Finite Group Databasebeta

← #28373375

Subgroups — #28373375

Order 13952.

392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 125 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#20295579C211yesmaximal, characteristic, complemented
2#20295572C211yesmaximal, characteristic
3#20295393C212yesmaximal, complemented
4#20295389C212yesmaximal, complemented
5#20295387C212yesmaximal, complemented
6#20295384C212yesmaximal, complemented
7#20295023C211yesmaximal, characteristic, complemented
8#20295022C211yesmaximal, characteristic, complemented
9#20295020C211yesmaximal, characteristic, complemented
10C2×#16812609C211yesmaximal, characteristic, complemented
11#416×C109C211yesmaximal, characteristic, complemented
12C2×#13182029C2211yescharacteristic
13C22×#11724784C2211yescharacteristic
14#16812698C2212yes—
15#16812697C2211yescharacteristic
16#16812695C2211yescharacteristic
17#16812690C2212yes—
18#16812688C2211yescharacteristic
19#16812686C2211yescharacteristic
20#16812676—22no—
21#16812671—22no—
22C4×Dic218—22no—
23C4×C22⋊D109—22no—
24#16812658C2211yescharacteristic
25C2×C4×Dic109C2211yescharacteristic
26#16812624C2212yes—
27#16812623C2212yes—
28#16812622C2212yes—
29#16812621C2212yes—
30#16812620C2212yes—
31#16812619C2212yes—
32#16812609C2212yes—
33#16812609C2212yes—
34C2×#41×C109C2211yescharacteristic
35C22×C8×C109C2211yescharacteristic
36#117×C109C2211yescharacteristic
37#103×C109C2212yes—
38#102×C109C2212yes—
39#13182029—22no—
40#13182029—22no—
41C2×Dic218—22no—
42C2×Dic218C2311yescharacteristic
43C2×D436C2311yescharacteristic
44C2×C22⋊D109—21no—
45C2×C22⋊D109—22no—
46C22×Dic109D412yes—
47C2×C4×D109—21no—
48C2×#11724784—22no—
49C2×#11724784C2312yes—
50C4⋊Dic109—22no—
51C4⋊Dic109C2312yes—
52#13182008—22no—
53#13182008—22no—
54#13182008—22no—
55C22⋊Dic109—21no—
56C22⋊Dic109—22no—
57#13182006—22no—
58C4×Dic109—21no—
59C4×Dic109D412yes—
60C4×Dic109C2311yescharacteristic
61C4×Dic109C2311yescharacteristic
62#41×C109—22no—
63#41×C109—22no—
64C2×Q8×C109C2311yescharacteristic
65C2×D4×C109—21no—
66C2×D4×C109C2311yescharacteristic
67C22×C4×C109—21no—
68C22×C4×C109C2311yescharacteristic
69C2×C8×C109—22no—
70C2×C8×C109C2312yes—
71C4⋊C4×C109C2312yes—
72C22⋊C4×C109—21no—
73C42×C109—21no—
74C23×C109—21no—
75C23×C109C2×D411yescharacteristic
76C22×D109—21no—
77Q8×C109—21no—
78Q8×C109—21no—
79D4×C109—21no—
80D4×C109—21no—
81D4×C109—42no—
82C2×C4×C109—22no—
83C2×C4×C109—21no—
84C2×C4×C109—42no—
85C2×C4×C109C2×D411yescharacteristic
86C2×C4×C109#4112yes—
87C2×C4×C109#4112yes—
88C2×C4×C109C2411yescharacteristic
89C22⋊D109—44no—
90C22⋊D109—42no—
91C2×Dic109—22no—
92C2×Dic109—21no—
93C2×Dic109—42no—
94C2×Dic109C2×D412yes—
95C2×Dic109C2×D412yes—
96D436—21no—
97D436—21no—
98C4×D109—42no—
99Dic218—21no—
100Dic218—21no—
101Dic218—44no—
102C8×C109—22no—
103#11724784—22no—
104C22×C109—22no—
105C22×C109—41no—
106C22×C109—42no—
107C22×C109#12412yes—
108C22×C109C22×D411yescharacteristic
109C2×D109—41no—
110C2×D109—42no—
111C4×C109—41no—
112C4×C109—42no—
113C4×C109#12412yes—
114C4×C109C2×#4111yescharacteristic
115C4×C109C2×#4111yescharacteristic
116Dic109—22no—
117Dic109—22no—
118Dic109—41no—
119Dic109—42no—
120C2×C109—22no—
121C2×C109—81no—
