Finite Group Databasebeta

← #28364684

Subgroups — #28364684

Order 13952.

234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 55 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#20295598C211yesmaximal, characteristic
2#20295007C211yesmaximal, characteristic
3#20294998C211yesmaximal, characteristic
4#20294817C211yesmaximal, characteristic, complemented
5#20294816C211yesmaximal, characteristic, complemented
6#20294815C211yesmaximal, characteristic, complemented
7#352×C109C211yesmaximal, characteristic, complemented
8C2×#13182028C2211yescharacteristic
9C22×Dic218C411yescharacteristic, complemented
10M16×D109—21no—
11#16812698—21no—
12#16812685—21no—
13#16812683C411yescharacteristic, complemented
14#16812682C411yescharacteristic, complemented
15#16812680C2211yescharacteristic
16#16812677—21no—
17#16812676—21no—
18#16812655—21no—
19#16812655C411yescharacteristic, complemented
20#16812617—21no—
21#16812616C2211yescharacteristic
22#16812614C2211yescharacteristic
23#16812613—21no—
24#123×C109C2211yescharacteristic
25#100×C109C2211yescharacteristic
26#99×C109C2211yescharacteristic
27#13182028—41no—
28#13182028—41no—
29C2×Dic218—21no—
30C2×Dic218—21no—
31C2×Dic218—41no—
32C2×Dic218—41no—
33C2×Dic218D411yescharacteristic
34C2×C22⋊D109C2×C411yescharacteristic
35C2×C22⋊D109D411yescharacteristic
36C22×Dic109C2×C411yescharacteristic
37C22×Dic109C2×C411yescharacteristic
38C22×Dic109D411yescharacteristic
39C2×C4×D109D411yescharacteristic
40#13182013—21no—
41#13182012—41no—
42C8×D109—41no—
43C4⋊Dic109—21no—
44#13182008—21no—
45#13182008—21no—
46#13182008—21no—
47#13182008—41no—
48C22⋊Dic109—21no—
49C22⋊Dic109—21no—
50C22⋊Dic109C2×C411yescharacteristic
51#13182006—21no—
52#13182006—21no—
53C4×Dic109—21no—
54C4×Dic109—41no—
55C2×D4×C109C2311yescharacteristic
56C22×C4×C109C2×C411yescharacteristic
57M16×C109—21no—
58C4⋊C4×C109—21no—
59C22⋊C4×C109—21no—
60C22⋊C4×C109—21no—
61C22⋊C4×C109C2×C411yescharacteristic
62C23×C109C22×C411yescharacteristic
63C23×C109C2×D411yescharacteristic
64C22×D109C22⋊C411yescharacteristic
65D4×C109—41no—
66C2×C4×C109—21no—
67C2×C4×C109—21no—
68C2×C4×C109—41no—
69C2×C4×C109—41no—
70C2×C4×C109C2×D411yescharacteristic
71C22⋊D109—41no—
72C22⋊D109—41no—
73C2×Dic109—21no—
74C2×Dic109—21no—
75C2×Dic109—21no—
76C2×Dic109—21no—
77C2×Dic109—21no—
78C2×Dic109—21no—
79C2×Dic109—41no—
80C2×Dic109—41no—
81C2×Dic109C22⋊C411yescharacteristic
82C2×Dic109C22⋊C411yescharacteristic
83C2×Dic109C22⋊C411yescharacteristic
84C4×D109—21no—
85C4×D109—21no—
86Dic218—41no—
87Dic218—42no—
88Dic218—41no—
89Dic218—41no—
90C8×C109—41no—
91#11724784—41no—
92C22×C109—21no—
93C22×C109—21no—
94C22×C109—41no—
95C22×C109—41no—
96C22×C109C2×C22⋊C411yescharacteristic
97C2×D109—21no—
98C2×D109—41no—
99C4×C109—21no—
100C4×C109—41no—
101C4×C109—41no—
102C4×C109—81no—
103Dic109—21no—
104Dic109—21no—
105Dic109—41no—
106Dic109—41no—
107Dic109—81no—
108Dic109#9911yescharacteristic
109Dic109#9911yescharacteristic
110C2×C109—21no—
