Finite Group Databasebeta

← #28363567

Subgroups — #28363567

Order 13952.

314 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 85 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#20295600C211yesmaximal, characteristic
2#20295504C211yesmaximal, characteristic, complemented
3#20295042C212yesmaximal
4#20294783C212yesmaximal, complemented
5C2×#101×C109C211yesmaximal, characteristic, complemented
6C2×#13182029C2211yescharacteristic
7#16812697C412yescomplemented
8#16812688C412yescomplemented
9#16812682—22no—
10#16812675—22no—
11Q8×Dic109—24no—
12#16812658—22no—
13#16812658C2211yescharacteristic
14#16812658C2212yes—
15#16812625—24no—
16C22×Q8×C109C2211yescharacteristic
17C2×M16×C109C2212yes—
18#101×C109—22no—
19#13182029—22no—
20#13182029—22no—
21C2×Dic218C2×C411yescharacteristic
22C2×D436C2×C411yescharacteristic
23C2×C22⋊D109—21no—
24C2×C4×D109—21no—
25C4⋊Dic109—24no—
26C4⋊Dic109—22no—
27C4⋊Dic109—21no—
28#13182008—24no—
29C22⋊Dic109—22no—
30C22⋊Dic109—21no—
31#13182006—24no—
32C4×Dic109—24no—
33C4×Dic109C2×C412yes—
34C4×Dic109D414yes—
35C2×Q8×C109—22no—
36C2×Q8×C109—22no—
37C2×Q8×C109C2×C412yes—
38C2×Q8×C109D412yes—
39C22×C4×C109D412yes—
40C22×C4×C109C2311yescharacteristic
41M16×C109—22no—
42M16×C109—22no—
43C2×C8×C109—22no—
44C23×C109C2×D411yescharacteristic
45C22×D109—21no—
46Q8×C109—24no—
47Q8×C109—24no—
48C2×C4×C109—22no—
49C2×C4×C109—22no—
50C2×C4×C109C22⋊C414yes—
51C2×C4×C109C22×C411yescharacteristic
52C2×C4×C109C2×D412yes—
53C2×C4×C109C2×D411yescharacteristic
54C2×C4×C109#4112yes—
55C22⋊D109—41no—
56C22⋊D109—41no—
57C2×Dic109—22no—
58C2×Dic109—21no—
59C2×Dic109—24no—
60D436—22no—
61C4×D109—42no—
62Dic218—22no—
63C8×C109—42no—
64C22×C109—41no—
65C22×C109C2×C22⋊C411yescharacteristic
66C22×C109#12011yescharacteristic
67C22×C109#12311yescharacteristic
68C2×D109—42no—
69C2×D109—41no—
70C4×C109—24no—
71C4×C109C4×D412yes—
72C4×C109#12112yes—
73Dic109—44no—
74Dic109—42no—
75Dic109—41no—
76C2×C109—21no—
77C2×C109—21no—
78C2×C109—21no—
79C2×C109#38611yescharacteristic
80D109—81no—
81#1912—1091nomaximal, Sylow
82C109#191211yescharacteristic, complemented, Sylow
83#536—1091no—
84#519—1091no—
85#421—1092no—
86C2×#101D10911yescharacteristic, complemented
87H(3,ℤ/4)—1092no—
88C2×#41—1091no—
89C22×Q8C2×D10911yescharacteristic
90C2×M16C2×D10912yes—
91C4⋊Q8—1092no—
92#124—1092no—
93#123—2182no—
94C22⋊Q8—2182no—
95C4×Q8—2184no—
96#117—1092no—
97#117—1091no—
98#117—2182no—
99#104—2184no—
100#101—22no—
101#41—2182no—
102#41—2182no—
103C2×Q8—22no—
104C2×Q8—22no—
105C2×Q8—1091no—
106C2×Q8C4×D10912yes—
107C2×Q8C22⋊D10912yes—
108C2×D4—1091no—
109C2×D4—2181no—
110C22×C4—2181no—
111C22×C4D43612yes—
112C22×C4C22×D10911yescharacteristic
113M16—22no—
114M16—22no—
115C2×C8—22no—
116C4⋊C4—2184no—
117C4⋊C4—2184no—
118C4⋊C4—2182no—
119C4⋊C4—2181no—
120C22⋊C4—2182no—
121C22⋊C4—2181no—
122C22⋊C4—2184no—
123C42—1092no—
124C42—1094no—
125C42—2184no—
126C23—2181no—
127C23C2×D43611yescharacteristic
128Q8—24no—
129Q8—24no—
130Q8—2182no—
131D4—4361no—
132D4—4361no—
133D4—2182no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—4362no—
137C2×C4—2182no—
138C2×C4—2181no—
139C2×C4—2184no—
140C2×C4#1318200614yes—
141C2×C4C2×C4×D10911yescharacteristic
142C2×C4D4×D10912yes—
143C2×C4C2×C22⋊D10911yescharacteristic
144C2×C4#1318202812yes—
145C8—42no—
146C22—41no—
147C22—4362no—
148C22—4361no—
149C22C2×#1318200611yescharacteristic
150C22#1681266911yescharacteristic
151C22#1681268311yescharacteristic
152C4—24no—
153C4—4364no—
154C4—4362no—
155C4—4361no—
156C4#1681265912yes—
157C4#1681267112yes—
158C2—21no—
159C2—21no—
160C2—21no—
161C2—8721no—
162C2#2029490311yescharacteristic
subgroupG/H
centerC2#20294903
commutatorC2×C4×C109C22×C4
FrattiniC22×C4C22×D109
FittingC2×#101×C109C2
socleC2×C109#386
prime radicalC2×#13182029C22
cosocleC22×C4×C109C23
hypercenterC2×#101D109
hypocenterC109#1912
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. #20295504C2semidirect
4. #20294783C2semidirect
5. C2×#101×C109C2semidirect
7. #16812697C4semidirect
8. #16812688C4semidirect
82. C109#1912semidirect
86. C2×#101D109semidirect

Maximal subgroups

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

subgroupindex
#202956002
#202955042
#202950422
#202947832
C2×#101×C1092
#1912109