Finite Group Databasebeta

← #28379169

Subgroups — #28379169

Order 13952.

320 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 70 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#20296030C211yesmaximal, characteristic, complemented
2C2×#16812764C212yesmaximal, complemented
3C2×#16812763C212yesmaximal, complemented
4#20295962C211yesmaximal, characteristic, complemented
5#20295575C211yesmaximal, characteristic
6C2×#13182039C2212yes—
7C2×C4×#89137C2212yes—
8C4⋊#11724786—22no—
9#16812764—24no—
10#16812763—24no—
11(C2×#89137)⋊C4—22no—
12C2×#13182030C2211yescharacteristic
13C2×#13182028C2211yescharacteristic
14#16812697C411yescharacteristic, complemented
15#16812695C411yescharacteristic, complemented
16#16812687C411yescharacteristic, complemented
17#16812672—22no—
18#16812659—22no—
19C42×D109C2211yescharacteristic
20#124×C109C411yescharacteristic, complemented
21C22×#89137—22no—
22#13182039—22no—
23#13182039—22no—
24C2×#11724786—22no—
25C4×#89137—22no—
26C4×#89137D414yescomplemented
27#13182030—22no—
28#13182030—22no—
29#13182028—22no—
30#13182028—22no—
31C2×Dic218C2×C411yescharacteristic
32C2×D436—21no—
33C2×D436C2×C411yescharacteristic
34C2×C22⋊D109—21no—
35C2×C22⋊D109—22no—
36C22×Dic109—21no—
37C2×C4×D109—21no—
38C2×C4×D109D412yes—
39C2×C4×D109C2311yescharacteristic
40#13182008—22no—
41#13182006—22no—
42C4×Dic109C2×C411yescharacteristic
43C4×Dic109D412yes—
44C2×Q8×C109C2×C411yescharacteristic
45C2×D4×C109C2×C411yescharacteristic
46C22⋊C4×C109—22no—
47C42×C109C2×C411yescharacteristic
48C23×C109—21no—
49C22×D109—21no—
50C22×D109C2×D411yescharacteristic
51C2×#89137—24no—
52C2×#89137—44no—
53Q8×C109—22no—
54D4×C109—22no—
55C2×C4×C109—21no—
56C2×C4×C109C22⋊C412yes—
57C2×C4×C109C22×C411yescharacteristic
58C22⋊D109—44no—
59C22⋊D109—42no—
60C2×Dic109—21no—
61C2×Dic109—41no—
62C2×Dic109—41no—
63C2×Dic109C22⋊C412yes—
64C2×Dic109C2×D411yescharacteristic
65D436—22no—
66D436—42no—
67C4×D109—42no—
68C4×D109—41no—
69C4×D109—41no—
70C4×D109C2×D412yes—
71C4×D109#4112yes—
72Dic218—22no—
73#11724786—42no—
74C22×C109—41no—
75C22×C109—42no—
76C22×C109C2×C22⋊C411yescharacteristic
77C2×D109—22no—
78C2×D109—41no—
79C2×D109—42no—
80C2×D109#12112yes—
81#89137—44no—
82C4×C109—22no—
83C4×C109—41no—
84C4×C109C4×D412yes—
85Dic109—22no—
86Dic109—41no—
87Dic109#12411yescharacteristic
88Dic109#12711yescharacteristic
89C2×C109—81no—
90C2×C109#39011yescharacteristic
91C2×C109#42112yes—
92D109—22no—
93D109—81no—
94#1963—1091nomaximal, Sylow
95C109#196311yescharacteristic, complemented, Sylow
96#532—1091no—
97#423—1091no—
98C2×#104—1092no—
99C2×#104—1092no—
100#376—1091no—
101C2×#41—1091no—
102C2×#41—1091no—
103C2×M16—1092no—
104C4⋊Q8—1091no—
105#127—1091no—
106#124—1091no—
107#124#8913711yescharacteristic, complemented
108#121—2182no—
109C4×D4—2182no—
110C2×C42—1091no—
111C2×C42—1092no—
112C4⋊C8—2182no—
113#104—2184no—
114#104—2184no—
115#95—2182no—
116#41—2182no—
117#41—2182no—
118#41—2182no—
119#41—2182no—
120C2×Q8—1091no—
121C2×Q8C2×#8913711yescharacteristic
122C2×D4—1091no—
123C2×D4—2181no—
124C2×D4—2182no—
125C2×D4—2181no—
126C2×D4C2×#8913711yescharacteristic
127C22×C4—1091no—
128C22×C4—1092no—
129C22×C4—2181no—
130C22×C4—2181no—
131C22×C4—2182no—
132M16—2182no—
133M16—2182no—
134C2×C8—2182no—
135C4⋊C4—2182no—
136C22⋊C4—22no—
137C22⋊C4—2182no—
138C42—1092no—
139C42—1091no—
140C42—1094no—
141C42—2182no—
142C42C2×#8913711yescharacteristic
143C23—21no—
144C23—1091no—
145C23—2181no—
146Q8—22no—
147Q8—2182no—
148D4—22no—
149D4—4362no—
150D4—4362no—
151D4—4364no—
152D4—2182no—
153C2×C4—21no—
154C2×C4—1091no—
155C2×C4—1092no—
156C2×C4—1092no—
157C2×C4—1092no—
158C2×C4—4362no—
159C2×C4—4361no—
160C2×C4—4361no—
161C2×C4—4361no—
162C2×C4—4361no—
163C2×C4—4364no—
164C2×C4—2184no—
165C2×C4—2181no—
166C2×C4C22⋊#8913712yes—
167C2×C4C22×#8913711yescharacteristic
168C8—4362no—
169C22—41no—
170C22—42no—
171C22—1092no—
172C22—4361no—
173C22—4362no—
174C22—2182no—
175C22C2×C22⋊#8913711yescharacteristic
176C4—22no—
177C4—41no—
178C4—1091no—
179C4—1091no—
180C4—4364no—
181C4—4361no—
182C4—2182no—
183C4D4×#8913712yes—
184C2—81no—
185C2—8721no—
186C2—2182no—
187C2#2029597811yescharacteristic
188C2#2029602312yes—
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
Fitting#124×C109C4
socleC22×C109C2×C22⋊C4
prime radical#20295575C2
cosocleC2×C4×D109C23
hypercenter#124#89137
hypocenterC109#1963
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #20296030C2semidirect
2. C2×#16812764C2semidirect
3. C2×#16812763C2semidirect
4. #20295962C2semidirect
14. #16812697C4semidirect
15. #16812695C4semidirect
16. #16812687C4semidirect
20. #124×C109C4semidirect
26. C4×#89137D4semidirect
95. C109#1963semidirect
107. #124#89137semidirect

Maximal subgroups

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

subgroupindex
#202960302
C2×#168127642
C2×#168127632
#202959622
#202955752
#1963109