Finite Group Databasebeta

← #13129367

Subgroups — #13129367

Order 1664.

1024 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#529C211yesmaximal, characteristic, complemented
2#11719412C214yesmaximal, complemented
3#11719404C212yesmaximal, complemented
4#11719389C212yesmaximal, complemented
5#11719360C214yesmaximal, complemented
6#11719350C212yesmaximal, complemented
7#11719302C212yesmaximal, complemented
8#11719284C212yesmaximal, complemented
9#11719270C212yesmaximal, complemented
10#11719270C212yesmaximal, complemented
11#11719260C212yesmaximal, complemented
12#11719240C212yesmaximal, complemented
13#11719224C212yesmaximal, complemented
14#11719182C211yesmaximal, characteristic, complemented
15C2×#88124C211yesmaximal, characteristic, complemented
16C2×#6129C2214yes—
17C2×#6127C2212yes—
18C13×#126C2212yes—
19C13×#125C2211yescharacteristic
20C13×#124C2211yescharacteristic
21C13×#123C2212yes—
22C13×C22⋊Q8C2211yescharacteristic
23C13×#121C2211yescharacteristic
24C4×Q8×C13C2211yescharacteristic
25C4×D4×C13C2212yes—
26C4×D4×C13C2211yescharacteristic
27C13×#117C2212yes—
28C2×C42×C13C2211yescharacteristic
29#88200C2214yes—
30#88193C2214yes—
31#88193C2214yes—
32#88184C2212yes—
33#88184C2212yes—
34#88184C2212yes—
35#88184C2212yes—
36#88180C2212yes—
37C2×C4⋊Dic13C2211yescharacteristic
38C2×C4⋊Dic13C2211yescharacteristic
39C2×C4⋊Dic13C2212yes—
40C2×#6101C2212yes—
41C2×#6101C2212yes—
42#88152C2214yes—
43#88152C2214yes—
44#88151C2214yes—
45#88150C2214yes—
46#88150C2214yes—
47#88148C2214yes—
48#88148C2214yes—
49C4⋊C4×D13C2214yes—
50#88144C2214yes—
51#88142C2214yes—
52#88140C2214yes—
53#88140C2214yes—
54#88138C2214yes—
55#88138C2214yes—
56#88137C2214yes—
57#88137C2214yes—
58#88135C2214yes—
59#88135C2214yes—
60#88132C2214yes—
61#88132C2214yes—
62#88129C2212yes—
63#88128C2211yescharacteristic
64C4×D52C2212yes—
65C4×D52C2212yes—
66C4×D52C2212yes—
67C4×D52C2212yes—
68#88124C2212yes—
69#88124C2212yes—
70#88124C2212yes—
71#88124C2212yes—
72#88124C2212yes—
73#88123C2211yescharacteristic
74#88123C2212yes—
75C2×Q8×C13C2311yescharacteristic
76C2×D4×C13C2312yes—
77C2×D4×C13C2311yescharacteristic
78C22×C4×C13C2311yescharacteristic
79C22×C4×C13C2311yescharacteristic
80C22×C4×C13C2312yes—
81C22×C4×C13C2311yescharacteristic
82C2×C22⋊D13C2314yes—
83C2×C22⋊D13C2314yes—
84C2×C22⋊D13C2314yes—
85C22×Dic13C2312yes—
86C22×Dic13C2314yes—
87C22×Dic13C2312yes—
88#6129—48no—
89#6127—44no—
90C2×D52C2312yes—
91C2×D52C2312yes—
92C2×D52C2312yes—
93C2×C4×D13C2314yes—
94C2×C4×D13C2314yes—
95C2×C4×D13C2314yes—
96C2×Dic26C2312yes—
97C2×Dic26C2314yes—
98C13×C4⋊C4C2312yes—
99C13×C4⋊C4C2312yes—
100C13×C4⋊C4C2312yes—
101C13×C4⋊C4C2311yescharacteristic
102C13×C4⋊C4C2312yes—
103C13×C4⋊C4C2311yescharacteristic
104C13×C22⋊C4C2312yes—
105C13×C22⋊C4C2312yes—
106C13×C22⋊C4C2312yes—
107C13×C22⋊C4C2312yes—
108C13×C22⋊C4C2312yes—
109C42×C13C2311yescharacteristic
110C42×C13C2312yes—
111C42×C13C2311yescharacteristic
112C42×C13C2311yescharacteristic
113C42×C13C2311yescharacteristic
114C22⋊Dic13C2314yes—
115#6103C2314yes—
116#6103C2314yes—
117#6103C2314yes—
118#6103C2314yes—
119#6103C2314yes—
120#6103C2314yes—
121C4⋊Dic13C2312yes—
122C4⋊Dic13C2312yes—
123C4⋊Dic13C2312yes—
