Finite Group Databasebeta

← #28337475

Subgroups — #28337475

Order 13696.

478 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 73 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×#16812134C211yesmaximal, characteristic, complemented
2#20293191C211yesmaximal, characteristic, complemented
3C2×#16812106C211yesmaximal, characteristic, complemented
4#20292633C211yesmaximal, characteristic, complemented
5C2×#16812025C211yesmaximal, characteristic, complemented
6#20292387C211yesmaximal, characteristic, complemented
7C2×#104×C107C211yesmaximal, characteristic, complemented
8C22×D428—22no—
9C22×D428C2211yescharacteristic
10C22×D428C2211yescharacteristic
11#16812134—22no—
12#16812134—22no—
13C2×#13133805—21no—
14C2×#13133803—21no—
15C2×#13133802C2211yescharacteristic
16#16812106—22no—
17#16812106—22no—
18#16812105—21no—
19#16812098—21no—
20#16812083—22no—
21#16812077—22no—
22#16812068C2211yescharacteristic
23#16812031—22no—
24#16812025—22no—
25C2×#41×C107C2211yescharacteristic
26C2×M16×C107C2211yescharacteristic
27C2×C42×C107C2211yescharacteristic
28#104×C107—22no—
29C23×D107—21no—
30C23×D107D412yes—
31C2×D428—21no—
32C2×D428—21no—
33C2×D428—21no—
34C2×D428—21no—
35C2×D428—28no—
36C2×D428—21no—
37C2×D428—21no—
38C2×D428—21no—
39C2×D428—21no—
40C2×D428—21no—
41C2×D428—21no—
42C2×D428—21no—
43C2×D428—48no—
44C2×D428D412yescomplemented
45C2×C22⋊D107—24no—
46#13133805—24no—
47#13133803—24no—
48#13133802—21no—
49#13133802D412yescomplemented
50C2×C107⋊C8—21no—
51C4⋊Dic107D412yescomplemented
52C22⋊Dic107—21no—
53(C2×D107)⋊C4—24no—
54C4×Dic107—21no—
55#41×C107—21no—
56#41×C107—21no—
57#41×C107—21no—
58#41×C107—21no—
59C2×Q8×C107D411yescharacteristic, complemented
60C2×D4×C107—21no—
61C2×D4×C107D411yescharacteristic, complemented
62C22×C4×C107—21no—
63C22×C4×C107—21no—
64C22×C4×C107C2311yescharacteristic
65M16×C107—21no—
66M16×C107—21no—
67C2×C8×C107—21no—
68C42×C107—21no—
69C42×C107D412yescomplemented
70C23×C107—21no—
71C23×C107C2×D411yescharacteristic
72C22×D107—22no—
73C22×D107—22no—
74C22×D107—22no—
75C22×D107—22no—
76C22×D107—44no—
77C22×D107—44no—
78C22×D107—41no—
79C22×D107—41no—
80Q8×C107—21no—
81Q8×C107—21no—
82D4×C107—21no—
83D4×C107—21no—
84D4×C107—41no—
85D4×C107—41no—
86C2×C4×C107—24no—
87C2×C4×C107—22no—
88C2×C4×C107—21no—
89C2×C4×C107—41no—
90C2×C4×C107—41no—
91C2×C4×C107C2×D411yescharacteristic
92C2×C4×C107C2×D411yescharacteristic
93C2×C4×C107C2×D411yescharacteristic
94C2×C4×C107C2×D411yescharacteristic
95C2×C4×C107C2×D411yescharacteristic
96C2×C4×C107#4111yescharacteristic
97C22⋊D107—84no—
98C2×Dic107—22no—
99D428—22no—
100D428—22no—
101D428—416no—
102D428—41no—
103D428—41no—
104D428—41no—
105D428—41no—
106D428—41no—
107D428—41no—
108C8×C107—41no—
109C107⋊C8—22no—
110C22×C107—22no—
111C22×C107—41no—
112C22×C107—42no—
113C22×C107#12011yescharacteristic
114C22×C107#12011yescharacteristic
115C22×C107#12111yescharacteristic
116C2×D107—44no—
117C2×D107—44no—
118C2×D107—42no—
119C2×D107—42no—
120C2×D107—44no—
121C2×D107—82no—
122C2×D107—82no—
123C2×D107—82no—
124C4×C107—24no—
125C4×C107—41no—
126C4×C107#12011yescharacteristic
127C4×C107#12111yescharacteristic
128C4×C107#12111yescharacteristic
129C4×C107#12711yescharacteristic
130Dic107—42no—
131C2×C107—21no—
132C2×C107—21no—
133C2×C107—81no—
134C2×C107#39211yescharacteristic
135C2×C107#45312yes—
136D107—82no—
137D107—82no—
138#2002—1071nomaximal, Sylow
139C107#200211yescharacteristic, complemented, Sylow
140C2×AGL(1,ℤ/8)—1071no—
