Finite Group Databasebeta

← C107×#2816 #28333499

Subgroups — C107×#2816 #28333499

Order 13696.

528 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 184 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×C22⋊Q8×C107C211yesmaximal, characteristic, complemented
2C2×#121×C107C211yesmaximal, characteristic
3#399×C107C212yesmaximal, complemented
4#398×C107C212yesmaximal, complemented
5#394×C107C212yesmaximal, complemented
6#394×C107C214yesmaximal, complemented
7#393×C107C212yesmaximal, complemented
8#381×C107C211yesmaximal, characteristic, complemented
9C22×Q8×C107C2211yescharacteristic
10C22×D4×C107C2212yes—
11C22×D4×C107C2211yescharacteristic
12C23×C4×C107C2211yescharacteristic
13C22⋊Q8×C107—24no—
14#121×C107—24no—
15C2×C4⋊C4×C107C2212yes—
16C2×C4⋊C4×C107C2211yescharacteristic
17C2×C4⋊C4×C107C2211yescharacteristic
18C2×C4⋊C4×C107C2214yes—
19C2×C22⋊C4×C107C2212yes—
20C2×C22⋊C4×C107C2212yes—
21C2×C22⋊C4×C107C2212yes—
22C2×C22⋊C4×C107C2214yes—
23C2×C22⋊C4×C107C2214yes—
24#95×C107C2212yes—
25#95×C107C2212yes—
26#95×C107C2214yes—
27C24×C107C2312yes—
28C24×C107C2311yescharacteristic
29C2×Q8×C107—22no—
30C2×Q8×C107—42no—
31C2×D4×C107—24no—
32C2×D4×C107—22no—
33C2×D4×C107—42no—
34C2×D4×C107—44no—
35C22×C4×C107—42no—
36C22×C4×C107D414yes—
37C22×C4×C107C2314yes—
38C22×C4×C107C2312yes—
39C22×C4×C107C2312yes—
40C22×C4×C107C2312yes—
41C22×C4×C107C2311yescharacteristic
42C22×C4×C107C2311yescharacteristic
43C4⋊C4×C107—22no—
44C4⋊C4×C107—22no—
45C4⋊C4×C107—24no—
46C4⋊C4×C107—44no—
47C22⋊C4×C107—24no—
48C22⋊C4×C107—24no—
49C22⋊C4×C107—42no—
50C22⋊C4×C107—44no—
51C22⋊C4×C107—44no—
52C23×C107—22no—
53C23×C107—22no—
54C23×C107—22no—
55C23×C107—22no—
56C23×C107—24no—
57C23×C107—24no—
58C23×C107—24no—
59C23×C107C2×D412yes—
60C23×C107C2411yescharacteristic
61Q8×C107—44no—
62D4×C107—44no—
63D4×C107—48no—
64C2×C4×C107—22no—
65C2×C4×C107—22no—
66C2×C4×C107—22no—
67C2×C4×C107—22no—
68C2×C4×C107—22no—
69C2×C4×C107—22no—
70C2×C4×C107—24no—
71C2×C4×C107—24no—
72C2×C4×C107—24no—
73C2×C4×C107—22no—
74C2×C4×C107—24no—
75C2×C4×C107—24no—
76C2×C4×C107—44no—
77C2×C4×C107C2×D412yes—
78C2×C4×C107C2×D412yes—
79C22×C107—22no—
80C22×C107—22no—
81C22×C107—22no—
82C22×C107—44no—
83C22×C107—42no—
84C22×C107—42no—
85C22×C107—42no—
86C22×C107—48no—
87C22×C107C22×D411yescharacteristic
88C22×C107H(5,𝔽2)12yes—
89C22×C107H(5,𝔽2)12yes—
90C22×C1072−1+412yes—
91C4×C107—22no—
92C4×C107—22no—
93C4×C107—42no—
94C4×C107—42no—
95C4×C107—42no—
96C4×C107—44no—
97C2×C107—42no—
98C2×C107—82no—
99C2×C107#53411yescharacteristic
100C2×C107#53511yescharacteristic
101C2×C107#53611yescharacteristic
102C2×C107#56214yes—
103#2816C10711yesmaximal, characteristic, direct product factor, Sylow
104C107#281611yescharacteristic, direct product factor, Sylow
105C2×C22⋊Q8C2×C10711yescharacteristic, complemented
