Finite Group Databasebeta

← #27206007

Subgroups — #27206007

Order 13184.

442 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268358C211yesmaximal, characteristic, complemented
2#20268357C211yesmaximal, characteristic, complemented
3#20268116C211yesmaximal, characteristic, complemented
4#20268114C211yesmaximal, characteristic, complemented
5#20268113C211yesmaximal, characteristic, complemented
6#20268112C211yesmaximal, characteristic, complemented
7#20268043C211yesmaximal, characteristic, complemented
8#20268041C211yesmaximal, characteristic, complemented
9#20268026C211yesmaximal, characteristic, complemented
10#20268024C211yesmaximal, characteristic, complemented
11#20267925C211yesmaximal, characteristic, complemented
12#20267923C211yesmaximal, characteristic, complemented
13#20267923C211yesmaximal, characteristic, complemented
14#20267756C211yesmaximal, characteristic, complemented
15#447×C103C211yesmaximal, characteristic, complemented
16C2×#13110105C2211yescharacteristic
17C2×D4×D103C2211yescharacteristic, complemented
18C2×#13110090C2211yescharacteristic
19C2×#13110090C2211yescharacteristic
20C2×#13110088C2211yescharacteristic, complemented
21C2×C8×D103C2211yescharacteristic, complemented
22#15693017—21no—
23#15693017—21no—
24#15693008—21no—
25#15693007—21no—
26#15692996C2211yescharacteristic, complemented
27#15692995C2211yescharacteristic
28#15692992C2211yescharacteristic
29#15692992C2211yescharacteristic
30#15692992C2211yescharacteristic, complemented
31#15692992C2211yescharacteristic, complemented
32#15692992C2211yescharacteristic, complemented
33#15692991—21no—
34#15692990—21no—
35#15692990—21no—
36#15692989—21no—
37#15692980C2211yescharacteristic, complemented
38#15692979C2211yescharacteristic, complemented
39#15692955C2211yescharacteristic, complemented
40#15692954C2211yescharacteristic, complemented
41#15692953C2211yescharacteristic, complemented
42#15692952C2211yescharacteristic, complemented
43#15692943C2211yescharacteristic, complemented
44#15692943C2211yescharacteristic, complemented
45#15692942C2211yescharacteristic, complemented
46#15692942C2211yescharacteristic, complemented
47#15692942C2211yescharacteristic, complemented
48#15692942C2211yescharacteristic, complemented
49C22⋊(C103⋊C8)C2211yescharacteristic, complemented
50(C2×D103)⋊C8C2211yescharacteristic, complemented
51(C2×D103)⋊C8C2211yescharacteristic, complemented
52C22×D4×C103C2211yescharacteristic, complemented
53C2×D8×C103C2211yescharacteristic
54C2×D8×C103C2211yescharacteristic
55#121×C103C2211yescharacteristic
56#102×C103C2211yescharacteristic, complemented
57#102×C103C2211yescharacteristic, complemented
58C22⋊C8×C103C2211yescharacteristic, complemented
59C23×D103—21no—
60#13110105—41no—
61#13110105—41no—
62C2×Dic206D411yescharacteristic
63C2×D412—21no—
64C2×D412D411yescharacteristic
65C2×D412C2311yescharacteristic
66C2×C22⋊D103—21no—
67C2×C22⋊D103—21no—
68C2×C22⋊D103—21no—
69C2×C22⋊D103—21no—
70C2×C22⋊D103—21no—
71C2×C22⋊D103—21no—
72C2×C22⋊D103—21no—
73C2×C22⋊D103D411yescharacteristic
74C2×C22⋊D103D411yescharacteristic
75D4×D103—41no—
76D4×D103—41no—
77C2×C4×D103C2311yescharacteristic
78C2×C4×D103C2311yescharacteristic
79#13110090—41no—
80#13110090—41no—
81#13110088—41no—
82C2×C103⋊C8C2311yescharacteristic
83C2×C103⋊C8C2311yescharacteristic
84C8×D103—41no—
85C4⋊Dic103C2311yescharacteristic
86C4⋊Dic103C2311yescharacteristic
87C4⋊Dic103C2311yescharacteristic
88C22⋊Dic103—21no—
89C22⋊Dic103—21no—
90C22⋊Dic103—21no—
91C22⋊Dic103—21no—
92C22⋊Dic103—21no—
93C22⋊Dic103—21no—
94(C2×D103)⋊C4—21no—
95(C2×D103)⋊C4—21no—
96(C2×D103)⋊C4—21no—
97C4×Dic103—21no—
98C4×Dic103—21no—
99C24×C103—21no—
100C2×D4×C103—21no—
101C2×D4×C103—21no—
102C2×D4×C103—41no—
103C2×D4×C103—41no—
104C2×D4×C103C2311yescharacteristic
