Finite Group Databasebeta

← #27205358

Subgroups — #27205358

Order 13184.

372 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#20268403C211yesmaximal, characteristic, complemented
2#20268126C211yesmaximal, characteristic, complemented
3#20268121C211yesmaximal, characteristic, complemented
4#20268098C211yesmaximal, characteristic, complemented
5#20268091C211yesmaximal, characteristic, complemented
6#20268001C211yesmaximal, characteristic, complemented
7#20267996C211yesmaximal, characteristic, complemented
8#20267953C211yesmaximal, characteristic
9#20267953C211yesmaximal, characteristic
10#20267896C211yesmaximal, characteristic, complemented
11#20267891C211yesmaximal, characteristic, complemented
12C4×#13110095C211yesmaximal, characteristic, complemented
13C4×#13110093C211yesmaximal, characteristic, complemented
14#20267852C211yesmaximal, characteristic, complemented
15#520×C103C211yesmaximal, characteristic
16C2×#13110095C2211yescharacteristic
17C2×#13110095C2211yescharacteristic
18C2×#13110093C2211yescharacteristic
19C2×#13110093C2211yescharacteristic
20#15693021C2211yescharacteristic
21#15693014—21no—
22#15693014—21no—
23#15693013C2211yescharacteristic
24#15693011—21no—
25#15693011—21no—
26#15693000C2211yescharacteristic
27#15693000C2211yescharacteristic
28C4×Dic206C2211yescharacteristic
29C4×Dic206C2211yescharacteristic
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
48C2×#41×C103C2211yescharacteristic
49C4×Q8×C103C2211yescharacteristic
50C4×Q8×C103C2211yescharacteristic
51C4×D4×C103—21no—
52C4×D4×C103—21no—
53C4×D4×C103C2211yescharacteristic
54C4×D4×C103C2211yescharacteristic
55#117×C103—21no—
56#117×C103C2211yescharacteristic
57C2×C4⋊C4×C103—21no—
58C2×C4⋊C4×C103C2211yescharacteristic
59C2×Dic206C2311yescharacteristic
60C2×Dic206C2311yescharacteristic
61#13110095—22no—
62#13110095—22no—
63#13110093—22no—
64#13110093—22no—
65C2×C103⋊C8C2311yescharacteristic
66C2×C103⋊C8C2311yescharacteristic
67C2×C103⋊C8C2311yescharacteristic
68C2×C103⋊C8C2311yescharacteristic
69C4⋊Dic103—21no—
70C4⋊Dic103—21no—
71C4⋊Dic103C2311yescharacteristic
72C4⋊Dic103C2311yescharacteristic
73Dic103⋊C4—21no—
74Dic103⋊C4—21no—
75Dic103⋊C4—21no—
76Dic103⋊C4—21no—
77Dic103⋊C4—21no—
78Dic103⋊C4—21no—
79C22⋊Dic103—21no—
80C22⋊Dic103—21no—
81C4×Dic103—21no—
82C4×Dic103—21no—
83#41×C103—22no—
84#41×C103—22no—
85C2×Q8×C103C2311yescharacteristic
86C2×D4×C103—21no—
87C2×D4×C103C2311yescharacteristic
88C22×C4×C103—21no—
89C22×C4×C103—21no—
90C22×C4×C103—21no—
91C22×C4×C103—21no—
92C22×C4×C103C2311yescharacteristic
93C4⋊C4×C103—21no—
94C4⋊C4×C103—21no—
95C4⋊C4×C103—21no—
96C4⋊C4×C103D411yescharacteristic
97C4⋊C4×C103D411yescharacteristic
98C4⋊C4×C103C2311yescharacteristic
99C4⋊C4×C103C2311yescharacteristic
100C22⋊C4×C103—21no—
101C22⋊C4×C103—21no—
102C22⋊C4×C103D411yescharacteristic
103C22⋊C4×C103D411yescharacteristic
104C42×C103—21no—
105C42×C103—21no—
106C42×C103C2311yescharacteristic
107C42×C103C2311yescharacteristic
108C23×C103—21no—
109C23×C103C2×D411yescharacteristic
110Q8×C103—21no—
111Q8×C103#4112yes—
112D4×C103—24no—
113D4×C103—21no—
114D4×C103#4112yes—
115C2×C4×C103—24no—
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×C103—81no—
123C2×C4×C103—81no—
124C2×C4×C103C2×D411yescharacteristic
125C2×C4×C103C2×D411yescharacteristic
126C2×C4×C103C2×D411yescharacteristic
127C2×C4×C103C2×D411yescharacteristic
128C2×C4×C103C2×D411yescharacteristic
129C2×C4×C103C2411yescharacteristic
130C2×Dic103—21no—
131C2×Dic103—21no—
132C2×Dic103—21no—
133C2×Dic103—21no—
134Dic206—21no—
135Dic206—21no—
136Dic206—21no—
137Dic206—21no—
138C103⋊C8—21no—
139C103⋊C8—21no—
140C103⋊C8—21no—
141C103⋊C8—21no—
142C22×C103—21no—
143C22×C103—22no—
144C22×C103—21no—
