Finite Group Databasebeta

← #27208734

Subgroups — #27208734

Order 13184.

1112 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
1#20268523C213yesmaximal, complemented
2#20268517C211yesmaximal, characteristic, complemented
3#20268512C213yesmaximal, complemented
4#20268493C213yesmaximal, complemented
5#20268487C213yesmaximal, complemented
6#20268460C211yesmaximal, characteristic, complemented
7#20268452C211yesmaximal, characteristic, complemented
8#20268336C213yesmaximal, complemented
9#20268327C213yesmaximal, complemented
10#20268320C213yesmaximal, complemented
11#41×Dic103C211yesmaximal, characteristic, complemented
12C4×#13110106C211yesmaximal, characteristic, complemented
13C4×#13110104C213yesmaximal, complemented
14C2×Q8×Dic103C211yesmaximal, characteristic, complemented
15#548×C103C211yesmaximal, characteristic, complemented
16C2×#13110106C2211yescharacteristic
17C2×#13110104C2213yes—
18#15693020C2213yes—
19#15693017C2213yes—
20#15693016C2216yes—
21#15693014C2216yes—
22#15693013C2213yes—
23#15693012C2213yes—
24#15693010C2213yes—
25#15693007C2216yes—
26#15693005C2216yes—
27#15693003C2216yes—
28#15692997C2213yes—
29#15692995C2213yes—
30#15692995C2213yes—
31#15692993C2216yes—
32#15692992C2213yes—
33Q8×Dic103C2213yes—
34Q8×Dic103C2211yescharacteristic
35Q8×Dic103C2211yescharacteristic
36Q8×Dic103C2213yes—
37Q8×Dic103C2211yescharacteristic
38C4×Dic206C2213yes—
39#15692986C2213yes—
40C4×D412C2213yes—
41D4×Dic103C2213yes—
42D4×Dic103C2213yes—
43D4×Dic103C2213yes—
44#15692983C2213yes—
45C4×C22⋊D103C2213yes—
46C4×C22⋊D103C2213yes—
47(C22⋊D103)⋊C4C2216yes—
48(C22⋊D103)⋊C4C2213yes—
49(C22⋊D103)⋊C4C2213yes—
50#15692980C2213yes—
51#15692979C2213yes—
52#15692979C2213yes—
53#15692977C2213yes—
54#15692977C2211yescharacteristic
55C2×C4⋊Dic103C2213yes—
56C2×C4×Dic103C2213yes—
57C2×C4×Dic103C2213yes—
58C42×D103C2213yes—
59C2×#41×C103C2211yescharacteristic
60C22×Q8×C103C2211yescharacteristic
61#124×C103C2213yes—
62C22⋊Q8×C103C2213yes—
63#121×C103C2213yes—
64C4×Q8×C103C2211yescharacteristic
65C4×D4×C103C2213yes—
66#13110106—24no—
67#13110104—212no—
68C2×Dic206C2313yes—
69C2×D412C2313yes—
70C2×C22⋊D103C2313yes—
71C2×C22⋊D103C2313yes—
72C2×C22⋊D103C2316yes—
73C22×Dic103C2313yes—
74C22×Dic103C2313yes—
75C22×Dic103C2313yes—
76C22×Dic103C2311yescharacteristic
77C2×C4×D103C2313yes—
78C2×C4×D103C2313yes—
79C2×C4×D103C2313yes—
80C4⋊Dic103C2313yes—
81C4⋊Dic103C2313yes—
82C4⋊Dic103C2316yes—
83C4⋊Dic103C2313yes—
84C4⋊Dic103C2313yes—
85Dic103⋊C4C2311yescharacteristic
86Dic103⋊C4C2313yes—
87Dic103⋊C4C2311yescharacteristic
88Dic103⋊C4C2313yes—
89Dic103⋊C4C2316yes—
90C22⋊Dic103C2311yescharacteristic
91C22⋊Dic103C2313yes—
92C22⋊Dic103C2316yes—
93(C2×D103)⋊C4C2313yes—
94(C2×D103)⋊C4C2313yes—
95(C2×D103)⋊C4C2316yes—
96(C2×D103)⋊C4C2316yes—
97C4×Dic103C2311yescharacteristic
98C4×Dic103C2313yes—
99C4×Dic103C2313yes—
100C4×Dic103C2311yescharacteristic
101C4×Dic103C2313yes—
102C4×Dic103C2313yes—
103C4×Dic103C2313yes—
104C4×Dic103C2313yes—
105C4×Dic103C2313yes—
106#41×C103—24no—
