Finite Group Databasebeta

← #28361572

Subgroups — #28361572

Order 13952.

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

normal subgroups only

This group has 286 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#20295536C211yesmaximal, characteristic
2#20294988C211yesmaximal, characteristic, complemented
3#20294885C211yesmaximal, characteristic, complemented
4#20294764C211yesmaximal, characteristic, complemented
5#20294762C211yesmaximal, characteristic, complemented
6#20294760C211yesmaximal, characteristic, complemented
7#327×C109C211yesmaximal, characteristic, complemented
8C2×#13182028C411yescharacteristic, complemented
9C22×C4×D109C2211yescharacteristic
10C2×#13182012—21no—
11#16812681—21no—
12#16812679C411yescharacteristic, complemented
13#16812678C2211yescharacteristic
14#16812670C411yescharacteristic, complemented
15#16812667—21no—
16D4×Dic109—21no—
17#16812659—21no—
18#16812657C411yescharacteristic, complemented
19C2×#13182008—21no—
20C2×#13182006—21no—
21C22⋊#11724784C2211yescharacteristic
22#16812611—21no—
23#16812606C2211yescharacteristic
24#121×C109C2211yescharacteristic
25C22⋊C8×C109C2211yescharacteristic
26#95×C109C2211yescharacteristic
27C23×D109D411yescharacteristic
28#13182028—42no—
29C2×Dic218C2×C411yescharacteristic
30C2×C22⋊D109—21no—
31C2×C22⋊D109—21no—
32C22×Dic109—21no—
33C22×Dic109—21no—
34C22×Dic109D411yescharacteristic
35C2×C4×D109—42no—
36C2×C4×D109C2×C411yescharacteristic
37C2×C4×D109C2×C411yescharacteristic
38C2×C4×D109D411yescharacteristic
39C2×C4×D109D411yescharacteristic
40#13182012—42no—
41C2×#11724784—21no—
42C4⋊Dic109—21no—
43C4⋊Dic109C2×C411yescharacteristic
44#13182008—21no—
45#13182008—42no—
46C22⋊Dic109—21no—
47C22⋊Dic109—21no—
48#13182006—21no—
49#13182006—21no—
50#13182006—42no—
51C4×Dic109—21no—
52C2×D4×C109—21no—
53C2×D4×C109C2×C411yescharacteristic
54C22×C4×C109—21no—
55C22×C4×C109C2311yescharacteristic
56C2×C8×C109—21no—
57C4⋊C4×C109C2×C411yescharacteristic
58C22⋊C4×C109—21no—
59C23×C109—21no—
60C23×C109C2×D411yescharacteristic
61C22×D109—21no—
62C22×D109—21no—
63C22×D109—41no—
64C22×D109—41no—
65C22×D109C22⋊C411yescharacteristic
66C22×D109C22⋊C411yescharacteristic
67D4×C109—41no—
68D4×C109—41no—
69D4×C109—41no—
70C2×C4×C109—21no—
71C2×C4×C109—41no—
72C2×C4×C109—41no—
73C2×C4×C109—41no—
74C2×C4×C109—41no—
75C2×C4×C109C22×C411yescharacteristic
76C2×C4×C109C2×D411yescharacteristic
77C22⋊D109—42no—
78C22⋊D109—42no—
79C2×Dic109—22no—
80C2×Dic109—21no—
81C2×Dic109—21no—
82C2×Dic109—42no—
83C2×Dic109—41no—
84C2×Dic109—41no—
85C2×Dic109—41no—
86C2×Dic109C22⋊C411yescharacteristic
87C2×Dic109C22⋊C411yescharacteristic
88C4×D109—22no—
89C4×D109—22no—
90C4×D109—41no—
91C4×D109—41no—
92Dic218—41no—
93C8×C109—41no—
94#11724784—41no—
95C22×C109—21no—
96C22×C109—21no—
97C22×C109—41no—
98C22×C109—41no—
99C22×C109—41no—
100C22×C109C2×C22⋊C411yescharacteristic
101C22×C109AGL(1,ℤ/8)11yescharacteristic
102C22×C109#13711yescharacteristic
103C2×D109—21no—
104C2×D109—21no—
105C2×D109—21no—
106C2×D109—21no—
107C2×D109—21no—
108C2×D109—21no—
109C2×D109—42no—
110C2×D109—42no—
111C4×C109—21no—
112C4×C109—21no—
113C4×C109—41no—
114C4×C109—81no—
115Dic109—21no—
116Dic109—41no—
117Dic109—41no—
118Dic109—81no—
119Dic109#9912yes—
120C2×C109—21no—
121C2×C109—21no—
122C2×C109—81no—
