Finite Group Databasebeta

← #28361554

Subgroups — #28361554

Order 13952.

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

normal subgroups only

This group has 242 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
1#20295557C211yesmaximal, characteristic
2#20295080C211yesmaximal, characteristic, complemented
3#20294877C211yesmaximal, characteristic, complemented
4#20294764C211yesmaximal, characteristic, complemented
5#20294762C211yesmaximal, characteristic, complemented
6#20294760C211yesmaximal, characteristic
7#327×C109C211yesmaximal, characteristic
8#16812692—21no—
9#16812690C411yescharacteristic, complemented
10#16812686C411yescharacteristic, complemented
11#16812680—21no—
12#16812678C2211yescharacteristic
13#16812664C411yescharacteristic, complemented
14D4×Dic109—21no—
15D4×Dic109C411yescharacteristic, complemented
16#16812655—21no—
17C2×#13182008—21no—
18C2×C4×Dic109—21no—
19C2×C4×Dic109C2211yescharacteristic
20#16812628—21no—
21C22⋊#11724784C2211yescharacteristic
22#16812609—21no—
23#16812606C2211yescharacteristic
24#121×C109C2211yescharacteristic
25C22⋊C8×C109C2211yescharacteristic
26#95×C109C2211yescharacteristic
27C2×Dic218C2×C411yescharacteristic
28C22×Dic109—21no—
29C22×Dic109—21no—
30C22×Dic109D411yescharacteristic
31C22×Dic109D411yescharacteristic
32C2×#11724784—21no—
33C4⋊Dic109—21no—
34C4⋊Dic109C2×C411yescharacteristic
35#13182008—24no—
36#13182008—21no—
37#13182008—21no—
38#13182008—21no—
39C22⋊Dic109—21no—
40C22⋊Dic109—21no—
41C22⋊Dic109—21no—
42C22⋊Dic109—21no—
43C4×Dic109—21no—
44C4×Dic109—42no—
45C4×Dic109C2×C411yescharacteristic
46C4×Dic109C2×C411yescharacteristic
47C4×Dic109D411yescharacteristic
48C4×Dic109D411yescharacteristic
49C2×D4×C109—21no—
50C2×D4×C109C2×C411yescharacteristic
51C22×C4×C109—21no—
52C22×C4×C109C2311yescharacteristic
53C2×C8×C109—21no—
54C4⋊C4×C109C2×C411yescharacteristic
55C22⋊C4×C109—21no—
56C23×C109—21no—
57C23×C109C2×D411yescharacteristic
58D4×C109—41no—
59D4×C109—41no—
60D4×C109—41no—
61C2×C4×C109—22no—
62C2×C4×C109—21no—
63C2×C4×C109—41no—
64C2×C4×C109—41no—
65C2×C4×C109—41no—
66C2×C4×C109C22×C411yescharacteristic
67C2×C4×C109C2×D411yescharacteristic
68C2×Dic109—21no—
69C2×Dic109—21no—
70C2×Dic109—22no—
71C2×Dic109—22no—
72C2×Dic109—21no—
73C2×Dic109—21no—
74C2×Dic109—41no—
75C2×Dic109—41no—
76C2×Dic109—42no—
77C2×Dic109C22⋊C411yescharacteristic
78C2×Dic109C22⋊C411yescharacteristic
79C2×Dic109C22⋊C411yescharacteristic
80C2×Dic109C22⋊C411yescharacteristic
81Dic218—41no—
82C8×C109—41no—
83#11724784—41no—
84C22×C109—21no—
85C22×C109—21no—
86C22×C109—41no—
87C22×C109—41no—
88C22×C109—41no—
89C22×C109C2×C22⋊C411yescharacteristic
90C22×C109AGL(1,ℤ/8)11yescharacteristic
91C22×C109#13711yescharacteristic
92C4×C109—21no—
93C4×C109—21no—
94C4×C109—42no—
95C4×C109—41no—
96Dic109—21no—
97Dic109—21no—
98Dic109—21no—
99Dic109—42no—
100Dic109—41no—
101Dic109—41no—
102Dic109#10412yes—
