Finite Group Databasebeta

← #27205907

Subgroups — #27205907

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#20268298C211yesmaximal, characteristic, complemented
2#121×D103C211yesmaximal, characteristic, complemented
3#20268125C211yesmaximal, characteristic, complemented
4#20268116C211yesmaximal, characteristic, complemented
5#20268112C211yesmaximal, characteristic, complemented
6#20268108C211yesmaximal, characteristic, complemented
7#20268026C211yesmaximal, characteristic, complemented
8#20268024C211yesmaximal, characteristic, complemented
9#20268023C211yesmaximal, characteristic, complemented
10#20268017C211yesmaximal, characteristic, complemented
11#20267940C211yesmaximal, characteristic, complemented
12#20267936C211yesmaximal, characteristic, complemented
13#20267923C211yesmaximal, characteristic, complemented
14C22⋊C8×D103C211yesmaximal, characteristic, complemented
15#449×C103C211yesmaximal, characteristic, complemented
16C2×D4×D103—21no—
17C2×D4×D103C2211yescharacteristic
18C22×C4×D103C2211yescharacteristic
19C2×#13110092C2211yescharacteristic, complemented
20C2×#13110090C2211yescharacteristic, complemented
21C2×C8×D103C2211yescharacteristic, complemented
22C2×C8×D103C2211yescharacteristic, complemented
23#15693002—21no—
24#15692997C2211yescharacteristic
25#15692997C2211yescharacteristic, complemented
26#15692996C2211yescharacteristic
27#15692995C2211yescharacteristic
28#15692994—21no—
29#15692993—21no—
30#15692992C2211yescharacteristic
31#15692992C2211yescharacteristic
32#15692992C2211yescharacteristic, complemented
33#15692989—21no—
34C4×C22⋊D103—21no—
35C4×C22⋊D103—21no—
36#15692980C2211yescharacteristic, complemented
37C4⋊C4×D103C2211yescharacteristic
38C22⋊C4×D103—21no—
39#15692955C2211yescharacteristic, complemented
40#15692954C2211yescharacteristic, complemented
41#15692953C2211yescharacteristic, complemented
42#15692952C2211yescharacteristic, complemented
43#15692945C2211yescharacteristic, complemented
44#15692943C2211yescharacteristic, complemented
45#15692943C2211yescharacteristic, complemented
46#15692942C2211yescharacteristic, complemented
47#15692942C2211yescharacteristic, complemented
48#15692942C2211yescharacteristic, complemented
49C22⋊(C103⋊C8)C2211yescharacteristic, complemented
50(C2×D103)⋊C8C2211yescharacteristic
51(C2×D103)⋊C8C2211yescharacteristic
52C2×#41×C103C2211yescharacteristic, complemented
53C2×SD16×C103C2211yescharacteristic, complemented
54C2×D8×C103C2211yescharacteristic, complemented
55#121×C103C2211yescharacteristic
56#103×C103C2211yescharacteristic, complemented
57#102×C103C2211yescharacteristic, complemented
58C22⋊C8×C103C2211yescharacteristic, complemented
59C23×D103—21no—
60C23×D103D411yescharacteristic
61C2×D412—21no—
62C2×D412C2311yescharacteristic
63C2×C22⋊D103—21no—
64C2×C22⋊D103—21no—
65C2×C22⋊D103—21no—
66C2×C22⋊D103—21no—
67C2×C22⋊D103—21no—
68D4×D103—41no—
69D4×D103—41no—
70D4×D103—44no—
71C22×Dic103D411yescharacteristic
72C2×C4×D103—21no—
73C2×C4×D103—41no—
74C2×C4×D103—41no—
75C2×C4×D103D411yescharacteristic
76C2×C4×D103D411yescharacteristic
77C2×C4×D103C2311yescharacteristic
78C2×C4×D103C2311yescharacteristic
79#13110092—41no—
80#13110090—41no—
81C2×C103⋊C8C2311yescharacteristic
82C2×C103⋊C8C2311yescharacteristic
83C8×D103—41no—
84C8×D103—41no—
85C4⋊Dic103C2311yescharacteristic
