Finite Group Databasebeta

← #27205910

Subgroups — #27205910

Order 13184.

472 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268304C211yesmaximal, characteristic, complemented
2#121×D103C211yesmaximal, characteristic, complemented
3#20268125C211yesmaximal, characteristic, complemented
4#20268117C211yesmaximal, characteristic, complemented
5#20268113C211yesmaximal, characteristic, complemented
6#20268111C211yesmaximal, characteristic, complemented
7#20268027C211yesmaximal, characteristic, complemented
8#20268025C211yesmaximal, characteristic, complemented
9#20268022C211yesmaximal, characteristic, complemented
10#20267940C211yesmaximal, characteristic, complemented
11#20267939C211yesmaximal, characteristic, complemented
12#20267935C211yesmaximal, characteristic, complemented
13#20267926C211yesmaximal, characteristic, complemented
14C2×(C2×D103)⋊C8C211yesmaximal, characteristic, complemented
15#465×C103C211yesmaximal, characteristic, complemented
16C2×#13110106C2211yescharacteristic, complemented
17C2×D4×D103—21no—
18C2×D4×D103C2211yescharacteristic
19C22×C4×D103C2211yescharacteristic
20C2×#13110092C2211yescharacteristic, complemented
21C2×D824C2211yescharacteristic, complemented
22C2×#13110090C2211yescharacteristic, complemented
23C22×C103⋊C8C2211yescharacteristic, complemented
24#15693006—21no—
25#15692997C2211yescharacteristic
26#15692996C2211yescharacteristic
27#15692996C2211yescharacteristic
28#15692995C2211yescharacteristic
29#15692995C2211yescharacteristic, complemented
30#15692994—21no—
31#15692993—21no—
32#15692992C2211yescharacteristic
33#15692991—21no—
34#15692983—21no—
35(C22⋊D103)⋊C4—21no—
36#15692979C2211yescharacteristic, complemented
37C4⋊C4×D103C2211yescharacteristic
38C22⋊C4×D103—21no—
39#15692955C2211yescharacteristic, complemented
40#15692954C2211yescharacteristic, complemented
41#15692952C2211yescharacteristic, complemented
42#15692945C2211yescharacteristic, complemented
43#15692943C2211yescharacteristic, complemented
44#15692943C2211yescharacteristic, complemented
45#15692942C2211yescharacteristic, complemented
46#15692941C2211yescharacteristic, complemented
47#15692941C2211yescharacteristic, complemented
48(C2×D103)⋊C8C2211yescharacteristic
49(C2×D103)⋊C8C2211yescharacteristic
50(C2×D103)⋊C8C2211yescharacteristic, complemented
51(C2×D103)⋊C8C2211yescharacteristic, complemented
52C2×SD16×C103C2211yescharacteristic, complemented
53C22×C8×C103C2211yescharacteristic, complemented
54C22⋊Q8×C103C2211yescharacteristic, complemented
55#121×C103C2211yescharacteristic
56#106×C103C2211yescharacteristic, complemented
57#103×C103C2211yescharacteristic, complemented
58#102×C103C2211yescharacteristic, complemented
59C23×D103—21no—
60C23×D103D411yescharacteristic
61#13110106—41no—
62#13110106—41no—
63C2×D412—21no—
64C2×D412—21no—
65C2×D412—21no—
66C2×D412C2311yescharacteristic
