Finite Group Databasebeta

← #28346747

Subgroups — #28346747

Order 13696.

382 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 121 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#20293104C211yesmaximal, characteristic, complemented
2#20292948C212yesmaximal, complemented
3#20292931C212yesmaximal, complemented
4#20292824C212yesmaximal, complemented
5#20292765C212yesmaximal, complemented
6#20292727C212yesmaximal, complemented
7C4×#13133806C212yesmaximal, complemented
8#20292688C211yesmaximal, characteristic, complemented
9#540×C107C211yesmaximal, characteristic
10C22×Dic214C2211yescharacteristic
11C2×#13133806C2212yes—
12C2×#13133806C2212yes—
13C4×Dic214C2212yes—
14C4×Dic214C2212yes—
15#16812074—22no—
16#16812068C2211yescharacteristic
17#16812065—22no—
18#16812042C2212yes—
19#16812040C2212yes—
20C4⋊(C107⋊C8)C2212yes—
21#16812032C2212yes—
22#16812032C2212yes—
23#16812030C2212yes—
24#16812030C2212yes—
25C22⋊(C107⋊C8)C2212yes—
26#16812020C2211yescharacteristic
27C4×C107⋊C8C2211yescharacteristic
28#127×C107C2211yescharacteristic
29#125×C107C2211yescharacteristic
30#123×C107—22no—
31#121×C107—22no—
32#121×C107C2212yes—
33C4×D4×C107C2212yes—
34#117×C107C2211yescharacteristic
35C2×Dic214—21no—
36C2×Dic214—24no—
37C2×Dic214C2312yes—
38C22×Dic107—21no—
39#13133806—24no—
40#13133806—24no—
41C2×C107⋊C8C2312yes—
42C2×C107⋊C8C2312yes—
43C4⋊Dic107C2312yes—
44Dic107⋊C4—22no—
45Dic107⋊C4—22no—
46C22⋊Dic107—21no—
47C4×Dic107—22no—
48C4×Dic107—22no—
49C4×Dic107—21no—
50C2×D4×C107—22no—
51C2×D4×C107—22no—
52C2×D4×C107C2312yes—
53C22×C4×C107—22no—
54C22×C4×C107C2311yescharacteristic
55C4⋊C4×C107—22no—
56C4⋊C4×C107D412yes—
57C4⋊C4×C107C2312yes—
58C22⋊C4×C107—22no—
59C22⋊C4×C107—22no—
60C22⋊C4×C107D412yes—
61C42×C107C2311yescharacteristic
62C42×C107C2311yescharacteristic
63C23×C107—22no—
64C23×C107C2×D411yescharacteristic
65D4×C107—22no—
66D4×C107—22no—
67D4×C107—82no—
68D4×C107—82no—
69C2×C4×C107—22no—
70C2×C4×C107—22no—
71C2×C4×C107—82no—
72C2×C4×C107C2×D412yes—
73C2×C4×C107C2×D412yes—
74C2×C4×C107C2×D411yescharacteristic
75C2×C4×C107C2411yescharacteristic
76C2×Dic107—24no—
77C2×Dic107—22no—
78C2×Dic107—22no—
79Dic214—24no—
80Dic214—22no—
81Dic214#4114yes—
82C107⋊C8—22no—
83C107⋊C8—22no—
84C22×C107—21no—
85C22×C107—22no—
86C22×C107—42no—
87C22×C107—42no—
88C22×C107—42no—
89C22×C107C22×D411yescharacteristic
90C4×C107—21no—
91C4×C107—22no—
92C4×C107—22no—
93C4×C107—42no—
94C4×C107C2×#4112yes—
95Dic107—24no—
96Dic107—42no—
97C2×C107—41no—
98C2×C107—82no—
99C2×C107#52511yescharacteristic
100C2×C107#57712yes—
101#3126—1071nomaximal, Sylow
102C107#312611yescharacteristic, complemented, Sylow
103#540D10711yescharacteristic
104#519—1071no—
105#482—1072no—
106#479—1072no—
107#460—1072no—
108#448—1072no—
109#440—1072no—
110C4×SD16—1072no—
111#433—1071no—
112C22×Q8—1071no—
113C2×SD16—1072no—
114C2×SD16—1072no—
115#127C2×D10711yescharacteristic
116#125C2×D10711yescharacteristic
117#123—22no—
118#121—22no—
119#121C2×D10712yes—
120C4×Q8—1072no—
121C4×Q8—1072no—
122C4×Q8—2142no—
123C4×D4C2×D10712yes—
124#117—1071no—
125#117—2142no—
126#117C2×D10711yescharacteristic
127#107—1072no—
128#106—1072no—
129C4⋊C8—1072no—
130#103—1072no—
131#103—1072no—
132#102—1072no—
133#102—1072no—
134C22⋊C8—1072no—
135#97—1071no—
136C4×C8—1071no—
137C2×Q8—1072no—
138C2×Q8—2144no—
139C2×Q8—2141no—
140C2×D4—22no—
141C2×D4—22no—
142C2×D4C22×D10712yes—
143C22×C4—22no—
144C22×C4—2141no—
145C22×C4C22×D10711yescharacteristic
146SD16—2144no—
147SD16—2144no—
148C2×C8—1072no—
149C2×C8—1072no—
150C4⋊C4—22no—
151C4⋊C4—1072no—
152C4⋊C4—2142no—
153C4⋊C4—2142no—
154C4⋊C4C22⋊D10712yes—
155C4⋊C4C22×D10712yes—
156C22⋊C4—22no—
157C22⋊C4—22no—
158C22⋊C4—2141no—
159C22⋊C4C22⋊D10712yes—
160C42—2141no—
161C42—2142no—
162C42—2142no—
163C42C22×D10711yescharacteristic
164C42C22×D10711yescharacteristic
165C23—22no—
166C23C2×C22⋊D10711yescharacteristic
167Q8—1074no—
168Q8—2144no—
169Q8—2142no—
170D4—22no—
171D4—22no—
172D4—82no—
173D4—82no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—82no—
177C2×C4—2142no—
178C2×C4—2144no—
179C2×C4—2142no—
180C2×C4C2×C22⋊D10712yes—
181C2×C4C2×C22⋊D10712yes—
182C2×C4C2×C22⋊D10711yescharacteristic
183C2×C4C23×D10711yescharacteristic
184C8—2142no—
185C8—2142no—
186C22—21no—
187C22—22no—
188C22—42no—
189C22—42no—
190C22—42no—
191C22C22×C22⋊D10711yescharacteristic
192C4—21no—
193C4—22no—
194C4—22no—
195C4—42no—
196C4—4282no—
197C4—2144no—
198C4#41×D10712yes—
199C2—41no—
200C2—82no—
201C2#2029313411yescharacteristic
202C2#2029343812yes—
subgroupG/H
centerC22C22×C22⋊D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting, prime radical#540×C107C2
socleC22×C107C22×D4
hypercenter#540D107
hypocenterC107#3126
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #20293104C2semidirect
2. #20292948C2semidirect
3. #20292931C2semidirect
4. #20292824C2semidirect
5. #20292765C2semidirect
6. #20292727C2semidirect
7. C4×#13133806C2semidirect
8. #20292688C2semidirect
102. C107#3126semidirect

Maximal subgroups

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

subgroupindex
#202931042
#202929482
#202929312
#202928242
#202927652
#202927272
C4×#131338062
#202926882
#540×C1072
#3126107