123C2×C109C2×#9911yescharacteristic
124C2×C109#41711yescharacteristic
125C2×C109#42111yescharacteristic
126D109—41no—
127D109—41no—
128#1513—1091nomaximal, Sylow
129C109#151311yescharacteristic, complemented, Sylow
130#525—1091no—
131#407—1091no—
132#380—1091no—
133#328—1091no—
134#328—1091no—
135#327—1091no—
136#327D10911yescharacteristic, complemented
137C2×#41—1091no—
138C23×C4—1091no—
139C2×M16—2181no—
140#123—2181no—
141C22⋊Q8—1091no—
142C22⋊Q8—1091no—
143#121—1091no—
144#121C2×D10911yescharacteristic
145#120—2181no—
146C4×D4—2181no—
147C4×D4—2181no—
148#117—1091no—
149C2×C4⋊C4—2181no—
150C2×C22⋊C4—2181no—
151C22⋊C8—1091no—
152C22⋊C8—2181no—
153C22⋊C8C2×D10911yescharacteristic
154#95—1091no—
155#95C2×D10911yescharacteristic
156C24—1091no—
157#41—4362no—
158C2×Q8—1091no—
159C2×D4—21no—
160C2×D4—2181no—
161C2×D4—2181no—
162C2×D4C4×D10911yescharacteristic
163C22×C4—21no—
164C22×C4—1091no—
165C22×C4—1091no—
166C22×C4—1091no—
167C22×C4—1091no—
168C22×C4—1091no—
169C22×C4—4362no—
170C22×C4—2181no—
171C22×C4—2181no—
172C22×C4C22×D10911yescharacteristic
173M16—4362no—
174C2×C8—21no—
175C2×C8—2181no—
176C4⋊C4—1091no—
177C4⋊C4—4362no—
178C4⋊C4—2181no—
179C4⋊C4—2181no—
180C4⋊C4C4×D10911yescharacteristic
181C22⋊C4—21no—
182C22⋊C4—4362no—
183C22⋊C4—2181no—
184C22⋊C4—2181no—
185C22⋊C4—2181no—
186C22⋊C4—2181no—
187C42—2181no—
188C23—21no—
189C23—1091no—
190C23—1091no—
191C23—4361no—
192C23—4361no—
193C23—2181no—
194C23—2181no—
195C23D4×D10911yescharacteristic
196Q8—4361no—
197D4—41no—
198D4—41no—
199D4—41no—
200D4—4362no—
201D4—4362no—
202C2×C4—21no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—1091no—
208C2×C4—1091no—
209C2×C4—4361no—
210C2×C4—4361no—
211C2×C4—4361no—
212C2×C4—4361no—
213C2×C4—4361no—
214C2×C4—4362no—
215C2×C4—2182no—
216C2×C4—2182no—
217C2×C4—2182no—
218C2×C4—2181no—
219C2×C4—2181no—
220C2×C4C2×C4×D10911yescharacteristic
221C2×C4D4×D10911yescharacteristic
222C8—41no—
223C8—4361no—
224C22—21no—
225C22—21no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—4362no—
230C22—4362no—
231C22—2181no—
232C22—2181no—
233C22—2181no—
234C22—2181no—
235C22—2181no—
236C22—2181no—
237C22C22⋊C4×D10911yescharacteristic
238C22#1681272311yescharacteristic
239C22#1681272811yescharacteristic
240C4—21no—
241C4—21no—
242C4—41no—
243C4—81no—
244C4—8721no—
245C4—1092no—
246C4—4361no—
247C4—4361no—
248C4—2181no—
249C2—21no—
250C2—21no—
251C2—81no—
252C2—4361no—
253C2—4361no—
254C2#99×D10911yescharacteristic
255C2#2029502411yescharacteristic
256C2#2029504111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D109
commutatorC2×C4×C109C22×C4
FrattiniC22×C4C22×D109
Fitting#327×C109C2
socleC22×C109C2×C22⋊C4
prime radical#20295536C2
cosocleC22×C4×C109C23
hypercenter#327D109
hypocenterC109#1513
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. #20294988C2semidirect
3. #20294885C2semidirect
4. #20294764C2semidirect
5. #20294762C2semidirect
6. #20294760C2semidirect
7. #327×C109C2semidirect
8. C2×#13182028C4semidirect
12. #16812679C4semidirect
14. #16812670C4semidirect
18. #16812657C4semidirect
129. C109#1513semidirect
136. #327D109semidirect

Maximal subgroups

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

subgroupindex
#202955362
#202949882
#202948852
#202947642
#202947622
#202947602
#327×C1092
#1513109