Finite Group Databasebeta

← #28373170

Subgroups — #28373170

Order 13952.

450 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 129 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#20295560C211yesmaximal, characteristic, complemented
2#20295356C211yesmaximal, characteristic, complemented
3#20295339C211yesmaximal, characteristic, complemented
4#20295326C212yesmaximal, complemented
5#20295241C212yesmaximal, complemented
6#20295177C211yesmaximal, characteristic, complemented
7#20295160C211yesmaximal, characteristic
8#20295136C212yesmaximal, complemented
9#20295126C212yesmaximal, complemented
10#20295083C211yesmaximal, characteristic, complemented
11C2×C4×D4×C109C211yesmaximal, characteristic, complemented
12C2×#13182017C2212yes—
13C2×#13182014C2212yes—
14#16812693—21no—
15#16812691C2211yescharacteristic, complemented
16#16812687C2211yescharacteristic, complemented
17#16812682—21no—
18#16812678C2211yescharacteristic
19#16812673C2211yescharacteristic
20C4×Dic218C2211yescharacteristic, complemented
21C4×D436C2211yescharacteristic, complemented
22C4×C22⋊D109—21no—
23#16812656—21no—
24#16812632C2212yescomplemented
25#16812630C2212yescomplemented
26C4⋊#11724784C2212yescomplemented
27#16812622C2212yescomplemented
28#16812620C2212yes—
29#16812620C2212yes—
30#16812619C2212yescomplemented
31C22⋊#11724784C2211yescharacteristic
32C22⋊#11724784C2211yescharacteristic
33#16812610C2212yescomplemented
34C22×D4×C109C2211yescharacteristic
35C23×C4×C109—21no—
36C4×D4×C109—21no—
37C4×D4×C109—21no—
38C4×D4×C109C2212yes—
39C4×D4×C109C2212yes—
40C2×C4⋊C4×C109C2211yescharacteristic
41C2×C22⋊C4×C109—21no—
42C2×C42×C109C2211yescharacteristic
43C2×Dic218C2311yescharacteristic
44C2×D436C2311yescharacteristic
45C2×C22⋊D109—21no—
46C2×C4×D109—21no—
47#13182017—24no—
48#13182014—24no—
49C2×#11724784C2312yes—
50C2×#11724784C2312yes—
51C4⋊Dic109C2311yescharacteristic
52C4⋊Dic109C2311yescharacteristic
53#13182008—21no—
54#13182008—21no—
55#13182008—21no—
56#13182008—21no—
57C22⋊Dic109—21no—
58#13182006—21no—
59#13182006—21no—
60#13182006—21no—
61#13182006—21no—
62C4×Dic109—21no—
63C24×C109—21no—
64C2×D4×C109—24no—
65C2×D4×C109—21no—
66C2×D4×C109C2312yes—
67C22×C4×C109—21no—
68C22×C4×C109—22no—
69C22×C4×C109—22no—
70C22×C4×C109—44no—
71C22×C4×C109D411yescharacteristic
72C22×C4×C109D411yescharacteristic
73C22×C4×C109C2311yescharacteristic
74C4⋊C4×C109—21no—
75C4⋊C4×C109C2312yes—
76C22⋊C4×C109—22no—
77C22⋊C4×C109—22no—
78C42×C109D411yescharacteristic
79C42×C109D411yescharacteristic
80C42×C109C2311yescharacteristic
81C42×C109C2311yescharacteristic
82C23×C109—24no—
83C23×C109—22no—
84C23×C109—42no—
85C23×C109—42no—
86C23×C109C2×D411yescharacteristic
87C22×D109—21no—
88D4×C109—24no—
89D4×C109—22no—
90D4×C109#4114yes—
91C2×C4×C109—22no—
92C2×C4×C109—22no—
93C2×C4×C109—22no—
94C2×C4×C109—41no—
95C2×C4×C109—44no—
96C2×C4×C109—44no—
97C2×C4×C109—42no—
98C2×C4×C109C2×D411yescharacteristic
99C2×C4×C109C2×D411yescharacteristic
100C2×C4×C109C2×D411yescharacteristic
101C2×C4×C109C2×D411yescharacteristic
102C2×C4×C109C2×D411yescharacteristic
103C2×C4×C109C2411yescharacteristic
104C22⋊D109—42no—
105C2×Dic109—21no—
106C2×Dic109—21no—
107C2×Dic109—21no—
108D436—22no—
109C4×D109—42no—
110Dic218—22no—
111#11724784—22no—
112#11724784—22no—
113C22×C109—21no—
114C22×C109—21no—
115C22×C109—24no—
116C22×C109—48no—
117C22×C109—42no—
118C22×C109—42no—
119C22×C109AGL(1,ℤ/8)12yes—
120C22×C109C22×D411yescharacteristic
121C2×D109—41no—
122C2×D109—41no—
123C2×D109—41no—
124C4×C109—21no—
125C4×C109—21no—
126C4×C109—21no—
127C4×C109—21no—
128C4×C109—21no—
129C4×C109—42no—
130C4×C109C2×#4112yes—
131Dic109—41no—
132Dic109—41no—
133Dic109—41no—
134C2×C109—22no—
135C2×C109—44no—
136C2×C109#52511yescharacteristic
137C2×C109C2×AGL(1,ℤ/8)11yescharacteristic