86C4⋊Dic103C2311yescharacteristic
87C4⋊Dic103C2311yescharacteristic
88Dic103⋊C4—21no—
89Dic103⋊C4—21no—
90Dic103⋊C4—21no—
91C22⋊Dic103—21no—
92C22⋊Dic103—21no—
93C22⋊Dic103—21no—
94C22⋊Dic103—21no—
95(C2×D103)⋊C4—21no—
96(C2×D103)⋊C4—21no—
97(C2×D103)⋊C4—21no—
98(C2×D103)⋊C4—21no—
99C4×Dic103—21no—
100#41×C103—41no—
101#41×C103—41no—
102C2×Q8×C103C2311yescharacteristic
103C2×D4×C103—21no—
104C2×D4×C103—21no—
105C2×D4×C103C2311yescharacteristic
106C2×D4×C103C2311yescharacteristic
107C22×C4×C103—21no—
108C22×C4×C103C2311yescharacteristic
109SD16×C103—41no—
110D8×C103—41no—
111C2×C8×C103C2311yescharacteristic
112C2×C8×C103C2311yescharacteristic
113C4⋊C4×C103C2311yescharacteristic
114C22⋊C4×C103—21no—
115C23×C103—21no—
116C23×C103—21no—
117C23×C103C2×D411yescharacteristic
118C22×D103—22no—
119C22×D103—22no—
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—21no—
132D4×C103—21no—
133D4×C103—42no—
134D4×C103—42no—
135C2×C4×C103—21no—
136C2×C4×C103—21no—
137C2×C4×C103—21no—
138C2×C4×C103—21no—
139C2×C4×C103—42no—
140C2×C4×C103C2×D411yescharacteristic
141C2×C4×C103C2411yescharacteristic
142C22⋊D103—42no—
143C22⋊D103—42no—
144C22⋊D103—42no—
145C22⋊D103—42no—
146C22⋊D103—42no—
147C2×Dic103—21no—
148C2×Dic103—21no—
149C2×Dic103—21no—
150C2×Dic103—41no—
151C2×Dic103C2×D411yescharacteristic
152C2×Dic103C2×D411yescharacteristic
153D412—21no—
154D412—21no—
155D412—42no—
156C4×D103—21no—
157C4×D103—21no—
158C4×D103—21no—
159C4×D103—21no—
160C4×D103—41no—
161C4×D103—41no—
162C4×D103—42no—
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×C103C22×D411yescharacteristic
177C2×D103—21no—
178C2×D103—21no—
179C2×D103—21no—
180C2×D103—21no—
181C2×D103—44no—
182C2×D103—41no—
183C2×D103—41no—
184C2×D103—41no—
185C2×D103—84no—
186C2×D103#13512yes—
187C2×D103AGL(1,ℤ/8)12yes—
188C4×C103—21no—
189C4×C103—41no—
190C4×C103—41no—
191C4×C103H(5,𝔽2)11yescharacteristic
192C4×C103H(5,𝔽2)11yescharacteristic
193Dic103—21no—
194Dic103—21no—
195Dic103—41no—
196Dic103—41no—
197Dic103—41no—
198C2×C103—41no—
199C2×C103—81no—
200C2×C103—81no—
201C2×C103#53411yescharacteristic
202C2×C103C2×#13511yescharacteristic
203C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
204D103—22no—
205D103—22no—
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#465—1031no—
219#450—1031no—
220#449—1031no—
221#449D10311yescharacteristic, complemented
222#447—1031no—
223C2×C22⋊C8—1031no—
224C2×#41C2×D10311yescharacteristic, complemented
225C22×D4—1031no—
226C22×D4—2061no—
227C23×C4—1031no—
228C2×SD16—1031no—
229C2×SD16C2×D10311yescharacteristic, complemented
230C2×D8—1031no—
231C2×D8C2×D10311yescharacteristic, complemented
232C22×C8—1031no—
233C22×C8—1031no—
234#123—2061no—
235C22⋊Q8—1031no—
236C22⋊Q8—1031no—
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#106—1031no—
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⋊C8C2×D10311yescharacteristic, complemented
267C24—1031no—
268C24—2061no—
269#41—41no—
270#41—41no—
271C2×Q8C22×D10311yescharacteristic
272C2×D4—21no—
273C2×D4—21no—
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×D4C22×D10311yescharacteristic
285C2×D4C22×D10311yescharacteristic
286C22×C4—21no—
287C22×C4—1031no—
288C22×C4—1031no—
289C22×C4—1031no—
290C22×C4—1031no—
291C22×C4—1031no—
292C22×C4—4121no—
293C22×C4—4121no—
294C22×C4—2061no—
