Finite Group Databasebeta

← #28337152

Subgroups — #28337152

Order 13696.

248 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C2×#16812034C211yesmaximal, characteristic
2C2×#16812032C211yesmaximal, characteristic
3C2×#16812019C211yesmaximal, characteristic
4#20292532C211yesmaximal, characteristic
5#20292526C211yesmaximal, characteristic
6#20292389C211yesmaximal, characteristic
7#340×C107C211yesmaximal, characteristic
8C22×Dic214C2211yescharacteristic
9C22×C107⋊C8C2211yescharacteristic
10C2×C4⋊Dic107—21no—
11C2×C4⋊Dic107C2211yescharacteristic
12C2×C4×Dic107C2211yescharacteristic
13#16812034—22no—
14#16812032C414yescomplemented
15#16812019—22no—
16C107⋊#95—21no—
17C107⋊#95—21no—
18C107⋊#95—21no—
19C22×C8×C107C2211yescharacteristic
20C2×C4⋊C4×C107C2211yescharacteristic
21C2×C4⋊C4×C107C2211yescharacteristic
22C2×Dic214—21no—
23C2×Dic214—21no—
24C2×Dic214—21no—
25C2×Dic214—21no—
26C2×Dic214—21no—
27C2×Dic214C2×C412yes—
28C22×Dic107—21no—
29C22×Dic107—21no—
30C22×Dic107D411yescharacteristic
31C22×Dic107D411yescharacteristic
32C2×C107⋊C8—21no—
33C2×C107⋊C8—21no—
34C2×C107⋊C8C2×C412yes—
35C4⋊Dic107—21no—
36C4⋊Dic107—21no—
37C4⋊Dic107—42no—
38C4×Dic107—21no—
39C4×Dic107—21no—
40C22×C4×C107—21no—
41C22×C4×C107—21no—
42C22×C4×C107C2311yescharacteristic
43C2×C8×C107—21no—
44C2×C8×C107—21no—
45C2×C8×C107D412yes—
46C4⋊C4×C107—21no—
47C4⋊C4×C107—21no—
48C4⋊C4×C107—21no—
49C4⋊C4×C107C2×C412yes—
50C23×C107C2×D411yescharacteristic
51C2×C4×C107—22no—
52C2×C4×C107—41no—
53C2×C4×C107—41no—
54C2×C4×C107—41no—
55C2×C4×C107—41no—
56C2×C4×C107—41no—
57C2×C4×C107C22×C411yescharacteristic
58C2×C4×C107C2×D411yescharacteristic
59C2×C4×C107#4111yescharacteristic
60C2×C4×C107#4111yescharacteristic
61C2×C4×C107#4111yescharacteristic
62C2×C4×C107#4111yescharacteristic
63C2×Dic107—22no—
64C2×Dic107—21no—
65C2×Dic107—21no—
66C2×Dic107—21no—
67C2×Dic107—21no—
68C2×Dic107—21no—
69C2×Dic107—21no—
70C2×Dic107—41no—
71C2×Dic107—41no—
72C2×Dic107—41no—
73C2×Dic107—41no—
74C2×Dic107—41no—
75Dic214—22no—
76Dic214—22no—
77Dic214—41no—
78Dic214—41no—
79C8×C107—22no—
80C107⋊C8—22no—
81C22×C107C4×D411yescharacteristic
82C22×C107#12111yescharacteristic
83C22×C107#12411yescharacteristic
84C22×C107AGL(1,ℤ/8)11yescharacteristic
85C22×C107#13711yescharacteristic
86C22×C107#13711yescharacteristic
87C22×C107#13711yescharacteristic
88C4×C107—42no—
89C4×C107—81no—
90C4×C107#11711yescharacteristic
91C4×C107C4×D411yescharacteristic
92C4×C107#12311yescharacteristic
93C4×C107#12611yescharacteristic
94Dic107—42no—
95Dic107—41no—
96Dic107—41no—
97Dic107—81no—
98C2×C107#38811yescharacteristic
99C2×C107#44011yescharacteristic
100C2×C107#44111yescharacteristic
101C2×C107#46811yescharacteristic
102C2×C107#47011yescharacteristic
103C2×C107#48911yescharacteristic
104C2×C107#49111yescharacteristic
105#1935—1071nomaximal, Sylow
