Finite Group Databasebeta

← #28335019

Subgroups — #28335019

Order 13696.

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

normal subgroups only

This group has 264 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#20293172C211yesmaximal, characteristic
2#20292677C211yesmaximal, characteristic, complemented
3#20292491C211yesmaximal, characteristic, complemented
4#20292362C211yesmaximal, characteristic, complemented
5#20292361C211yesmaximal, characteristic, complemented
6#20292360C211yesmaximal, characteristic, complemented
7#327×C107C211yesmaximal, characteristic, complemented
8C2×#13133817—21no—
9#16812108C411yescharacteristic, complemented
10#16812105C411yescharacteristic, complemented
11#16812095—21no—
12#16812083C2211yescharacteristic
13#16812081—21no—
14D4×Dic107C411yescharacteristic, complemented
15#16812071C411yescharacteristic, complemented
16(C22⋊D107)⋊C4—21no—
17C2×Dic107⋊C4—21no—
18C2×C4×Dic107C2211yescharacteristic
19Dic107⋊C8—21no—
20C22⋊(C107⋊C8)C2211yescharacteristic
21C8×Dic107—21no—
22C107⋊#95—21no—
23C107⋊#95C2211yescharacteristic
24#121×C107C2211yescharacteristic
25C22⋊C8×C107C2211yescharacteristic
26#95×C107C2211yescharacteristic
27#13133817—42no—
28#13133817—42no—
29C2×Dic214—21no—
30C2×D428C2×C411yescharacteristic
31C2×C22⋊D107—21no—
32C2×C22⋊D107—21no—
33C2×C22⋊D107—21no—
34C22×Dic107—21no—
35C22×Dic107—21no—
36C22×Dic107D411yescharacteristic
37C22×Dic107D411yescharacteristic
38C2×C4×D107—21no—
39C2×C107⋊C8—21no—
40C4⋊Dic107C2×C411yescharacteristic
41Dic107⋊C4—21no—
42Dic107⋊C4—42no—
43C22⋊Dic107—21no—
44(C2×D107)⋊C4—21no—
45(C2×D107)⋊C4—21no—
46C4×Dic107C2×C411yescharacteristic
47C4×Dic107C2×C411yescharacteristic
48C4×Dic107D411yescharacteristic
49C4×Dic107D411yescharacteristic
50C2×D4×C107—21no—
51C2×D4×C107C2×C411yescharacteristic
52C22×C4×C107—21no—
53C22×C4×C107C2311yescharacteristic
54C2×C8×C107—21no—
55C4⋊C4×C107C2×C411yescharacteristic
56C22⋊C4×C107—21no—
57C23×C107—21no—
58C23×C107C2×D411yescharacteristic
59C22×D107—21no—
60D4×C107—41no—
61D4×C107—41no—
62D4×C107—41no—
63C2×C4×C107—21no—
64C2×C4×C107—41no—
65C2×C4×C107—41no—
66C2×C4×C107—41no—
67C2×C4×C107—41no—
68C2×C4×C107C22×C411yescharacteristic
69C2×C4×C107C2×D411yescharacteristic
70C22⋊D107—42no—
71C22⋊D107—41no—
72C22⋊D107—41no—
73C22⋊D107—42no—
74C2×Dic107—21no—
75C2×Dic107—41no—
76C2×Dic107—42no—
77C2×Dic107—41no—
78C2×Dic107—41no—
79C2×Dic107—41no—
80C2×Dic107C22⋊C411yescharacteristic
81C2×Dic107C22⋊C411yescharacteristic
82C2×Dic107C22⋊C411yescharacteristic
83C2×Dic107C22⋊C411yescharacteristic
84C2×Dic107D812yes—
85C2×Dic107SD1612yes—
86D428—41no—
87C4×D107—42no—
88Dic214—42no—
89C8×C107—41no—
90C107⋊C8—41no—
91C22×C107—21no—
92C22×C107—21no—
93C22×C107—41no—
94C22×C107—41no—
95C22×C107—41no—
96C22×C107C2×C22⋊C411yescharacteristic
97C22×C107C2×D811yescharacteristic
98C22×C107C2×SD1611yescharacteristic
99C2×D107—41no—
100C2×D107—41no—
101C2×D107—41no—
102C4×C107—21no—
103C4×C107—21no—
104C4×C107—41no—
105C4×C107—81no—
106Dic107—21no—
107Dic107—21no—
108Dic107—41no—
109Dic107—81no—
110Dic107#10212yes—
111Dic107#10212yes—
112C2×C107—21no—
