Finite Group Databasebeta

← #38751036

Subgroups — #38751036

Order 25216.

582 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#20263311C211yesmaximal, characteristic
2C2×C42×D197C211yesmaximal, characteristic, complemented
3#27160971C211yesmaximal, characteristic, complemented
4#27160970C211yesmaximal, characteristic, complemented
5#27160969C211yesmaximal, characteristic, complemented
6#27160968C211yesmaximal, characteristic, complemented
7#27160962C211yesmaximal, characteristic, complemented
8#27160961C211yesmaximal, characteristic, complemented
9#27160960C211yesmaximal, characteristic, complemented
10#27160957C211yesmaximal, characteristic
11#27160957C211yesmaximal, characteristic
12#27160953C211yesmaximal, characteristic, complemented
13#27160950C211yesmaximal, characteristic, complemented
14#27160941C211yesmaximal, characteristic, complemented
15#387×C197C211yesmaximal, characteristic, complemented
16C22×D788C2211yescharacteristic
17C22×C4×D197C2211yescharacteristic
18C22×C4×D197C2211yescharacteristic
19C22×C4×D197C2211yescharacteristic
20#20263311—24no—
21C2×C4⋊Dic197C2211yescharacteristic
22C2×#15691337C2211yescharacteristic
23C2×#15691337C2211yescharacteristic
24C2×#15691337C2211yescharacteristic
25C2×#15691335C2211yescharacteristic
26C2×#15691335C2211yescharacteristic
27C2×#15691335C2211yescharacteristic
28C2×#15691335C2211yescharacteristic
29C2×#15691335C2211yescharacteristic
30C2×#15691335C2211yescharacteristic
31C2×#15691335C2211yescharacteristic
32C2×#15691335C2211yescharacteristic
33C2×#15691335C2211yescharacteristic
34C2×C4×Dic197C2211yescharacteristic
35C2×C4×Dic197C2211yescharacteristic
36C2×C4×Dic197C2211yescharacteristic
37C42×D197—24no—
38#20263233C2211yescharacteristic
39#20263233C2211yescharacteristic
40#20263233C2211yescharacteristic
41#20263233C2211yescharacteristic
42#20263233C2211yescharacteristic
43#20263233C2211yescharacteristic
44#20263233C2211yescharacteristic
45#20263233C2211yescharacteristic
46C2×C4⋊C4×C197C2211yescharacteristic
47C2×C4⋊C4×C197C2211yescharacteristic
48C2×C42×C197C2211yescharacteristic
49#95×C197C2211yescharacteristic
50#95×C197C2211yescharacteristic
51#95×C197C2211yescharacteristic
52#95×C197C2211yescharacteristic
53C23×D197C2311yescharacteristic
54C23×D197C2311yescharacteristic
55C2×D788—22no—
56C2×D788—22no—
57C2×D788—22no—
58C22×Dic197C2311yescharacteristic
59C22×Dic197C2311yescharacteristic
60C22×Dic197C2311yescharacteristic
61C22×Dic197C2311yescharacteristic
62C22×Dic197C2311yescharacteristic
63C22×Dic197C2311yescharacteristic
64C2×C4×D197—22no—
65C2×C4×D197—22no—
66C2×C4×D197—22no—
67C2×C4×D197—22no—
68C2×C4×D197—22no—
69C2×C4×D197—22no—
70C2×C4×D197—22no—
71C2×C4×D197—22no—
72C2×C4×D197D414yes—
73C4⋊Dic197—22no—
74#15691337—22no—
75#15691337—22no—
76#15691337—22no—
77#15691335—22no—
78#15691335—22no—
79#15691335—22no—
80#15691335—22no—
81#15691335—22no—
82#15691335—22no—
83#15691335—22no—
84#15691335—22no—
85#15691335—22no—
86C4×Dic197—22no—
87C4×Dic197—22no—
88C4×Dic197—22no—
89C22×C4×C197C2311yescharacteristic
90C22×C4×C197C2311yescharacteristic
91C22×C4×C197C2311yescharacteristic
92C22×C4×C197C2311yescharacteristic
93C22×C4×C197C2311yescharacteristic
94C22×C4×C197C2311yescharacteristic
95C22×C4×C197C2311yescharacteristic
96C4⋊C4×C197—22no—
97C4⋊C4×C197—22no—
98C42×C197—22no—
99C22×D197—21no—
100C22×D197—21no—
