Finite Group Databasebeta

← #27206650

Subgroups — #27206650

Order 13184.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15693051C211yesmaximal, characteristic, complemented
2C22×#13110093C211yesmaximal, characteristic, complemented
3D4×Dic206C211yesmaximal, characteristic, complemented
4#20268186C211yesmaximal, characteristic, complemented
5#20268035C211yesmaximal, characteristic, complemented
6#20268030C211yesmaximal, characteristic, complemented
7#20268010C211yesmaximal, characteristic, complemented
8#20267996C211yesmaximal, characteristic, complemented
9#20267953C211yesmaximal, characteristic, complemented
10#20267946C211yesmaximal, characteristic, complemented
11#20267942C211yesmaximal, characteristic, complemented
12#20267929C211yesmaximal, characteristic, complemented
13#20267891C211yesmaximal, characteristic, complemented
14#20267863C211yesmaximal, characteristic, complemented
15#546×C103C211yesmaximal, characteristic
16C22×Dic206C2211yescharacteristic
17C22×Dic206C2211yescharacteristic, complemented
18#15693051—24no—
19C2×#13110095C2211yescharacteristic, complemented
20C2×#13110095C2211yescharacteristic, complemented
21C2×#13110095C2211yescharacteristic, complemented
22C2×#13110093—24no—
23C2×#13110093C2211yescharacteristic
24C2×#13110093C2211yescharacteristic
25C2×#13110093C2211yescharacteristic
26C2×#13110093C2211yescharacteristic
27C2×#13110093C2211yescharacteristic
28C2×#13110093C2211yescharacteristic
29C2×#13110089C2211yescharacteristic, complemented
30C22×C103⋊C8C2211yescharacteristic
31#15693021C2211yescharacteristic, complemented
32#15693020—21no—
33#15693000C2211yescharacteristic
34#15693000C2211yescharacteristic, complemented
35#15692998—21no—
36#15692998—21no—
37C4×Dic206C2211yescharacteristic, complemented
38D4×Dic103—21no—
39#15692954C2211yescharacteristic, complemented
40C4⋊(C103⋊C8)C2211yescharacteristic, complemented
41#15692945C2211yescharacteristic, complemented
42#15692944C2211yescharacteristic, complemented
43#15692944C2211yescharacteristic, complemented
44#15692944C2211yescharacteristic, complemented
45#15692942C2211yescharacteristic
46#15692942C2211yescharacteristic
47C22⋊(C103⋊C8)C2211yescharacteristic
48C22⋊(C103⋊C8)C2211yescharacteristic, complemented
49#15692932C2211yescharacteristic, complemented
50C2×#41×C103C2211yescharacteristic
51C22×D4×C103C2211yescharacteristic
52#124×C103C2211yescharacteristic
53#123×C103—21no—
54C22⋊Q8×C103C2211yescharacteristic
55#121×C103—21no—
56#121×C103C2211yescharacteristic
57#120×C103—21no—
58C4×D4×C103C2211yescharacteristic
59C4×D4×C103C2211yescharacteristic
60C2×C22⋊C4×C103—21no—
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—41no—
75#13110093—22no—
76#13110093—22no—
77#13110093—22no—
78#13110093—22no—
79#13110093—41no—
80#13110093D414yescomplemented
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—
96C24×C103—21no—
97#41×C103—22no—
98#41×C103—41no—
99C2×Q8×C103C2311yescharacteristic
100C2×D4×C103—22no—
101C2×D4×C103—21no—
102C2×D4×C103—21no—
103C2×D4×C103—21no—
104C2×D4×C103—41no—
105C2×D4×C103D411yescharacteristic
106C2×D4×C103C2311yescharacteristic
107C2×D4×C103C2311yescharacteristic
108C22×C4×C103—21no—
109C22×C4×C103—21no—
110C22×C4×C103C2311yescharacteristic
111C22×C4×C103C2311yescharacteristic
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×C103—21no—
120C22⋊C4×C103D411yescharacteristic
121C22⋊C4×C103D411yescharacteristic
122C42×C103C2311yescharacteristic
