Finite Group Databasebeta

← #27205932

Subgroups — #27205932

Order 13184.

424 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268302C211yesmaximal, characteristic, complemented
2#20268132C211yesmaximal, characteristic, complemented
3#20268129C211yesmaximal, characteristic, complemented
4#20268115C211yesmaximal, characteristic, complemented
5#20268112C211yesmaximal, characteristic, complemented
6#20268030C211yesmaximal, characteristic, complemented
7#20268025C211yesmaximal, characteristic, complemented
8#20268022C211yesmaximal, characteristic, complemented
9#20268018C211yesmaximal, characteristic, complemented
10#20267953C211yesmaximal, characteristic, complemented
11#20267951C211yesmaximal, characteristic, complemented
12#20267936C211yesmaximal, characteristic, complemented
13#20267934C211yesmaximal, characteristic, complemented
14C2×C22⋊(C103⋊C8)C211yesmaximal, characteristic, complemented
15#525×C103C211yesmaximal, characteristic, complemented
16C2×#13110105C2211yescharacteristic
17C2×#13110095C2211yescharacteristic, complemented
18C2×#13110093C2211yescharacteristic, complemented
19C2×#13110092C2211yescharacteristic, complemented
20C2×#13110090C2211yescharacteristic, complemented
21C22×C103⋊C8C2211yescharacteristic
22C22×C103⋊C8C2211yescharacteristic
23#15693004—21no—
24#15693000C2211yescharacteristic
25#15693000C2211yescharacteristic
26#15692995C2211yescharacteristic
27#15692995C2211yescharacteristic
28#15692990—21no—
29C4×C22⋊D103—21no—
30C4×C22⋊D103—21no—
31#15692980C2211yescharacteristic
32#15692954C2211yescharacteristic, complemented
33#15692954C2211yescharacteristic, complemented
34#15692952C2211yescharacteristic, complemented
35#15692952C2211yescharacteristic, complemented
36#15692945C2211yescharacteristic, complemented
37#15692945C2211yescharacteristic, complemented
38#15692944C2211yescharacteristic, complemented
39#15692944C2211yescharacteristic, complemented
40#15692942C2211yescharacteristic, complemented
41#15692942C2211yescharacteristic, complemented
42#15692941C2211yescharacteristic, complemented
43#15692941C2211yescharacteristic, complemented
44C22⋊(C103⋊C8)C2211yescharacteristic
45C22⋊(C103⋊C8)C2211yescharacteristic
46C22⋊(C103⋊C8)C2211yescharacteristic
47C22⋊(C103⋊C8)C2211yescharacteristic
48C2×#41×C103C2211yescharacteristic
49C23×C4×C103C2211yescharacteristic
50#123×C103—21no—
51C22⋊Q8×C103C2211yescharacteristic
52C22⋊Q8×C103C2211yescharacteristic
53#121×C103C2211yescharacteristic
54#121×C103C2211yescharacteristic
55#120×C103—21no—
56C4×D4×C103—21no—
57C4×D4×C103—21no—
58#117×C103C2211yescharacteristic
59#13110105—41no—
60#13110105—41no—
61C2×Dic206C2311yescharacteristic
62C2×D412C2311yescharacteristic
63C2×C22⋊D103—21no—
64C2×C22⋊D103—21no—
65C2×C22⋊D103—21no—
66C2×C4×D103—21no—
67#13110095—41no—
68#13110093—41no—
69#13110092—41no—
70#13110090—41no—
71C2×C103⋊C8—41no—
72C2×C103⋊C8—41no—
73C2×C103⋊C8C2311yescharacteristic
74C2×C103⋊C8C2311yescharacteristic
75C2×C103⋊C8C2311yescharacteristic
76C2×C103⋊C8C2311yescharacteristic
77C4⋊Dic103C2311yescharacteristic
78C4⋊Dic103C2311yescharacteristic
79Dic103⋊C4—21no—
80Dic103⋊C4—21no—
81C22⋊Dic103—21no—
82C22⋊Dic103—21no—
83C22⋊Dic103—21no—
84(C2×D103)⋊C4—21no—
85(C2×D103)⋊C4—21no—
86C4×Dic103—21no—
87C24×C103D411yescharacteristic
88#41×C103—41no—
89#41×C103—41no—
90C2×Q8×C103C2311yescharacteristic
91C2×D4×C103—21no—
92C2×D4×C103—21no—
93C2×D4×C103—21no—
94C2×D4×C103C2311yescharacteristic
95C22×C4×C103—21no—
96C22×C4×C103—41no—
97C22×C4×C103—41no—
