Finite Group Databasebeta

← #38751453

Subgroups — #38751453

Order 25216.

492 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#20263334C211yesmaximal, characteristic, complemented
2C2×#20263332C211yesmaximal, characteristic, complemented
3#27161626C211yesmaximal, characteristic
4#27161155C211yesmaximal, characteristic, complemented
5#27161154C211yesmaximal, characteristic, complemented
6#27161152C211yesmaximal, characteristic, complemented
7#27161151C211yesmaximal, characteristic, complemented
8#27161149C211yesmaximal, characteristic, complemented
9C8×C22⋊D197C211yesmaximal, characteristic, complemented
10#27161142C211yesmaximal, characteristic, complemented
11C4⋊C8×D197C211yesmaximal, characteristic, complemented
12#27161044C211yesmaximal, characteristic, complemented
13#27161044C211yesmaximal, characteristic, complemented
14#27161031C211yesmaximal, characteristic, complemented
15#435×C197C211yesmaximal, characteristic, complemented
16C2×#15691358C2211yescharacteristic
17C2×#15691358C2211yescharacteristic
18#20263334—24no—
19#20263332—24no—
20C2×#15691342C2211yescharacteristic
21C2×#15691341C2211yescharacteristic
22C2×#15691341C2211yescharacteristic
23C2×#15691341C2211yescharacteristic
24C2×#15691341C2211yescharacteristic
25C22×#13096802C2211yescharacteristic
26C2×C8×D197C2211yescharacteristic
27C2×C8×D197C2211yescharacteristic
28C2×C8×D197C2211yescharacteristic
29C2×C8×D197C2211yescharacteristic
30#20263325C411yescharacteristic
31#20263322C411yescharacteristic
32#20263312C411yescharacteristic
33#20263312C411yescharacteristic
34#20263301C411yescharacteristic
35#20263299C411yescharacteristic
36#20263299C411yescharacteristic
37#20263297C411yescharacteristic
38C4×D788C2211yescharacteristic
39C4×C22⋊D197C2211yescharacteristic
40C4×C22⋊D197C2211yescharacteristic
41C42×D197C2211yescharacteristic
42C4⋊#13096802C2211yescharacteristic
43#20263255C2211yescharacteristic
44#20263255C2211yescharacteristic
45C22⋊#13096802C2211yescharacteristic
46C22⋊#13096802C2211yescharacteristic
47#20263238C2211yescharacteristic
48#20263238C2211yescharacteristic
49#20263238C2211yescharacteristic
50#20263238C2211yescharacteristic
51#20263237C2211yescharacteristic
52C8×Dic197C2211yescharacteristic
53C8×Dic197C2211yescharacteristic
54C2×M16×C197C2211yescharacteristic
55C22×C8×C197C2211yescharacteristic
56C4×D4×C197C2211yescharacteristic
57C4⋊C8×C197C2211yescharacteristic
58C22⋊C8×C197C2211yescharacteristic
59C22⋊C8×C197C2211yescharacteristic
60#97×C197C2211yescharacteristic
61#15691358—22no—
62#15691358—22no—
63#15691358—22no—
64#15691358—22no—
65C2×Dic394C2×C411yescharacteristic
66C2×Dic394C2×C411yescharacteristic
67C2×D788C2×C411yescharacteristic
68C2×D788C2×C411yescharacteristic
69C2×D788C2×C411yescharacteristic
70C2×C22⋊D197C2×C411yescharacteristic
