Finite Group Databasebeta

← #28336932

Subgroups — #28336932

Order 13696.

304 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 85 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×#16812139C211yesmaximal, characteristic
2#20293394C211yesmaximal, characteristic
3#20292635C211yesmaximal, characteristic, complemented
4C2×#16812027C211yesmaximal, characteristic, complemented
5#20292397C211yesmaximal, characteristic, complemented
6C107⋊#338C211yesmaximal, characteristic, complemented
7#421×C107C211yesmaximal, characteristic
8C22×Dic214C2211yescharacteristic
9#16812139—22no—
10#16812139—22no—
11C2×#13133808C412yescomplemented
12C2×#13133806C412yescomplemented
13#16812116—22no—
14#16812116—22no—
15C2×#13133802—22no—
16C2×#13133802C2211yescharacteristic
17C2×#13133802C2211yescharacteristic
18C2×#13133802C2211yescharacteristic
19#16812032—22no—
20#16812027—22no—
21C2×#41×C107C2211yescharacteristic
22C2×M16×C107C2211yescharacteristic
23#117×C107C2211yescharacteristic
24#104×C107—22no—
25C2×Dic214—21no—
26C2×Dic214—21no—
27C2×Dic214—21no—
28C2×Dic214—21no—
29C2×Dic214—21no—
30C2×Dic214C2×C412yes—
31C22×Dic107—21no—
32#13133808—24no—
33#13133806—24no—
34#13133802—24no—
35#13133802—21no—
36#13133802—21no—
37#13133802—21no—
38#13133802—21no—
39#13133802—21no—
40#13133802D412yes—
41C2×C107⋊C8—24no—
42C2×C107⋊C8—21no—
43C2×C107⋊C8C2×C412yes—
44C2×C107⋊C8D412yes—
45#41×C107—21no—
46#41×C107—21no—
47#41×C107D412yes—
48#41×C107D412yes—
49C2×Q8×C107C2×C411yescharacteristic
50C2×D4×C107—21no—
51C2×D4×C107C2×C411yescharacteristic
52C22×C4×C107—21no—
53C22×C4×C107C2311yescharacteristic
54M16×C107—21no—
55M16×C107—21no—
56C2×C8×C107—21no—
57C4⋊C4×C107—21no—
58C22⋊C4×C107—21no—
59C42×C107—21no—
60C23×C107—21no—
61C23×C107#4111yescharacteristic
62Q8×C107—21no—
63Q8×C107C22⋊C412yes—
64D4×C107—22no—
65D4×C107—22no—
66D4×C107—21no—
67D4×C107C22⋊C412yes—
68C2×C4×C107—21no—
69C2×C4×C107—22no—
70C2×C4×C107—22no—
71C2×C4×C107—41no—
72C2×C4×C107C22×C411yescharacteristic
73C2×C4×C107C2×D411yescharacteristic
74C2×C4×C107C2×D411yescharacteristic
75C2×C4×C107C2×D411yescharacteristic
76C2×C4×C107C2×D411yescharacteristic
77C2×C4×C107#4111yescharacteristic
78C2×Dic107—22no—
79C2×Dic107—41no—
80C2×Dic107—41no—
81Dic214—22no—
82Dic214—22no—
83Dic214—41no—
84Dic214—41no—
85C8×C107—41no—
86C107⋊C8—22no—
87C107⋊C8—22no—
88C107⋊C8—22no—
89C22×C107—22no—
90C22×C107—41no—
91C22×C107—81no—
92C22×C107C4×D411yescharacteristic
93C22×C107#12111yescharacteristic
94C22×C107#12311yescharacteristic
95C4×C107—22no—
96C4×C107—81no—
97C4×C107C2×C22⋊C411yescharacteristic
98C4×C107C4×D411yescharacteristic
99C4×C107#12011yescharacteristic
100C4×C107#12111yescharacteristic
101Dic107—42no—
102C2×C107—21no—
103C2×C107—21no—
104C2×C107—21no—
105C2×C107—42no—
106C2×C107#38611yescharacteristic
107#1902—1071nomaximal, Sylow
