Finite Group Databasebeta

← #27209256

Subgroups — #27209256

Order 13184.

1030 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268526C213yesmaximal, complemented
2#20268507C213yesmaximal, complemented
3#20268494C213yesmaximal, complemented
4#20268479C213yesmaximal, complemented
5#20268463C211yesmaximal, characteristic, complemented
6#20268453C211yesmaximal, characteristic, complemented
7#20268453C211yesmaximal, characteristic, complemented
8#20268415C213yesmaximal, complemented
9#20268397C213yesmaximal, complemented
10#20268328C213yesmaximal, complemented
11#20268326C213yesmaximal, complemented
12#20268273C211yesmaximal, characteristic, complemented
13#20268267C211yesmaximal, characteristic, complemented
14C4×#13110106C211yesmaximal, characteristic, complemented
15#557×C103C211yesmaximal, characteristic, complemented
16C2×#13110106C2211yescharacteristic
17C2×#13110106C2211yescharacteristic
18C2×Q8×D103C2211yescharacteristic
19#15693018C2213yes—
20#15693016C2213yes—
21#15693016C2211yescharacteristic
22#15693016C2216yes—
23#15693012C2213yes—
24#15693010C2213yes—
25#15693010C2216yes—
26#15693009C2213yes—
27#15693009C2213yes—
28#15693006C2216yes—
29#15693006C2213yes—
30#15693006C2213yes—
31#15693006C2216yes—
32#15693001C2213yes—
33#15693001C2213yes—
34#15692997C2213yes—
35#15692996C2213yes—
36#15692996C2213yes—
37#15692996C2213yes—
38#15692996C2213yes—
39#15692996C2216yes—
40#15692996C2213yes—
41Q8×Dic103C2211yescharacteristic
42C4×Dic206C2213yes—
43#15692986C2213yes—
44C4×D412C2213yes—
45C4×D412C2213yes—
46C4×D412C2213yes—
47C4×D412C2213yes—
48C4×D412C2213yes—
49#15692983C2213yes—
50#15692983C2216yes—
51#15692983C2213yes—
52#15692979C2216yes—
53#15692979C2213yes—
54#15692979C2213yes—
55#15692978C2213yes—
56#15692978C2213yes—
57C4⋊C4×D103C2213yes—
58C42×D103C2213yes—
59C4⋊Q8×C103C2213yes—
60#125×C103C2213yes—
61#125×C103C2213yes—
62C4×Q8×C103C2213yes—
63C4×Q8×C103C2211yescharacteristic
64C4×Q8×C103C2211yescharacteristic
65C4×Q8×C103C2211yescharacteristic
66#13110106—24no—
67#13110106—24no—
68C2×Dic206C2313yes—
69Q8×D103—24no—
70C2×D412C2313yes—
71C2×D412C2313yes—
72C2×D412C2316yes—
73C2×D412C2313yes—
74C2×D412C2313yes—
75C2×D412C2313yes—
76C2×C4×D103C2313yes—
77C2×C4×D103C2313yes—
78C2×C4×D103C2313yes—
79C2×C4×D103C2313yes—
80C2×C4×D103C2313yes—
81C2×C4×D103C2316yes—
82C4⋊Dic103C2313yes—
83C4⋊Dic103C2313yes—
84C4⋊Dic103C2311yescharacteristic
85C4⋊Dic103C2313yes—
86Dic103⋊C4C2313yes—
87Dic103⋊C4C2311yescharacteristic
88Dic103⋊C4C2313yes—
89Dic103⋊C4C2313yes—
90(C2×D103)⋊C4C2311yescharacteristic
91(C2×D103)⋊C4C2313yes—
92(C2×D103)⋊C4C2313yes—
93(C2×D103)⋊C4C2313yes—
94(C2×D103)⋊C4C2313yes—
95(C2×D103)⋊C4C2316yes—
96(C2×D103)⋊C4C2316yes—
97(C2×D103)⋊C4C2313yes—
98(C2×D103)⋊C4C2316yes—
99(C2×D103)⋊C4C2311yescharacteristic
100(C2×D103)⋊C4C2311yescharacteristic
101(C2×D103)⋊C4C2313yes—
102(C2×D103)⋊C4C2313yes—
103C4×Dic103C2311yescharacteristic
104C4×Dic103C2313yes—