71C2×C22⋊D197C2×C411yescharacteristic
72C2×C22⋊D197C2×C411yescharacteristic
73C2×C22⋊D197C2×C411yescharacteristic
74C2×C22⋊D197C2×C411yescharacteristic
75C2×C22⋊D197C2×C411yescharacteristic
76C2×C4×D197C2×C411yescharacteristic
77C2×C4×D197C2×C411yescharacteristic
78C2×C4×D197C2311yescharacteristic
79C2×C4×D197C2311yescharacteristic
80C2×C4×D197C2311yescharacteristic
81#15691342—22no—
82#15691341—22no—
83#15691341—22no—
84#15691341—22no—
85#15691341D414yescomplemented
86C2×#13096802—22no—
87C2×#13096802C2311yescharacteristic
88C2×#13096802C2311yescharacteristic
89C2×#13096802C2311yescharacteristic
90C2×#13096802C2311yescharacteristic
91C8×D197—22no—
92C8×D197—22no—
93C8×D197—22no—
94C8×D197—22no—
95C4⋊Dic197C2×C411yescharacteristic
96#15691337C2×C411yescharacteristic
97#15691337C2×C411yescharacteristic
98C22⋊Dic197C2×C411yescharacteristic
99C22⋊Dic197C2×C411yescharacteristic
100#15691335C2×C411yescharacteristic
101#15691335C2×C411yescharacteristic
102#15691335C2×C411yescharacteristic
103#15691335C2×C411yescharacteristic
104C4×Dic197C2×C411yescharacteristic
105C4×Dic197C2×C411yescharacteristic
106C4×Dic197C2311yescharacteristic
107C2×D4×C197C2×C411yescharacteristic
108C22×C4×C197C2311yescharacteristic
109C22×C4×C197C2311yescharacteristic
110M16×C197—22no—
111C2×C8×C197—22no—
112C2×C8×C197C2311yescharacteristic
113C2×C8×C197C2311yescharacteristic
114C2×C8×C197C2311yescharacteristic
115C2×C8×C197C2311yescharacteristic
116C4⋊C4×C197C2×C411yescharacteristic
117C22⋊C4×C197C2×C411yescharacteristic
118C22⋊C4×C197C2×C411yescharacteristic
119C42×C197C2311yescharacteristic
120C22×D197C22×C411yescharacteristic
121C22×D197C22×C411yescharacteristic
122C22×D197C22×C411yescharacteristic
123Dic394—22no—
124Dic394—22no—
125D788—22no—
126D788—22no—
127D788—41no—
128C22⋊D197—22no—
129C22⋊D197—22no—
130C22⋊D197—22no—
131C22⋊D197—22no—
132C22⋊D197—22no—
133C22⋊D197—22no—
134C2×Dic197C22×C411yescharacteristic
135C2×Dic197C22×C411yescharacteristic
136C2×Dic197C22×C411yescharacteristic
137C2×Dic197C22×C411yescharacteristic
138C2×Dic197C22×C411yescharacteristic
139C4×D197—21no—
140C4×D197—21no—
141C4×D197—21no—
142C4×D197—21no—
143C4×D197—22no—
144C4×D197—41no—
145C4×D197C2×D412yes—
146C4×D197#4112yes—
147#13096802—21no—
148#13096802—21no—
149#13096802—21no—
150#13096802C2×D412yes—
151C23×C197C22×C411yescharacteristic
152C23×C197C22×C411yescharacteristic
153D4×C197—41no—
154C2×C4×C197—21no—
155C2×C4×C197—21no—
156C2×C4×C197—21no—
157C2×C4×C197—21no—
158C2×C4×C197C22×C411yescharacteristic
159C2×C4×C197C22×C411yescharacteristic
160C2×C4×C197C22×C411yescharacteristic
161C2×C4×C197C22×C411yescharacteristic
162C2×C4×C197C2411yescharacteristic
163C8×C197—21no—
164C8×C197—21no—
165C8×C197—21no—
166C8×C197C2×D412yes—
167C22×C197—21no—
168C22×C197—21no—
