Finite Group Databasebeta

← #28336805

Subgroups — #28336805

Order 13696.

338 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 103 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×C4×Dic214C211yesmaximal, characteristic
3C2×#16812033C211yesmaximal, characteristic
4C2×#16812032C211yesmaximal, characteristic
5#20292389C211yesmaximal, characteristic
6#20292382C211yesmaximal, characteristic
7#391×C107C211yesmaximal, characteristic
8C22×Dic214C2211yescharacteristic
9C2×#13133808—22no—
10C2×#13133808—22no—
11C2×#13133808C414yescomplemented
12C22×C107⋊C8C2211yescharacteristic
13C22×C107⋊C8C2211yescharacteristic
14C4×Dic214—22no—
15C4×Dic214—22no—
16C2×C4⋊Dic107C2211yescharacteristic
17C2×Dic107⋊C4—21no—
18C2×C4×Dic107—21no—
19#16812033—22no—
20#16812032—22no—
21C22×Q8×C107C2211yescharacteristic
22C2×C4⋊C4×C107C2211yescharacteristic
23C2×C42×C107C2211yescharacteristic
24#95×C107—21no—
25#95×C107—21no—
26C2×Dic214—21no—
27C2×Dic214—21no—
28C2×Dic214—21no—
29C2×Dic214C2×C412yes—
30C2×Dic214D412yes—
31C2×Dic214D412yes—
32C22×Dic107—21no—
33C22×Dic107—21no—
34#13133808—28no—
35C2×C107⋊C8—21no—
36C2×C107⋊C8—21no—
37C2×C107⋊C8—21no—
38C2×C107⋊C8—21no—
39C2×C107⋊C8—21no—
40C2×C107⋊C8C2×C412yes—
41C4⋊Dic107—21no—
42C4⋊Dic107D412yes—
43Dic107⋊C4—24no—
44C4×Dic107—24no—
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×C107—21no—
53C22×C4×C107D411yescharacteristic
54C22×C4×C107D411yescharacteristic
55C22×C4×C107C2311yescharacteristic
56C4⋊C4×C107—21no—
57C4⋊C4×C107—21no—
58C42×C107—21no—
59C42×C107—21no—
60C23×C107C2×D411yescharacteristic
61Q8×C107—22no—
62Q8×C107—22no—
63Q8×C107—41no—
64Q8×C107—41no—
65C2×C4×C107—21no—
66C2×C4×C107—21no—
67C2×C4×C107—22no—
68C2×C4×C107—21no—
69C2×C4×C107—21no—
70C2×C4×C107—21no—
71C2×C4×C107—41no—
72C2×C4×C107—41no—
73C2×C4×C107—41no—
74C2×C4×C107—41no—
75C2×C4×C107—41no—
76C2×C4×C107Q1612yescomplemented
77C2×C4×C107C22×C411yescharacteristic
78C2×C4×C107C2×D411yescharacteristic
79C2×C4×C107C2×D411yescharacteristic
80C2×C4×C107C2×D411yescharacteristic
81C2×C4×C107#4111yescharacteristic
82C2×C4×C107#4111yescharacteristic
83C2×Dic107—22no—
84C2×Dic107—22no—
85C2×Dic107—22no—
86C2×Dic107—22no—
87C2×Dic107—41no—
88C2×Dic107—41no—
89Dic214—22no—
90Dic214—22no—
91Dic214—22no—
92Dic214C22⋊C414yes—
93C107⋊C8—22no—
94C107⋊C8—41no—
95C22×C107C4×D411yescharacteristic
96C22×C107#12011yescharacteristic
97C22×C107#12111yescharacteristic
98C22×C107C2×Q1611yescharacteristic
99C22×C107#13511yescharacteristic
100C22×C107#13711yescharacteristic
101C22×C107#13711yescharacteristic
102C4×C107—22no—
103C4×C107—42no—
104C4×C107—41no—
105C4×C107—81no—
106C4×C107C2×C22⋊C411yescharacteristic
107C4×C107C4×D411yescharacteristic
108C4×C107#12111yescharacteristic
109C4×C107#12311yescharacteristic
110Dic107—24no—
111Dic107—42no—
112C2×C107#38611yescharacteristic
113C2×C107C4×Q1611yescharacteristic
114C2×C107#44111yescharacteristic
115C2×C107#45111yescharacteristic
116C2×C107#45211yescharacteristic
117C2×C107#46211yescharacteristic
118C2×C107#46411yescharacteristic