67C2×D412C2311yescharacteristic
68C2×C22⋊D103—21no—
69C2×C22⋊D103—21no—
70C2×C22⋊D103—21no—
71C2×C22⋊D103—21no—
72D4×D103—41no—
73D4×D103—41no—
74D4×D103—44no—
75C22×Dic103D411yescharacteristic
76C2×C4×D103—21no—
77C2×C4×D103—21no—
78C2×C4×D103—41no—
79C2×C4×D103—41no—
80C2×C4×D103D411yescharacteristic
81C2×C4×D103D411yescharacteristic
82C2×C4×D103C2311yescharacteristic
83C2×C4×D103C2311yescharacteristic
84#13110092—41no—
85D824—41no—
86#13110090—41no—
87C2×C103⋊C8—41no—
88C2×C103⋊C8C2311yescharacteristic
89C2×C103⋊C8C2311yescharacteristic
90C4⋊Dic103C2311yescharacteristic
91C4⋊Dic103C2311yescharacteristic
92Dic103⋊C4—21no—
93Dic103⋊C4—21no—
94C22⋊Dic103—21no—
95(C2×D103)⋊C4—21no—
96(C2×D103)⋊C4—21no—
97(C2×D103)⋊C4—21no—
98(C2×D103)⋊C4—21no—
99(C2×D103)⋊C4—21no—
100(C2×D103)⋊C4—21no—
101C4×Dic103—21no—
102C2×Q8×C103C2311yescharacteristic
103C2×D4×C103—21no—
104C2×D4×C103C2311yescharacteristic
105C22×C4×C103C2311yescharacteristic
106SD16×C103—41no—
107C2×C8×C103—41no—
108C2×C8×C103C2311yescharacteristic
109C2×C8×C103C2311yescharacteristic
110C4⋊C4×C103—21no—
111C4⋊C4×C103C2311yescharacteristic
112C4⋊C4×C103C2311yescharacteristic
113C22⋊C4×C103—21no—
114C22⋊C4×C103—21no—
115C23×C103—21no—
116C23×C103C2×D411yescharacteristic
117C22×D103—22no—
118C22×D103—22no—
119C22×D103—21no—
120C22×D103—21no—
121C22×D103—41no—
122C22×D103—42no—
123C22×D103—42no—
124C22×D103—42no—
125C22×D103C2×D411yescharacteristic
126C22×D103C2×D411yescharacteristic
127Q8×C103—21no—
128Q8×C103—21no—
129D4×C103—21no—
130D4×C103—21no—
131D4×C103—42no—
132C2×C4×C103—21no—
133C2×C4×C103—21no—
134C2×C4×C103—21no—
135C2×C4×C103—21no—
136C2×C4×C103—21no—
137C2×C4×C103C2×D411yescharacteristic
138C2×C4×C103C2411yescharacteristic
139C22⋊D103—42no—
140C22⋊D103—42no—
141C22⋊D103—42no—
142C22⋊D103—42no—
143C2×Dic103—21no—
144C2×Dic103—21no—
145C2×Dic103—41no—
146C2×Dic103C2×D411yescharacteristic
147C2×Dic103C2×D411yescharacteristic
148D412—21no—
149D412—21no—
150D412—21no—
151D412—21no—
152D412—42no—
153D412—42no—
154D412—42no—
155C4×D103—21no—
156C4×D103—21no—
157C4×D103—21no—
158C4×D103—21no—
159C4×D103—41no—
160C4×D103—41no—
161C4×D103—42no—
162C4×D103—42no—
163C8×C103—21no—
164C8×C103—21no—
165C103⋊C8—21no—
166C103⋊C8—21no—
167C22×C103—21no—
168C22×C103—21no—
169C22×C103—41no—
170C22×C103—41no—
171C22×C103—41no—
172C22×C103AGL(1,ℤ/8)12yes—
173C22×C103C22×D411yescharacteristic
174C2×D103—21no—
175C2×D103—21no—
176C2×D103—21no—
177C2×D103—21no—
178C2×D103—21no—
179C2×D103—44no—
180C2×D103—41no—
181C2×D103—41no—
182C2×D103—41no—
183C2×D103—41no—
184C2×D103—41no—
185C2×D103—41no—
186C2×D103—84no—
187C2×D103#13512yes—
188C4×C103—21no—
189C4×C103—41no—
190C4×C103—41no—
191C4×C103—41no—
192C4×C103H(5,𝔽2)11yescharacteristic
193C4×C103H(5,𝔽2)11yescharacteristic
194Dic103—21no—
195Dic103—21no—
196Dic103—41no—
197Dic103—41no—
198C2×C103—22no—
