Finite Group Databasebeta

← #27195163

Subgroups — #27195163

Order 13184.

312 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 87 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#20268259C211yesmaximal, characteristic
2#20267814C211yesmaximal, characteristic, complemented
3C2×#15692949C211yesmaximal, characteristic
4C2×#15692947C211yesmaximal, characteristic
5C4×Dic103⋊C4C211yesmaximal, characteristic, complemented
6#20267550C211yesmaximal, characteristic, complemented
7#339×C103C211yesmaximal, characteristic, complemented
8C2×#13110105C2211yescharacteristic
9C2×#13110089C2211yescharacteristic
10#15692986C411yescharacteristic, complemented
11#15692986C411yescharacteristic, complemented
12#15692983C411yescharacteristic, complemented
13#15692983C411yescharacteristic, complemented
14(C22⋊D103)⋊C4—21no—
15(C22⋊D103)⋊C4—21no—
16#15692978—21no—
17C2×Dic103⋊C4—21no—
18C2×C4×Dic103C2211yescharacteristic
19C2×C4×Dic103C2211yescharacteristic
20C42×D103—21no—
21Dic103⋊C8—21no—
22Dic103⋊C8—21no—
23#15692949—22no—
24#15692947—22no—
25C103⋊#95—21no—
26C2×M16×C103C2211yescharacteristic
27#117×C103C2211yescharacteristic
28C2×C42×C103C2211yescharacteristic
29#13110105—21no—
30#13110105—21no—
31#13110105D412yes—
32#13110105Q812yes—
33C2×Dic206C2×C411yescharacteristic
34C2×D412C2×C411yescharacteristic
35C2×C22⋊D103—21no—
36C22×Dic103—21no—
37C22×Dic103D411yescharacteristic
38C22×Dic103D411yescharacteristic
39C2×C4×D103—21no—
40C2×C4×D103—21no—
41C2×C4×D103—21no—
42#13110089—21no—
43#13110089—21no—
44C2×C103⋊C8—21no—
45Dic103⋊C4—24no—
46Dic103⋊C4—21no—
47Dic103⋊C4—21no—
48(C2×D103)⋊C4—21no—
49(C2×D103)⋊C4—21no—
50C4×Dic103—21no—
51C4×Dic103—21no—
52C4×Dic103—21no—
53C4×Dic103—21no—
54C4×Dic103C2×C411yescharacteristic
55C4×Dic103C2×C411yescharacteristic
56C4×Dic103D411yescharacteristic
57C4×Dic103D411yescharacteristic
58C22×C4×C103—21no—
59C22×C4×C103C2311yescharacteristic
60M16×C103—21no—
61M16×C103—21no—
62C2×C8×C103—21no—
63C4⋊C4×C103C2×C411yescharacteristic
64C4⋊C4×C103C2×C411yescharacteristic
65C22⋊C4×C103—21no—
66C42×C103—21no—
67C42×C103—21no—
68C42×C103—21no—
69C23×C103C2×D411yescharacteristic
70C22×D103—21no—
71C2×C4×C103—22no—
72C2×C4×C103—21no—
73C2×C4×C103—21no—
74C2×C4×C103—41no—
75C2×C4×C103—41no—
76C2×C4×C103C22×C411yescharacteristic
77C2×C4×C103C2×D411yescharacteristic
78C2×C4×C103C2×D411yescharacteristic
79C2×C4×C103C2×Q811yescharacteristic
80C2×C4×C103#4111yescharacteristic
81C2×C4×C103#4111yescharacteristic
82C22⋊D103—22no—
83C22⋊D103—22no—
84C2×Dic103—21no—
85C2×Dic103—22no—
86C2×Dic103—22no—
87C2×Dic103—41no—
88C2×Dic103—41no—
89C2×Dic103—41no—
90C2×Dic103C22⋊C411yescharacteristic
91C2×Dic103C22⋊C411yescharacteristic
92C2×Dic103C22⋊C411yescharacteristic
93C2×Dic103C22⋊C411yescharacteristic
94D412—21no—
95D412C4⋊C412yescomplemented
96C4×D103—22no—
97C4×D103—22no—
98C4×D103—42no—
99C4×D103—42no—
100Dic206—21no—
101Dic206C4⋊C412yescomplemented
102C8×C103—41no—
103C103⋊C8—41no—
104C22×C103—21no—
105C22×C103—21no—
106C22×C103C2×C22⋊C411yescharacteristic
107C22×C103#12111yescharacteristic
108C22×C103C22⋊Q811yescharacteristic
109C2×D103—22no—
110C2×D103—41no—
111C2×D103—41no—
112C4×C103—42no—
113C4×C103—41no—
114C4×C103—41no—
115C4×C103C2×C4⋊C411yescharacteristic
116C4×C103#11711yescharacteristic
117C4×C103#12111yescharacteristic
118C4×C103C22⋊Q811yescharacteristic
119Dic103—22no—
120Dic103—21no—
121Dic103—21no—
122Dic103—21no—
123Dic103—42no—
124Dic103#10412yescomplemented
125C2×C103—21no—
126C2×C103—21no—