169C22×C197—21no—
170C22×C197—21no—
171C22×C197—21no—
172C22×C197—21no—
173C22×C197C23×C411yescharacteristic
174C2×D197—21no—
175C2×D197—21no—
176C2×D197—21no—
177C2×D197—21no—
178C2×D197—21no—
179C2×D197—21no—
180C2×D197—21no—
181C2×D197—21no—
182C2×D197C4×D412yes—
183C4×C197—21no—
184C4×C197—21no—
185C4×C197—21no—
186C4×C197—21no—
187C4×C197C22×D411yescharacteristic
188C4×C197C2×#4111yescharacteristic
189Dic197—21no—
190Dic197—21no—
191Dic197—21no—
192Dic197C4×D412yes—
193Dic197#13112yescomplemented
194C2×C197—41no—
195C2×C197—41no—
196C2×C197C2×C4×D411yescharacteristic
197C2×C197C2×#13111yescharacteristic
198C2×C197#56811yescharacteristic
199D197—22no—
200D197—41no—
201D197—41no—
202C197#293511yescharacteristic, complemented, Sylow
203#2935—1971nomaximal, Sylow
204C2×#131—1971no—
205C2×#131—1971no—
206#532—1971no—
207#436—1971no—
208#436—1971no—
209#435—1971no—
210#435—1971no—
211#435—1971no—
212#435D19711yescharacteristic, complemented
213C8×D4—1971no—
214C8×D4—1971no—
215C2×C4⋊C8—1971no—
216#408—1971no—
217#408—1971no—
218C4×M16—1971no—
219C2×#41—1971no—
220C2×#41—1971no—
221#131—3944no—
222#131—3944no—
223C2×M16—1971no—
224C2×M16—1971no—
225C2×M16—1971no—
226C2×M16—1971no—
227C2×M16—1971no—
228C2×M16C2×D19711yescharacteristic
229C22×C8—1971no—
230C22×C8—1971no—
231C22×C8—1971no—
232C22×C8—1971no—
233C22×C8—1971no—
234C22×C8C2×D19711yescharacteristic
235C4⋊Q8—1971no—
236#127—1971no—
237#124—1971no—
238#124—1971no—
239#121—1971no—
240#121—1971no—
241#121—1971no—
242#121—1971no—
243C4×D4—1971no—
244C4×D4—1971no—
245C4×D4—1971no—
246C4×D4C2×D19711yescharacteristic
247C2×C42—1971no—
248C4⋊C8—1971no—
249C4⋊C8—1971no—
250C4⋊C8—1971no—
251C4⋊C8C2×D19711yescharacteristic
252C22⋊C8—1971no—
253C22⋊C8—1971no—
254C22⋊C8—1971no—
255C22⋊C8—1971no—
256C22⋊C8—1971no—
257C22⋊C8—1971no—
258C22⋊C8C2×D19711yescharacteristic
259C22⋊C8C2×D19711yescharacteristic
260#97—1971no—
261#97C2×D19711yescharacteristic
262C4×C8—1971no—
263C4×C8—1971no—
264#41—3942no—
265#41—3942no—
266#41—3942no—
267#41—3942no—
268C2×Q8—1971no—
269C2×Q8—1971no—
270C2×D4—1971no—
271C2×D4—1971no—
272C2×D4—1971no—
273C2×D4—1971no—
274C2×D4—1971no—
275C2×D4—1971no—
276C2×D4—1971no—
277C2×D4—1971no—
278C2×D4—1971no—
279C2×D4C4×D19711yescharacteristic
280C22×C4—1971no—
281C22×C4—1971no—
282C22×C4—1971no—
283C22×C4—1971no—
284C22×C4—1971no—
285C22×C4C22×D19711yescharacteristic
286C22×C4C22×D19711yescharacteristic
287M16—22no—
288M16—3942no—
289M16—3942no—
290M16—3942no—
291M16—3942no—
292M16—1974no—
293C2×C8—22no—
294C2×C8—3942no—
295C2×C8—3942no—
296C2×C8—3942no—
297C2×C8—3942no—
298C2×C8—3942no—
299C2×C8—1971no—
300C2×C8—1971no—
301C2×C8—1971no—
302C2×C8—1971no—
303C2×C8C22×D19711yescharacteristic
304C2×C8C22×D19711yescharacteristic
305C2×C8C22×D19711yescharacteristic