106C2×#121C2×C10711yescharacteristic
107#399C2×C10712yescomplemented
108#398C2×C10712yescomplemented
109#394C2×C10712yescomplemented
110#394C2×C10714yescomplemented
111#393C2×C10712yescomplemented
112#381C2×C10711yescharacteristic, complemented
113C22×Q8C22×C10711yescharacteristic
114C22×D4C22×C10712yes—
115C22×D4C22×C10711yescharacteristic
116C23×C4C22×C10711yescharacteristic
117C22⋊Q8—24no—
118#121—24no—
119C2×C4⋊C4C22×C10711yescharacteristic
120C2×C4⋊C4C22×C10712yes—
121C2×C4⋊C4C22×C10711yescharacteristic
122C2×C4⋊C4C22×C10714yes—
123C2×C22⋊C4C22×C10712yes—
124C2×C22⋊C4C22×C10712yes—
125C2×C22⋊C4C22×C10712yes—
126C2×C22⋊C4C22×C10714yes—
127C2×C22⋊C4C22×C10714yes—
128#95C22×C10712yes—
129#95C22×C10712yes—
130#95C22×C10714yes—
131C24C23×C10712yes—
132C24C23×C10711yescharacteristic
133C2×Q8—22no—
134C2×Q8—42no—
135C2×D4—24no—
136C2×D4—22no—
137C2×D4—42no—
138C2×D4—44no—
139C22×C4—42no—
140C22×C4D4×C10714yes—
141C22×C4C23×C10714yes—
142C22×C4C23×C10712yes—
143C22×C4C23×C10712yes—
144C22×C4C23×C10712yes—
145C22×C4C23×C10711yescharacteristic
146C22×C4C23×C10711yescharacteristic
147C4⋊C4—22no—
148C4⋊C4—22no—
149C4⋊C4—24no—
150C4⋊C4—44no—
151C22⋊C4—24no—
152C22⋊C4—24no—
153C22⋊C4—42no—
154C22⋊C4—44no—
155C22⋊C4—44no—
156C23—22no—
157C23—22no—
158C23—22no—
159C23—22no—
160C23—24no—
161C23—24no—
162C23—24no—
163C23C2×D4×C10712yes—
164C23C24×C10711yescharacteristic
165Q8—44no—
166D4—44no—
167D4—48no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—24no—
175C2×C4—24no—
176C2×C4—24no—
177C2×C4—22no—
178C2×C4—24no—
179C2×C4—24no—
180C2×C4—44no—
181C2×C4C2×D4×C10712yes—
182C2×C4C2×D4×C10712yes—
183C22—22no—
184C22—22no—
185C22—22no—
186C22—44no—
187C22—42no—
188C22—42no—
189C22—42no—
190C22—48no—
191C22C22×D4×C10711yescharacteristic
192C22H(5,𝔽2)×C10712yes—
193C22H(5,𝔽2)×C10712yes—
194C222−1+4×C10712yes—
195C4—22no—
196C4—22no—
197C4—42no—
198C4—42no—
199C4—42no—
200C4—44no—
201C2—42no—
202C2—82no—
203C2#534×C10711yescharacteristic
204C2#535×C10711yescharacteristic
205C2#536×C10711yescharacteristic
206C2#562×C10714yes—
subgroupG/H
center, socleC23×C107C24
commutator, Frattini, cosocleC23C24×C107
prime radicalC2×#121×C107C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C22⋊Q8×C107C2semidirect
3. #399×C107C2semidirect
4. #398×C107C2semidirect
5. #394×C107C2semidirect
6. #394×C107C2semidirect
7. #393×C107C2semidirect
8. #381×C107C2semidirect
103. #2816C107direct (N × H)
104. C107#2816direct (N × H)
105. C2×C22⋊Q8C2×C107semidirect
107. #399C2×C107semidirect
108. #398C2×C107semidirect
109. #394C2×C107semidirect
110. #394C2×C107semidirect
111. #393C2×C107semidirect
112. #381C2×C107semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×C1072
C2×#121×C1072
#399×C1072
#398×C1072
#394×C1072
#393×C1072
#381×C1072
#2816107