Finite Group Databasebeta

← #28364253

Subgroups — #28364253

Order 13952.

306 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 71 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×#16812626C212yesmaximal, complemented
2#20295027C212yesmaximal, complemented
3#20294895C211yesmaximal, characteristic, complemented
4#20294795C211yesmaximal, characteristic, complemented
5#537×C109C211yesmaximal, characteristic
6C2×#13182013C2212yes—
7C2×C4⋊Dic109C2211yescharacteristic
8C2×#13182008—22no—
9C2×C4×Dic109C2211yescharacteristic
10#16812626—24no—
11#16812623—22no—
12#16812620—22no—
13C2×#41×C109C2212yes—
14C22⋊Q8×C109—22no—
15#121×C109—22no—
16#121×C109—22no—
17C2×C4⋊C4×C109C2211yescharacteristic
18C22×Dic109—21no—
19C22×Dic109—21no—
20#13182013—22no—
21#13182013—22no—
22C2×#11724784—22no—
23C4⋊Dic109—22no—
24#13182008—44no—
25C4×Dic109—21no—
26C4×Dic109D412yescomplemented
27#41×C109—22no—
28#41×C109—22no—
29#41×C109—22no—
30#41×C109—22no—
31C2×Q8×C109D412yes—
32C2×D4×C109—22no—
33C2×D4×C109—22no—
34C2×D4×C109D412yes—
35C22×C4×C109—22no—
36C22×C4×C109D412yes—
37C22×C4×C109C2311yescharacteristic
38C4⋊C4×C109—22no—
39C4⋊C4×C109—22no—
40C22⋊C4×C109—24no—
41C23×C109—22no—
42C23×C109C2×D411yescharacteristic
43Q8×C109—22no—
44Q8×C109—22no—
45D4×C109—22no—
46D4×C109—22no—
47D4×C109—42no—
48D4×C109—42no—
49D4×C109—82no—
50C2×C4×C109—22no—
51C2×C4×C109—22no—
52C2×C4×C109—42no—
53C2×C4×C109—42no—
54C2×C4×C109—42no—
55C2×C4×C109C2×D411yescharacteristic
56C2×C4×C109C2×D412yes—
57C2×C4×C109#4112yes—
58C2×C4×C109#4111yescharacteristic
59C2×Dic109—22no—
60C2×Dic109—22no—
61C2×Dic109—22no—
62C2×Dic109—42no—
63C2×Dic109—41no—
64#11724784—42no—
65C22×C109—21no—
66C22×C109—21no—
67C22×C109—42no—
68C22×C109—42no—
69C22×C109—42no—
70C22×C109#12011yescharacteristic
71C22×C109#12111yescharacteristic
72C22×C109#12411yescharacteristic
73C4×C109—42no—
74C4×C109—42no—
75C4×C109#12112yes—
76C4×C109#12312yes—
77Dic109—24no—
78Dic109—81no—
79C2×C109—21no—
80C2×C109—21no—
81C2×C109—82no—
82C2×C109#39411yescharacteristic
83C2×C109#45311yescharacteristic
84C2×C109#45611yescharacteristic
85#2039—1091nomaximal, Sylow
86C109#203911yescharacteristic, complemented, Sylow
87#537D10911yescharacteristic
88C2×#104—1092no—
89#417—1092no—
90#384—1091no—
91#343—1091no—
92C2×#41C2×D10912yes—
93C2×M16—1092no—
94C22⋊Q8—22no—
95#121—22no—
96#121—22no—
97C2×C4⋊C4—1091no—
98C2×C4⋊C4—2182no—
99C2×C4⋊C4C2×D10911yescharacteristic
100C2×C42—1091no—
101#104—2184no—
102#103—2182no—
103#102—2182no—
104#41—22no—
105#41—22no—
106#41—22no—
107#41—22no—
108C2×Q8C22⋊D10912yes—
109C2×D4—22no—
110C2×D4—22no—
111C2×D4C22⋊D10912yes—
112C22×C4—22no—
113C22×C4—2181no—
114C22×C4—2181no—
115C22×C4C22⋊D10912yes—
116C22×C4C22×D10911yescharacteristic
117M16—2182no—
118M16—2182no—
119C2×C8—2182no—
120C4⋊C4—22no—
121C4⋊C4—22no—
122C4⋊C4—4364no—
123C4⋊C4—2182no—
124C22⋊C4—24no—
125C42—1092no—
126C42—2181no—
127C23—22no—
128C23C2×C22⋊D10911yescharacteristic
129Q8—22no—
130Q8—22no—
131D4—22no—
132D4—22no—
133D4—42no—
134D4—42no—
135D4—82no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—42no—
139C2×C4—42no—
140C2×C4—42no—
141C2×C4—4362no—
142C2×C4—4361no—
143C2×C4—2182no—
144C2×C4—2182no—
145C2×C4—2182no—
146C2×C4D4×D10911yescharacteristic
147C2×C4C2×C22⋊D10912yes—
148C2×C4#1318202812yes—
149C2×C4#1318202811yescharacteristic
150C8—4362no—
151C22—21no—
152C22—21no—
153C22—42no—
154C22—42no—
155C22—42no—
156C22#1681266811yescharacteristic
157C22#1681267011yescharacteristic
158C22#1681268611yescharacteristic
159C4—42no—
160C4—42no—
161C4—8721no—
162C4—2184no—
163C4#1681267112yes—
164C4#1681268012yes—
165C2—21no—
166C2—21no—
167C2—82no—
168C2#2029494011yescharacteristic
169C2#2029519411yescharacteristic
170C2#2029520911yescharacteristic
subgroupG/H
centerC22#16812668
commutator, cosocleC22×C4×C109C23
FrattiniC22×C4C22×D109
Fitting, prime radical#537×C109C2
socleC22×C109#120
hypercenter#537D109
hypocenterC109#2039
LCSG ▷ C22×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C2×#16812626C2semidirect
2. #20295027C2semidirect
3. #20294895C2semidirect
4. #20294795C2semidirect
26. C4×Dic109D4semidirect
86. C109#2039semidirect

Maximal subgroups

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

subgroupindex
C2×#168126262
#202950272
#202948952
#202947952
#537×C1092
#2039109