Finite Group Databasebeta

← #15867284

Subgroups — #15867284

Order 3328.

862 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×#11718372C211yesmaximal, characteristic
2#13117480C212yesmaximal, complemented
3#13115712C211yesmaximal, characteristic
4#13115702C211yesmaximal, characteristic
5#13115579C211yesmaximal, characteristic, complemented
6#13115564C211yesmaximal, characteristic, complemented
7#13115533C212yesmaximal, complemented
8#13115519C212yesmaximal, complemented
9#13114733C211yesmaximal, characteristic, complemented
10C4×#88061C212yesmaximal, complemented
11C13×#1726C211yesmaximal, characteristic, complemented
12C22×D104C2211yescharacteristic
13C2×C4×D52C2212yes—
14C2×C13×#97C2211yescharacteristic
15C2×C13×#97C2211yescharacteristic
16C2×C13×#97C2211yescharacteristic
17C2×C4×C8×C13C2211yescharacteristic
18C2×C4×C8×C13C2211yescharacteristic
19C2×C4×C8×C13C2211yescharacteristic
20C13×#376C2211yescharacteristic
21C2×#88061C2212yes—
22C2×#88061C2212yes—
23C2×#88061C2212yes—
24C2×#88058C2211yescharacteristic
25C2×#88057C2211yescharacteristic
26C2×#88057C2211yescharacteristic
27#11718600C2212yes—
28#11718600C2212yes—
29C4×C4⋊Dic13C2212yes—
30#11718589C2212yes—
31#11718589C2212yes—
32#11718372C418yescomplemented
33#11718330—22no—
34#11718330—22no—
35#11718328—22no—
36#11718325—22no—
37#11718143C2212yes—
38#11718143C2212yes—
39#11718143C2212yes—
40C22×D52C2312yes—
41C22×C4×D13—22no—
42C22×C8×C13C2311yescharacteristic
43C22×C8×C13C2311yescharacteristic
44C22×C8×C13C2311yescharacteristic
45C22×C8×C13C2311yescharacteristic
46C2×C42×C13C2311yescharacteristic
47C2×C42×C13C2311yescharacteristic
48C2×C42×C13C2311yescharacteristic
49C2×#6103—22no—
50C2×#6103—22no—
51C2×#6103—22no—
52C2×#6103—22no—
53C2×#6103—22no—
54C2×C4⋊Dic13C2312yes—
55C2×C4⋊Dic13C2312yes—
56C2×C4⋊Dic13C2312yes—
57C2×#6101—22no—
58C2×#6101—22no—
59C2×C4×Dic13—22no—
60C2×D104—22no—
61C2×D104—22no—
62C2×D104C2×C414yes—
63C4×D52—24no—
64C4×D52C2×C418yes—
65C13×#97—22no—
66C13×#97—22no—
67C13×#97C2×C414yes—
68C4×C8×C13—22no—
69C4×C8×C13—22no—
70C4×C8×C13—22no—
71C13×#95D412yes—
72C13×#95D412yes—
73#88071—22no—
74#88071—22no—
75#88071—22no—
76#88061—24no—
77#88061—24no—
78#88061C2×C418yes—
79#88058—22no—
80#88057—22no—
81#88057C2×C414yes—
82#21290—131nomaximal, Sylow
83C23×D13—22no—
84C22×C4×C13C2×D411yescharacteristic
85C22×C4×C13C2×D412yes—
86C22×C4×C13C2×D411yescharacteristic
87C22×C4×C13C2×D412yes—
88C22×C4×C13C2411yescharacteristic
89C22×Dic13—22no—
90C22×Dic13—22no—
91C22×Dic13—22no—
92C2×D52—22no—
93C2×D52—22no—
94C2×D52—22no—
95C2×D52—22no—
96C2×D52—22no—
97C2×D52C22×C414yes—
98C2×C4×D13—28no—
99C2×C4×D13—82no—
100C2×C4×D13—82no—
101C2×C8×C13—21no—
102C2×C8×C13—21no—
103C2×C8×C13—21no—
104C2×C8×C13—21no—
105C2×C8×C13—21no—
106C2×C8×C13—21no—
107C2×C8×C13C22×C412yes—
108C2×C8×C13C22×C412yes—
109C2×C8×C13#4112yes—
110C2×C8×C13#4112yes—
111C2×C8×C13#4112yes—
112C2×C8×C13#4112yes—
113C42×C13—21no—
114C42×C13—21no—
115C42×C13—21no—
116C42×C13—21no—
117C42×C13C22×C412yes—
118C42×C13#4112yes—
119#6103—28no—
120#6103—82no—
121#6103—82no—
122#6103—82no—
123#6103—82no—
124C4⋊Dic13—22no—
125C4⋊Dic13—22no—
126C4⋊Dic13—22no—
127C4⋊Dic13—22no—
128C4⋊Dic13—22no—
129C4⋊Dic13C22×C414yes—