101C22×D197—21no—
102C22×D197—21no—
103C22×D197—21no—
104C22×D197—21no—
105C22×D197—21no—
106C22×D197—21no—
107C22×D197—21no—
108C22×D197—21no—
109C22×D197—21no—
110C22×D197C2×D412yes—
111C22×D197#4112yes—
112C22×D197#4112yes—
113D788—44no—
114C2×Dic197—21no—
115C2×Dic197—21no—
116C2×Dic197—21no—
117C2×Dic197—21no—
118C2×Dic197—21no—
119C2×Dic197—21no—
120C2×Dic197—21no—
121C2×Dic197—21no—
122C2×Dic197—21no—
123C2×Dic197—21no—
124C2×Dic197—21no—
125C2×Dic197—21no—
126C2×Dic197—21no—
127C2×Dic197—21no—
128C2×Dic197—21no—
129C2×Dic197C2×D412yes—
130C2×Dic197#4112yes—
131C2×Dic197#4112yes—
132C4×D197—28no—
133C4×D197—28no—
134C4×D197—28no—
135C23×C197C2411yescharacteristic
136C2×C4×C197—21no—
137C2×C4×C197—21no—
138C2×C4×C197—21no—
139C2×C4×C197—21no—
140C2×C4×C197—21no—
141C2×C4×C197—21no—
142C2×C4×C197—21no—
143C2×C4×C197—21no—
144C2×C4×C197—21no—
145C2×C4×C197—21no—
146C2×C4×C197—21no—
147C2×C4×C197—21no—
148C2×C4×C197—21no—
149C2×C4×C197—21no—
150C2×C4×C197—21no—
151C2×C4×C197—21no—
152C2×C4×C197—21no—
153C2×C4×C197—21no—
154C2×C4×C197C2×D412yes—
155C2×C4×C197#4112yes—
156C2×C4×C197#4112yes—
157C22×C197C22×D411yescharacteristic
158C22×C197C2×#4111yescharacteristic
159C22×C197C2×#4111yescharacteristic
160C22×C197C2×#4111yescharacteristic
161C22×C197C2×#4111yescharacteristic
162C22×C197C2×#4111yescharacteristic
163C22×C197C2×#4111yescharacteristic
164C2×D197—22no—
165C2×D197—22no—
166C2×D197—22no—
167C2×D197—22no—
168C2×D197—22no—
169C2×D197—22no—
170C2×D197—41no—
171C2×D197—41no—
172C2×D197—41no—
173C2×D197—41no—
174C2×D197—41no—
175C2×D197—41no—
176C2×D197—41no—
177C2×D197#12314yes—
178C4×C197—22no—
179C4×C197—22no—
180C4×C197—22no—
181C4×C197—41no—
182C4×C197—41no—
183C4×C197—41no—
184C4×C197—41no—
185Dic197—22no—
186Dic197—22no—
187Dic197—22no—
188Dic197—41no—
189Dic197—41no—
190Dic197—41no—
191C2×C197C2×#12311yescharacteristic
192C2×C197#52511yescharacteristic
193C2×C197#52511yescharacteristic
194C2×C197#52911yescharacteristic
195C2×C197#52911yescharacteristic
196C2×C197#52911yescharacteristic
197C2×C197#52911yescharacteristic
198D197—24no—
199D197—81no—
200C197#285311yescharacteristic, complemented, Sylow
201#2853—1971nomaximal, Sylow
202C2×#123—1971no—
203C22×C42—1971no—
204#388—1971no—
205#388—1971no—
206#388—1971no—
207#388—1971no—
208#387—1971no—
209#387—1971no—
210#387—1971no—
211#387D19711yescharacteristic, complemented
212#386—1971no—
213#386—1971no—
214#385—1971no—
215#385—1971no—
216#381—1971no—
217C22×D4—1971no—
218C23×C4—1971no—
219C23×C4—1971no—
220C23×C4—1971no—
221#123—3944no—
222C2×C4⋊C4—1971no—
223C2×C4⋊C4—1971no—
224C2×C4⋊C4—1971no—
225C2×C4⋊C4—1971no—
226C2×C4⋊C4C2×D19711yescharacteristic
227C2×C4⋊C4C2×D19711yescharacteristic
228C2×C22⋊C4—1971no—
229C2×C22⋊C4—1971no—
230C2×C22⋊C4—1971no—
231C2×C22⋊C4—1971no—
232C2×C22⋊C4—1971no—
233C2×C22⋊C4—1971no—
234C2×C22⋊C4—1971no—
235C2×C22⋊C4—1971no—
236C2×C22⋊C4—1971no—
237C2×C42—3944no—
238C2×C42—1971no—
239C2×C42—1971no—
240C2×C42—1971no—
241C2×C42C2×D19711yescharacteristic
242#95—1971no—
243#95—1971no—
244#95—1971no—
245#95—1971no—
246#95—1971no—
247#95—1971no—
248#95—1971no—
249#95—1971no—
250#95C2×D19711yescharacteristic
251#95C2×D19711yescharacteristic
252#95C2×D19711yescharacteristic
253#95C2×D19711yescharacteristic
254C24—1971no—
255C24—1971no—
256C2×D4—3942no—
257C2×D4—3942no—
258C2×D4—3942no—