199C2×C103—81no—
200C2×C103#53411yescharacteristic
201C2×C103C2×#13511yescharacteristic
202C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
203D103—22no—
204D103—41no—
205D103—81no—
206D103—81no—
207#3188—1031nomaximal, Sylow
208C103#318811yescharacteristic, complemented, Sylow
209#525—1031no—
210C2×#121—1031no—
211#484—1031no—
212#482—1031no—
213#482—1031no—
214#481—1031no—
215#466—1031no—
216#466—1031no—
217#465—1031no—
218#465D10311yescharacteristic, complemented
219#450—1031no—
220#449—1031no—
221#449—1031no—
222#447—1031no—
223C2×C22⋊C8—1031no—
224C2×#41—1031no—
225C22×D4—1031no—
226C22×D4—2061no—
227C23×C4—1031no—
228C2×SD16—1031no—
229C2×SD16C2×D10311yescharacteristic, complemented
230C2×D8—1031no—
231C2×D8—1031no—
232C22×C8—1031no—
233C22×C8C2×D10311yescharacteristic, complemented
234#123—2061no—
235C22⋊Q8—1031no—
236C22⋊Q8C2×D10311yescharacteristic, complemented
237#121—1031no—
238#121—1031no—
239#121—1031no—
240#121—1031no—
241#121—1031no—
242#121—2061no—
243#121—2061no—
244#121C2×D10311yescharacteristic
245#120—2061no—
246C4×D4—2061no—
247C4×D4—2061no—
248#117—1031no—
249C2×C4⋊C4—1031no—
250C2×C22⋊C4—2061no—
251#107—1031no—
252#107—1031no—
253#106—1031no—
254#106C2×D10311yescharacteristic, complemented
255#103—1031no—
256#103C2×D10311yescharacteristic, complemented
257#102—1031no—
258#102—1031no—
259#102—1031no—
260#102—1031no—
261#102—1031no—
262#102C2×D10311yescharacteristic, complemented
263C22⋊C8—1031no—
264C22⋊C8—1031no—
265C22⋊C8—1031no—
266C22⋊C8—1031no—
267C24—1031no—
268C24—2061no—
269#41—4121no—
270#41—4121no—
271C2×Q8C22×D10311yescharacteristic
272C2×D4—21no—
273C2×D4—1031no—
274C2×D4—1031no—
275C2×D4—4124no—
276C2×D4—4121no—
277C2×D4—4121no—
278C2×D4—2061no—
279C2×D4—2061no—
280C2×D4—2061no—
281C2×D4—2061no—
282C2×D4—2061no—
283C2×D4—2061no—
284C2×D4—2061no—
285C2×D4C22×D10311yescharacteristic
286C22×C4—1031no—
287C22×C4—1031no—
288C22×C4—1031no—
289C22×C4—1031no—
290C22×C4—1031no—
291C22×C4—4121no—
292C22×C4—4121no—
293C22×C4—2061no—
294C22×C4—2061no—
295C22×C4C22×D10311yescharacteristic
296SD16—41no—
297SD16—4121no—
298D8—4121no—
299D8—4121no—
300C2×C8—41no—
301C2×C8—1031no—
302C2×C8—1031no—
303C2×C8—4121no—
304C2×C8C22×D10311yescharacteristic
305C2×C8C22×D10311yescharacteristic
306C4⋊C4—21no—
307C4⋊C4—1031no—
308C4⋊C4—1031no—
309C4⋊C4—2061no—
310C4⋊C4—2061no—
311C4⋊C4C22×D10311yescharacteristic
312C4⋊C4C22×D10311yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—2061no—
316C22⋊C4—2061no—
317C22⋊C4—2061no—
318C22⋊C4—2061no—
319C22⋊C4—2061no—
320C22⋊C4—2061no—
321C22⋊C4—2061no—
322C42—2061no—
323C23—21no—
324C23—1031no—
325C23—1031no—
326C23—4121no—
327C23—4122no—
328C23—4122no—
329C23—4122no—
330C23—2062no—
331C23—2061no—
332C23—2061no—
333C23—2062no—
334C23D4×D10311yescharacteristic
335Q8—21no—
336Q8—21no—
337D4—21no—
338D4—21no—
339D4—42no—
340D4—4122no—
