Finite Group Databasebeta

← #27206987

Subgroups — #27206987

Order 13184.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268488C211yesmaximal, characteristic, complemented
2#20268429C211yesmaximal, characteristic, complemented
3#20268147C211yesmaximal, characteristic, complemented
4#20268125C211yesmaximal, characteristic, complemented
5#20268116C211yesmaximal, characteristic, complemented
6#20268093C211yesmaximal, characteristic, complemented
7#20268025C211yesmaximal, characteristic, complemented
8#20268017C211yesmaximal, characteristic, complemented
9#20268008C211yesmaximal, characteristic, complemented
10#20267923C211yesmaximal, characteristic, complemented
11D8×Dic103C211yesmaximal, characteristic, complemented
12(C22⋊D103)⋊C8C211yesmaximal, characteristic, complemented
13#20267787C211yesmaximal, characteristic, complemented
14#102×D103C211yesmaximal, characteristic, complemented
15#449×C103C211yesmaximal, characteristic, complemented
16C2×D4×D103C2211yescharacteristic
17C2×#13110090C2211yescharacteristic
18C22×C103⋊C8C2211yescharacteristic, complemented
19C2×C8×D103C2211yescharacteristic
20#15693014—21no—
21#15693012C2211yescharacteristic, complemented
22#15693010C2211yescharacteristic
23#15693004—21no—
24#15693002—21no—
25#15692997C2211yescharacteristic
26#15692995C2211yescharacteristic
27#15692993—21no—
28#15692992—21no—
29#15692992C2211yescharacteristic
30#15692989—21no—
31D4×Dic103C2211yescharacteristic
32D4×Dic103C2211yescharacteristic, complemented
33C4×C22⋊D103C2211yescharacteristic
34(C22⋊D103)⋊C4—21no—
35#15692980C2211yescharacteristic, complemented
36C4⋊C4×D103C2211yescharacteristic
37C2×(C2×D103)⋊C4—21no—
38#15692955C2211yescharacteristic, complemented
39#15692954C2211yescharacteristic, complemented
40#15692953C2211yescharacteristic, complemented
41Dic103⋊C8C2211yescharacteristic, complemented
42#15692945C2211yescharacteristic, complemented
43#15692945C2211yescharacteristic, complemented
44#15692943C2211yescharacteristic
45#15692943C2211yescharacteristic
46#15692942C2211yescharacteristic
47#15692942C2211yescharacteristic
48#15692942C2211yescharacteristic, complemented
49#15692941C2211yescharacteristic
50(C2×D103)⋊C8C2211yescharacteristic
51C8×Dic103C2211yescharacteristic, complemented
52C2×#41×C103C2211yescharacteristic
53C2×SD16×C103C2211yescharacteristic, complemented
54C2×D8×C103C2211yescharacteristic
55#121×C103C2211yescharacteristic, complemented
56#103×C103C2211yescharacteristic, complemented
57#102×C103C2211yescharacteristic
58C22⋊C8×C103C2211yescharacteristic, complemented
59C23×D103—21no—
60C2×D412C2311yescharacteristic
61C2×C22⋊D103—21no—
62C2×C22⋊D103—21no—
63C2×C22⋊D103—21no—
64C2×C22⋊D103D411yescharacteristic
65D4×D103—22no—
66D4×D103—41no—
67C22×Dic103—21no—
68C22×Dic103—21no—
69C2×C4×D103—21no—
70C2×C4×D103C2311yescharacteristic
71#13110090—41no—
72C2×C103⋊C8—41no—
73C2×C103⋊C8C2311yescharacteristic
74C2×C103⋊C8C2311yescharacteristic
75C8×D103—41no—
76C4⋊Dic103—21no—
77C4⋊Dic103C2311yescharacteristic
78C4⋊Dic103C2311yescharacteristic
79C4⋊Dic103C2311yescharacteristic
80Dic103⋊C4—21no—
81Dic103⋊C4—21no—
82Dic103⋊C4—21no—
83Dic103⋊C4D411yescharacteristic
84C22⋊Dic103—21no—
85C22⋊Dic103—21no—
86C22⋊Dic103—21no—
87C22⋊Dic103—21no—
88C22⋊Dic103D411yescharacteristic
89(C2×D103)⋊C4—21no—
90(C2×D103)⋊C4—21no—
91(C2×D103)⋊C4—21no—
92(C2×D103)⋊C4—21no—
93(C2×D103)⋊C4D411yescharacteristic
94C4×Dic103—21no—
95C4×Dic103C2311yescharacteristic
96#41×C103—22no—
97#41×C103—41no—
