Finite Group Databasebeta

← #27205996

Subgroups — #27205996

Order 13184.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268369C211yesmaximal, characteristic, complemented
2#20268132C211yesmaximal, characteristic, complemented
3#20268115C211yesmaximal, characteristic, complemented
4#20268107C211yesmaximal, characteristic, complemented
5#20268102C211yesmaximal, characteristic, complemented
6#20268042C211yesmaximal, characteristic, complemented
7#20268035C211yesmaximal, characteristic, complemented
8#20268025C211yesmaximal, characteristic, complemented
9#20268018C211yesmaximal, characteristic, complemented
10#20267942C211yesmaximal, characteristic, complemented
11#20267934C211yesmaximal, characteristic, complemented
12#20267934C211yesmaximal, characteristic, complemented
13#20267925C211yesmaximal, characteristic, complemented
14#20267758C211yesmaximal, characteristic, complemented
15#535×C103C211yesmaximal, characteristic, complemented
16C2×#13110105C2211yescharacteristic, complemented
17C2×#13110093C2211yescharacteristic
18C2×#13110093C2211yescharacteristic
19C2×#13110090C2211yescharacteristic
20C2×#13110090C2211yescharacteristic
21C2×#13110089C2211yescharacteristic, complemented
22C22×C103⋊C8C2211yescharacteristic, complemented
23#15693000C2211yescharacteristic
24#15693000C2211yescharacteristic, complemented
25#15692997—21no—
26#15692995C2211yescharacteristic
27#15692995C2211yescharacteristic, complemented
28#15692993—21no—
29#15692993—21no—
30#15692992—21no—
31C2×C4⋊Dic103C2211yescharacteristic, complemented
32#15692954C2211yescharacteristic, complemented
33#15692954C2211yescharacteristic, complemented
34#15692952C2211yescharacteristic, complemented
35#15692952C2211yescharacteristic, complemented
36#15692944C2211yescharacteristic, complemented
37#15692944C2211yescharacteristic, complemented
38#15692942C2211yescharacteristic
39#15692942C2211yescharacteristic
40#15692942C2211yescharacteristic
41#15692942C2211yescharacteristic
42#15692941C2211yescharacteristic, complemented
43#15692941C2211yescharacteristic, complemented
44C22⋊(C103⋊C8)C2211yescharacteristic
45C22⋊(C103⋊C8)C2211yescharacteristic
46C22⋊(C103⋊C8)C2211yescharacteristic, complemented
47C22⋊(C103⋊C8)C2211yescharacteristic, complemented
48C2×#41×C103C2211yescharacteristic
49C22×D4×C103C2211yescharacteristic
50#127×C103—21no—
51#124×C103—21no—
52#121×C103C2211yescharacteristic
53#121×C103C2211yescharacteristic
54#121×C103C2211yescharacteristic
55#121×C103C2211yescharacteristic
56#120×C103—21no—
57#120×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—
66C22×Dic103—21no—
67C2×C4×D103—21no—
68#13110093—41no—
69#13110093—41no—
70#13110090—41no—
71#13110090—41no—
72#13110089—41no—
73C2×C103⋊C8—41no—
74C2×C103⋊C8C2311yescharacteristic
75C2×C103⋊C8C2311yescharacteristic
76C2×C103⋊C8C2311yescharacteristic
77C2×C103⋊C8C2311yescharacteristic
78C4⋊Dic103—21no—
79C4⋊Dic103C2311yescharacteristic
80C4⋊Dic103C2311yescharacteristic
81Dic103⋊C4—21no—
82Dic103⋊C4—21no—
83C22⋊Dic103—21no—
84C22⋊Dic103—21no—
85(C2×D103)⋊C4—21no—
86(C2×D103)⋊C4—21no—
87C24×C103—21no—
88#41×C103—41no—
89#41×C103—41no—
90C2×Q8×C103D411yescharacteristic
91C2×D4×C103—21no—
92C2×D4×C103—21no—
93C2×D4×C103—21no—
94C2×D4×C103—21no—
95C2×D4×C103—21no—
96C2×D4×C103—41no—
97C2×D4×C103—41no—
98C2×D4×C103D411yescharacteristic
99C2×D4×C103D411yescharacteristic
