Finite Group Databasebeta

← #27193740

Subgroups — #27193740

Order 13184.

264 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 61 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#124×D103C211yesmaximal, characteristic
2#20267846C211yesmaximal, characteristic, complemented
3#20267743C211yesmaximal, characteristic, complemented
4#20267531C211yesmaximal, characteristic, complemented
5#20267530C211yesmaximal, characteristic, complemented
6#20267530C211yesmaximal, characteristic, complemented
7#329×C103C211yesmaximal, characteristic, complemented
8C2×Q8×D103C411yescharacteristic
9C2×D4×D103C411yescharacteristic
10C2×#13110088—21no—
11#15693010C411yescharacteristic
12#15693009C2211yescharacteristic
13#15693008C411yescharacteristic
14#15693007—21no—
15#15693007—21no—
16C22⋊C4×D103—21no—
17C22⋊C4×D103—21no—
18C42×D103C2211yescharacteristic
19Dic103⋊C8—21no—
20(C2×D103)⋊C8—21no—
21#15692932C2211yescharacteristic, complemented
22#15692932C2211yescharacteristic, complemented
23C8×Dic103—21no—
24#124×C103C2211yescharacteristic
25#97×C103C2211yescharacteristic, complemented
26#97×C103C2211yescharacteristic, complemented
27C23×D103—21no—
28C2×Dic206—21no—
29C2×Dic206C2×C411yescharacteristic
30Q8×D103—42no—
31C2×D412C2×C411yescharacteristic
32C2×C22⋊D103—21no—
33D4×D103—42no—
34C2×C4×D103—21no—
35C2×C4×D103C2×C411yescharacteristic
36C2×C4×D103D411yescharacteristic
37C2×C4×D103D411yescharacteristic
38#13110088—24no—
39C2×C103⋊C8—21no—
40C2×C103⋊C8—21no—
41C22⋊Dic103—21no—
42C22⋊Dic103—21no—
43(C2×D103)⋊C4—21no—
44(C2×D103)⋊C4—21no—
45(C2×D103)⋊C4—21no—
46(C2×D103)⋊C4—21no—
47C4×Dic103C2×C411yescharacteristic
48C4×Dic103D411yescharacteristic
49C4×Dic103D411yescharacteristic
50C2×Q8×C103C2×C411yescharacteristic
51C2×D4×C103C2×C411yescharacteristic
52C2×C8×C103—21no—
53C2×C8×C103—21no—
54C22⋊C4×C103—21no—
55C22⋊C4×C103—21no—
56C42×C103C2311yescharacteristic
57C23×C103—21no—
58C22×D103—21no—
59C22×D103—42no—
60C22×D103—42no—
61C22×D103—42no—
62C22×D103C22⋊C411yescharacteristic
63Q8×C103—41no—
64D4×C103—41no—
65C2×C4×C103—21no—
66C2×C4×C103C22×C411yescharacteristic
67C2×C4×C103C2×D411yescharacteristic
68C2×C4×C103C2×D411yescharacteristic
69C22⋊D103—42no—
70C2×Dic103—21no—
71C2×Dic103C22⋊C411yescharacteristic
72C2×Dic103C22⋊C411yescharacteristic
73C2×Dic103C22⋊C411yescharacteristic
74D412—41no—
75C4×D103—22no—
76C4×D103—22no—
77C4×D103—41no—
78C4×D103—42no—
79Dic206—42no—
80Dic206—41no—
81C8×C103—22no—
82C8×C103—41no—
83C103⋊C8—22no—
84C103⋊C8—41no—
85C22×C103—41no—
86C22×C103—41no—
87C22×C103—41no—
88C22×C103C2×C22⋊C411yescharacteristic
89C2×D103—21no—
90C2×D103—21no—
91C2×D103—41no—
92C2×D103—41no—
93C2×D103—41no—
94C2×D103—84no—
95C2×D103#10412yes—
96C4×C103—21no—
97C4×C103—21no—
98C4×C103—21no—
99C4×C103—41no—
100Dic103—21no—
101Dic103—21no—
102Dic103—41no—
103Dic103#10012yes—
104C2×C103—81no—
105C2×C103C2×#10011yescharacteristic
106C2×C103C2×#10411yescharacteristic
