Finite Group Databasebeta

← #27208742

Subgroups — #27208742

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#20268524C213yesmaximal, complemented
2#20268517C211yesmaximal, characteristic, complemented
3#20268509C213yesmaximal, complemented
4#20268491C213yesmaximal, complemented
5#20268485C213yesmaximal, complemented
6#20268460C211yesmaximal, characteristic, complemented
7#20268453C211yesmaximal, characteristic, complemented
8#20268448C211yesmaximal, characteristic, complemented
9#20268338C213yesmaximal, complemented
10#20268325C213yesmaximal, complemented
11#20268323C213yesmaximal, complemented
12C4×#13110106C211yesmaximal, characteristic, complemented
13C4×#13110105C213yesmaximal, complemented
14C4×Q8×D103C211yesmaximal, characteristic, complemented
15C4×#41×C103C211yesmaximal, characteristic, complemented
16C2×#13110106C2211yescharacteristic
17C2×#13110105C2213yes—
18C2×Q8×D103C2211yescharacteristic
19#15693020C2213yes—
20#15693017C2213yes—
21#15693015C2216yes—
22#15693014C2216yes—
23#15693013C2213yes—
24#15693012C2213yes—
25#15693009C2213yes—
26#15693008C2213yes—
27#15693007C2216yes—
28#15693004C2216yes—
29#15693003C2216yes—
30#15693001C2213yes—
31#15693000C2213yes—
32#15692996C2213yes—
33#15692995C2213yes—
34#15692994C2216yes—
35#15692992C2213yes—
36#15692992C2213yes—
37Q8×Dic103C2211yescharacteristic
38Q8×Dic103C2211yescharacteristic
39C4×Dic206C2213yes—
40C4×Dic206C2213yes—
41C4×Dic206C2213yes—
42#15692986C2213yes—
43C4×D412C2213yes—
44C4×D412C2213yes—
45C4×D412C2213yes—
46#15692983C2213yes—
47C4×C22⋊D103C2216yes—
48C4×C22⋊D103C2213yes—
49C4×C22⋊D103C2213yes—
50C4×C22⋊D103C2213yes—
51C4×C22⋊D103C2213yes—
52#15692980C2213yes—
53#15692979C2213yes—
54#15692978C2213yes—
55#15692978C2211yescharacteristic
56C4⋊C4×D103C2213yes—
57C42×D103C2213yes—
58C42×D103C2213yes—
59C2×#41×C103C2211yescharacteristic
60C4×Q8×C103C2211yescharacteristic
61C4×Q8×C103C2211yescharacteristic
62C4×D4×C103C2213yes—
63C4×D4×C103C2213yes—
64#117×C103C2213yes—
65C2×C42×C103C2213yes—
66#13110106—24no—
67#13110105—212no—
68C2×Dic206C2313yes—
69C2×Dic206C2313yes—
70Q8×D103—24no—
71C2×D412C2313yes—
72C2×D412C2313yes—
73C2×C22⋊D103C2313yes—
74C2×C22⋊D103C2313yes—
75C2×C22⋊D103C2316yes—
76C2×C4×D103C2313yes—
77C2×C4×D103C2313yes—
78C2×C4×D103C2313yes—
79C2×C4×D103C2313yes—
80C2×C4×D103C2313yes—
81C2×C4×D103C2311yescharacteristic
82C4⋊Dic103C2313yes—
83C4⋊Dic103C2313yes—
84C4⋊Dic103C2313yes—
85C4⋊Dic103C2313yes—
86Dic103⋊C4C2316yes—
87Dic103⋊C4C2311yescharacteristic
88Dic103⋊C4C2311yescharacteristic
89Dic103⋊C4C2313yes—
90Dic103⋊C4C2313yes—
91Dic103⋊C4C2316yes—
92C22⋊Dic103C2313yes—
93C22⋊Dic103C2313yes—
94C22⋊Dic103C2316yes—
95(C2×D103)⋊C4C2311yescharacteristic
96(C2×D103)⋊C4C2311yescharacteristic
97(C2×D103)⋊C4C2313yes—
98(C2×D103)⋊C4C2313yes—
99(C2×D103)⋊C4C2316yes—
100(C2×D103)⋊C4C2316yes—
101C4×Dic103C2311yescharacteristic
102C4×Dic103C2313yes—
103C4×Dic103C2313yes—
104C4×Dic103C2313yes—