111C2×C109—41no—
112C2×C109—41no—
113C2×C109C2×#9911yescharacteristic
114D109—41no—
115#2123—1091nomaximal, Sylow
116C109#212311yescharacteristic, complemented, Sylow
117#536—1091no—
118#413—1091no—
119#410—1091no—
120#352—1091no—
121#352—1091no—
122#352—1091no—
123#352D10911yescharacteristic, complemented
124C2×#41—1091no—
125C22×Q8—1091no—
126C2×M16—2181no—
127C4⋊Q8—2181no—
128#124—2181no—
129#123—1091no—
130#123—1091no—
131#123—1091no—
132#123C2×D10911yescharacteristic
133C22⋊Q8—2181no—
134C22⋊Q8—2181no—
135#117—1091no—
136#117—2181no—
137#101—2181no—
138#100—1091no—
139#100C2×D10911yescharacteristic
140#99—1091no—
141#99—2181no—
142#99C2×D10911yescharacteristic
143#41—4361no—
144#41—4361no—
145C2×Q8—1091no—
146C2×Q8—4361no—
147C2×Q8—4361no—
148C2×Q8—2181no—
149C2×Q8—2181no—
150C2×D4—1091no—
151C2×D4—1091no—
152C2×D4C22×D10911yescharacteristic
153C22×C4—1091no—
154C22×C4—1091no—
155C22×C4—1091no—
156C22×C4—1091no—
157C22×C4C4×D10911yescharacteristic
158M16—21no—
159M16—4361no—
160M16—2181no—
161C2×C8—4361no—
162C4⋊C4—21no—
163C4⋊C4—4361no—
164C4⋊C4—2181no—
165C4⋊C4—2181no—
166C4⋊C4—2181no—
167C4⋊C4—2181no—
168C22⋊C4—21no—
169C22⋊C4—21no—
170C22⋊C4—1091no—
171C22⋊C4—2181no—
172C22⋊C4—2181no—
173C22⋊C4—2181no—
174C22⋊C4—2181no—
175C22⋊C4C4×D10911yescharacteristic
176C42—4361no—
177C42—2181no—
178C23—1091no—
179C23C2×C4×D10911yescharacteristic
180C23D4×D10911yescharacteristic
181Q8—4361no—
182Q8—4361no—
183Q8—4361no—
184Q8—4362no—
185D4—41no—
186D4—4361no—
187D4—4361no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—1091no—
193C2×C4—1091no—
194C2×C4—1091no—
195C2×C4—4361no—
196C2×C4—4361no—
197C2×C4—2181no—
198C2×C4—2181no—
199C2×C4—2181no—
200C2×C4—2181no—
201C2×C4—2181no—
202C2×C4—2181no—
203C2×C4—2181no—
204C2×C4—2181no—
205C2×C4D4×D10911yescharacteristic
206C8—41no—
207C8—4361no—
208C22—21no—
209C22—21no—
210C22—41no—
211C22—41no—
212C22—4361no—
213C22—2181no—
214C22C22⋊C4×D10911yescharacteristic
215C4—21no—
216C4—41no—
217C4—41no—
218C4—81no—
219C4—8721no—
220C4—1091no—
221C4—1091no—
222C4—4361no—
223C4—4361no—
224C4—2181no—
225C4—2181no—
226C2—21no—
227C2—41no—
228C2—41no—
229C2—4361no—
230C2#99×D10911yescharacteristic
subgroupG/H
centerC2#99×D109
commutatorC23×C109C22×C4
FrattiniC2×D4C22×D109
Fitting#352×C109C2
socleC2×C109C2×#99
prime radicalC2×#13182028C22
cosocleC2×D4×C109C23
hypercenter#352D109
hypocenterC109#2123
LCSG ▷ C23×C109 ▷ C22×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #352

Complements

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

NH ≅ G/Ntype
4. #20294817C2semidirect
5. #20294816C2semidirect
6. #20294815C2semidirect
7. #352×C109C2semidirect
9. C22×Dic218C4semidirect
13. #16812683C4semidirect
14. #16812682C4semidirect
19. #16812655C4semidirect
116. C109#2123semidirect
123. #352D109semidirect

Maximal subgroups

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

subgroupindex
#202955982
#202950072
#202949982
#202948172
#202948162
#202948152
#352×C1092
#2123109