Finite Group Databasebeta

← #28361377

Subgroups — #28361377

Order 13952.

280 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 63 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×#16812681C211yesmaximal, characteristic
2#20294988C211yesmaximal, characteristic, complemented
3C22⋊C8×D109C211yesmaximal, characteristic, complemented
4#20294751C211yesmaximal, characteristic, complemented
5#20294751C211yesmaximal, characteristic, complemented
6#20294750C211yesmaximal, characteristic, complemented
7#323×C109C211yesmaximal, characteristic, complemented
8C22×C22⋊D109C411yescharacteristic
9C22×C4×D109C2211yescharacteristic
10C2×#13182012—21no—
11C2×C8×D109—21no—
12#16812681—21no—
13#16812681—21no—
14#16812681—21no—
15#16812681—21no—
16C2×C4⋊Dic109C411yescharacteristic
17C2×#13182008C2211yescharacteristic
18C2×C22⋊Dic109C411yescharacteristic
19C2×#13182006C411yescharacteristic
20C22⋊#11724784C2211yescharacteristic
21C22⋊#11724784C2211yescharacteristic
22#16812611—21no—
23#16812611—21no—
24C2×C22⋊C4×C109C2211yescharacteristic
25C22⋊C8×C109C2211yescharacteristic
26C22⋊C8×C109C2211yescharacteristic
27C23×D109C2×C411yescharacteristic
28C2×C22⋊D109—21no—
29C2×C22⋊D109—21no—
30C2×C22⋊D109—42no—
31C22×Dic109C2×C411yescharacteristic
32C22×Dic109C2×C411yescharacteristic
33C22×Dic109C2×C411yescharacteristic
34C2×C4×D109—42no—
35C2×C4×D109D411yescharacteristic
36C2×C4×D109D411yescharacteristic
37C2×C4×D109D411yescharacteristic
38C2×C4×D109D411yescharacteristic
39#13182012—42no—
40C2×#11724784—21no—
41C2×#11724784—21no—
42C8×D109—42no—
43C4⋊Dic109—21no—
44C4⋊Dic109—21no—
45#13182008—21no—
46#13182008—21no—
47C22⋊Dic109—21no—
48C22⋊Dic109—21no—
49#13182006—21no—
50#13182006—21no—
51C24×C109C2×C411yescharacteristic
52C22×C4×C109C2×C411yescharacteristic
53C22×C4×C109C2311yescharacteristic
54C2×C8×C109—21no—
55C2×C8×C109—21no—
56C22⋊C4×C109—21no—
57C22⋊C4×C109—21no—
58C23×C109—21no—
59C23×C109—21no—
60C23×C109—21no—
61C23×C109—41no—
62C23×C109—41no—
63C23×C109C22×C411yescharacteristic
64C22×D109—21no—
65C22×D109—21no—
66C22×D109—22no—
67C22×D109—41no—
68C22×D109C22⋊C411yescharacteristic
69C22×D109C22⋊C411yescharacteristic
70C2×C4×C109—21no—
71C2×C4×C109—41no—
72C2×C4×C109—41no—
73C2×C4×C109C2×D411yescharacteristic
74C2×C4×C109C2×D411yescharacteristic
75C22⋊D109—42no—
76C22⋊D109—42no—
77C2×Dic109—21no—
78C2×Dic109—21no—
79C2×Dic109—21no—
80C2×Dic109—21no—
81C2×Dic109—41no—
82C2×Dic109—41no—
83C2×Dic109C22⋊C411yescharacteristic
84C2×Dic109C22⋊C411yescharacteristic
85C4×D109—22no—
86C4×D109—22no—
87C4×D109—41no—
88C4×D109—41no—
89C8×C109—41no—
90C8×C109—41no—
91#11724784—41no—
92#11724784—41no—
93C22×C109—21no—
94C22×C109—21no—
95C22×C109—41no—
96C22×C109—41no—
97C22×C109—41no—
98C22×C109—81no—
99C22×C109—81no—
100C22×C109C2×C22⋊C411yescharacteristic
101C22×C109#13111yescharacteristic
102C22×C109#13111yescharacteristic
103C2×D109—21no—
104C2×D109—21no—
105C2×D109—21no—
106C2×D109—21no—
107C2×D109—21no—
108C2×D109—42no—
109C2×D109—42no—
110C2×D109#9912yes—
111C4×C109—21no—
112C4×C109—21no—
113C4×C109—41no—
114Dic109—21no—
115Dic109—21no—
116Dic109—41no—
117Dic109—41no—
118C2×C109—21no—
119C2×C109—21no—
120C2×C109—81no—
