Finite Group Databasebeta

← #28363130

Subgroups — #28363130

Order 13952.

306 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 79 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#117×D109C211yesmaximal, characteristic
2#20294989C211yesmaximal, characteristic
3C4×#13182006C211yesmaximal, characteristic
4#20294787C211yesmaximal, characteristic, complemented
5#20294786C211yesmaximal, characteristic, complemented
6#20294785C211yesmaximal, characteristic, complemented
7#339×C109C211yesmaximal, characteristic, complemented
8C22×C4×D109C2211yescharacteristic
9C2×#13182013C2211yescharacteristic
10#16812658C2211yescharacteristic
11#16812657C411yescharacteristic, complemented
12#16812657C411yescharacteristic, complemented
13#16812656—21no—
14#16812655—21no—
15C4⋊C4×D109C411yescharacteristic, complemented
16C4⋊C4×D109C411yescharacteristic, complemented
17C2×#13182006—21no—
18C22⋊C4×D109—21no—
19C2×C4×Dic109C2211yescharacteristic
20C42×D109—21no—
21#16812611—21no—
22#16812611—21no—
23#16812606—21no—
24C2×M16×C109C2211yescharacteristic
25#117×C109C2211yescharacteristic
26C2×C42×C109C2211yescharacteristic
27C23×D109D411yescharacteristic
28C22×Dic109—21no—
29C22×Dic109D411yescharacteristic
30C2×C4×D109—21no—
31C2×C4×D109—21no—
32C2×C4×D109—21no—
33C2×C4×D109—21no—
34C2×C4×D109—21no—
35C2×C4×D109—21no—
36C2×C4×D109C2×C411yescharacteristic
37C2×C4×D109C2×C411yescharacteristic
38C2×C4×D109D411yescharacteristic
39C2×C4×D109D411yescharacteristic
40#13182013—21no—
41#13182013—21no—
42C2×#11724784—21no—
43C4⋊Dic109C2×C411yescharacteristic
44C4⋊Dic109C2×C411yescharacteristic
45#13182008—21no—
46#13182008—21no—
47C22⋊Dic109—21no—
48#13182006—24no—
49#13182006—21no—
50#13182006—21no—
51C4×Dic109—21no—
52C4×Dic109—21no—
53C4×Dic109—21no—
54C4×Dic109—21no—
55C4×Dic109—21no—
56C22×C4×C109—21no—
57C22×C4×C109C2311yescharacteristic
58M16×C109—21no—
59M16×C109—21no—
60C2×C8×C109—21no—
61C4⋊C4×C109C2×C411yescharacteristic
62C4⋊C4×C109C2×C411yescharacteristic
63C22⋊C4×C109—21no—
64C42×C109—21no—
65C42×C109—21no—
66C42×C109—21no—
67C23×C109C2×D411yescharacteristic
68C22×D109—21no—
69C22×D109—21no—
70C22×D109—22no—
71C22×D109—41no—
72C22×D109C22⋊C411yescharacteristic
73C22×D109C22⋊C411yescharacteristic
74C2×C4×C109—22no—
75C2×C4×C109—21no—
76C2×C4×C109—21no—
77C2×C4×C109—41no—
78C2×C4×C109—41no—
79C2×C4×C109C22×C411yescharacteristic
80C2×C4×C109C2×D411yescharacteristic
81C2×C4×C109#4111yescharacteristic
82C2×C4×C109#4111yescharacteristic
83C2×C4×C109#4111yescharacteristic
84C2×C4×C109#4111yescharacteristic
85C2×Dic109—21no—
86C2×Dic109—21no—
87C2×Dic109—22no—
88C2×Dic109—21no—
89C2×Dic109—21no—
90C2×Dic109—41no—
91C2×Dic109—41no—
92C2×Dic109C22⋊C411yescharacteristic
93C2×Dic109C22⋊C411yescharacteristic
94C4×D109—21no—
95C4×D109—21no—
96C4×D109—21no—
97C4×D109—21no—
98C4×D109—21no—
99C4×D109—21no—
100C4×D109—21no—
101C4×D109—21no—
102C4×D109—42no—
103C4×D109—42no—
104C8×C109—41no—
105#11724784—41no—
106C22×C109—21no—
107C22×C109—21no—
108C22×C109C2×C22⋊C411yescharacteristic
109C22×C109#12311yescharacteristic
110C22×C109#12311yescharacteristic
111C2×D109—21no—
112C2×D109—21no—
113C2×D109—21no—
114C2×D109—21no—
115C2×D109—21no—
116C2×D109—42no—
117C2×D109—42no—
118C2×D109#10412yes—
119C4×C109—42no—
120C4×C109—41no—
121C4×C109—41no—
122C4×C109#11711yescharacteristic
123C4×C109#11711yescharacteristic
124C4×C109#12311yescharacteristic
125C4×C109#12311yescharacteristic
126Dic109—21no—
127Dic109—21no—
128Dic109—42no—
129Dic109—41no—
130Dic109—41no—
131C2×C109—21no—
132C2×C109—21no—
