Finite Group Databasebeta

← #27206992

Subgroups — #27206992

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#20268489C211yesmaximal, characteristic, complemented
2#20268432C211yesmaximal, characteristic, complemented
3#20268147C211yesmaximal, characteristic, complemented
4#20268118C211yesmaximal, characteristic, complemented
5#20268094C211yesmaximal, characteristic, complemented
6#20268028C211yesmaximal, characteristic, complemented
7#20268022C211yesmaximal, characteristic, complemented
8#20268009C211yesmaximal, characteristic, complemented
9#20267939C211yesmaximal, characteristic, complemented
10#20267927C211yesmaximal, characteristic, complemented
11#20267873C211yesmaximal, characteristic, complemented
12(C22⋊D103)⋊C8C211yesmaximal, characteristic, complemented
13#20267786C211yesmaximal, characteristic, complemented
14C2×#15692941C211yesmaximal, characteristic, complemented
15#484×C103C211yesmaximal, characteristic, complemented
16C2×#13110106C2211yescharacteristic
17C22×D412C2211yescharacteristic
18C2×#13110092C2211yescharacteristic, complemented
19C2×D824C2211yescharacteristic
20C2×D824C2211yescharacteristic
21C22×C103⋊C8C2211yescharacteristic
22C2×C8×D103C2211yescharacteristic, complemented
23#15693016—21no—
24#15693012C2211yescharacteristic, complemented
25#15693010C2211yescharacteristic
26#15693006—21no—
27#15693006—21no—
28#15692996—21no—
29#15692996C2211yescharacteristic
30#15692996C2211yescharacteristic, complemented
31#15692995—21no—
32#15692995C2211yescharacteristic
33#15692991—21no—
34#15692983C2211yescharacteristic
35#15692983C2211yescharacteristic, complemented
36C4×C22⋊D103—21no—
37C4×C22⋊D103C2211yescharacteristic
38#15692979C2211yescharacteristic, complemented
39C22⋊C4×D103—21no—
40#15692952C2211yescharacteristic, complemented
41Dic103⋊C8C2211yescharacteristic, complemented
42#15692945C2211yescharacteristic, complemented
43#15692943C2211yescharacteristic
44#15692943C2211yescharacteristic
45#15692941C2211yescharacteristic
46#15692941C2211yescharacteristic
47#15692941C2211yescharacteristic
48#15692941C2211yescharacteristic
49#15692941C2211yescharacteristic, complemented
50(C2×D103)⋊C8C2211yescharacteristic, complemented
51C8×Dic103C2211yescharacteristic, complemented
52C22⋊Q8×C103C2211yescharacteristic
53C2×C4⋊C4×C103C2211yescharacteristic
54#107×C103C2211yescharacteristic, complemented
55#107×C103C2211yescharacteristic, complemented
56#103×C103C2211yescharacteristic, complemented
57#103×C103C2211yescharacteristic, complemented
58C22⋊C8×C103C2211yescharacteristic
59C23×D103—21no—
60#13110106—22no—
61#13110106—41no—
62C2×D412—22no—
63C2×D412—21no—
64C2×D412—21no—
65C2×D412—21no—
66C2×D412—21no—
67C2×D412—41no—
68C2×D412C2311yescharacteristic
69C2×D412C2311yescharacteristic
70C2×D412C2311yescharacteristic
71C2×C22⋊D103—21no—
72C2×C22⋊D103D411yescharacteristic
73C2×C4×D103—21no—
74C2×C4×D103—21no—
75C2×C4×D103—21no—
76C2×C4×D103C2311yescharacteristic
77#13110092—41no—
78D824—22no—
79D824—41no—
80C2×C103⋊C8—41no—
81C2×C103⋊C8C2311yescharacteristic
82C2×C103⋊C8C2311yescharacteristic
83C8×D103—41no—
84C4⋊Dic103—21no—
85C4⋊Dic103C2311yescharacteristic
86Dic103⋊C4—21no—
87Dic103⋊C4D411yescharacteristic
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)⋊C4—21no—
94(C2×D103)⋊C4—21no—
95(C2×D103)⋊C4—21no—