98C22×C4×C103D411yescharacteristic
99C22×C4×C103D411yescharacteristic
100C22×C4×C103D411yescharacteristic
101C22×C4×C103C2311yescharacteristic
102C22×C4×C103C2311yescharacteristic
103C22×C4×C103C2311yescharacteristic
104C4⋊C4×C103—21no—
105C4⋊C4×C103—21no—
106C4⋊C4×C103C2311yescharacteristic
107C4⋊C4×C103C2311yescharacteristic
108C22⋊C4×C103—21no—
109C22⋊C4×C103—21no—
110C22⋊C4×C103—21no—
111C22⋊C4×C103—21no—
112C22⋊C4×C103—21no—
113C42×C103—21no—
114C23×C103—22no—
115C23×C103—21no—
116C23×C103—41no—
117C23×C103—41no—
118C23×C103C2×D411yescharacteristic
119C23×C103C2×D411yescharacteristic
120C23×C103C2×D411yescharacteristic
121C22×D103—21no—
122Q8×C103—21no—
123Q8×C103—21no—
124D4×C103—21no—
125D4×C103—21no—
126D4×C103—42no—
127D4×C103—42no—
128D4×C103—42no—
129C2×C4×C103—21no—
130C2×C4×C103—21no—
131C2×C4×C103—21no—
132C2×C4×C103—21no—
133C2×C4×C103—21no—
134C2×C4×C103—21no—
135C2×C4×C103—21no—
136C2×C4×C103—21no—
137C2×C4×C103—21no—
138C2×C4×C103—41no—
139C2×C4×C103—41no—
140C2×C4×C103—41no—
141C2×C4×C103—42no—
142C2×C4×C103C2×D411yescharacteristic
143C2×C4×C103C2×D411yescharacteristic
144C2×C4×C103C2×D411yescharacteristic
145C2×C4×C103C2411yescharacteristic
146C22⋊D103—42no—
147C22⋊D103—42no—
148C22⋊D103—42no—
149C2×Dic103—21no—
150C2×Dic103—21no—
151C2×Dic103—21no—
152D412—21no—
153D412—21no—
154C4×D103—42no—
155Dic206—21no—
156Dic206—21no—
157C103⋊C8—21no—
158C103⋊C8—21no—
159C103⋊C8—21no—
160C103⋊C8—21no—
161C22×C103—21no—
162C22×C103—21no—
163C22×C103—21no—
164C22×C103—21no—
165C22×C103—21no—
166C22×C103—21no—
167C22×C103—21no—
168C22×C103—21no—
169C22×C103—44no—
170C22×C103—41no—
171C22×C103—41no—
172C22×C103—41no—
173C22×C103#13512yes—
174C22×C103C22×D411yescharacteristic
175C2×D103—41no—
176C2×D103—41no—
177C2×D103—41no—
178C4×C103—21no—
179C4×C103—21no—
180C4×C103—21no—
181C4×C103—41no—
182C4×C103—41no—
183C4×C103—41no—
184C4×C103H(5,𝔽2)11yescharacteristic
185C4×C103H(5,𝔽2)11yescharacteristic
186Dic103—41no—
187Dic103—41no—
188Dic103—41no—
189C2×C103—22no—
190C2×C103—41no—
191C2×C103—41no—
192C2×C103—81no—
193C2×C103#53411yescharacteristic
194C2×C103C2×#13511yescharacteristic
195C2×C103#57511yescharacteristic
196D103—81no—
197#3191—1031nomaximal, Sylow
198C103#319111yescharacteristic, complemented, Sylow
199#525—1031no—
200#525D10311yescharacteristic, complemented
201#485—1031no—
202#485—1031no—
203#482—1031no—
204#482—1031no—
205#467—1031no—
206#466—1031no—
207#465—1031no—
208#465—1031no—
209#452—1031no—
210#452—1031no—
211#449—1031no—
212#449—1031no—
213C2×C22⋊C8—1031no—
214C2×#41—1031no—
215C2×#41C2×D10311yescharacteristic
216C23×C4C2×D10311yescharacteristic
217C2×Q16—1031no—
218C2×SD16—1031no—
219C2×SD16—1031no—
220C2×D8—1031no—
221C22×C8—1031no—
222C22×C8—1031no—
223#123—21no—
224#123—2061no—
225C22⋊Q8—1031no—
226C22⋊Q8—1031no—
227C22⋊Q8C2×D10311yescharacteristic
228C22⋊Q8C2×D10311yescharacteristic
229#121—1031no—
230#121—1031no—
231#121C2×D10311yescharacteristic
232#121C2×D10311yescharacteristic
233#120—21no—
234#120—2061no—
235C4×D4—21no—
236C4×D4—21no—
237C4×D4—2061no—
238C4×D4—2061no—
239#117—1031no—
240#117C2×D10311yescharacteristic
241#107—1031no—
242#107—1031no—
243#106—1031no—
244#106—1031no—
245#103—1031no—
246#103—1031no—
247#103—1031no—
248#103—1031no—
249#102—1031no—
250#102—1031no—
251#102—1031no—
252#102—1031no—
253C22⋊C8—1031no—
254C22⋊C8—1031no—
255C22⋊C8—1031no—
256C22⋊C8—1031no—
257C24C22⋊D10311yescharacteristic
258#41—41no—
259#41—41no—
260#41—4121no—
261#41—4121no—
262C2×Q8—1031no—