138C2×C109#57511yescharacteristic
139D109—81no—
140#3114—1091nomaximal, Sylow
141C109#311411yescharacteristic, complemented, Sylow
142#529—1091no—
143C2×C4×D4D10911yescharacteristic, complemented
144#483—1091no—
145#480—1091no—
146#478—1092no—
147#463—1092no—
148#450—1091no—
149#447—1091no—
150#442—1092no—
151#440—1092no—
152#432—1091no—
153C22×D4C2×D10911yescharacteristic
154C23×C4—21no—
155C2×SD16—1092no—
156C2×D8—1092no—
157#126—2181no—
158#125—1091no—
159#124—1091no—
160#123—2181no—
161C22⋊Q8—1091no—
162#121—1091no—
163C4×Q8—1091no—
164C4×D4—21no—
165C4×D4—21no—
166C4×D4—1091no—
167C4×D4—2181no—
168C4×D4C2×D10912yes—
169C4×D4C2×D10912yes—
170#117—2181no—
171C2×C4⋊C4C2×D10911yescharacteristic
172C2×C22⋊C4—21no—
173C2×C42C2×D10911yescharacteristic
174#107—1092no—
175#106—1092no—
176C4⋊C8—1092no—
177#103—1092no—
178#102—1092no—
179#102—1092no—
180#102—1092no—
181C22⋊C8—1091no—
182C22⋊C8—1091no—
183#97—1092no—
184C24—21no—
185C2×Q8—1091no—
186C2×D4—24no—
187C2×D4—21no—
188C2×D4—1091no—
189C2×D4—2181no—
190C2×D4C22×D10912yes—
191C22×C4—21no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—44no—
195C22×C4—2181no—
196C22×C4C22⋊D10911yescharacteristic
197C22×C4C22⋊D10911yescharacteristic
198C22×C4C22×D10911yescharacteristic
199SD16—2184no—
200D8—2184no—
201C2×C8—1092no—
202C2×C8—1092no—
203C4⋊C4—21no—
204C4⋊C4—1091no—
205C4⋊C4—1091no—
206C4⋊C4—2181no—
207C4⋊C4—2181no—
208C4⋊C4—2181no—
209C4⋊C4—2181no—
210C4⋊C4C22×D10912yes—
211C22⋊C4—22no—
212C22⋊C4—22no—
213C22⋊C4—2181no—
214C22⋊C4—2181no—
215C22⋊C4—2181no—
216C22⋊C4—2181no—
217C22⋊C4—2181no—
218C42—2181no—
219C42C22⋊D10911yescharacteristic
220C42C22⋊D10911yescharacteristic
221C42C22×D10911yescharacteristic
222C42C22×D10911yescharacteristic
223C23—24no—
224C23—22no—
225C23—42no—
226C23—42no—
227C23—2181no—
228C23C2×C22⋊D10911yescharacteristic
229Q8—2182no—
230D4—24no—
231D4—22no—
232D4—4362no—
233D4—2182no—
234D4#1318202914yes—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—41no—
239C2×C4—44no—
240C2×C4—44no—
241C2×C4—42no—
242C2×C4—4362no—
243C2×C4—2181no—
244C2×C4—2181no—
245C2×C4—2181no—
246C2×C4C2×C22⋊D10911yescharacteristic
247C2×C4C2×C22⋊D10911yescharacteristic
248C2×C4C2×C22⋊D10911yescharacteristic
249C2×C4C2×C22⋊D10911yescharacteristic
250C2×C4C2×C22⋊D10911yescharacteristic
251C2×C4C23×D10911yescharacteristic
252C8—2182no—
253C8—2182no—
254C22—21no—
255C22—21no—
256C22—24no—
257C22—48no—
258C22—42no—
259C22—42no—
260C22—4361no—
261C22—4361no—
262C22—4361no—
263C22#1681272512yes—
264C22C22×C22⋊D10911yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—42no—
271C4—4361no—
272C4—4361no—
273C4—4361no—
274C4C2×#1318202912yes—
275C2—22no—
276C2—44no—
277C2—8721no—
278C2#2029553711yescharacteristic
279C2C2×#1681272511yescharacteristic
280C2#2029582411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
FittingC2×C4×D4×C109C2
socleC22×C109C22×D4
prime radical#20295160C2
hypercenterC2×C4×D4D109
hypocenterC109#3114
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #20295560C2semidirect
2. #20295356C2semidirect
3. #20295339C2semidirect
4. #20295326C2semidirect
5. #20295241C2semidirect
6. #20295177C2semidirect
8. #20295136C2semidirect
9. #20295126C2semidirect
10. #20295083C2semidirect
11. C2×C4×D4×C109C2semidirect
15. #16812691C22semidirect
16. #16812687C22semidirect
20. C4×Dic218C22semidirect
21. C4×D436C22semidirect
24. #16812632C22semidirect
25. #16812630C22semidirect
26. C4⋊#11724784C22semidirect
27. #16812622C22semidirect
30. #16812619C22semidirect
33. #16812610C22semidirect
141. C109#3114semidirect
143. C2×C4×D4D109semidirect

Maximal subgroups

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

subgroupindex
#202955602
#202953562
#202953392
#202953262
#202952412
#202951772
#202951602
#202951362
#202951262
#202950832
C2×C4×D4×C1092
#3114109