Finite Group Databasebeta

← #13129245

Subgroups — #13129245

Order 1664.

1002 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
1C13×#536C211yesmaximal, characteristic, complemented
2#11719537C211yesmaximal, characteristic
3#11719530C211yesmaximal, characteristic, complemented
4Q8×C22⋊D13C212yesmaximal, complemented
5#11719440C212yesmaximal, complemented
6#11719427C212yesmaximal, complemented
7#11719374C214yesmaximal, complemented
8#11719369C212yesmaximal, complemented
9#11719367C214yesmaximal, complemented
10#11719356C212yesmaximal, complemented
11#11719346C212yesmaximal, complemented
12#11719337C212yesmaximal, complemented
13#11719333C212yesmaximal, complemented
14#11719327C212yesmaximal, complemented
15#11719238C212yesmaximal, complemented
16C2×C13×#41C2211yescharacteristic
17C22×Q8×C13C2211yescharacteristic
18C2×Q8×D13C2212yes—
19C2×#6127C2211yescharacteristic
20C22×Dic26C2211yescharacteristic
21C13×C4⋊Q8C2212yes—
22C13×#124C2212yes—
23C13×#123C2212yes—
24C13×#123C2212yes—
25C13×C22⋊Q8C2212yes—
26C13×C22⋊Q8C2212yes—
27C13×#117C2211yescharacteristic
28#88201C2211yescharacteristic
29#88200C2214yes—
30#88200C2212yes—
31Q8×Dic13C2212yes—
32#88198C2211yescharacteristic
33#88198C2212yes—
34#88198C2214yes—
35#88198C2212yes—
36#88194C2211yescharacteristic
37#88193C2212yes—
38#88193C2212yes—
39#88190C2212yes—
40#88190C2211yescharacteristic
41#88189C2212yes—
42#88189C2212yes—
43C4×C22⋊D13C2212yes—
44C4×C22⋊D13C2214yes—
45C4×C22⋊D13C2212yes—
46#88180C2211yescharacteristic
47#88178C2212yes—
48#88178C2214yes—
49#88178C2212yes—
50C2×C4×Dic13C2211yescharacteristic
51#88152C2214yes—
52#88151C2212yes—
53#88150C2214yes—
54#88148C2214yes—
55#88146C2212yes—
56#88143C2214yes—
57#88142C2214yes—
58#88142C2214yes—
59#88142C2212yes—
60#88141C2214yes—
61#88141C2214yes—
62#88141C2212yes—
63#88139C2214yes—
64#88139C2214yes—
65#88139C2214yes—
66#88137C2214yes—
67#88135C2214yes—
68#88133C2214yes—
69#88133C2214yes—
70#88132C2214yes—
71#88132C2214yes—
72#88131C2214yes—
73#88130C2214yes—
74C4×Dic26C2214yes—
75C13×#41—42no—
76C2×Q8×C13—42no—
77C2×Q8×C13C2312yes—
78C2×Q8×C13C2311yescharacteristic
79C2×Q8×C13C2312yes—
80C2×D4×C13C2311yescharacteristic
81C2×D4×C13C2311yescharacteristic
82C2×D4×C13C2311yescharacteristic
83C22×C4×C13C2311yescharacteristic
84C22×C4×C13C2311yescharacteristic
85C22×C4×C13C2311yescharacteristic
86C22×C4×C13C2312yes—
87C2×C22⋊D13C2312yes—
88C2×C22⋊D13C2312yes—
89C2×C22⋊D13C2312yes—
90C22×Dic13C2312yes—
91C22×Dic13C2312yes—
92Q8×D13—44no—
93#6127—42no—
94C2×D52C2311yescharacteristic
95C2×C4×D13C2312yes—
96C2×C4×D13C2314yes—
97C2×Dic26—42no—
98C2×Dic26C2314yes—
99C2×Dic26C2312yes—
100C2×Dic26C2314yes—
101C2×Dic26C2311yescharacteristic
102C2×Dic26C2312yes—
103C13×C4⋊C4C2314yes—
104C13×C4⋊C4C2312yes—
105C13×C4⋊C4C2314yes—
106C13×C22⋊C4C2314yes—
107C13×C22⋊C4C2314yes—
108C13×C22⋊C4C2312yes—
109C42×C13C2312yes—
110C22⋊Dic13C2314yes—
111C22⋊Dic13C2312yes—
112C22⋊Dic13C2312yes—
113C22⋊Dic13C2312yes—
114C22⋊Dic13C2314yes—
115#6103C2312yes—
116#6103C2314yes—
117#6103C2314yes—
118#6103C2314yes—
119#6103C2312yes—
