Finite Group Databasebeta

← #27204016

Subgroups — #27204016

Order 13184.

484 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15693042C211yesmaximal, characteristic
2#20268273C211yesmaximal, characteristic, complemented
3#20268270C211yesmaximal, characteristic, complemented
4#20267893C211yesmaximal, characteristic, complemented
5#20267892C211yesmaximal, characteristic, complemented
6#20267890C211yesmaximal, characteristic, complemented
7C4×#13110095C211yesmaximal, characteristic, complemented
8#20267883C211yesmaximal, characteristic, complemented
9C4×#13110090C211yesmaximal, characteristic, complemented
10#20267871C211yesmaximal, characteristic, complemented
11#107×D103C211yesmaximal, characteristic, complemented
12#20267791C211yesmaximal, characteristic, complemented
13#20267789C211yesmaximal, characteristic, complemented
14#20267748C211yesmaximal, characteristic, complemented
15#440×C103C211yesmaximal, characteristic, complemented
16C2×#13110106C2211yescharacteristic
17C2×#13110104C2211yescharacteristic
18#15693042C418yescomplemented
19C2×#13110095C2211yescharacteristic
20C2×#13110094C2211yescharacteristic
21C2×#13110090C2211yescharacteristic
22C2×#13110088C2211yescharacteristic
23C2×C8×D103C2211yescharacteristic
24Q8×Dic103C2211yescharacteristic
25C4×Dic206C2211yescharacteristic
26#15692986C2211yescharacteristic
27C4×D412—21no—
28C4×D412C2211yescharacteristic
29D4×Dic103C2211yescharacteristic
30#15692983—21no—
31#15692983C2211yescharacteristic
32C4×C22⋊D103—21no—
33(C22⋊D103)⋊C4—21no—
34#15692978—21no—
35#15692978C2211yescharacteristic
36#15692977—21no—
37C2×Dic103⋊C4—21no—
38C4⋊C4×D103—21no—
39C4⋊C4×D103C2211yescharacteristic
40C4⋊C4×D103C2211yescharacteristic
41#15692955C2211yescharacteristic
42#15692954C2211yescharacteristic
43#15692954C2211yescharacteristic
44#15692946C2211yescharacteristic
45#15692945C2211yescharacteristic
46#15692944C2211yescharacteristic
47#15692943C2211yescharacteristic
48#15692942C2211yescharacteristic
49#15692941C2211yescharacteristic
50#15692931C2211yescharacteristic
51C4×C103⋊C8C2211yescharacteristic
52C8×Dic103C2211yescharacteristic
53C2×SD16×C103C2211yescharacteristic
54C4×Q8×C103C2211yescharacteristic
55C4×D4×C103C2211yescharacteristic
56#107×C103C2211yescharacteristic
57#103×C103C2211yescharacteristic
58#102×C103C2211yescharacteristic
59#97×C103C2211yescharacteristic
60#13110106—22no—
61#13110106C2×C414yescomplemented
62#13110104—22no—
63#13110104C2×C414yescomplemented
64C2×Dic206C2311yescharacteristic
65C2×D412—21no—
66C2×D412C2311yescharacteristic
67C2×C22⋊D103—21no—
68C22×Dic103—21no—
69C22×Dic103—21no—
70C2×C4×D103—21no—
71C2×C4×D103—21no—
72C2×C4×D103—21no—
73C2×C4×D103—21no—
74C2×C4×D103—21no—
75C2×C4×D103C2311yescharacteristic
76#13110095C2×C414yescomplemented
77#13110094C2×C414yescomplemented
78#13110090C2×C414yescomplemented
79#13110088—22no—
80C2×C103⋊C8C2311yescharacteristic
81C2×C103⋊C8C2311yescharacteristic
82C8×D103C2×C414yescomplemented
83C4⋊Dic103—21no—
84C4⋊Dic103C2311yescharacteristic
85C4⋊Dic103C2311yescharacteristic
86Dic103⋊C4—21no—
87Dic103⋊C4—21no—
88Dic103⋊C4—21no—
89Dic103⋊C4—21no—
90Dic103⋊C4D411yescharacteristic
91Dic103⋊C4D411yescharacteristic
92C22⋊Dic103—21no—
93(C2×D103)⋊C4—21no—
94(C2×D103)⋊C4—21no—
95(C2×D103)⋊C4D411yescharacteristic
