Finite Group Databasebeta

← #28379323

Subgroups — #28379323

Order 13952.

250 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 54 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#20296012C212yesmaximal, complemented
2#20295936C212yesmaximal, complemented
3#20295934C212yesmaximal, complemented
4#20295572C211yesmaximal, characteristic
5D109⋊M16—22no—
6#16812760C2214yes—
7#16812759—22no—
8C2×#13182029C2211yescharacteristic
9#16812697C2211yescharacteristic
10#16812695C411yescharacteristic
11#16812688C411yescharacteristic
12#16812686C2211yescharacteristic
13#16812671—22no—
14C4×C22⋊D109—22no—
15C2×C4×Dic109C411yescharacteristic
16C2×#41×C109C411yescharacteristic
17#13182039—42no—
18#13182038—24no—
19D109⋊C8—42no—
20#13182029—41no—
21#13182029—41no—
22C2×Dic218C2311yescharacteristic
23C2×D436C2×C411yescharacteristic
24C2×C22⋊D109—22no—
25C2×C22⋊D109D412yes—
26C22×Dic109—21no—
27C2×C4×D109D412yes—
28#13182008—22no—
29C22⋊Dic109—22no—
30#13182006—22no—
31C4×Dic109—21no—
32C4×Dic109C2×C411yescharacteristic
33C4×Dic109C2×C411yescharacteristic
34#41×C109—41no—
35#41×C109—41no—
36C2×Q8×C109C2×C411yescharacteristic
37C2×D4×C109—21no—
38C2×D4×C109C2×C411yescharacteristic
39C22×C4×C109—21no—
40C22×C4×C109C2×C411yescharacteristic
41C23×C109—21no—
42C23×C109C22⋊C411yescharacteristic
43C22×D109C22⋊C412yes—
44Q8×C109—41no—
45D4×C109—41no—
46D4×C109—42no—
47C2×C4×C109—21no—
48C2×C4×C109—21no—
49C2×C4×C109—21no—
50C2×C4×C109—41no—
51C2×C4×C109—41no—
52C2×C4×C109C22⋊C411yescharacteristic
53C2×C4×C109C22×C411yescharacteristic
54C22⋊D109—42no—
55C22⋊D109—44no—
56C2×Dic109—21no—
57C2×Dic109—21no—
58C2×Dic109—42no—
59C2×Dic109C2×D412yes—
60D436—41no—
61C4×D109—22no—
62C4×D109—22no—
63Dic218—41no—
64#11724786—44no—
65C22×C109—21no—
66C22×C109—41no—
67C22×C109—42no—
68C22×C109—41no—
69C22×C109C2×C22⋊C411yescharacteristic
70C2×D109—22no—
71C2×D109—42no—
72C4×C109—21no—
73C4×C109—41no—
74C4×C109#9911yescharacteristic
75C4×C109#9911yescharacteristic
76Dic109—22no—
77Dic109—22no—
78Dic109—41no—
79C2×C109—21no—
80C2×C109—41no—
81C2×C109—81no—
82C2×C109C2×#9911yescharacteristic
83D109—42no—
84#2132—1091nomaximal, Sylow
85C109#213211yescharacteristic, complemented, Sylow
86#532—1091no—
87#413—1092no—
88#356—1092no—
89#355—1092no—
90C2×#41—1091no—
91C2×#41#8913711yescharacteristic
92C2×M16—2182no—
93C4⋊Q8—1091no—
94#127—1091no—
95#124—1091no—
96#124—1091no—
97#121—2182no—
98C4×D4—2182no—
99C2×C42—1091no—
100#101—1094no—
101#100—2182no—
102#41—41no—
103#41—41no—
104#41—4361no—
105#41—4361no—
106C2×Q8—1091no—
107C2×Q8C2×#8913711yescharacteristic
108C2×D4—21no—
109C2×D4—1092no—
110C2×D4—1091no—
111C2×D4—2182no—
112C2×D4C2×#8913711yescharacteristic
113C22×C4—21no—
114C22×C4—1092no—
115C22×C4—2181no—
116C22×C4C2×#8913711yescharacteristic
117M16—4362no—
118M16—2184no—
119C2×C8—4362no—
120C4⋊C4—2182no—
121C22⋊C4—2182no—
122C22⋊C4—2182no—
123C42—1091no—
124C42—1091no—
125C42—2181no—
126C23—21no—
127C23—1092no—
128C23C22⋊#8913711yescharacteristic
129Q8—41no—
130Q8—4361no—
131D4—41no—
132D4—42no—
133D4—4361no—
134D4—4362no—
135D4—4364no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—1092no—
142C2×C4—4362no—
143C2×C4—2181no—
144C2×C4—2181no—
145C2×C4—2182no—
146C2×C4—2182no—
147C2×C4C22⋊#8913711yescharacteristic
148C2×C4C22×#8913711yescharacteristic
149C8—4364no—
150C22—21no—
151C22—41no—
152C22—42no—
153C22—41no—
154C22—4362no—
155C22—2182no—
156C22C2×C22⋊#8913711yescharacteristic
157C4—21no—
158C4—41no—
159C4—4361no—
160C4—2182no—
161C4—2182no—
162C4#1681275711yescharacteristic
163C4#1681275711yescharacteristic
164C2—21no—
165C2—41no—
166C2—81no—
167C2—4362no—
168C2C2×#1681275711yescharacteristic
subgroupG/H
centerC4#16812757
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
FittingC2×#41×C109C4
socleC2×C109C2×#99
prime radical#20295572C2
cosocleC2×Dic218C23
hypercenterC2×#41#89137
hypocenterC109#2132
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #20296012C2semidirect
2. #20295936C2semidirect
3. #20295934C2semidirect
85. C109#2132semidirect

Maximal subgroups

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

subgroupindex
#202960122
#202959362
#202959342
#202955722
#2132109