100C2×D4×C103D411yescharacteristic
101C2×D4×C103C2311yescharacteristic
102C2×D4×C103C2311yescharacteristic
103C22×C4×C103C2311yescharacteristic
104C22×C4×C103C2311yescharacteristic
105C22×C4×C103C2311yescharacteristic
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—21no—
115C23×C103—21no—
116C23×C103—42no—
117C23×C103—81no—
118C23×C103—81no—
119C23×C103C2×D411yescharacteristic
120C23×C103C2×D411yescharacteristic
121C23×C103C2×D411yescharacteristic
122C22×D103—21no—
123Q8×C103—41no—
124D4×C103—21no—
125D4×C103—21no—
126D4×C103—21no—
127D4×C103—21no—
128D4×C103—41no—
129D4×C103—41no—
130D4×C103—41no—
131D4×C103—42no—
132D4×C103—81no—
133D4×C103—81no—
134D4×C103—81no—
135D4×C103—81no—
136C2×C4×C103—21no—
137C2×C4×C103—21no—
138C2×C4×C103—21no—
139C2×C4×C103—21no—
140C2×C4×C103—21no—
141C2×C4×C103—21no—
142C2×C4×C103—21no—
143C2×C4×C103—21no—
144C2×C4×C103C2×D411yescharacteristic
145C2×C4×C103C2×D411yescharacteristic
146C2×C4×C103C2×D411yescharacteristic
147C2×C4×C103C2411yescharacteristic
148C22⋊D103—42no—
149C22⋊D103—81no—
150C22⋊D103—81no—
151C2×Dic103—21no—
152C2×Dic103—21no—
153C2×Dic103—21no—
154C2×Dic103—81no—
155D412—21no—
156D412—21no—
157C4×D103—42no—
158Dic206—21no—
159Dic206—21no—
160C103⋊C8—21no—
161C103⋊C8—21no—
162C103⋊C8—21no—
163C103⋊C8—21no—
164C22×C103—21no—
165C22×C103—21no—
166C22×C103—21no—
167C22×C103—21no—
168C22×C103—21no—
169C22×C103—21no—
170C22×C103—21no—
171C22×C103—21no—
172C22×C103—21no—
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—41no—
182C2×D103—41no—
183C2×D103—41no—
184C4×C103—21no—
185C4×C103—21no—
186C4×C103—21no—
187C4×C103—41no—
188C4×C103—41no—
189C4×C103H(5,𝔽2)11yescharacteristic
190C4×C103H(5,𝔽2)11yescharacteristic
191Dic103—41no—
192Dic103—41no—
193Dic103—41no—
194C2×C103—41no—
195C2×C103—41no—
196C2×C103—41no—
197C2×C103—81no—
198C2×C103—81no—
199C2×C103#53411yescharacteristic
200C2×C103#57611yescharacteristic
201C2×C103#57711yescharacteristic
202D103—81no—
203#3198—1031nomaximal, Sylow
204C103#319811yescharacteristic, complemented, Sylow
205#537—1031no—
206#535D10311yescharacteristic, complemented
207#485—1031no—
208#482—1031no—
209#481—1031no—
210#480—1031no—
211#469—1031no—
212#468—1031no—
213#466—1031no—
214#465—1031no—
215#450—1031no—
216#449—1031no—
217#449—1031no—
218#447—1031no—
219#408—1031no—
220C2×#41—1031no—
221C2×#41C2×D10311yescharacteristic
222C22×D4C2×D10311yescharacteristic
223C2×SD16—1031no—
224C2×SD16—1031no—
225C2×D8—1031no—
226C2×D8—1031no—
227C2×M16—1031no—
228C22×C8—1031no—
229#127—21no—
230#124—21no—
231C22⋊Q8—1031no—
232C22⋊Q8—1031no—
233C22⋊Q8—2061no—
234#121—1031no—
235#121—1031no—
236#121—2061no—
237#121—2061no—
238#121—2061no—
239#121C2×D10311yescharacteristic
240#121C2×D10311yescharacteristic
241#121C2×D10311yescharacteristic
242#121C2×D10311yescharacteristic
243#120—21no—
244#120—21no—
245#117C2×D10311yescharacteristic
246C2×C4⋊C4—1031no—
247#107—1031no—
248#107—1031no—
249#106—1031no—
250#106—1031no—
251#103—1031no—
252#103—1031no—
253#102—1031no—
254#102—1031no—
255#102—1031no—
256#102—1031no—
257#102—1031no—
258#102—1031no—
259C22⋊C8—1031no—
260C22⋊C8—1031no—
261C22⋊C8—1031no—
262C22⋊C8—1031no—
263C24—21no—
264#41—41no—
265#41—41no—
266#41—4121no—
267#41—4121no—
268C2×Q8—1031no—
269C2×Q8C22⋊D10311yescharacteristic
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—1031no—
278C2×D4—2061no—
279C2×D4—2061no—