306C2×C8C22×D19711yescharacteristic
307C4⋊C4—1971no—
308C4⋊C4—1971no—
309C4⋊C4—1971no—
310C4⋊C4C4×D19711yescharacteristic
311C22⋊C4—1971no—
312C22⋊C4—1971no—
313C22⋊C4—1971no—
314C22⋊C4—1971no—
315C22⋊C4—1971no—
316C22⋊C4—1971no—
317C22⋊C4C4×D19711yescharacteristic
318C22⋊C4C4×D19711yescharacteristic
319C42—1971no—
320C42—1971no—
321C42—1971no—
322C42C22×D19711yescharacteristic
323C23—1971no—
324C23—1971no—
325C23—1971no—
326C23C2×C4×D19711yescharacteristic
327C23C2×C4×D19711yescharacteristic
328Q8—3942no—
329Q8—3942no—
330D4—41no—
331D4—7881no—
332D4—3942no—
333D4—3942no—
334D4—3942no—
335D4—3942no—
336D4—3942no—
337D4—3942no—
338D4—3942no—
339D4—3942no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—7881no—
345C2×C4—3942no—
346C2×C4—3941no—
347C2×C4—3941no—
348C2×C4—3941no—
349C2×C4—3941no—
350C2×C4—1971no—
351C2×C4—1971no—
352C2×C4—1971no—
353C2×C4—1971no—
354C2×C4—1971no—
355C2×C4—1972no—
356C2×C4—1972no—
357C2×C4C2×C4×D19711yescharacteristic
358C2×C4C2×C4×D19711yescharacteristic
359C2×C4C2×C4×D19711yescharacteristic
360C2×C4C2×C4×D19711yescharacteristic
361C2×C4C23×D19711yescharacteristic
362C8—21no—
363C8—21no—
364C8—21no—
365C8—3941no—
366C8—3941no—
367C8—3941no—
368C8—1972no—
369C8D4×D19712yes—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—3941no—
377C22—3941no—
378C22—3941no—
379C22—3941no—
380C22—3941no—
381C22—3941no—
382C22—3941no—
383C22—3941no—
384C22—1972no—
385C22C22×C4×D19711yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—21no—
390C4—3941no—
391C4—3941no—
392C4—3941no—
393C4—1972no—
394C4—1972no—
395C4C2×D4×D19711yescharacteristic
396C4#41×D19711yescharacteristic
397C2—41no—
398C2—41no—
399C2—7881no—
400C2—7881no—
401C2—3942no—
402C2C4×D4×D19711yescharacteristic
403C2#131×D19711yescharacteristic
404C2#2716184511yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D197
commutator, socleC22×C197C23×C4
Fitting#435×C197C2
prime radical#27161626C2
cosocleC2×C4×C197C24
hypercenter#435D197
hypocenterC197#2935
LCSG ▷ C22×C197 ▷ C197
UCSC1 ◁ C2×C4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#20263334C2semidirect
2. C2×#20263332C2semidirect
4. #27161155C2semidirect
5. #27161154C2semidirect
6. #27161152C2semidirect
7. #27161151C2semidirect
8. #27161149C2semidirect
9. C8×C22⋊D197C2semidirect
10. #27161142C2semidirect
11. C4⋊C8×D197C2semidirect
12. #27161044C2semidirect
13. #27161044C2semidirect
14. #27161031C2semidirect
15. #435×C197C2semidirect
85. #15691341D4semidirect
193. Dic197#131semidirect
202. C197#2935semidirect
212. #435D197semidirect

Maximal subgroups

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

subgroupindex
C2×#202633342
C2×#202633322
#271616262
#271611552
#271611542
#271611522
#271611512
#271611492
C8×C22⋊D1972
#271611422
C4⋊C8×D1972
#271610442
#271610312
#435×C1972
#2935197