Finite Group Databasebeta

← #27196796

Subgroups — #27196796

Order 13184.

234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 55 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#20268363C211yesmaximal, characteristic
2#20267772C211yesmaximal, characteristic
3#20267763C211yesmaximal, characteristic
4#20267582C211yesmaximal, characteristic, complemented
5#20267581C211yesmaximal, characteristic, complemented
6#20267580C211yesmaximal, characteristic, complemented
7#352×C103C211yesmaximal, characteristic, complemented
8C2×#13110104C2211yescharacteristic
9C22×Dic206C411yescharacteristic, complemented
10M16×D103—21no—
11#15693020—21no—
12#15693007—21no—
13#15693005C411yescharacteristic, complemented
14#15693004C411yescharacteristic, complemented
15#15693002C2211yescharacteristic
16#15692999—21no—
17#15692998—21no—
18#15692977—21no—
19#15692977C411yescharacteristic, complemented
20#15692939—21no—
21#15692938C2211yescharacteristic
22#15692936C2211yescharacteristic
23#15692935—21no—
24#123×C103C2211yescharacteristic
25#100×C103C2211yescharacteristic
26#99×C103C2211yescharacteristic
27#13110104—41no—
28#13110104—41no—
29C2×Dic206—21no—
30C2×Dic206—21no—
31C2×Dic206—41no—
32C2×Dic206—41no—
33C2×Dic206D411yescharacteristic
34C2×C22⋊D103C2×C411yescharacteristic
35C2×C22⋊D103D411yescharacteristic
36C22×Dic103C2×C411yescharacteristic
37C22×Dic103C2×C411yescharacteristic
38C22×Dic103D411yescharacteristic
39C2×C4×D103D411yescharacteristic
40#13110089—21no—
41#13110088—41no—
42C8×D103—41no—
43C4⋊Dic103—21no—
44Dic103⋊C4—21no—
45Dic103⋊C4—21no—
46Dic103⋊C4—21no—
47Dic103⋊C4—41no—
48C22⋊Dic103—21no—
49C22⋊Dic103—21no—
50C22⋊Dic103C2×C411yescharacteristic
51(C2×D103)⋊C4—21no—
52(C2×D103)⋊C4—21no—
53C4×Dic103—21no—
54C4×Dic103—41no—
55C2×D4×C103C2311yescharacteristic
56C22×C4×C103C2×C411yescharacteristic
57M16×C103—21no—
58C4⋊C4×C103—21no—
59C22⋊C4×C103—21no—
60C22⋊C4×C103—21no—
61C22⋊C4×C103C2×C411yescharacteristic
62C23×C103C22×C411yescharacteristic
63C23×C103C2×D411yescharacteristic
64C22×D103C22⋊C411yescharacteristic
65D4×C103—41no—
66C2×C4×C103—21no—
67C2×C4×C103—21no—
68C2×C4×C103—41no—
69C2×C4×C103—41no—
70C2×C4×C103C2×D411yescharacteristic
71C22⋊D103—41no—
72C22⋊D103—41no—
73C2×Dic103—21no—
74C2×Dic103—21no—
75C2×Dic103—21no—
76C2×Dic103—21no—
77C2×Dic103—21no—
78C2×Dic103—21no—
79C2×Dic103—41no—
80C2×Dic103—41no—
81C2×Dic103C22⋊C411yescharacteristic
82C2×Dic103C22⋊C411yescharacteristic
83C2×Dic103C22⋊C411yescharacteristic
84C4×D103—21no—
85C4×D103—21no—
86Dic206—41no—
87Dic206—42no—
88Dic206—41no—
89Dic206—41no—
90C8×C103—41no—
91C103⋊C8—41no—
92C22×C103—21no—
93C22×C103—21no—
94C22×C103—41no—
95C22×C103—41no—
96C22×C103C2×C22⋊C411yescharacteristic
97C2×D103—21no—
98C2×D103—41no—
99C4×C103—21no—
100C4×C103—41no—
101C4×C103—41no—
102C4×C103—81no—
103Dic103—21no—
104Dic103—21no—
105Dic103—41no—
106Dic103—41no—
107Dic103—81no—
108Dic103#9911yescharacteristic
109Dic103#9911yescharacteristic
110C2×C103—21no—