280C2×D4—2061no—
281C2×D4C22⋊D10311yescharacteristic
282C2×D4C22⋊D10311yescharacteristic
283C2×D4C22⋊D10311yescharacteristic
284C2×D4C22×D10311yescharacteristic
285C2×D4C22×D10311yescharacteristic
286C22×C4—2061no—
287C22×C4—2061no—
288C22×C4C22×D10311yescharacteristic
289C22×C4C22×D10311yescharacteristic
290C22×C4C22×D10311yescharacteristic
291SD16—4121no—
292SD16—4121no—
293D8—4121no—
294D8—4121no—
295M16—4121no—
296C2×C8—1031no—
297C2×C8—1031no—
298C2×C8—1031no—
299C2×C8—1031no—
300C2×C8—4121no—
301C4⋊C4—1031no—
302C4⋊C4—1031no—
303C4⋊C4—2061no—
304C4⋊C4—2061no—
305C4⋊C4—2061no—
306C4⋊C4C22×D10311yescharacteristic
307C4⋊C4C22×D10311yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—21no—
313C22⋊C4—2061no—
314C22⋊C4—2061no—
315C22⋊C4—2061no—
316C22⋊C4—2061no—
317C42—21no—
318C23—21no—
319C23—21no—
320C23—42no—
321C23—81no—
322C23—81no—
323C23—2061no—
324C23C2×C22⋊D10311yescharacteristic
325C23C2×C22⋊D10311yescharacteristic
326C23C2×C22⋊D10311yescharacteristic
327Q8—41no—
328Q8—2061no—
329Q8—2061no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—41no—
335D4—41no—
336D4—41no—
337D4—42no—
338D4—81no—
339D4—81no—
340D4—81no—
341D4—81no—
342D4—8241no—
343D4—8241no—
344D4—4122no—
345D4—2061no—
346D4—2061no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—8241no—
356C2×C4—4122no—
357C2×C4—2061no—
358C2×C4—2061no—
359C2×C4—2061no—
360C2×C4C2×C22⋊D10311yescharacteristic
361C2×C4C2×C22⋊D10311yescharacteristic
362C2×C4C2×C22⋊D10311yescharacteristic
363C2×C4C23×D10311yescharacteristic
364C8—2061no—
365C8—2061no—
366C8—2061no—
367C8—2061no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—84no—
384C22—4121no—
385C22—4121no—
386C22—4121no—
387C22C22×C22⋊D10311yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—41no—
392C4—41no—
393C4—4121no—
394C4—4121no—
395C4—4121no—
396C4#1569306611yescharacteristic
397C4#1569306611yescharacteristic
398C2—41no—
399C2—41no—
400C2—41no—
401C2—81no—
402C2—81no—
403C2—8241no—
404C2#2026835011yescharacteristic
405C2#2026859411yescharacteristic
406C2#2026860211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#535×C103C2
socleC22×C103C22×D4
hypercenter#535D103
hypocenterC103#3198
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #20268369C2semidirect
2. #20268132C2semidirect
3. #20268115C2semidirect
4. #20268107C2semidirect
5. #20268102C2semidirect
6. #20268042C2semidirect
7. #20268035C2semidirect
8. #20268025C2semidirect
9. #20268018C2semidirect
10. #20267942C2semidirect
11. #20267934C2semidirect
12. #20267934C2semidirect
13. #20267925C2semidirect
14. #20267758C2semidirect
15. #535×C103C2semidirect
16. C2×#13110105C22semidirect
21. C2×#13110089C22semidirect
22. C22×C103⋊C8C22semidirect
24. #15693000C22semidirect
27. #15692995C22semidirect
31. C2×C4⋊Dic103C22semidirect
32. #15692954C22semidirect
33. #15692954C22semidirect
34. #15692952C22semidirect
35. #15692952C22semidirect
36. #15692944C22semidirect
37. #15692944C22semidirect
42. #15692941C22semidirect
43. #15692941C22semidirect
46. C22⋊(C103⋊C8)C22semidirect
47. C22⋊(C103⋊C8)C22semidirect
204. C103#3198semidirect
206. #535D103semidirect

Maximal subgroups

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

subgroupindex
#202683692
#202681322
#202681152
#202681072
#202681022
#202680422
#202680352
#202680252
#202680182
#202679422
#202679342
#202679252
#202677582
#535×C1032
#3198103