105C4×Dic103C2313yes—
106C4×Dic103C2316yes—
107C2×Q8×C103C2313yes—
108C2×Q8×C103C2311yescharacteristic
109C4⋊C4×C103C2311yescharacteristic
110C4⋊C4×C103C2313yes—
111C4⋊C4×C103C2313yes—
112C4⋊C4×C103C2313yes—
113C4⋊C4×C103C2313yes—
114C4⋊C4×C103C2313yes—
115C4⋊C4×C103C2316yes—
116C42×C103C2313yes—
117C42×C103C2313yes—
118C42×C103C2313yes—
119C22×D103C2411yescharacteristic
120C22×D103C2413yes—
121C22×D103C2413yes—
122Q8×C103—43no—
123Q8×C103#4114yes—
124C2×C4×C103C2411yescharacteristic
125C2×C4×C103C2411yescharacteristic
126C2×C4×C103C2411yescharacteristic
127C2×C4×C103C2413yes—
128C2×C4×C103C2413yes—
129C2×C4×C103C2413yes—
130C2×C4×C103C2413yes—
131C2×Dic103C2411yescharacteristic
132C2×Dic103C2413yes—
133C2×Dic103C2411yescharacteristic
134C2×Dic103C2413yes—
135C2×Dic103C2411yescharacteristic
136D412—26no—
137D412—26no—
138D412—43no—
139D412—43no—
140D412—43no—
141D412—46no—
142C4×D103—26no—
143C4×D103—26no—
144C4×D103—26no—
145C4×D103—43no—
146C4×D103—46no—
147C4×D103—43no—
148Dic206—26no—
149C22×C103C2511yescharacteristic
150C2×D103—21no—
151C2×D103—23no—
152C2×D103—23no—
153C2×D103—23no—
154C2×D103—23no—
155C2×D103—23no—
156C2×D103—21no—
157C2×D103—23no—
158C2×D103—21no—
159C4×C103—21no—
160C4×C103—23no—
161C4×C103—23no—
162C4×C103—21no—
163C4×C103—23no—
164C4×C103—21no—
165C4×C103C2×#4116yes—
166Dic103—23no—
167Dic103—21no—
168Dic103—21no—
169Dic103—21no—
170Dic103—23no—
171C2×C103C22×#4111yescharacteristic
172C2×C103#58511yescharacteristic
173C2×C103#58511yescharacteristic
174D103—41no—
175D103—43no—
176D103—43no—
177#3524—1031nomaximal, Sylow
178C103#352411yescharacteristic, complemented, Sylow
179#559—1033no—
180#557D10311yescharacteristic, complemented
181#555—1033no—
182#553—1033no—
183#552—1033no—
184#550—1031no—
185#548—1031no—
186#548—1031no—
187#542—1033no—
188#540—1033no—
189#529—1033no—
190#529—1033no—
191#520—1031no—
192#519—1031no—
193C4×#41—1031no—
194C2×#41—1031no—
195C2×#41—1031no—
196C22×Q8—1031no—
197C4⋊Q8C2×D10313yes—
198#127—1033no—
199#126—1031no—
200#126—1033no—
201#126—1036no—
202#125—1033no—
203#125C2×D10313yes—
204#125C2×D10313yes—
205#124—1033no—
206#124—1036no—
207#124—1033no—
208#124—1033no—
209#123—1036no—
210#123—1033no—
211#123—1033no—
212#123—1036no—
213C22⋊Q8—1033no—
214C22⋊Q8—1033no—
215C22⋊Q8—1033no—
216#121—1033no—
217#121—1033no—
218#121—1033no—
219#121—1033no—
220#121—1036no—
221#121—1033no—
222C4×Q8—1031no—
223C4×Q8—1033no—
224C4×Q8—1033no—
225C4×Q8C2×D10311yescharacteristic
226C4×Q8C2×D10311yescharacteristic
227C4×Q8C2×D10311yescharacteristic
228C4×Q8C2×D10313yes—
229C4×D4—1033no—
230C4×D4—1033no—
231C4×D4—1036no—
232C4×D4—1033no—
233C4×D4—1033no—
234C4×D4—1033no—
235C4×D4—1033no—
236C4×D4—1033no—
237#117—1033no—
238#117—1033no—
239#117—1036no—
240#117—1033no—
241#117—1033no—
242C2×C4⋊C4—1033no—
243C2×C42—1033no—
244#41—2064no—
245#41—2064no—
246C2×Q8—1033no—
247C2×Q8—2064no—
248C2×Q8C22×D10313yes—