263C2×Q8C22×D10311yescharacteristic
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—1031no—
268C2×D4—2061no—
269C2×D4—2061no—
270C2×D4—2061no—
271C2×D4C22×D10311yescharacteristic
272C22×C4—21no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—2061no—
276C22×C4C22⋊D10311yescharacteristic
277C22×C4C22⋊D10311yescharacteristic
278C22×C4C22⋊D10311yescharacteristic
279C22×C4C22×D10311yescharacteristic
280C22×C4C22×D10311yescharacteristic
281C22×C4C22×D10311yescharacteristic
282Q16—4121no—
283SD16—4121no—
284SD16—4121no—
285D8—4121no—
286C2×C8—1031no—
287C2×C8—1031no—
288C2×C8—1031no—
289C2×C8—1031no—
290C2×C8—4121no—
291C2×C8—4121no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—1031no—
295C4⋊C4—1031no—
296C4⋊C4—2061no—
297C4⋊C4—2061no—
298C4⋊C4C22×D10311yescharacteristic
299C4⋊C4C22×D10311yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—2061no—
306C22⋊C4—2061no—
307C22⋊C4—2061no—
308C22⋊C4—2061no—
309C22⋊C4—2061no—
310C42—21no—
311C42—2061no—
312C23—22no—
313C23—21no—
314C23—41no—
315C23—41no—
316C23—2061no—
317C23C2×C22⋊D10311yescharacteristic
318C23C2×C22⋊D10311yescharacteristic
319C23C2×C22⋊D10311yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—2061no—
323Q8—2061no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—42no—
328D4—42no—
329D4—4122no—
330D4—4122no—
331D4—4122no—
332D4—2061no—
333D4—2061no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—4122no—
348C2×C4—2061no—
349C2×C4—2061no—
350C2×C4—2061no—
351C2×C4C2×C22⋊D10311yescharacteristic
352C2×C4C2×C22⋊D10311yescharacteristic
353C2×C4C2×C22⋊D10311yescharacteristic
354C2×C4C23×D10311yescharacteristic
355C8—2061no—
356C8—2061no—
357C8—2061no—
358C8—2061no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—44no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—4121no—
372C22—4121no—
373C22—4121no—
374C22#1569304112yes—
375C22C22×C22⋊D10311yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—4121no—
383C4—4121no—
384C4—4121no—
385C4#1569306611yescharacteristic
386C4#1569306611yescharacteristic
387C2—22no—
388C2—41no—
389C2—41no—
390C2—81no—
391C2—8241no—
392C2#2026835011yescharacteristic
393C2C2×#1569304111yescharacteristic
394C2#2026858911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#525×C103C2
socleC22×C103C22×D4
hypercenter#525D103
hypocenterC103#3191
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #20268302C2semidirect
2. #20268132C2semidirect
3. #20268129C2semidirect
4. #20268115C2semidirect
5. #20268112C2semidirect
6. #20268030C2semidirect
7. #20268025C2semidirect
8. #20268022C2semidirect
9. #20268018C2semidirect
10. #20267953C2semidirect
11. #20267951C2semidirect
12. #20267936C2semidirect
13. #20267934C2semidirect
14. C2×C22⋊(C103⋊C8)C2semidirect
15. #525×C103C2semidirect
17. C2×#13110095C22semidirect
18. C2×#13110093C22semidirect
19. C2×#13110092C22semidirect
20. C2×#13110090C22semidirect
32. #15692954C22semidirect
33. #15692954C22semidirect
34. #15692952C22semidirect
35. #15692952C22semidirect
36. #15692945C22semidirect
37. #15692945C22semidirect
38. #15692944C22semidirect
39. #15692944C22semidirect
40. #15692942C22semidirect
41. #15692942C22semidirect
42. #15692941C22semidirect
43. #15692941C22semidirect
198. C103#3191semidirect
200. #525D103semidirect

Maximal subgroups

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

subgroupindex
#202683022
#202681322
#202681292
#202681152
#202681122
#202680302
#202680252
#202680222
#202680182
#202679532
#202679512
#202679362
#202679342
C2×C22⋊(C103⋊C8)2
#525×C1032
#3191103