259C22×C4—3942no—
260C22×C4—3942no—
261C22×C4—3942no—
262C22×C4—3942no—
263C22×C4—3942no—
264C22×C4—3942no—
265C22×C4—3942no—
266C22×C4—3942no—
267C22×C4—1971no—
268C22×C4—1971no—
269C22×C4—1971no—
270C22×C4—1971no—
271C22×C4—1971no—
272C22×C4—1971no—
273C22×C4—1974no—
274C22×C4C22×D19711yescharacteristic
275C22×C4C22×D19711yescharacteristic
276C22×C4C22×D19711yescharacteristic
277C22×C4C22×D19711yescharacteristic
278C22×C4C22×D19711yescharacteristic
279C22×C4C22×D19711yescharacteristic
280C22×C4C22×D19711yescharacteristic
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—3942no—
284C4⋊C4—3942no—
285C4⋊C4—3942no—
286C4⋊C4—3942no—
287C22⋊C4—3942no—
288C22⋊C4—3942no—
289C22⋊C4—3942no—
290C22⋊C4—3942no—
291C22⋊C4—3942no—
292C22⋊C4—3942no—
293C22⋊C4—3942no—
294C22⋊C4—3942no—
295C22⋊C4—3942no—
296C42—22no—
297C42—3942no—
298C42—3942no—
299C42—3942no—
300C23—3941no—
301C23—3941no—
302C23—3941no—
303C23—3941no—
304C23—3941no—
305C23—3941no—
306C23—3941no—
307C23—3941no—
308C23—3941no—
309C23—3941no—
310C23—3941no—
311C23—1972no—
312C23—1972no—
313C23—1972no—
314C23C23×D19711yescharacteristic
315D4—7884no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—3948no—
335C2×C4—3948no—
336C2×C4—3948no—
337C2×C4—3941no—
338C2×C4—3941no—
339C2×C4—3941no—
340C2×C4—3941no—
341C2×C4—3941no—
342C2×C4—3941no—
343C2×C4—3941no—
344C2×C4—3941no—
345C2×C4—3941no—
346C2×C4—3941no—
347C2×C4—3941no—
348C2×C4—3941no—
349C2×C4—3941no—
350C2×C4—3941no—
351C2×C4—3941no—
352C2×C4—1972no—
353C2×C4—1972no—
354C2×C4—1972no—
355C2×C4D4×D19712yes—
356C2×C4#1569135812yes—
357C2×C4#1569135912yes—
358C22—7881no—
359C22—7881no—
360C22—7881no—
361C22—7881no—
362C22—7881no—
363C22—7881no—
364C22—7881no—
365C22—3942no—
366C22—3942no—
367C22—3942no—
368C22—3942no—
369C22—3942no—
370C22—3942no—
371C22—1974no—
372C22C2×D4×D19711yescharacteristic
373C22#41×D19711yescharacteristic
374C22#41×D19711yescharacteristic
375C22#41×D19711yescharacteristic
376C22#41×D19711yescharacteristic
377C22C2×#1569135811yescharacteristic
378C22C2×#1569135911yescharacteristic
379C4—22no—
380C4—22no—
381C4—22no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—7881no—
387C4—7881no—
388C4—7881no—
389C4—3942no—
390C4—3942no—
391C4—3942no—
392C2—15761no—
393C2—3944no—
394C2#123×D19711yescharacteristic
395C2#2716158811yescharacteristic
396C2#2716159211yescharacteristic
397C2#2716160711yescharacteristic
398C2#2716161211yescharacteristic
399C2#2716161411yescharacteristic
400C2#2716161611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D197
commutator, socle, cosocleC23×C197C24
Fitting#387×C197C2
prime radicalC22×D788C22
hypercenter#387D197
hypocenterC197#2853
LCSG ▷ C23×C197 ▷ C197
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. C2×C42×D197C2semidirect
3. #27160971C2semidirect
4. #27160970C2semidirect
5. #27160969C2semidirect
6. #27160968C2semidirect
7. #27160962C2semidirect
8. #27160961C2semidirect
9. #27160960C2semidirect
12. #27160953C2semidirect
13. #27160950C2semidirect
14. #27160941C2semidirect
15. #387×C197C2semidirect
200. C197#2853semidirect
211. #387D197semidirect

Maximal subgroups

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

subgroupindex
C2×#202633112
C2×C42×D1972
#271609712
#271609702
#271609692
#271609682
#271609622
#271609612
#271609602
#271609572
#271609532
#271609502
#271609412
#387×C1972
#2853197