Finite Group Databasebeta

← #27193634

Subgroups — #27193634

Order 13184.

304 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 65 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#20268304C211yesmaximal, characteristic
2C22⋊C8×D103C211yesmaximal, characteristic, complemented
3#20267638C211yesmaximal, characteristic, complemented
4#20267528C211yesmaximal, characteristic, complemented
5#20267526C211yesmaximal, characteristic, complemented
6#20267524C211yesmaximal, characteristic, complemented
7#328×C103C211yesmaximal, characteristic, complemented
8C2×#13110106C411yescharacteristic, complemented
9C22×C4×D103C2211yescharacteristic
10C2×C8×D103—21no—
11#15693006—21no—
12#15692997C411yescharacteristic, complemented
13#15692996C411yescharacteristic, complemented
14#15692995C2211yescharacteristic
15#15692991—21no—
16#15692983—21no—
17(C22⋊D103)⋊C4—21no—
18#15692979C411yescharacteristic, complemented
19C2×(C2×D103)⋊C4—21no—
20C2×C4×Dic103—21no—
21C22⋊(C103⋊C8)C2211yescharacteristic
22(C2×D103)⋊C8—21no—
23C103⋊#95C2211yescharacteristic
24C22⋊Q8×C103C2211yescharacteristic
25C22⋊C8×C103C2211yescharacteristic
26#95×C103C2211yescharacteristic
27C23×D103D411yescharacteristic
28#13110106—42no—
29C2×D412—21no—
30C2×D412—21no—
31C2×D412C2×C411yescharacteristic
32C2×C22⋊D103—21no—
33C22×Dic103—21no—
34C22×Dic103D411yescharacteristic
35C2×C4×D103—21no—
36C2×C4×D103—42no—
37C2×C4×D103C2×C411yescharacteristic
38C2×C4×D103C2×C411yescharacteristic
39C2×C4×D103D411yescharacteristic
40C2×C4×D103D411yescharacteristic
41C2×C103⋊C8—21no—
42C8×D103—42no—
43C4⋊Dic103C2×C411yescharacteristic
44Dic103⋊C4—21no—
45(C2×D103)⋊C4—24no—
46(C2×D103)⋊C4—21no—
47(C2×D103)⋊C4—21no—
48(C2×D103)⋊C4—21no—
49(C2×D103)⋊C4—21no—
50C4×Dic103—21no—
51C4×Dic103—42no—
52C2×Q8×C103C2×C411yescharacteristic
53C22×C4×C103—21no—
54C22×C4×C103C2311yescharacteristic
55C2×C8×C103—21no—
56C4⋊C4×C103—21no—
57C4⋊C4×C103C2×C411yescharacteristic
58C22⋊C4×C103—21no—
59C23×C103C2×D411yescharacteristic
60C22×D103—21no—
61C22×D103—21no—
62C22×D103—22no—
63C22×D103—21no—
64C22×D103—41no—
65C22×D103C22⋊C411yescharacteristic
66C22×D103C22⋊C411yescharacteristic
67Q8×C103—41no—
68C2×C4×C103—22no—
69C2×C4×C103—21no—
70C2×C4×C103—21no—
71C2×C4×C103—41no—
72C2×C4×C103—41no—
73C2×C4×C103—41no—
74C2×C4×C103C22×C411yescharacteristic
75C2×C4×C103C2×D411yescharacteristic
76C22⋊D103—41no—
77C22⋊D103—41no—
78C2×Dic103—22no—
79C2×Dic103—22no—
80C2×Dic103—21no—
81C2×Dic103—41no—
82C2×Dic103—41no—
83C2×Dic103C22⋊C411yescharacteristic
84C2×Dic103C22⋊C411yescharacteristic
85D412—41no—
86D412—42no—
87D412—42no—
88C4×D103—22no—
89C4×D103—22no—
90C4×D103—41no—
91C4×D103—41no—
92C4×D103—42no—
93C8×C103—41no—
94C103⋊C8—41no—
95C22×C103—21no—
96C22×C103—21no—
97C22×C103C2×C22⋊C411yescharacteristic
98C22×C103#13511yescharacteristic
99C22×C103#13511yescharacteristic
100C2×D103—21no—
101C2×D103—21no—
102C2×D103—21no—
103C2×D103—21no—
104C2×D103—21no—
105C2×D103—42no—
106C2×D103—42no—
107C2×D103—41no—
108C2×D103—41no—
109C2×D103—41no—
110C2×D103#10412yes—
111C4×C103—21no—
112C4×C103—21no—
113C4×C103—42no—
114C4×C103—41no—
115C4×C103—41no—
116Dic103—21no—
117Dic103—42no—
118Dic103—41no—
119Dic103#9912yes—
120C2×C103—21no—
121C2×C103—21no—
122C2×C103C2×#9911yescharacteristic
