Finite Group Databasebeta

← #28378796

Subgroups — #28378796

Order 13952.

320 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C2×#16812764C212yesmaximal
2C4×#13182039C211yesmaximal, characteristic, complemented
3#20295962C211yesmaximal, characteristic, complemented
4#20295896C212yesmaximal, complemented
5C4×#13182030C211yesmaximal, characteristic
6C2×#13182039C2212yes—
7C2×C4×#89137C2212yes—
8#16812764C418yescomplemented
9#16812754—21no—
10C4×#11724786—21no—
11(C2×#89137)⋊C4—21no—
12(C2×#89137)⋊C4—21no—
13C2×#13182030C2211yescharacteristic
14Q8×Dic109C411yescharacteristic, complemented
15C4×D436—21no—
16C4×D436C411yescharacteristic, complemented
17#16812661—21no—
18#16812661C411yescharacteristic, complemented
19#16812657—21no—
20#16812657C2211yescharacteristic
21C42×D109—21no—
22C42×D109C2211yescharacteristic
23C4×Q8×C109C411yescharacteristic, complemented
24C22×#89137—22no—
25#13182039—22no—
26#13182039C2×C414yescomplemented
27C2×#11724786—22no—
28C4×#89137—22no—
29C4×#89137C2×C414yescomplemented
30#13182030—22no—
31#13182030C2×C414yes—
32C2×D436—21no—
33C2×D436C2×C411yescharacteristic
34C2×C4×D109—21no—
35C2×C4×D109—21no—
36C2×C4×D109—21no—
37C2×C4×D109D411yescharacteristic
38C2×C4×D109D411yescharacteristic
39C2×C4×D109C2311yescharacteristic
40C4⋊Dic109—21no—
41C4⋊Dic109C2×C411yescharacteristic
42#13182006—21no—
43#13182006—21no—
44#13182006—21no—
45C4×Dic109—21no—
46C4×Dic109—21no—
47C4×Dic109C2×C411yescharacteristic
48C4×Dic109D411yescharacteristic
49C4×Dic109D411yescharacteristic
50C2×Q8×C109C2×C411yescharacteristic
51C4⋊C4×C109—21no—
52C4⋊C4×C109C2×C411yescharacteristic
53C42×C109—21no—
54C42×C109C2×C411yescharacteristic
55C22×D109—21no—
56C22×D109C2×D411yescharacteristic
57C2×#89137—24no—
58C2×#89137—42no—
59C2×#89137—42no—
60Q8×C109—21no—
61Q8×C109C4212yes—
62C2×C4×C109—21no—
63C2×C4×C109—21no—
64C2×C4×C109C22⋊C411yescharacteristic
65C2×C4×C109C22⋊C411yescharacteristic
66C2×C4×C109C22×C411yescharacteristic
67C2×Dic109—21no—
68C2×Dic109C22⋊C411yescharacteristic
69C2×Dic109C22⋊C411yescharacteristic
70C2×Dic109C2×D411yescharacteristic
71D436—24no—
72D436—21no—
73D436C4212yes—
74C4×D109—24no—
75C4×D109—41no—
76C4×D109—41no—
77C4×D109—42no—
78C4×D109—42no—
79C4×D109C22×C412yes—
80C4×D109#4112yes—
81#11724786—24no—
82C22×C109C2×C22⋊C411yescharacteristic
83C2×D109—21no—
84C2×D109—21no—
85C2×D109—22no—
86C2×D109—41no—
87C2×D109—41no—
88C2×D109C4×D412yes—
89#89137—44no—
90C4×C109—22no—
91C4×C109—21no—
92C4×C109—21no—
93C4×C109—41no—
94C4×C109C2×C4211yescharacteristic
95C4×C109#11711yescharacteristic
96Dic109—21no—
97Dic109—21no—
98Dic109—41no—
99Dic109C4×D412yes—
100C2×C109C4×C22⋊C411yescharacteristic
101C2×C109#42111yescharacteristic
102C2×C109#42111yescharacteristic
103D109—22no—
104D109—42no—