96(C2×D103)⋊C4D411yescharacteristic
97C4×Dic103—21no—
98C4×Dic103—21no—
99C4×Dic103—21no—
100C4×Dic103C2311yescharacteristic
101C2×Q8×C103C2311yescharacteristic
102C2×D4×C103C2311yescharacteristic
103C22×C4×C103—21no—
104SD16×C103C2×C414yescomplemented
105C2×C8×C103C2311yescharacteristic
106C2×C8×C103C2311yescharacteristic
107C4⋊C4×C103—21no—
108C4⋊C4×C103C2311yescharacteristic
109C4⋊C4×C103C2311yescharacteristic
110C22⋊C4×C103—21no—
111C42×C103—21no—
112C42×C103C2311yescharacteristic
113C23×C103—21no—
114C22×D103—21no—
115C22×D103C2×D411yescharacteristic
116Q8×C103—21no—
117Q8×C103C22×C412yes—
118D4×C103—21no—
119D4×C103C22×C412yes—
120C2×C4×C103—21no—
121C2×C4×C103—21no—
122C2×C4×C103—21no—
123C2×C4×C103—81no—
124C2×C4×C103C2×D411yescharacteristic
125C2×C4×C103C2×D411yescharacteristic
126C2×C4×C103C2411yescharacteristic
127C22⋊D103—24no—
128C2×Dic103—21no—
129C2×Dic103—24no—
130C2×Dic103—21no—
131C2×Dic103—21no—
132C2×Dic103—81no—
133C2×Dic103C2×D411yescharacteristic
134C2×Dic103C2×D411yescharacteristic
135C2×Dic103C2×D411yescharacteristic
136D412—24no—
137D412—21no—
138D412C22×C412yes—
139C4×D103—24no—
140C4×D103—81no—
141C4×D103—81no—
142C4×D103—81no—
143C4×D103—81no—
144C4×D103C22×C412yes—
145C4×D103#4112yes—
146Dic206—21no—
147Dic206C22×C412yes—
148C8×C103—21no—
149C8×C103C22×C412yes—
150C103⋊C8—21no—
151C103⋊C8C22×C412yes—
152C22×C103—22no—
153C22×C103—41no—
154C22×C103—41no—
155C22×C103C22×D411yescharacteristic
156C2×D103—21no—
157C2×D103—21no—
158C2×D103—22no—
159C2×D103—41no—
160C2×D103—41no—
161C2×D103C4×D412yes—
162C4×C103—22no—
163C4×C103—21no—
164C4×C103—21no—
165C4×C103—41no—
166C4×C103—41no—
167C4×C103C23×C411yescharacteristic
168C4×C103C2×#4111yescharacteristic
169Dic103—22no—
170Dic103—21no—
171Dic103—21no—
172Dic103—41no—
173Dic103—41no—
174Dic103C4×D412yes—
175C2×C103—42no—
176C2×C103C2×C4×D411yescharacteristic
177C2×C103#57611yescharacteristic
178C2×C103#57811yescharacteristic
179D103—22no—
180D103—42no—
181#2951—1031nomaximal, Sylow
182C103#295111yescharacteristic, complemented, Sylow
183C2×#135—1031no—
184#520—1031no—
185#520—1031no—
186#440—1031no—
187#440—1031no—
188#440—1031no—
189#440D10311yescharacteristic, complemented
190C4×Q16—1031no—
191C4×Q16—1031no—
192C4×D8—1031no—
193C4×D8—1031no—
194C2×#107—1031no—
195#417—1031no—
196#417—1031no—
197#405—1031no—
198C2×#41—1031no—
199C2×#41—1031no—
200#135—1038no—
201C2×Q16—1031no—
202C2×SD16—1031no—
203C2×SD16C2×D10311yescharacteristic
204C2×D8—1031no—
205C2×M16—1031no—
206C22×C8—1031no—
207C4×Q8—1031no—
208C4×Q8—1031no—
209C4×Q8—1031no—
210C4×Q8C2×D10311yescharacteristic
211C4×D4—1031no—
212C4×D4—1031no—
213C4×D4—1031no—
214C4×D4—2061no—
215C4×D4—2061no—
216C4×D4—2061no—
217C4×D4—2061no—
218C4×D4C2×D10311yescharacteristic
219#117—1031no—
220#117—2061no—
221#117—2061no—
222C2×C4⋊C4—1031no—
223C2×C4⋊C4—1031no—
224C2×C4⋊C4—2061no—
225C2×C4⋊C4—2061no—
226#107—1031no—
227#107—1031no—
228#107—1031no—
229#107C2×D10311yescharacteristic
230#103—1031no—
231#103—1031no—
232#103—1031no—
233#103C2×D10311yescharacteristic
234#102—1031no—
235#102—1031no—
236#102—1031no—
237#102C2×D10311yescharacteristic
238#97—1031no—
239#97C2×D10311yescharacteristic
240C4×C8—1031no—
241C4×C8—1031no—
242#41—1034no—
243#41—1034no—
244#41—2062no—
245#41—2062no—
246C2×Q8—1031no—
247C2×Q8C22×D10311yescharacteristic
