Finite Group Databasebeta

← #28362012

Subgroups — #28362012

Order 13952.

260 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 53 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#20295181C211yesmaximal, characteristic, complemented
2#20295164C211yesmaximal, characteristic, complemented
3#20294938C211yesmaximal, characteristic, complemented
4#20294763C211yesmaximal, characteristic, complemented
5#20294760C211yesmaximal, characteristic, complemented
6#20294750C211yesmaximal, characteristic, complemented
7#538×C109C211yesmaximal, characteristic
8C22×Dic218C2211yescharacteristic
9C2×#13182019—21no—
10C2×#13182017—21no—
11C2×C22⋊Dic109—21no—
12#16812622—21no—
13#16812622—21no—
14C22⋊#11724784C2211yescharacteristic
15C22⋊#11724784C2211yescharacteristic
16#16812606—21no—
17#16812606C2211yescharacteristic
18#126×C109—21no—
19#124×C109—21no—
20#123×C109—21no—
21C22⋊Q8×C109C2211yescharacteristic
22#121×C109—21no—
23#121×C109C2211yescharacteristic
24#120×C109—21no—
25C4×D4×C109—21no—
26C2×C22⋊C4×C109C2211yescharacteristic
27C2×Dic218—21no—
28C2×Dic218—21no—
29C2×Dic218—42no—
30C22×Dic109—21no—
31C22×Dic109—21no—
32#13182019—42no—
33#13182017—42no—
34C2×#11724784—21no—
35C2×#11724784—21no—
36C22⋊Dic109—42no—
37C24×C109D411yescharacteristic
38C2×Q8×C109D411yescharacteristic
39C2×D4×C109—21no—
40C2×D4×C109—21no—
41C2×D4×C109—21no—
42C2×D4×C109D411yescharacteristic
43C22×C4×C109—21no—
44C22×C4×C109D411yescharacteristic
45C22×C4×C109C2311yescharacteristic
46C4⋊C4×C109—21no—
47C4⋊C4×C109—21no—
48C4⋊C4×C109D411yescharacteristic
49C4⋊C4×C109D411yescharacteristic
50C22⋊C4×C109—21no—
51C22⋊C4×C109—21no—
52C22⋊C4×C109—21no—
53C22⋊C4×C109—21no—
54C22⋊C4×C109—21no—
55C22⋊C4×C109—21no—
56C22⋊C4×C109—21no—
57C42×C109—21no—
58C23×C109—21no—
59C23×C109—21no—
60C23×C109—21no—
61C23×C109—21no—
62C23×C109—41no—
63C23×C109—41no—
64C23×C109C2×D411yescharacteristic
65Q8×C109—41no—
66D4×C109—41no—
67D4×C109—41no—
68D4×C109—41no—
69D4×C109—81no—
70D4×C109—81no—
71C2×C4×C109—21no—
72C2×C4×C109—21no—
73C2×C4×C109—21no—
74C2×C4×C109—21no—
75C2×C4×C109—41no—
76C2×C4×C109—41no—
77C2×C4×C109—81no—
78C2×C4×C109C2×D411yescharacteristic
79C2×C4×C109C2×D411yescharacteristic
80C2×Dic109—22no—
81C2×Dic109—41no—
82C2×Dic109—41no—
83C2×Dic109—41no—
84C2×Dic109—41no—
85C2×Dic109—41no—
86Dic218—22no—
87Dic218—22no—
88Dic218—41no—
89Dic218—41no—
90#11724784—41no—
91#11724784—41no—
92C22×C109—21no—
93C22×C109—21no—
94C22×C109—42no—
95C22×C109—41no—
96C22×C109—41no—
97C22×C109—41no—
98C22×C109—41no—
99C22×C109—41no—
100C22×C109—41no—
101C22×C109—81no—
102C22×C109#12011yescharacteristic
103C22×C109#13511yescharacteristic
104C22×C109#13711yescharacteristic
105C4×C109—21no—
106C4×C109—21no—
107C4×C109—41no—
108C4×C109—41no—
109C4×C109—41no—
110C4×C109—41no—
111Dic109—42no—
112Dic109—81no—
113C2×C109—21no—
114C2×C109—21no—
115C2×C109—81no—
116C2×C109—81no—
117C2×C109#45211yescharacteristic
118C2×C109#45511yescharacteristic
