Finite Group Databasebeta

← #28363416

Subgroups — #28363416

Order 13952.

332 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 93 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#20295793C211yesmaximal, characteristic, complemented
2#20295043C212yesmaximal, complemented
3#20295000C211yesmaximal, characteristic, complemented
4#20294786C212yesmaximal, complemented
5#532×C109C211yesmaximal, characteristic
6#16812706—24no—
7C2×#13182013—22no—
8C2×#13182013C2212yes—
9#16812658C2212yes—
10#16812626—24no—
11#16812614—22no—
12C2×#41×C109C2211yescharacteristic
13C2×#41×C109C2211yescharacteristic
14C4⋊Q8×C109C411yescharacteristic, complemented
15#127×C109C411yescharacteristic, complemented
16#124×C109C411yescharacteristic, complemented
17#124×C109C411yescharacteristic, complemented
18#121×C109—22no—
19C4×D4×C109—22no—
20C2×C42×C109C2211yescharacteristic
21#13182013—24no—
22#13182013—22no—
23#13182013D414yescomplemented
24C2×#11724784—24no—
25C2×#11724784—22no—
26C4⋊Dic109—22no—
27C22⋊Dic109—22no—
28C4×Dic109—22no—
29#41×C109—22no—
30#41×C109—22no—
31#41×C109—22no—
32#41×C109—22no—
33C2×Q8×C109C2×C411yescharacteristic
34C2×Q8×C109C2×C411yescharacteristic
35C2×D4×C109—22no—
36C2×D4×C109—21no—
37C2×D4×C109C2×C411yescharacteristic
38C2×D4×C109C2×C411yescharacteristic
39C2×D4×C109D412yes—
40C22×C4×C109—21no—
41C22×C4×C109—21no—
42C22×C4×C109D412yes—
43C22×C4×C109C2311yescharacteristic
44C4⋊C4×C109—22no—
45C22⋊C4×C109—22no—
46C22⋊C4×C109—22no—
47C42×C109—21no—
48C42×C109C2×C411yescharacteristic
49C42×C109C2×C411yescharacteristic
50C23×C109—21no—
51C23×C109C22⋊C412yes—
52C23×C109C2×D411yescharacteristic
53Q8×C109—22no—
54Q8×C109—22no—
55D4×C109—24no—
56D4×C109—22no—
57D4×C109—22no—
58D4×C109—44no—
59D4×C109—42no—
60C2×C4×C109—21no—
61C2×C4×C109—22no—
62C2×C4×C109—22no—
63C2×C4×C109—21no—
64C2×C4×C109—21no—
65C2×C4×C109—42no—
66C2×C4×C109—41no—
67C2×C4×C109—41no—
68C2×C4×C109C22⋊C412yes—
69C2×C4×C109C22×C411yescharacteristic
70C2×C4×C109C2×D412yes—
71C2×C4×C109C2×D411yescharacteristic
72C2×C4×C109#4112yes—
73C2×Dic109—42no—
74#11724784—24no—
75C22×C109—22no—
76C22×C109—41no—
77C22×C109—42no—
78C22×C109—42no—
79C22×C109—41no—
80C22×C109C2×C22⋊C411yescharacteristic
81C22×C109#12112yes—
82C4×C109—22no—
83C4×C109—22no—
84C4×C109—41no—
85C4×C109—41no—
86C4×C109C4×D412yes—
87C4×C109#12011yescharacteristic
88C4×C109#12311yescharacteristic
89Dic109—82no—
90C2×C109—22no—
91C2×C109—21no—
92C2×C109—42no—
93C2×C109—81no—
94C2×C109#38611yescharacteristic
95#1884—1091nomaximal, Sylow
96C109#188411yescharacteristic, complemented, Sylow
97#568—1091no—
98#532D10911yescharacteristic
99#421—1092no—
100#410—1091no—
101#339—1092no—
102C2×#41C2×D10911yescharacteristic
103C2×#41C2×D10911yescharacteristic
104#131—2184no—
105C2×M16—1092no—
106C2×M16—2182no—
107C4⋊Q8Dic10911yescharacteristic, complemented
108#127Dic10911yescharacteristic, complemented
109#124Dic10911yescharacteristic, complemented
110#124Dic10911yescharacteristic, complemented
111#121—22no—
112C4×D4—22no—
113#117—1092no—
114C2×C42C2×D10911yescharacteristic
115#104—2184no—
116#99—2182no—
117#41—22no—
118#41—22no—
119#41—22no—
120#41—22no—
121C2×Q8C2×Dic10911yescharacteristic
122C2×Q8C2×Dic10911yescharacteristic
123C2×D4—22no—
124C2×D4—21no—
125C2×D4C2×Dic10911yescharacteristic
126C2×D4C2×Dic10911yescharacteristic
127C2×D4C22⋊D10912yes—
128C22×C4—21no—
129C22×C4—21no—
130C22×C4C22⋊D10912yes—
131C22×C4C22×D10911yescharacteristic
132M16—1094no—
133M16—2184no—
134M16—2182no—
135C2×C8—2184no—
136C2×C8—2182no—
137C4⋊C4—22no—
138C4⋊C4—2182no—
139C22⋊C4—22no—
140C22⋊C4—22no—
141C22⋊C4—2182no—
142C42—21no—
143C42—2182no—
144C42C2×Dic10911yescharacteristic
145C42C2×Dic10911yescharacteristic
146C23—21no—
147C23C22⋊Dic10912yes—
148C23C2×C22⋊D10911yescharacteristic
149Q8—22no—
150Q8—22no—
151D4—24no—
152D4—22no—
153D4—22no—
154D4—44no—
155D4—42no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—42no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—4362no—
165C2×C4C22⋊Dic10912yes—
166C2×C4C22×Dic10911yescharacteristic
167C2×C4D4×D10912yes—
168C2×C4C2×C22⋊D10911yescharacteristic
169C2×C4#1318202812yes—
170C8—2184no—
171C22—22no—
172C22—41no—
173C22—42no—
174C22—42no—
175C22—41no—
176C22C2×C22⋊Dic10911yescharacteristic
177C22#1681267112yes—
178C4—22no—
179C4—22no—
180C4—41no—
181C4—41no—
182C4—8722no—
183C4D4×Dic10912yes—
184C4#1681266711yescharacteristic
185C4#1681268011yescharacteristic
186C2—21no—
187C2—22no—
188C2—42no—
189C2—81no—
190C2#2029490611yescharacteristic
subgroupG/H
centerC4#16812667
commutatorC2×C4×C109C22×C4
FrattiniC22×C4C22×D109
Fitting, prime radical#532×C109C2
socleC2×C109#386
cosocleC22×C4×C109C23
hypercenter#532D109
hypocenterC109#1884
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C4 ◁ C22×C4 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #20295793C2semidirect
2. #20295043C2semidirect
3. #20295000C2semidirect
4. #20294786C2semidirect
14. C4⋊Q8×C109C4semidirect
15. #127×C109C4semidirect
16. #124×C109C4semidirect
17. #124×C109C4semidirect
23. #13182013D4semidirect
96. C109#1884semidirect
107. C4⋊Q8Dic109semidirect
108. #127Dic109semidirect
109. #124Dic109semidirect
110. #124Dic109semidirect

Maximal subgroups

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

subgroupindex
#202957932
#202950432
#202950002
#202947862
#532×C1092
#1884109