96(C2×D103)⋊C4—21no—
97(C2×D103)⋊C4D411yescharacteristic
98C4×Dic103—21no—
99C4×Dic103C2311yescharacteristic
100C2×Q8×C103C2311yescharacteristic
101C22×C4×C103—21no—
102C22×C4×C103C2311yescharacteristic
103C2×C8×C103C2311yescharacteristic
104C2×C8×C103C2311yescharacteristic
105C4⋊C4×C103—21no—
106C4⋊C4×C103—21no—
107C4⋊C4×C103C2311yescharacteristic
108C4⋊C4×C103C2311yescharacteristic
109C4⋊C4×C103C2311yescharacteristic
110C22⋊C4×C103—21no—
111C23×C103C2×D411yescharacteristic
112C22×D103—21no—
113C22×D103—21no—
114C22×D103—21no—
115C22×D103—42no—
116C22×D103—42no—
117C22×D103—81no—
118C22×D103C2×D411yescharacteristic
119Q8×C103—21no—
120Q8×C103—21no—
121C2×C4×C103—21no—
122C2×C4×C103—21no—
123C2×C4×C103—21no—
124C2×C4×C103—21no—
125C2×C4×C103—21no—
126C2×C4×C103—21no—
127C2×C4×C103—81no—
128C2×C4×C103C2×D411yescharacteristic
129C2×C4×C103C2411yescharacteristic
130C22⋊D103—22no—
131C22⋊D103—42no—
132C2×Dic103—21no—
133C2×Dic103C2×D411yescharacteristic
134C2×Dic103C2×D411yescharacteristic
135C2×Dic103C2×D411yescharacteristic
136D412—21no—
137D412—21no—
138D412—21no—
139D412—21no—
140D412—21no—
141D412—42no—
142D412—42no—
143D412—81no—
144D412—81no—
145D412#4112yes—
146C4×D103—21no—
147C4×D103—21no—
148C4×D103—42no—
149C4×D103—81no—
150C4×D103—81no—
151C8×C103—21no—
152C8×C103—21no—
153C103⋊C8—21no—
154C103⋊C8—21no—
155C22×C103—21no—
156C22×C103—21no—
157C22×C103#13512yes—
158C22×C103C22×D411yescharacteristic
159C2×D103—21no—
160C2×D103—22no—
161C2×D103—21no—
162C2×D103—21no—
163C2×D103—41no—
164C2×D103—41no—
165C2×D103—41no—
166C2×D103—41no—
167C2×D103—41no—
168C2×D103—41no—
169C2×D103—41no—
170C2×D103—41no—
171C2×D103—84no—
172C4×C103—21no—
173C4×C103—41no—
174C4×C103—41no—
175C4×C103—41no—
176C4×C103—41no—
177C4×C103C2×#4111yescharacteristic
178C4×C103H(5,𝔽2)11yescharacteristic
179Dic103—21no—
180Dic103—21no—
181Dic103—21no—
182Dic103—41no—
183C2×C103—22no—
184C2×C103#54611yescharacteristic
185C2×C103C2×#13511yescharacteristic
186C2×C103#57611yescharacteristic
187D103—41no—
188D103—42no—
189D103—81no—
190D103—81no—
191#3297—1031nomaximal, Sylow
192C103#329711yescharacteristic, complemented, Sylow
193#553—1031no—
194#546—1031no—
195#488—1031no—
196#484D10311yescharacteristic, complemented
197#482—1031no—
198#478—1031no—
199#466—1031no—
200#465—1031no—
201#463—1031no—
202#449—1031no—
203#447—1031no—
204C4×D8—1031no—
205C8×D4—1031no—
206#416—1031no—
207C2×#102—1031no—
208C2×#41—1031no—
209C22×D4—1031no—
210C2×SD16—1031no—
211C2×D8—1031no—
212C2×D8—1031no—
213C22×C8—1031no—
214C22×C8—1031no—
215#126—2061no—
216#125—1031no—
217#124—1031no—
218#123—2061no—
219#123—2061no—
220C22⋊Q8C2×D10311yescharacteristic
221#121—1031no—
222#121—1031no—
223#121—1031no—
224#121—2061no—
225#121—2061no—
226#120—2061no—
227C4×D4—1031no—
228C4×D4—1031no—
229C4×D4—1031no—
230C4×D4—2061no—
231#117—1031no—
232C2×C4⋊C4C2×D10311yescharacteristic
233C2×C22⋊C4—2061no—
234#107C2×D10311yescharacteristic, complemented
235#107C2×D10311yescharacteristic, complemented
236#106—1031no—
237C4⋊C8—1031no—
238#103—1031no—
239#103C2×D10311yescharacteristic, complemented
240#103C2×D10311yescharacteristic, complemented
241#102—1031no—
242#102—1031no—
243#102—1031no—
244#102—1031no—
245#102—1031no—
246#102—1031no—
247#102—1031no—
248C22⋊C8—1031no—
249C22⋊C8C2×D10311yescharacteristic
