Finite Group Databasebeta

← #28337684

Subgroups — #28337684

Order 13696.

306 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 69 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#20293205C211yesmaximal, characteristic
2C2×#16812037C211yesmaximal, characteristic, complemented
3#20292629C211yesmaximal, characteristic, complemented
4#20292628C211yesmaximal, characteristic, complemented
5#20292497C211yesmaximal, characteristic, complemented
6#20292395C211yesmaximal, characteristic, complemented
7C2×#104×C107C211yesmaximal, characteristic, complemented
8C2×#13133818C2211yescharacteristic
9C2×#13133802C2211yescharacteristic
10#16812088—21no—
11#16812085—21no—
12#16812083—21no—
13#16812081—22no—
14#16812080—21no—
15C2×C4⋊Dic107—22no—
16C2×C4⋊Dic107C2211yescharacteristic
17C2×C4⋊Dic107C2211yescharacteristic
18#16812037—22no—
19#16812034—21no—
20#16812033—21no—
21#16812031—21no—
22#16812030—21no—
23C2×#41×C107C2211yescharacteristic
24C2×M16×C107C2211yescharacteristic
25C2×C42×C107C2211yescharacteristic
26#104×C107—22no—
27#13133818—21no—
28#13133818—21no—
29#13133818—21no—
30#13133818—21no—
31C2×Dic214D411yescharacteristic
32C2×D428D411yescharacteristic
33C2×C22⋊D107—21no—
34C2×C22⋊D107—22no—
35C22×Dic107—21no—
36C22×Dic107D412yes—
37C2×C4×D107—21no—
38#13133802—21no—
39#13133802—21no—
40C2×C107⋊C8—21no—
41C4⋊Dic107—21no—
42C4⋊Dic107—21no—
43C4⋊Dic107—21no—
44C4⋊Dic107—21no—
45C4⋊Dic107—44no—
46Dic107⋊C4—22no—
47C22⋊Dic107—22no—
48(C2×D107)⋊C4—22no—
49#41×C107—21no—
50#41×C107—21no—
51#41×C107—21no—
52#41×C107—21no—
53C2×Q8×C107D411yescharacteristic
54C2×D4×C107—21no—
55C2×D4×C107D411yescharacteristic
56C22×C4×C107—21no—
57C22×C4×C107—21no—
58C22×C4×C107C2311yescharacteristic
59M16×C107—21no—
60M16×C107—21no—
61C2×C8×C107—21no—
62C42×C107—21no—
63C42×C107D412yescomplemented
64C23×C107—21no—
65C23×C107C2×D411yescharacteristic
66C22×D107—21no—
67Q8×C107—21no—
68Q8×C107—21no—
69D4×C107—21no—
70D4×C107—21no—
71D4×C107—41no—
72D4×C107—41no—
73C2×C4×C107—22no—
74C2×C4×C107—22no—
75C2×C4×C107—22no—
76C2×C4×C107—21no—
77C2×C4×C107—41no—
78C2×C4×C107—41no—
79C2×C4×C107C2×D411yescharacteristic
80C2×C4×C107C2×D411yescharacteristic
81C2×C4×C107C2×D411yescharacteristic
82C2×C4×C107#4111yescharacteristic
83C2×C4×C107#4111yescharacteristic
84C2×C4×C107#4111yescharacteristic
85C22⋊D107—41no—
86C22⋊D107—41no—
87C22⋊D107—82no—
88C2×Dic107—22no—
89C2×Dic107—21no—
90C2×Dic107—42no—
91C2×Dic107—42no—
92C2×Dic107—41no—
93D428—21no—
94D428—21no—
95C4×D107—41no—
96C4×D107—41no—
97Dic214—21no—
98Dic214—21no—
99C8×C107—41no—
100C107⋊C8—41no—
101C22×C107—21no—
102C22×C107—21no—
103C22×C107—41no—
104C22×C107—41no—
105C22×C107—41no—
106C22×C107#12011yescharacteristic
107C22×C107#12111yescharacteristic
108C22×C107#12411yescharacteristic
109C2×D107—41no—
110C2×D107—41no—
111C2×D107—41no—
112C4×C107—24no—
113C4×C107—41no—
114C4×C107#12111yescharacteristic
115C4×C107#12111yescharacteristic
116C4×C107#12311yescharacteristic
117C4×C107#12311yescharacteristic
118Dic107—41no—
119Dic107—42no—
120Dic107—81no—
121C2×C107—21no—
122C2×C107—21no—
123C2×C107—81no—
124C2×C107#39411yescharacteristic
125C2×C107#45311yescharacteristic
126C2×C107#45611yescharacteristic
