Finite Group Databasebeta

← #28373434

Subgroups — #28373434

Order 13952.

392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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#20295577C211yesmaximal, characteristic
2#125×D109C211yesmaximal, characteristic, complemented
3#20295394C211yesmaximal, characteristic, complemented
4#20295392C211yesmaximal, characteristic, complemented
5#20295391C211yesmaximal, characteristic, complemented
6#20295382C214yesmaximal, complemented
7#20295026C214yesmaximal, complemented
8#20294978C211yesmaximal, characteristic, complemented
9#491×C109C211yesmaximal, characteristic, complemented
10C2×#13182030C2212yes—
11C2×#13182012C2212yes—
12#16812696C2211yescharacteristic
13#16812691C2211yescharacteristic
14#16812690C2212yes—
15#16812689—22no—
16#16812688C2212yes—
17#16812674—22no—
18#16812661—22no—
19C4⋊C4×D109—22no—
20C4⋊C4×D109C2212yes—
21C42×D109C2211yescharacteristic
22#16812623C2214yes—
23#16812621C2214yes—
24#16812619C2214yes—
25#16812610C2211yescharacteristic
26C8×Dic109C2212yes—
27C4⋊Q8×C109C2211yescharacteristic
28#125×C109C2211yescharacteristic
29#103×C109C2214yes—
30#97×C109C2211yescharacteristic
31#13182030—28no—
32C2×D436—22no—
33C2×D436—22no—
34C2×D436C2312yes—
35C2×C4×D109—22no—
36C2×C4×D109—22no—
37C2×C4×D109D412yes—
38C2×C4×D109C2311yescharacteristic
39#13182012—24no—
40C2×#11724784C2312yes—
41C4⋊Dic109—22no—
42C4⋊Dic109C2312yes—
43#13182008—22no—
44#13182008—22no—
45#13182008—22no—
46#13182006—24no—
47C4×Dic109D412yes—
48C4×Dic109C2311yescharacteristic
49C2×Q8×C109C2312yes—
50C2×C8×C109C2312yes—
51C4⋊C4×C109—22no—
52C4⋊C4×C109—22no—
53C4⋊C4×C109C2312yes—
54C42×C109C2311yescharacteristic
55C22×D109—22no—
56C22×D109C2×D411yescharacteristic
57Q8×C109—24no—
58C2×C4×C109—22no—
59C2×C4×C109—22no—
60C2×C4×C109C2×D412yes—
61C2×C4×C109C2411yescharacteristic
62C2×Dic109—22no—
63C2×Dic109C2×D412yes—
64C2×Dic109C2×D411yescharacteristic
65D436—24no—
66D436—44no—
67D436—44no—
68C4×D109—42no—
69C4×D109—44no—
70C4×D109—44no—
71C4×D109#4114yes—
72C8×C109—22no—
73#11724784—22no—
74C22×C109C22×D411yescharacteristic
75C2×D109—22no—
76C2×D109—42no—
77C2×D109—44no—
78C2×D109#12412yes—
79C4×C109—22no—
80C4×C109—42no—
81C4×C109—42no—
82C4×C109C2×#4112yes—
83Dic109—22no—
84Dic109—42no—
85Dic109#12412yes—
86C2×C109C2×#12411yescharacteristic
87C2×C109#57512yes—
88D109—22no—
89D109—82no—
90#3142—1091nomaximal, Sylow
91C109#314211yescharacteristic, complemented, Sylow
92#532—1091no—
93C2×#125—1091no—
94#491—1091no—
95#491D10911yescharacteristic, complemented
96#490—1091no—
97#490—1091no—
98#488—1094no—
99#417—1094no—
100C4×M16—1091no—
101C2×#41—1092no—
102C2×M16—1092no—
103C4⋊Q8C2×D10911yescharacteristic
104#127—1091no—
105#125—1092no—
106#125—1091no—
107#125—2182no—
108#125C2×D10911yescharacteristic
109#124—1092no—
110#121—2182no—
111C4×D4—2182no—
112C2×C4⋊C4—1092no—
113C2×C4⋊C4—2182no—
114C2×C42—1091no—
115#103—1094no—
116#103C2×D10914yes—
117#102—1094no—
118#102—1094no—
119#97—1091no—
120#97C2×D10911yescharacteristic
121C4×C8—1092no—
122#41—2188no—
123C2×Q8C22×D10912yes—
124C2×D4—1092no—
125C2×D4—2182no—
126C2×D4—2182no—
127C22×C4—1091no—
128C22×C4—1092no—
129C22×C4—2182no—
130C22×C4—2182no—
131M16—2184no—
132C2×C8—1092no—
133C2×C8C22×D10912yes—
134C4⋊C4—22no—
135C4⋊C4—22no—
136C4⋊C4—1092no—
137C4⋊C4—2182no—
138C4⋊C4—2182no—
139C4⋊C4—2182no—
140C4⋊C4—2182no—
141C4⋊C4C22×D10912yes—
142C22⋊C4—2184no—
143C42—1092no—
144C42—1091no—
145C42C22×D10911yescharacteristic
146C23—1091no—
147C23—2182no—
148Q8—24no—
149D4—4364no—
150D4—4364no—
151D4—2184no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—1091no—
155C2×C4—1094no—
156C2×C4—1092no—
157C2×C4—4362no—
158C2×C4—4364no—
159C2×C4—4364no—
160C2×C4—2182no—
161C2×C4D4×D10912yes—
162C2×C4C23×D10911yescharacteristic
163C8—22no—
164C8—2182no—
165C22—1092no—
166C22—4362no—
167C22—4364no—
168C22—2182no—
169C22C2×D4×D10911yescharacteristic
170C4—22no—
171C4—42no—
172C4—42no—
173C4—1092no—
174C4—4362no—
175C4—2182no—
176C4#41×D10912yes—
177C2—8722no—
178C2—2182no—
179C2#124×D10911yescharacteristic
180C2#2029582512yes—
subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#491×C109C2
socleC22×C109C22×D4
prime radical#20295577C2
hypercenter#491D109
hypocenterC109#3142
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #125×D109C2semidirect
3. #20295394C2semidirect
4. #20295392C2semidirect
5. #20295391C2semidirect
6. #20295382C2semidirect
7. #20295026C2semidirect
8. #20294978C2semidirect
9. #491×C109C2semidirect
91. C109#3142semidirect
95. #491D109semidirect

Maximal subgroups

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

subgroupindex
#202955772
#125×D1092
#202953942
#202953922
#202953912
#202953822
#202950262
#202949782
#491×C1092
#3142109