123C2×C103#41611yescharacteristic
124C2×C103C2×#10411yescharacteristic
125D103—22no—
126D103—41no—
127D103—81no—
128#1501—1031nomaximal, Sylow
129C103#150111yescharacteristic, complemented, Sylow
130#525—1031no—
131C2×C22⋊C8—1031no—
132C4×C22⋊C4—1031no—
133#328—1031no—
134#328D10311yescharacteristic, complemented
135#327—1031no—
136#327—1031no—
137C2×#41—1031no—
138C23×C4—1031no—
139C22×C8—2061no—
140#123—2061no—
141C22⋊Q8—1031no—
142C22⋊Q8C2×D10311yescharacteristic
143#121—1031no—
144#121—1031no—
145#120—2061no—
146C4×D4—2061no—
147C4×D4—2061no—
148#117—1031no—
149C2×C22⋊C4—2061no—
150C2×C42—2061no—
151C22⋊C8—1031no—
152C22⋊C8—2061no—
153C22⋊C8C2×D10311yescharacteristic
154#95—1031no—
155#95C2×D10311yescharacteristic
156C24—1031no—
157#41—4122no—
158C2×Q8C4×D10311yescharacteristic
159C2×D4—1031no—
160C2×D4—2061no—
161C2×D4—2061no—
162C2×D4—2061no—
163C22×C4—21no—
164C22×C4—1031no—
165C22×C4—1031no—
166C22×C4—1031no—
167C22×C4—1031no—
168C22×C4—1031no—
169C22×C4—4122no—
170C22×C4—2061no—
171C22×C4—2061no—
172C22×C4C22×D10311yescharacteristic
173C2×C8—21no—
174C2×C8—4122no—
175C2×C8—2061no—
176C4⋊C4—21no—
177C4⋊C4—1031no—
178C4⋊C4—2061no—
179C4⋊C4C4×D10311yescharacteristic
180C22⋊C4—21no—
181C22⋊C4—2061no—
182C22⋊C4—2061no—
183C22⋊C4—2061no—
184C22⋊C4—2064no—
185C22⋊C4—2061no—
186C42—4122no—
187C42—2061no—
188C23—1031no—
189C23—1031no—
190C23—4121no—
191C23—2062no—
192C23—2061no—
193C23—2061no—
194C23—2061no—
195C23D4×D10311yescharacteristic
196Q8—41no—
197D4—4121no—
198D4—4122no—
199D4—4122no—
200D4—4121no—
201D4—4121no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—1031no—
209C2×C4—1031no—
210C2×C4—4121no—
211C2×C4—4121no—
212C2×C4—4122no—
213C2×C4—4121no—
214C2×C4—4121no—
215C2×C4—2062no—
216C2×C4—2062no—
217C2×C4—2062no—
218C2×C4—2062no—
219C2×C4—2061no—
220C2×C4C2×C4×D10311yescharacteristic
221C2×C4D4×D10311yescharacteristic
222C8—41no—
223C8—4121no—
224C22—21no—
225C22—21no—
226C22—1032no—
227C22—4122no—
228C22—4122no—
229C22—4121no—
230C22—4121no—
231C22—4121no—
232C22—2061no—
233C22—2061no—
234C22—2061no—
235C22—2061no—
236C22—2061no—
237C22C22⋊C4×D10311yescharacteristic
238C22#1569304211yescharacteristic
239C22#1569304411yescharacteristic
240C4—21no—
241C4—21no—
242C4—42no—
243C4—41no—
244C4—41no—
245C4—1032no—
246C4—4122no—
247C4—4121no—
248C4—2061no—
249C2—21no—
250C2—21no—
251C2—8241no—
252C2—4121no—
253C2—2062no—
254C2#99×D10311yescharacteristic
255C2#2026778611yescharacteristic
256C2#104×D10311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D103
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#328×C103C2
socleC22×C103C2×C22⋊C4
prime radical#20268304C2
cosocleC22×C4×C103C23
hypercenter#328D103
hypocenterC103#1501
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. C22⋊C8×D103C2semidirect
3. #20267638C2semidirect
4. #20267528C2semidirect
5. #20267526C2semidirect
6. #20267524C2semidirect
7. #328×C103C2semidirect
8. C2×#13110106C4semidirect
12. #15692997C4semidirect
13. #15692996C4semidirect
18. #15692979C4semidirect
129. C103#1501semidirect
134. #328D103semidirect

Maximal subgroups

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

subgroupindex
#202683042
C22⋊C8×D1032
#202676382
#202675282
#202675262
#202675242
#328×C1032
#1501103