130#6101—82no—
131#6101—82no—
132C4×Dic13—82no—
133D104—28no—
134C2×#442—131no—
135#2319—132no—
136#1972—131no—
137#1970—131no—
138#1944—131no—
139#1941—131no—
140#1936—132no—
141#1934—132no—
142#1776—131no—
143C4×#102—132no—
144#1726D1311yescharacteristic, complemented
145C23×C13C22×D411yescharacteristic
146C22×D13—24no—
147C22×D13—42no—
148C22×D13—42no—
149C22×D13—42no—
150C22×D13—42no—
151C22×D13—42no—
152C22×D13—42no—
153C2×C4×C13—22no—
154C2×C4×C13—22no—
155C2×C4×C13—21no—
156C2×C4×C13—21no—
157C2×C4×C13—22no—
158C2×C4×C13—22no—
159C2×C4×C13—22no—
160C2×C4×C13—22no—
161C2×C4×C13—22no—
162C2×C4×C13C4×D414yes—
163C2×C4×C13C23×C411yescharacteristic
164C2×C4×C13C2×#4111yescharacteristic
165C2×C4×C13C2×#4111yescharacteristic
166C2×C4×C13C2×#4111yescharacteristic
167C2×C4×C13C2×#4111yescharacteristic
168C2×C4×C13C2×#4111yescharacteristic
169C2×Dic13—24no—
170C2×Dic13—42no—
171C2×Dic13—42no—
172C2×Dic13—42no—
173C2×Dic13—42no—
174C2×Dic13—42no—
175C2×Dic13—42no—
176C2×Dic13—42no—
177C2×Dic13—42no—
178D52—24no—
179D52—24no—
180D52—42no—
181D52—42no—
182C4×D13—88no—
183C8×C13—22no—
184C8×C13—22no—
185C8×C13—22no—
186C8×C13#11714yes—
187C22×D8—131no—
188C2×C4×D4—132no—
189#442—138no—
190C2×#107—131no—
191C2×#106—131no—
192C2×#106—131no—
193C2×#102—132no—
194C2×#102—132no—
195C2×#102—132no—
196C2×#97C2×D1311yescharacteristic
197C2×#97C2×D1311yescharacteristic
198C2×#97C2×D1311yescharacteristic
199C2×C4×C8C2×D1311yescharacteristic
200C2×C4×C8C2×D1311yescharacteristic
201C2×C4×C8C2×D1311yescharacteristic
202#390—132no—
203#390—132no—
204#389—132no—
205#389—132no—
206#388—262no—
207#388—262no—
208#381—262no—
209#380—262no—
210C4×C4⋊C4—132no—
211#376C2×D1311yescharacteristic
212#340—132no—
213#340—132no—
214#340—132no—
215C22×C13C2×C4×D411yescharacteristic
216C22×C13#53211yescharacteristic
217C22×C13#53211yescharacteristic
218C22×C13#57612yes—
219C22×C13#57712yes—
220C2×D13—44no—
221C2×D13—44no—
222C2×D13—44no—
223C2×D13—82no—
224C2×D13—82no—
225C2×D13—82no—
226C2×D13—82no—
227C4×C13—24no—
228C4×C13—41no—
229C4×C13—41no—
230C4×C13—42no—
231C4×C13C2×#11711yescharacteristic
232C4×C13C4×#4111yescharacteristic
233C4×C13#52911yescharacteristic
234C4×C13#52911yescharacteristic
235Dic13—44no—
236Dic13—82no—
237Dic13—82no—
238C22×D4—132no—
239C23×C4—262no—
240C2×D8—134no—
241C2×D8—262no—
242C2×D8—262no—
243C22×C8C22×D1311yescharacteristic
244C22×C8C22×D1311yescharacteristic
245C22×C8C22×D1311yescharacteristic
246C22×C8C22×D1311yescharacteristic
247C4×D4—138no—
248C4×D4—264no—
249C2×C4⋊C4—132no—
250C2×C4⋊C4—132no—
251C2×C4⋊C4—132no—
252C2×C4⋊C4—262no—
253C2×C4⋊C4—262no—
254C2×C22⋊C4—262no—
255C2×C22⋊C4—262no—
256C2×C22⋊C4—262no—
257C2×C22⋊C4—262no—
258C2×C22⋊C4—262no—
259C2×C42—262no—
260C2×C42C22×D1311yescharacteristic
261C2×C42C22×D1311yescharacteristic
262C2×C42C22×D1311yescharacteristic
263#107—262no—
264#106—134no—
265#106—262no—
266#102—138no—
267#102—264no—
268#102—264no—
269#97—22no—
270#97—22no—
271#97C4×D1314yes—
272C4×C8—22no—
273C4×C8—22no—
274C4×C8—22no—
275#95—262no—
276#95—262no—
277#95—262no—
278#95D5212yes—
279#95D5212yes—
280C2×C13#229311yescharacteristic
281C2×C13#294612yes—
282C2×C13#317311yescharacteristic
