Finite Group Databasebeta

← #28362107

Subgroups — #28362107

Order 13952.

236 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 55 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#20295736C211yesmaximal, characteristic, complemented
2#20295399C211yesmaximal, characteristic, complemented
3#20295226C211yesmaximal, characteristic, complemented
4#20295222C211yesmaximal, characteristic
5#20294774C211yesmaximal, characteristic, complemented
6#20294755C211yesmaximal, characteristic, complemented
7Q8⋊C8×C109C211yesmaximal, characteristic, complemented
8C2×#13182018—22no—
9C2×#13182016—21no—
10C2×D872—21no—
11#16812699C2211yescharacteristic
12#16812696C2211yescharacteristic
13#16812691—21no—
14#16812677—22no—
15#16812675—21no—
16C4×D436—21no—
17C4×D436C2211yescharacteristic
18C4⋊C4×D109—21no—
19C4⋊#11724784C2211yescharacteristic
20#16812621—21no—
21#16812619—21no—
22C4×Q8×C109C2211yescharacteristic
23C4⋊C8×C109C2211yescharacteristic
24C4×C8×C109C2211yescharacteristic
25C2×Dic218D412yes—
26C2×D436—21no—
27C2×D436—21no—
28C2×D436—21no—
29C2×D436D411yescharacteristic
30C2×C4×D109—21no—
31C2×C4×D109—22no—
32#13182018—44no—
33#13182016—42no—
34D872—42no—
35C2×#11724784—21no—
36C4⋊Dic109—21no—
37C4⋊Dic109—21no—
38C4⋊Dic109D411yescharacteristic
39#13182008—22no—
40#13182008—22no—
41#13182006—22no—
42#13182006—21no—
43C2×Q8×C109D411yescharacteristic
44C2×C8×C109—21no—
45C2×C8×C109—21no—
46C4⋊C4×C109—21no—
47C4⋊C4×C109D411yescharacteristic
48C42×C109—21no—
49C42×C109C2311yescharacteristic
50C22×D109—21no—
51C22×D109—41no—
52Q8×C109—21no—
53Q8×C109—21no—
54C2×C4×C109—21no—
55C2×C4×C109—21no—
56C2×C4×C109C2×D411yescharacteristic
57C2×C4×C109C2×D411yescharacteristic
58C2×C4×C109C2×D411yescharacteristic
59C2×Dic109—21no—
60C2×Dic109—22no—
61D436—21no—
62D436—42no—
63D436—41no—
64D436—41no—
65D436—41no—
66D436—41no—
67D436SD1612yescomplemented
68C4×D109—41no—
69C4×D109—41no—
70C4×D109—82no—
71Dic218—42no—
72C8×C109—22no—
73C8×C109—41no—
74#11724784—41no—
75C22×C109#12011yescharacteristic
76C2×D109—22no—
77C2×D109—41no—
78C2×D109—41no—
79C2×D109—81no—
80C2×D109—81no—
81C2×D109—81no—
82C4×C109—21no—
83C4×C109—41no—
84C4×C109—41no—
85C4×C109C2×SD1611yescharacteristic
86C4×C109#13511yescharacteristic
87C4×C109AGL(1,ℤ/8)11yescharacteristic
88C4×C109#13711yescharacteristic
89Dic109—41no—
90Dic109—42no—
91C2×C109#44811yescharacteristic
92C2×C109#44911yescharacteristic
93C2×C109#45311yescharacteristic
94D109—42no—
95D109—161no—
96#1622—1091nomaximal, Sylow
97C109#162211yescharacteristic, complemented, Sylow
98#554—1091no—
99#492—1091no—
100#460—1091no—
101#459—1091no—
102#333—1091no—
103Q8⋊C8D10911yescharacteristic, complemented
104D4⋊C8—1091no—
105C2×SD16—2182no—
106C2×SD16—2181no—
107C2×D8—2181no—
108C4⋊Q8—1091no—
109#127—1091no—
110#125—2181no—
111C22⋊Q8—2182no—
112C22⋊Q8—2181no—
113C4×Q8C2×D10911yescharacteristic
114C4×D4—1091no—
115C4×D4—2181no—
116C2×C4⋊C4—2181no—
117C4⋊C8—1091no—
118C4⋊C8C2×D10911yescharacteristic
119#102—2181no—
120#102—2181no—
121C4×C8C2×D10911yescharacteristic
122C2×Q8—1092no—
123C2×Q8D43611yescharacteristic
124C2×D4—1091no—
125C2×D4—2181no—
126C2×D4—2181no—
127C2×D4—2181no—
128C22×C4—2182no—
129C22×C4—2181no—
130SD16—4364no—
131SD16—4362no—
132D8—4362no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—2181no—
136C4⋊C4—21no—
137C4⋊C4—1091no—
138C4⋊C4—2182no—
139C4⋊C4—2182no—
140C4⋊C4—2181no—
141C4⋊C4—2181no—
142C4⋊C4D43611yescharacteristic
143C22⋊C4—2182no—
144C22⋊C4—2181no—
145C42—21no—
146C42C22×D10911yescharacteristic
147C23—4361no—
148C23—2181no—
149Q8—21no—
150Q8—21no—
151Q8—4362no—
152D4—1092no—
153D4—4362no—
154D4—4361no—
155D4—4361no—
156D4—4361no—
157D4—4361no—
158D4—2181no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—8722no—
162C2×C4—4361no—
163C2×C4—4361no—
164C2×C4—2181no—
165C2×C4—2182no—
166C2×C4D4×D10911yescharacteristic
167C2×C4D4×D10911yescharacteristic
168C2×C4C2×D43611yescharacteristic
169C8—22no—
170C8—41no—
171C8—4361no—
172C22—8721no—
173C22—8721no—
174C22—8721no—
175C22—4361no—
176C22—4361no—
177C22—2182no—
178C22#1681266911yescharacteristic
179C4—21no—
180C4—41no—
181C4—41no—
182C4—4361no—
183C4—4362no—
184C4SD16×D10911yescharacteristic
185C4#1681272111yescharacteristic
186C4#1681272711yescharacteristic
187C4#1681273111yescharacteristic
188C2—4362no—
189C2—17441no—
190C2#2029516611yescharacteristic
191C2#2029517311yescharacteristic
192C2#2029519511yescharacteristic
subgroupG/H
centerC22#16812669
commutator, cosocleC42×C109C23
FrattiniC42C22×D109
FittingQ8⋊C8×C109C2
socleC22×C109#120
prime radical#20295222C2
hypercenterQ8⋊C8D109
hypocenterC109#1622
LCSG ▷ C42×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. #20295736C2semidirect
2. #20295399C2semidirect
3. #20295226C2semidirect
5. #20294774C2semidirect
6. #20294755C2semidirect
7. Q8⋊C8×C109C2semidirect
67. D436SD16semidirect
97. C109#1622semidirect
103. Q8⋊C8D109semidirect

Maximal subgroups

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

subgroupindex
#202957362
#202953992
#202952262
#202952222
#202947742
#202947552
Q8⋊C8×C1092
#1622109