Finite Group Databasebeta

← #28335689

Subgroups — #28335689

Order 13696.

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

normal subgroups only

This group has 212 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#20292977C211yesmaximal, characteristic, complemented
2#20292907C211yesmaximal, characteristic, complemented
3#20292832C211yesmaximal, characteristic, complemented
4#20292376C211yesmaximal, characteristic, complemented
5D4⋊(C107⋊C8)C211yesmaximal, characteristic, complemented
6D4⋊(C107⋊C8)C211yesmaximal, characteristic, complemented
7#555×C107C211yesmaximal, characteristic
8C2×#13133806—21no—
9#16812109C2211yescharacteristic
10#16812042—21no—
11C4⋊(C107⋊C8)C2211yescharacteristic
12C4⋊(C107⋊C8)C2211yescharacteristic
13#16812033—22no—
14#16812032—21no—
15#16812030—21no—
16C4×C107⋊C8C2211yescharacteristic
17C4⋊Q8×C107C2211yescharacteristic
18#124×C107—22no—
19#121×C107—21no—
20#121×C107—21no—
21C4×D4×C107C2211yescharacteristic
22C4×D4×C107C2211yescharacteristic
23#117×C107—21no—
24#117×C107—21no—
25C2×Dic214—21no—
26#13133806—42no—
27C2×C107⋊C8—21no—
28C2×C107⋊C8—21no—
29C2×C107⋊C8—21no—
30C4⋊Dic107—21no—
31C4⋊Dic107—21no—
32C2×Q8×C107D412yes—
33C2×D4×C107—22no—
34C2×D4×C107D411yescharacteristic
35C2×D4×C107D411yescharacteristic
36C22×C4×C107—21no—
37C22×C4×C107—21no—
38C4⋊C4×C107—21no—
39C4⋊C4×C107—21no—
40C4⋊C4×C107D411yescharacteristic
41C4⋊C4×C107D411yescharacteristic
42C22⋊C4×C107—22no—
43C22⋊C4×C107—22no—
44C22⋊C4×C107—21no—
45C22⋊C4×C107—21no—
46C42×C107—22no—
47C42×C107C2311yescharacteristic
48C23×C107—21no—
49C23×C107—21no—
50Q8×C107—42no—
51D4×C107—21no—
52D4×C107—21no—
53D4×C107—21no—
54D4×C107—21no—
55D4×C107—82no—
56C2×C4×C107—21no—
57C2×C4×C107—21no—
58C2×C4×C107—22no—
59C2×C4×C107—41no—
60C2×C4×C107—41no—
61C2×C4×C107—41no—
62C2×C4×C107—41no—
63C2×C4×C107C2×D411yescharacteristic
64C2×C4×C107C2×D411yescharacteristic
65C2×C4×C107C2×D411yescharacteristic
66C2×Dic107—41no—
67Dic214—41no—
68Dic214—41no—
69C107⋊C8—41no—
70C107⋊C8—41no—
71C107⋊C8—41no—
72C22×C107—41no—
73C22×C107—41no—
74C22×C107—41no—
75C22×C107—41no—
76C22×C107—41no—
77C22×C107—41no—
78C22×C107#12011yescharacteristic
79C4×C107—21no—
80C4×C107—41no—
81C4×C107—41no—
82C4×C107—42no—
83C4×C107#13511yescharacteristic
84C4×C107#13511yescharacteristic
85C4×C107AGL(1,ℤ/8)11yescharacteristic
86C4×C107#13711yescharacteristic
87Dic107—81no—
88C2×C107—81no—
89C2×C107—81no—
90C2×C107#44911yescharacteristic
91C2×C107#45211yescharacteristic
92C2×C107#45511yescharacteristic
93#1646—1071nomaximal, Sylow
94C107#164611yescharacteristic, complemented, Sylow
95#555D10711yescharacteristic
96#487—1071no—
97#474—1071no—
98#461—1071no—
99#333—1071no—
100D4⋊C8—1071no—
101D4⋊C8—1071no—
102C2×SD16—2141no—
103C4⋊Q8—1071no—
104C4⋊Q8C2×D10711yescharacteristic
105#124—22no—
106#121—21no—
107#121—21no—
108C4×D4C2×D10711yescharacteristic
109C4×D4C2×D10711yescharacteristic
110#117—21no—
111#117—21no—
112#107—2141no—
113C4⋊C8—1071no—
114C4⋊C8—1071no—
115#103—2142no—
116#103—2141no—
117#102—2141no—
118C4×C8—1071no—
119C2×Q8—2141no—
120C2×Q8C22⋊D10712yes—
121C2×D4—22no—
122C2×D4C22⋊D10711yescharacteristic
123C2×D4C22⋊D10711yescharacteristic
124C22×C4—21no—
125C22×C4—21no—
126SD16—4282no—
127C2×C8—2141no—
128C2×C8—2141no—
129C2×C8—2141no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—2141no—
133C4⋊C4—2141no—
134C4⋊C4C22⋊D10711yescharacteristic
135C4⋊C4C22⋊D10711yescharacteristic
136C22⋊C4—22no—
137C22⋊C4—22no—
138C22⋊C4—21no—
139C22⋊C4—21no—
140C42—22no—
141C42C22×D10711yescharacteristic
142C23—21no—
143C23—21no—
144Q8—42no—
145Q8—4281no—
146Q8—4281no—
147D4—21no—
148D4—21no—
149D4—21no—
150D4—21no—
151D4—82no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—22no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—4281no—
160C2×C4C2×C22⋊D10711yescharacteristic
161C2×C4C2×C22⋊D10711yescharacteristic
162C2×C4C2×C22⋊D10711yescharacteristic
163C8—4281no—
164C8—4281no—
165C8—4281no—
166C22—41no—
167C22—41no—
168C22—41no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22#1681207811yescharacteristic
173C4—21no—
174C4—41no—
175C4—41no—
176C4—42no—
177C4—8561no—
178C4#1681212911yescharacteristic
179C4#1681212911yescharacteristic
180C4#1681213411yescharacteristic
181C4#1681213911yescharacteristic
182C2—81no—
183C2—81no—
184C2#2029277211yescharacteristic
185C2#2029278911yescharacteristic
186C2#2029280511yescharacteristic
subgroupG/H
centerC22#16812078
commutator, cosocleC42×C107C23
FrattiniC42C22×D107
Fitting, prime radical#555×C107C2
socleC22×C107#120
hypercenter#555D107
hypocenterC107#1646
LCSG ▷ C42×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #555

Complements

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

NH ≅ G/Ntype
1. #20292977C2semidirect
2. #20292907C2semidirect
3. #20292832C2semidirect
4. #20292376C2semidirect
5. D4⋊(C107⋊C8)C2semidirect
6. D4⋊(C107⋊C8)C2semidirect
94. C107#1646semidirect

Maximal subgroups

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

subgroupindex
#202929772
#202929072
#202928322
#202923762
D4⋊(C107⋊C8)2
#555×C1072
#1646107