Finite Group Databasebeta

← #38769149

Subgroups — #38769149

Order 25472.

376 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 85 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×M16×D199C211yesmaximal, characteristic, complemented
2#27164525C211yesmaximal, characteristic
3C2×#20263882C211yesmaximal, characteristic, complemented
4C4×(C2×D199)⋊C4C211yesmaximal, characteristic, complemented
5#27163779C211yesmaximal, characteristic, complemented
6#27163778C211yesmaximal, characteristic, complemented
7C2×#104×C199C211yesmaximal, characteristic, complemented
8C22×C4×D199C2211yescharacteristic
9C2×#15691870C2211yescharacteristic
10C2×#15691869—21no—
11M16×D199—22no—
12M16×D199—22no—
13C2×C8×D199—21no—
14#20263936—21no—
15#20263931C411yescharacteristic, complemented
16#20263931C411yescharacteristic, complemented
17#20263926C411yescharacteristic, complemented
18#20263926C411yescharacteristic, complemented
19#20263923—21no—
20C4×C22⋊D199—21no—
21C4×C22⋊D199—21no—
22#20263914C2211yescharacteristic
23C2×(C2×D199)⋊C4—21no—
24C2×C4×Dic199C2211yescharacteristic
25#20263882—22no—
26C199⋊#95—21no—
27C2×#41×C199C2211yescharacteristic
28C2×M16×C199C2211yescharacteristic
29C2×C42×C199C2211yescharacteristic
30#104×C199—22no—
31C23×D199D411yescharacteristic
32C2×C22⋊D199—21no—
33C2×C22⋊D199—21no—
34C22×Dic199—21no—
35C22×Dic199D411yescharacteristic
36C2×C4×D199—21no—
37C2×C4×D199—21no—
38C2×C4×D199—21no—
39C2×C4×D199—21no—
40C2×C4×D199C2×C411yescharacteristic
41C2×C4×D199C2×C411yescharacteristic
42C2×C4×D199D411yescharacteristic
43C2×C4×D199D411yescharacteristic
44#15691870—21no—
45#15691870D412yescomplemented
46#15691869—24no—
47C2×C199⋊C8—21no—
48C8×D199—24no—
49C4⋊Dic199C2×C411yescharacteristic
50C4⋊Dic199C2×C411yescharacteristic
51Dic199⋊C4—21no—
52Dic199⋊C4—21no—
53C22⋊Dic199—21no—
54C22⋊Dic199—21no—
55C22⋊Dic199—21no—
56(C2×D199)⋊C4—24no—
57(C2×D199)⋊C4—21no—
58(C2×D199)⋊C4—21no—
59C4×Dic199—21no—
60C4×Dic199—21no—
61C4×Dic199—21no—
62#41×C199—21no—
63#41×C199—21no—
64#41×C199—21no—
65#41×C199—21no—
66C2×Q8×C199C2×C411yescharacteristic
67C2×D4×C199—21no—
68C2×D4×C199C2×C411yescharacteristic
69C22×C4×C199—21no—
70C22×C4×C199—21no—
71C22×C4×C199C2311yescharacteristic
72M16×C199—21no—
73M16×C199D412yescomplemented
74C2×C8×C199—21no—
75C42×C199—21no—
76C42×C199—21no—
77C22×D199—21no—
78C22×D199—21no—
79C22×D199—22no—
80C22×D199—41no—
81C22×D199C22⋊C411yescharacteristic
82C22×D199C22⋊C411yescharacteristic
83C22⋊D199—42no—
84C22⋊D199—42no—
85C2×Dic199—21no—
86C2×Dic199—21no—
87C2×Dic199—22no—
88C2×Dic199—21no—
89C2×Dic199—21no—
90C2×Dic199—41no—
91C2×Dic199—41no—
92C2×Dic199C22⋊C411yescharacteristic
93C2×Dic199C22⋊C411yescharacteristic
94C4×D199—21no—
