Finite Group Databasebeta

← #11859099

Subgroups — #11859099

Order 1152.

702 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 702 conjugacy classes of subgroups — too many to draw. Only its 158 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×#3832C211yesmaximal, characteristic
2#10593834C212yesmaximal
3#10593753C214yesmaximal, complemented
4#10593748C212yesmaximal, complemented
5#10593730C212yesmaximal, complemented
6#10593728C211yesmaximal, characteristic, complemented
7#10593727C212yesmaximal, complemented
8#10593726C211yesmaximal, characteristic, complemented
9C2×#3832C2211yescharacteristic
10C2×#3788C2212yes—
11C2×#3787C2212yes—
12C32×C4×Q8C411yescharacteristic
13Q8×C3⋊Dic3C411yescharacteristic
14#64102C412yes—
15#64102C411yescharacteristic
16#64101C2211yescharacteristic
17#64101C2212yes—
18C4×C4⋊(C3⋊D3)C412yes—
19C4×C4⋊(C3⋊D3)C411yescharacteristic
20C42×C3⋊D3C2211yescharacteristic
21C42×C3⋊D3C2212yes—
22#63779C2212yes—
23#63778C2214yes—
24#63778C2214yes—
25#63777C2214yes—
26C4⋊#622C2211yescharacteristic
27C4⋊#622C2211yescharacteristic
28C4⋊#622C2212yes—
29C4⋊#622C2212yes—
30C4×#622C2214yes—
31C4×#239—62no—
32C2×C32×Q8C2×C411yescharacteristic
33#3832—22no—
34#3832—22no—
35C2×C4⋊(C3⋊D3)C2×C412yes—
36C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
37C2×C4×C3⋊D3C2×C412yes—
38C2×C4×C3⋊D3C2×C411yescharacteristic
39C2×C4×C3⋊D3C2×C412yes—
40C2×C4×C3⋊D3C2×C411yescharacteristic
41C2×C4×C3⋊D3C2312yes—
42C2×C4×C3⋊D3C2311yescharacteristic
43C2×#622C2312yes—
44C2×#622C2312yes—
45C2×#622C2314yes—
46#3788—24no—
47#3787—24no—
48C32×C4⋊C4C2×C412yes—
49C32×C4⋊C4C2×C411yescharacteristic
50C32×C42C2×C412yes—
51C32×C42C2×C411yescharacteristic
52#3752C2×C412yes—
53#3752C2×C412yes—
54#3752C2×C412yes—
55C4⋊(C3⋊Dic3)C2×C412yes—
56C4⋊(C3⋊Dic3)C2×C411yescharacteristic
57C4×C3⋊Dic3C2×C412yes—
58C4×C3⋊Dic3C2×C411yescharacteristic
59C4×C3⋊Dic3C2312yes—
60C4×C3⋊Dic3C2311yescharacteristic
61C4×C3⋊Dic3C2311yescharacteristic
62#2925—91nomaximal, Sylow
63C2×#239—62no—
64C3×C4×Q8—22no—
65Q8×Dic3—62no—
66#893—64no—
67#893—62no—
68#892—62no—
69#892—64no—
70C4×D12—64no—
71C4×D12—62no—
72C42×D3—62no—
73C42×D3—64no—
74C22×C3⋊D3C22×C412yes—
75C22×C3⋊D3C22×C411yescharacteristic
76C32×Q8—22no—
77C2×C32×C4C22×C412yes—
78C2×C32×C4C22×C412yes—
79C2×C32×C4C22×C411yescharacteristic
80C2×C32×C4C22×C411yescharacteristic
81C2×C32×C4C22×C411yescharacteristic
82C2×C3⋊Dic3C22×C411yescharacteristic
83C2×C3⋊Dic3C22×C412yes—
84C2×C3⋊Dic3C22×C411yescharacteristic
85C2×C3⋊Dic3C2411yescharacteristic
86C4⋊(C3⋊D3)—24no—
87C4⋊(C3⋊D3)—22no—
88C4×C3⋊D3—22no—
89C4×C3⋊D3—22no—
90C4×C3⋊D3—22no—
91C4×C3⋊D3—24no—
92C4×C3⋊D3—41no—
93C4×C3⋊D3—42no—
94C4×C3⋊D3#4112yes—
95C4×C3⋊D3#4112yes—
96#622—22no—
97#622—22no—
98#622—24no—
99C4×#41—91no—
100#433—94no—
101#432—92no—
102#431—92no—
103#423—91no—
104C2×C4⋊C8—91no—
105#408—92no—
106#405—92no—
107C2×C3×Q8—22no—
108#239—68no—
109#239—68no—
110C2×D12—64no—
111C2×D12—62no—
112C2×C4×D3—62no—
113C2×C4×D3—64no—
114C2×C4×D3—62no—
115C2×C4×D3—64no—
116C2×C4×D3—62no—
117C2×C4×D3—64no—
118C3×C4⋊C4—24no—
119C3×C4⋊C4—22no—
120C3×C42—24no—
121C3×C42—22no—
122(C2×D3)⋊C4—64no—
123(C2×D3)⋊C4—64no—
124(C2×D3)⋊C4—64no—
125C4⋊Dic3—64no—
126C4⋊Dic3—62no—
127C4×Dic3—62no—
128C4×Dic3—64no—
129C4×Dic3—62no—
130C4×Dic3—64no—
131C4×Dic3—62no—
132C22×C32C23×C411yescharacteristic
133C2×C3⋊D3—22no—
134C2×C3⋊D3—21no—
135C2×C3⋊D3—21no—
136C2×C3⋊D3—22no—
137C2×C3⋊D3—22no—
