Finite Group Databasebeta

← #355×D107 #28338137

Subgroups — #355×D107 #28338137

Order 13696.

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×D107C211yesmaximal, characteristic
2#101×D107C212yesmaximal, complemented
3#20292424C211yesmaximal, characteristic, complemented
4#20292423C212yesmaximal, complemented
5#355×C107C211yesmaximal, characteristic, complemented
6C2×Q8×D107C2211yescharacteristic
7C2×D4×D107C411yescharacteristic
8M16×D107—22no—
9#16812098C2211yescharacteristic
10#16812097C411yescharacteristic
11#16812096C411yescharacteristic
12#16812095—22no—
13C22⋊C4×D107—22no—
14C42×D107C411yescharacteristic
15#16812028C2212yescomplemented
16#16812027—22no—
17#124×C107C2211yescharacteristic
18#101×C107C2212yescomplemented
19C23×D107—21no—
20C2×Dic214C2×C411yescharacteristic
21C2×Dic214D412yes—
22Q8×D107—41no—
23Q8×D107—41no—
24C2×D428C2×C411yescharacteristic
25C2×C22⋊D107—21no—
26D4×D107—41no—
27D4×D107—41no—
28C2×C4×D107—21no—
29C2×C4×D107C2×C411yescharacteristic
30C2×C4×D107D412yes—
31#13133802—22no—
32#13133801—42no—
33C8×D107—42no—
34C22⋊Dic107—22no—
35(C2×D107)⋊C4—22no—
36(C2×D107)⋊C4—22no—
37C4×Dic107—21no—
38C4×Dic107C2×C411yescharacteristic
39C2×Q8×C107C2311yescharacteristic
40C2×D4×C107C2×C411yescharacteristic
41M16×C107—22no—
42C22⋊C4×C107—22no—
43C42×C107C2×C411yescharacteristic
44C23×C107—21no—
45C22×D107—21no—
46C22×D107—44no—
47C22×D107—41no—
48C22×D107—41no—
49C22×D107C22⋊C411yescharacteristic
50Q8×C107—41no—
51D4×C107—41no—
52C2×C4×C107—21no—
53C2×C4×C107C22×C411yescharacteristic
54C2×C4×C107C2×D412yes—
55C22⋊D107—42no—
56C2×Dic107—21no—
57C2×Dic107C22⋊C411yescharacteristic
58C2×Dic107C22⋊C412yes—
59D428—41no—
60C4×D107—22no—
61C4×D107—22no—
62C4×D107—21no—
63C4×D107—21no—
64C4×D107—42no—
65Dic214—41no—
66Dic214—42no—
67C8×C107—42no—
68C107⋊C8—42no—
69C22×C107—42no—
70C22×C107—41no—
71C22×C107C2×C22⋊C411yescharacteristic
72C2×D107—22no—
73C2×D107—42no—
74C2×D107—41no—
75C2×D107—82no—
76C2×D107—82no—
77C2×D107#9911yescharacteristic
78C2×D107#9911yescharacteristic
79C4×C107—22no—
80C4×C107—21no—
81C4×C107—41no—
82Dic107—22no—
83Dic107—21no—
84Dic107—41no—
85C2×C107—21no—
86C2×C107—81no—
87C2×C107C2×#9911yescharacteristic
88D107—21no—
89D107—81no—
90D107#35512yesdirect product factor
91C2×#355—1071nomaximal, Sylow
92C107C2×#35511yescharacteristic, complemented, Sylow
93C2×#124—1071no—
94C2×#101—1072no—
95#355—1071no—
96#355—1072no—
97#355D10711yescharacteristic, direct product factor
98C22×Q8—1071no—
99C22×D4—1071no—
100C2×M16—2142no—
101#124—1071no—
102#124—1071no—
103#124—1071no—
104#124—2142no—
105#124C2×D10711yescharacteristic
106C2×C22⋊C4—2142no—
107C2×C42—1071no—
108#101—1072no—
109#101—2142no—
110#101C2×D10712yescomplemented
111C24—2141no—
112C2×Q8—1071no—
113C2×Q8—1072no—
114C2×Q8—4281no—
115C2×Q8—4281no—
116C2×Q8C22×D10711yescharacteristic
117C2×D4—1071no—
118C2×D4—4281no—
119C2×D4—4281no—
120C2×D4—2141no—
121C2×D4C4×D10711yescharacteristic
122C22×C4—1071no—
123C22×C4—1072no—
124C22×C4—2141no—
125M16—22no—
126M16—4282no—
127M16—2142no—
128C2×C8—4282no—
129C22⋊C4—22no—
130C22⋊C4—2142no—
131C22⋊C4—2142no—
132C22⋊C4—2142no—
133C42—1071no—
134C42—2141no—
135C42C4×D10711yescharacteristic
136C23—21no—
137C23—1071no—
138C23—4281no—
139C23—4281no—
140C23—4284no—
141C23—2141no—
142Q8—41no—
143Q8—4282no—
144Q8—4281no—
145D4—41no—
146D4—4281no—
147D4—4282no—
148C2×C4—21no—
149C2×C4—1071no—
150C2×C4—1072no—
151C2×C4—4282no—
152C2×C4—2142no—
153C2×C4—2142no—
154C2×C4—2141no—
155C2×C4—2141no—
156C2×C4—2141no—
157C2×C4C2×C4×D10711yescharacteristic
158C2×C4D4×D10712yes—
159C8—42no—
160C8—4282no—
161C22—42no—
162C22—41no—
163C22—8562no—
164C22—8562no—
165C22—1071no—
166C22—1071no—
167C22—4282no—
168C22—4281no—
169C22—2142no—
170C22C22⋊C4×D10711yescharacteristic
171C4—22no—
172C4—21no—
173C4—41no—
174C4—4281no—
175C4—2141no—
176C4—2142no—
177C2—21no—
178C2—81no—
179C2—8561no—
180C2—1072no—
181C2—2141no—
182C2#99×D10711yescharacteristic
subgroupG/H
centerC2#99×D107
commutatorC2×C4×C107C22×C4
FrattiniC2×Q8C22×D107
Fitting#355×C107C2
socleC2×C107C2×#99
prime radicalC2×D4×D107C4
cosocleC2×Q8×C107C23
hypercenter#355D107
hypocenterC107C2×#355
LCSG ▷ C2×C4×C107 ▷ C22×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #101×D107C2semidirect
3. #20292424C2semidirect
4. #20292423C2semidirect
5. #355×C107C2semidirect
15. #16812028C22semidirect
18. #101×C107C22semidirect
90. D107#355direct (N × H)
92. C107C2×#355semidirect
97. #355D107direct (N × H)
110. #101C2×D107semidirect

Maximal subgroups

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

subgroupindex
#124×D1072
#101×D1072
#202924242
#202924232
#355×C1072
C2×#355107