249C2×Q8C22×D10311yescharacteristic
250C2×D4—1033no—
251C2×D4—1033no—
252C2×D4—1036no—
253C2×D4—1033no—
254C2×D4—1033no—
255C2×D4—1033no—
256C22×C4—1033no—
257C22×C4—1033no—
258C22×C4—1036no—
259C22×C4—1033no—
260C22×C4—1033no—
261C22×C4—1033no—
262C4⋊C4—1033no—
263C4⋊C4—1031no—
264C4⋊C4—1033no—
265C4⋊C4—1033no—
266C4⋊C4—1033no—
267C4⋊C4—1033no—
268C4⋊C4—1031no—
269C4⋊C4—1033no—
270C4⋊C4C22×D10313yes—
271C4⋊C4C22×D10313yes—
272C4⋊C4C22×D10313yes—
273C4⋊C4C22×D10316yes—
274C4⋊C4C22×D10313yes—
275C4⋊C4C22×D10311yescharacteristic
276C4⋊C4C22×D10313yes—
277C22⋊C4—1031no—
278C22⋊C4—1033no—
279C22⋊C4—1033no—
280C22⋊C4—1033no—
281C22⋊C4—1036no—
282C22⋊C4—1033no—
283C22⋊C4—1036no—
284C22⋊C4—1031no—
285C22⋊C4—1033no—
286C22⋊C4—1031no—
287C22⋊C4—1033no—
288C22⋊C4—1036no—
289C22⋊C4—1033no—
290C42—1031no—
291C42—1033no—
292C42—1033no—
293C42—1036no—
294C42C22×D10313yes—
295C42C22×D10313yes—
296C42C22×D10313yes—
297C23—1031no—
298C23—1033no—
299C23—1033no—
300Q8—43no—
301Q8—2066no—
302Q8#1311010614yes—
303D4—4123no—
304D4—4126no—
305D4—4123no—
306D4—4123no—
307D4—2066no—
308D4—2066no—
309C2×C4—1031no—
310C2×C4—1031no—
311C2×C4—1033no—
312C2×C4—1033no—
313C2×C4—1031no—
314C2×C4—4123no—
315C2×C4—4123no—
316C2×C4—4126no—
317C2×C4—2066no—
318C2×C4—2066no—
319C2×C4—2066no—
320C2×C4C23×D10313yes—
321C2×C4C23×D10311yescharacteristic
322C2×C4C23×D10313yes—
323C2×C4C23×D10311yescharacteristic
324C2×C4C23×D10311yescharacteristic
325C2×C4C23×D10313yes—
326C2×C4C23×D10313yes—
327C22—2061no—
328C22—2063no—
329C22—2063no—
330C22—2063no—
331C22—2061no—
332C22—2063no—
333C22—2063no—
334C22—2063no—
335C22—2061no—
336C22C24×D10311yescharacteristic
337C4—23no—
338C4—23no—
339C4—21no—
340C4—21no—
341C4—23no—
342C4—21no—
343C4—2061no—
344C4—2061no—
345C4—2063no—
346C4—2061no—
347C4—2063no—
348C4C2×#1311010616yes—
349C2—4121no—
350C2—4123no—
351C2—4123no—
352C2C22×#1311010611yescharacteristic
353C2#2026862711yescharacteristic
354C2#2026862811yescharacteristic
subgroupG/H
center, FrattiniC22C24×D103
commutator, socle, cosocleC22×C103C25
Fitting#557×C103C2
hypercenter#557D103
hypocenterC103#3524
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ #557

Complements

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

NH ≅ G/Ntype
1. #20268526C2semidirect
2. #20268507C2semidirect
3. #20268494C2semidirect
4. #20268479C2semidirect
5. #20268463C2semidirect
6. #20268453C2semidirect
7. #20268453C2semidirect
8. #20268415C2semidirect
9. #20268397C2semidirect
10. #20268328C2semidirect
11. #20268326C2semidirect
12. #20268273C2semidirect
13. #20268267C2semidirect
14. C4×#13110106C2semidirect
15. #557×C103C2semidirect
178. C103#3524semidirect
180. #557D103semidirect

Maximal subgroups

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

subgroupindex
#202685262
#202685072
#202684942
#202684792
#202684632
#202684532
#202684152
#202683972
#202683282
#202683262
#202682732
#202682672
C4×#131101062
#557×C1032
#3524103