Finite Group Databasebeta

← #27205829

Subgroups — #27205829

Order 13184.

374 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268412C211yesmaximal, characteristic, complemented
2#20268201C211yesmaximal, characteristic, complemented
3#20268178C211yesmaximal, characteristic, complemented
4#20268148C211yesmaximal, characteristic, complemented
5#20268137C211yesmaximal, characteristic, complemented
6#20268042C211yesmaximal, characteristic, complemented
7#20268035C211yesmaximal, characteristic, complemented
8#20268025C211yesmaximal, characteristic, complemented
9#20268018C211yesmaximal, characteristic, complemented
10#20267901C211yesmaximal, characteristic, complemented
11#20267891C211yesmaximal, characteristic, complemented
12C4×#13110093C211yesmaximal, characteristic, complemented
13C4×#13110090C211yesmaximal, characteristic, complemented
14#20267747C211yesmaximal, characteristic, complemented
15#540×C103C211yesmaximal, characteristic, complemented
16C2×#13110093C2211yescharacteristic
17C2×#13110093C2211yescharacteristic
18C2×#13110090C2211yescharacteristic
19C2×#13110090C2211yescharacteristic
20C2×#13110089C2211yescharacteristic
21C22×C103⋊C8C2211yescharacteristic
22#15693021C2211yescharacteristic
23#15693016—21no—
24#15693009C2211yescharacteristic
25#15693007—21no—
26#15693003—21no—
27#15693000C2211yescharacteristic
28#15692999—21no—
29#15692995C2211yescharacteristic
30C4×Dic206C2211yescharacteristic
31C4×D412C2211yescharacteristic
32#15692954C2211yescharacteristic
33#15692954C2211yescharacteristic
34#15692952C2211yescharacteristic
35#15692952C2211yescharacteristic
36#15692944C2211yescharacteristic
37#15692944C2211yescharacteristic
38#15692942C2211yescharacteristic
39#15692942C2211yescharacteristic
40#15692942C2211yescharacteristic
41#15692942C2211yescharacteristic
42#15692941C2211yescharacteristic
43#15692941C2211yescharacteristic
44#15692932C2211yescharacteristic
45#15692932C2211yescharacteristic
46C4×C103⋊C8C2211yescharacteristic
47C4×C103⋊C8C2211yescharacteristic
48#127×C103C2211yescharacteristic
49#125×C103C2211yescharacteristic
50#123×C103—21no—
51#123×C103—21no—
52#121×C103—21no—
53#121×C103—21no—
54#121×C103C2211yescharacteristic
55#121×C103C2211yescharacteristic
56C4×D4×C103C2211yescharacteristic
57C4×D4×C103C2211yescharacteristic
58#117×C103C2211yescharacteristic
59C2×Dic206—21no—
60C2×Dic206C2311yescharacteristic
61C2×D412C2311yescharacteristic
62C2×C22⋊D103—21no—
63C2×C4×D103—21no—
64#13110093—22no—
65#13110093—22no—
66#13110090—22no—
67#13110090—22no—
68#13110089—22no—
69C2×C103⋊C8—22no—
70C2×C103⋊C8C2311yescharacteristic
71C2×C103⋊C8C2311yescharacteristic
72C2×C103⋊C8C2311yescharacteristic
73C2×C103⋊C8C2311yescharacteristic
74C4⋊Dic103—21no—
75C4⋊Dic103C2311yescharacteristic
76C4⋊Dic103C2311yescharacteristic
77Dic103⋊C4—21no—
78Dic103⋊C4—21no—
79C22⋊Dic103—21no—
80(C2×D103)⋊C4—21no—
81(C2×D103)⋊C4—21no—
82(C2×D103)⋊C4—21no—
83(C2×D103)⋊C4—21no—
84C4×Dic103—21no—
85C2×D4×C103—21no—
86C2×D4×C103—21no—
87C2×D4×C103—21no—