124C4⋊Dic13C2314yes—
125C4⋊Dic13C2312yes—
126C4⋊Dic13C2312yes—
127C4⋊Dic13C2312yes—
128C4⋊Dic13C2314yes—
129#6101C2314yes—
130#6101C2314yes—
131#6101C2314yes—
132#6101C2314yes—
133#6101C2314yes—
134#6101C2314yes—
135C4×Dic13C2314yes—
136#3559—131nomaximal, Sylow
137C23×C13C2412yes—
138C23×C13C2411yescharacteristic
139C22×D13C2414yes—
140Q8×C13—41no—
141D4×C13—24no—
142D4×C13—41no—
143C2×C4×C13—22no—
144C2×C4×C13—22no—
145C2×C4×C13—24no—
146C2×C4×C13—41no—
147C2×C4×C13C2412yes—
148C2×C4×C13C2411yescharacteristic
149C2×C4×C13C2411yescharacteristic
150C2×C4×C13C2411yescharacteristic
151C2×C4×C13C2411yescharacteristic
152C2×C4×C13C2412yes—
153C2×C4×C13C2412yes—
154C2×C4×C13C2411yescharacteristic
155C2×C4×C13C2411yescharacteristic
156C22⋊D13—28no—
157C22⋊D13—44no—
158C22⋊D13—44no—
159C2×Dic13—24no—
160C2×Dic13—44no—
161C2×Dic13—42no—
162C2×Dic13C2414yes—
163C2×Dic13C2414yes—
164C2×Dic13C2414yes—
165D52—24no—
166D52—42no—
167D52—42no—
168C4×D13—44no—
169C4×D13—44no—
170C4×D13—44no—
171Dic26—42no—
172Dic26—44no—
173#563—132no—
174#562—132no—
175#554—132no—
176#553—132no—
177#553—132no—
178#547—134no—
179#547—132no—
180#544—132no—
181#540—132no—
182#539—134no—
183#539—132no—
184#537—132no—
185#532—131no—
186#529D1311yescharacteristic, complemented
187C2×#125—131no—
188C22×C13—21no—
189C22×C13—21no—
190C22×C13—22no—
191C22×C13—22no—
192C22×C13—22no—
193C22×C13H(5,𝔽2)12yes—
194C22×C13C2511yescharacteristic
195C2×D13—24no—
196C2×D13—24no—
197C2×D13—24no—
198C4×C13—22no—
199C4×C13—21no—
200C4×C13—21no—
201C4×C13—22no—
202C4×C13—21no—
203C4×C13—22no—
204C4×C13—21no—
205C4×C13—21no—
206C4×C132−1+412yes—
207Dic13—24no—
208Dic13—24no—
209Dic13—24no—
210C2×#41—134no—
211C2×#41—132no—
212C4⋊Q8—134no—
213C4⋊Q8—131no—
214C4⋊Q8—132no—
215#127—131no—
216#126—134no—
217#126—134no—
218#126C2×D1312yes—
219#125—134no—
220#125—132no—
221#125—132no—
222#125—132no—
223#125—132no—
224#125—132no—
225#125C2×D1311yescharacteristic
226#124—132no—
227#124C2×D1311yescharacteristic
228#123—134no—
229#123—134no—
230#123—134no—
231#123—134no—
232#123—134no—
233#123—134no—
234#123C2×D1312yes—
235C22⋊Q8—134no—
236C22⋊Q8—134no—
237C22⋊Q8—134no—
238C22⋊Q8—134no—
239C22⋊Q8—134no—
240C22⋊Q8—134no—
241C22⋊Q8C2×D1311yescharacteristic
242#121—134no—
243#121—134no—
244#121—132no—
245#121—132no—
246#121—132no—
247#121—132no—
248#121—134no—
249#121—134no—
250#121C2×D1311yescharacteristic
251C4×Q8C2×D1311yescharacteristic
252C4×D4—134no—
253C4×D4—134no—
254C4×D4—132no—
255C4×D4—132no—
256C4×D4—132no—
257C4×D4—132no—
258C4×D4C2×D1312yes—
259C4×D4C2×D1311yescharacteristic
260#117—132no—
261#117C2×D1312yes—
262C2×C4⋊C4—132no—
263C2×C4⋊C4—132no—
264C2×C4⋊C4—131no—
265C2×C4⋊C4—131no—
266C2×C4⋊C4—132no—
267C2×C4⋊C4—134no—
268C2×C42C2×D1311yescharacteristic
269C2×C13—22no—
270C2×C13—42no—
271C2×C13C2×H(5,𝔽2)11yescharacteristic
272C2×C13C2×2−1+411yescharacteristic
273C2×C13#58511yescharacteristic
274D13—44no—
275#41—524no—
276#41—528no—
277C2×Q8—134no—
278C2×Q8—132no—
279C2×Q8C22×D1311yescharacteristic
280C2×D4—134no—
281C2×D4—134no—
282C2×D4—134no—
283C2×D4—132no—
284C2×D4—132no—
285C2×D4—132no—
286C2×D4C22×D1312yes—
287C2×D4C22×D1311yescharacteristic
