Finite Group Databasebeta

← #355×D109 #28364708

Subgroups — #355×D109 #28364708

Order 13952.

260 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 57 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#124×D109C211yesmaximal, characteristic
2#101×D109C212yesmaximal, complemented
3#20294823C211yesmaximal, characteristic, complemented
4#20294822C212yesmaximal, complemented
5#355×C109C211yesmaximal, characteristic, complemented
6C2×Q8×D109C2211yescharacteristic
7C2×D4×D109C411yescharacteristic
8M16×D109—22no—
9#16812688C2211yescharacteristic
10#16812687C411yescharacteristic
11#16812686C411yescharacteristic
12#16812685—22no—
13C22⋊C4×D109—22no—
14C42×D109C411yescharacteristic
15#16812618C2212yescomplemented
16#16812617—22no—
17#124×C109C2211yescharacteristic
18#101×C109C2212yescomplemented
19C23×D109—21no—
20C2×Dic218C2×C411yescharacteristic
21C2×Dic218D412yes—
22Q8×D109—41no—
23Q8×D109—41no—
24C2×D436C2×C411yescharacteristic
25C2×C22⋊D109—21no—
26D4×D109—41no—
27D4×D109—41no—
28C2×C4×D109—21no—
29C2×C4×D109C2×C411yescharacteristic
30C2×C4×D109D412yes—
31#13182013—22no—
32#13182012—42no—
33C8×D109—42no—
34C22⋊Dic109—22no—
35#13182006—22no—
36#13182006—22no—
37C4×Dic109—21no—
38C4×Dic109C2×C411yescharacteristic
39C2×Q8×C109C2311yescharacteristic
40C2×D4×C109C2×C411yescharacteristic
41M16×C109—22no—
42C22⋊C4×C109—22no—
43C42×C109C2×C411yescharacteristic
44C23×C109—21no—
45C22×D109—21no—
46C22×D109—44no—
47C22×D109—41no—
48C22×D109—41no—
49C22×D109C22⋊C411yescharacteristic
50Q8×C109—41no—
51D4×C109—41no—
52C2×C4×C109—21no—
53C2×C4×C109C22×C411yescharacteristic
54C2×C4×C109C2×D412yes—
55C22⋊D109—42no—
56C2×Dic109—21no—
57C2×Dic109C22⋊C411yescharacteristic
58C2×Dic109C22⋊C412yes—
59D436—41no—
60C4×D109—22no—
61C4×D109—22no—
62C4×D109—21no—
63C4×D109—21no—
64C4×D109—42no—
65Dic218—41no—
66Dic218—42no—
67C8×C109—42no—
68#11724784—42no—
69C22×C109—42no—
70C22×C109—41no—
71C22×C109C2×C22⋊C411yescharacteristic
72C2×D109—22no—
73C2×D109—42no—
74C2×D109—41no—
75C2×D109—82no—
76C2×D109—82no—
77C2×D109#9911yescharacteristic
78C2×D109#9911yescharacteristic
79C4×C109—22no—
80C4×C109—21no—
81C4×C109—41no—
82Dic109—22no—
83Dic109—21no—
84Dic109—41no—
85C2×C109—21no—
86C2×C109—81no—
87C2×C109C2×#9911yescharacteristic
88D109—21no—
89D109—81no—
90D109#35512yesdirect product factor
91C2×#355—1091nomaximal, Sylow
92C109C2×#35511yescharacteristic, complemented, Sylow
93C2×#124—1091no—
94C2×#101—1092no—
95#355—1091no—
96#355—1092no—
97#355D10911yescharacteristic, direct product factor
98C22×Q8—1091no—
99C22×D4—1091no—
100C2×M16—2182no—
101#124—1091no—
102#124—1091no—
103#124—1091no—
104#124—2182no—
105#124C2×D10911yescharacteristic
106C2×C22⋊C4—2182no—
107C2×C42—1091no—
108#101—1092no—
109#101—2182no—
110#101C2×D10912yescomplemented
111C24—2181no—
112C2×Q8—1091no—
113C2×Q8—1092no—
114C2×Q8—4361no—
115C2×Q8—4361no—
116C2×Q8C22×D10911yescharacteristic
117C2×D4—1091no—
118C2×D4—4361no—
119C2×D4—4361no—
120C2×D4—2181no—
121C2×D4C4×D10911yescharacteristic
122C22×C4—1091no—
123C22×C4—1092no—
124C22×C4—2181no—
125M16—22no—
126M16—4362no—
127M16—2182no—
128C2×C8—4362no—
129C22⋊C4—22no—
130C22⋊C4—2182no—
131C22⋊C4—2182no—
132C22⋊C4—2182no—
133C42—1091no—
134C42—2181no—
135C42C4×D10911yescharacteristic
136C23—21no—
137C23—1091no—
138C23—4361no—
139C23—4361no—
140C23—4364no—
141C23—2181no—
142Q8—41no—
143Q8—4362no—
144Q8—4361no—
145D4—41no—
146D4—4361no—
147D4—4362no—
148C2×C4—21no—
149C2×C4—1091no—
150C2×C4—1092no—
151C2×C4—4362no—
152C2×C4—2182no—
153C2×C4—2182no—
154C2×C4—2181no—
155C2×C4—2181no—
156C2×C4—2181no—
157C2×C4C2×C4×D10911yescharacteristic
158C2×C4D4×D10912yes—
159C8—42no—
160C8—4362no—
161C22—42no—
162C22—41no—
163C22—8722no—
164C22—8722no—
165C22—1091no—
166C22—1091no—
167C22—4362no—
168C22—4361no—
169C22—2182no—
170C22C22⋊C4×D10911yescharacteristic
171C4—22no—
172C4—21no—
173C4—41no—
174C4—4361no—
175C4—2181no—
176C4—2182no—
177C2—21no—
178C2—81no—
179C2—8721no—
180C2—1092no—
181C2—2181no—
182C2#99×D10911yescharacteristic
subgroupG/H
centerC2#99×D109
commutatorC2×C4×C109C22×C4
FrattiniC2×Q8C22×D109
Fitting#355×C109C2
socleC2×C109C2×#99
prime radicalC2×D4×D109C4
cosocleC2×Q8×C109C23
hypercenter#355D109
hypocenterC109C2×#355
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. #20294823C2semidirect
4. #20294822C2semidirect
5. #355×C109C2semidirect
15. #16812618C22semidirect
18. #101×C109C22semidirect
90. D109#355direct (N × H)
92. C109C2×#355semidirect
97. #355D109direct (N × H)
110. #101C2×D109semidirect

Maximal subgroups

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

subgroupindex
#124×D1092
#101×D1092
#202948232
#202948222
#355×C1092
C2×#355109