Finite Group Databasebeta

← #27205367

Subgroups — #27205367

Order 13184.

370 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268268C211yesmaximal, characteristic, complemented
2#20268129C211yesmaximal, characteristic, complemented
3#20268112C211yesmaximal, characteristic
4#20268083C211yesmaximal, characteristic, complemented
5#20268073C211yesmaximal, characteristic, complemented
6#20268010C211yesmaximal, characteristic, complemented
7#20268010C211yesmaximal, characteristic, complemented
8#20267946C211yesmaximal, characteristic, complemented
9#20267929C211yesmaximal, characteristic
10#20267896C211yesmaximal, characteristic, complemented
11#20267891C211yesmaximal, characteristic, complemented
12C4×#13110095C211yesmaximal, characteristic, complemented
13C4×#13110093C211yesmaximal, characteristic, complemented
14#20267852C211yesmaximal, characteristic, complemented
15#542×C103C211yesmaximal, characteristic
16C22×Dic206C2211yescharacteristic
17C2×#13110095C2211yescharacteristic
18C2×#13110095C2211yescharacteristic
19C2×#13110093C2211yescharacteristic
20C2×#13110093C2211yescharacteristic
21C4×Dic206C2211yescharacteristic
22C4×Dic206C2211yescharacteristic
23C4×Dic206C2211yescharacteristic
24C4×Dic206C2211yescharacteristic
25#15692986—21no—
26#15692986—21no—
27#15692980C2211yescharacteristic
28#15692977—21no—
29#15692977—21no—
30#15692954C2211yescharacteristic
31#15692954C2211yescharacteristic
32#15692952C2211yescharacteristic
33#15692952C2211yescharacteristic
34C4⋊(C103⋊C8)C2211yescharacteristic
35C4⋊(C103⋊C8)C2211yescharacteristic
36#15692945C2211yescharacteristic
37#15692945C2211yescharacteristic
38#15692944C2211yescharacteristic
39#15692944C2211yescharacteristic
40#15692944C2211yescharacteristic
41#15692944C2211yescharacteristic
42#15692942C2211yescharacteristic
43#15692942C2211yescharacteristic
44C22⋊(C103⋊C8)C2211yescharacteristic
45C22⋊(C103⋊C8)C2211yescharacteristic
46#15692932C2211yescharacteristic
47C4×C103⋊C8C2211yescharacteristic
48C4⋊Q8×C103C2211yescharacteristic
49#126×C103—21no—
50#124×C103—21no—
51#124×C103C2211yescharacteristic
52#123×C103—21no—
53C22⋊Q8×C103—21no—
54C22⋊Q8×C103C2211yescharacteristic
55#121×C103C2211yescharacteristic
56C4×Q8×C103C2211yescharacteristic
57C4×D4×C103C2211yescharacteristic
58#117×C103C2211yescharacteristic
59C2×Dic206—21no—
60C2×Dic206—22no—
61C2×Dic206—22no—
62C2×Dic206C2311yescharacteristic
63C2×Dic206C2311yescharacteristic
64C22×Dic103—21no—
65#13110095—22no—
66#13110095—22no—
67#13110093—22no—
68#13110093—22no—
69C2×C103⋊C8C2311yescharacteristic
70C2×C103⋊C8C2311yescharacteristic
71C2×C103⋊C8C2311yescharacteristic
72C2×C103⋊C8C2311yescharacteristic
73C4⋊Dic103C2311yescharacteristic
74C4⋊Dic103C2311yescharacteristic
75Dic103⋊C4—21no—
76Dic103⋊C4—21no—
77Dic103⋊C4—21no—
78Dic103⋊C4—21no—
79C22⋊Dic103—21no—
80C4×Dic103—21no—
81C4×Dic103—21no—
82C4×Dic103—21no—
83C4×Dic103—21no—
84C4×Dic103—21no—
