Finite Group Databasebeta

← #38767364

Subgroups — #38767364

Order 25472.

346 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 65 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#121×D199C211yesmaximal, characteristic
2#27163980C211yesmaximal, characteristic, complemented
3#27163865C211yesmaximal, characteristic, complemented
4#27163753C211yesmaximal, characteristic, complemented
5#27163752C211yesmaximal, characteristic, complemented
6#27163751C211yesmaximal, characteristic, complemented
7#327×C199C211yesmaximal, characteristic, complemented
8C2×D4×D199—21no—
9C2×D4×D199C411yescharacteristic, complemented
10C22×C4×D199C2211yescharacteristic
11C2×#15691869—21no—
12#20263930C411yescharacteristic, complemented
13#20263929C2211yescharacteristic
14#20263928—21no—
15#20263927—21no—
16#20263926C411yescharacteristic, complemented
17C4⋊C4×D199C411yescharacteristic, complemented
18C2×(C2×D199)⋊C4—21no—
19C22⋊C4×D199—21no—
20C2×C4×Dic199—21no—
21C22⋊(C199⋊C8)C2211yescharacteristic, complemented
22(C2×D199)⋊C8—21no—
23C199⋊#95C2211yescharacteristic, complemented
24#121×C199C2211yescharacteristic
25C22⋊C8×C199C2211yescharacteristic, complemented
26#95×C199C2211yescharacteristic, complemented
27C23×D199—21no—
28C23×D199D411yescharacteristic
29C2×D796—21no—
30C2×D796C2×C411yescharacteristic
31C2×C22⋊D199—21no—
32C2×C22⋊D199—21no—
33C2×C22⋊D199—21no—
34D4×D199—42no—
35D4×D199—42no—
36D4×D199—42no—
37C22×Dic199—21no—
38C22×Dic199D411yescharacteristic
39C2×C4×D199—21no—
40C2×C4×D199—42no—
41C2×C4×D199C2×C411yescharacteristic
42C2×C4×D199C2×C411yescharacteristic
43C2×C4×D199D411yescharacteristic
44C2×C4×D199D411yescharacteristic
45#15691869—42no—
46C2×C199⋊C8—21no—
47C4⋊Dic199C2×C411yescharacteristic
48Dic199⋊C4—21no—
49C22⋊Dic199—21no—
50(C2×D199)⋊C4—24no—
51(C2×D199)⋊C4—21no—
52(C2×D199)⋊C4—21no—
53C4×Dic199—42no—
54C2×D4×C199—21no—
55C2×D4×C199C2×C411yescharacteristic
56C22×C4×C199—21no—
57C22×C4×C199C2311yescharacteristic
58C2×C8×C199—21no—
59C4⋊C4×C199C2×C411yescharacteristic
60C22⋊C4×C199—21no—
61C22×D199—21no—
62C22×D199—21no—
63C22×D199—22no—
64C22×D199—21no—
65C22×D199—41no—
66C22×D199—42no—
67C22×D199—42no—
68C22×D199—42no—
69C22×D199C22⋊C411yescharacteristic
70C22×D199C22⋊C411yescharacteristic
71D796—41no—
72D796—42no—
73C22⋊D199—42no—
74C22⋊D199—41no—
75C22⋊D199—41no—
76C22⋊D199—42no—
77C2×Dic199—22no—
78C2×Dic199—22no—
79C2×Dic199—21no—
80C2×Dic199—41no—
81C2×Dic199—41no—
82C2×Dic199C22⋊C411yescharacteristic
83C2×Dic199C22⋊C411yescharacteristic
84C4×D199—22no—
85C4×D199—22no—
86C4×D199—41no—
87C4×D199—41no—
88C4×D199—42no—
89C199⋊C8—41no—
90C23×C199—21no—
91C23×C199C2×D411yescharacteristic
92D4×C199—41no—
93D4×C199—41no—
94D4×C199—41no—
95C2×C4×C199—22no—
96C2×C4×C199—21no—
97C2×C4×C199—41no—
98C2×C4×C199—41no—
99C2×C4×C199—41no—
100C2×C4×C199C22×C411yescharacteristic
101C2×C4×C199C2×D411yescharacteristic
102C8×C199—41no—
103C22×C199—21no—
104C22×C199—21no—
105C22×C199—41no—
106C22×C199—41no—
107C22×C199—41no—
108C22×C199C2×C22⋊C411yescharacteristic
109C22×C199AGL(1,ℤ/8)11yescharacteristic
110C22×C199AGL(1,ℤ/8)11yescharacteristic
111C2×D199—21no—
112C2×D199—21no—
113C2×D199—21no—
114C2×D199—21no—
115C2×D199—21no—
116C2×D199—42no—
117C2×D199—42no—
118C2×D199—41no—
119C2×D199—41no—
120C2×D199—41no—
121C2×D199—84no—
122C2×D199#10412yes—
123C4×C199—21no—
124C4×C199—21no—
125C4×C199—42no—
126C4×C199—41no—
127Dic199—21no—
128Dic199—42no—
129Dic199—41no—
130Dic199#9912yes—
131C2×C199—21no—
132C2×C199—21no—
133C2×C199—81no—
134C2×C199C2×#9911yescharacteristic
135C2×C199#41811yescharacteristic