88C2×D4×C103—21no—
89C2×D4×C103C2311yescharacteristic
90C2×D4×C103C2311yescharacteristic
91C22×C4×C103—21no—
92C22×C4×C103—21no—
93C22×C4×C103C2311yescharacteristic
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×C103—21no—
103C22⋊C4×C103—21no—
104C22⋊C4×C103D411yescharacteristic
105C22⋊C4×C103D411yescharacteristic
106C42×C103C2311yescharacteristic
107C42×C103C2311yescharacteristic
108C23×C103—21no—
109C23×C103—21no—
110C23×C103C2×D411yescharacteristic
111C22×D103—21no—
112D4×C103—21no—
113D4×C103—21no—
114D4×C103—21no—
115D4×C103—21no—
116D4×C103—81no—
117D4×C103—81no—
118D4×C103—81no—
119D4×C103—81no—
120C2×C4×C103—21no—
121C2×C4×C103—21no—
122C2×C4×C103—21no—
123C2×C4×C103—21no—
124C2×C4×C103—81no—
125C2×C4×C103—81no—
126C2×C4×C103C2×D411yescharacteristic
127C2×C4×C103C2×D411yescharacteristic
128C2×C4×C103C2×D411yescharacteristic
129C2×C4×C103C2×D411yescharacteristic
130C2×C4×C103C2×D411yescharacteristic
131C2×C4×C103C2411yescharacteristic
132C22⋊D103—81no—
133C2×Dic103—21no—
134C2×Dic103—21no—
135C2×Dic103—21no—
136D412—21no—
137D412—21no—
138C4×D103—81no—
139Dic206—21no—
140Dic206—21no—
141Dic206—81no—
142C103⋊C8—21no—
143C103⋊C8—21no—
144C103⋊C8#4112yes—
145C103⋊C8#4112yes—
146C22×C103—21no—
147C22×C103—21no—
148C22×C103—21no—
149C22×C103—41no—
150C22×C103—41no—
151C22×C103—41no—
152C22×C103—41no—
153C22×C103—41no—
154C22×C103—41no—
155C22×C103C22×D411yescharacteristic
156C2×D103—41no—
157C2×D103—41no—
158C2×D103—41no—
159C4×C103—21no—
160C4×C103—21no—
161C4×C103—21no—
162C4×C103—21no—
163C4×C103—21no—
164C4×C103—41no—
165C4×C103—41no—
166C4×C103C2×#4111yescharacteristic
167C4×C103C2×#4111yescharacteristic
168Dic103—41no—
169Dic103—41no—
170Dic103—41no—
171C2×C103—41no—
172C2×C103—81no—
173C2×C103—81no—
174C2×C103#53211yescharacteristic
175C2×C103#57611yescharacteristic
176C2×C103#57711yescharacteristic
177D103—81no—
178#3179—1031nomaximal, Sylow
179C103#317911yescharacteristic, complemented, Sylow
180#542—1031no—
181#540D10311yescharacteristic, complemented
182#501—1031no—
183#496—1031no—
184#488—1031no—
185#486—1031no—
186#469—1031no—
187#468—1031no—
188#466—1031no—
189#465—1031no—
190#442—1031no—
191#440—1031no—
192C4×SD16—1031no—
193C4×D8—1031no—
194#405—1031no—
195C2×SD16—1031no—
196C2×SD16—1031no—
197C2×D8—1031no—
198C2×D8—1031no—
199C2×M16—1031no—
200C22×C8—1031no—
201C4⋊Q8—1031no—
202#127C2×D10311yescharacteristic
203#126—2061no—
204#125C2×D10311yescharacteristic
205#124—1031no—
206#124—2061no—
207#123—21no—
208#123—21no—
209#123—2061no—
210C22⋊Q8—1031no—
211C22⋊Q8—2061no—
212#121—21no—
213#121—21no—
214#121—1031no—
215#121C2×D10311yescharacteristic
216#121C2×D10311yescharacteristic
217C4×Q8—1031no—
218C4×D4—1031no—
219C4×D4C2×D10311yescharacteristic
220C4×D4C2×D10311yescharacteristic
221#117C2×D10311yescharacteristic
222#107—1031no—
223#107—1031no—
224#106—1031no—
225#106—1031no—
226#103—1031no—
227#103—1031no—
228#102—1031no—
229#102—1031no—
230#102—1031no—
231#102—1031no—
232#102—1031no—
233#102—1031no—