123C23×C103—21no—
124C23×C103—21no—
125C23×C103—42no—
126C23×C103—42no—
127C23×C103—81no—
128C23×C103C2×D411yescharacteristic
129C23×C103C2×D411yescharacteristic
130Q8×C103—21no—
131Q8×C103—21no—
132D4×C103—22no—
133D4×C103—21no—
134D4×C103—21no—
135D4×C103—21no—
136D4×C103—42no—
137D4×C103—42no—
138D4×C103—81no—
139D4×C103C2×D412yes—
140C2×C4×C103—21no—
141C2×C4×C103—21no—
142C2×C4×C103—21no—
143C2×C4×C103—21no—
144C2×C4×C103—21no—
145C2×C4×C103—21no—
146C2×C4×C103—42no—
147C2×C4×C103—81no—
148C2×C4×C103C2×D411yescharacteristic
149C2×C4×C103C2×D411yescharacteristic
150C2×C4×C103C2×D411yescharacteristic
151C2×C4×C103C2×D411yescharacteristic
152C2×C4×C103C2411yescharacteristic
153C2×Dic103—21no—
154C2×Dic103—21no—
155C2×Dic103—21no—
156C2×Dic103—21no—
157C2×Dic103—42no—
158C2×Dic103—42no—
159Dic206—21no—
160Dic206—21no—
161Dic206—21no—
162Dic206—21no—
163Dic206—21no—
164Dic206—42no—
165Dic206—42no—
166Dic206C2×D412yes—
167C103⋊C8—21no—
168C103⋊C8—21no—
169C103⋊C8—21no—
170C103⋊C8C2×D412yes—
171C22×C103—21no—
172C22×C103—21no—
173C22×C103—21no—
174C22×C103—22no—
175C22×C103—21no—
176C22×C103—21no—
177C22×C103—41no—
178C22×C103—41no—
179C22×C103—41no—
180C22×C103—41no—
181C22×C103—41no—
182C22×C103—84no—
183C22×C103#13712yescomplemented
184C22×C103C22×D411yescharacteristic
185C4×C103—21no—
186C4×C103—21no—
187C4×C103—21no—
188C4×C103—21no—
189C4×C103—41no—
190C4×C103—41no—
191C4×C103C22×D411yescharacteristic
192C4×C103H(5,𝔽2)11yescharacteristic
193Dic103—22no—
194Dic103—41no—
195Dic103—41no—
196Dic103—41no—
197C2×C103—22no—
198C2×C103—41no—
199C2×C103—42no—
200C2×C103—81no—
201C2×C103D4211yescharacteristic
202C2×C103C2×#13711yescharacteristic
203C2×C103#57711yescharacteristic
204#3266—1031nomaximal, Sylow
205C103#326611yescharacteristic, complemented, Sylow
206C2×#137—1031no—
207C22×SD16—1031no—
208D4×Q8—1031no—
209#546D10311yescharacteristic
210#497—1031no—
211#468—1031no—
212#467—1031no—
213#464—1031no—
214#461—1031no—
215#452—1031no—
216#451—1031no—
217#450—1031no—
218#448—1031no—
219#440—1031no—
220#435—1031no—
221C2×#41C2×D10311yescharacteristic
222C22×Q8—1031no—
223C22×Q8—1031no—
224C22×D4C2×D10311yescharacteristic
225#137—2064no—
226C2×Q16—1031no—
227C2×Q16—1031no—
228C2×Q16—1031no—
229C2×SD16—1031no—
230C2×SD16—1031no—
231C2×SD16—1031no—
232C2×SD16—1031no—
233C2×SD16—1031no—
234C2×SD16—1031no—
235C2×SD16—2064no—
236C2×M16—1031no—
237C22×C8—1031no—
238C4⋊Q8—1031no—
239C4⋊Q8—2061no—
240#124C2×D10311yescharacteristic
241#123—21no—
242C22⋊Q8—1031no—
243C22⋊Q8—1031no—
244C22⋊Q8—2061no—
245C22⋊Q8—2061no—
246C22⋊Q8C2×D10311yescharacteristic
247#121—21no—
248#121C2×D10311yescharacteristic
249#120—21no—
250C4×Q8—1031no—
251C4×D4—2061no—
252C4×D4C2×D10311yescharacteristic
253C4×D4C2×D10311yescharacteristic
254C2×C22⋊C4—21no—
255#107—1031no—
256C4⋊C8—1031no—
257#103—1031no—
258#103—1031no—
259#103—1031no—
260#103—1031no—
261#102—1031no—
262#102—1031no—
263C22⋊C8—1031no—
264C22⋊C8—1031no—
265#97—1031no—
266C24—21no—
267#41—22no—
268#41—41no—
269C2×Q8—1031no—
270C2×Q8—1031no—
271C2×Q8—1031no—
272C2×Q8—4121no—
273C2×Q8—4121no—
274C2×Q8—2062no—
275C2×Q8—2062no—
276C2×Q8—2061no—
277C2×Q8—2061no—
278C2×Q8C22×D10311yescharacteristic
279C2×D4—22no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—41no—
284C2×D4C22⋊D10311yescharacteristic
285C2×D4C22×D10311yescharacteristic
286C2×D4C22×D10311yescharacteristic
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—2061no—