105C4×Dic103C2313yes—
106C4×Dic103C2313yes—
107#41×C103—24no—
108C2×Q8×C103C2311yescharacteristic
109C2×D4×C103C2313yes—
110C22×C4×C103C2313yes—
111C22×C4×C103C2313yes—
112C22×C4×C103C2313yes—
113C4⋊C4×C103C2313yes—
114C4⋊C4×C103C2313yes—
115C22⋊C4×C103C2316yes—
116C42×C103C2311yescharacteristic
117C42×C103C2313yes—
118C42×C103C2313yes—
119C42×C103C2313yes—
120C23×C103C2413yes—
121C22×D103C2413yes—
122C22×D103C2411yescharacteristic
123Q8×C103#4114yescomplemented
124D4×C103—26no—
125C2×C4×C103—26no—
126C2×C4×C103—26no—
127C2×C4×C103—43no—
128C2×C4×C103C2411yescharacteristic
129C2×C4×C103C2411yescharacteristic
130C2×C4×C103C2413yes—
131C2×C4×C103C2413yes—
132C2×C4×C103C2413yes—
133C2×C4×C103C2411yescharacteristic
134C22⋊D103—26no—
135C22⋊D103—26no—
136C22⋊D103—46no—
137C2×Dic103C2411yescharacteristic
138C2×Dic103C2411yescharacteristic
139C2×Dic103C2413yes—
140C2×Dic103C2413yes—
141C2×Dic103C2413yes—
142C2×Dic103C2411yescharacteristic
143D412—26no—
144D412—26no—
145C4×D103—26no—
146C4×D103—26no—
147C4×D103—26no—
148C4×D103—43no—
149C4×D103—43no—
150C4×D103#4114yescomplemented
151Dic206—26no—
152Dic206—26no—
153C22×C103—23no—
154C22×C103—23no—
155C22×C103—23no—
156C22×C103C2511yescharacteristic
157C2×D103—21no—
158C2×D103—21no—
159C2×D103—23no—
160C2×D103—23no—
161C2×D103—23no—
162C2×D103C2×#4112yes—
163C4×C103—23no—
164C4×C103—21no—
165C4×C103—23no—
166C4×C103—21no—
167C4×C103C2×#4112yes—
168C4×C103C2×#4116yes—
169Dic103—23no—
170Dic103—23no—
171Dic103—21no—
172Dic103—21no—
173Dic103—23no—
174Dic103C2×#4112yes—
175C2×C103—43no—
176C2×C103C22×#4111yescharacteristic
177C2×C103C22×#4111yescharacteristic
178C2×C103#58511yescharacteristic
179D103—22no—
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#548—1031no—
191#532—1033no—
192#529—1033no—
193#529—1033no—
194C4×#41—1031no—
195C4×#41—1033no—
196C4×#41D10311yescharacteristic, complemented
197C2×C4×Q8—1031no—
198C2×#41—1031no—
199C2×#41—1033no—
200C2×#41C2×D10311yescharacteristic
201C22×Q8—1031no—
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#124—1033no—
211#123—1036no—
212#123—1036no—
213C22⋊Q8—1033no—
214C22⋊Q8—1033no—
215#121—1033no—
216#121—1033no—
217#121—1033no—
218#121—1033no—
219#121—1036no—
220C4×Q8—1031no—
221C4×Q8—1031no—
222C4×Q8—1033no—
223C4×Q8—1033no—
224C4×Q8—1033no—
225C4×Q8—1033no—
226C4×Q8C2×D10311yescharacteristic
227C4×Q8C2×D10311yescharacteristic
228C4×D4—1033no—
229C4×D4—1033no—
230C4×D4—1033no—
231C4×D4—1033no—
232C4×D4—1036no—
233C4×D4—1033no—
234C4×D4—1033no—
235C4×D4—1033no—
236C4×D4—1033no—
237C4×D4C2×D10313yes—
238C4×D4C2×D10313yes—
239#117—1033no—
240#117—1033no—
241#117—1031no—
242#117—1033no—
243#117C2×D10313yes—
244C2×C4⋊C4—1033no—
245C2×C42—1033no—
246C2×C42—1033no—
247C2×C42C2×D10313yes—
248#41—24no—
249#41—20612no—
250#41—2064no—
251C2×Q8—1033no—
252C2×Q8—1033no—
253C2×Q8—2064no—
254C2×Q8C22×D10311yescharacteristic
255C2×D4—1036no—
256C2×D4—1033no—
257C2×D4—1033no—
258C2×D4—1033no—