234#97—1031no—
235#97—1031no—
236C4×C8—1031no—
237C4×C8—1031no—
238C2×Q8—1031no—
239C2×Q8—2061no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—1031no—
245C2×D4—2061no—
246C2×D4C22×D10311yescharacteristic
247C2×D4C22×D10311yescharacteristic
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—2061no—
251C22×C4C22×D10311yescharacteristic
252SD16—2062no—
253SD16—2062no—
254D8—2062no—
255D8—2062no—
256M16—2062no—
257C2×C8—1031no—
258C2×C8—1031no—
259C2×C8—1031no—
260C2×C8—1031no—
261C2×C8—2062no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—1031no—
265C4⋊C4—1031no—
266C4⋊C4—2061no—
267C4⋊C4—2061no—
268C4⋊C4—2061no—
269C4⋊C4C22⋊D10311yescharacteristic
270C4⋊C4C22⋊D10311yescharacteristic
271C4⋊C4C22×D10311yescharacteristic
272C4⋊C4C22×D10311yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—2061no—
278C22⋊C4—2061no—
279C22⋊C4—2061no—
280C22⋊C4—2061no—
281C22⋊C4—2061no—
282C22⋊C4C22⋊D10311yescharacteristic
283C22⋊C4C22⋊D10311yescharacteristic
284C42—2061no—
285C42C22×D10311yescharacteristic
286C42C22×D10311yescharacteristic
287C23—21no—
288C23—21no—
289C23—2061no—
290C23C2×C22⋊D10311yescharacteristic
291Q8—8241no—
292Q8—2061no—
293Q8—2061no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—81no—
299D4—81no—
300D4—81no—
301D4—81no—
302D4—8241no—
303D4—2061no—
304D4—2061no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—8241no—
312C2×C4—2061no—
313C2×C4—2061no—
314C2×C4—2061no—
315C2×C4C2×C22⋊D10311yescharacteristic
316C2×C4C2×C22⋊D10311yescharacteristic
317C2×C4C2×C22⋊D10311yescharacteristic
318C2×C4C2×C22⋊D10311yescharacteristic
319C2×C4C2×C22⋊D10311yescharacteristic
320C2×C4C23×D10311yescharacteristic
321C8—1032no—
322C8—1032no—
323C8—2061no—
324C8—2061no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—4121no—
335C22—4121no—
336C22—4121no—
337C22C22×C22⋊D10311yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—4121no—
346C4—4121no—
347C4—4121no—
348C4#41×D10311yescharacteristic
349C4#41×D10311yescharacteristic
350C2—41no—
351C2—81no—
352C2—81no—
353C2—8241no—
354C2#2026833711yescharacteristic
355C2#2026859411yescharacteristic
356C2#2026860211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#540×C103C2
socleC22×C103C22×D4
hypercenter#540D103
hypocenterC103#3179
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #20268412C2semidirect
2. #20268201C2semidirect
3. #20268178C2semidirect
4. #20268148C2semidirect
5. #20268137C2semidirect
6. #20268042C2semidirect
7. #20268035C2semidirect
8. #20268025C2semidirect
9. #20268018C2semidirect
10. #20267901C2semidirect
11. #20267891C2semidirect
12. C4×#13110093C2semidirect
13. C4×#13110090C2semidirect
14. #20267747C2semidirect
15. #540×C103C2semidirect
179. C103#3179semidirect
181. #540D103semidirect

Maximal subgroups

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

subgroupindex
#202684122
#202682012
#202681782
#202681482
#202681372
#202680422
#202680352
#202680252
#202680182
#202679012
#202678912
C4×#131100932
C4×#131100902
#202677472
#540×C1032
#3179103