106C107#193511yescharacteristic, complemented, Sylow
107C2×#103—1071no—
108C2×#103—1071no—
109C2×#97—1071no—
110#391—1071no—
111#389—1071no—
112#340—1071no—
113#340D10711yescharacteristic
114C22×Q8—1071no—
115C22×C8—1071no—
116C22×C8C2×D10711yescharacteristic
117C2×C4⋊C4—1071no—
118C2×C4⋊C4—2141no—
119C2×C4⋊C4C2×D10711yescharacteristic
120C2×C4⋊C4C2×D10711yescharacteristic
121C2×C42—1071no—
122#103—1074no—
123#103—2142no—
124#97—2142no—
125#95—2141no—
126#95—2141no—
127#95—2141no—
128C2×Q8—1072no—
129C2×Q8—2141no—
130C2×Q8—2141no—
131C2×Q8—2141no—
132C2×Q8—2141no—
133C2×Q8—2141no—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—1071no—
137C22×C4—1071no—
138C22×C4—2141no—
139C22×C4—2141no—
140C22×C4C22×D10711yescharacteristic
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—1072no—
144C2×C8—2141no—
145C2×C8—2141no—
146C2×C8D42812yes—
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4—21no—
150C4⋊C4—4282no—
151C4⋊C4—2141no—
152C4⋊C4—2141no—
153C4⋊C4C4×D10712yes—
154C42—2141no—
155C42—2141no—
156C23D4×D10711yescharacteristic
157Q8—4281no—
158Q8—4281no—
159Q8—2142no—
160Q8—2142no—
161C2×C4—22no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—4281no—
168C2×C4—4281no—
169C2×C4—4281no—
170C2×C4—4281no—
171C2×C4—4281no—
172C2×C4—2142no—
173C2×C4—2141no—
174C2×C4—2141no—
175C2×C4—2141no—
176C2×C4—2141no—
177C2×C4—2141no—
178C2×C4—2141no—
179C2×C4C2×C4×D10711yescharacteristic
180C2×C4C2×D42811yescharacteristic
181C2×C4#1313381711yescharacteristic
182C2×C4#1313381711yescharacteristic
183C2×C4#1313381811yescharacteristic
184C2×C4#1313381911yescharacteristic
185C8—22no—
186C8—2142no—
187C22(C22⋊D107)⋊C411yescharacteristic
188C22#1681208411yescharacteristic
189C22#1681209511yescharacteristic
190C22#1681213311yescharacteristic
191C22#1681213811yescharacteristic
192C22#1681213811yescharacteristic
193C22#1681214111yescharacteristic
194C4—42no—
195C4—81no—
196C4—8561no—
197C4—4281no—
198C4—4281no—
199C4—4282no—
200C4#1681206711yescharacteristic
201C4C4×D42811yescharacteristic
202C4#1681209311yescharacteristic
203C4#1681210411yescharacteristic
204C2#2029251911yescharacteristic
205C2#2029272411yescharacteristic
206C2#2029273111yescharacteristic
207C2#2029287411yescharacteristic
208C2#2029288611yescharacteristic
209C2#2029298511yescharacteristic
210C2#2029299411yescharacteristic
subgroupG/H
centerC23D4×D107
commutatorC2×C4×C107C22×C4
FrattiniC22×C4C22×D107
Fitting#340×C107C2
socle, prime radicalC23×C107C2×D4
cosocleC22×C4×C107C23
hypercenter#340D107
hypocenterC107#1935
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
14. #16812032C4semidirect
106. C107#1935semidirect

Maximal subgroups

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

subgroupindex
C2×#168120342
C2×#168120322
C2×#168120192
#202925322
#202925262
#202923892
#340×C1072
#1935107