Finite Group Databasebeta

← #28363862

Subgroups — #28363862

Order 13952.

320 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 83 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#20295572C211yesmaximal, characteristic
2#20295049C211yesmaximal, characteristic, complemented
3C2×#16812627C211yesmaximal, characteristic, complemented
4C2×#16812626C211yesmaximal, characteristic, complemented
5C2×#16812625C211yesmaximal, characteristic, complemented
6#20294872C211yesmaximal, characteristic, complemented
7C2×#104×C109C211yesmaximal, characteristic, complemented
8C2×#13182029C2211yescharacteristic
9C2×#13182013C2211yescharacteristic
10#16812697C411yescharacteristic, complemented
11#16812695C411yescharacteristic, complemented
12#16812688C411yescharacteristic, complemented
13#16812686C411yescharacteristic, complemented
14#16812671—22no—
15C4×C22⋊D109—22no—
16C2×C4×Dic109C2211yescharacteristic
17C2×C4×Dic109C2211yescharacteristic
18#16812628—22no—
19#16812627—22no—
20#16812626—22no—
21#16812625—22no—
22#16812606—22no—
23C2×#41×C109C2211yescharacteristic
24C2×M16×C109C2211yescharacteristic
25C2×C42×C109C2211yescharacteristic
26#104×C109—22no—
27#13182029—21no—
28#13182029—21no—
29#13182029—21no—
30#13182029—21no—
31C2×Dic218C2×C411yescharacteristic
32C2×D436C2×C411yescharacteristic
33C2×C22⋊D109—21no—
34C2×C22⋊D109—22no—
35C22×Dic109—21no—
36C22×Dic109D412yes—
37C2×C4×D109—21no—
38#13182013—21no—
39#13182013—21no—
40C2×#11724784—21no—
41#13182008—22no—
42C22⋊Dic109—22no—
43#13182006—22no—
44C4×Dic109—21no—
45C4×Dic109C2×C411yescharacteristic
46C4×Dic109C2×C411yescharacteristic
47C4×Dic109D412yes—
48C4×Dic109D412yescomplemented
49#41×C109—21no—
50#41×C109—21no—
51#41×C109—21no—
52#41×C109—21no—
53C2×Q8×C109C2×C411yescharacteristic
54C2×D4×C109—21no—
55C2×D4×C109C2×C411yescharacteristic
56C22×C4×C109—21no—
57C22×C4×C109—21no—
58C22×C4×C109C2311yescharacteristic
59M16×C109—21no—
60M16×C109—21no—
61C2×C8×C109—21no—
62C42×C109—21no—
63C42×C109D412yescomplemented
64C23×C109—21no—
65C23×C109C2×D411yescharacteristic
66C22×D109—21no—
67Q8×C109—21no—
68Q8×C109—21no—
69D4×C109—21no—
70D4×C109—21no—
71D4×C109—41no—
72D4×C109—41no—
73C2×C4×C109—21no—
74C2×C4×C109—22no—
75C2×C4×C109—42no—
76C2×C4×C109—41no—
77C2×C4×C109—41no—
78C2×C4×C109C22×C411yescharacteristic
79C2×C4×C109C2×D411yescharacteristic
80C2×C4×C109C2×D411yescharacteristic
81C2×C4×C109C2×D411yescharacteristic
82C2×C4×C109#4111yescharacteristic
83C2×C4×C109#4111yescharacteristic
84C22⋊D109—44no—
85C22⋊D109—41no—
86C22⋊D109—41no—
87C2×Dic109—21no—
88C2×Dic109—22no—
89C2×Dic109—42no—
90C2×Dic109—42no—
91C2×Dic109C22⋊C412yes—
92C2×Dic109C22⋊C412yes—
93D436—21no—
94D436—21no—
95C4×D109—41no—
96C4×D109—41no—
97Dic218—21no—
98Dic218—21no—
99C8×C109—41no—
100#11724784—41no—
101C22×C109—22no—
102C22×C109—41no—
103C22×C109—42no—
104C22×C109C2×C22⋊C411yescharacteristic
105C22×C109#12111yescharacteristic
106C22×C109#12111yescharacteristic
107C2×D109—41no—
108C2×D109—42no—
109C4×C109—42no—
110C4×C109—41no—
111C4×C109C4×D411yescharacteristic
112C4×C109C4×D411yescharacteristic
113C4×C109#12411yescharacteristic
114C4×C109#12711yescharacteristic
115Dic109—22no—
116Dic109—22no—
117Dic109—42no—
118Dic109—41no—
119C2×C109—21no—
120C2×C109—21no—
121C2×C109—81no—
122C2×C109#39011yescharacteristic
123C2×C109#42112yes—