107C2×Q8×C103—24no—
108C2×Q8×C103C2313yes—
109C2×Q8×C103C2311yescharacteristic
110C2×D4×C103C2313yes—
111C2×D4×C103C2313yes—
112C22×C4×C103C2313yes—
113C22×C4×C103C2313yes—
114C4⋊C4×C103C2313yes—
115C4⋊C4×C103C2313yes—
116C22⋊C4×C103C2311yescharacteristic
117C22⋊C4×C103C2313yes—
118C22⋊C4×C103C2316yes—
119C42×C103C2313yes—
120C23×C103C2413yes—
121C23×C103C2411yescharacteristic
122C22×D103C2413yes—
123Q8×C103—26no—
124Q8×C103#4114yescomplemented
125D4×C103—26no—
126D4×C103—26no—
127C2×C4×C103—26no—
128C2×C4×C103—26no—
129C2×C4×C103C2411yescharacteristic
130C2×C4×C103C2413yes—
131C2×C4×C103C2413yes—
132C2×C4×C103C2411yescharacteristic
133C2×C4×C103C2413yes—
134C22⋊D103—26no—
135C22⋊D103—26no—
136C22⋊D103—46no—
137C2×Dic103—26no—
138C2×Dic103—43no—
139C2×Dic103—43no—
140C2×Dic103#4114yescomplemented
141C2×Dic103C2411yescharacteristic
142C2×Dic103C2413yes—
143C2×Dic103C2411yescharacteristic
144C2×Dic103C2413yes—
145C2×Dic103C2413yes—
146C2×Dic103C2411yescharacteristic
147C2×Dic103C2411yescharacteristic
148D412—26no—
149C4×D103—26no—
150C4×D103—26no—
151C4×D103—43no—
152Dic206—26no—
153C22×C103—21no—
154C22×C103—21no—
155C22×C103—23no—
156C22×C103—23no—
157C22×C103—23no—
158C22×C103C2×#4112yes—
159C22×C103C2511yescharacteristic
160C2×D103—23no—
161C2×D103—23no—
162C2×D103—23no—
163C4×C103—23no—
164C4×C103—21no—
165C4×C103—23no—
166C4×C103—21no—
167C4×C103C2×#4116yes—
168Dic103—23no—
169Dic103—21no—
170Dic103—23no—
171Dic103—21no—
172Dic103—23no—
173Dic103C2×#4112yes—
174Dic103C2×#4112yes—
175C2×C103—22no—
176C2×C103—43no—
177C2×C103C22×#4111yescharacteristic
178C2×C103C22×#4111yescharacteristic
179C2×C103#58511yescharacteristic
180D103—43no—
181#3480—1031nomaximal, Sylow
182C103#348011yescharacteristic, complemented, Sylow
183#559—1033no—
184#557—1031no—
185#556—1033no—
186#553—1033no—
187#553—1033no—
188#550—1031no—
189#548—1031no—
190#548D10311yescharacteristic, complemented
191#532—1033no—
192#529—1033no—
193#529—1033no—
194C4×#41—1031no—
195C4×#41—1031no—
196C4×#41—1033no—
197C2×C4×Q8—1031no—
198C2×#41—1031no—
199C2×#41—1033no—
200C2×#41C2×D10311yescharacteristic
201C22×Q8C2×D10311yescharacteristic
202C4⋊Q8—1033no—
203#127—1033no—
204#126—1036no—
205#126—1036no—
206#125—1033no—
207#125—1033no—
208#124—1033no—
209#124—1036no—
210#124C2×D10313yes—
211#123—1036no—
212#123—1036no—
213C22⋊Q8—1033no—
214C22⋊Q8C2×D10313yes—
215#121—1033no—
216#121—1036no—
217#121—1033no—
218#121—1033no—
219#121C2×D10313yes—
220C4×Q8—1031no—
221C4×Q8—1033no—
222C4×Q8—1031no—
223C4×Q8—1033no—
224C4×Q8—1031no—
225C4×Q8—1033no—
226C4×Q8—1033no—
227C4×Q8C2×D10311yescharacteristic
228C4×D4—1033no—
229C4×D4—1033no—
230C4×D4—1033no—
231C4×D4—1033no—
232C4×D4—1033no—
233C4×D4—1033no—
234C4×D4—1033no—
235C4×D4—1033no—
236C4×D4—1036no—
237C4×D4—1033no—
238C4×D4C2×D10313yes—
239#117—1033no—
240#117—1033no—
241#117—1033no—
242#117—1031no—
243#117—1033no—
244C2×C4⋊C4—1033no—
245C2×C42—1033no—
246C2×C42—1033no—
247C2×C42—1033no—
248#41—24no—
249#41—20612no—
250#41—2064no—
251C2×Q8—24no—
252C2×Q8—1033no—