341D4—4122no—
342D4—4122no—
343D4—4122no—
344D4—4122no—
345D4—4122no—
346D4—4122no—
347D4—2061no—
348D4—2061no—
349D4—2061no—
350D4—2061no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—1031no—
357C2×C4—1031no—
358C2×C4—4121no—
359C2×C4—4121no—
360C2×C4—4122no—
361C2×C4—4122no—
362C2×C4—4121no—
363C2×C4—2061no—
364C2×C4—2061no—
365C2×C4—2061no—
366C2×C4—2061no—
367C2×C4—2061no—
368C2×C4—2061no—
369C2×C4D4×D10311yescharacteristic
370C2×C4C23×D10311yescharacteristic
371C8—21no—
372C8—21no—
373C8—2061no—
374C8—2061no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—8244no—
381C22—1032no—
382C22—4124no—
383C22—4121no—
384C22—4121no—
385C22—4121no—
386C22—4121no—
387C22—4121no—
388C22—4121no—
389C22—2061no—
390C22—2061no—
391C22—2061no—
392C22—2061no—
393C22—2061no—
394C22#1569304812yes—
395C22C2×D4×D10311yescharacteristic
396C4—21no—
397C4—41no—
398C4—41no—
399C4—41no—
400C4—4121no—
401C4—4121no—
402C4—2061no—
403C4—2061no—
404C4#1569306611yescharacteristic
405C4#1569306711yescharacteristic
406C2—22no—
407C2—81no—
408C2—8241no—
409C2—8241no—
410C2—4121no—
411C2—2062no—
412C2#2026834911yescharacteristic
413C2#135×D10311yescharacteristic
414C2C2×#1569304811yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#465×C103C2
socleC22×C103C22×D4
hypercenter#465D103
hypocenterC103#3188
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #20268304C2semidirect
2. #121×D103C2semidirect
3. #20268125C2semidirect
4. #20268117C2semidirect
5. #20268113C2semidirect
6. #20268111C2semidirect
7. #20268027C2semidirect
8. #20268025C2semidirect
9. #20268022C2semidirect
10. #20267940C2semidirect
11. #20267939C2semidirect
12. #20267935C2semidirect
13. #20267926C2semidirect
14. C2×(C2×D103)⋊C8C2semidirect
15. #465×C103C2semidirect
16. C2×#13110106C22semidirect
20. C2×#13110092C22semidirect
21. C2×D824C22semidirect
22. C2×#13110090C22semidirect
23. C22×C103⋊C8C22semidirect
29. #15692995C22semidirect
36. #15692979C22semidirect
39. #15692955C22semidirect
40. #15692954C22semidirect
41. #15692952C22semidirect
42. #15692945C22semidirect
43. #15692943C22semidirect
44. #15692943C22semidirect
45. #15692942C22semidirect
46. #15692941C22semidirect
47. #15692941C22semidirect
50. (C2×D103)⋊C8C22semidirect
51. (C2×D103)⋊C8C22semidirect
52. C2×SD16×C103C22semidirect
53. C22×C8×C103C22semidirect
54. C22⋊Q8×C103C22semidirect
56. #106×C103C22semidirect
57. #103×C103C22semidirect
58. #102×C103C22semidirect
208. C103#3188semidirect
218. #465D103semidirect
229. C2×SD16C2×D103semidirect
233. C22×C8C2×D103semidirect
236. C22⋊Q8C2×D103semidirect
254. #106C2×D103semidirect
256. #103C2×D103semidirect
262. #102C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202683042
#121×D1032
#202681252
#202681172
#202681132
#202681112
#202680272
#202680252
#202680222
#202679402
#202679392
#202679352
#202679262
C2×(C2×D103)⋊C82
#465×C1032
#3188103