Finite Group Databasebeta

← #28373404

Subgroups — #28373404

Order 13952.

484 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 129 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#20295579C211yesmaximal, characteristic, complemented
2C2×#16812695C211yesmaximal, characteristic
3#20295389C214yesmaximal, complemented
4#20295371C214yesmaximal, complemented
5#20295032C211yesmaximal, characteristic, complemented
6#20295031C211yesmaximal, characteristic, complemented
7#20295030C211yesmaximal, characteristic, complemented
8M16×Dic109C211yesmaximal, characteristic, complemented
9#418×C109C211yesmaximal, characteristic, complemented
10C22×D436C2211yescharacteristic
11C22×C22⋊D109—22no—
12C2×#13182013C2211yescharacteristic
13#16812698C2212yescomplemented
14#16812695—22no—
15#16812695C2212yes—
16#16812695C2212yes—
17#16812690C2212yescomplemented
18#16812676—22no—
19C4×Dic218—22no—
20#16812658C2211yescharacteristic
21C2×C4×Dic109C2211yescharacteristic
22#16812621C2214yescomplemented
23#16812620C2214yescomplemented
24#16812619C2214yescomplemented
25#16812609C2212yescomplemented
26C8×Dic109C2212yescomplemented
27C22×D4×C109C2211yescharacteristic
28C2×M16×C109C2211yescharacteristic
29#117×C109C2211yescharacteristic
30#102×C109C2214yescomplemented
31C23×D109—21no—
32C2×Dic218—22no—
33C2×D436—22no—
34C2×D436—22no—
35C2×D436—21no—
36C2×D436C2312yes—
37C2×C22⋊D109—24no—
38C2×C22⋊D109—24no—
39C2×C22⋊D109—48no—
40C22×Dic109D412yes—
41#13182013—22no—
42C2×#11724784C2312yes—
43C4⋊Dic109—22no—
44C4⋊Dic109C2312yes—
45#13182008—22no—
46#13182008—22no—
47C22⋊Dic109—21no—
48C4×Dic109—21no—
49C4×Dic109D412yes—
50C4×Dic109C2311yescharacteristic
51C4×Dic109C2311yescharacteristic
52C24×C109—21no—
53C2×D4×C109—21no—
54C2×D4×C109—22no—
55C2×D4×C109—22no—
56C2×D4×C109C2312yes—
57C22×C4×C109C2311yescharacteristic
58M16×C109—22no—
59C2×C8×C109C2312yes—
60C4⋊C4×C109C2312yes—
61C22⋊C4×C109—21no—
62C42×C109—21no—
63C23×C109—22no—
64C23×C109—44no—
65C23×C109—42no—
66C23×C109C2×D411yescharacteristic
67C22×D109—22no—
68C22×D109—44no—
69C22×D109—42no—
70D4×C109—22no—
71D4×C109—22no—
72D4×C109—42no—
73C2×C4×C109—22no—
74C2×C4×C109C2×D411yescharacteristic
75C2×C4×C109#4112yes—
76C2×C4×C109#4112yes—
77C2×C4×C109C2411yescharacteristic
78C22⋊D109—48no—
79C22⋊D109—48no—
80C2×Dic109—24no—
81C2×Dic109—22no—
82C2×Dic109C2×D412yes—
83C2×Dic109C2×D412yes—
84D436—22no—
85D436—22no—
86D436—42no—
87Dic218—44no—
88C8×C109—22no—
89#11724784—22no—
90C22×C109—22no—
91C22×C109—42no—
92C22×C109—44no—
93C22×C109—84no—
94C22×C109#12412yes—
95C22×C109C22×D411yescharacteristic
96C2×D109—42no—
97C2×D109—44no—
98C2×D109—84no—
99C4×C109—42no—
100C4×C109#12412yes—
101C4×C109C2×#4111yescharacteristic
102C4×C109C2×#4111yescharacteristic
103Dic109—22no—
104Dic109—42no—
105Dic109AGL(1,ℤ/8)14yes—
106C2×C109—22no—
107C2×C109—82no—
108C2×C109C2×#12411yescharacteristic
109C2×C109C2×AGL(1,ℤ/8)12yes—
110D109—82no—
111#3138—1091nomaximal, Sylow
