Finite Group Databasebeta

← #28372945

Subgroups — #28372945

Order 13952.

420 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 137 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#20295537C211yesmaximal, characteristic
2#20295367C212yesmaximal, complemented
3#20295361C211yesmaximal, characteristic, complemented
4#20295356C211yesmaximal, characteristic, complemented
5#20295350C212yesmaximal, complemented
6#20295344C211yesmaximal, characteristic, complemented
7#20295339C211yesmaximal, characteristic, complemented
8#20295062C212yesmaximal, complemented
9#20295020C212yesmaximal, complemented
10C2×C22⋊#11724784C211yesmaximal, characteristic, complemented
11C2×#117×C109C211yesmaximal, characteristic, complemented
12C2×#13182029C2211yescharacteristic
13C22×#11724784C2212yes—
14#16812682—21no—
15#16812678C2211yescharacteristic
16#16812678C2211yescharacteristic
17#16812673C2211yescharacteristic
18#16812673C2211yescharacteristic
19#16812668—21no—
20C4×C22⋊D109—21no—
21C4×C22⋊D109—21no—
22#16812658C2211yescharacteristic
23#16812632C2212yescomplemented
24#16812632C2212yescomplemented
25#16812630C2212yescomplemented
26#16812630C2212yescomplemented
27#16812622C2212yescomplemented
28#16812622C2212yescomplemented
29#16812619C2212yescomplemented
30#16812619C2212yescomplemented
31C22⋊#11724784C2211yescharacteristic
32C22⋊#11724784C2211yescharacteristic
33C22⋊#11724784C2212yes—
34C23×C4×C109C2211yescharacteristic
35#117×C109—21no—
36#117×C109—21no—
37#117×C109C2212yes—
38#117×C109C2212yes—
39C2×C4⋊C4×C109C2211yescharacteristic
40C2×C4⋊C4×C109C2211yescharacteristic
41C2×C22⋊C4×C109—21no—
42C2×C42×C109—21no—
43#13182029—24no—
44C2×Dic218C2311yescharacteristic
45C2×D436C2311yescharacteristic
46C2×C22⋊D109—21no—
47C2×C22⋊D109—21no—
48C2×C22⋊D109—21no—
49C2×C4×D109—21no—
50C2×#11724784—24no—
51C2×#11724784C2312yes—
52C2×#11724784C2312yes—
53C4⋊Dic109C2311yescharacteristic
54C4⋊Dic109C2311yescharacteristic
55#13182008—21no—
56#13182008—21no—
57C22⋊Dic109—21no—
58C22⋊Dic109—21no—
59C22⋊Dic109—21no—
60#13182006—21no—
61#13182006—21no—
62C4×Dic109—21no—
63C24×C109D411yescharacteristic
64C22×C4×C109—24no—
65C22×C4×C109—21no—
66C22×C4×C109—21no—
67C22×C4×C109D411yescharacteristic
68C22×C4×C109D411yescharacteristic
69C22×C4×C109D411yescharacteristic
70C22×C4×C109C2311yescharacteristic
71C22×C4×C109C2311yescharacteristic
72C22×C4×C109C2311yescharacteristic
73C4⋊C4×C109—21no—
74C4⋊C4×C109—21no—
75C4⋊C4×C109C2312yes—
76C4⋊C4×C109C2312yes—
77C22⋊C4×C109—22no—
78C22⋊C4×C109—22no—
79C42×C109—22no—
80C42×C109—22no—
81C23×C109—22no—
82C23×C109—22no—
83C23×C109—41no—
84C23×C109C2×D411yescharacteristic
85C23×C109C2×D411yescharacteristic
86C23×C109C2×D411yescharacteristic
87C22×D109—21no—
88C2×C4×C109—22no—
89C2×C4×C109—22no—
90C2×C4×C109—22no—
91C2×C4×C109—22no—
92C2×C4×C109—22no—
93C2×C4×C109—22no—
94C2×C4×C109—22no—
95C2×C4×C109—42no—
96C2×C4×C109—42no—
97C2×C4×C109C2×D411yescharacteristic
98C2×C4×C109C2×D411yescharacteristic
99C2×C4×C109C2×D411yescharacteristic
100C2×C4×C109#4114yes—
101C2×C4×C109C2411yescharacteristic
102C22⋊D109—42no—
103C22⋊D109—42no—
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—21no—
116C22×C109—21no—
117C22×C109—21no—
118C22×C109—21no—
119C22×C109—21no—
120C22×C109—44no—
121C22×C109#12312yes—
122C22×C109#13512yes—
123C22×C109C22×D411yescharacteristic
124C2×D109—41no—
125C2×D109—41no—
126C2×D109—41no—
127C4×C109—21no—
128C4×C109—21no—
129C4×C109—42no—
130C4×C109—42no—
131C4×C109#12312yes—
132C4×C109C2×#4112yes—
133Dic109—41no—
134Dic109—41no—
135Dic109—41no—
136C2×C109—22no—
137C2×C109—22no—
138C2×C109—41no—
139C2×C109C2×#12311yescharacteristic
140C2×C109C2×#13511yescharacteristic
141C2×C109#57511yescharacteristic