250C4×C8—1031no—
251C24—2061no—
252#41—4121no—
253#41—2062no—
254C2×Q8C22×D10311yescharacteristic
255C2×D4—1031no—
256C2×D4—1031no—
257C2×D4—1031no—
258C2×D4—1031no—
259C2×D4—4121no—
260C2×D4—2061no—
261C2×D4—2061no—
262C2×D4—2062no—
263C2×D4—2061no—
264C2×D4—2061no—
265C2×D4—2061no—
266C22×C4—21no—
267C22×C4—1031no—
268C22×C4—2061no—
269C22×C4—2061no—
270C22×C4—2061no—
271C22×C4C22×D10311yescharacteristic
272SD16—4121no—
273D8—4121no—
274D8—2062no—
275C2×C8—1031no—
276C2×C8—1031no—
277C2×C8—4121no—
278C2×C8—4121no—
279C2×C8C22×D10311yescharacteristic
280C2×C8C22×D10311yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—1031no—
284C4⋊C4—1031no—
285C4⋊C4—2061no—
286C4⋊C4—2061no—
287C4⋊C4C22×D10311yescharacteristic
288C4⋊C4C22×D10311yescharacteristic
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—8241no—
304C23—1031no—
305C23—4122no—
306C23—4122no—
307C23—2061no—
308C23—2061no—
309C23—2061no—
310C23D4×D10311yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—8241no—
314D4—8241no—
315D4—1032no—
316D4—4122no—
317D4—4122no—
318D4—4122no—
319D4—2062no—
320D4—2061no—
321D4—2061no—
322D4—2061no—
323D4—2061no—
324D4—2061no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—81no—
332C2×C4—8241no—
333C2×C4—8241no—
334C2×C4—1031no—
335C2×C4—1031no—
336C2×C4—1031no—
337C2×C4—4122no—
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—8244no—
350C22—4121no—
351C22—4121no—
352C22—4121no—
353C22—4121no—
354C22—4121no—
355C22—4121no—
356C22—4121no—
357C22—4121no—
358C22—2061no—
359C22—2061no—
360C22—2062no—
361C22—2061no—
362C22#1569304412yes—
363C22C2×D4×D10311yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—4121no—
370C4—2061no—
371C4—2061no—
372C4—2061no—
373C4#41×D10311yescharacteristic
374C4#1569306711yescharacteristic
375C2—22no—
376C2—8241no—
377C2—8241no—
378C2—4122no—
379C2—4121no—
380C2#2026843311yescharacteristic
381C2C2×#1569304411yescharacteristic
382C2#2026859511yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#484×C103C2
socleC22×C103C22×D4
hypercenter#484D103
hypocenterC103#3297
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
1. #20268489C2semidirect
2. #20268432C2semidirect
3. #20268147C2semidirect
4. #20268118C2semidirect
5. #20268094C2semidirect
6. #20268028C2semidirect
7. #20268022C2semidirect
8. #20268009C2semidirect
9. #20267939C2semidirect
10. #20267927C2semidirect
11. #20267873C2semidirect
12. (C22⋊D103)⋊C8C2semidirect
13. #20267786C2semidirect
14. C2×#15692941C2semidirect
15. #484×C103C2semidirect
18. C2×#13110092C22semidirect
22. C2×C8×D103C22semidirect
24. #15693012C22semidirect
30. #15692996C22semidirect
35. #15692983C22semidirect
38. #15692979C22semidirect
40. #15692952C22semidirect
41. Dic103⋊C8C22semidirect
42. #15692945C22semidirect
49. #15692941C22semidirect
50. (C2×D103)⋊C8C22semidirect
51. C8×Dic103C22semidirect
54. #107×C103C22semidirect
55. #107×C103C22semidirect
56. #103×C103C22semidirect
57. #103×C103C22semidirect
192. C103#3297semidirect
196. #484D103semidirect
234. #107C2×D103semidirect
235. #107C2×D103semidirect
239. #103C2×D103semidirect
240. #103C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202684892
#202684322
#202681472
#202681182
#202680942
#202680282
#202680222
#202680092
#202679392
#202679272
#202678732
(C22⋊D103)⋊C82
#202677862
C2×#156929412
#484×C1032
#3297103