288C22×C4—132no—
289C22×C4—132no—
290C22×C4—134no—
291C22×C4—134no—
292C22×C4—134no—
293C22×C4—134no—
294C22×C4C22×D1311yescharacteristic
295C22×C4C22×D1311yescharacteristic
296C22×C4C22×D1312yes—
297C22×C4C22×D1311yescharacteristic
298C4⋊C4—132no—
299C4⋊C4—134no—
300C4⋊C4—132no—
301C4⋊C4—132no—
302C4⋊C4—134no—
303C4⋊C4—134no—
304C4⋊C4—134no—
305C4⋊C4—134no—
306C4⋊C4—132no—
307C4⋊C4—134no—
308C4⋊C4—134no—
309C4⋊C4—132no—
310C4⋊C4—132no—
311C4⋊C4—134no—
312C4⋊C4C22×D1312yes—
313C4⋊C4C22×D1312yes—
314C4⋊C4C22×D1312yes—
315C4⋊C4C22×D1312yes—
316C4⋊C4C22×D1311yescharacteristic
317C4⋊C4C22×D1311yescharacteristic
318C22⋊C4—134no—
319C22⋊C4—134no—
320C22⋊C4—134no—
321C22⋊C4—134no—
322C22⋊C4—134no—
323C22⋊C4—134no—
324C22⋊C4—134no—
325C22⋊C4C22×D1312yes—
326C22⋊C4C22×D1312yes—
327C22⋊C4C22×D1312yes—
328C22⋊C4C22×D1312yes—
329C22⋊C4C22×D1312yes—
330C42—134no—
331C42C22×D1311yescharacteristic
332C42C22×D1311yescharacteristic
333C42C22×D1311yescharacteristic
334C42C22×D1311yescharacteristic
335C42C22×D1312yes—
336C13#355911yescharacteristic, complemented, Sylow
337C23—134no—
338C23C23×D1312yes—
339C23C23×D1311yescharacteristic
340Q8—41no—
341Q8—522no—
342Q8—524no—
343D4—24no—
344D4—41no—
345D4—268no—
346D4—264no—
347D4—522no—
348D4—522no—
349D4—524no—
350D4—524no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—24no—
354C2×C4—41no—
355C2×C4—134no—
356C2×C4—134no—
357C2×C4—134no—
358C2×C4—264no—
359C2×C4—524no—
360C2×C4—524no—
361C2×C4—524no—
362C2×C4—522no—
363C2×C4—524no—
364C2×C4C23×D1312yes—
365C2×C4C23×D1311yescharacteristic
366C2×C4C23×D1311yescharacteristic
367C2×C4C23×D1311yescharacteristic
368C2×C4C23×D1311yescharacteristic
369C2×C4C23×D1311yescharacteristic
370C2×C4C23×D1312yes—
371C2×C4C23×D1312yes—
372C2×C4C23×D1311yescharacteristic
373C22—21no—
374C22—21no—
375C22—22no—
376C22—22no—
377C22—22no—
378C22—264no—
379C22—264no—
380C22—264no—
381C22#8825612yes—
382C22C24×D1311yescharacteristic
383C4—21no—
384C4—21no—
385C4—22no—
386C4—22no—
387C4—21no—
388C4—21no—
389C4—21no—
390C4—22no—
391C4—264no—
392C4—264no—
393C4—264no—
394C4#8825712yes—
395C2—22no—
396C2—42no—
397C2—524no—
398C2C2×#8825611yescharacteristic
399C2C2×#8825711yescharacteristic
400C2#1171964811yescharacteristic
subgroupG/H
center, FrattiniC22C24×D13
commutator, socle, cosocleC22×C13C25
FittingC13×#529C2
hypercenter#529D13
hypocenterC13#3559
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #529

Complements

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

NH ≅ G/Ntype
1. C13×#529C2semidirect
2. #11719412C2semidirect
3. #11719404C2semidirect
4. #11719389C2semidirect
5. #11719360C2semidirect
6. #11719350C2semidirect
7. #11719302C2semidirect
8. #11719284C2semidirect
9. #11719270C2semidirect
10. #11719270C2semidirect
11. #11719260C2semidirect
12. #11719240C2semidirect
13. #11719224C2semidirect
14. #11719182C2semidirect
15. C2×#88124C2semidirect
186. #529D13semidirect
336. C13#3559semidirect

Maximal subgroups

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

subgroupindex
C13×#5292
#117194122
#117194042
#117193892
#117193602
#117193502
#117193022
#117192842
#117192702
#117192602
#117192402
#117192242
#117191822
C2×#881242
#355913