Finite Group Databasebeta

← #28335641

Subgroups — #28335641

Order 13696.

308 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 57 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#20293262C211yesmaximal, characteristic
2#20292973C211yesmaximal, characteristic, complemented
3#20292908C211yesmaximal, characteristic, complemented
4#20292833C211yesmaximal, characteristic, complemented
5#20292354C211yesmaximal, characteristic, complemented
6#20292354C211yesmaximal, characteristic, complemented
7#331×C107C211yesmaximal, characteristic, complemented
8C2×D4×D107—21no—
9C2×D4×D107—21no—
10C2×#13133807—21no—
11#16812109C2211yescharacteristic, complemented
12#16812080—21no—
13#16812080—21no—
14#16812077—22no—
15C4×D428C2211yescharacteristic
16C4×D428C2211yescharacteristic
17#16812043—21no—
18#16812034—21no—
19#16812031—21no—
20#16812030—22no—
21C4×C107⋊C8C2211yescharacteristic, complemented
22#127×C107C2211yescharacteristic
23C4⋊C8×C107C2211yescharacteristic, complemented
24C4⋊C8×C107C2211yescharacteristic, complemented
25C23×D107—22no—
26C2×Dic214—21no—
27C2×D428D411yescharacteristic
28C2×D428D411yescharacteristic
29C2×C22⋊D107—22no—
30C2×C22⋊D107—22no—
31D4×D107—42no—
32D4×D107—42no—
33D4×D107—42no—
34D4×D107—42no—
35C2×C4×D107—21no—
36C2×C4×D107—21no—
37#13133807—42no—
38C2×C107⋊C8—21no—
39C4⋊Dic107—21no—
40C4⋊Dic107—21no—
41C4⋊Dic107D411yescharacteristic
42C4⋊Dic107D411yescharacteristic
43C22⋊Dic107—22no—
44(C2×D107)⋊C4—21no—
45(C2×D107)⋊C4—21no—
46C2×D4×C107—21no—
47C2×D4×C107—21no—
48C2×D4×C107D412yes—
49C2×C8×C107—21no—
50C2×C8×C107—21no—
51C42×C107C2311yescharacteristic
52C23×C107—22no—
53C22×D107—21no—
54C22×D107—21no—
55C22×D107—44no—
56C22×D107—44no—
57C22×D107—82no—
58D4×C107—42no—
59D4×C107—41no—
60D4×C107—41no—
61D4×C107—41no—
62D4×C107—41no—
63C2×C4×C107C2×D411yescharacteristic
64C2×C4×C107C2×D411yescharacteristic
65C2×C4×C107C2×D411yescharacteristic
66C22⋊D107—44no—
67C22⋊D107—44no—
68C2×Dic107—21no—
69C2×Dic107—21no—
70C2×Dic107—41no—
71D428—21no—
72D428—21no—
73D428D812yes—
74D428SD1612yescomplemented
75C4×D107—41no—
76C4×D107—41no—
77C4×D107—41no—
78C4×D107—41no—
79Dic214—41no—
80Dic214—41no—
81C8×C107—41no—
82C8×C107—41no—
83C107⋊C8—41no—
84C22×C107—42no—
85C22×C107—42no—
86C22×C107—42no—
87C22×C107#12011yescharacteristic
88C2×D107—22no—
89C2×D107—22no—
90C2×D107—41no—
91C2×D107—41no—
92C2×D107—41no—
93C2×D107—41no—
94C2×D107—88no—
95C4×C107—21no—
96C4×C107C2×D811yescharacteristic
97C4×C107C2×SD1611yescharacteristic
98C4×C107AGL(1,ℤ/8)11yescharacteristic
99C4×C107AGL(1,ℤ/8)11yescharacteristic
100Dic107—41no—
101Dic107—41no—
102Dic107—81no—
103C2×C107—82no—
104C2×C107#44711yescharacteristic
105C2×C107#45011yescharacteristic
106C2×C107#45511yescharacteristic
107D107—42no—
108D107—42no—
109#1639—1071nomaximal, Sylow
110C107#163911yescharacteristic, complemented, Sylow