111C2×C103—41no—
112C2×C103—41no—
113C2×C103C2×#9911yescharacteristic
114D103—41no—
115#2123—1031nomaximal, Sylow
116C103#212311yescharacteristic, complemented, Sylow
117#536—1031no—
118#413—1031no—
119#410—1031no—
120#352—1031no—
121#352—1031no—
122#352—1031no—
123#352D10311yescharacteristic, complemented
124C2×#41—1031no—
125C22×Q8—1031no—
126C2×M16—2061no—
127C4⋊Q8—2061no—
128#124—2061no—
129#123—1031no—
130#123—1031no—
131#123—1031no—
132#123C2×D10311yescharacteristic
133C22⋊Q8—2061no—
134C22⋊Q8—2061no—
135#117—1031no—
136#117—2061no—
137#101—2061no—
138#100—1031no—
139#100C2×D10311yescharacteristic
140#99—1031no—
141#99—2061no—
142#99C2×D10311yescharacteristic
143#41—4121no—
144#41—4121no—
145C2×Q8—1031no—
146C2×Q8—4121no—
147C2×Q8—4121no—
148C2×Q8—2061no—
149C2×Q8—2061no—
150C2×D4—1031no—
151C2×D4—1031no—
152C2×D4C22×D10311yescharacteristic
153C22×C4—1031no—
154C22×C4—1031no—
155C22×C4—1031no—
156C22×C4—1031no—
157C22×C4C4×D10311yescharacteristic
158M16—21no—
159M16—4121no—
160M16—2061no—
161C2×C8—4121no—
162C4⋊C4—21no—
163C4⋊C4—4121no—
164C4⋊C4—2061no—
165C4⋊C4—2061no—
166C4⋊C4—2061no—
167C4⋊C4—2061no—
168C22⋊C4—21no—
169C22⋊C4—21no—
170C22⋊C4—1031no—
171C22⋊C4—2061no—
172C22⋊C4—2061no—
173C22⋊C4—2061no—
174C22⋊C4—2061no—
175C22⋊C4C4×D10311yescharacteristic
176C42—4121no—
177C42—2061no—
178C23—1031no—
179C23C2×C4×D10311yescharacteristic
180C23D4×D10311yescharacteristic
181Q8—4121no—
182Q8—4121no—
183Q8—4121no—
184Q8—4122no—
185D4—41no—
186D4—4121no—
187D4—4121no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—1031no—
193C2×C4—1031no—
194C2×C4—1031no—
195C2×C4—4121no—
196C2×C4—4121no—
197C2×C4—2061no—
198C2×C4—2061no—
199C2×C4—2061no—
200C2×C4—2061no—
201C2×C4—2061no—
202C2×C4—2061no—
203C2×C4—2061no—
204C2×C4—2061no—
205C2×C4D4×D10311yescharacteristic
206C8—41no—
207C8—4121no—
208C22—21no—
209C22—21no—
210C22—41no—
211C22—41no—
212C22—4121no—
213C22—2061no—
214C22C22⋊C4×D10311yescharacteristic
215C4—21no—
216C4—41no—
217C4—41no—
218C4—81no—
219C4—8241no—
220C4—1031no—
221C4—1031no—
222C4—4121no—
223C4—4121no—
224C4—2061no—
225C4—2061no—
226C2—21no—
227C2—41no—
228C2—41no—
229C2—4121no—
230C2#99×D10311yescharacteristic
subgroupG/H
centerC2#99×D103
commutatorC23×C103C22×C4
FrattiniC2×D4C22×D103
Fitting#352×C103C2
socleC2×C103C2×#99
prime radicalC2×#13110104C22
cosocleC2×D4×C103C23
hypercenter#352D103
hypocenterC103#2123
LCSG ▷ C23×C103 ▷ C22×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #352

Complements

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

NH ≅ G/Ntype
4. #20267582C2semidirect
5. #20267581C2semidirect
6. #20267580C2semidirect
7. #352×C103C2semidirect
9. C22×Dic206C4semidirect
13. #15693005C4semidirect
14. #15693004C4semidirect
19. #15692977C4semidirect
116. C103#2123semidirect
123. #352D103semidirect

Maximal subgroups

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

subgroupindex
#202683632
#202677722
#202677632
#202675822
#202675812
#202675802
#352×C1032
#2123103