138C2×C3⋊D3#11712yes—
139C32×C4—22no—
140C32×C4—21no—
141C32×C4—22no—
142C32×C4#11712yes—
143C32×C4#13112yes—
144C3⋊Dic3—21no—
145C3⋊Dic3—21no—
146C3⋊Dic3—22no—
147C3⋊Dic3C2×#4111yescharacteristic
148C3⋊Dic3C2×#4111yescharacteristic
149C2×#41—91no—
150C2×M16—92no—
151C22×C8—92no—
152C4×Q8—91no—
153C4×Q8#15711yescharacteristic
154C4×D4—92no—
155C4×D4—91no—
156C4×D4—92no—
157C4×D4—91no—
158#117—91no—
159#117—92no—
160C2×C42—91no—
161C2×C42—92no—
162C4⋊C8—91no—
163C4⋊C8—91no—
164C4⋊C8—92no—
165C4⋊C8—92no—
166C4⋊C8—92no—
167C22⋊C8—94no—
168C22⋊C8—94no—
169#97—94no—
170C4×C8—94no—
171C22×D3—62no—
172C22×D3—64no—
173C3×Q8—28no—
174C2×C3×C4—24no—
175C2×C3×C4—22no—
176C2×C3×C4—22no—
177C2×C3×C4—24no—
178C2×C3×C4—22no—
179C2×Dic3—62no—
180C2×Dic3—62no—
181C2×Dic3—64no—
182C2×Dic3—62no—
183D12—616no—
184D12—68no—
185C4×D3—64no—
186C4×D3—64no—
187C4×D3—68no—
188C4×D3—68no—
189C4×D3—124no—
190C4×D3—128no—
191C4×D3—124no—
192C4×D3—128no—
193C2×C32C2×#11711yescharacteristic
194C2×C32C2×#13111yescharacteristic
195C2×C32#56811yescharacteristic
196C3⋊D3—22no—
197C3⋊D3—42no—
198#41—182no—
199#41—182no—
200C2×Q8C2×#15711yescharacteristic
201C2×D4—92no—
202C2×D4—91no—
203C22×C4—91no—
204C22×C4—92no—
205C22×C4—91no—
206C22×C4—92no—
207C22×C4—91no—
208C22×C4—92no—
209M16—184no—
210C2×C8—92no—
211C2×C8—94no—
212C2×C8—92no—
213C2×C8—184no—
214C4⋊C4—92no—
215C4⋊C4—91no—
216C4⋊C4C2×#15712yes—
217C4⋊C4C2×#15711yescharacteristic
218C22⋊C4—92no—
219C22⋊C4—92no—
220C22⋊C4—92no—
221C42—92no—
222C42—91no—
223C42—91no—
224C42—92no—
225C42—91no—
226C42C2×#15712yes—
227C42C2×#15711yescharacteristic
228C22×C3—22no—
229C2×D3—64no—
230C2×D3—68no—
231C2×D3—122no—
232C2×D3—122no—
233C2×D3—124no—
234C2×D3—124no—
235C3×C4—28no—
236C3×C4—24no—
237C3×C4—24no—
238C3×C4—42no—
239C3×C4—44no—
240Dic3—62no—
241Dic3—62no—
242Dic3—64no—
243Dic3—124no—
244Dic3—122no—
245C32#292511yescharacteristic, complemented, Sylow
246C23—91no—
247C23—92no—
248Q8—22no—
249D4—184no—
250D4—182no—
251C2×C4—91no—
252C2×C4—92no—
253C2×C4—92no—
254C2×C4—91no—
255C2×C4—92no—
256C2×C4—91no—
257C2×C4—182no—
258C2×C4—182no—
259C2×C4—182no—
260C2×C4—184no—
261C2×C4—361no—
262C2×C4—362no—
263C2×C4C22×#15712yes—
264C2×C4C22×#15711yescharacteristic
265C2×C4C22×#15712yes—
266C2×C4C22×#15711yescharacteristic
267C2×C4C22×#15711yescharacteristic
268C8—182no—
269C8—182no—
270C8—184no—
271C2×C3—22no—
272C2×C3—22no—
273C2×C3—22no—
274D3—124no—
275D3—128no—
276C22—92no—
277C22—181no—
278C22—181no—
279C22—182no—
280C22—182no—
281C22—182no—
282C22C23×#15711yescharacteristic
283C4—22no—
284C4—21no—
285C4—22no—
286C4—91no—
287C4—91no—
288C4—182no—
289C4—181no—
290C4—181no—
291C4#6428612yes—
292C4#6428912yes—
293C3—22no—
294C2—182no—
295C2—362no—
296C2C2×#6428611yescharacteristic
297C2C2×#6428911yescharacteristic
298C2#1059664811yescharacteristic
subgroupG/H
center, FrattiniC22C23×#157
commutator, socleC22×C32C23×C4
FittingC32×C4×Q8C4
prime radicalC2×#3832C22
cosocleC2×C3⋊Dic3C24
hypercenterC4×Q8#157
hypocenterC32#2925
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
3. #10593753C2semidirect
4. #10593748C2semidirect
5. #10593730C2semidirect
6. #10593728C2semidirect
7. #10593727C2semidirect
8. #10593726C2semidirect
245. C32#2925semidirect

Maximal subgroups

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

subgroupindex
C4×#38322
#105938342
#105937532
#105937482
#105937302
#105937282
#105937272
#105937262
#29259