295C22×C4C22×D10311yescharacteristic
296SD16—41no—
297SD16—4121no—
298D8—41no—
299D8—4121no—
300C2×C8—1031no—
301C2×C8—1031no—
302C2×C8—4121no—
303C2×C8—4121no—
304C2×C8C22×D10311yescharacteristic
305C2×C8C22×D10311yescharacteristic
306C4⋊C4—1031no—
307C4⋊C4—1031no—
308C4⋊C4—1031no—
309C4⋊C4—2061no—
310C4⋊C4—2061no—
311C4⋊C4—2061no—
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—
322C42—2061no—
323C23—21no—
324C23—21no—
325C23—1031no—
326C23—1031no—
327C23—4121no—
328C23—4122no—
329C23—4122no—
330C23—4122no—
331C23—2062no—
332C23—2062no—
333C23—2061no—
334C23D4×D10311yescharacteristic
335Q8—21no—
336Q8—21no—
337D4—21no—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—42no—
342D4—42no—
343D4—4122no—
344D4—4122no—
345D4—4122no—
346D4—4122no—
347D4—4122no—
348D4—4122no—
349D4—2061no—
350D4—2061no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—42no—
356C2×C4—1031no—
357C2×C4—1031no—
358C2×C4—4121no—
359C2×C4—4121no—
360C2×C4—4122no—
361C2×C4—4121no—
362C2×C4—2061no—
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—21no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—8244no—
385C22—1032no—
386C22—1032no—
387C22—4124no—
388C22—4121no—
389C22—4121no—
390C22—4121no—
391C22—2061no—
392C22—2061no—
393C22—2061no—
394C22—2061no—
395C22C2×D4×D10311yescharacteristic
396C4—21no—
397C4—41no—
398C4—41no—
399C4—4121no—
400C4—4121no—
401C4—4121no—
402C4—2061no—
403C4—2061no—
404C4#1569306611yescharacteristic
405C4#1569306611yescharacteristic
406C2—41no—
407C2—81no—
408C2—81no—
409C2—8241no—
410C2—2062no—
411C2—2062no—
412C2#2026835111yescharacteristic
413C2#135×D10311yescharacteristic
414C2AGL(1,ℤ/8)×D10311yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#449×C103C2
socleC22×C103C22×D4
hypercenter#449D103
hypocenterC103#3188
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #20268298C2semidirect
2. #121×D103C2semidirect
3. #20268125C2semidirect
4. #20268116C2semidirect
5. #20268112C2semidirect
6. #20268108C2semidirect
7. #20268026C2semidirect
8. #20268024C2semidirect
9. #20268023C2semidirect
10. #20268017C2semidirect
11. #20267940C2semidirect
12. #20267936C2semidirect
13. #20267923C2semidirect
14. C22⋊C8×D103C2semidirect
15. #449×C103C2semidirect
19. C2×#13110092C22semidirect
20. C2×#13110090C22semidirect
21. C2×C8×D103C22semidirect
22. C2×C8×D103C22semidirect
25. #15692997C22semidirect
32. #15692992C22semidirect
36. #15692980C22semidirect
39. #15692955C22semidirect
40. #15692954C22semidirect
41. #15692953C22semidirect
42. #15692952C22semidirect
43. #15692945C22semidirect
44. #15692943C22semidirect
45. #15692943C22semidirect
46. #15692942C22semidirect
47. #15692942C22semidirect
48. #15692942C22semidirect
49. C22⋊(C103⋊C8)C22semidirect
52. C2×#41×C103C22semidirect
53. C2×SD16×C103C22semidirect
54. C2×D8×C103C22semidirect
56. #103×C103C22semidirect
57. #102×C103C22semidirect
58. C22⋊C8×C103C22semidirect
208. C103#3188semidirect
221. #449D103semidirect
224. C2×#41C2×D103semidirect
229. C2×SD16C2×D103semidirect
231. C2×D8C2×D103semidirect
256. #103C2×D103semidirect
262. #102C2×D103semidirect
266. C22⋊C8C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202682982
#121×D1032
#202681252
#202681162
#202681122
#202681082
#202680262
#202680242
#202680232
#202680172
#202679402
#202679362
#202679232
C22⋊C8×D1032
#449×C1032
#3188103