105#1759—1091nomaximal, Sylow
106C109#175911yescharacteristic, complemented, Sylow
107C4×#41—1091no—
108C2×#104—1092no—
109C4×M16—1091no—
110#376—1091no—
111#339—1092no—
112C2×#41—1091no—
113C2×M16—1092no—
114C4×Q8—1091no—
115C4×Q8#8913711yescharacteristic, complemented
116C4×D4—1091no—
117C4×D4—1091no—
118C4×D4—2181no—
119C4×D4—2181no—
120#117—1091no—
121#117—2181no—
122C2×C42—1091no—
123C2×C42—1092no—
124C2×C42—2181no—
125#104—1098no—
126#97—2181no—
127C4×C8—2181no—
128#95—2181no—
129#95—2181no—
130#41—1094no—
131#41—2182no—
132C2×Q8C2×#8913711yescharacteristic
133C2×D4—1091no—
134C2×D4—2181no—
135C22×C4—1091no—
136C22×C4—1091no—
137C22×C4—1091no—
138C22×C4—2181no—
139C22×C4—2181no—
140C22×C4—2182no—
141C22×C4—2181no—
142M16—1094no—
143M16—2182no—
144C2×C8—2182no—
145C4⋊C4—21no—
146C4⋊C4—1091no—
147C4⋊C4—2181no—
148C4⋊C4C2×#8913711yescharacteristic
149C22⋊C4—2181no—
150C22⋊C4—2181no—
151C22⋊C4—2181no—
152C42—21no—
153C42—1091no—
154C42—1091no—
155C42—1091no—
156C42—1094no—
157C42—2181no—
158C42—2181no—
159C42—2182no—
160C42C2×#8913711yescharacteristic
161C23—1091no—
162C23—2181no—
163Q8—21no—
164Q8C4×#8913712yes—
165D4—1092no—
166D4—2184no—
167D4—2181no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—1091no—
171C2×C4—1092no—
172C2×C4—1092no—
173C2×C4—1091no—
174C2×C4—1091no—
175C2×C4—4362no—
176C2×C4—4361no—
177C2×C4—4361no—
178C2×C4—4362no—
179C2×C4—4362no—
180C2×C4—4362no—
181C2×C4—2184no—
182C2×C4—2184no—
183C2×C4—2181no—
184C2×C4C22⋊#8913711yescharacteristic
185C2×C4C22⋊#8913711yescharacteristic
186C2×C4C22×#8913711yescharacteristic
187C8—2184no—
188C22—1092no—
189C22—4361no—
190C22—4361no—
191C22—2182no—
192C22—2181no—
193C22—2181no—
194C22C2×C22⋊#8913711yescharacteristic
195C4—22no—
196C4—21no—
197C4—21no—
198C4—41no—
199C4—1092no—
200C4—4364no—
201C4—4361no—
202C4—2181no—
203C4—2181no—
204C4C2×C4×#8913711yescharacteristic
205C4#1681277811yescharacteristic
206C2—4362no—
207C2—2182no—
208C2C4×C22⋊#8913711yescharacteristic
209C2#2029602311yescharacteristic
210C2#2029602511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC4×C109C2×C42
FrattiniC2×C4C22×#89137
FittingC4×Q8×C109C4
socleC22×C109C2×C22⋊C4
prime radicalC2×#13182030C22
cosocleC2×C4×D109C23
hypercenterC4×Q8#89137
hypocenterC109#1759
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. C4×#13182039C2semidirect
3. #20295962C2semidirect
4. #20295896C2semidirect
8. #16812764C4semidirect
14. Q8×Dic109C4semidirect
16. C4×D436C4semidirect
18. #16812661C4semidirect
23. C4×Q8×C109C4semidirect
26. #13182039C2×C4semidirect
29. C4×#89137C2×C4semidirect
106. C109#1759semidirect
115. C4×Q8#89137semidirect

Maximal subgroups

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

subgroupindex
C2×#168127642
C4×#131820392
#202959622
#202958962
C4×#131820302
#1759109