107C2×C103#42111yescharacteristic
108D103—22no—
109D103—81no—
110#1527—1031nomaximal, Sylow
111C103#152711yescharacteristic, complemented, Sylow
112C2×#124—1031no—
113#432—1031no—
114C4×M16—1031no—
115#329—1031no—
116#329—1031no—
117#329—1031no—
118#329D10311yescharacteristic, complemented
119C22×Q8—1031no—
120C22×D4—1031no—
121C2×M16—2061no—
122#124—1031no—
123#124—1031no—
124#124—1031no—
125#124—2061no—
126#124—2061no—
127#124C2×D10311yescharacteristic
128C2×C22⋊C4—2061no—
129C2×C22⋊C4—2061no—
130C2×C42—1031no—
131C4⋊C8—2061no—
132C22⋊C8—2061no—
133#97—1031no—
134#97—1031no—
135#97C2×D10311yescharacteristic, complemented
136#97C2×D10311yescharacteristic, complemented
137C4×C8—2061no—
138C24—2061no—
139C2×Q8—1031no—
140C2×Q8—4122no—
141C2×Q8—2061no—
142C2×Q8C4×D10311yescharacteristic
143C2×D4—1031no—
144C2×D4—4122no—
145C2×D4—2061no—
146C2×D4C4×D10311yescharacteristic
147C22×C4—1031no—
148C22×C4—1031no—
149C22×C4—1031no—
150C22×C4—2061no—
151M16—2064no—
152C2×C8—21no—
153C2×C8—21no—
154C2×C8—2061no—
155C2×C8—2061no—
156C22⋊C4—21no—
157C22⋊C4—21no—
158C22⋊C4—2061no—
159C22⋊C4—2061no—
160C22⋊C4—2061no—
161C22⋊C4—2061no—
162C22⋊C4—2061no—
163C22⋊C4—2061no—
164C42—1031no—
165C42—1031no—
166C42—1031no—
167C42C22×D10311yescharacteristic
168C23—21no—
169C23—1031no—
170C23—4122no—
171C23—4122no—
172C23—4122no—
173C23—2061no—
174Q8—41no—
175Q8—4121no—
176Q8—4122no—
177D4—41no—
178D4—4121no—
179D4—4122no—
180C2×C4—21no—
181C2×C4—1031no—
182C2×C4—1031no—
183C2×C4—1031no—
184C2×C4—4121no—
185C2×C4—4122no—
186C2×C4—2062no—
187C2×C4—2062no—
188C2×C4—2061no—
189C2×C4C2×C4×D10311yescharacteristic
190C2×C4D4×D10311yescharacteristic
191C2×C4D4×D10311yescharacteristic
192C8—22no—
193C8—41no—
194C8—4121no—
195C8—2062no—
196C22—41no—
197C22—41no—
198C22—41no—
199C22—8244no—
200C22—1032no—
201C22—4121no—
202C22—4121no—
203C22—4121no—
204C22—2061no—
205C22—2061no—
206C22C22⋊C4×D10311yescharacteristic
207C4—21no—
208C4—21no—
209C4—21no—
210C4—41no—
211C4—1032no—
212C4—4121no—
213C4—2061no—
214C4—2061no—
215C2—81no—
216C2—8241no—
217C2—2062no—
218C2#100×D10311yescharacteristic
219C2#104×D10311yescharacteristic
220C2#2026780611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D103
commutatorC2×C4×C103C22×C4
FrattiniC42C22×D103
Fitting#329×C103C2
socleC22×C103C2×C22⋊C4
prime radicalC2×D4×D103C4
cosocleC42×C103C23
hypercenter#329D103
hypocenterC103#1527
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #20267846C2semidirect
3. #20267743C2semidirect
4. #20267531C2semidirect
5. #20267530C2semidirect
6. #20267530C2semidirect
7. #329×C103C2semidirect
21. #15692932C22semidirect
22. #15692932C22semidirect
25. #97×C103C22semidirect
26. #97×C103C22semidirect
111. C103#1527semidirect
118. #329D103semidirect
135. #97C2×D103semidirect
136. #97C2×D103semidirect

Maximal subgroups

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

subgroupindex
#124×D1032
#202678462
#202677432
#202675312
#202675302
#329×C1032
#1527103