248C2×D4—1031no—
249C2×D4—2061no—
250C2×D4—2061no—
251C2×D4C22×D10311yescharacteristic
252C22×C4—21no—
253C22×C4—1031no—
254C22×C4—2061no—
255C22×C4—2061no—
256C22×C4—2061no—
257C22×C4—2061no—
258C22×C4—2061no—
259C22×C4—2061no—
260C22×C4—2061no—
261Q16—1034no—
262SD16—1034no—
263SD16C4×D10314yescomplemented
264D8—1034no—
265M16—2062no—
266C2×C8—1031no—
267C2×C8—1034no—
268C2×C8—1031no—
269C2×C8C22×D10311yescharacteristic
270C2×C8C22×D10311yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—1031no—
273C4⋊C4—1031no—
274C4⋊C4—1031no—
275C4⋊C4—1031no—
276C4⋊C4—2061no—
277C4⋊C4—2061no—
278C4⋊C4—2061no—
279C4⋊C4—2061no—
280C4⋊C4—2061no—
281C4⋊C4C22×D10311yescharacteristic
282C4⋊C4C22×D10311yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—1031no—
285C22⋊C4—1031no—
286C22⋊C4—2061no—
287C22⋊C4—2061no—
288C22⋊C4—2061no—
289C42—21no—
290C42—1031no—
291C42—2061no—
292C42—2061no—
293C42—2061no—
294C42C22×D10311yescharacteristic
295C23—21no—
296C23—1031no—
297C23—2061no—
298Q8—21no—
299Q8—1032no—
300Q8—2061no—
301Q8C2×C4×D10312yes—
302D4—21no—
303D4—1032no—
304D4—2064no—
305D4—2064no—
306D4—2061no—
307D4C2×C4×D10312yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—8241no—
313C2×C4—8241no—
314C2×C4—8241no—
315C2×C4—8241no—
316C2×C4—8241no—
317C2×C4—1031no—
318C2×C4—1032no—
319C2×C4—1032no—
320C2×C4—1031no—
321C2×C4—1031no—
322C2×C4—2064no—
323C2×C4—2064no—
324C2×C4—2061no—
325C2×C4—2061no—
326C2×C4—2061no—
327C2×C4D4×D10311yescharacteristic
328C2×C4D4×D10311yescharacteristic
329C2×C4C23×D10311yescharacteristic
330C8—21no—
331C8—1032no—
332C8—2061no—
333C8C2×C4×D10312yes—
334C22—22no—
335C22—41no—
336C22—41no—
337C22—1032no—
338C22—4121no—
339C22—4121no—
340C22—2062no—
341C22—2061no—
342C22—2061no—
343C22C2×D4×D10311yescharacteristic
344C4—21no—
345C4—21no—
346C4—22no—
347C4—41no—
348C4—41no—
349C4—1032no—
350C4—4121no—
351C4—4121no—
352C4—2061no—
353C4—2061no—
354C4—2062no—
355C4C22×C4×D10311yescharacteristic
356C4#41×D10311yescharacteristic
357C2—42no—
358C2—4122no—
359C2—2062no—
360C2C4×D4×D10311yescharacteristic
361C2#2026859511yescharacteristic
362C2#2026860711yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutatorC4×C103C23×C4
FrattiniC2×C4C23×D103
Fitting#440×C103C2
socleC22×C103C22×D4
prime radicalC2×#15693042C2
cosocleC2×C4×C103C24
hypercenter#440D103
hypocenterC103#2951
LCSG ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. #20268273C2semidirect
3. #20268270C2semidirect
4. #20267893C2semidirect
5. #20267892C2semidirect
6. #20267890C2semidirect
7. C4×#13110095C2semidirect
8. #20267883C2semidirect
9. C4×#13110090C2semidirect
10. #20267871C2semidirect
11. #107×D103C2semidirect
12. #20267791C2semidirect
13. #20267789C2semidirect
14. #20267748C2semidirect
15. #440×C103C2semidirect
18. #15693042C4semidirect
61. #13110106C2×C4semidirect
63. #13110104C2×C4semidirect
76. #13110095C2×C4semidirect
77. #13110094C2×C4semidirect
78. #13110090C2×C4semidirect
82. C8×D103C2×C4semidirect
104. SD16×C103C2×C4semidirect
182. C103#2951semidirect
189. #440D103semidirect
263. SD16C4×D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156930422
#202682732
#202682702
#202678932
#202678922
#202678902
C4×#131100952
#202678832
C4×#131100902
#202678712
#107×D1032
#202677912
#202677892
#202677482
#440×C1032
#2951103