103C2×C109—21no—
104C2×C109—21no—
105C2×C109—81no—
106C2×C109#41011yescharacteristic
107C2×C109#41711yescharacteristic
108C2×C109C2×#10411yescharacteristic
109#1509—1091nomaximal, Sylow
110C109#150911yescharacteristic, complemented, Sylow
111#529—1091no—
112#432—1091no—
113C4×C4⋊C4—1091no—
114#328—1091no—
115#328—1091no—
116#327—1091no—
117#327D10911yescharacteristic
118#126—2181no—
119#125—1091no—
120#124—1091no—
121#123—2181no—
122C22⋊Q8—1091no—
123#121C2×D10911yescharacteristic
124C4×Q8—1091no—
125C4×D4—1091no—
126C4×D4—2181no—
127#117—2181no—
128C2×C4⋊C4—2181no—
129C2×C42—1091no—
130C2×C42—2181no—
131C4⋊C8—2181no—
132C22⋊C8—1091no—
133C22⋊C8C2×D10911yescharacteristic
134#97—2181no—
135#95—1091no—
136#95C2×D10911yescharacteristic
137C2×Q8—1091no—
138C2×D4—21no—
139C2×D4C4×D10911yescharacteristic
140C22×C4—21no—
141C22×C4—1091no—
142C22×C4—1091no—
143C22×C4—2181no—
144C22×C4—2181no—
145C22×C4C22×D10911yescharacteristic
146C2×C8—21no—
147C2×C8—2181no—
148C4⋊C4—1091no—
149C4⋊C4—2181no—
150C4⋊C4—2181no—
151C4⋊C4—2181no—
152C4⋊C4—2184no—
153C4⋊C4—2181no—
154C4⋊C4C4×D10911yescharacteristic
155C22⋊C4—21no—
156C22⋊C4—2181no—
157C22⋊C4—2181no—
158C22⋊C4—2181no—
159C22⋊C4—2181no—
160C42—1091no—
161C42—1091no—
162C42—1091no—
163C42—1091no—
164C42—4362no—
165C42—2181no—
166C23—21no—
167C23D4×D10911yescharacteristic
168Q8—4361no—
169D4—41no—
170D4—41no—
171D4—41no—
172C2×C4—22no—
173C2×C4—21no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—1091no—
178C2×C4—1091no—
179C2×C4—1091no—
180C2×C4—1091no—
181C2×C4—4362no—
182C2×C4—4361no—
183C2×C4—4361no—
184C2×C4—2182no—
185C2×C4—2182no—
186C2×C4—2181no—
187C2×C4—2181no—
188C2×C4—2181no—
189C2×C4—2181no—
190C2×C4C2×C4×D10911yescharacteristic
191C2×C4D4×D10911yescharacteristic
192C8—41no—
193C8—4361no—
194C22—21no—
195C22—21no—
196C22—41no—
197C22—41no—
198C22—41no—
199C22C22⋊C4×D10911yescharacteristic
200C22#1681272311yescharacteristic
201C22#1681272811yescharacteristic
202C4—21no—
203C4—21no—
204C4—42no—
205C4—41no—
206C4—1092no—
207C4—4362no—
208C4—4361no—
209C4—4361no—
210C4—2181no—
211C4—2181no—
212C4—2181no—
213C2—21no—
214C2—21no—
215C2—81no—
216C2#2029499811yescharacteristic
217C2#2029502411yescharacteristic
218C2#104×D10911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D109
commutatorC2×C4×C109C22×C4
FrattiniC22×C4C22×D109
Fitting#327×C109C2
socleC22×C109C2×C22⋊C4
prime radical#121×C109C22
cosocleC22×C4×C109C23
hypercenter#327D109
hypocenterC109#1509
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #20295080C2semidirect
3. #20294877C2semidirect
4. #20294764C2semidirect
5. #20294762C2semidirect
9. #16812690C4semidirect
10. #16812686C4semidirect
13. #16812664C4semidirect
15. D4×Dic109C4semidirect
110. C109#1509semidirect

Maximal subgroups

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

subgroupindex
#202955572
#202950802
#202948772
#202947642
#202947622
#202947602
#327×C1092
#1509109