142D109—81no—
143#3091—1091nomaximal, Sylow
144C109#309111yescharacteristic, complemented, Sylow
145#525—1091no—
146C2×#117D10911yescharacteristic, complemented
147#485—1092no—
148#484—1091no—
149#483—1091no—
150#482—1092no—
151#481—1091no—
152#480—1091no—
153#427—1092no—
154#416—1092no—
155C2×C22⋊C8—1091no—
156C2×#41—1091no—
157C23×C4C2×D10911yescharacteristic
158C22×C8—1092no—
159#123—2181no—
160C22⋊Q8—1091no—
161C22⋊Q8—1091no—
162#121—1091no—
163#121—1091no—
164#120—2181no—
165C4×D4—2181no—
166C4×D4—2181no—
167#117—21no—
168#117—21no—
169#117—1091no—
170#117C2×D10912yes—
171#117C2×D10912yes—
172C2×C4⋊C4C2×D10911yescharacteristic
173C2×C4⋊C4C2×D10911yescharacteristic
174C2×C22⋊C4—21no—
175C2×C42—21no—
176#107—1092no—
177#107—1092no—
178#106—1092no—
179#106—1092no—
180#103—1092no—
181#103—1092no—
182#102—1092no—
183#102—1092no—
184C22⋊C8—1091no—
185C22⋊C8—1091no—
186C22⋊C8—1092no—
187C24C22⋊D10911yescharacteristic
188#41—2184no—
189C2×Q8—1091no—
190C2×D4—1091no—
191C2×D4—2181no—
192C2×D4—2181no—
193C2×D4—2181no—
194C22×C4—24no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—2181no—
198C22×C4C22⋊D10911yescharacteristic
199C22×C4C22⋊D10911yescharacteristic
200C22×C4C22⋊D10911yescharacteristic
201C22×C4C22×D10911yescharacteristic
202C22×C4C22×D10911yescharacteristic
203C22×C4C22×D10911yescharacteristic
204C2×C8—1092no—
205C2×C8—1092no—
206C2×C8—2184no—
207C4⋊C4—21no—
208C4⋊C4—21no—
209C4⋊C4—1091no—
210C4⋊C4—1091no—
211C4⋊C4—2181no—
212C4⋊C4—2181no—
213C4⋊C4C22×D10912yes—
214C4⋊C4C22×D10912yes—
215C22⋊C4—22no—
216C22⋊C4—22no—
217C22⋊C4—2181no—
218C22⋊C4—2181no—
219C22⋊C4—2181no—
220C22⋊C4—2181no—
221C22⋊C4—2181no—
222C42—22no—
223C42—22no—
224C42—2181no—
225C23—22no—
226C23—22no—
227C23—41no—
228C23—2181no—
229C23C2×C22⋊D10911yescharacteristic
230C23C2×C22⋊D10911yescharacteristic
231C23C2×C22⋊D10911yescharacteristic
232Q8—2182no—
233D4—4362no—
234D4—4362no—
235D4—4362no—
236D4—2182no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—4362no—
247C2×C4—2181no—
248C2×C4—2181no—
249C2×C4—2181no—
250C2×C4C2×C22⋊D10911yescharacteristic
251C2×C4C2×C22⋊D10911yescharacteristic
252C2×C4C2×C22⋊D10911yescharacteristic
253C2×C4#1318202914yes—
254C2×C4C23×D10911yescharacteristic
255C8—2182no—
256C8—2182no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22—44no—
265C22—4361no—
266C22—4361no—
267C22—4361no—
268C22#1681268212yes—
269C22#1681271912yes—
270C22C22×C22⋊D10911yescharacteristic
271C4—21no—
272C4—21no—
273C4—42no—
274C4—42no—
275C4—4361no—
276C4—4361no—
277C4—4361no—
278C4#1681268212yes—
279C4C2×#1318202912yes—
280C2—22no—
281C2—22no—
282C2—41no—
283C2—8721no—
284C2C2×#1681268211yescharacteristic
285C2C2×#1681271911yescharacteristic
286C2#2029582411yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
FittingC2×#117×C109C2
socleC22×C109C22×D4
prime radical#20295537C2
hypercenterC2×#117D109
hypocenterC109#3091
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #20295367C2semidirect
3. #20295361C2semidirect
4. #20295356C2semidirect
5. #20295350C2semidirect
6. #20295344C2semidirect
7. #20295339C2semidirect
8. #20295062C2semidirect
9. #20295020C2semidirect
10. C2×C22⋊#11724784C2semidirect
11. C2×#117×C109C2semidirect
23. #16812632C22semidirect
24. #16812632C22semidirect
25. #16812630C22semidirect
26. #16812630C22semidirect
27. #16812622C22semidirect
28. #16812622C22semidirect
29. #16812619C22semidirect
30. #16812619C22semidirect
144. C109#3091semidirect
146. C2×#117D109semidirect

Maximal subgroups

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

subgroupindex
#202955372
#202953672
#202953612
#202953562
#202953502
#202953442
#202953392
#202950622
#202950202
C2×C22⋊#117247842
C2×#117×C1092
#3091109