98C2×Q8×C103C2311yescharacteristic
99C2×D4×C103—21no—
100C2×D4×C103—21no—
101C2×D4×C103C2311yescharacteristic
102C2×D4×C103C2311yescharacteristic
103C22×C4×C103—21no—
104C22×C4×C103C2311yescharacteristic
105SD16×C103—41no—
106D8×C103—22no—
107C2×C8×C103C2311yescharacteristic
108C2×C8×C103C2311yescharacteristic
109C4⋊C4×C103C2311yescharacteristic
110C22⋊C4×C103—21no—
111C23×C103—21no—
112C23×C103—21no—
113C23×C103C2×D411yescharacteristic
114C22×D103—21no—
115C22×D103—42no—
116C22×D103—42no—
117C22×D103—81no—
118C22×D103C2×D411yescharacteristic
119Q8×C103—21no—
120Q8×C103—21no—
121D4×C103—21no—
122D4×C103—21no—
123D4×C103—21no—
124D4×C103—42no—
125D4×C103—81no—
126D4×C103#4112yes—
127C2×C4×C103—21no—
128C2×C4×C103—21no—
129C2×C4×C103—21no—
130C2×C4×C103—21no—
131C2×C4×C103—42no—
132C2×C4×C103C2×D411yescharacteristic
133C2×C4×C103C2411yescharacteristic
134C22⋊D103—22no—
135C22⋊D103—42no—
136C22⋊D103—42no—
137C22⋊D103—81no—
138C2×Dic103—21no—
139C2×Dic103—21no—
140C2×Dic103—21no—
141C2×Dic103—81no—
142C2×Dic103—81no—
143C2×Dic103C2×D411yescharacteristic
144C2×Dic103C2×D411yescharacteristic
145C2×Dic103C2×D411yescharacteristic
146D412—21no—
147D412—21no—
148C4×D103—21no—
149C4×D103—21no—
150C4×D103—81no—
151C8×C103—21no—
152C8×C103—21no—
153C103⋊C8—21no—
154C103⋊C8—21no—
155C22×C103—22no—
156C22×C103—21no—
157C22×C103—21no—
158C22×C103—21no—
159C22×C103—41no—
160C22×C103—41no—
161C22×C103—41no—
162C22×C103—41no—
163C22×C103—41no—
164C22×C103C22×D411yescharacteristic
165C2×D103—21no—
166C2×D103—21no—
167C2×D103—41no—
168C2×D103—41no—
169C2×D103—41no—
170C2×D103—84no—
171C2×D103#13512yes—
172C4×C103—21no—
173C4×C103—41no—
174C4×C103—41no—
175C4×C103C2×#4111yescharacteristic
176C4×C103H(5,𝔽2)11yescharacteristic
177Dic103—21no—
178Dic103—21no—
179Dic103—21no—
180Dic103—41no—
181Dic103—41no—
182Dic103—41no—
183C2×C103—42no—
184C2×C103—41no—
185C2×C103—81no—
186C2×C103#54611yescharacteristic
187C2×C103C2×#13511yescharacteristic
188C2×C103#57611yescharacteristic
189D103—22no—
190D103—81no—
191#3297—1031nomaximal, Sylow
192C103#329711yescharacteristic, complemented, Sylow
193#553—1031no—
194#546—1031no—
195#488—1031no—
196#484—1031no—
197#482—1031no—
198#478—1031no—
199#466—1031no—
200#465—1031no—
201#463—1031no—
202#449D10311yescharacteristic, complemented
203#447—1031no—
204C4×D8—1031no—
205C8×D4—1031no—
206#416—1031no—
207C2×#102—1031no—
208C2×#41C2×D10311yescharacteristic
209C22×D4—1031no—
210C2×SD16C2×D10311yescharacteristic, complemented
211C2×D8—1031no—
212C2×D8C2×D10311yescharacteristic
213C22×C8—1031no—
214C22×C8—1031no—
215#126—2061no—
216#125—1031no—
217#124—1031no—
218#123—2061no—
219#123—2061no—
220C22⋊Q8—1031no—
221#121—1031no—
222#121—1031no—
223#121—2061no—
224#121—2061no—
225#121C2×D10311yescharacteristic, complemented
226#120—2061no—
227C4×D4—1031no—
228C4×D4—1031no—
229C4×D4—1031no—
230C4×D4—2061no—
231#117—1031no—
232C2×C4⋊C4—1031no—
233C2×C22⋊C4—2061no—
234#107—1031no—
235#107—1031no—
236#106—1031no—
237C4⋊C8—1031no—
238#103—1031no—
239#103—1031no—
240#103C2×D10311yescharacteristic, complemented
241#102—1031no—
242#102—1031no—
243#102—1031no—
244#102—1031no—
245#102—1031no—
246#102—1031no—
247#102C2×D10311yescharacteristic
248C22⋊C8—1031no—
249C22⋊C8C2×D10311yescharacteristic, complemented
250C4×C8—1031no—
251C24—2061no—
252#41—22no—
253#41—41no—
254C2×Q8C22×D10311yescharacteristic
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—1031no—
258C2×D4—1031no—
259C2×D4—4121no—