112C109#313811yescharacteristic, complemented, Sylow
113#533—1091no—
114C2×#127—1091no—
115#490—1094no—
116#486—1094no—
117#418—1091no—
118#418—1091no—
119#418—1091no—
120#418D10911yescharacteristic, complemented
121C4×M16—1091no—
122C22×D4—1091no—
123C22×D4—2182no—
124C22×D4C2×D10911yescharacteristic
125C2×M16—1091no—
126C2×M16C2×D10911yescharacteristic
127C4⋊Q8—1092no—
128#127—1092no—
129#127—1092no—
130#127—2182no—
131#125—1092no—
132C22⋊Q8—2182no—
133C4×Q8—2182no—
134#117—1091no—
135#117C2×D10911yescharacteristic
136C2×C42—1091no—
137#102—1094no—
138#102—1094no—
139#102—1094no—
140#102C2×D10914yescomplemented
141#97—1092no—
142C4×C8—1092no—
143C24—21no—
144C24—2181no—
145C2×Q8—2182no—
146C2×D4—21no—
147C2×D4—22no—
148C2×D4—22no—
149C2×D4—1092no—
150C2×D4—4368no—
151C2×D4—2184no—
152C2×D4—2184no—
153C2×D4—2181no—
154C2×D4—2182no—
155C2×D4—2182no—
156C2×D4C22×D10912yes—
157C22×C4—1092no—
158C22×C4C22×D10911yescharacteristic
159M16—22no—
160M16—2182no—
161C2×C8—1092no—
162C2×C8C22×D10912yes—
163C4⋊C4—1092no—
164C4⋊C4—2182no—
165C4⋊C4—2182no—
166C4⋊C4—2182no—
167C4⋊C4C22×D10912yes—
168C22⋊C4—21no—
169C22⋊C4—2181no—
170C42—21no—
171C42—1092no—
172C42—1091no—
173C42—1091no—
174C42—2181no—
175C23—22no—
176C23—44no—
177C23—42no—
178C23—4364no—
179C23—4362no—
180C23—2182no—
181C23D4×D10911yescharacteristic
182Q8—4364no—
183D4—22no—
184D4—22no—
185D4—42no—
186D4—4368no—
187D4—4368no—
188D4—4362no—
189D4—2182no—
190D4—2182no—
191C2×C4—22no—
192C2×C4—1092no—
193C2×C4—1092no—
194C2×C4—2184no—
195C2×C4—2182no—
196C2×C4D4×D10911yescharacteristic
197C2×C4#1318202812yes—
198C2×C4#1318202912yes—
199C2×C4C23×D10911yescharacteristic
200C8—22no—
201C8—2182no—
202C22—22no—
203C22—42no—
204C22—44no—
205C22—84no—
206C22—8724no—
207C22—4362no—
208C22—4364no—
209C22#1681268512yes—
210C22C2×D4×D10911yescharacteristic
211C4—42no—
212C4—1094no—
213C4—4362no—
214C4—2182no—
215C4#1681268512yes—
216C4C2×#1318202811yescharacteristic
217C4C2×#1318202911yescharacteristic
218C2—22no—
219C2—82no—
220C2—8722no—
221C2C2×#1681268511yescharacteristic
222C2AGL(1,ℤ/8)×D10912yes—
subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#418×C109C2
socleC22×C109C22×D4
prime radicalC2×#16812695C2
hypercenter#418D109
hypocenterC109#3138
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #20295579C2semidirect
3. #20295389C2semidirect
4. #20295371C2semidirect
5. #20295032C2semidirect
6. #20295031C2semidirect
7. #20295030C2semidirect
8. M16×Dic109C2semidirect
9. #418×C109C2semidirect
13. #16812698C22semidirect
17. #16812690C22semidirect
22. #16812621C22semidirect
23. #16812620C22semidirect
24. #16812619C22semidirect
25. #16812609C22semidirect
26. C8×Dic109C22semidirect
30. #102×C109C22semidirect
112. C109#3138semidirect
120. #418D109semidirect
140. #102C2×D109semidirect

Maximal subgroups

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

subgroupindex
#202955792
C2×#168126952
#202953892
#202953712
#202950322
#202950312
#202950302
M16×Dic1092
#418×C1092
#3138109