111D42—1071no—
112#486—1071no—
113#474—1071no—
114#461—1071no—
115#331D10711yescharacteristic, complemented
116D4⋊C8—1071no—
117D4⋊C8—1071no—
118C22×D4—2141no—
119C22×D4—2141no—
120C2×SD16—2141no—
121C4⋊Q8—1071no—
122#127C2×D10711yescharacteristic
123#121—2141no—
124#121—2141no—
125#120—2142no—
126C4×D4—1071no—
127C4×D4—1071no—
128#107—2141no—
129C4⋊C8C2×D10711yescharacteristic, complemented
130C4⋊C8C2×D10711yescharacteristic, complemented
131#103—2141no—
132#102—2141no—
133#102—2142no—
134C4×C8—1071no—
135C24—2142no—
136C2×Q8—2141no—
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—1071no—
140C2×D4—1071no—
141C2×D4—4282no—
142C2×D4—4282no—
143C2×D4—4282no—
144C2×D4—4282no—
145C2×D4—2142no—
146C2×D4—2142no—
147C2×D4D42812yes—
148C22×C4—2141no—
149C22×C4—2141no—
150SD16—4282no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—2141no—
154C4⋊C4—1071no—
155C4⋊C4—1071no—
156C4⋊C4—2141no—
157C4⋊C4—2141no—
158C22⋊C4—2142no—
159C22⋊C4—2141no—
160C22⋊C4—2141no—
161C42C22×D10711yescharacteristic
162C23—22no—
163C23—8562no—
164C23—4284no—
165C23—4284no—
166C23—2141no—
167C23—2141no—
168Q8—4281no—
169Q8—4281no—
170D4—42no—
171D4—41no—
172D4—41no—
173D4—41no—
174D4—41no—
175D4—1072no—
176D4—1072no—
177D4—4284no—
178D4—4284no—
179D4—2141no—
180D4—2141no—
181C2×C4—4281no—
182C2×C4—4281no—
183C2×C4—4281no—
184C2×C4—4281no—
185C2×C4—4281no—
186C2×C4—2141no—
187C2×C4—2141no—
188C2×C4D4×D10711yescharacteristic
189C2×C4D4×D10711yescharacteristic
190C2×C4C2×D42811yescharacteristic
191C8—41no—
192C8—41no—
193C8—4281no—
194C22—42no—
195C22—42no—
196C22—42no—
197C22—8568no—
198C22—4281no—
199C22—4281no—
200C22—4281no—
201C22—4281no—
202C22—2142no—
203C22—2142no—
204C22#1681207911yescharacteristic
205C4—21no—
206C4—8561no—
207C4—4281no—
208C4—4281no—
209C4D8×D10711yescharacteristic
210C4SD16×D10711yescharacteristic
211C4#1681213311yescharacteristic
212C4#1681213611yescharacteristic
213C2—82no—
214C2—4282no—
215C2—4282no—
216C2#2029276211yescharacteristic
217C2#2029277911yescharacteristic
218C2#2029280711yescharacteristic
subgroupG/H
centerC22#16812079
commutator, cosocleC42×C107C23
FrattiniC42C22×D107
Fitting#331×C107C2
socleC22×C107#120
prime radical#20293262C2
hypercenter#331D107
hypocenterC107#1639
LCSG ▷ C42×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #20292973C2semidirect
3. #20292908C2semidirect
4. #20292833C2semidirect
5. #20292354C2semidirect
6. #20292354C2semidirect
7. #331×C107C2semidirect
11. #16812109C22semidirect
21. C4×C107⋊C8C22semidirect
23. C4⋊C8×C107C22semidirect
24. C4⋊C8×C107C22semidirect
74. D428SD16semidirect
110. C107#1639semidirect
115. #331D107semidirect
129. C4⋊C8C2×D107semidirect
130. C4⋊C8C2×D107semidirect

Maximal subgroups

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

subgroupindex
#202932622
#202929732
#202929082
#202928332
#202923542
#331×C1072
#1639107