145C22×C103—21no—
146C22×C103—41no—
147C22×C103—41no—
148C22×C103C22×D411yescharacteristic
149C4×C103—21no—
150C4×C103—22no—
151C4×C103—21no—
152C4×C103—21no—
153C4×C103—21no—
154C4×C103—21no—
155C4×C103—41no—
156C4×C103—41no—
157C4×C103C2×#4111yescharacteristic
158C4×C103C2×#4111yescharacteristic
159Dic103—41no—
160Dic103—41no—
161Dic103—41no—
162Dic103—41no—
163C2×C103—41no—
164C2×C103—42no—
165C2×C103#52511yescharacteristic
166C2×C103#57711yescharacteristic
167C2×C103#57811yescharacteristic
168#3120—1031nomaximal, Sylow
169C103#312011yescharacteristic, complemented, Sylow
170#541—1031no—
171#520D10311yescharacteristic
172#484—1031no—
173#483—1031no—
174#479—1031no—
175#478—1031no—
176#462—1031no—
177#461—1031no—
178#452—1031no—
179#452—1031no—
180#441—1031no—
181#440—1031no—
182C4×Q16—1031no—
183C4×SD16—1031no—
184#433—1031no—
185C2×#41C2×D10311yescharacteristic
186C2×Q16—1031no—
187C2×Q16—1031no—
188C2×SD16—1031no—
189C2×SD16—1031no—
190C4⋊Q8—1031no—
191#126—2061no—
192#126—2061no—
193#125—1031no—
194#125—2061no—
195#125—2061no—
196C22⋊Q8—1031no—
197C22⋊Q8—1031no—
198C4×Q8—1031no—
199C4×Q8—1031no—
200C4×Q8C2×D10311yescharacteristic
201C4×Q8C2×D10311yescharacteristic
202C4×D4—21no—
203C4×D4—21no—
204C4×D4C2×D10311yescharacteristic
205C4×D4C2×D10311yescharacteristic
206#117—21no—
207#117C2×D10311yescharacteristic
208C2×C4⋊C4—21no—
209C2×C4⋊C4C2×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—
228#41—22no—
229#41—22no—
230C2×Q8—1031no—
231C2×Q8—1031no—
232C2×Q8C22×D10311yescharacteristic
233C2×D4—21no—
234C2×D4C22×D10311yescharacteristic
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
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⋊C4—2061no—
258C4⋊C4—2061no—
259C4⋊C4—2061no—
260C4⋊C4—2061no—
261C4⋊C4C22⋊D10311yescharacteristic
262C4⋊C4C22⋊D10311yescharacteristic
263C4⋊C4C22×D10311yescharacteristic
264C4⋊C4C22×D10311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—2061no—
268C22⋊C4—2061no—
269C22⋊C4C22⋊D10311yescharacteristic
270C22⋊C4C22⋊D10311yescharacteristic
271C42—21no—
272C42—21no—
273C42—2061no—
274C42—2061no—
275C42C22×D10311yescharacteristic
276C42C22×D10311yescharacteristic
277C23—21no—
278C23C2×C22⋊D10311yescharacteristic
279Q8—21no—
280Q8—2061no—
281Q8—2061no—
282Q8—2061no—
283Q8—2061no—
284Q8#1311010512yes—
285D4—24no—
286D4—21no—
287D4#1311010512yes—
288C2×C4—24no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—2061no—
298C2×C4—2061no—
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—22no—
313C22—21no—
314C22—21no—
315C22—41no—
316C22—41no—
317C22C22×C22⋊D10311yescharacteristic
318C4—21no—
319C4—22no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—4121no—
327C4—4121no—
328C4—4121no—
329C4—4121no—
330C4C2×#1311010511yescharacteristic
331C4C2×#1311010511yescharacteristic
332C2—41no—
333C2—42no—
334C2#2026830211yescharacteristic
335C2#2026860211yescharacteristic
336C2#2026860611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#520×C103C2
socleC22×C103C22×D4
prime radicalC2×#41×C103C22
hypercenter#520D103
hypocenterC103#3120
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #20268403C2semidirect
2. #20268126C2semidirect
3. #20268121C2semidirect
4. #20268098C2semidirect
5. #20268091C2semidirect
6. #20268001C2semidirect
7. #20267996C2semidirect
10. #20267896C2semidirect
11. #20267891C2semidirect
12. C4×#13110095C2semidirect
13. C4×#13110093C2semidirect
14. #20267852C2semidirect
169. C103#3120semidirect

Maximal subgroups

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

subgroupindex
#202684032
#202681262
#202681212
#202680982
#202680912
#202680012
#202679962
#202679532
#202678962
#202678912
C4×#131100952
C4×#131100932
#202678522
#520×C1032
#3120103