Finite Group Databasebeta

← #27206996

Subgroups — #27206996

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#20268487C211yesmaximal, characteristic, complemented
2#20268437C211yesmaximal, characteristic, complemented
3#20268146C211yesmaximal, characteristic, complemented
4#20268127C211yesmaximal, characteristic, complemented
5#20268116C211yesmaximal, characteristic, complemented
6#20268092C211yesmaximal, characteristic, complemented
7#20268027C211yesmaximal, characteristic, complemented
8#20268020C211yesmaximal, characteristic, complemented
9#20268007C211yesmaximal, characteristic, complemented
10#20267938C211yesmaximal, characteristic, complemented
11#20267927C211yesmaximal, characteristic, complemented
12C4×D824C211yesmaximal, characteristic, complemented
13#20267788C211yesmaximal, characteristic, complemented
14C2×#15692943C211yesmaximal, characteristic, complemented
15C8×D4×C103C211yesmaximal, characteristic, complemented
16C2×#13110105C2211yescharacteristic
17C22×D412C2211yescharacteristic
18C2×#13110094C2211yescharacteristic, complemented
19C2×D824C2211yescharacteristic
20C2×D824C2211yescharacteristic
21#15693016—21no—
22#15693013C2211yescharacteristic, complemented
23#15693009C2211yescharacteristic
24#15693006—21no—
25#15693003—21no—
26#15693000C2211yescharacteristic
27#15692995C2211yescharacteristic
28#15692995C2211yescharacteristic
29#15692995C2211yescharacteristic, complemented
30#15692994—21no—
31#15692993—21no—
32#15692989—21no—
33C4×D412C2211yescharacteristic
34C4×D412C2211yescharacteristic, complemented
35(C22⋊D103)⋊C4—21no—
36#15692980C2211yescharacteristic, complemented
37C2×C4⋊Dic103C2211yescharacteristic
38C22⋊C4×D103—21no—
39#15692955C2211yescharacteristic, complemented
40#15692955C2211yescharacteristic, complemented
41#15692953C2211yescharacteristic, complemented
42#15692946C2211yescharacteristic, complemented
43#15692946C2211yescharacteristic, complemented
44#15692946C2211yescharacteristic, complemented
45#15692943C2211yescharacteristic
46#15692943C2211yescharacteristic
47#15692943C2211yescharacteristic
48#15692943C2211yescharacteristic
49#15692943C2211yescharacteristic
50#15692943C2211yescharacteristic
51#15692943C2211yescharacteristic, complemented
52C22×C8×C103C2211yescharacteristic
53C22×C8×C103C2211yescharacteristic, complemented
54C4×D4×C103C2211yescharacteristic
55C4⋊C8×C103C2211yescharacteristic, complemented
56C22⋊C8×C103C2211yescharacteristic
57C22⋊C8×C103C2211yescharacteristic, complemented
58C4×C8×C103C2211yescharacteristic, complemented
59C23×D103—21no—
60#13110105—22no—
61#13110105—41no—
62C2×Dic206C2311yescharacteristic
63C2×D412—22no—
64C2×D412—21no—
65C2×D412—41no—
66C2×D412C2311yescharacteristic
67C2×D412C2311yescharacteristic
68C2×D412C2311yescharacteristic
69C2×C22⋊D103—21no—
70C2×C22⋊D103—21no—
71C2×C22⋊D103—21no—
72C2×C22⋊D103—21no—
73C22×Dic103—21no—
74C2×C4×D103—21no—
75C2×C4×D103—21no—
76C2×C4×D103—21no—
77#13110094—41no—
78D824—22no—
79D824—41no—
80C4⋊Dic103—21no—
81C4⋊Dic103C2311yescharacteristic
82C4⋊Dic103C2311yescharacteristic
83C4⋊Dic103C2311yescharacteristic
84C4⋊Dic103C2311yescharacteristic
85Dic103⋊C4—21no—
86Dic103⋊C4—21no—
87Dic103⋊C4—21no—
88C22⋊Dic103—21no—
89C22⋊Dic103—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—
