Finite Group Databasebeta

← #28374844

Subgroups — #28374844

Order 13952.

494 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 123 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#20295679C211yesmaximal, characteristic, complemented
2#20295661C211yesmaximal, characteristic, complemented
3#20295338C212yesmaximal, complemented
4#20295303C211yesmaximal, characteristic, complemented
5#20295261C212yesmaximal, complemented
6#20295218C211yesmaximal, characteristic, complemented
7#20295161C212yesmaximal, complemented
8C4×D872C211yesmaximal, characteristic, complemented
9C8×D436C211yesmaximal, characteristic, complemented
10#102×D109C212yesmaximal, complemented
11#486×C109C211yesmaximal, characteristic, complemented
12C2×#13182030—21no—
13C2×D4×D109—21no—
14C2×D4×D109C2212yes—
15C2×D872C2211yescharacteristic
16C2×#13182014C2212yescomplemented
17C2×C8×D109C2212yescomplemented
18#16812684—22no—
19#16812675—21no—
20#16812674C2212yescomplemented
21#16812670—21no—
22#16812670C2212yes—
23#16812667—22no—
24C4×D436C2211yescharacteristic
25C4×D436C2211yescharacteristic
26C4×D436C2211yescharacteristic, complemented
27C4⋊C4×D109C2212yescomplemented
28#16812633C2211yescharacteristic, complemented
29#16812632C2212yescomplemented
30C4⋊#11724784C2211yescharacteristic, complemented
31#16812621C2211yescharacteristic
32#16812621C2211yescharacteristic, complemented
33#16812620C2212yescomplemented
34#16812619C2212yes—
35#16812611C2212yescomplemented
36C4⋊Q8×C109C2211yescharacteristic, complemented
37#127×C109C2211yescharacteristic
38#102×C109C2212yescomplemented
39#102×C109C2212yescomplemented
40C4×C8×C109C2211yescharacteristic, complemented
41C23×D109—22no—
42#13182030—44no—
43C2×D436—22no—
44C2×D436D411yescharacteristic
45C2×D436C2311yescharacteristic
46C2×D436C2311yescharacteristic
47C2×C22⋊D109—22no—
48C2×C22⋊D109—22no—
49D4×D109—24no—
50D4×D109—42no—
51D4×D109—44no—
52C2×C4×D109—22no—
53C2×C4×D109—21no—
54C2×C4×D109—21no—
55C2×C4×D109C2312yes—
56D872—22no—
57#13182014—42no—
58C2×#11724784C2312yes—
59C8×D109—42no—
60C4⋊Dic109D411yescharacteristic
61C4⋊Dic109C2311yescharacteristic
62C4⋊Dic109C2311yescharacteristic
63#13182008—22no—
64C22⋊Dic109—22no—
65#13182006—21no—
66#13182006—21no—
67#13182006—22no—
68#13182006D412yes—
69C2×Q8×C109—21no—
70C2×D4×C109—21no—
71C2×D4×C109—21no—
72C2×D4×C109C2312yes—
73C2×C8×C109C2311yescharacteristic
74C2×C8×C109C2311yescharacteristic
75C4⋊C4×C109—21no—
76C4⋊C4×C109C2312yes—
77C42×C109C2311yescharacteristic
78C23×C109—22no—
79C22×D109—21no—
80C22×D109—21no—
81C22×D109—44no—
82C22×D109—44no—
83C22×D109—82no—
84C22×D109C2×D412yes—
85Q8×C109—42no—
86D4×C109—22no—
87D4×C109—22no—
88D4×C109—42no—
89D4×C109—81no—
90C2×C4×C109—22no—
91C2×C4×C109C2×D411yescharacteristic
92C2×C4×C109C2×D411yescharacteristic
93C2×C4×C109C2411yescharacteristic
94C22⋊D109—44no—
95C22⋊D109—44no—
96C2×Dic109—21no—
97C2×Dic109—21no—
98C2×Dic109C2×D412yes—
99D436—21no—
100D436—21no—
101D436—21no—
102D436—44no—
103D436D814yescomplemented
104D436#4112yescomplemented
105C4×D109—22no—
106C4×D109—22no—
107C4×D109—44no—
108C4×D109—42no—
109C4×D109—42no—
110C8×C109—21no—
111C8×C109—21no—
112#11724784—22no—
113C22×C109—42no—
114C22×C109—42no—
115C22×C109—42no—
116C22×C109C22×D411yescharacteristic
117C2×D109—22no—
118C2×D109—22no—
119C2×D109—22no—
120C2×D109—41no—
121C2×D109—41no—
122C2×D109—41no—
123C2×D109—41no—
124C2×D109—41no—
125C2×D109—88no—
126C2×D109C2×D814yes—
127C4×C109—21no—
128C4×C109—42no—
129C4×C109C2×D812yes—
130C4×C109C2×#4111yescharacteristic
131C4×C109H(5,𝔽2)11yescharacteristic
132Dic109—22no—
133Dic109—41no—
134Dic109—41no—
135C2×C109—82no—
136C2×C109#54611yescharacteristic
137C2×C109C22×D811yescharacteristic
138C2×C109#57711yescharacteristic
139D109—24no—
140D109—42no—
141D109—81no—
142#3294—1091nomaximal, Sylow
143C109#329411yescharacteristic, complemented, Sylow
144#547—1091no—
145D42—1091no—