122C2×C109C2×#12411yescharacteristic
123C2×C109#57512yes—
124D109—81no—
125#3135—1091nomaximal, Sylow
126C109#313511yescharacteristic, complemented, Sylow
127#533—1091no—
128#532—1091no—
129#491—1092no—
130#490—1092no—
131#489—1092no—
132#489—1092no—
133#416—1091no—
134#416—1091no—
135#416—1091no—
136#416D10911yescharacteristic, complemented
137C2×#97—1091no—
138C2×#41—1091no—
139C2×#41C2×D10911yescharacteristic
140C22×C8—1091no—
141C22×C8C2×D10911yescharacteristic
142C4⋊Q8—1092no—
143C4⋊Q8—1091no—
144#127—1091no—
145#125—1092no—
146#124—1091no—
147#124—1091no—
148C22⋊Q8—2182no—
149#121—2182no—
150C4×Q8—2182no—
151C4×D4—2182no—
152#117—1091no—
153#117C2×D10911yescharacteristic
154C2×C42—1091no—
155#103—1092no—
156#103—1092no—
157#103—1092no—
158#103C2×D10912yes—
159#102—1092no—
160#102—1092no—
161#102—1092no—
162#102C2×D10912yes—
163#97—1092no—
164#97—1092no—
165#41—22no—
166#41—22no—
167#41—2182no—
168#41—2182no—
169C2×Q8—1091no—
170C2×Q8—2182no—
171C2×Q8C22×D10911yescharacteristic
172C2×D4—21no—
173C2×D4—1091no—
174C2×D4—2182no—
175C2×D4—2181no—
176C2×D4C22×D10911yescharacteristic
177C22×C4—21no—
178C22×C4—1092no—
179C22×C4—2181no—
180C22×C4C22×D10911yescharacteristic
181C2×C8—22no—
182C2×C8—1092no—
183C2×C8—2182no—
184C2×C8C22×D10912yes—
185C4⋊C4—1092no—
186C4⋊C4—2182no—
187C4⋊C4—2182no—
188C4⋊C4—2182no—
189C4⋊C4—2182no—
190C4⋊C4C22×D10912yes—
191C22⋊C4—21no—
192C22⋊C4—2182no—
193C22⋊C4—2182no—
194C22⋊C4—2181no—
195C42—21no—
196C42—1092no—
197C42—1091no—
198C42—1091no—
199C42—2181no—
200C23—21no—
201C23—2181no—
202C23D4×D10911yescharacteristic
203Q8—21no—
204Q8—21no—
205Q8—4364no—
206Q8—2181no—
207Q8—2181no—
208D4—21no—
209D4—21no—
210D4—42no—
211D4—4362no—
212D4—4364no—
213D4—2181no—
214D4—2181no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—42no—
218C2×C4—1092no—
219C2×C4—1092no—
220C2×C4—4362no—
221C2×C4—4362no—
222C2×C4—2182no—
223C2×C4—2181no—
224C2×C4D4×D10911yescharacteristic
225C2×C4#1318202812yes—
226C2×C4#1318202912yes—
227C2×C4C23×D10911yescharacteristic
228C8—22no—
229C8—2182no—
230C22—22no—
231C22—41no—
232C22—42no—
233C22—4361no—
234C22—4362no—
235C22#1681268512yes—
236C22C2×D4×D10911yescharacteristic
237C4—41no—
238C4—42no—
239C4—4361no—
240C4—4362no—
241C4—2182no—
242C4—2182no—
243C4#1681268512yes—
244C4C2×#1318202811yescharacteristic
245C4C2×#1318202911yescharacteristic
246C2—22no—
247C2—81no—
248C2—8721no—
249C2C2×#1681268511yescharacteristic
250C2#2029582312yes—
subgroupG/H
centerC2×C4D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#416×C109C2
socleC22×C109C22×D4
prime radical#20295572C2
hypercenter#416D109
hypocenterC109#3135
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #20295579C2semidirect
3. #20295393C2semidirect
4. #20295389C2semidirect
5. #20295387C2semidirect
6. #20295384C2semidirect
7. #20295023C2semidirect
8. #20295022C2semidirect
9. #20295020C2semidirect
10. C2×#16812609C2semidirect
11. #416×C109C2semidirect
126. C109#3135semidirect
136. #416D109semidirect

Maximal subgroups

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

subgroupindex
#202955792
#202955722
#202953932
#202953892
#202953872
#202953842
#202950232
#202950222
#202950202
C2×#168126092
#416×C1092
#3135109