97C4×Dic103—21no—
98C2×D4×C103D411yescharacteristic
99C22×C4×C103C2311yescharacteristic
100C22×C4×C103C2311yescharacteristic
101C2×C8×C103—41no—
102C2×C8×C103—41no—
103C2×C8×C103C2311yescharacteristic
104C2×C8×C103C2311yescharacteristic
105C2×C8×C103C2311yescharacteristic
106C2×C8×C103C2311yescharacteristic
107C4⋊C4×C103D411yescharacteristic
108C22⋊C4×C103D411yescharacteristic
109C22⋊C4×C103D411yescharacteristic
110C42×C103C2311yescharacteristic
111C23×C103C2×D411yescharacteristic
112C23×C103C2×D411yescharacteristic
113C22×D103—21no—
114C22×D103—21no—
115C22×D103—21no—
116C22×D103—42no—
117C22×D103—42no—
118C22×D103—81no—
119D4×C103—22no—
120C2×C4×C103—21no—
121C2×C4×C103—21no—
122C2×C4×C103—21no—
123C2×C4×C103—21no—
124C2×C4×C103C2×D411yescharacteristic
125C2×C4×C103C2×D411yescharacteristic
126C2×C4×C103C2×D411yescharacteristic
127C2×C4×C103C2×D411yescharacteristic
128C2×C4×C103C2411yescharacteristic
129C22⋊D103—42no—
130C22⋊D103—42no—
131C22⋊D103—81no—
132C22⋊D103—81no—
133C2×Dic103—21no—
134C2×Dic103—21no—
135C2×Dic103—21no—
136C2×Dic103—21no—
137C2×Dic103—21no—
138C2×Dic103—81no—
139D412—21no—
140D412—21no—
141D412—21no—
142D412—21no—
143D412—21no—
144D412—42no—
145D412#4112yes—
146C4×D103—42no—
147C4×D103—81no—
148C4×D103—81no—
149Dic206—21no—
150Dic206—21no—
151C8×C103—21no—
152C8×C103—21no—
153C8×C103—21no—
154C8×C103—21no—
155C22×C103—21no—
156C22×C103—21no—
157C22×C103—21no—
158C22×C103—21no—
159C22×C103—21no—
160C22×C103#13512yes—
161C22×C103C22×D411yescharacteristic
162C2×D103—22no—
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—21no—
174C4×C103—21no—
175C4×C103—21no—
176C4×C103C2×#4111yescharacteristic
177C4×C103H(5,𝔽2)11yescharacteristic
178Dic103—41no—
179Dic103—41no—
180Dic103—41no—
181Dic103—41no—
182Dic103—41no—
183C2×C103—22no—
184C2×C103—41no—
185C2×C103#54611yescharacteristic
186C2×C103C2×#13511yescharacteristic
187C2×C103#57611yescharacteristic
188D103—42no—
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×D4D10311yescharacteristic, complemented
206#416—1031no—
207C2×#102—1031no—
208C2×#41—1031no—
209C22×D4—1031no—
210C2×SD16—1031no—
211C2×D8—1031no—
212C2×D8—1031no—
213C22×C8C2×D10311yescharacteristic
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—2061no—
230C4×D4C2×D10311yescharacteristic
231#117—1031no—
232C2×C4⋊C4—1031no—
233C2×C22⋊C4—2061no—
234#107—1031no—
235#107—1031no—
236#106—1031no—
237C4⋊C8C2×D10311yescharacteristic, complemented
238#103—1031no—
239#103—1031no—
240#103—1031no—
241#102—1031no—
242#102—1031no—
243#102—1031no—
244#102—1031no—
245#102—1031no—
246#102—1031no—
247#102—1031no—
248C22⋊C8C2×D10311yescharacteristic
249C22⋊C8C2×D10311yescharacteristic, complemented
250C4×C8C2×D10311yescharacteristic, complemented
251C24—2061no—
252#41—4121no—
253#41—2062no—
254C2×Q8—1031no—
255C2×D4—1031no—
256C2×D4—1031no—
257C2×D4—1031no—
258C2×D4—4121no—
259C2×D4—2062no—
260C2×D4—2061no—
261C2×D4—2061no—
262C2×D4—2061no—
263C2×D4—2061no—
264C2×D4—2061no—
265C2×D4D41211yescharacteristic
266C22×C4—2061no—
267C22×C4—2061no—
268C22×C4—2061no—
269C22×C4—2061no—
270C22×C4C22×D10311yescharacteristic
271C22×C4C22×D10311yescharacteristic
272SD16—4121no—
273D8—4121no—