105C2×D4×C103C2311yescharacteristic
106C2×D4×C103C2311yescharacteristic
107C22×C4×C103C2311yescharacteristic
108D8×C103—41no—
109D8×C103—41no—
110C2×C8×C103C2311yescharacteristic
111C2×C8×C103C2311yescharacteristic
112C4⋊C4×C103C2311yescharacteristic
113C22⋊C4×C103—21no—
114C23×C103—21no—
115C23×C103—21no—
116C23×C103—21no—
117C23×C103—42no—
118C23×C103—81no—
119C23×C103—81no—
120C23×C103C2×D411yescharacteristic
121C22×D103—21no—
122C22×D103—42no—
123C22×D103—81no—
124C22×D103—81no—
125C22×D103C2×D411yescharacteristic
126C22×D103C2×D411yescharacteristic
127D4×C103—21no—
128D4×C103—21no—
129D4×C103—21no—
130D4×C103—21no—
131D4×C103—21no—
132D4×C103—21no—
133D4×C103—42no—
134D4×C103—81no—
135C2×C4×C103—21no—
136C2×C4×C103—21no—
137C2×C4×C103—21no—
138C2×C4×C103C2×D411yescharacteristic
139C2×C4×C103C2411yescharacteristic
140C22⋊D103—41no—
141C22⋊D103—41no—
142C22⋊D103—42no—
143C22⋊D103—81no—
144C22⋊D103—81no—
145C22⋊D103—81no—
146C22⋊D103—81no—
147C22⋊D103—81no—
148C22⋊D103—81no—
149C2×Dic103—21no—
150C2×Dic103—21no—
151C2×Dic103—21no—
152C2×Dic103C2×D411yescharacteristic
153C2×Dic103C2×D411yescharacteristic
154D412—21no—
155D412—21no—
156D412—41no—
157D412—81no—
158C4×D103—21no—
159C4×D103—21no—
160C4×D103—21no—
161C4×D103—21no—
162Dic206—41no—
163C8×C103—21no—
164C8×C103—21no—
165C103⋊C8—21no—
166C103⋊C8—21no—
167C22×C103—21no—
168C22×C103—21no—
169C22×C103—21no—
170C22×C103—41no—
171C22×C103—41no—
172C22×C103—41no—
173C22×C103—41no—
174C22×C103—41no—
175C22×C103—41no—
176C22×C103—41no—
177C22×C103—41no—
178C22×C103—41no—
179C22×C103—84no—
180C22×C103C22×D411yescharacteristic
181C2×D103—21no—
182C2×D103—21no—
183C2×D103—21no—
184C2×D103—21no—
185C2×D103—21no—
186C2×D103—21no—
187C2×D103—41no—
188C2×D103—41no—
189C2×D103—41no—
190C2×D103—84no—
191C4×C103—21no—
192C4×C103—41no—
193C4×C103H(5,𝔽2)11yescharacteristic
194C4×C103H(5,𝔽2)11yescharacteristic
195Dic103—21no—
196Dic103—21no—
197Dic103—41no—
198Dic103—41no—
199Dic103—41no—
200C2×C103—41no—
201C2×C103—81no—
202C2×C103—81no—
203C2×C103—81no—
204C2×C103#53411yescharacteristic
205C2×C103#57611yescharacteristic
206C2×C103#57611yescharacteristic
207D103—41no—
208D103—41no—
209D103—81no—
210#3199—1031nomaximal, Sylow
211C103#319911yescharacteristic, complemented, Sylow
212#535—1031no—
213#535—1031no—
214#482—1031no—
215#482—1031no—
216#482—1031no—
217#482—1031no—
218#469—1031no—
219#469—1031no—
220#466—1031no—
221#466—1031no—
222#447—1031no—
223#447—1031no—
224#447—1031no—
225#447D10311yescharacteristic, complemented
226#408—1031no—
227C2×#41—1031no—
228C22×D4—1031no—
229C22×D4C2×D10311yescharacteristic, complemented
230C2×D8—1031no—
231C2×D8—1031no—
232C2×D8C2×D10311yescharacteristic
233C2×D8C2×D10311yescharacteristic
234C2×M16—1031no—
235C22×C8—1031no—
236#127—2061no—
237#127—2061no—
238#124—2061no—
239#124—2061no—
240#121—1031no—
241#121—1031no—
242#121—1031no—
243#121—1031no—
244#121—1031no—
245#121—1031no—
246#121—1031no—
247#121C2×D10311yescharacteristic
248#120—2061no—
249#120—2061no—
250#120—2061no—
251#120—2061no—
252#117—1031no—
253#117—1031no—
254#107—1031no—
255#107—1031no—
256#106—1031no—
257#106—1031no—
258#102—1031no—
259#102—1031no—
260#102—1031no—
261#102—1031no—
262#102—1031no—
263#102—1031no—
264#102C2×D10311yescharacteristic, complemented
265#102C2×D10311yescharacteristic, complemented
266C22⋊C8—1031no—
267C22⋊C8—1031no—
268C22⋊C8—1031no—
269C22⋊C8C2×D10311yescharacteristic, complemented
270C24—21no—
271C24—2061no—
272#41—4121no—
273#41—4121no—
274C2×Q8—1031no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—1031no—
280C2×D4—1031no—
281C2×D4—1031no—
282C2×D4—1031no—
283C2×D4—4121no—
284C2×D4—4121no—
285C2×D4—2061no—
286C2×D4—2061no—
287C2×D4—2061no—
288C2×D4—2061no—
289C2×D4—2061no—
290C2×D4—2061no—