124D109—81no—
125#1963—1091nomaximal, Sylow
126C109#196311yescharacteristic, complemented, Sylow
127#532—1091no—
128#423—1091no—
129C2×#104—1091no—
130C2×#104—1091no—
131C2×#104—1091no—
132C2×#104D10911yescharacteristic, complemented
133#376—1091no—
134C2×#41—1091no—
135C2×#41C2×D10911yescharacteristic
136C2×M16—1091no—
137C2×M16C2×D10911yescharacteristic
138C4⋊Q8—1091no—
139#127—1091no—
140#124—1091no—
141#124—1091no—
142#121—2182no—
143C4×D4—2182no—
144C2×C42—1091no—
145C2×C42—1091no—
146C2×C42C2×D10911yescharacteristic
147C4⋊C8—2182no—
148#104—22no—
149#104—2182no—
150#104—2182no—
151#104—2182no—
152#95—2182no—
153#41—21no—
154#41—21no—
155#41—21no—
156#41—21no—
157#41—2181no—
158#41—2181no—
159#41—2181no—
160#41—2181no—
161C2×Q8—1091no—
162C2×Q8C4×D10911yescharacteristic
163C2×D4—21no—
164C2×D4—1091no—
165C2×D4—2182no—
166C2×D4—2181no—
167C2×D4C4×D10911yescharacteristic
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—1092no—
171C22×C4—2181no—
172C22×C4—2181no—
173C22×C4C22×D10911yescharacteristic
174M16—21no—
175M16—21no—
176M16—2181no—
177M16—2181no—
178C2×C8—21no—
179C2×C8—2181no—
180C4⋊C4—2182no—
181C22⋊C4—2182no—
182C22⋊C4—2182no—
183C42—21no—
184C42—1091no—
185C42—1091no—
186C42—1092no—
187C42—1092no—
188C42—2181no—
189C42C22⋊D10912yescomplemented
190C23—21no—
191C23—2181no—
192C23D4×D10911yescharacteristic
193Q8—21no—
194Q8—21no—
195Q8—2181no—
196Q8—2181no—
197D4—21no—
198D4—21no—
199D4—41no—
200D4—41no—
201D4—4361no—
202D4—4361no—
203D4—4364no—
204D4—2181no—
205D4—2181no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—1092no—
212C2×C4—1092no—
213C2×C4—4362no—
214C2×C4—4361no—
215C2×C4—4361no—
216C2×C4—4362no—
217C2×C4—2181no—
218C2×C4—2182no—
219C2×C4C2×C4×D10911yescharacteristic
220C2×C4D4×D10911yescharacteristic
221C2×C4D4×D10911yescharacteristic
222C2×C4C2×C22⋊D10911yescharacteristic
223C2×C4#1318202811yescharacteristic
224C2×C4#1318202911yescharacteristic
225C8—41no—
226C8—4361no—
227C22—22no—
228C22—41no—
229C22—42no—
230C22—4361no—
231C22—4362no—
232C22C22⋊C4×D10911yescharacteristic
233C22#1681267111yescharacteristic
234C22#1681267211yescharacteristic
235C4—42no—
236C4—41no—
237C4—4362no—
238C4—4361no—
239C4—2182no—
240C4—2182no—
241C4#1681265911yescharacteristic
242C4C4×C22⋊D10911yescharacteristic
243C4#1681268511yescharacteristic
244C4#1681269511yescharacteristic
245C2—21no—
246C2—21no—
247C2—81no—
248C2—8721no—
249C2#2029492611yescharacteristic
250C2#2029504112yes—
subgroupG/H
centerC2×C4D4×D109
commutatorC2×C4×C109C22×C4
FrattiniC22×C4C22×D109
FittingC2×#104×C109C2
socleC22×C109C2×C22⋊C4
prime radical#20295572C2
cosocleC22×C4×C109C23
hypercenterC2×#104D109
hypocenterC109#1963
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. #20295049C2semidirect
3. C2×#16812627C2semidirect
4. C2×#16812626C2semidirect
5. C2×#16812625C2semidirect
6. #20294872C2semidirect
7. C2×#104×C109C2semidirect
10. #16812697C4semidirect
11. #16812695C4semidirect
12. #16812688C4semidirect
13. #16812686C4semidirect
48. C4×Dic109D4semidirect
63. C42×C109D4semidirect
126. C109#1963semidirect
132. C2×#104D109semidirect
189. C42C22⋊D109semidirect

Maximal subgroups

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

subgroupindex
#202955722
#202950492
C2×#168126272
C2×#168126262
C2×#168126252
#202948722
C2×#104×C1092
#1963109