133C2×C109#38111yescharacteristic
134C2×C109C2×#10411yescharacteristic
135C2×C109#42111yescharacteristic
136D109—22no—
137D109—41no—
138#1826—1091nomaximal, Sylow
139C109#182611yescharacteristic, complemented, Sylow
140C2×#117—1091no—
141#407—1091no—
142C4×C22⋊C4—1091no—
143#339—1091no—
144#339—1091no—
145#339—1091no—
146#339D10911yescharacteristic, complemented
147C23×C4—1091no—
148C2×M16—1091no—
149C2×M16C2×D10911yescharacteristic
150#117—1091no—
151#117—1091no—
152#117—1091no—
153#117—2181no—
154#117—2181no—
155#117C2×D10911yescharacteristic
156C2×C4⋊C4—1091no—
157C2×C4⋊C4—1091no—
158C2×C22⋊C4—2181no—
159C2×C22⋊C4—2181no—
160C2×C42—1091no—
161C2×C42—2181no—
162C2×C42C2×D10911yescharacteristic
163C22⋊C8—2181no—
164C22⋊C8—2181no—
165#95—2181no—
166C24—1091no—
167C22×C4—21no—
168C22×C4—1091no—
169C22×C4—1091no—
170C22×C4—1091no—
171C22×C4—1091no—
172C22×C4—1091no—
173C22×C4—2181no—
174C22×C4—2181no—
175C22×C4—2181no—
176C22×C4—2181no—
177C22×C4—2181no—
178C22×C4—2181no—
179C22×C4—2181no—
180C22×C4C22×D10911yescharacteristic
181M16—21no—
182M16—21no—
183M16—2181no—
184M16—2181no—
185C2×C8—21no—
186C2×C8—2181no—
187C4⋊C4—1091no—
188C4⋊C4—1091no—
189C4⋊C4—2181no—
190C4⋊C4—2181no—
191C4⋊C4C4×D10911yescharacteristic
192C4⋊C4C4×D10911yescharacteristic
193C22⋊C4—21no—
194C22⋊C4—2181no—
195C22⋊C4—2181no—
196C22⋊C4—2184no—
197C22⋊C4—2181no—
198C42—21no—
199C42—21no—
200C42—21no—
201C42—2181no—
202C42—2181no—
203C42—2181no—
204C42—2181no—
205C42—2181no—
206C23—1091no—
207C23—1091no—
208C23—4361no—
209C23—2182no—
210C23—2181no—
211C23—2181no—
212C23D4×D10911yescharacteristic
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—1091no—
219C2×C4—1091no—
220C2×C4—4362no—
221C2×C4—4362no—
222C2×C4—4361no—
223C2×C4—4361no—
224C2×C4—2182no—
225C2×C4—2181no—
226C2×C4—2181no—
227C2×C4—2181no—
228C2×C4—2181no—
229C2×C4—2181no—
230C2×C4—2181no—
231C2×C4—2181no—
232C2×C4—2181no—
233C2×C4—2181no—
234C2×C4—2181no—
235C2×C4—2181no—
236C2×C4—2181no—
237C2×C4C2×C4×D10911yescharacteristic
238C2×C4D4×D10911yescharacteristic
239C2×C4#1318202811yescharacteristic
240C2×C4#1318202911yescharacteristic
241C2×C4#1318202911yescharacteristic
242C2×C4#1318203011yescharacteristic
243C8—41no—
244C8—4361no—
245C22—21no—
246C22—21no—
247C22—1092no—
248C22—4362no—
249C22—4362no—
250C22—2181no—
251C22—2181no—
252C22—2181no—
253C22—2181no—
254C22—2181no—
255C22C22⋊C4×D10911yescharacteristic
256C22#1681268111yescharacteristic
257C22#1681268411yescharacteristic
258C4—42no—
259C4—41no—
260C4—41no—
261C4—4362no—
262C4—4361no—
263C4—4361no—
264C4—2181no—
265C4—2181no—
266C4#1681265611yescharacteristic
267C4#1681265711yescharacteristic
268C4#1681268111yescharacteristic
269C4#1681268411yescharacteristic
270C2—21no—
271C2—21no—
272C2—4361no—
273C2—2182no—
274C2#2029488811yescharacteristic
275C2#104×D10911yescharacteristic
276C2#2029504111yescharacteristic
subgroupG/H
centerC2×C4D4×D109
commutatorC2×C4×C109C22×C4
FrattiniC22×C4C22×D109
Fitting#339×C109C2
socleC22×C109C2×C22⋊C4
prime radicalC23×D109D4
cosocleC22×C4×C109C23
hypercenter#339D109
hypocenterC109#1826
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
4. #20294787C2semidirect
5. #20294786C2semidirect
6. #20294785C2semidirect
7. #339×C109C2semidirect
11. #16812657C4semidirect
12. #16812657C4semidirect
15. C4⋊C4×D109C4semidirect
16. C4⋊C4×D109C4semidirect
139. C109#1826semidirect
146. #339D109semidirect

Maximal subgroups

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

subgroupindex
#117×D1092
#202949892
C4×#131820062
#202947872
#202947862
#202947852
#339×C1092
#1826109