119#1878—1071nomaximal, Sylow
120C107#187811yescharacteristic, complemented, Sylow
121C22×Q16—1071no—
122C2×C4×Q8—1071no—
123C2×#103—1071no—
124C2×#103—1071no—
125#391D10711yescharacteristic
126#340—1071no—
127#336—1071no—
128C22×Q8—1071no—
129C22×Q8C2×D10711yescharacteristic
130C2×Q16—1074no—
131C2×Q16—2142no—
132C2×Q16—2142no—
133C22×C8—1071no—
134C22×C8—1071no—
135C4×Q8—2142no—
136C4×Q8—2142no—
137C2×C4⋊C4—1071no—
138C2×C4⋊C4—2141no—
139C2×C4⋊C4C2×D10711yescharacteristic
140C2×C42—2141no—
141C2×C42C2×D10711yescharacteristic
142#103—2142no—
143#103—2142no—
144#95—21no—
145#95—21no—
146C2×Q8—21no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—1072no—
152C2×Q8—1072no—
153C2×Q8—1072no—
154C2×Q8—2141no—
155C2×Q8—2141no—
156C2×Q8—2141no—
157C2×Q8C4×D10712yes—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—2141no—
161C22×C4—2141no—
162C22×C4C22⋊D10711yescharacteristic
163C22×C4C22⋊D10711yescharacteristic
164C22×C4C22×D10711yescharacteristic
165Q16—2148no—
166C2×C8—1072no—
167C2×C8—2141no—
168C2×C8—2141no—
169C2×C8—2141no—
170C2×C8—2141no—
171C2×C8—2141no—
172C4⋊C4—21no—
173C4⋊C4—21no—
174C4⋊C4—1072no—
175C4⋊C4—2144no—
176C4⋊C4—2141no—
177C42—21no—
178C42—21no—
179C42—2144no—
180C23C2×C22⋊D10711yescharacteristic
181Q8—22no—
182Q8—22no—
183Q8—41no—
184Q8—41no—
185Q8—1074no—
186Q8—2142no—
187Q8—2142no—
188Q8—2142no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—4281no—
201C2×C4—4281no—
202C2×C4—2142no—
203C2×C4—2142no—
204C2×C4—2142no—
205C2×C4—2142no—
206C2×C4#1313380812yescomplemented
207C2×C4C2×C4×D10711yescharacteristic
208C2×C4D4×D10711yescharacteristic
209C2×C4D4×D10711yescharacteristic
210C2×C4D4×D10711yescharacteristic
211C2×C4#1313381711yescharacteristic
212C2×C4#1313381811yescharacteristic
213C8—4281no—
214C8—2142no—
215C22C4×C22⋊D10711yescharacteristic
216C22#1681207711yescharacteristic
217C22#1681208011yescharacteristic
218C22C2×#1313380811yescharacteristic
219C22#1681212911yescharacteristic
220C22#1681213911yescharacteristic
221C22#1681214011yescharacteristic
222C4—22no—
223C4—42no—
224C4—41no—
225C4—81no—
226C4—4282no—
227C4—2144no—
228C4C22⋊C4×D10711yescharacteristic
229C4(C22⋊D107)⋊C411yescharacteristic
230C4#1681208211yescharacteristic
231C4#1681209111yescharacteristic
232C2#2029250311yescharacteristic
233C2C4×#1313380811yescharacteristic
234C2#2029273211yescharacteristic
235C2#2029278211yescharacteristic
236C2#2029278711yescharacteristic
237C2#2029283411yescharacteristic
238C2#2029284611yescharacteristic
subgroupG/H
centerC23C2×C22⋊D107
commutatorC2×C4×C107C22×C4
FrattiniC22×C4C22×D107
Fitting#391×C107C2
socle, prime radicalC23×C107C2×D4
cosocleC22×C4×C107C23
hypercenter#391D107
hypocenterC107#1878
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
11. C2×#13133808C4semidirect
76. C2×C4×C107Q16semidirect
120. C107#1878semidirect
206. C2×C4#13133808semidirect

Maximal subgroups

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

subgroupindex
C22×#131338082
C2×C4×Dic2142
C2×#168120332
C2×#168120322
#202923892
#202923822
#391×C1072
#1878107