108C107#190211yescharacteristic, complemented, Sylow
109C2×#137—1071no—
110#568—1071no—
111#421D10711yescharacteristic
112#419—1071no—
113C2×#101—1071no—
114#344—1071no—
115#338—1071no—
116C2×#41C2×D10711yescharacteristic
117C22×Q8—1071no—
118#137—2142no—
119#137—2142no—
120C2×Q16—1072no—
121C2×SD16—1072no—
122#131—2142no—
123#131—2142no—
124C2×M16—1071no—
125C2×M16—1071no—
126C2×M16—1071no—
127C2×M16—2142no—
128C2×M16C2×D10711yescharacteristic
129#117C2×D10711yescharacteristic
130#104—22no—
131#103—2142no—
132#101—2142no—
133#41—21no—
134#41—21no—
135#41D42812yes—
136#41C22⋊D10712yes—
137C2×Q8—1072no—
138C2×Q8—2141no—
139C2×Q8—2141no—
140C2×Q8—2141no—
141C2×Q8—2141no—
142C2×Q8—2141no—
143C2×Q8C4×D10711yescharacteristic
144C2×D4—21no—
145C2×D4C4×D10711yescharacteristic
146C22×C4—21no—
147C22×C4—2141no—
148C22×C4C22×D10711yescharacteristic
149Q16—2144no—
150SD16—2144no—
151M16—21no—
152M16—21no—
153M16—1072no—
154M16—2144no—
155M16—2141no—
156M16—2141no—
157M16—2141no—
158M16—2141no—
159M16—2141no—
160C2×C8—21no—
161C2×C8—1072no—
162C2×C8—1072no—
163C2×C8—2144no—
164C2×C8—2141no—
165C4⋊C4—21no—
166C22⋊C4—21no—
167C42—21no—
168C23—21no—
169C23#1313381711yescharacteristic
170Q8—21no—
171Q8—4281no—
172Q8—4281no—
173Q8—2142no—
174Q8—2142no—
175Q8(C2×D107)⋊C412yes—
176D4—22no—
177D4—22no—
178D4—21no—
179D4(C2×D107)⋊C412yes—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—41no—
184C2×C4—4281no—
185C2×C4—4281no—
186C2×C4—2142no—
187C2×C4C2×C4×D10711yescharacteristic
188C2×C4D4×D10711yescharacteristic
189C2×C4D4×D10711yescharacteristic
190C2×C4C2×C22⋊D10711yescharacteristic
191C2×C4C2×D42811yescharacteristic
192C2×C4#1313381711yescharacteristic
193C8—41no—
194C8—2142no—
195C8—2142no—
196C8—2142no—
197C22—22no—
198C22—41no—
199C22—81no—
200C22(C22⋊D107)⋊C411yescharacteristic
201C22#1681208111yescharacteristic
202C22#1681209311yescharacteristic
203C4—22no—
204C4—81no—
205C4—4282no—
206C4C2×(C2×D107)⋊C411yescharacteristic
207C4(C22⋊D107)⋊C411yescharacteristic
208C4#1681207911yescharacteristic
209C4#1681208111yescharacteristic
210C2—21no—
211C2—21no—
212C2—21no—
213C2—42no—
214C2#2029250411yescharacteristic
subgroupG/H
centerC2#20292504
commutatorC2×C4×C107C22×C4
FrattiniC22×C4C22×D107
Fitting#421×C107C2
socleC2×C107#386
prime radicalC2×#41×C107C22
cosocleC22×C4×C107C23
hypercenter#421D107
hypocenterC107#1902
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C2 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
3. #20292635C2semidirect
4. C2×#16812027C2semidirect
5. #20292397C2semidirect
6. C107⋊#338C2semidirect
11. C2×#13133808C4semidirect
12. C2×#13133806C4semidirect
108. C107#1902semidirect

Maximal subgroups

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

subgroupindex
C2×#168121392
#202933942
#202926352
C2×#168120272
#202923972
C107⋊#3382
#421×C1072
#1902107