Finite Group Databasebeta

← #28379035

Subgroups — #28379035

Order 13952.

332 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 66 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#20296104C211yesmaximal, characteristic, complemented
2#20296024C212yesmaximal, complemented
3#20296006C211yesmaximal, characteristic, complemented
4#20295897C212yesmaximal, complemented
5#20295574C211yesmaximal, characteristic
6#16812786—24no—
7D109⋊M16C2212yes—
8C2×#13182038—22no—
9#16812778C2212yes—
10#16812763—24no—
11#16812757—22no—
12C2×#13182028C2211yescharacteristic
13C2×#13182028C2211yescharacteristic
14#16812699C411yescharacteristic, complemented
15#16812686C411yescharacteristic, complemented
16#16812686C411yescharacteristic, complemented
17#16812670—22no—
18D4×Dic109—22no—
19C42×D109C2211yescharacteristic
20#127×C109C411yescharacteristic, complemented
21#13182039D414yescomplemented
22#13182038—24no—
23#13182038—22no—
24D109⋊C8—22no—
25C2×#11724786—24no—
26C4⋊#89137—22no—
27C22⋊#89137—22no—
28C4×#89137—22no—
29#13182028—22no—
30#13182028—22no—
31#13182028—22no—
32#13182028—22no—
33C2×Dic218C2×C411yescharacteristic
34C2×Dic218C2×C411yescharacteristic
35C2×C22⋊D109—21no—
36C2×C22⋊D109D412yes—
37C22×Dic109—21no—
38C22×Dic109D412yes—
39C2×C4×D109—21no—
40C2×C4×D109C2311yescharacteristic
41C4⋊Dic109—22no—
42C22⋊Dic109—22no—
43C22⋊Dic109—22no—
44C4×Dic109—21no—
45C4×Dic109C2×C411yescharacteristic
46C2×D4×C109—22no—
47C2×D4×C109C2×C411yescharacteristic
48C2×D4×C109C2×C411yescharacteristic
49C42×C109C2×C411yescharacteristic
50C23×C109—21no—
51C23×C109C22⋊C412yes—
52C22×D109C2×D411yescharacteristic
53C2×#89137—42no—
54D4×C109—22no—
55D4×C109—22no—
56D4×C109—44no—
57C2×C4×C109—21no—
58C2×C4×C109C22×C411yescharacteristic
59C22⋊D109—24no—
60C22⋊D109—42no—
61C2×Dic109—22no—
62C2×Dic109—22no—
63C2×Dic109—21no—
64C2×Dic109—21no—
65C2×Dic109—41no—
66C2×Dic109—41no—
67C2×Dic109C22⋊C412yes—
68C2×Dic109C2×D411yescharacteristic
69C4×D109—42no—
70C4×D109C2×D412yes—
71C4×D109#4112yes—
72Dic218—22no—
73Dic218—22no—
74#11724786—24no—
75C22×C109—22no—
76C22×C109—42no—
77C22×C109—42no—
78C22×C109—41no—
79C22×C109C2×C22⋊C411yescharacteristic
80C2×D109—41no—
81C2×D109#12112yes—
82#89137—82no—
83C4×C109—22no—
84C4×C109C4×D412yes—
85Dic109—22no—
86Dic109—41no—
87Dic109—41no—
88Dic109#12011yescharacteristic
89Dic109#12311yescharacteristic
90C2×C109—21no—
91C2×C109—42no—
92C2×C109—81no—
93C2×C109#38611yescharacteristic
94D109—22no—
95#1884—1091nomaximal, Sylow
96C109#188411yescharacteristic, complemented, Sylow
97#568—1091no—
98#532—1091no—
99#421—1092no—
100#410—1091no—
101#339—1092no—
102C2×#41—1091no—
103C2×#41—1091no—
104#131—2184no—
105C2×M16—1092no—
106C2×M16—2182no—
107C4⋊Q8—1091no—
108#127#8913711yescharacteristic, complemented
109#124—1091no—
110#124—1091no—
111#121—2182no—
112C4×D4—2182no—
113#117—1092no—
114C2×C42—1091no—
115#104—2184no—
116#99—2182no—
117#41—2182no—
118#41—2182no—
119#41—2182no—
120#41—2182no—
121C2×Q8—1091no—
122C2×Q8—1091no—
123C2×D4—22no—
124C2×D4—1092no—
125C2×D4—2181no—
126C2×D4C2×#8913711yescharacteristic
127C2×D4C2×#8913711yescharacteristic
128C22×C4—1091no—
129C22×C4—1092no—
130C22×C4—2181no—
131C22×C4—2181no—
132M16—1094no—
133M16—2182no—
134M16—2184no—
135C2×C8—2182no—
136C2×C8—2184no—
137C4⋊C4—2182no—
138C4⋊C4—2182no—
139C22⋊C4—2182no—
140C22⋊C4—2182no—
141C22⋊C4—2182no—
142C42—1091no—
143C42—2181no—
144C42—2182no—
145C42C2×#8913711yescharacteristic
146C23—21no—
147C23—1091no—
148C23C22⋊#8913712yes—
149Q8—2182no—
150Q8—2182no—
151D4—22no—
152D4—22no—
153D4—44no—
154D4—4362no—
155D4—2184no—
156C2×C4—21no—
157C2×C4—1091no—
158C2×C4—1092no—
159C2×C4—1092no—
160C2×C4—1092no—
161C2×C4—4362no—
162C2×C4—4362no—
163C2×C4—4361no—
164C2×C4—4361no—
165C2×C4—2182no—
166C2×C4—2182no—
167C2×C4—2181no—
168C2×C4—2181no—
169C2×C4C22×#8913711yescharacteristic
170C8—2184no—
171C22—22no—
172C22—42no—
173C22—42no—
174C22—41no—
175C22—1092no—
176C22—4361no—
177C22C2×C22⋊#8913711yescharacteristic
178C4—22no—
179C4—8722no—
180C4—1091no—
181C4—1091no—
182C4—4361no—
183C4—4361no—
184C4—2182no—
185C4D4×#8913712yes—
186C2—21no—
187C2—42no—
188C2—81no—
189C2—2182no—
190C2#2029597411yescharacteristic
subgroupG/H
centerC2#20295974
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
Fitting#127×C109C4
socleC2×C109#386
prime radical#20295574C2
cosocleC2×C4×D109C23
hypercenter#127#89137
hypocenterC109#1884
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C2×C4 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #20296104C2semidirect
2. #20296024C2semidirect
3. #20296006C2semidirect
4. #20295897C2semidirect
14. #16812699C4semidirect
15. #16812686C4semidirect
16. #16812686C4semidirect
20. #127×C109C4semidirect
21. #13182039D4semidirect
96. C109#1884semidirect
108. #127#89137semidirect

Maximal subgroups

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

subgroupindex
#202961042
#202960242
#202960062
#202958972
#202955742
#1884109