Finite Group Databasebeta

← #28361608

Subgroups — #28361608

Order 13952.

218 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 61 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#20295562C211yesmaximal, characteristic
2#20295076C211yesmaximal, characteristic, complemented
3#20294893C211yesmaximal, characteristic, complemented
4#20294763C211yesmaximal, characteristic, complemented
5#20294761C211yesmaximal, characteristic
6#20294759C211yesmaximal, characteristic
7#328×C109C211yesmaximal, characteristic, complemented
8#16812694—21no—
9#16812690C411yescharacteristic, complemented
10#16812688C411yescharacteristic, complemented
11#16812683—21no—
12#16812673C2211yescharacteristic
13Q8×Dic109C411yescharacteristic, complemented
14#16812661C411yescharacteristic, complemented
15#16812659—21no—
16#16812657—21no—
17C2×C4×Dic109C2211yescharacteristic
18#16812628—21no—
19C22⋊#11724784C2211yescharacteristic
20C8×Dic109—21no—
21#16812606—21no—
22#16812606—21no—
23#16812606C2211yescharacteristic
24C22⋊Q8×C109C2211yescharacteristic
25C22⋊C8×C109C2211yescharacteristic
26#95×C109C2211yescharacteristic
27C2×D436C2×C411yescharacteristic
28C2×C22⋊D109—21no—
29C22×Dic109—21no—
30C22×Dic109D411yescharacteristic
31C22×Dic109D411yescharacteristic
32C2×C4×D109—21no—
33C2×#11724784—21no—
34C4⋊Dic109—21no—
35C4⋊Dic109—21no—
36C4⋊Dic109C2×C411yescharacteristic
37#13182008—21no—
38#13182006—21no—
39#13182006—21no—
40#13182006—21no—
41#13182006—21no—
42C4×Dic109—21no—
43C4×Dic109C2×C411yescharacteristic
44C4×Dic109C2×C411yescharacteristic
45C4×Dic109D411yescharacteristic
46C4×Dic109D411yescharacteristic
47C2×Q8×C109C2×C411yescharacteristic
48C22×C4×C109—21no—
49C22×C4×C109C2311yescharacteristic
50C2×C8×C109—21no—
51C4⋊C4×C109—21no—
52C4⋊C4×C109C2×C411yescharacteristic
53C22⋊C4×C109—21no—
54C23×C109C2×D411yescharacteristic
55C22×D109—21no—
56Q8×C109—41no—
57C2×C4×C109—21no—
58C2×C4×C109—21no—
59C2×C4×C109—41no—
60C2×C4×C109—41no—
61C2×C4×C109—41no—
62C2×C4×C109—41no—
63C2×C4×C109C22×C411yescharacteristic
64C2×C4×C109C2×D411yescharacteristic
65C22⋊D109—41no—
66C22⋊D109—41no—
67C2×Dic109—21no—
68C2×Dic109—21no—
69C2×Dic109—21no—
70C2×Dic109—41no—
71C2×Dic109—41no—
72C2×Dic109—41no—
73C2×Dic109—41no—
74C2×Dic109C22⋊C411yescharacteristic
75C2×Dic109C22⋊C411yescharacteristic
76C2×Dic109C22⋊C411yescharacteristic
77C2×Dic109C22⋊C411yescharacteristic
78D436—41no—
79C4×D109—42no—
80C8×C109—41no—
81#11724784—41no—
82C22×C109—21no—
83C22×C109—21no—
84C22×C109C2×C22⋊C411yescharacteristic
85C22×C109#13511yescharacteristic
86C22×C109#13511yescharacteristic
87C2×D109—41no—
88C2×D109—41no—
89C2×D109—41no—
90C4×C109—21no—
91C4×C109—21no—
92C4×C109—41no—
93C4×C109—41no—
94C4×C109—81no—
95Dic109—21no—
96Dic109—21no—
97Dic109—21no—
98Dic109—21no—
99Dic109—41no—
100Dic109—81no—
101C2×C109—21no—
102C2×C109—21no—