146#486D10911yescharacteristic, complemented
147#480—1092no—
148#474—1091no—
149#466—1092no—
150#459—1091no—
151#447—1092no—
152C4×D8—1091no—
153C8×D4—1091no—
154C2×#102—1092no—
155C2×#41—2181no—
156C22×D4—1092no—
157C22×D4—2181no—
158C2×D8—1092no—
159C2×D8—1091no—
160C22×C8—1092no—
161C4⋊Q8C2×D10911yescharacteristic, complemented
162#127C2×D10911yescharacteristic
163#123—2182no—
164C22⋊Q8—2181no—
165#121—1092no—
166#121—1092no—
167#121—2181no—
168#120—2182no—
169C4×D4—1091no—
170C4×D4—1091no—
171C4×D4—1091no—
172C2×C4⋊C4—1092no—
173#107—1091no—
174#107—1092no—
175C4⋊C8—1091no—
176#102—1092no—
177#102—1091no—
178#102—1091no—
179#102—1092no—
180#102C2×D10912yescomplemented
181#102C2×D10912yescomplemented
182C22⋊C8—1092no—
183C4×C8C2×D10911yescharacteristic, complemented
184C24—2182no—
185#41—4364no—
186C2×Q8—21no—
187C2×D4—21no—
188C2×D4—21no—
189C2×D4—1091no—
190C2×D4—1091no—
191C2×D4—1091no—
192C2×D4—4364no—
193C2×D4—4362no—
194C2×D4—2182no—
195C2×D4—2182no—
196C2×D4—2184no—
197C2×D4—2182no—
198C2×D4C22×D10912yes—
199C22×C4—1092no—
200C22×C4—2182no—
201C22×C4—2181no—
202C22×C4—2181no—
203D8—4362no—
204D8—2182no—
205C2×C8—1092no—
206C2×C8—4362no—
207C2×C8C22×D10911yescharacteristic
208C2×C8C22×D10911yescharacteristic
209C4⋊C4—21no—
210C4⋊C4—1091no—
211C4⋊C4—1091no—
212C4⋊C4—1091no—
213C4⋊C4—2182no—
214C4⋊C4C22×D10912yes—
215C22⋊C4—1092no—
216C22⋊C4—2182no—
217C22⋊C4—2182no—
218C22⋊C4—2181no—
219C22⋊C4—2181no—
220C42C22×D10911yescharacteristic
221C23—22no—
222C23—8722no—
223C23—1092no—
224C23—4364no—
225C23—4364no—
226C23—2181no—
227C23—2181no—
228Q8—42no—
229D4—22no—
230D4—22no—
231D4—42no—
232D4—81no—
233D4—1094no—
234D4—1092no—
235D4—4364no—
236D4—4364no—
237D4—4364no—
238D4—2181no—
239D4—2181no—
240D4—2181no—
241C2×C4—22no—
242C2×C4—1092no—
243C2×C4—4364no—
244C2×C4—4362no—
245C2×C4—4362no—
246C2×C4—2181no—
247C2×C4—2181no—
248C2×C4—2182no—
249C2×C4—2182no—
250C2×C4D4×D10911yescharacteristic
251C2×C4D4×D10911yescharacteristic
252C2×C4C23×D10911yescharacteristic
253C8—21no—
254C8—21no—
255C8—2182no—
256C22—42no—
257C22—42no—
258C22—42no—
259C22—8728no—
260C22—1094no—
261C22—4361no—
262C22—4361no—
263C22—4361no—
264C22—4361no—
265C22—4361no—
266C22—2182no—
267C22—2182no—
268C22—2182no—
269C22C2×D4×D10911yescharacteristic
270C4—21no—
271C4—42no—
272C4—4361no—
273C4—4361no—
274C4—2182no—
275C4D8×D10912yes—
276C4#41×D10911yescharacteristic
277C4#1681274511yescharacteristic
278C2—82no—
279C2—8721no—
280C2—4362no—
281C2—2184no—
282C2#2029566911yescharacteristic
283C2C2×D8×D10911yescharacteristic
284C2#2029583211yescharacteristic
subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#486×C109C2
socleC22×C109C22×D4
hypercenter#486D109
hypocenterC109#3294
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #20295679C2semidirect
2. #20295661C2semidirect
3. #20295338C2semidirect
4. #20295303C2semidirect
5. #20295261C2semidirect
6. #20295218C2semidirect
7. #20295161C2semidirect
8. C4×D872C2semidirect
9. C8×D436C2semidirect
10. #102×D109C2semidirect
11. #486×C109C2semidirect
16. C2×#13182014C22semidirect
17. C2×C8×D109C22semidirect
20. #16812674C22semidirect
26. C4×D436C22semidirect
27. C4⋊C4×D109C22semidirect
28. #16812633C22semidirect
29. #16812632C22semidirect
30. C4⋊#11724784C22semidirect
32. #16812621C22semidirect
33. #16812620C22semidirect
35. #16812611C22semidirect
36. C4⋊Q8×C109C22semidirect
38. #102×C109C22semidirect
39. #102×C109C22semidirect
40. C4×C8×C109C22semidirect
103. D436D8semidirect
104. D436#41semidirect
143. C109#3294semidirect
146. #486D109semidirect
161. C4⋊Q8C2×D109semidirect
180. #102C2×D109semidirect
181. #102C2×D109semidirect
183. C4×C8C2×D109semidirect

Maximal subgroups

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

subgroupindex
#202956792
#202956612
#202953382
#202953032
#202952612
#202952182
#202951612
C4×D8722
C8×D4362
#102×D1092
#486×C1092
#3294109