121C2×C109#40811yescharacteristic
122C2×C109C2×#9911yescharacteristic
123C2×C109#41311yescharacteristic
124D109—22no—
125D109—41no—
126#1468—1091nomaximal, Sylow
127C109#146811yescharacteristic, complemented, Sylow
128C2×#123—1091no—
129#407—1091no—
130C2×C22⋊C8—1091no—
131#324—1091no—
132#324—1091no—
133#323—1091no—
134#323D10911yescharacteristic, complemented
135C22×D4—1091no—
136C23×C4—1091no—
137C2×M16—2181no—
138C22×C8—2181no—
139#123—2181no—
140#123—2181no—
141#123—2181no—
142#123—2181no—
143C2×C4⋊C4—1091no—
144C2×C4⋊C4—1091no—
145C2×C22⋊C4—1091no—
146C2×C22⋊C4—1091no—
147C2×C22⋊C4C2×D10911yescharacteristic
148C22⋊C8—1091no—
149C22⋊C8—1091no—
150C22⋊C8—2181no—
151C22⋊C8—2181no—
152C22⋊C8C2×D10911yescharacteristic
153C22⋊C8C2×D10911yescharacteristic
154C24—1091no—
155C24C4×D10911yescharacteristic
156C2×D4—4362no—
157C2×D4—2181no—
158C2×D4—2181no—
159C22×C4—1091no—
160C22×C4—1091no—
161C22×C4—1091no—
162C22×C4—1091no—
163C22×C4—1091no—
164C22×C4—1091no—
165C22×C4—1091no—
166C22×C4—4362no—
167C22×C4C4×D10911yescharacteristic
168C22×C4C22×D10911yescharacteristic
169M16—4362no—
170C2×C8—21no—
171C2×C8—21no—
172C2×C8—4362no—
173C2×C8—2181no—
174C2×C8—2181no—
175C4⋊C4—2181no—
176C4⋊C4—2181no—
177C4⋊C4—2181no—
178C4⋊C4—2181no—
179C22⋊C4—21no—
180C22⋊C4—21no—
181C22⋊C4—2181no—
182C22⋊C4—2181no—
183C22⋊C4—2181no—
184C22⋊C4—2181no—
185C23—21no—
186C23—21no—
187C23—21no—
188C23—41no—
189C23—41no—
190C23—1091no—
191C23—1091no—
192C23—4361no—
193C23—2182no—
194C23—2181no—
195C23—2181no—
196C23C2×C4×D10911yescharacteristic
197D4—4362no—
198D4—4362no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—1091no—
203C2×C4—1091no—
204C2×C4—4361no—
205C2×C4—4361no—
206C2×C4—4361no—
207C2×C4—4361no—
208C2×C4—2182no—
209C2×C4—2182no—
210C2×C4—2181no—
211C2×C4—2181no—
212C2×C4—2181no—
213C2×C4—2181no—
214C2×C4D4×D10911yescharacteristic
215C2×C4D4×D10911yescharacteristic
216C8—41no—
217C8—41no—
218C8—4361no—
219C8—4361no—
220C22—21no—
221C22—21no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—81no—
226C22—81no—
227C22—1092no—
228C22—4362no—
229C22—4362no—
230C22—2181no—
231C22—2181no—
232C22—2181no—
233C22—2181no—
234C22—2181no—
235C22C22⋊C4×D10911yescharacteristic
236C22#1681270511yescharacteristic
237C22#1681270711yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—4361no—
242C4—4361no—
243C4—2181no—
244C4—2181no—
245C2—21no—
246C2—21no—
247C2—81no—
248C2—4361no—
249C2—2182no—
250C2#2029499111yescharacteristic
251C2#99×D10911yescharacteristic
252C2#2029500711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D109
commutatorC23×C109C22×C4
FrattiniC22×C4C22×D109
Fitting#323×C109C2
socleC22×C109C2×C22⋊C4
prime radicalC22×C22⋊D109C4
cosocleC22×C4×C109C23
hypercenter#323D109
hypocenterC109#1468
LCSG ▷ C23×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #20294988C2semidirect
3. C22⋊C8×D109C2semidirect
4. #20294751C2semidirect
5. #20294751C2semidirect
6. #20294750C2semidirect
7. #323×C109C2semidirect
127. C109#1468semidirect
134. #323D109semidirect

Maximal subgroups

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

subgroupindex
C2×#168126812
#202949882
C22⋊C8×D1092
#202947512
#202947502
#323×C1092
#1468109