127C2×C103#38011yescharacteristic
128C2×C103C2×#10411yescharacteristic
129C2×C103#42111yescharacteristic
130D103—42no—
131#1806—1031nomaximal, Sylow
132C103#180611yescharacteristic, complemented, Sylow
133C4×#41—1031no—
134#423—1031no—
135C2×#104—1031no—
136C2×#104—1031no—
137C4×C4⋊C4—1031no—
138#339—1031no—
139#339D10311yescharacteristic, complemented
140C2×#41—1031no—
141C2×M16—1031no—
142C2×M16C2×D10311yescharacteristic
143C4×Q8—1031no—
144C4×Q8—1031no—
145C4×D4—1031no—
146C4×D4—1031no—
147C4×D4—2061no—
148C4×D4—2061no—
149#117—2061no—
150#117C2×D10311yescharacteristic
151C2×C4⋊C4—2061no—
152C2×C42—1031no—
153C2×C42—1031no—
154C2×C42—2061no—
155C2×C42C2×D10311yescharacteristic
156C4⋊C8—2061no—
157C4⋊C8—2061no—
158#104—2062no—
159#104—2062no—
160#95—2061no—
161#41—1032no—
162#41—1032no—
163#41—2061no—
164#41—2061no—
165C2×Q8—1031no—
166C2×D4—1031no—
167C2×D4—2061no—
168C22×C4—21no—
169C22×C4—1031no—
170C22×C4—1031no—
171C22×C4—2061no—
172C22×C4—2061no—
173C22×C4—2061no—
174C22×C4—2061no—
175C22×C4C22×D10311yescharacteristic
176M16—21no—
177M16—21no—
178M16—2061no—
179M16—2061no—
180C2×C8—21no—
181C2×C8—2061no—
182C4⋊C4—2061no—
183C4⋊C4—2061no—
184C4⋊C4—2064no—
185C4⋊C4C4×D10311yescharacteristic
186C4⋊C4C4×D10311yescharacteristic
187C22⋊C4—21no—
188C22⋊C4—2061no—
189C22⋊C4—2061no—
190C42—21no—
191C42—21no—
192C42—21no—
193C42—1031no—
194C42—1031no—
195C42—1031no—
196C42—1031no—
197C42—2061no—
198C42—2061no—
199C42—2061no—
200C42—2061no—
201C23—2061no—
202C23D4×D10311yescharacteristic
203Q8—1032no—
204Q8—2061no—
205D4—1032no—
206D4—2062no—
207D4—2062no—
208D4—2061no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—1031no—
215C2×C4—1031no—
216C2×C4—1031no—
217C2×C4—1031no—
218C2×C4—4122no—
219C2×C4—4122no—
220C2×C4—4121no—
221C2×C4—4121no—
222C2×C4—4121no—
223C2×C4—2062no—
224C2×C4—2062no—
225C2×C4—2061no—
226C2×C4—2062no—
227C2×C4—2062no—
228C2×C4C2×C4×D10311yescharacteristic
229C2×C4D4×D10311yescharacteristic
230C2×C4D4×D10311yescharacteristic
231C2×C4Q8×D10311yescharacteristic
232C2×C4#1311010511yescharacteristic
233C2×C4#1311010511yescharacteristic
234C8—41no—
235C8—4121no—
236C22—21no—
237C22—21no—
238C22—4121no—
239C22—4121no—
240C22—2062no—
241C22C22⋊C4×D10311yescharacteristic
242C22#1569299411yescharacteristic
243C22#1569299911yescharacteristic
244C4—42no—
245C4—41no—
246C4—41no—
247C4—1032no—
248C4—4122no—
249C4—2061no—
250C4—2061no—
251C4—2061no—
252C4—2062no—
253C4C4⋊C4×D10311yescharacteristic
254C4#1569297811yescharacteristic
255C4#1569299411yescharacteristic
256C4#1569299911yescharacteristic
257C2—21no—
258C2—21no—
259C2—4122no—
260C2#2026765011yescharacteristic
261C2#104×D10311yescharacteristic
262C2#2026780611yescharacteristic
subgroupG/H
centerC2×C4D4×D103
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#339×C103C2
socleC22×C103C2×C22⋊C4
prime radicalC2×#13110105C22
cosocleC22×C4×C103C23
hypercenter#339D103
hypocenterC103#1806
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #20267814C2semidirect
5. C4×Dic103⋊C4C2semidirect
6. #20267550C2semidirect
7. #339×C103C2semidirect
10. #15692986C4semidirect
11. #15692986C4semidirect
12. #15692983C4semidirect
13. #15692983C4semidirect
95. D412C4⋊C4semidirect
101. Dic206C4⋊C4semidirect
124. Dic103#104semidirect
132. C103#1806semidirect
139. #339D103semidirect

Maximal subgroups

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

subgroupindex
#202682592
#202678142
C2×#156929492
C2×#156929472
C4×Dic103⋊C42
#202675502
#339×C1032
#1806103