Finite Group Databasebeta

← #27206995

Subgroups — #27206995

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#20268485C211yesmaximal, characteristic, complemented
2#20268429C211yesmaximal, characteristic, complemented
3#20268147C211yesmaximal, characteristic, complemented
4#20268125C211yesmaximal, characteristic, complemented
5#20268115C211yesmaximal, characteristic, complemented
6#20268089C211yesmaximal, characteristic, complemented
7#20268027C211yesmaximal, characteristic, complemented
8#20268023C211yesmaximal, characteristic, complemented
9#20268009C211yesmaximal, characteristic, complemented
10#20267936C211yesmaximal, characteristic, complemented
11#20267926C211yesmaximal, characteristic, complemented
12#20267871C211yesmaximal, characteristic, complemented
13C8×C22⋊D103C211yesmaximal, characteristic, complemented
14#102×D103C211yesmaximal, characteristic, complemented
15#416×C103C211yesmaximal, characteristic, complemented
16C2×D4×D103C2211yescharacteristic
17C2×#13110092C2211yescharacteristic, complemented
18C2×D824C2211yescharacteristic
19C2×#13110090C2211yescharacteristic
20C2×C8×D103C2211yescharacteristic
21#15693015—21no—
22#15693012C2211yescharacteristic, complemented
23#15693010C2211yescharacteristic
24#15693004—21no—
25#15693003—21no—
26#15692997C2211yescharacteristic
27#15692996C2211yescharacteristic
28#15692995C2211yescharacteristic
29#15692995C2211yescharacteristic, complemented
30#15692994—21no—
31#15692993—21no—
32#15692989—21no—
33C4×D412—21no—
34D4×Dic103C2211yescharacteristic
35#15692983C2211yescharacteristic, complemented
36C4×C22⋊D103C2211yescharacteristic
37C4⋊C4×D103C2211yescharacteristic
38C2×(C2×D103)⋊C4—21no—
39#15692955C2211yescharacteristic, complemented
40#15692954C2211yescharacteristic, complemented
41#15692952C2211yescharacteristic, complemented
42Dic103⋊C8C2211yescharacteristic, complemented
43#15692945C2211yescharacteristic, complemented
44#15692943C2211yescharacteristic
45#15692943C2211yescharacteristic, complemented
46#15692942C2211yescharacteristic
47#15692941C2211yescharacteristic
48#15692941C2211yescharacteristic
49C22⋊(C103⋊C8)C2211yescharacteristic, complemented
50(C2×D103)⋊C8C2211yescharacteristic
51C8×Dic103C2211yescharacteristic, complemented
52C2×#41×C103C2211yescharacteristic
53C22×C8×C103C2211yescharacteristic, complemented
54#117×C103C2211yescharacteristic, complemented
55#103×C103C2211yescharacteristic, complemented
56#103×C103C2211yescharacteristic, complemented
57#102×C103C2211yescharacteristic
58#102×C103C2211yescharacteristic
59C23×D103—21no—
60C2×D412—21no—
61C2×D412C2311yescharacteristic
62C2×D412C2311yescharacteristic
63C2×C22⋊D103—21no—
64C2×C22⋊D103—21no—
65C2×C22⋊D103—21no—
66C2×C22⋊D103D411yescharacteristic
67D4×D103—22no—
68D4×D103—41no—
69C22×Dic103—21no—
70C2×C4×D103—21no—
71C2×C4×D103—21no—
72C2×C4×D103C2311yescharacteristic
73#13110092—41no—
74D824—41no—
75#13110090—22no—
76C2×C103⋊C8C2311yescharacteristic
77C2×C103⋊C8C2311yescharacteristic
78C8×D103—41no—
79C4⋊Dic103—21no—
80C4⋊Dic103C2311yescharacteristic
81C4⋊Dic103C2311yescharacteristic
82Dic103⋊C4—21no—
83Dic103⋊C4—21no—
84Dic103⋊C4—21no—
85Dic103⋊C4D411yescharacteristic
86C22⋊Dic103—21no—
87C22⋊Dic103D411yescharacteristic
88(C2×D103)⋊C4—21no—
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)⋊C4D411yescharacteristic
96C4×Dic103C2311yescharacteristic
97#41×C103—22no—
98#41×C103—41no—
99C2×Q8×C103C2311yescharacteristic
100C2×D4×C103—21no—
101C2×D4×C103C2311yescharacteristic
102C22×C4×C103—21no—
103C22×C4×C103C2311yescharacteristic
104C2×C8×C103—41no—
105C2×C8×C103C2311yescharacteristic
106C2×C8×C103C2311yescharacteristic
107C4⋊C4×C103C2311yescharacteristic
108C4⋊C4×C103C2311yescharacteristic
109C22⋊C4×C103—21no—
110C42×C103—21no—
111C23×C103—21no—
112C23×C103C2×D411yescharacteristic
113C22×D103—21no—
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—42no—
123D4×C103#4112yes—
124C2×C4×C103—21no—
125C2×C4×C103—21no—
126C2×C4×C103—21no—
127C2×C4×C103—21no—
128C2×C4×C103—21no—
129C2×C4×C103—42no—
130C2×C4×C103C2×D411yescharacteristic
131C2×C4×C103C2411yescharacteristic
132C22⋊D103—22no—
133C22⋊D103—42no—
134C22⋊D103—81no—
135C22⋊D103—81no—
136C2×Dic103—21no—
137C2×Dic103—21no—
138C2×Dic103—81no—
139C2×Dic103C2×D411yescharacteristic
140C2×Dic103C2×D411yescharacteristic
141C2×Dic103C2×D411yescharacteristic
142D412—21no—
143D412—21no—
144D412—21no—
145D412—21no—
146D412—42no—
147C4×D103—21no—