95C4×D199—21no—
96C4×D199—21no—
97C4×D199—21no—
98C4×D199—21no—
99C4×D199—21no—
100C4×D199—21no—
101C4×D199—21no—
102C199⋊C8—22no—
103C23×C199—21no—
104C23×C199C2×D411yescharacteristic
105Q8×C199—21no—
106Q8×C199—21no—
107D4×C199—21no—
108D4×C199—21no—
109D4×C199—41no—
110D4×C199—41no—
111C2×C4×C199—22no—
112C2×C4×C199—21no—
113C2×C4×C199—41no—
114C2×C4×C199—41no—
115C2×C4×C199—41no—
116C2×C4×C199—41no—
117C2×C4×C199C22×C411yescharacteristic
118C2×C4×C199C2×D411yescharacteristic
119C2×C4×C199C2×D411yescharacteristic
120C2×C4×C199C2×D411yescharacteristic
121C2×C4×C199#4111yescharacteristic
122C2×C4×C199#4111yescharacteristic
123C8×C199—22no—
124C22×C199—21no—
125C22×C199—21no—
126C22×C199—41no—
127C22×C199—41no—
128C22×C199—41no—
129C22×C199C2×C22⋊C411yescharacteristic
130C22×C199#12111yescharacteristic
131C22×C199#12111yescharacteristic
132C2×D199—21no—
133C2×D199—21no—
134C2×D199—21no—
135C2×D199—21no—
136C2×D199—21no—
137C2×D199—42no—
138C2×D199—42no—
139C2×D199#10412yescomplemented
140C4×C199—42no—
141C4×C199—41no—
142C4×C199C4×D411yescharacteristic
143C4×C199C4×D411yescharacteristic
144C4×C199#12011yescharacteristic
145C4×C199#12311yescharacteristic
146Dic199—21no—
147Dic199—21no—
148Dic199—42no—
149Dic199—41no—
150Dic199—41no—
151C2×C199—21no—
152C2×C199—21no—
153C2×C199—81no—
154C2×C199#38611yescharacteristic
155C2×C199C2×#10411yescharacteristic
156C2×C199#42111yescharacteristic
157D199—22no—
158D199—41no—
159C199#187111yescharacteristic, complemented, Sylow
160#1871—1991nomaximal, Sylow
161C22×M16—1991no—
162#525—1991no—
163C2×#104—1991no—
164C2×#104D19911yescharacteristic, complemented
165C4×C22⋊C4—1991no—
166#339—1991no—
167#339—1991no—
168C2×#41C2×D19911yescharacteristic
169C23×C4—1991no—
170C2×M16—3981no—
171C2×M16—3982no—
172C2×M16—3982no—
173C2×M16—1991no—
174C2×M16C2×D19911yescharacteristic
175C22×C8—3981no—
176#123—3981no—
177C22⋊Q8—1991no—
178C22⋊Q8—1991no—
179#121—1991no—
180#121—1991no—
181#120—3981no—
182C4×D4—3981no—
183C4×D4—3981no—
184#117—1991no—
185C2×C22⋊C4—3981no—
186C2×C42—1991no—
187C2×C42C2×D19911yescharacteristic
188#104—22no—
189#104—3982no—
190#95—3981no—
191C24—1991no—
192#41—21no—
193#41—21no—
194#41—21no—
195#41—21no—
196C2×Q8C4×D19911yescharacteristic
197C2×D4—21no—
198C2×D4—3981no—
199C2×D4—3981no—
200C2×D4C4×D19911yescharacteristic
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—3981no—
204C22×C4—3981no—
205C22×C4—3981no—
206C22×C4—3981no—
207C22×C4—3981no—
208C22×C4—1991no—
209C22×C4—1991no—
210C22×C4—1991no—
211C22×C4—1991no—
212C22×C4—1991no—
213C22×C4C22×D19911yescharacteristic
214M16—21no—
215M16—3984no—
216M16—3981no—
217M16—1992no—
218M16C22⋊D19912yescomplemented
219C2×C8—21no—
220C2×C8—3984no—