136C2×C199C2×#10411yescharacteristic
137D199—22no—
138D199—41no—
139D199—81no—
140C199#150711yescharacteristic, complemented, Sylow
141#1507—1991nomaximal, Sylow
142C2×#121—1991no—
143#407—1991no—
144C4×C22⋊C4—1991no—
145#327—1991no—
146#327—1991no—
147#327—1991no—
148#327D19911yescharacteristic, complemented
149C22×D4—3981no—
150C22×D4—1991no—
151C23×C4—1991no—
152C2×M16—3981no—
153#121—3981no—
154#121—3981no—
155#121—1991no—
156#121—1991no—
157#121—1991no—
158#121C2×D19911yescharacteristic
159C2×C4⋊C4—1991no—
160C2×C22⋊C4—3981no—
161C2×C22⋊C4—3981no—
162C2×C42—3981no—
163C22⋊C8—3981no—
164C22⋊C8—1991no—
165C22⋊C8C2×D19911yescharacteristic, complemented
166#95—1991no—
167#95C2×D19911yescharacteristic, complemented
168C24—3981no—
169C24—1991no—
170C2×D4—21no—
171C2×D4—7962no—
172C2×D4—7962no—
173C2×D4—7962no—
174C2×D4—3981no—
175C2×D4—3981no—
176C2×D4—3981no—
177C2×D4—3981no—
178C2×D4—1991no—
179C2×D4C4×D19911yescharacteristic
180C22×C4—21no—
181C22×C4—7962no—
182C22×C4—3981no—
183C22×C4—3981no—
184C22×C4—1991no—
185C22×C4—1991no—
186C22×C4—1991no—
187C22×C4—1991no—
188C22×C4—1991no—
189C22×C4C22×D19911yescharacteristic
190M16—7962no—
191C2×C8—21no—
192C2×C8—3981no—
193C4⋊C4—3981no—
194C4⋊C4—1991no—
195C4⋊C4C4×D19911yescharacteristic
196C22⋊C4—21no—
197C22⋊C4—3984no—
198C22⋊C4—3981no—
199C22⋊C4—3981no—
200C22⋊C4—3981no—
201C42—7962no—
202C23—21no—
203C23—7961no—
204C23—7962no—
205C23—7962no—
206C23—7962no—
207C23—3982no—
208C23—3981no—
209C23—3981no—
210C23—3981no—
211C23—1991no—
212C23—1991no—
213C23D4×D19911yescharacteristic
214D4—41no—
215D4—41no—
216D4—41no—
217D4—7961no—
218D4—7962no—
219D4—7962no—
220D4—7961no—
221D4—7961no—
222D4—7962no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—7961no—
229C2×C4—7961no—
230C2×C4—7962no—
231C2×C4—7961no—
232C2×C4—7961no—
233C2×C4—3982no—
234C2×C4—3982no—
235C2×C4—3982no—
236C2×C4—3981no—
237C2×C4—3982no—
238C2×C4—1991no—
239C2×C4—1991no—
240C2×C4C2×C4×D19911yescharacteristic
241C2×C4D4×D19911yescharacteristic
242C8—41no—
243C8—7961no—
244C22—21no—
245C22—21no—
246C22—41no—
247C22—41no—
248C22—41no—
249C22—7962no—
250C22—7962no—
251C22—7961no—
252C22—7961no—
253C22—7961no—
254C22—15924no—
255C22—3981no—
256C22—3981no—
257C22—3981no—
258C22—3981no—
259C22—3981no—
260C22—1992no—
261C22C22⋊C4×D19911yescharacteristic
262C22#2026397911yescharacteristic
263C22#2026398211yescharacteristic
264C4—21no—
265C4—21no—
266C4—42no—
267C4—41no—
268C4—7962no—
269C4—7961no—
270C4—3981no—
271C4—1992no—
272C2—21no—
273C2—21no—
274C2—81no—
275C2—7961no—
276C2—15921no—
277C2—3982no—
278C2#99×D19911yescharacteristic
279C2#2716402111yescharacteristic
280C2#104×D19911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D199
commutatorC2×C4×C199C22×C4
FrattiniC22×C4C22×D199
Fitting#327×C199C2
socleC22×C199C2×C22⋊C4
prime radical#121×D199C2
cosocleC22×C4×C199C23
hypercenter#327D199
hypocenterC199#1507
LCSG ▷ C2×C4×C199 ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #27163980C2semidirect
3. #27163865C2semidirect
4. #27163753C2semidirect
5. #27163752C2semidirect
6. #27163751C2semidirect
7. #327×C199C2semidirect
9. C2×D4×D199C4semidirect
12. #20263930C4semidirect
16. #20263926C4semidirect
17. C4⋊C4×D199C4semidirect
21. C22⋊(C199⋊C8)C22semidirect
23. C199⋊#95C22semidirect
25. C22⋊C8×C199C22semidirect
26. #95×C199C22semidirect
140. C199#1507semidirect
148. #327D199semidirect
165. C22⋊C8C2×D199semidirect
167. #95C2×D199semidirect

Maximal subgroups

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

subgroupindex
#121×D1992
#271639802
#271638652
#271637532
#271637522
#271637512
#327×C1992
#1507199