127D107—81no—
128#2039—1071nomaximal, Sylow
129C107#203911yescharacteristic, complemented, Sylow
130#537—1071no—
131C2×#104—1071no—
132C2×#104D10711yescharacteristic, complemented
133#417—1071no—
134#417—1071no—
135#384—1071no—
136#343—1071no—
137C2×#41—1071no—
138C2×#41C2×D10711yescharacteristic
139C2×M16—1071no—
140C2×M16C2×D10711yescharacteristic
141C22⋊Q8—2141no—
142C22⋊Q8—2141no—
143#121—2141no—
144#121—2142no—
145#121—2141no—
146C2×C4⋊C4—1071no—
147C2×C4⋊C4—1071no—
148C2×C4⋊C4—2142no—
149C2×C42C2×D10711yescharacteristic
150#104—22no—
151#104—2142no—
152#103—2141no—
153#103—2141no—
154#102—2141no—
155#102—2141no—
156#41—21no—
157#41—21no—
158#41—21no—
159#41—21no—
160#41—2141no—
161#41—2141no—
162#41—2141no—
163#41—2141no—
164C2×Q8—1071no—
165C2×Q8D42811yescharacteristic
166C2×D4—21no—
167C2×D4—1071no—
168C2×D4—2142no—
169C2×D4—2141no—
170C2×D4D42811yescharacteristic
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—1072no—
174C22×C4—2141no—
175C22×C4—2141no—
176C22×C4C22×D10711yescharacteristic
177M16—21no—
178M16—21no—
179M16—2141no—
180M16—2141no—
181C2×C8—21no—
182C2×C8—2141no—
183C4⋊C4—4284no—
184C4⋊C4—2142no—
185C4⋊C4—2141no—
186C4⋊C4—2141no—
187C4⋊C4—2141no—
188C4⋊C4—2141no—
189C22⋊C4—2142no—
190C22⋊C4—2142no—
191C42—21no—
192C42C22⋊D10712yescomplemented
193C23—21no—
194C23—2141no—
195C23D4×D10711yescharacteristic
196Q8—21no—
197Q8—21no—
198Q8—2141no—
199Q8—2141no—
200D4—21no—
201D4—21no—
202D4—41no—
203D4—41no—
204D4—8562no—
205D4—4281no—
206D4—4281no—
207D4—2141no—
208D4—2141no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—4282no—
216C2×C4—4281no—
217C2×C4—4281no—
218C2×C4—4281no—
219C2×C4—4282no—
220C2×C4—2142no—
221C2×C4—2141no—
222C2×C4D4×D10711yescharacteristic
223C2×C4C2×C22⋊D10711yescharacteristic
224C2×C4C2×D42811yescharacteristic
225C2×C4#1313381711yescharacteristic
226C2×C4#1313381711yescharacteristic
227C2×C4#1313381811yescharacteristic
228C8—41no—
229C8—4281no—
230C22—21no—
231C22—21no—
232C22—41no—
233C22—41no—
234C22—41no—
235C22—4281no—
236C22—4281no—
237C22—4281no—
238C22#1681207911yescharacteristic
239C22#1681208111yescharacteristic
240C22#1681209511yescharacteristic
241C4—24no—
242C4—41no—
243C4—8561no—
244C4—4282no—
245C4—4281no—
246C4#1681208011yescharacteristic
247C4#1681208311yescharacteristic
248C4#1681209111yescharacteristic
249C4#1681209311yescharacteristic
250C2—21no—
251C2—21no—
252C2—81no—
253C2—8561no—
254C2#2029254311yescharacteristic
255C2#2029279611yescharacteristic
256C2#2029281111yescharacteristic
subgroupG/H
centerC22#16812079
commutator, cosocleC22×C4×C107C23
FrattiniC22×C4C22×D107
FittingC2×#104×C107C2
socleC22×C107#120
prime radical#20293205C2
hypercenterC2×#104D107
hypocenterC107#2039
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
2. C2×#16812037C2semidirect
3. #20292629C2semidirect
4. #20292628C2semidirect
5. #20292497C2semidirect
6. #20292395C2semidirect
7. C2×#104×C107C2semidirect
63. C42×C107D4semidirect
129. C107#2039semidirect
132. C2×#104D107semidirect
192. C42C22⋊D107semidirect

Maximal subgroups

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

subgroupindex
#202932052
C2×#168120372
#202926292
#202926282
#202924972
#202923952
C2×#104×C1072
#2039107