Finite Group Databasebeta

← #27206710

Subgroups — #27206710

Order 13184.

472 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15693051C211yesmaximal, characteristic, complemented
2C22×#13110095C211yesmaximal, characteristic, complemented
3D4×Dic206C211yesmaximal, characteristic, complemented
4#20268186C211yesmaximal, characteristic, complemented
5#20268047C211yesmaximal, characteristic, complemented
6#20268018C211yesmaximal, characteristic, complemented
7#20268010C211yesmaximal, characteristic, complemented
8#20268001C211yesmaximal, characteristic, complemented
9#20267953C211yesmaximal, characteristic, complemented
10#20267947C211yesmaximal, characteristic, complemented
11#20267946C211yesmaximal, characteristic, complemented
12#20267929C211yesmaximal, characteristic, complemented
13#20267896C211yesmaximal, characteristic, complemented
14#20267863C211yesmaximal, characteristic, complemented
15#548×C103C211yesmaximal, characteristic
16C22×Dic206C2211yescharacteristic
17C22×Dic206C2211yescharacteristic
18#15693051—24no—
19C2×#13110095—24no—
20C2×#13110095C2211yescharacteristic
21C2×#13110095C2211yescharacteristic
22C2×#13110095C2211yescharacteristic
23C2×#13110095C2211yescharacteristic
24C2×#13110095C2211yescharacteristic
25C2×#13110095C2211yescharacteristic
26C2×#13110093C2211yescharacteristic
27C2×#13110093C2211yescharacteristic
28C2×#13110093C2211yescharacteristic
29C2×#13110089C2211yescharacteristic
30C22×C103⋊C8C2211yescharacteristic
31#15693021C2211yescharacteristic
32#15693020—21no—
33#15693000C2211yescharacteristic
34#15693000C2211yescharacteristic
35#15692998—21no—
36#15692998—21no—
37C4×Dic206C2211yescharacteristic
38D4×Dic103—21no—
39#15692952C2211yescharacteristic
40C4⋊(C103⋊C8)C2211yescharacteristic
41#15692945C2211yescharacteristic
42#15692945C2211yescharacteristic
43#15692944C2211yescharacteristic
44#15692944C2211yescharacteristic
45#15692944C2211yescharacteristic
46#15692942C2211yescharacteristic
47C22⋊(C103⋊C8)C2211yescharacteristic
48C22⋊(C103⋊C8)C2211yescharacteristic
49#15692932C2211yescharacteristic
50C2×#41×C103C2211yescharacteristic
51C22×Q8×C103C2211yescharacteristic
52#124×C103—21no—
53#124×C103C2211yescharacteristic
54C22⋊Q8×C103—21no—
55C22⋊Q8×C103C2211yescharacteristic
56#121×C103—21no—
57#121×C103C2211yescharacteristic
58C4×Q8×C103C2211yescharacteristic
59C4×D4×C103—21no—
60C4×D4×C103C2211yescharacteristic
61C2×Dic206—22no—
62C2×Dic206—22no—
63C2×Dic206—21no—
64C2×Dic206—21no—
65C2×Dic206—41no—
66C2×Dic206—41no—
67C2×Dic206C2311yescharacteristic
68C2×Dic206C2311yescharacteristic
69C2×Dic206C2311yescharacteristic
70C22×Dic103—21no—
71C22×Dic103—21no—
72#13110095—22no—
73#13110095—22no—
74#13110095—22no—
75#13110095—22no—
76#13110095—41no—
77#13110095D414yescomplemented
78#13110093—22no—
79#13110093—22no—
80#13110093—41no—
81#13110089—22no—
82C2×C103⋊C8—22no—
83C2×C103⋊C8C2311yescharacteristic
84C2×C103⋊C8C2311yescharacteristic
85C2×C103⋊C8C2311yescharacteristic
86C2×C103⋊C8C2311yescharacteristic
87C4⋊Dic103—21no—
88C4⋊Dic103—21no—
89C4⋊Dic103C2311yescharacteristic
90Dic103⋊C4—21no—
91Dic103⋊C4—21no—
92Dic103⋊C4—21no—
93C22⋊Dic103—21no—
94C22⋊Dic103—21no—
95C4×Dic103—21no—
96#41×C103—22no—
97#41×C103—41no—
98C2×Q8×C103—21no—
99C2×Q8×C103—22no—
100C2×Q8×C103—41no—
101C2×Q8×C103C2311yescharacteristic
102C2×Q8×C103C2311yescharacteristic