148C4×D103—21no—
149C4×D103—81no—
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×C103C22×D411yescharacteristic
162C2×D103—21no—
163C2×D103—21no—
164C2×D103—41no—
165C2×D103—41no—
166C2×D103—41no—
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×C103—41no—
176C4×C103C2×#4111yescharacteristic
177C4×C103H(5,𝔽2)11yescharacteristic
178Dic103—21no—
179Dic103—21no—
180Dic103—21no—
181Dic103—41no—
182Dic103—41no—
183C2×C103—42no—
184C2×C103—41no—
185C2×C103#54611yescharacteristic
186C2×C103C2×#13511yescharacteristic
187C2×C103#57611yescharacteristic
188D103—22no—
189D103—81no—
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#449—1031no—
203#447—1031no—
204C4×D8—1031no—
205C8×D4—1031no—
206#416D10311yescharacteristic, complemented
207C2×#102—1031no—
208C2×#41C2×D10311yescharacteristic
209C22×D4—1031no—
210C2×SD16—1031no—
211C2×D8—1031no—
212C2×D8—1031no—
213C22×C8—1031no—
214C22×C8C2×D10311yescharacteristic, complemented
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—1031no—
224#121—2061no—
225#121—2061no—
226#120—2061no—
227C4×D4—1031no—
228C4×D4—1031no—
229C4×D4—1031no—
230C4×D4—2061no—
231#117C2×D10311yescharacteristic, complemented
232C2×C4⋊C4—1031no—
233C2×C22⋊C4—2061no—
234#107—1031no—
235#107—1031no—
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#102C2×D10311yescharacteristic
247#102C2×D10311yescharacteristic
248C22⋊C8—1031no—
249C22⋊C8—1031no—
250C4×C8—1031no—
251C24—2061no—
252#41—22no—
253#41—41no—
254C2×Q8C22×D10311yescharacteristic
255C2×D4—21no—
256C2×D4—1031no—
257C2×D4—1031no—
258C2×D4—1031no—
259C2×D4—4121no—
260C2×D4—2061no—
261C2×D4—2061no—
262C2×D4—2061no—
263C2×D4—2061no—
264C2×D4—2062no—
265C2×D4C22×D10311yescharacteristic
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—41no—
276C2×C8—1031no—
277C2×C8—1031no—
278C2×C8—4121no—
279C2×C8C22×D10311yescharacteristic
280C2×C8C22×D10311yescharacteristic
281C4⋊C4—1031no—
282C4⋊C4—1031no—
283C4⋊C4—1031no—
284C4⋊C4—2061no—
285C4⋊C4—2061no—
286C4⋊C4—2061no—
287C4⋊C4—2061no—
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—21no—
302C42—1031no—
303C23—21no—
304C23—8241no—
305C23—1031no—
306C23—4122no—
307C23—4122no—
308C23—2061no—
309C23—2061no—
310C23D4×D10311yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—42no—
315D4—8241no—
316D4—8241no—
317D4—4122no—
318D4—4122no—
319D4—2062no—
320D4—2061no—
321D4—2061no—
322D4—2061no—
323D4—2061no—
324D4#1311010512yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—8241no—
332C2×C4—8241no—
333C2×C4—8241no—
334C2×C4—1031no—
335C2×C4—1031no—
336C2×C4—1031no—
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—8244no—
354C22—1032no—
355C22—4121no—
356C22—4121no—
357C22—4121no—
358C22—4121no—
359C22—4121no—
360C22—4121no—
361C22—2061no—
362C22—2061no—
363C22C2×D4×D10311yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—4121no—
369C4—4121no—
370C4—2061no—
371C4—2061no—
372C4—2061no—
373C4C2×#1311010511yescharacteristic
374C4#1569306611yescharacteristic
375C2—41no—
376C2—42no—
377C2—8241no—
378C2—8241no—
379C2—2062no—
380C2#2026843111yescharacteristic
381C2#135×D10311yescharacteristic
382C2#2026859311yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#416×C103C2
socleC22×C103C22×D4
hypercenter#416D103
hypocenterC103#3297
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #20268485C2semidirect
2. #20268429C2semidirect
3. #20268147C2semidirect
4. #20268125C2semidirect
5. #20268115C2semidirect
6. #20268089C2semidirect
7. #20268027C2semidirect
8. #20268023C2semidirect
9. #20268009C2semidirect
10. #20267936C2semidirect
11. #20267926C2semidirect
12. #20267871C2semidirect
13. C8×C22⋊D103C2semidirect
14. #102×D103C2semidirect
15. #416×C103C2semidirect
17. C2×#13110092C22semidirect
22. #15693012C22semidirect
29. #15692995C22semidirect
35. #15692983C22semidirect
39. #15692955C22semidirect
40. #15692954C22semidirect
41. #15692952C22semidirect
42. Dic103⋊C8C22semidirect
43. #15692945C22semidirect
45. #15692943C22semidirect
49. C22⋊(C103⋊C8)C22semidirect
51. C8×Dic103C22semidirect
53. C22×C8×C103C22semidirect
54. #117×C103C22semidirect
55. #103×C103C22semidirect
56. #103×C103C22semidirect
192. C103#3297semidirect
206. #416D103semidirect
214. C22×C8C2×D103semidirect
231. #117C2×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
#202684852
#202684292
#202681472
#202681252
#202681152
#202680892
#202680272
#202680232
#202680092
#202679362
#202679262
#202678712
C8×C22⋊D1032
#102×D1032
#416×C1032
#3297103