Finite Group Databasebeta

← #28373166

Subgroups — #28373166

Order 13952.

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

normal subgroups only

This group has 450 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
1C2×C4×D436C211yesmaximal, characteristic, complemented
2#20295354C211yesmaximal, characteristic, complemented
3#20295337C211yesmaximal, characteristic, complemented
4#20295323C212yesmaximal, complemented
5#20295238C212yesmaximal, complemented
6#20295176C211yesmaximal, characteristic, complemented
7#20295159C211yesmaximal, characteristic
8#20295136C212yesmaximal, complemented
9#20295124C212yesmaximal, complemented
10#20295083C211yesmaximal, characteristic, complemented
11#529×C109C211yesmaximal, characteristic, complemented
12C22×D436C2211yescharacteristic
13C22×C4×D109—21no—
14C2×#13182016C2212yes—
15C2×#13182014C2212yes—
16C4×D436—21no—
17C4×D436—21no—
18C4×D436C2212yes—
19C4×D436C2212yes—
20C2×C4⋊Dic109C2211yescharacteristic
21C2×#13182006—21no—
22#16812632C2212yescomplemented
23#16812630C2212yescomplemented
24C4⋊#11724784C2212yescomplemented
25#16812623C2212yescomplemented
26#16812620C2212yescomplemented
27#16812619C2212yes—
28#16812619C2212yes—
29C22⋊#11724784C2211yescharacteristic
30C22⋊#11724784C2211yescharacteristic
31#16812610C2212yescomplemented
32#126×C109—21no—
33#125×C109C2211yescharacteristic, complemented
34#124×C109C2211yescharacteristic, complemented
35#123×C109—21no—
36C22⋊Q8×C109C2211yescharacteristic
37#121×C109C2211yescharacteristic
38C4×Q8×C109C2211yescharacteristic, complemented
39C4×D4×C109—21no—
40C4×D4×C109C2211yescharacteristic, complemented
41#117×C109—21no—
42C2×C42×C109C2211yescharacteristic
43C23×D109—21no—
44C2×D436—21no—
45C2×D436—24no—
46C2×D436C2312yes—
47C22×Dic109—21no—
48C2×C4×D109—22no—
49C2×C4×D109—22no—
50C2×C4×D109—44no—
51#13182016—24no—
52#13182014—24no—
53C2×#11724784C2312yes—
54C2×#11724784C2312yes—
55C4⋊Dic109—21no—
56C4⋊Dic109C2312yes—
57#13182006—22no—
58#13182006—22no—
59C2×Q8×C109C2311yescharacteristic
60C2×D4×C109—21no—
61C2×D4×C109C2311yescharacteristic
62C22×C4×C109—21no—
63C22×C4×C109D411yescharacteristic
64C22×C4×C109D411yescharacteristic
65C22×C4×C109C2311yescharacteristic
66C4⋊C4×C109—21no—
67C4⋊C4×C109—21no—
68C4⋊C4×C109—21no—
69C4⋊C4×C109—21no—
70C4⋊C4×C109C2311yescharacteristic
71C4⋊C4×C109C2311yescharacteristic
72C22⋊C4×C109—21no—
73C22⋊C4×C109—21no—
74C22⋊C4×C109—21no—
75C22⋊C4×C109—21no—
76C22⋊C4×C109—21no—
77C42×C109—21no—
78C42×C109D411yescharacteristic
79C42×C109D411yescharacteristic
80C42×C109C2311yescharacteristic
81C42×C109C2311yescharacteristic
82C23×C109—21no—
83C23×C109C2×D411yescharacteristic
84C22×D109—24no—
85C22×D109—22no—
86C22×D109—42no—
87C22×D109—42no—
88Q8×C109—22no—
89D4×C109—22no—
90D4×C109—42no—
91C2×C4×C109—22no—
92C2×C4×C109—22no—
93C2×C4×C109—21no—
94C2×C4×C109—21no—
95C2×C4×C109—21no—
96C2×C4×C109—41no—
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
104C2×Dic109—22no—
105C2×Dic109—42no—
106D436—24no—
107D436—22no—
108D436#4114yes—
109C4×D109—44no—
110C4×D109—44no—
111#11724784—22no—
112#11724784—22no—
113C22×C109—21no—
114C22×C109—21no—
115C22×C109—41no—
116C22×C109—41no—
117C22×C109—41no—
118C22×C109AGL(1,ℤ/8)12yes—
119C22×C109C22×D411yescharacteristic
120C2×D109—24no—
121C2×D109—48no—
122C2×D109—42no—
123C2×D109—42no—
124C4×C109—21no—
125C4×C109—21no—
126C4×C109—21no—
127C4×C109—21no—
128C4×C109—21no—
129C4×C109—41no—
130C4×C109—41no—
131C4×C109—41no—
132C4×C109C2×#4112yes—
133Dic109—42no—
134C2×C109—22no—
135C2×C109—81no—