103C2×D4×C103—21no—
104C2×D4×C103—21no—
105C2×D4×C103D411yescharacteristic
106C2×D4×C103C2311yescharacteristic
107C22×C4×C103—21no—
108C22×C4×C103—21no—
109C22×C4×C103C2311yescharacteristic
110C22×C4×C103C2311yescharacteristic
111C4⋊C4×C103—21no—
112C4⋊C4×C103—21no—
113C4⋊C4×C103D411yescharacteristic
114C4⋊C4×C103C2311yescharacteristic
115C22⋊C4×C103—21no—
116C22⋊C4×C103—21no—
117C22⋊C4×C103—21no—
118C22⋊C4×C103—21no—
119C22⋊C4×C103D411yescharacteristic
120C22⋊C4×C103D411yescharacteristic
121C42×C103—21no—
122C42×C103C2311yescharacteristic
123C23×C103—21no—
124C23×C103C2×D411yescharacteristic
125C23×C103C2×D411yescharacteristic
126Q8×C103—21no—
127Q8×C103—21no—
128Q8×C103—21no—
129Q8×C103—42no—
130Q8×C103C2×D412yes—
131D4×C103—22no—
132D4×C103—21no—
133D4×C103—21no—
134D4×C103—42no—
135D4×C103—42no—
136C2×C4×C103—21no—
137C2×C4×C103—21no—
138C2×C4×C103—21no—
139C2×C4×C103—21no—
140C2×C4×C103—21no—
141C2×C4×C103—21no—
142C2×C4×C103—21no—
143C2×C4×C103—42no—
144C2×C4×C103—42no—
145C2×C4×C103C2×D411yescharacteristic
146C2×C4×C103C2×D411yescharacteristic
147C2×C4×C103C2×D411yescharacteristic
148C2×C4×C103C2×D411yescharacteristic
149C2×C4×C103C2411yescharacteristic
150C2×Dic103—21no—
151C2×Dic103—21no—
152C2×Dic103—21no—
153C2×Dic103—21no—
154C2×Dic103—42no—
155C2×Dic103—42no—
156Dic206—21no—
157Dic206—21no—
158Dic206—21no—
159Dic206—21no—
160Dic206—21no—
161Dic206—42no—
162Dic206—42no—
163Dic206C2×D412yes—
164C103⋊C8—21no—
165C103⋊C8—21no—
166C103⋊C8—21no—
167C103⋊C8C2×D412yes—
168C22×C103—21no—
169C22×C103—21no—
170C22×C103—21no—
171C22×C103—21no—
172C22×C103—21no—
173C22×C103—41no—
174C22×C103—41no—
175C22×C103—41no—
176C22×C103#13712yescomplemented
177C22×C103C22×D411yescharacteristic
178C4×C103—21no—
179C4×C103—21no—
180C4×C103—22no—
181C4×C103—21no—
182C4×C103—21no—
183C4×C103—41no—
184C4×C103—41no—
185C4×C103C22×D411yescharacteristic
186C4×C103H(5,𝔽2)11yescharacteristic
187Dic103—22no—
188Dic103—41no—
189Dic103—41no—
190Dic103—41no—
191C2×C103—22no—
192C2×C103—41no—
193C2×C103—81no—
194C2×C103D4211yescharacteristic
195C2×C103C2×#13711yescharacteristic
196C2×C103#57811yescharacteristic
197#3270—1031nomaximal, Sylow
198C103#327011yescharacteristic, complemented, Sylow
199C2×#137—1031no—
200C22×Q16—1031no—
201D4×Q8—1031no—
202#548D10311yescharacteristic
203#497—1031no—
204#470—1031no—
205#465—1031no—
206#464—1031no—
207#462—1031no—
208#452—1031no—
209#451—1031no—
210#451—1031no—
211#448—1031no—
212#441—1031no—
213#435—1031no—
214C2×#41C2×D10311yescharacteristic
215C22×Q8—1031no—
216C22×Q8—1031no—
217C22×Q8C2×D10311yescharacteristic
218#137—2064no—
219C2×Q16—1031no—
220C2×Q16—1031no—
221C2×Q16—1031no—
222C2×Q16—1031no—
223C2×Q16—1031no—
224C2×Q16—1031no—
225C2×Q16—2064no—
226C2×SD16—1031no—
227C2×SD16—1031no—
228C2×SD16—1031no—
229C2×M16—1031no—
230C22×C8—1031no—
231C4⋊Q8—1031no—
232C4⋊Q8—2061no—
233#124—21no—
234#124C2×D10311yescharacteristic
235C22⋊Q8—21no—
236C22⋊Q8—1031no—
237C22⋊Q8—1031no—
238C22⋊Q8—2061no—
239C22⋊Q8—2061no—
240C22⋊Q8C2×D10311yescharacteristic
241#121—21no—
242#121C2×D10311yescharacteristic
243C4×Q8—1031no—
244C4×Q8C2×D10311yescharacteristic
245C4×D4—21no—
246C4×D4—2061no—
247C4×D4C2×D10311yescharacteristic
248#106—1031no—
249C4⋊C8—1031no—
250#103—1031no—
251#103—1031no—
252#103—1031no—
253#103—1031no—
254#103—1031no—
255#102—1031no—
256C22⋊C8—1031no—