85C2×Q8×C103—21no—
86C2×Q8×C103C2311yescharacteristic
87C2×D4×C103—21no—
88C2×D4×C103C2311yescharacteristic
89C22×C4×C103—21no—
90C22×C4×C103C2311yescharacteristic
91C4⋊C4×C103—21no—
92C4⋊C4×C103—21no—
93C4⋊C4×C103—21no—
94C4⋊C4×C103D411yescharacteristic
95C4⋊C4×C103D411yescharacteristic
96C4⋊C4×C103C2311yescharacteristic
97C4⋊C4×C103C2311yescharacteristic
98C22⋊C4×C103—21no—
99C22⋊C4×C103—21no—
100C22⋊C4×C103—21no—
101C22⋊C4×C103—21no—
102C22⋊C4×C103—21no—
103C22⋊C4×C103D411yescharacteristic
104C22⋊C4×C103D411yescharacteristic
105C42×C103—21no—
106C42×C103C2311yescharacteristic
107C42×C103C2311yescharacteristic
108C23×C103—21no—
109C23×C103C2×D411yescharacteristic
110Q8×C103—21no—
111Q8×C103—21no—
112Q8×C103—81no—
113D4×C103—21no—
114D4×C103—21no—
115D4×C103—81no—
116C2×C4×C103—21no—
117C2×C4×C103—21no—
118C2×C4×C103—21no—
119C2×C4×C103—21no—
120C2×C4×C103—21no—
121C2×C4×C103—81no—
122C2×C4×C103C2×D411yescharacteristic
123C2×C4×C103C2×D411yescharacteristic
124C2×C4×C103C2×D411yescharacteristic
125C2×C4×C103C2×D411yescharacteristic
126C2×C4×C103C2×D411yescharacteristic
127C2×C4×C103C2411yescharacteristic
128C2×Dic103—24no—
129C2×Dic103—21no—
130C2×Dic103—21no—
131C2×Dic103—21no—
132C2×Dic103—21no—
133Dic206—24no—
134Dic206—21no—
135Dic206—21no—
136Dic206#4112yes—
137Dic206#4112yes—
138C103⋊C8—21no—
139C103⋊C8—21no—
140C103⋊C8—21no—
141C103⋊C8—21no—
142C22×C103—21no—
143C22×C103—21no—
144C22×C103—21no—
145C22×C103—41no—
146C22×C103—41no—
147C22×C103—41no—
148C22×C103C22×D411yescharacteristic
149C4×C103—21no—
150C4×C103—21no—
151C4×C103—21no—
152C4×C103—21no—
153C4×C103—21no—
154C4×C103—41no—
155C4×C103—41no—
156C4×C103—41no—
157C4×C103C2×#4111yescharacteristic
158C4×C103C2×#4111yescharacteristic
159Dic103—22no—
160Dic103—22no—
161Dic103—41no—
162Dic103—41no—
163C2×C103—41no—
164C2×C103—81no—
165C2×C103#52511yescharacteristic
166C2×C103#57711yescharacteristic
167C2×C103#57811yescharacteristic
168#3121—1031nomaximal, Sylow
169C103#312111yescharacteristic, complemented, Sylow
170#542D10311yescharacteristic
171#519—1031no—
172#485—1031no—
173#482—1031no—
174#477—1031no—
175#475—1031no—
176#464—1031no—
177#464—1031no—
178#451—1031no—
179#448—1031no—
180#441—1031no—
181#440—1031no—
182C4×Q16—1031no—
183C4×SD16—1031no—
184#433—1031no—
185C22×Q8—1031no—
186C2×Q16—1031no—
187C2×Q16—1031no—
188C2×SD16—1031no—
189C2×SD16—1031no—
190C4⋊Q8C2×D10311yescharacteristic
191#126—21no—
192#124—21no—
193#124C2×D10311yescharacteristic
194#123—21no—
195C22⋊Q8—21no—
196C22⋊Q8C2×D10311yescharacteristic
197#121C2×D10311yescharacteristic
198C4×Q8—1031no—
199C4×Q8—1031no—
200C4×Q8—1031no—
201C4×Q8—1031no—
202C4×Q8—2061no—
203C4×Q8—2061no—
204C4×Q8C2×D10311yescharacteristic
205C4×D4C2×D10311yescharacteristic
206#117—1031no—
207#117—2061no—
208#117—2061no—
209#117C2×D10311yescharacteristic
210#107—1031no—
211#107—1031no—
212#106—1031no—
213#106—1031no—
214C4⋊C8—1031no—
215C4⋊C8—1031no—