259C2×D4—1033no—
260C2×D4C22×D10313yes—
261C22×C4—1031no—
262C22×C4—1033no—
263C22×C4—1033no—
264C22×C4—1033no—
265C22×C4—1033no—
266C22×C4—1033no—
267C22×C4C22×D10313yes—
268C22×C4C22×D10313yes—
269C22×C4C22×D10313yes—
270C4⋊C4—1036no—
271C4⋊C4—1031no—
272C4⋊C4—1031no—
273C4⋊C4—1033no—
274C4⋊C4—1033no—
275C4⋊C4—1036no—
276C4⋊C4—1033no—
277C4⋊C4—1033no—
278C4⋊C4—1033no—
279C4⋊C4—1033no—
280C4⋊C4C22×D10313yes—
281C4⋊C4C22×D10313yes—
282C22⋊C4—1033no—
283C22⋊C4—1033no—
284C22⋊C4—1036no—
285C22⋊C4—1031no—
286C22⋊C4—1031no—
287C22⋊C4—1033no—
288C22⋊C4—1036no—
289C22⋊C4—1033no—
290C22⋊C4—1036no—
291C22⋊C4C22×D10316yes—
292C42—1033no—
293C42—1033no—
294C42—1033no—
295C42—1033no—
296C42—1031no—
297C42—1033no—
298C42C22×D10313yes—
299C42C22×D10313yes—
300C42C22×D10313yes—
301C42C22×D10311yescharacteristic
302C23—1031no—
303C23—1033no—
304C23C23×D10313yes—
305Q8—2066no—
306Q8—2066no—
307Q8#1311010514yescomplemented
308D4—26no—
309D4—4126no—
310D4—2066no—
311D4—2066no—
312D4—2066no—
313D4—2066no—
314C2×C4—26no—
315C2×C4—26no—
316C2×C4—43no—
317C2×C4—1031no—
318C2×C4—1034no—
319C2×C4—1031no—
320C2×C4—1031no—
321C2×C4—1033no—
322C2×C4—1033no—
323C2×C4—1033no—
324C2×C4—4123no—
325C2×C4—4123no—
326C2×C4—2066no—
327C2×C4—2066no—
328C2×C4—2066no—
329C2×C4C23×D10313yes—
330C2×C4C23×D10311yescharacteristic
331C2×C4C23×D10311yescharacteristic
332C2×C4C23×D10313yes—
333C2×C4C23×D10313yes—
334C2×C4C23×D10311yescharacteristic
335C22—23no—
336C22—23no—
337C22—23no—
338C22—1032no—
339C22—2063no—
340C22—2063no—
341C22—2063no—
342C22—2061no—
343C22—2061no—
344C22C24×D10311yescharacteristic
345C4—23no—
346C4—21no—
347C4—21no—
348C4—23no—
349C4—1032no—
350C4—2063no—
351C4—2061no—
352C4—2063no—
353C4—2061no—
354C4—2063no—
355C4#41×D10312yes—
356C4C2×#1311010516yes—
357C2—43no—
358C2—4123no—
359C2—2062no—
360C2C2×#41×D10311yescharacteristic
361C2C22×#1311010511yescharacteristic
362C2#2026862711yescharacteristic
subgroupG/H
centerC2×C4C23×D103
commutator, socle, cosocleC22×C103C25
FrattiniC22C24×D103
FittingC4×#41×C103C2
hypercenterC4×#41D103
hypocenterC103#3480
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. #20268524C2semidirect
2. #20268517C2semidirect
3. #20268509C2semidirect
4. #20268491C2semidirect
5. #20268485C2semidirect
6. #20268460C2semidirect
7. #20268453C2semidirect
8. #20268448C2semidirect
9. #20268338C2semidirect
10. #20268325C2semidirect
11. #20268323C2semidirect
12. C4×#13110106C2semidirect
13. C4×#13110105C2semidirect
14. C4×Q8×D103C2semidirect
15. C4×#41×C103C2semidirect
123. Q8×C103#41semidirect
150. C4×D103#41semidirect
182. C103#3480semidirect
196. C4×#41D103semidirect
307. Q8#13110105semidirect

Maximal subgroups

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

subgroupindex
#202685242
#202685172
#202685092
#202684912
#202684852
#202684602
#202684532
#202684482
#202683382
#202683252
#202683232
C4×#131101062
C4×#131101052
C4×Q8×D1032
C4×#41×C1032
#3480103