141#535—1071no—
142C2×#127—1071no—
143C2×#104D10711yescharacteristic, complemented
144#418—1071no—
145C2×#100—1071no—
146#339—1071no—
147C2×#41C2×D10711yescharacteristic
148C22×D4—1071no—
149C22×D4—1071no—
150C22×D4—2142no—
151AGL(1,ℤ/8)—2142no—
152AGL(1,ℤ/8)—2142no—
153C2×SD16—2141no—
154C2×D8—2141no—
155C2×M16—1071no—
156C2×M16C2×D10711yescharacteristic
157#127—2142no—
158#127—2141no—
159#127—2142no—
160#124—2141no—
161#121—2142no—
162#120—2142no—
163#117—1071no—
164C2×C42C2×D10711yescharacteristic
165#104—22no—
166#102—2142no—
167#100—2142no—
168C24—1072no—
169C24—2141no—
170#41—21no—
171#41—21no—
172#41—21no—
173#41—21no—
174C2×Q8D42811yescharacteristic, complemented
175C2×D4—21no—
176C2×D4—1072no—
177C2×D4—4288no—
178C2×D4—2148no—
179C2×D4—2144no—
180C2×D4—2141no—
181C2×D4—2141no—
182C2×D4—2141no—
183C2×D4—2141no—
184C2×D4—2141no—
185C2×D4—2141no—
186C2×D4—2141no—
187C2×D4—2141no—
188C2×D4—2141no—
189C2×D4—2141no—
190C2×D4—2141no—
191C2×D4D42811yescharacteristic, complemented
192C22×C4—21no—
193C22×C4—21no—
194C22×C4C22×D10711yescharacteristic
195SD16—2144no—
196D8—2144no—
197M16—21no—
198M16—21no—
199M16—1072no—
200M16—2141no—
201C2×C8—21no—
202C2×C8—2141no—
203C4⋊C4—1072no—
204C22⋊C4—2144no—
205C22⋊C4—2141no—
206C42—21no—
207C42—2141no—
208C42C22⋊D10712yescomplemented
209C23—21no—
210C23—4284no—
211C23—4284no—
212C23—4281no—
213C23—4281no—
214C23—2142no—
215C23—2142no—
216C23—2142no—
217C23—2142no—
218C23D4×D10711yescharacteristic
219Q8—21no—
220Q8—21no—
221D4—21no—
222D4—21no—
223D4—41no—
224D4—41no—
225D4—8564no—
226D4—42816no—
227D4—4281no—
228D4—4281no—
229D4—4281no—
230D4—4281no—
231D4—4281no—
232D4—4281no—
233D4—2142no—
234D4—2142no—
235C2×C4—24no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—2142no—
241C2×C4D4×D10711yescharacteristic
242C2×C4D4×D10711yescharacteristic
243C2×C4D4×D10711yescharacteristic
244C2×C4C2×C22⋊D10711yescharacteristic
245C2×C4C2×D42811yescharacteristic
246C2×C4#1313381811yescharacteristic
247C8—41no—
248C8—2142no—
249C22—22no—
250C22—41no—
251C22—42no—
252C22—8562no—
253C22—8562no—
254C22—8562no—
255C22—4284no—
256C22—4284no—
257C22—4282no—
258C22—4282no—
259C22—4284no—
260C22#1681207711yescharacteristic
261C22#1681207911yescharacteristic
262C22#1681208211yescharacteristic
263C4—24no—
264C4—41no—
265C4—4282no—
266C4#1681207911yescharacteristic
267C4#1681208211yescharacteristic
268C4#1681208311yescharacteristic
269C4#1681210511yescharacteristic
270C2—21no—
271C2—21no—
272C2—81no—
273C2—8562no—
274C2—8562no—
275C2#2029253611yescharacteristic
276C2#2029279612yes—
subgroupG/H
centerC22#16812079
commutator, cosocleC22×C4×C107C23
FrattiniC22×C4C22×D107
FittingC2×#104×C107C2
socleC22×C107#120
hypercenterC2×#104D107
hypocenterC107#2002
LCSG ▷ C22×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
1. C2×#16812134C2semidirect
2. #20293191C2semidirect
3. C2×#16812106C2semidirect
4. #20292633C2semidirect
5. C2×#16812025C2semidirect
6. #20292387C2semidirect
7. C2×#104×C107C2semidirect
44. C2×D428D4semidirect
49. #13133802D4semidirect
51. C4⋊Dic107D4semidirect
59. C2×Q8×C107D4semidirect
61. C2×D4×C107D4semidirect
69. C42×C107D4semidirect
139. C107#2002semidirect
143. C2×#104D107semidirect
174. C2×Q8D428semidirect
191. C2×D4D428semidirect
208. C42C22⋊D107semidirect

Maximal subgroups

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

subgroupindex
C2×#168121342
#202931912
C2×#168121062
#202926332
C2×#168120252
#202923872
C2×#104×C1072
#2002107