291C2×D4—2061no—
292C2×D4—2061no—
293C2×D4C22×D10311yescharacteristic
294C2×D4C22×D10311yescharacteristic
295C2×D4C22×D10311yescharacteristic
296C22×C4—1031no—
297C22×C4—1031no—
298C22×C4C22×D10311yescharacteristic
299D8—41no—
300D8—41no—
301D8—4121no—
302D8—4121no—
303M16—4121no—
304C2×C8—1031no—
305C2×C8—1031no—
306C2×C8—4121no—
307C2×C8C22×D10311yescharacteristic
308C2×C8C22×D10311yescharacteristic
309C4⋊C4—1031no—
310C4⋊C4—1031no—
311C4⋊C4—1031no—
312C4⋊C4C22×D10311yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—2061no—
315C22⋊C4—2061no—
316C22⋊C4—2061no—
317C22⋊C4—2061no—
318C22⋊C4—2061no—
319C22⋊C4—2061no—
320C22⋊C4—2061no—
321C22⋊C4—2061no—
322C22⋊C4—2061no—
323C42—2061no—
324C42—2061no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—42no—
329C23—81no—
330C23—81no—
331C23—8241no—
332C23—8241no—
333C23—1031no—
334C23—1031no—
335C23—4122no—
336C23—2061no—
337C23D4×D10311yescharacteristic
338Q8—4121no—
339D4—21no—
340D4—21no—
341D4—21no—
342D4—21no—
343D4—21no—
344D4—21no—
345D4—42no—
346D4—81no—
347D4—8241no—
348D4—8241no—
349D4—8241no—
350D4—8241no—
351D4—8241no—
352D4—8241no—
353D4—8241no—
354D4—4121no—
355D4—4121no—
356D4—4121no—
357D4—4122no—
358D4—2061no—
359D4—2061no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—1031no—
364C2×C4—1031no—
365C2×C4—2061no—
366C2×C4—2061no—
367C2×C4—2061no—
368C2×C4—2061no—
369C2×C4—2061no—
370C2×C4—2061no—
371C2×C4—2061no—
372C2×C4D4×D10311yescharacteristic
373C2×C4C23×D10311yescharacteristic
374C8—21no—
375C8—21no—
376C8—2061no—
377C8—2061no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—84no—
391C22—8244no—
392C22—4121no—
393C22—4121no—
394C22—4121no—
395C22—2061no—
396C22—2061no—
397C22—2061no—
398C22—2061no—
399C22—2061no—
400C22—2061no—
401C22C2×D4×D10311yescharacteristic
402C4—21no—
403C4—41no—
404C4—4121no—
405C4—4121no—
406C4—4121no—
407C4—2061no—
408C4—2061no—
409C4#1569306611yescharacteristic
410C4#1569306611yescharacteristic
411C2—41no—
412C2—81no—
413C2—81no—
414C2—81no—
415C2—8241no—
416C2—4121no—
417C2—4121no—
418C2#2026835111yescharacteristic
419C2#2026859211yescharacteristic
420C2#2026859511yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#447×C103C2
socleC22×C103C22×D4
hypercenter#447D103
hypocenterC103#3199
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #20268358C2semidirect
2. #20268357C2semidirect
3. #20268116C2semidirect
4. #20268114C2semidirect
5. #20268113C2semidirect
6. #20268112C2semidirect
7. #20268043C2semidirect
8. #20268041C2semidirect
9. #20268026C2semidirect
10. #20268024C2semidirect
11. #20267925C2semidirect
12. #20267923C2semidirect
13. #20267923C2semidirect
14. #20267756C2semidirect
15. #447×C103C2semidirect
17. C2×D4×D103C22semidirect
20. C2×#13110088C22semidirect
21. C2×C8×D103C22semidirect
26. #15692996C22semidirect
30. #15692992C22semidirect
31. #15692992C22semidirect
32. #15692992C22semidirect
37. #15692980C22semidirect
38. #15692979C22semidirect
39. #15692955C22semidirect
40. #15692954C22semidirect
41. #15692953C22semidirect
42. #15692952C22semidirect
43. #15692943C22semidirect
44. #15692943C22semidirect
45. #15692942C22semidirect
46. #15692942C22semidirect
47. #15692942C22semidirect
48. #15692942C22semidirect
49. C22⋊(C103⋊C8)C22semidirect
50. (C2×D103)⋊C8C22semidirect
51. (C2×D103)⋊C8C22semidirect
52. C22×D4×C103C22semidirect
56. #102×C103C22semidirect
57. #102×C103C22semidirect
58. C22⋊C8×C103C22semidirect
211. C103#3199semidirect
225. #447D103semidirect
229. C22×D4C2×D103semidirect
264. #102C2×D103semidirect
265. #102C2×D103semidirect
269. C22⋊C8C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202683582
#202683572
#202681162
#202681142
#202681132
#202681122
#202680432
#202680412
#202680262
#202680242
#202679252
#202679232
#202677562
#447×C1032
#3199103