274D8—2062no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8C22×D10311yescharacteristic
278C2×C8C22×D10311yescharacteristic
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⋊C4D41211yescharacteristic
290C22⋊C4—2061no—
291C22⋊C4—2061no—
292C22⋊C4—2061no—
293C22⋊C4—2061no—
294C22⋊C4—2061no—
295C22⋊C4—2061no—
296C22⋊C4—2061no—
297C22⋊C4—2061no—
298C22⋊C4—2061no—
299C22⋊C4D41211yescharacteristic
300C22⋊C4D41211yescharacteristic
301C42—2061no—
302C42C22×D10311yescharacteristic
303C23—8241no—
304C23—4122no—
305C23—4122no—
306C23—2061no—
307C23—2061no—
308C23—2061no—
309C23C2×D41211yescharacteristic
310C23C2×D41211yescharacteristic
311Q8—2061no—
312Q8—2061no—
313D4—22no—
314D4—8241no—
315D4—8241no—
316D4—1032no—
317D4—4122no—
318D4—4122no—
319D4—4122no—
320D4—2061no—
321D4—2061no—
322D4—2061no—
323D4—2061no—
324D4—2061no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—8241no—
330C2×C4—8241no—
331C2×C4—8241no—
332C2×C4—4122no—
333C2×C4—2061no—
334C2×C4—2061no—
335C2×C4—2061no—
336C2×C4—2061no—
337C2×C4—2061no—
338C2×C4C2×D41211yescharacteristic
339C2×C4C2×D41211yescharacteristic
340C2×C4C2×D41211yescharacteristic
341C2×C4C2×D41211yescharacteristic
342C2×C4C23×D10311yescharacteristic
343C8—21no—
344C8—21no—
345C8—21no—
346C8—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—8244no—
353C22—4121no—
354C22—4121no—
355C22—4121no—
356C22—4121no—
357C22—4121no—
358C22—4121no—
359C22—4121no—
360C22—4121no—
361C22—2062no—
362C22#1569304312yes—
363C22C22×D41211yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—4121no—
369C4—4121no—
370C4—4121no—
371C4—4121no—
372C4—4121no—
373C4#41×D10311yescharacteristic
374C4#1569306611yescharacteristic
375C2—22no—
376C2—41no—
377C2—8241no—
378C2—8241no—
379C2—4122no—
380C2#2026843611yescharacteristic
381C2C2×#1569304311yescharacteristic
382C2#2026859611yescharacteristic
subgroupG/H
centerC22C22×D412
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC8×D4×C103C2
socleC22×C103C22×D4
hypercenterC8×D4D103
hypocenterC103#3297
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #20268487C2semidirect
2. #20268437C2semidirect
3. #20268146C2semidirect
4. #20268127C2semidirect
5. #20268116C2semidirect
6. #20268092C2semidirect
7. #20268027C2semidirect
8. #20268020C2semidirect
9. #20268007C2semidirect
10. #20267938C2semidirect
11. #20267927C2semidirect
12. C4×D824C2semidirect
13. #20267788C2semidirect
14. C2×#15692943C2semidirect
15. C8×D4×C103C2semidirect
18. C2×#13110094C22semidirect
22. #15693013C22semidirect
29. #15692995C22semidirect
34. C4×D412C22semidirect
36. #15692980C22semidirect
39. #15692955C22semidirect
40. #15692955C22semidirect
41. #15692953C22semidirect
42. #15692946C22semidirect
43. #15692946C22semidirect
44. #15692946C22semidirect
51. #15692943C22semidirect
53. C22×C8×C103C22semidirect
55. C4⋊C8×C103C22semidirect
57. C22⋊C8×C103C22semidirect
58. C4×C8×C103C22semidirect
192. C103#3297semidirect
205. C8×D4D103semidirect
214. C22×C8C2×D103semidirect
237. C4⋊C8C2×D103semidirect
249. C22⋊C8C2×D103semidirect
250. C4×C8C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202684872
#202684372
#202681462
#202681272
#202681162
#202680922
#202680272
#202680202
#202680072
#202679382
#202679272
C4×D8242
#202677882
C2×#156929432
C8×D4×C1032
#3297103