253C2×Q8C22×D10313yes—
254C2×Q8C22×D10311yescharacteristic
255C2×D4—1036no—
256C2×D4—1033no—
257C2×D4—1033no—
258C2×D4—1033no—
259C2×D4C22×D10313yes—
260C2×D4C22×D10313yes—
261C22×C4—1031no—
262C22×C4—1033no—
263C22×C4—1033no—
264C22×C4—1033no—
265C22×C4—1033no—
266C22×C4—1033no—
267C22×C4—1033no—
268C22×C4C22×D10313yes—
269C22×C4C22×D10313yes—
270C4⋊C4—1031no—
271C4⋊C4—1031no—
272C4⋊C4—1033no—
273C4⋊C4—1033no—
274C4⋊C4—1036no—
275C4⋊C4—1033no—
276C4⋊C4—1033no—
277C4⋊C4—1036no—
278C4⋊C4—1033no—
279C4⋊C4—1033no—
280C4⋊C4C22×D10313yes—
281C4⋊C4C22×D10313yes—
282C22⋊C4—1031no—
283C22⋊C4—1033no—
284C22⋊C4—1036no—
285C22⋊C4—1033no—
286C22⋊C4—1036no—
287C22⋊C4—1033no—
288C22⋊C4—1036no—
289C22⋊C4C22×D10311yescharacteristic
290C22⋊C4C22×D10313yes—
291C22⋊C4C22×D10316yes—
292C42—1031no—
293C42—1031no—
294C42—1033no—
295C42—1033no—
296C42—1033no—
297C42—1033no—
298C42—1033no—
299C42—1033no—
300C42—1033no—
301C42C22×D10313yes—
302C23—1033no—
303C23C23×D10313yes—
304C23C23×D10311yescharacteristic
305Q8—26no—
306Q8—2066no—
307Q8#1311010414yescomplemented
308D4—26no—
309D4—26no—
310D4—4126no—
311D4—2066no—
312D4—2066no—
313D4—2066no—
314C2×C4—26no—
315C2×C4—26no—
316C2×C4—1034no—
317C2×C4—1031no—
318C2×C4—1031no—
319C2×C4—1031no—
320C2×C4—1031no—
321C2×C4—1033no—
322C2×C4—1033no—
323C2×C4—1033no—
324C2×C4—4123no—
325C2×C4—4123no—
326C2×C4—4123no—
327C2×C4—2066no—
328C2×C4—2066no—
329C2×C4—2066no—
330C2×C4C23×D10311yescharacteristic
331C2×C4C23×D10313yes—
332C2×C4C23×D10311yescharacteristic
333C2×C4C23×D10313yes—
334C2×C4C23×D10313yes—
335C22—21no—
336C22—21no—
337C22—23no—
338C22—23no—
339C22—23no—
340C22—2063no—
341C22—2063no—
342C22—2063no—
343C22#41×D10312yes—
344C22C24×D10311yescharacteristic
345C4—23no—
346C4—21no—
347C4—23no—
348C4—21no—
349C4—1032no—
350C4—1032no—
351C4—2063no—
352C4—2061no—
353C4—2063no—
354C4—2061no—
355C4—2063no—
356C4C2×#1311010416yes—
357C2—22no—
358C2—43no—
359C2—4123no—
360C2C2×#41×D10311yescharacteristic
361C2C22×#1311010411yescharacteristic
362C2#2026862811yescharacteristic
subgroupG/H
center, FrattiniC22C24×D103
commutator, socle, cosocleC22×C103C25
Fitting#548×C103C2
hypercenter#548D103
hypocenterC103#3480
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #20268523C2semidirect
2. #20268517C2semidirect
3. #20268512C2semidirect
4. #20268493C2semidirect
5. #20268487C2semidirect
6. #20268460C2semidirect
7. #20268452C2semidirect
8. #20268336C2semidirect
9. #20268327C2semidirect
10. #20268320C2semidirect
11. #41×Dic103C2semidirect
12. C4×#13110106C2semidirect
13. C4×#13110104C2semidirect
14. C2×Q8×Dic103C2semidirect
15. #548×C103C2semidirect
124. Q8×C103#41semidirect
140. C2×Dic103#41semidirect
182. C103#3480semidirect
190. #548D103semidirect
307. Q8#13110104semidirect

Maximal subgroups

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

subgroupindex
#202685232
#202685172
#202685122
#202684932
#202684872
#202684602
#202684522
#202683362
#202683272
#202683202
#41×Dic1032
C4×#131101062
C4×#131101042
C2×Q8×Dic1032
#548×C1032
#3480103