257C22⋊C8—1031no—
258#97—1031no—
259#41—22no—
260#41—41no—
261C2×Q8—21no—
262C2×Q8—22no—
263C2×Q8—41no—
264C2×Q8—1031no—
265C2×Q8—1031no—
266C2×Q8—1031no—
267C2×Q8—4121no—
268C2×Q8—4121no—
269C2×Q8—2062no—
270C2×Q8—2062no—
271C2×Q8—2061no—
272C2×Q8—2061no—
273C2×Q8C22×D10311yescharacteristic
274C2×Q8C22×D10311yescharacteristic
275C2×D4—21no—
276C2×D4—21no—
277C2×D4C22⋊D10311yescharacteristic
278C2×D4C22×D10311yescharacteristic
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—2061no—
282C22×C4—2061no—
283C22×C4C22×D10311yescharacteristic
284C22×C4C22×D10311yescharacteristic
285Q16—1034no—
286Q16—4121no—
287Q16—2062no—
288Q16—2062no—
289Q16—2062no—
290Q16—2062no—
291SD16—4121no—
292SD16—2062no—
293SD16—2062no—
294M16—2062no—
295C2×C8—1031no—
296C2×C8—1031no—
297C2×C8—1031no—
298C2×C8—1031no—
299C2×C8—2062no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—1031no—
303C4⋊C4—2061no—
304C4⋊C4—2061no—
305C4⋊C4—2061no—
306C4⋊C4—2061no—
307C4⋊C4—2061no—
308C4⋊C4C22⋊D10311yescharacteristic
309C4⋊C4C22×D10311yescharacteristic
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—2061no—
315C22⋊C4—2061no—
316C22⋊C4C22⋊D10311yescharacteristic
317C22⋊C4C22⋊D10311yescharacteristic
318C42—21no—
319C42—2061no—
320C42C22×D10311yescharacteristic
321C23—21no—
322C23C2×C22⋊D10311yescharacteristic
323C23C2×C22⋊D10311yescharacteristic
324Q8—21no—
325Q8—21no—
326Q8—21no—
327Q8—42no—
328Q8—1032no—
329Q8—4122no—
330Q8—4122no—
331Q8—2061no—
332Q8—2061no—
333Q8—2061no—
334Q8—2061no—
335Q8—2061no—
336Q8D4×D10312yes—
337D4—22no—
338D4—21no—
339D4—21no—
340D4—42no—
341D4—42no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—4122no—
352C2×C4—4122no—
353C2×C4—2061no—
354C2×C4—2061no—
355C2×C4—2061no—
356C2×C4—2061no—
357C2×C4C2×C22⋊D10311yescharacteristic
358C2×C4C2×C22⋊D10311yescharacteristic
359C2×C4C2×C22⋊D10311yescharacteristic
360C2×C4C2×C22⋊D10311yescharacteristic
361C2×C4C23×D10311yescharacteristic
362C8—1032no—
363C8—2061no—
364C8—2061no—
365C8—2061no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22#1569305112yescomplemented
375C22C22×C22⋊D10311yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—22no—
381C4—41no—
382C4—41no—
383C4—4121no—
384C4—4121no—
385C4—4121no—
386C4—2062no—
387C4C2×D4×D10311yescharacteristic
388C4#1569306611yescharacteristic
389C2—22no—
390C2—41no—
391C2—81no—
392C2D4×C22⋊D10311yescharacteristic
393C2C2×#1569305111yescharacteristic
394C2#2026860611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting, prime radical#548×C103C2
socleC22×C103C22×D4
hypercenter#548D103
hypocenterC103#3270
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#15693051C2semidirect
2. C22×#13110095C2semidirect
3. D4×Dic206C2semidirect
4. #20268186C2semidirect
5. #20268047C2semidirect
6. #20268018C2semidirect
7. #20268010C2semidirect
8. #20268001C2semidirect
9. #20267953C2semidirect
10. #20267947C2semidirect
11. #20267946C2semidirect
12. #20267929C2semidirect
13. #20267896C2semidirect
14. #20267863C2semidirect
77. #13110095D4semidirect
176. C22×C103#137semidirect
198. C103#3270semidirect
374. C22#15693051semidirect

Maximal subgroups

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

subgroupindex
C2×#156930512
C22×#131100952
D4×Dic2062
#202681862
#202680472
#202680182
#202680102
#202680012
#202679532
#202679472
#202679462
#202679292
#202678962
#202678632
#548×C1032
#3270103