119C2×C109B(4,𝔽2)11yescharacteristic
120#1606—1091nomaximal, Sylow
121C109#160611yescharacteristic, complemented, Sylow
122#538D10911yescharacteristic
123#451—1091no—
124#448—1091no—
125#393—1091no—
126#328—1091no—
127#327—1091no—
128#323—1091no—
129C22×Q8—1091no—
130C2×Q16—2181no—
131C2×SD16—2181no—
132#126—21no—
133#124—21no—
134#123—21no—
135C22⋊Q8C2×D10911yescharacteristic
136#121—21no—
137#121C2×D10911yescharacteristic
138#120—21no—
139C4×D4—21no—
140C2×C22⋊C4—2181no—
141C2×C22⋊C4C2×D10911yescharacteristic
142#103—2181no—
143#103—2181no—
144C22⋊C8—1091no—
145C22⋊C8—1091no—
146#95—1091no—
147#95—2181no—
148C24C22⋊D10911yescharacteristic
149C2×Q8—4362no—
150C2×Q8—2181no—
151C2×Q8—2181no—
152C2×Q8C22⋊D10911yescharacteristic
153C2×D4—21no—
154C2×D4—21no—
155C2×D4—21no—
156C2×D4C22⋊D10911yescharacteristic
157C22×C4—21no—
158C22×C4—2181no—
159C22×C4—2181no—
160C22×C4C22⋊D10911yescharacteristic
161C22×C4C22×D10911yescharacteristic
162Q16—4362no—
163SD16—4362no—
164C2×C8—2181no—
165C2×C8—2181no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4C22⋊D10911yescharacteristic
169C4⋊C4C22⋊D10911yescharacteristic
170C22⋊C4—21no—
171C22⋊C4—21no—
172C22⋊C4—21no—
173C22⋊C4—21no—
174C22⋊C4—21no—
175C22⋊C4—21no—
176C22⋊C4—21no—
177C22⋊C4—4362no—
178C42—21no—
179C23—21no—
180C23—21no—
181C23—21no—
182C23—21no—
183C23—41no—
184C23—41no—
185C23C2×C22⋊D10911yescharacteristic
186Q8—41no—
187Q8—4361no—
188Q8—4361no—
189Q8—2182no—
190Q8—2182no—
191D4—41no—
192D4—41no—
193D4—41no—
194D4—81no—
195D4—81no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—81no—
203C2×C4—4361no—
204C2×C4—4361no—
205C2×C4—4361no—
206C2×C4—4361no—
207C2×C4—4361no—
208C2×C4—2182no—
209C2×C4C2×C22⋊D10911yescharacteristic
210C2×C4C2×C22⋊D10911yescharacteristic
211C8—4361no—
212C8—4361no—
213C22—21no—
214C22—21no—
215C22—42no—
216C22—41no—
217C22—41no—
218C22—41no—
219C22—41no—
220C22—41no—
221C22—41no—
222C22—81no—
223C22#1681266811yescharacteristic
224C22#1681271911yescharacteristic
225C22#1681272911yescharacteristic
226C4—21no—
227C4—21no—
228C4—41no—
229C4—41no—
230C4—41no—
231C4—41no—
232C4—8721no—
233C4—4362no—
234C2—21no—
235C2—21no—
236C2—81no—
237C2—81no—
238C2#2029518811yescharacteristic
239C2#2029520411yescharacteristic
240C2#2029521311yescharacteristic
subgroupG/H
centerC22#16812668
commutator, cosocleC22×C4×C109C23
FrattiniC22×C4C22×D109
Fitting, prime radical#538×C109C2
socleC22×C109#120
hypercenter#538D109
hypocenterC109#1606
LCSG ▷ C22×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #538

Complements

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

NH ≅ G/Ntype
1. #20295181C2semidirect
2. #20295164C2semidirect
3. #20294938C2semidirect
4. #20294763C2semidirect
5. #20294760C2semidirect
6. #20294750C2semidirect
121. C109#1606semidirect

Maximal subgroups

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

subgroupindex
#202951812
#202951642
#202949382
#202947632
#202947602
#202947502
#538×C1092
#1606109