290C22×C4—2061no—
291C22×C4C22×D10311yescharacteristic
292C22×C4C22×D10311yescharacteristic
293Q16—4121no—
294Q16—2062no—
295Q16—2062no—
296SD16—1034no—
297SD16—4121no—
298SD16—2062no—
299SD16—2062no—
300SD16—2062no—
301SD16—2062no—
302M16—2062no—
303C2×C8—1031no—
304C2×C8—1031no—
305C2×C8—1031no—
306C2×C8—1031no—
307C2×C8—2062no—
308C4⋊C4—21no—
309C4⋊C4—1031no—
310C4⋊C4—2061no—
311C4⋊C4—2061no—
312C4⋊C4—2061no—
313C4⋊C4—2061no—
314C4⋊C4—2061no—
315C4⋊C4C22⋊D10311yescharacteristic
316C4⋊C4C22×D10311yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—21no—
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—2061no—
323C22⋊C4—2061no—
324C22⋊C4C22⋊D10311yescharacteristic
325C22⋊C4C22⋊D10311yescharacteristic
326C42—2061no—
327C42C22×D10311yescharacteristic
328C23—21no—
329C23—21no—
330C23—42no—
331C23—42no—
332C23—81no—
333C23C2×C22⋊D10311yescharacteristic
334C23C2×C22⋊D10311yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—1032no—
338Q8—4122no—
339Q8—4122no—
340Q8—2061no—
341Q8—2061no—
342Q8—2061no—
343Q8—2061no—
344Q8—2061no—
345D4—22no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—42no—
350D4—42no—
351D4—81no—
352D4D4×D10312yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—42no—
360C2×C4—81no—
361C2×C4—4122no—
362C2×C4—4122no—
363C2×C4—2061no—
364C2×C4—2061no—
365C2×C4—2061no—
366C2×C4—2061no—
367C2×C4C2×C22⋊D10311yescharacteristic
368C2×C4C2×C22⋊D10311yescharacteristic
369C2×C4C2×C22⋊D10311yescharacteristic
370C2×C4C2×C22⋊D10311yescharacteristic
371C2×C4C23×D10311yescharacteristic
372C8—1032no—
373C8—2061no—
374C8—2061no—
375C8—2061no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—22no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—84no—
388C22#1569305112yescomplemented
389C22C22×C22⋊D10311yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—41no—
395C4—41no—
396C4—4121no—
397C4—4121no—
398C4—4121no—
399C4—2062no—
400C4C2×D4×D10311yescharacteristic
401C4#1569306611yescharacteristic
402C2—22no—
403C2—41no—
404C2—42no—
405C2—81no—
406C2D4×C22⋊D10311yescharacteristic
407C2C2×#1569305111yescharacteristic
408C2#2026860211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting, prime radical#546×C103C2
socleC22×C103C22×D4
hypercenter#546D103
hypocenterC103#3266
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C2×#15693051C2semidirect
2. C22×#13110093C2semidirect
3. D4×Dic206C2semidirect
4. #20268186C2semidirect
5. #20268035C2semidirect
6. #20268030C2semidirect
7. #20268010C2semidirect
8. #20267996C2semidirect
9. #20267953C2semidirect
10. #20267946C2semidirect
11. #20267942C2semidirect
12. #20267929C2semidirect
13. #20267891C2semidirect
14. #20267863C2semidirect
17. C22×Dic206C22semidirect
19. C2×#13110095C22semidirect
20. C2×#13110095C22semidirect
21. C2×#13110095C22semidirect
29. C2×#13110089C22semidirect
31. #15693021C22semidirect
34. #15693000C22semidirect
37. C4×Dic206C22semidirect
39. #15692954C22semidirect
40. C4⋊(C103⋊C8)C22semidirect
41. #15692945C22semidirect
42. #15692944C22semidirect
43. #15692944C22semidirect
44. #15692944C22semidirect
48. C22⋊(C103⋊C8)C22semidirect
49. #15692932C22semidirect
80. #13110093D4semidirect
183. C22×C103#137semidirect
205. C103#3266semidirect
388. 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×#131100932
D4×Dic2062
#202681862
#202680352
#202680302
#202680102
#202679962
#202679532
#202679462
#202679422
#202679292
#202678912
#202678632
#546×C1032
#3266103