136C2×C109#52511yescharacteristic
137C2×C109C2×AGL(1,ℤ/8)11yescharacteristic
138C2×C109#57511yescharacteristic
139D109—44no—
140#3114—1091nomaximal, Sylow
141C109#311411yescharacteristic, complemented, Sylow
142#529D10911yescharacteristic, complemented
143C2×C4×D4—1091no—
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×D4—1091no—
154C23×C4—2181no—
155C2×SD16—1092no—
156C2×D8—1092no—
157#126—21no—
158#125C2×D10911yescharacteristic, complemented
159#124C2×D10911yescharacteristic, complemented
160#123—21no—
161C22⋊Q8C2×D10911yescharacteristic
162#121C2×D10911yescharacteristic
163C4×Q8C2×D10911yescharacteristic, complemented
164C4×D4—21no—
165C4×D4—1092no—
166C4×D4—1092no—
167C4×D4—2181no—
168C4×D4—2181no—
169C4×D4C2×D10911yescharacteristic, complemented
170#117—21no—
171C2×C4⋊C4—1091no—
172C2×C22⋊C4—2181no—
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—2181no—
185C2×Q8C22×D10911yescharacteristic
186C2×D4—21no—
187C2×D4—1092no—
188C2×D4—2184no—
189C2×D4—2181no—
190C2×D4C22×D10911yescharacteristic
191C22×C4—21no—
192C22×C4—4364no—
193C22×C4—2181no—
194C22×C4—2182no—
195C22×C4—2182no—
196C22×C4C22⋊D10911yescharacteristic
197C22×C4C22⋊D10911yescharacteristic
198C22×C4C22×D10911yescharacteristic
199SD16—2184no—
200D8—2184no—
201C2×C8—1092no—
202C2×C8—1092no—
203C4⋊C4—21no—
204C4⋊C4—21no—
205C4⋊C4—21no—
206C4⋊C4—21no—
207C4⋊C4—1092no—
208C4⋊C4—2181no—
209C4⋊C4C22×D10911yescharacteristic
210C4⋊C4C22×D10911yescharacteristic
211C22⋊C4—21no—
212C22⋊C4—21no—
213C22⋊C4—21no—
214C22⋊C4—21no—
215C22⋊C4—21no—
216C22⋊C4—2182no—
217C22⋊C4—2182no—
218C42—21no—
219C42C22⋊D10911yescharacteristic
220C42C22⋊D10911yescharacteristic
221C42C22×D10911yescharacteristic
222C42C22×D10911yescharacteristic
223C23—21no—
224C23—4362no—
225C23—4362no—
226C23—2184no—
227C23—2182no—
228C23C2×C22⋊D10911yescharacteristic
229Q8—22no—
230D4—22no—
231D4—42no—
232D4—1094no—
233D4—2184no—
234D4—2182no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—4364no—
243C2×C4—4364no—
244C2×C4—4362no—
245C2×C4—2182no—
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—41no—
257C22—41no—
258C22—41no—
259C22—4368no—
260C22—4362no—
261C22—4362no—
262C22—2184no—
263C22#1681272412yes—
264C22C22×C22⋊D10911yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—41no—
271C4—41no—
272C4—41no—
273C4—4362no—
274C4#41×D10912yes—
275C2—22no—
276C2—81no—
277C2—4364no—
278C2#2029553311yescharacteristic
279C2C2×#1681272411yescharacteristic
280C2#2029582411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#529×C109C2
socleC22×C109C22×D4
prime radical#20295159C2
hypercenter#529D109
hypocenterC109#3114
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. C2×C4×D436C2semidirect
2. #20295354C2semidirect
3. #20295337C2semidirect
4. #20295323C2semidirect
5. #20295238C2semidirect
6. #20295176C2semidirect
8. #20295136C2semidirect
9. #20295124C2semidirect
10. #20295083C2semidirect
11. #529×C109C2semidirect
22. #16812632C22semidirect
23. #16812630C22semidirect
24. C4⋊#11724784C22semidirect
25. #16812623C22semidirect
26. #16812620C22semidirect
31. #16812610C22semidirect
33. #125×C109C22semidirect
34. #124×C109C22semidirect
38. C4×Q8×C109C22semidirect
40. C4×D4×C109C22semidirect
141. C109#3114semidirect
142. #529D109semidirect
158. #125C2×D109semidirect
159. #124C2×D109semidirect
163. C4×Q8C2×D109semidirect
169. C4×D4C2×D109semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4362
#202953542
#202953372
#202953232
#202952382
#202951762
#202951592
#202951362
#202951242
#202950832
#529×C1092
#3114109