103C2×C109#41011yescharacteristic
104C2×C109#41611yescharacteristic
105C2×C109#42111yescharacteristic
106D109—81no—
107#1521—1091nomaximal, Sylow
108C109#152111yescharacteristic, complemented, Sylow
109#529—1091no—
110#431—1091no—
111#383—1091no—
112#328—1091no—
113#328D10911yescharacteristic, complemented
114#327—1091no—
115#327—1091no—
116#126—2181no—
117#125—1091no—
118#124—1091no—
119#123—2181no—
120C22⋊Q8C2×D10911yescharacteristic
121#121—1091no—
122C4×Q8—1091no—
123C4×D4—1091no—
124C4×D4—2181no—
125#117—2181no—
126C2×C42—1091no—
127C4⋊C8—2181no—
128C22⋊C8—1091no—
129C22⋊C8C2×D10911yescharacteristic
130C4×C8—2181no—
131#95—1091no—
132#95—2181no—
133#95—2181no—
134#95C2×D10911yescharacteristic
135C2×Q8C4×D10911yescharacteristic
136C2×D4—1091no—
137C2×D4—2181no—
138C22×C4—21no—
139C22×C4—1091no—
140C22×C4—1091no—
141C22×C4—2181no—
142C22×C4—2181no—
143C22×C4C22×D10911yescharacteristic
144C2×C8—21no—
145C2×C8—2181no—
146C4⋊C4—21no—
147C4⋊C4—1091no—
148C4⋊C4—2181no—
149C4⋊C4—2181no—
150C4⋊C4—2181no—
151C4⋊C4C4×D10911yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—2181no—
154C22⋊C4—2181no—
155C22⋊C4—2181no—
156C22⋊C4—2181no—
157C42—1091no—
158C42—1091no—
159C42—1091no—
160C42—1091no—
161C42—2181no—
162C23—2181no—
163C23D4×D10911yescharacteristic
164Q8—41no—
165D4—4361no—
166D4—4361no—
167D4—4361no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—1091no—
175C2×C4—1091no—
176C2×C4—1091no—
177C2×C4—1091no—
178C2×C4—4362no—
179C2×C4—4361no—
180C2×C4—4361no—
181C2×C4—4361no—
182C2×C4—4361no—
183C2×C4—2181no—
184C2×C4—2181no—
185C2×C4—2181no—
186C2×C4C2×C4×D10911yescharacteristic
187C2×C4D4×D10911yescharacteristic
188C8—41no—
189C8—4361no—
190C22—21no—
191C22—21no—
192C22—4361no—
193C22—4361no—
194C22—4361no—
195C22C22⋊C4×D10911yescharacteristic
196C22#1681272011yescharacteristic
197C22#1681272211yescharacteristic
198C4—21no—
199C4—21no—
200C4—41no—
201C4—41no—
202C4—81no—
203C4—8721no—
204C4—4361no—
205C4—2181no—
206C4—2181no—
207C4—2181no—
208C4—2181no—
209C2—21no—
210C2—21no—
211C2—8721no—
212C2#2029499811yescharacteristic
213C2#2029502111yescharacteristic
214C2#2029504111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D109
commutatorC2×C4×C109C22×C4
FrattiniC22×C4C22×D109
Fitting#328×C109C2
socleC22×C109C2×C22⋊C4
prime radical#16812673C22
cosocleC22×C4×C109C23
hypercenter#328D109
hypocenterC109#1521
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #20295076C2semidirect
3. #20294893C2semidirect
4. #20294763C2semidirect
7. #328×C109C2semidirect
9. #16812690C4semidirect
10. #16812688C4semidirect
13. Q8×Dic109C4semidirect
14. #16812661C4semidirect
108. C109#1521semidirect
113. #328D109semidirect

Maximal subgroups

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

subgroupindex
#202955622
#202950762
#202948932
#202947632
#202947612
#202947592
#328×C1092
#1521109