Finite Group Databasebeta

← #28364078

Subgroups — #28364078

Order 13952.

370 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 73 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×#16812730C212yesmaximal, complemented
2#20295607C211yesmaximal, characteristic
3C2×#16812627C212yesmaximal, complemented
4#20294795C211yesmaximal, characteristic, complemented
5#391×C109C211yesmaximal, characteristic, complemented
6C2×#13182029C2212yes—
7#16812730—24no—
8#16812730—24no—
9C2×#13182019—22no—
10C2×#13182016—22no—
11C2×#13182013C2212yes—
12#16812679—22no—
13#16812674—22no—
14#16812673—22no—
15#16812627—24no—
16C22×Q8×C109C2211yescharacteristic
17C2×C4⋊C4×C109C2211yescharacteristic
18C2×C42×C109C2211yescharacteristic
19#95×C109—22no—
20#13182029—22no—
21#13182029—22no—
22#13182029—22no—
23#13182029—22no—
24C2×Dic218D412yes—
25C2×D436—22no—
26C2×D436D412yes—
27C2×C22⋊D109—22no—
28C2×C4×D109—22no—
29#13182019—28no—
30#13182016—28no—
31#13182013—22no—
32#13182013D414yescomplemented
33C2×#11724784—22no—
34C4⋊Dic109—22no—
35#13182006—24no—
36C2×Q8×C109—21no—
37C2×Q8×C109—22no—
38C2×Q8×C109—22no—
39C2×Q8×C109D412yescomplemented
40C22×C4×C109—21no—
41C22×C4×C109—21no—
42C22×C4×C109D412yes—
43C22×C4×C109C2311yescharacteristic
44C4⋊C4×C109—22no—
45C42×C109—22no—
46C23×C109C2×D411yescharacteristic
47C22×D109—22no—
48Q8×C109—24no—
49Q8×C109—42no—
50C2×C4×C109—22no—
51C2×C4×C109—22no—
52C2×C4×C109—22no—
53C2×C4×C109—41no—
54C2×C4×C109—41no—
55C2×C4×C109—41no—
56C2×C4×C109—41no—
57C2×C4×C109—42no—
58C2×C4×C109C2×D412yes—
59C2×C4×C109C2×D412yes—
60C2×C4×C109C2×D411yescharacteristic
61C2×C4×C109#4111yescharacteristic
62C22⋊D109—42no—
63C22⋊D109—42no—
64C2×Dic109—22no—
65D436—22no—
66D436—22no—
67D436—82no—
68C4×D109—42no—
69C4×D109—42no—
70Dic218—22no—
71Dic218—22no—
72#11724784—24no—
73C22×C109—21no—
74C22×C109—21no—
75C22×C109#12011yescharacteristic
76C22×C109#12111yescharacteristic
77C22×C109#12711yescharacteristic
78C2×D109—42no—
79C2×D109—42no—
80C2×D109—42no—
81C4×C109—42no—
82C4×C109—42no—
83C4×C109—42no—
84C4×C109#12012yes—
85C4×C109#12112yes—
86Dic109—42no—
87C2×C109—21no—
88C2×C109—21no—
89C2×C109#39211yescharacteristic
90C2×C109#45511yescharacteristic
91C2×C109#45611yescharacteristic
92D109—82no—
93#2007—1091nomaximal, Sylow
94C109#200711yescharacteristic, complemented, Sylow
95C2×#137—1092no—
96#537—1091no—
97C2×#104—1092no—
98#391D10911yescharacteristic, complemented
99#343—1091no—
100C2×#41—1092no—
101C22×Q8C2×D10911yescharacteristic
102#137—2184no—
103#137—2184no—
104C2×Q16—2182no—
105C2×SD16—2182no—
106C2×M16—1092no—
107C22⋊Q8—2182no—
108#121—2182no—
109#121—2182no—
110C2×C4⋊C4C2×D10911yescharacteristic
111C2×C42C2×D10911yescharacteristic
112#104—2184no—
113#95—22no—
114#41—2182no—
115#41—2182no—
116#41—2182no—
117#41—2182no—
118C2×Q8—21no—
119C2×Q8—22no—
120C2×Q8—22no—
121C2×Q8—1092no—
122C2×Q8D43612yescomplemented
123C2×D4—1092no—
124C2×D4—2182no—
125C2×D4—2182no—
126C22×C4—21no—
127C22×C4—21no—
128C22×C4—2182no—
129C22×C4C22⋊D10912yes—
130C22×C4C22×D10911yescharacteristic
131Q16—2188no—
132SD16—2188no—
133M16—1094no—
134M16—2182no—
135C2×C8—2182no—
136C4⋊C4—22no—
137C4⋊C4—2182no—
138C22⋊C4—2184no—
139C42—22no—
140C23—2182no—
141C23C2×C22⋊D10911yescharacteristic
142Q8—24no—
143Q8—42no—
144Q8—2182no—
145Q8—2182no—
146D4—8722no—
147D4—4362no—
148D4—4362no—
149D4—2182no—
150D4—2182no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—42no—
159C2×C4—4362no—
160C2×C4—4362no—
161C2×C4—2182no—
162C2×C4D4×D10912yes—
163C2×C4D4×D10912yes—
164C2×C4C2×D43611yescharacteristic
165C2×C4#1318202911yescharacteristic
166C8—2184no—
167C22—21no—
168C22—21no—
169C22—4362no—
170C22—4362no—
171C22—4362no—
172C22#1681266711yescharacteristic
173C22#1681267311yescharacteristic
174C22#1681269511yescharacteristic
175C4—42no—
176C4—42no—
177C4—42no—
178C4—4362no—
179C4#1681266912yes—
180C4#1681267212yes—
181C2—21no—
182C2—21no—
183C2—8722no—
184C2#2029493511yescharacteristic
185C2#2029520311yescharacteristic
186C2#2029520811yescharacteristic
subgroupG/H
centerC22#16812667
commutator, cosocleC22×C4×C109C23
FrattiniC22×C4C22×D109
Fitting#391×C109C2
socleC22×C109#120
prime radical#20295607C2
hypercenter#391D109
hypocenterC109#2007
LCSG ▷ C22×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#16812730C2semidirect
3. C2×#16812627C2semidirect
4. #20294795C2semidirect
5. #391×C109C2semidirect
32. #13182013D4semidirect
39. C2×Q8×C109D4semidirect
94. C109#2007semidirect
98. #391D109semidirect
122. C2×Q8D436semidirect

Maximal subgroups

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

subgroupindex
C2×#168127302
#202956072
C2×#168126272
#202947952
#391×C1092
#2007109