C3×C4—22no—
175C2×C3×C4—22no—
176C2×Dic3—62no—
177C2×Dic3—62no—
178C2×Dic3—62no—
179C2×Dic3—64no—
180C2×Dic3—64no—
181C4×D3—62no—
182C4×D3—62no—
183C4×D3—62no—
184C4×D3—62no—
185C4×D3—68no—
186C4×D3—68no—
187C4×D3—68no—
188C4×D3—124no—
189C4×D3—128no—
190Dic6—64no—
191Dic6—68no—
192Dic6—68no—
193Dic6—64no—
194C2×C32#38011yescharacteristic
195C2×C32#41611yescharacteristic
196C2×C32#41911yescharacteristic
197C3⋊D3#46412yes—
198C3⋊D3#47912yes—
199C2×Q8—92no—
200C2×Q8—92no—
201C2×Q8—91no—
202C2×Q8—181no—
203C2×Q8—181no—
204C2×Q8—181no—
205C2×Q8C2×#15711yescharacteristic
206C22×C4—91no—
207C22×C4—91no—
208C22×C4—91no—
209C22×C4—181no—
210C22×C4—181no—
211C22×C4—182no—
212C2×C8—182no—
213C2×C8—182no—
214C2×C8—182no—
215C4⋊C4—21no—
216C4⋊C4—91no—
217C4⋊C4—181no—
218C4⋊C4—181no—
219C4⋊C4—181no—
220C4⋊C4—182no—
221C4⋊C4—182no—
222C4⋊C4—181no—
223C4⋊C4C2×#15711yescharacteristic
224C42—21no—
225C42—91no—
226C42—91no—
227C42—91no—
228C42—181no—
229C42—181no—
230C42—181no—
231C42C2×#15711yescharacteristic
232C22×C3—22no—
233C2×D3—62no—
234C2×D3—62no—
235C2×D3—64no—
236C2×D3—64no—
237C3×C4—28no—
238C3×C4—24no—
239C3×C4—22no—
240C3×C4—22no—
241C3×C4—42no—
242C3×C4—44no—
243Dic3—62no—
244Dic3—62no—
245Dic3—68no—
246Dic3—64no—
247Dic3—122no—
248Dic3—124no—
249C32#180511yescharacteristic, complemented, Sylow
250C23—91no—
251Q8—21no—
252Q8—92no—
253Q8—182no—
254Q8—182no—
255Q8—181no—
256Q8C4⋊#15712yes—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—91no—
260C2×C4—91no—
261C2×C4—91no—
262C2×C4—91no—
263C2×C4—91no—
264C2×C4—91no—
265C2×C4—91no—
266C2×C4—182no—
267C2×C4—182no—
268C2×C4—182no—
269C2×C4—182no—
270C2×C4—181no—
271C2×C4—181no—
272C2×C4—362no—
273C2×C4—362no—
274C2×C4—362no—
275C2×C4—362no—
276C2×C4C22⋊#15711yescharacteristic
277C2×C4C22⋊#15711yescharacteristic
278C2×C4C22×#15711yescharacteristic
279C8—362no—
280C2×C3—22no—
281C2×C3—22no—
282C2×C3—22no—
283D3—64no—
284D3—64no—
285C22—91no—
286C22—91no—
287C22—92no—
288C22—92no—
289C22C2×C22⋊#15711yescharacteristic
290C4—22no—
291C4—21no—
292C4—21no—
293C4—41no—
294C4—91no—
295C4—91no—
296C4—182no—
297C4—181no—
298C4—181no—
299C4—361no—
300C4—722no—
301C4C2×C4⋊#15711yescharacteristic
302C4#6428611yescharacteristic
303C3—22no—
304C2—92no—
305C2—92no—
306C2#1059381211yescharacteristic
307C2#1059382911yescharacteristic
308C2#1059384111yescharacteristic
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#1805
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
9. C32×C4×Q8C4semidirect
10. Q8×C3⋊Dic3C4semidirect
14. #64096C4semidirect
18. C4×#634C4semidirect
157. C4×Q8#157semidirect
249. C32#1805semidirect

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
#105937362
#105937262
#105901632
#18059