216#103—1031no—
217#103—1031no—
218#103—1031no—
219#103—1031no—
220#103—1031no—
221#103—1031no—
222#102—1031no—
223#102—1031no—
224C22⋊C8—1031no—
225C22⋊C8—1031no—
226#97—1031no—
227C4×C8—1031no—
228C2×Q8—21no—
229C2×Q8—1031no—
230C2×Q8—1031no—
231C2×Q8—2062no—
232C2×Q8—2062no—
233C2×Q8—2061no—
234C2×Q8C22×D10311yescharacteristic
235C2×D4—21no—
236C2×D4C22×D10311yescharacteristic
237C22×C4—21no—
238C22×C4—2061no—
239C22×C4C22×D10311yescharacteristic
240Q16—2062no—
241Q16—2062no—
242SD16—2062no—
243SD16—2062no—
244C2×C8—1031no—
245C2×C8—1031no—
246C2×C8—1031no—
247C2×C8—1031no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—1031no—
252C4⋊C4—1031no—
253C4⋊C4—2061no—
254C4⋊C4—2061no—
255C4⋊C4—2061no—
256C4⋊C4—2061no—
257C4⋊C4C22⋊D10311yescharacteristic
258C4⋊C4C22⋊D10311yescharacteristic
259C4⋊C4C22×D10311yescharacteristic
260C4⋊C4C22×D10311yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—2061no—
267C22⋊C4C22⋊D10311yescharacteristic
268C22⋊C4C22⋊D10311yescharacteristic
269C42—21no—
270C42—2061no—
271C42—2061no—
272C42—2061no—
273C42—2061no—
274C42—2061no—
275C42C22×D10311yescharacteristic
276C42C22×D10311yescharacteristic
277C23—21no—
278C23C2×C22⋊D10311yescharacteristic
279Q8—21no—
280Q8—21no—
281Q8—81no—
282Q8—1032no—
283Q8—1032no—
284Q8—2064no—
285Q8—2061no—
286Q8—2061no—
287D4—21no—
288D4—21no—
289D4—81no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—81no—
296C2×C4—2061no—
297C2×C4—2061no—
298C2×C4—2064no—
299C2×C4—2061no—
300C2×C4—2061no—
301C2×C4C2×C22⋊D10311yescharacteristic
302C2×C4C2×C22⋊D10311yescharacteristic
303C2×C4C2×C22⋊D10311yescharacteristic
304C2×C4C2×C22⋊D10311yescharacteristic
305C2×C4C2×C22⋊D10311yescharacteristic
306C2×C4C23×D10311yescharacteristic
307C8—2061no—
308C8—2061no—
309C8—2061no—
310C8—2061no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22C22×C22⋊D10311yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—4121no—
327C4—4121no—
328C4—2062no—
329C4—2062no—
330C4#41×D10311yescharacteristic
331C4#41×D10311yescharacteristic
332C2—41no—
333C2—81no—
334C2#2026829811yescharacteristic
335C2#2026860211yescharacteristic
336C2#2026860611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#542×C103C2
socleC22×C103C22×D4
prime radical#121×C103C22
hypercenter#542D103
hypocenterC103#3121
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #20268268C2semidirect
2. #20268129C2semidirect
4. #20268083C2semidirect
5. #20268073C2semidirect
6. #20268010C2semidirect
7. #20268010C2semidirect
8. #20267946C2semidirect
10. #20267896C2semidirect
11. #20267891C2semidirect
12. C4×#13110095C2semidirect
13. C4×#13110093C2semidirect
14. #20267852C2semidirect
169. C103#3121semidirect

Maximal subgroups

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

subgroupindex
#202682682
#202681292
#202681122
#202680832
#202680732
#202680102
#202679462
#202679292
#202678962
#202678912
C4×#131100952
C4×#131100932
#202678522
#542×C1032
#3121103