Finite Group Databasebeta

← #28334944

Subgroups — #28334944

Order 13696.

238 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 63 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#20293158C211yesmaximal, characteristic
2#20292677C211yesmaximal, characteristic, complemented
3#20292472C211yesmaximal, characteristic, complemented
4#20292365C211yesmaximal, characteristic, complemented
5#20292363C211yesmaximal, characteristic, complemented
6#20292361C211yesmaximal, characteristic
7#327×C107C211yesmaximal, characteristic
8#16812102—21no—
9#16812100C411yescharacteristic, complemented
10#16812096C411yescharacteristic, complemented
11#16812090—21no—
12#16812088C2211yescharacteristic
13#16812074C411yescharacteristic, complemented
14D4×Dic107—21no—
15D4×Dic107C411yescharacteristic, complemented
16#16812065—21no—
17C2×C4×Dic107—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
27C2×Dic214C2×C411yescharacteristic
28C22×Dic107—21no—
29C22×Dic107—21no—
30C22×Dic107D411yescharacteristic
31C22×Dic107D411yescharacteristic
32C2×C107⋊C8—21no—
33C4⋊Dic107—21no—
34C4⋊Dic107C2×C411yescharacteristic
35Dic107⋊C4—21no—
36Dic107⋊C4—21no—
37Dic107⋊C4—21no—
38C22⋊Dic107—21no—
39C22⋊Dic107—21no—
40C22⋊Dic107—21no—
41C22⋊Dic107—21no—
42C4×Dic107—24no—
43C4×Dic107—21no—
44C4×Dic107C2×C411yescharacteristic
45C4×Dic107C2×C411yescharacteristic
46C4×Dic107D411yescharacteristic
47C4×Dic107D411yescharacteristic
48C2×D4×C107—21no—
49C2×D4×C107C2×C411yescharacteristic
50C22×C4×C107—21no—
51C22×C4×C107C2311yescharacteristic
52C2×C8×C107—21no—
53C4⋊C4×C107C2×C411yescharacteristic
54C22⋊C4×C107—21no—
55C23×C107—21no—
56C23×C107C2×D411yescharacteristic
57D4×C107—41no—
58D4×C107—41no—
59D4×C107—41no—
60C2×C4×C107—22no—
61C2×C4×C107—21no—
62C2×C4×C107—41no—
63C2×C4×C107—41no—
64C2×C4×C107—41no—
65C2×C4×C107C22×C411yescharacteristic
66C2×C4×C107C2×D411yescharacteristic
67C2×Dic107—21no—
68C2×Dic107—21no—
69C2×Dic107—22no—
70C2×Dic107—22no—
71C2×Dic107—21no—
72C2×Dic107—21no—
73C2×Dic107—41no—
74C2×Dic107—41no—
75C2×Dic107—42no—
76C2×Dic107C22⋊C411yescharacteristic
77C2×Dic107C22⋊C411yescharacteristic
78C2×Dic107C22⋊C411yescharacteristic
79C2×Dic107C22⋊C411yescharacteristic
80Dic214—41no—
81C8×C107—41no—
82C107⋊C8—41no—
83C22×C107—21no—
84C22×C107—21no—
85C22×C107—41no—
86C22×C107—41no—
87C22×C107—41no—
88C22×C107C2×C22⋊C411yescharacteristic
89C22×C107#13511yescharacteristic
90C22×C107#13511yescharacteristic
91C4×C107—21no—
92C4×C107—21no—
93C4×C107—42no—
94C4×C107—41no—
95Dic107—21no—
96Dic107—21no—
97Dic107—21no—
98Dic107—42no—
99Dic107—41no—
100Dic107—41no—
101Dic107#10412yes—
102C2×C107—21no—
103C2×C107—21no—
104C2×C107—81no—
105C2×C107#41011yescharacteristic
106C2×C107#41611yescharacteristic
107C2×C107C2×#10411yescharacteristic
108#1500—1071nomaximal, Sylow
109C107#150011yescharacteristic, complemented, Sylow
110#529—1071no—
111#431—1071no—
112#376—1071no—
113#328—1071no—
114#328—1071no—
115#327—1071no—
116#327D10711yescharacteristic
117#126—2141no—
118#125—1071no—
119#124—1071no—
120#123—2141no—
121C22⋊Q8—1071no—
122#121C2×D10711yescharacteristic
123C4×Q8—1071no—
124C4×D4—1071no—
125C4×D4—2141no—
126#117—2141no—
127C2×C42—1071no—
128C2×C42—2141no—
129C4⋊C8—2141no—
130C22⋊C8—1071no—
131C22⋊C8C2×D10711yescharacteristic
132C4×C8—2141no—
133#95—1071no—
134#95—2141no—
135#95C2×D10711yescharacteristic
136C2×Q8—1071no—
137C2×D4—21no—
138C2×D4C4×D10711yescharacteristic
139C22×C4—21no—
140C22×C4—1071no—
141C22×C4—1071no—
142C22×C4—2141no—
143C22×C4—2141no—
144C22×C4C22×D10711yescharacteristic
145C2×C8—21no—
146C2×C8—2141no—
147C4⋊C4—1071no—
148C4⋊C4—2141no—
149C4⋊C4—2141no—
150C4⋊C4—2141no—
151C4⋊C4—2141no—
152C4⋊C4C4×D10711yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—2141no—
155C22⋊C4—2141no—
156C22⋊C4—2141no—
157C22⋊C4—2141no—
158C42—1071no—
159C42—1071no—
160C42—1071no—
161C42—1071no—
162C42—2141no—
163C42—2144no—
164C23—21no—
165C23D4×D10711yescharacteristic
166Q8—4281no—
167D4—41no—
168D4—41no—
169D4—41no—
170C2×C4—22no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—1071no—
176C2×C4—1071no—
177C2×C4—1071no—
178C2×C4—1071no—
179C2×C4—4282no—
180C2×C4—4281no—
181C2×C4—4281no—
182C2×C4—2142no—
183C2×C4—2142no—
184C2×C4—2141no—
185C2×C4—2141no—
186C2×C4—2141no—
187C2×C4—2141no—
188C2×C4C2×C4×D10711yescharacteristic
189C2×C4D4×D10711yescharacteristic
190C8—41no—
191C8—4281no—
192C22—21no—
193C22—21no—
194C22—41no—
195C22—41no—
196C22—41no—
197C22C22⋊C4×D10711yescharacteristic
198C22#1681212811yescharacteristic
199C22#1681213011yescharacteristic
200C4—21no—
201C4—21no—
202C4—42no—
203C4—41no—
204C4—1072no—
205C4—4282no—
206C4—4281no—
207C4—4281no—
208C4—2141no—
209C4—2141no—
210C4—2141no—
211C2—21no—
212C2—21no—
213C2—81no—
214C2#2029259911yescharacteristic
215C2#2029262011yescharacteristic
216C2#104×D10711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D107
commutatorC2×C4×C107C22×C4
FrattiniC22×C4C22×D107
Fitting#327×C107C2
socleC22×C107C2×C22⋊C4
prime radical#121×C107C22
cosocleC22×C4×C107C23
hypercenter#327D107
hypocenterC107#1500
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. #20292472C2semidirect
4. #20292365C2semidirect
5. #20292363C2semidirect
9. #16812100C4semidirect
10. #16812096C4semidirect
13. #16812074C4semidirect
15. D4×Dic107C4semidirect
109. C107#1500semidirect

Maximal subgroups

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

subgroupindex
#202931582
#202926772
#202924722
#202923652
#202923632
#202923612
#327×C1072
#1500107