Finite Group Databasebeta

← #28337375

Subgroups — #28337375

Order 13696.

276 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C22×#13133808C211yesmaximal, characteristic
2C2×#16812044C211yesmaximal, characteristic
3#20292635C211yesmaximal, characteristic
4C2×#16812028C211yesmaximal, characteristic
5C2×#16812027C211yesmaximal, characteristic
6#20292583C211yesmaximal, characteristic
7#419×C107C211yesmaximal, characteristic
8C22×Dic214C2211yescharacteristic
9C2×#13133808—22no—
10C2×#13133808—21no—
11C2×#13133808—21no—
12C2×#13133808C414yescomplemented
13C2×#13133802C2211yescharacteristic
14C2×#13133802C2211yescharacteristic
15C22×C107⋊C8C2211yescharacteristic
16#16812044—22no—
17#16812032—22no—
18#16812028—22no—
19#16812027—22no—
20#16812020—21no—
21C4×C107⋊C8—21no—
22C22×Q8×C107C2211yescharacteristic
23C2×M16×C107C2211yescharacteristic
24#117×C107C2211yescharacteristic
25#103×C107—22no—
26C2×Dic214—21no—
27C2×Dic214—21no—
28C2×Dic214—21no—
29C2×Dic214—21no—
30C2×Dic214—21no—
31C2×Dic214C2×C412yes—
32C22×Dic107—21no—
33#13133808—24no—
34#13133808—24no—
35#13133802—21no—
36#13133802—21no—
37#13133802—21no—
38#13133802D412yes—
39C2×C107⋊C8—21no—
40C2×C107⋊C8—21no—
41C2×C107⋊C8C2×C412yes—
42C2×C107⋊C8D412yes—
43C2×C107⋊C8D411yescharacteristic
44C2×C107⋊C8D411yescharacteristic
45C2×Q8×C107—21no—
46C2×Q8×C107—21no—
47C2×Q8×C107—21no—
48C2×Q8×C107—21no—
49C2×Q8×C107—21no—
50C2×Q8×C107C2×C412yes—
51C22×C4×C107—21no—
52C22×C4×C107C2311yescharacteristic
53M16×C107—21no—
54M16×C107—21no—
55C2×C8×C107—21no—
56C4⋊C4×C107D412yes—
57C22⋊C4×C107—21no—
58C42×C107—21no—
59C23×C107#4111yescharacteristic
60Q8×C107—22no—
61Q8×C107—22no—
62Q8×C107—41no—
63Q8×C107—41no—
64C2×C4×C107—22no—
65C2×C4×C107—22no—
66C2×C4×C107—41no—
67C2×C4×C107—41no—
68C2×C4×C107C22×C411yescharacteristic
69C2×C4×C107C2×D411yescharacteristic
70C2×C4×C107C2×D411yescharacteristic
71C2×C4×C107C2×D411yescharacteristic
72C2×C4×C107C2×D411yescharacteristic
73C2×C4×C107#4111yescharacteristic
74C2×Dic107—22no—
75C2×Dic107—41no—
76C2×Dic107—41no—
77Dic214—22no—
78Dic214—22no—
79Dic214—41no—
80Dic214—41no—
81C8×C107—41no—
82C107⋊C8—22no—
83C107⋊C8—41no—
84C107⋊C8C22⋊C412yes—
85C107⋊C8C22⋊C412yes—
86C22×C107—22no—
87C22×C107C4×D411yescharacteristic
88C22×C107#12111yescharacteristic
89C22×C107#12411yescharacteristic
90C4×C107—42no—
91C4×C107—42no—
92C4×C107C2×C22⋊C411yescharacteristic
93C4×C107C4×D411yescharacteristic
94C4×C107#12111yescharacteristic
95C4×C107#12711yescharacteristic
96Dic107—42no—
97C2×C107—21no—
98C2×C107—21no—
99C2×C107#39011yescharacteristic
100C2×C107#47312yes—
101#1979—1071nomaximal, Sylow
102C107#197911yescharacteristic, complemented, Sylow
103C22×Q16—1071no—
104C2×#108—1071no—
105#419—1071no—
106#419D10711yescharacteristic
107C2×#101—1071no—
108C2×#101—1071no—
109#405—1071no—
110C22×Q8—1071no—
111C22×Q8C2×D10711yescharacteristic
112C2×Q16—1074no—
113C2×Q16—2141no—
114C2×Q16—2141no—
115C2×Q16—2142no—
116C2×M16—1071no—
117C2×M16—1071no—
118C2×M16C2×D10711yescharacteristic
119C22×C8—1071no—
120#117C2×D10711yescharacteristic
121#108—2142no—
122#103—22no—
123#103—2142no—
124#101—2142no—
125#101—2142no—
126#97—2141no—
127C4×C8—2141no—
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—1072no—
134C2×Q8—2141no—
135C2×Q8—2141no—
136C2×Q8—2141no—
137C2×Q8—2141no—
138C2×Q8—2141no—
139C2×Q8C4×D10712yes—
140C22×C4—21no—
141C22×C4—2141no—
142C22×C4C22×D10711yescharacteristic
143Q16—2144no—
144Q16—2144no—
145M16—21no—
146M16—21no—
147M16—1072no—
148M16—2141no—
149M16—2141no—
150M16—2141no—
151C2×C8—21no—
152C2×C8—1072no—
153C2×C8—1071no—
154C2×C8—1071no—
155C2×C8—1072no—
156C2×C8—2141no—
157C2×C8—2141no—
158C4⋊C4C22⋊D10712yes—
159C22⋊C4—21no—
160C42—21no—
161C23#1313381711yescharacteristic
162Q8—22no—
163Q8—22no—
164Q8—41no—
165Q8—41no—
166Q8—4281no—
167Q8—4281no—
168Q8—2142no—
169Q8—2142no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—4281no—
175C2×C4—4281no—
176C2×C4—2142no—
177C2×C4C2×C4×D10711yescharacteristic
178C2×C4D4×D10711yescharacteristic
179C2×C4D4×D10711yescharacteristic
180C2×C4D4×D10711yescharacteristic
181C2×C4C2×C22⋊D10711yescharacteristic
182C2×C4#1313381811yescharacteristic
183C8—41no—
184C8—1072no—
185C8—1072no—
186C8—4281no—
187C8—2142no—
188C22—22no—
189C22(C22⋊D107)⋊C411yescharacteristic
190C22#1681208111yescharacteristic
191C22#1681209511yescharacteristic
192C4—42no—
193C4—42no—
194C4—4282no—
195C4C22⋊C4×D10711yescharacteristic
196C4C4×C22⋊D10711yescharacteristic
197C4#1681208211yescharacteristic
198C4#1681210511yescharacteristic
199C2—21no—
200C2—21no—
201C2#2029252711yescharacteristic
202C2#2029290012yes—
subgroupG/H
centerC22#16812081
commutatorC2×C4×C107C22×C4
FrattiniC22×C4C22×D107
Fitting#419×C107C2
socleC22×C107#121
prime radicalC23×C107#41
cosocleC22×C4×C107C23
hypercenter#419D107
hypocenterC107#1979
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
12. C2×#13133808C4semidirect
102. C107#1979semidirect

Maximal subgroups

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

subgroupindex
C22×#131338082
C2×#168120442
#202926352
C2×#168120282
C2×#168120272
#202925832
#419×C1072
#1979107