260C2×D4—2061no—
261C2×D4—2061no—
262C2×D4—2061no—
263C2×D4—2062no—
264C2×D4C22×D10311yescharacteristic
265C2×D4C22×D10311yescharacteristic
266C22×C4—21no—
267C22×C4—1031no—
268C22×C4—2061no—
269C22×C4—2061no—
270C22×C4—2061no—
271C22×C4C22×D10311yescharacteristic
272SD16—41no—
273D8—22no—
274D8—4121no—
275C2×C8—1031no—
276C2×C8—1031no—
277C2×C8—4121no—
278C2×C8—4121no—
279C2×C8C22×D10311yescharacteristic
280C2×C8C22×D10311yescharacteristic
281C4⋊C4—1031no—
282C4⋊C4—1031no—
283C4⋊C4—1031no—
284C4⋊C4—1031no—
285C4⋊C4—2061no—
286C4⋊C4—2061no—
287C4⋊C4—2061no—
288C4⋊C4—2061no—
289C4⋊C4C22×D10311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—1031no—
292C22⋊C4—1031no—
293C22⋊C4—2061no—
294C22⋊C4—2061no—
295C22⋊C4—2061no—
296C22⋊C4—2061no—
297C22⋊C4—2061no—
298C22⋊C4—2061no—
299C22⋊C4—2061no—
300C22⋊C4—2061no—
301C42—1031no—
302C42—2061no—
303C23—21no—
304C23—21no—
305C23—8241no—
306C23—1031no—
307C23—4122no—
308C23—4122no—
309C23—2061no—
310C23D4×D10311yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—42no—
317D4—81no—
318D4—8241no—
319D4—4122no—
320D4—4122no—
321D4—2062no—
322D4—2061no—
323D4—2061no—
324D4#1311010412yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—8241no—
331C2×C4—8241no—
332C2×C4—8241no—
333C2×C4—1031no—
334C2×C4—1031no—
335C2×C4—1031no—
336C2×C4—2061no—
337C2×C4—2061no—
338C2×C4—2061no—
339C2×C4—2061no—
340C2×C4—2061no—
341C2×C4D4×D10311yescharacteristic
342C2×C4C23×D10311yescharacteristic
343C8—21no—
344C8—21no—
345C8—2061no—
346C8—2061no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—22no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—8244no—
357C22—1032no—
358C22—4121no—
359C22—4121no—
360C22—4121no—
361C22—2061no—
362C22—2061no—
363C22C2×D4×D10311yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—4121no—
368C4—4121no—
369C4—4121no—
370C4—2061no—
371C4—2061no—
372C4—2061no—
373C4C2×#1311010411yescharacteristic
374C4#1569306611yescharacteristic
375C2—41no—
376C2—42no—
377C2—81no—
378C2—8241no—
379C2—2062no—
380C2#2026842811yescharacteristic
381C2#135×D10311yescharacteristic
382C2#2026859511yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#449×C103C2
socleC22×C103C22×D4
hypercenter#449D103
hypocenterC103#3297
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. #20268488C2semidirect
2. #20268429C2semidirect
3. #20268147C2semidirect
4. #20268125C2semidirect
5. #20268116C2semidirect
6. #20268093C2semidirect
7. #20268025C2semidirect
8. #20268017C2semidirect
9. #20268008C2semidirect
10. #20267923C2semidirect
11. D8×Dic103C2semidirect
12. (C22⋊D103)⋊C8C2semidirect
13. #20267787C2semidirect
14. #102×D103C2semidirect
15. #449×C103C2semidirect
18. C22×C103⋊C8C22semidirect
21. #15693012C22semidirect
32. D4×Dic103C22semidirect
35. #15692980C22semidirect
38. #15692955C22semidirect
39. #15692954C22semidirect
40. #15692953C22semidirect
41. Dic103⋊C8C22semidirect
42. #15692945C22semidirect
43. #15692945C22semidirect
48. #15692942C22semidirect
51. C8×Dic103C22semidirect
53. C2×SD16×C103C22semidirect
55. #121×C103C22semidirect
56. #103×C103C22semidirect
58. C22⋊C8×C103C22semidirect
192. C103#3297semidirect
202. #449D103semidirect
210. C2×SD16C2×D103semidirect
225. #121C2×D103semidirect
240. #103C2×D103semidirect
249. C22⋊C8C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202684882
#202684292
#202681472
#202681252
#202681162
#202680932
#202680252
#202680172
#202680082
#202679232
D8×Dic1032
(C22⋊D103)⋊C82
#202677872
#102×D1032
#449×C1032
#3297103