Finite Group Databasebeta

← #28364718

Subgroups — #28364718

Order 13952.

230 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 55 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#20295596C211yesmaximal, characteristic
2#101×D109C212yesmaximal, complemented
3#20294824C212yesmaximal, complemented
4#20294823C211yesmaximal, characteristic, complemented
5#355×C109C211yesmaximal, characteristic, complemented
6C2×#13182028C411yescharacteristic
7C2×Q8×D109C2211yescharacteristic
8M16×D109—22no—
9#16812699C411yescharacteristic
10#16812697C2211yescharacteristic
11#16812686C411yescharacteristic
12#16812681—22no—
13#16812676—22no—
14#16812656C411yescharacteristic
15#16812618C2212yes—
16#16812617—22no—
17#124×C109C2211yescharacteristic
18#101×C109C2212yes—
19#13182028—42no—
20C2×Dic218C2×C411yescharacteristic
21C2×Dic218C2×C411yescharacteristic
22C2×Dic218D412yes—
23Q8×D109—42no—
24C2×C22⋊D109—21no—
25C22×Dic109—21no—
26C2×C4×D109C2×C411yescharacteristic
27C2×C4×D109D412yes—
28#13182013—22no—
29#13182012—42no—
30C8×D109—42no—
31C4⋊Dic109—22no—
32#13182008—22no—
33#13182008—21no—
34C22⋊Dic109—22no—
35#13182006—21no—
36C4×Dic109C2×C411yescharacteristic
37C2×Q8×C109C2311yescharacteristic
38C2×D4×C109C2×C411yescharacteristic
39M16×C109—22no—
40C22⋊C4×C109—22no—
41C42×C109C2×C411yescharacteristic
42C23×C109—21no—
43C22×D109C22⋊C411yescharacteristic
44Q8×C109—41no—
45D4×C109—41no—
46C2×C4×C109—21no—
47C2×C4×C109C22×C411yescharacteristic
48C2×C4×C109C2×D412yes—
49C22⋊D109—42no—
50C2×Dic109—21no—
51C2×Dic109—21no—
52C2×Dic109—42no—
53C2×Dic109C22⋊C412yes—
54C2×Dic109C22⋊C411yescharacteristic
55C4×D109—22no—
56C4×D109—22no—
57C4×D109—22no—
58Dic218—41no—
59Dic218—42no—
60Dic218—41no—
61C8×C109—42no—
62#11724784—42no—
63C22×C109—42no—
64C22×C109—41no—
65C22×C109C2×C22⋊C411yescharacteristic
66C2×D109—41no—
67C2×D109#9912yes—
68C4×C109—22no—
69C4×C109—21no—
70C4×C109—41no—
71Dic109—21no—
72Dic109—22no—
73Dic109—41no—
74Dic109—41no—
75C2×C109—21no—
76C2×C109—81no—
77C2×C109C2×#9911yescharacteristic
78D109—22no—
79#2133—1091nomaximal, Sylow
80C109#213311yescharacteristic, complemented, Sylow
81#536—1091no—
82C2×#101—1092no—
83#356—1092no—
84#355—1091no—
85#355D10911yescharacteristic, complemented
86C2×#41—1091no—
87C22×Q8—1091no—
88C2×M16—2182no—
89C4⋊Q8—1091no—
90C4⋊Q8—1091no—
91#124—1091no—
92#124C2×D10911yescharacteristic
93#123—2182no—
94C22⋊Q8—2182no—
95#117—1091no—
96#101—1092no—
97#101—2182no—
98#101C2×D10912yes—
99#41—4362no—
100C2×Q8—1091no—
101C2×Q8—1092no—
102C2×Q8—1091no—
103C2×Q8—4362no—
104C2×Q8C22×D10911yescharacteristic
105C2×D4—2181no—
106C2×D4C4×D10911yescharacteristic
107C22×C4—1091no—
108C22×C4—1092no—
109C22×C4—2181no—
110M16—22no—
111M16—4362no—
112M16—2182no—
113C2×C8—4362no—
114C4⋊C4—2181no—
115C4⋊C4—2182no—
116C4⋊C4—2182no—
117C22⋊C4—22no—
118C22⋊C4—2181no—
119C22⋊C4—2182no—
120C42—1091no—
121C42C4×D10911yescharacteristic
122C23—21no—
123C23—1091no—
124Q8—41no—
125Q8—4361no—
126Q8—4362no—
127Q8—4361no—
128D4—41no—
129D4—4362no—
130C2×C4—21no—
131C2×C4—1092no—
132C2×C4—1091no—
133C2×C4—4362no—
134C2×C4—2182no—
135C2×C4—2182no—
136C2×C4—2182no—
137C2×C4—2181no—
138C2×C4—2181no—
139C2×C4C2×C4×D10911yescharacteristic
140C2×C4D4×D10912yes—
141C8—42no—
142C8—4362no—
143C22—42no—
144C22—41no—
145C22—1092no—
146C22—4361no—
147C22C22⋊C4×D10911yescharacteristic
148C4—22no—
149C4—21no—
150C4—41no—
151C4—4361no—
152C4—4361no—
153C4—2181no—
154C4—2182no—
155C2—21no—
156C2—81no—
157C2—2182no—
158C2#99×D10911yescharacteristic
subgroupG/H
centerC2#99×D109
commutatorC2×C4×C109C22×C4
FrattiniC2×Q8C22×D109
Fitting#355×C109C2
socleC2×C109C2×#99
prime radicalC2×#13182028C4
cosocleC2×Q8×C109C23
hypercenter#355D109
hypocenterC109#2133
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #101×D109C2semidirect
3. #20294824C2semidirect
4. #20294823C2semidirect
5. #355×C109C2semidirect
80. C109#2133semidirect
85. #355D109semidirect

Maximal subgroups

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

subgroupindex
#202955962
#101×D1092
#202948242
#202948232
#355×C1092
#2133109