Finite Group Databasebeta

← #28375608

Subgroups — #28375608

Order 13952.

336 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 113 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#20295717C212yesmaximal
2#20295428C211yesmaximal, characteristic, complemented
3#20295366C212yesmaximal, complemented
4#20295360C212yesmaximal, complemented
5#20295333C212yesmaximal, complemented
6#20295281C212yesmaximal, complemented
7#20295105C211yesmaximal, characteristic
8#20295067C212yesmaximal, complemented
9C4×Q16×C109C211yesmaximal, characteristic, complemented
10C2×#13182012C2212yes—
11#16812693—22no—
12#16812691C2212yes—
13#16812689—22no—
14#16812684—22no—
15#16812675C2212yes—
16#16812675C2212yes—
17C4×D436C2211yescharacteristic
18#16812657C2212yes—
19#16812656—22no—
20C4⋊C4×D109C2212yes—
21#16812633C2211yescharacteristic
22#16812633C2211yescharacteristic
23#16812632C2212yes—
24#16812631C2212yes—
25#16812630C2212yes—
26C4⋊#11724784C2211yescharacteristic
27#16812623C2212yes—
28#16812623C2212yes—
29#16812611C2212yes—
30C2×Q16×C109C2211yescharacteristic
31C4×Q8×C109C2212yes—
32#107×C109C2211yescharacteristic
33#103×C109C2212yes—
34C4×C8×C109C2211yescharacteristic
35C2×D436D411yescharacteristic
36C2×C4×D109—22no—
37C2×C4×D109C2312yes—
38#13182012—24no—
39C2×#11724784C2312yes—
40C4⋊Dic109D411yescharacteristic
41C4⋊Dic109C2312yes—
42C4⋊Dic109C2312yes—
43#13182008—22no—
44#13182008—22no—
45#13182008—22no—
46#13182008—22no—
47#13182008—22no—
48#13182006—22no—
49#13182006—22no—
50#13182006—22no—
51#13182006D412yes—
52C4×Dic109—22no—
53C2×Q8×C109C2312yes—
54Q16×C109—22no—
55C2×C8×C109C2311yescharacteristic
56C2×C8×C109C2311yescharacteristic
57C4⋊C4×C109—22no—
58C4⋊C4×C109C2312yes—
59C42×C109—22no—
60C42×C109C2311yescharacteristic
61C22×D109C2×D412yes—
62Q8×C109—22no—
63Q8×C109—22no—
64C2×C4×C109—22no—
65C2×C4×C109—22no—
66C2×C4×C109C2×D411yescharacteristic
67C2×C4×C109C2×D411yescharacteristic
68C2×C4×C109C2411yescharacteristic
69C2×Dic109—22no—
70C2×Dic109—22no—
71C2×Dic109C2×D412yes—
72D436—41no—
73C4×D109—22no—
74C4×D109—22no—
75C4×D109—44no—
76C8×C109—21no—
77C8×C109#4112yes—
78#11724784—22no—
79C22×C109C22×D411yescharacteristic
80C2×D109—22no—
81C2×D109—22no—
82C2×D109—22no—
83C4×C109—21no—
84C4×C109—21no—
85C4×C109—42no—
86C4×C109—42no—
87C4×C109C2×#4111yescharacteristic
88C4×C1092−1+411yescharacteristic
89Dic109—22no—
90Dic109—42no—
91Dic109—42no—
92C2×C109#54711yescharacteristic
93C2×C109#57511yescharacteristic
94C2×C109#57811yescharacteristic
95D109—42no—
96#3352—1091nomaximal, Sylow
97C109#335211yescharacteristic, complemented, Sylow
98#552—1092no—
99#499—1091no—
100#485—1092no—
101#484—1092no—
102#479—1092no—
103#470—1092no—
104C4×Q16D10911yescharacteristic, complemented
105#436—1091no—
106#428—1092no—
107C2×Q16C2×D10911yescharacteristic
108C2×M16—1092no—
109#126—2182no—
110#125—1092no—
111#125—2182no—
112#123—2182no—
113C22⋊Q8—1092no—
114C22⋊Q8—1092no—
115C4×Q8C2×D10912yes—
116C4×D4—1091no—
117#117—1092no—
118#117—2182no—
119C2×C4⋊C4—1092no—
120#107—1091no—
121#107—1091no—
122#107—1092no—
123#107C2×D10911yescharacteristic
124#106—1092no—
125#106—1092no—
126C4⋊C8—1091no—
127#103—1092no—
128#103—1092no—
129#103C2×D10912yes—
130C22⋊C8—1092no—
131C4×C8C2×D10911yescharacteristic
132C2×Q8C22×D10912yes—
133C2×D4—1091no—
134C22×C4—1092no—
135C22×C4—2182no—
136Q16—22no—
137M16—2184no—
138C2×C8—1092no—
139C2×C8C22×D10911yescharacteristic
140C2×C8C22×D10911yescharacteristic
141C4⋊C4—22no—
142C4⋊C4—1091no—
143C4⋊C4—1092no—
144C4⋊C4—1092no—
145C4⋊C4—2182no—
146C4⋊C4—2182no—
147C4⋊C4—2182no—
148C4⋊C4—2182no—
149C4⋊C4—2182no—
150C4⋊C4C22×D10912yes—
151C22⋊C4—1092no—
152C22⋊C4—2182no—
153C22⋊C4—2182no—
154C22⋊C4—2182no—
155C42—22no—
156C42—2182no—
157C42C22×D10911yescharacteristic
158C23—1092no—
159Q8—22no—
160Q8—22no—
161D4—4361no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—1092no—
165C2×C4—4364no—
166C2×C4—2182no—
167C2×C4—2182no—
168C2×C4—2182no—
169C2×C4—2182no—
170C2×C4D4×D10911yescharacteristic
171C2×C4D4×D10911yescharacteristic
172C2×C4C23×D10911yescharacteristic
173C8—21no—
174C8—2182no—
175C8#1318202912yes—
176C22—2182no—
177C22—2182no—
178C22—2182no—
179C22C2×D4×D10911yescharacteristic
180C4—21no—
181C4—21no—
182C4—42no—
183C4—42no—
184C4—4362no—
185C4—4362no—
186C4—2182no—
187C4C2×#1318202911yescharacteristic
188C4#1681274611yescharacteristic
189C2—4362no—
190C2#2029568111yescharacteristic
191C2#2029582311yescharacteristic
192C2#2029583911yescharacteristic
subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
FittingC4×Q16×C109C2
socleC22×C109C22×D4
prime radicalC2×D436D4
hypercenterC4×Q16D109
hypocenterC109#3352
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
2. #20295428C2semidirect
3. #20295366C2semidirect
4. #20295360C2semidirect
5. #20295333C2semidirect
6. #20295281C2semidirect
8. #20295067C2semidirect
9. C4×Q16×C109C2semidirect
97. C109#3352semidirect
104. C4×Q16D109semidirect

Maximal subgroups

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

subgroupindex
#202957172
#202954282
#202953662
#202953602
#202953332
#202952812
#202951052
#202950672
C4×Q16×C1092
#3352109