113C2×C107—21no—
114C2×C107—81no—
115C2×C107#41011yescharacteristic
116C2×C107C2×#10211yescharacteristic
117C2×C107#42111yescharacteristic
118D107—81no—
119#1517—1071nomaximal, Sylow
120C107#151711yescharacteristic, complemented, Sylow
121#532—1071no—
122#431—1071no—
123#382—1071no—
124#327—1071no—
125#327—1071no—
126#327—1071no—
127#327D10711yescharacteristic, complemented
128C2×#41—2141no—
129C4⋊Q8—1071no—
130#127—1071no—
131#124—2141no—
132#121—1071no—
133#121—2141no—
134#121C2×D10711yescharacteristic
135C4×D4—1071no—
136C4×D4—1071no—
137C4×D4—2141no—
138C2×C4⋊C4—2141no—
139C2×C42—1071no—
140C4⋊C8—2141no—
141C22⋊C8—1071no—
142C22⋊C8C2×D10711yescharacteristic
143C4×C8—2141no—
144#95—1071no—
145#95—2141no—
146#95C2×D10711yescharacteristic
147#41—4282no—
148#41—4282no—
149C2×Q8—2141no—
150C2×D4—21no—
151C2×D4—1071no—
152C2×D4—2141no—
153C2×D4—2141no—
154C2×D4—2141no—
155C2×D4C4×D10711yescharacteristic
156C22×C4—21no—
157C22×C4—1071no—
158C22×C4—1071no—
159C22×C4—2141no—
160C22×C4—2141no—
161C22×C4—2141no—
162C22×C4C22×D10711yescharacteristic
163C2×C8—21no—
164C2×C8—2141no—
165C4⋊C4—1071no—
166C4⋊C4—4282no—
167C4⋊C4—2141no—
168C4⋊C4C4×D10711yescharacteristic
169C22⋊C4—21no—
170C22⋊C4—2141no—
171C22⋊C4—2141no—
172C22⋊C4—2141no—
173C42—1071no—
174C42—1071no—
175C42—1071no—
176C42—1071no—
177C23—21no—
178C23—2141no—
179C23D4×D10711yescharacteristic
180Q8—4282no—
181D4—41no—
182D4—41no—
183D4—41no—
184D4—4281no—
185D4—4282no—
186D4—4281no—
187D4—4281no—
188D4—4282no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—1071no—
195C2×C4—1071no—
196C2×C4—1072no—
197C2×C4—1072no—
198C2×C4—1071no—
199C2×C4—1071no—
200C2×C4—4282no—
201C2×C4—4281no—
202C2×C4—4281no—
203C2×C4—4281no—
204C2×C4—4282no—
205C2×C4—4281no—
206C2×C4—2141no—
207C2×C4C2×C4×D10711yescharacteristic
208C2×C4D4×D10711yescharacteristic
209C8—41no—
210C8—4281no—
211C22—21no—
212C22—21no—
213C22—41no—
214C22—41no—
215C22—41no—
216C22—4281no—
217C22—4281no—
218C22—4281no—
219C22C22⋊C4×D10711yescharacteristic
220C22D8×D10711yescharacteristic
221C22SD16×D10711yescharacteristic
222C4—21no—
223C4—21no—
224C4—41no—
225C4—81no—
226C4—8561no—
227C4—1072no—
228C4—1072no—
229C4—4281no—
230C4—2141no—
231C4—2141no—
232C2—21no—
233C2—21no—
234C2—81no—
235C2—8561no—
236C2#2029259911yescharacteristic
237C2#102×D10711yescharacteristic
238C2#2029264211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D107
commutatorC2×C4×C107C22×C4
FrattiniC22×C4C22×D107
Fitting#327×C107C2
socleC22×C107C2×C22⋊C4
prime radical#20293172C2
cosocleC22×C4×C107C23
hypercenter#327D107
hypocenterC107#1517
LCSG ▷ C2×C4×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #20292677C2semidirect
3. #20292491C2semidirect
4. #20292362C2semidirect
5. #20292361C2semidirect
6. #20292360C2semidirect
7. #327×C107C2semidirect
9. #16812108C4semidirect
10. #16812105C4semidirect
14. D4×Dic107C4semidirect
15. #16812071C4semidirect
120. C107#1517semidirect
127. #327D107semidirect

Maximal subgroups

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

subgroupindex
#202931722
#202926772
#202924912
#202923622
#202923612
#202923602
#327×C1072
#1517107