221C2×C8—3981no—
222C4⋊C4—3981no—
223C4⋊C4—3981no—
224C4⋊C4—1991no—
225C4⋊C4—1991no—
226C22⋊C4—3984no—
227C22⋊C4—3981no—
228C22⋊C4—3981no—
229C22⋊C4—3981no—
230C22⋊C4—3981no—
231C22⋊C4—3981no—
232C42—21no—
233C42—21no—
234C42—3981no—
235C42—3981no—
236C42—3981no—
237C23—21no—
238C23—7961no—
239C23—3982no—
240C23—3981no—
241C23—3981no—
242C23—1991no—
243C23—1991no—
244C23D4×D19911yescharacteristic
245Q8—21no—
246Q8—21no—
247D4—21no—
248D4—21no—
249D4—41no—
250D4—41no—
251D4—7962no—
252D4—7962no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—7961no—
260C2×C4—7961no—
261C2×C4—3982no—
262C2×C4—3981no—
263C2×C4—3981no—
264C2×C4—3981no—
265C2×C4—3981no—
266C2×C4—3981no—
267C2×C4—3981no—
268C2×C4—3981no—
269C2×C4—3981no—
270C2×C4—3981no—
271C2×C4—3981no—
272C2×C4—3981no—
273C2×C4—3981no—
274C2×C4—1991no—
275C2×C4—1991no—
276C2×C4C2×C4×D19911yescharacteristic
277C2×C4D4×D19911yescharacteristic
278C2×C4D4×D19911yescharacteristic
279C2×C4C2×C22⋊D19911yescharacteristic
280C2×C4#1569188511yescharacteristic
281C2×C4#1569188611yescharacteristic
282C8—22no—
283C8—3982no—
284C22—21no—
285C22—21no—
286C22—41no—
287C22—41no—
288C22—41no—
289C22—7962no—
290C22—7962no—
291C22—3981no—
292C22—3981no—
293C22—3981no—
294C22—3981no—
295C22—3981no—
296C22—1992no—
297C22C22⋊C4×D19911yescharacteristic
298C22#2026392611yescharacteristic
299C22#2026392811yescharacteristic
300C4—42no—
301C4—41no—
302C4—7962no—
303C4—7961no—
304C4—7961no—
305C4—3981no—
306C4—3981no—
307C4(C22⋊D199)⋊C411yescharacteristic
308C4C4×C22⋊D19911yescharacteristic
309C4#2026392311yescharacteristic
310C4#2026393711yescharacteristic
311C2—21no—
312C2—21no—
313C2—81no—
314C2—7961no—
315C2—3982no—
316C2#2716389411yescharacteristic
317C2#104×D19911yescharacteristic
318C2#2716403311yescharacteristic
subgroupG/H
centerC2×C4D4×D199
commutatorC2×C4×C199C22×C4
FrattiniC22×C4C22×D199
FittingC2×#104×C199C2
socleC22×C199C2×C22⋊C4
prime radical#27164525C2
cosocleC22×C4×C199C23
hypercenterC2×#104D199
hypocenterC199#1871
LCSG ▷ C2×C4×C199 ▷ C2×C199 ▷ C199
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
1. C2×M16×D199C2semidirect
3. C2×#20263882C2semidirect
4. C4×(C2×D199)⋊C4C2semidirect
5. #27163779C2semidirect
6. #27163778C2semidirect
7. C2×#104×C199C2semidirect
15. #20263931C4semidirect
16. #20263931C4semidirect
17. #20263926C4semidirect
18. #20263926C4semidirect
45. #15691870D4semidirect
73. M16×C199D4semidirect
139. C2×D199#104semidirect
159. C199#1871semidirect
164. C2×#104D199semidirect
218. M16C22⋊D199semidirect

Maximal subgroups

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

subgroupindex
C2×M16×D1992
#271645252
C2×#202638822
C4×(C2×D199)⋊C42
#271637792
#271637782
C2×#104×C1992
#1871199