283C2×C13#317611yescharacteristic
284C2×C13#317912yes—
285D13—84no—
286C24—262no—
287C2×D4—134no—
288C2×D4—262no—
289C2×D4—262no—
290C2×D4—262no—
291C2×D4—262no—
292C2×D4—262no—
293C22×C4—262no—
294C22×C4—268no—
295C22×C4—262no—
296C22×C4—262no—
297C22×C4—1042no—
298C22×C4—1042no—
299C22×C4C2×D5211yescharacteristic
300C22×C4C2×D5212yes—
301C22×C4C2×D5211yescharacteristic
302C22×C4C2×D5212yes—
303C22×C4C23×D1311yescharacteristic
304D8—268no—
305C2×C8—21no—
306C2×C8—21no—
307C2×C8—21no—
308C2×C8—21no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8C2×C4×D1312yes—
312C2×C8C2×C4×D1312yes—
313C2×C8#612712yes—
314C2×C8#612712yes—
315C2×C8#612712yes—
316C2×C8#612712yes—
317C4⋊C4—134no—
318C4⋊C4—262no—
319C4⋊C4—262no—
320C4⋊C4—262no—
321C4⋊C4—262no—
322C4⋊C4—262no—
323C4⋊C4—1042no—
324C4⋊C4—1042no—
325C22⋊C4—268no—
326C22⋊C4—1042no—
327C22⋊C4—1042no—
328C22⋊C4—1042no—
329C22⋊C4—1042no—
330C42—21no—
331C42—21no—
332C42—21no—
333C42—21no—
334C42—1042no—
335C42C2×C4×D1312yes—
336C42#612712yes—
337C13#2129011yescharacteristic, complemented, Sylow
338C23—264no—
339C23—522no—
340C23—522no—
341C23—522no—
342C23—522no—
343C23—522no—
344C23—522no—
345C23C22×D5211yescharacteristic
346D4—264no—
347D4—264no—
348D4—522no—
349D4—522no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—264no—
360C2×C4—522no—
361C2×C4—522no—
362C2×C4—522no—
363C2×C4—522no—
364C2×C4—522no—
365C2×C4—522no—
366C2×C4—522no—
367C2×C4—522no—
368C2×C4—1048no—
369C2×C4C4×D5214yes—
370C2×C4C22×C4×D1311yescharacteristic
371C2×C4C2×#612711yescharacteristic
372C2×C4C2×#612711yescharacteristic
373C2×C4C2×#612711yescharacteristic
374C2×C4C2×#612711yescharacteristic
375C2×C4C2×#612711yescharacteristic
376C8—22no—
377C8—22no—
378C8—22no—
379C8#8812614yes—
380C22—524no—
381C22—524no—
382C22—524no—
383C22—1042no—
384C22—1042no—
385C22—1042no—
386C22—1042no—
387C22C2×C4×D5211yescharacteristic
388C22#1171918211yescharacteristic
389C22#1171918211yescharacteristic
390C22#1171945612yes—
391C22#1171945712yes—
392C4—24no—
393C4—41no—
394C4—41no—
395C4—42no—
396C4—524no—
397C4—1042no—
398C4—1042no—
399C4C2×#8812611yescharacteristic
400C4C4×#612711yescharacteristic
401C4#1171918411yescharacteristic
402C4#1171918411yescharacteristic
403C2—1044no—
404C2#1311730011yescharacteristic
405C2#1312367012yes—
406C2#1312545311yescharacteristic
407C2#1312548611yescharacteristic
408C2#1312551912yes—
subgroupG/H
centerC23C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1726C2
socleC23×C13C22×D4
prime radicalC22×D104C22
cosocleC22×C4×C13C24
hypercenter#1726D13
hypocenterC13#21290
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ #376 ◁ #1726

Complements

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

NH ≅ G/Ntype
2. #13117480C2semidirect
5. #13115579C2semidirect
6. #13115564C2semidirect
7. #13115533C2semidirect
8. #13115519C2semidirect
9. #13114733C2semidirect
10. C4×#88061C2semidirect
11. C13×#1726C2semidirect
32. #11718372C4semidirect
144. #1726D13semidirect
337. C13#21290semidirect

Maximal subgroups

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

subgroupindex
C2×#117183722
#131174802
#131157122
#131157022
#131155792
#131155642
#131155332
#131155192
#131147332
C4×#880612
C13×#17262
#2129013