120C4⋊Dic13C2314yes—
121C4⋊Dic13C2314yes—
122C4⋊Dic13C2312yes—
123#6101C2312yes—
124#6101C2314yes—
125#6101C2314yes—
126#6101C2314yes—
127#6101C2314yes—
128#6101C2314yes—
129#6101C2314yes—
130#6101C2312yes—
131#6101C2314yes—
132C4×Dic13C2314yes—
133C4×Dic13C2314yes—
134C4×Dic13C2314yes—
135C4×Dic13C2311yescharacteristic
136C4×Dic13C2312yes—
137C4×Dic13C2312yes—
138C4×Dic13C2311yescharacteristic
139#3550—131nomaximal, Sylow
140C23×C13C2411yescharacteristic
141C23×C13C2411yescharacteristic
142C23×C13C2411yescharacteristic
143C22×D13C2412yes—
144Q8×C13—24no—
145Q8×C13—42no—
146Q8×C13—41no—
147D4×C13—41no—
148D4×C13—41no—
149D4×C13—41no—
150C2×C4×C13—22no—
151C2×C4×C13—22no—
152C2×C4×C13—22no—
153C2×C4×C13—42no—
154C2×C4×C13C2411yescharacteristic
155C2×C4×C13C2414yes—
156C2×C4×C13C2411yescharacteristic
157C2×C4×C13C2414yes—
158C2×C4×C13C2411yescharacteristic
159C2×C4×C13C2411yescharacteristic
160C22⋊D13—24no—
161C22⋊D13—24no—
162C22⋊D13—42no—
163C2×Dic13—24no—
164C2×Dic13—42no—
165C2×Dic13C2414yes—
166C2×Dic13C2412yes—
167C2×Dic13C2412yes—
168C2×Dic13C2414yes—
169C2×Dic13C2412yes—
170D52—41no—
171C4×D13—24no—
172C4×D13—44no—
173Dic26—24no—
174Dic26—28no—
175Dic26—42no—
176Dic26—41no—
177Dic26—44no—
178#563—132no—
179#563—132no—
180#559—132no—
181Q82—132no—
182#556—132no—
183#556—132no—
184D4×Q8—132no—
185D4×Q8—132no—
186#542—134no—
187#542—134no—
188#536—131no—
189#536—132no—
190#536D1311yescharacteristic, complemented
191#533—132no—
192#532—131no—
193C22×C13—21no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13—22no—
197C22×C13—22no—
198C22×C13—22no—
199C22×C13C2511yescharacteristic
200C2×D13—22no—
201C2×D13—22no—
202C2×D13—22no—
203C4×C13—21no—
204C4×C13—24no—
205C4×C13—21no—
206C4×C13—21no—
207C4×C13—24no—
208C4×C13H(5,𝔽2)12yes—
209Dic13—24no—
210Dic13—22no—
211Dic13—24no—
212Dic13—22no—
213Dic132−1+414yes—
214C2×#41—131no—
215C2×#41C2×D1311yescharacteristic
216C22×Q8—132no—
217C22×Q8—131no—
218C22×Q8C2×D1311yescharacteristic
219C4⋊Q8—131no—
220C4⋊Q8—132no—
221C4⋊Q8—132no—
222C4⋊Q8—134no—
223C4⋊Q8—132no—
224C4⋊Q8—134no—
225C4⋊Q8—134no—
226C4⋊Q8C2×D1312yes—
227#127—131no—
228#126—134no—
229#126—134no—
230#126—134no—
231#126—134no—
232#125—134no—
233#124—131no—
234#124—131no—
235#124—132no—
236#124—134no—
237#124—134no—
238#124—134no—
239#124C2×D1312yes—
240#123—132no—
241#123—132no—
242#123—134no—
243#123—134no—
244#123C2×D1312yes—
245#123C2×D1312yes—
246C22⋊Q8—132no—
247C22⋊Q8—134no—
248C22⋊Q8—132no—
249C22⋊Q8—132no—
250C22⋊Q8—134no—
251C22⋊Q8—132no—
252C22⋊Q8—134no—
253C22⋊Q8—134no—
254C22⋊Q8—134no—
255C22⋊Q8C2×D1312yes—
256C22⋊Q8C2×D1312yes—
257#121—132no—
258#121—132no—
259C4×Q8—132no—
260C4×Q8—132no—
261C4×Q8—134no—
262C4×Q8—134no—
263C4×Q8—134no—
264C4×D4—132no—
265C4×D4—132no—
266C4×D4—134no—
267C4×D4—134no—
268#117—131no—
269#117—132no—
270#117—134no—
271#117C2×D1311yescharacteristic
272C2×C42—131no—
273C2×C13—41no—
274C2×C13—41no—
275C2×C13—41no—
276C2×C13C2×H(5,𝔽2)11yescharacteristic
277C2×C13C2×2−1+412yes—
278D13—42no—
279#41—42no—
280#41—522no—
281C2×Q8—42no—
282C2×Q8—134no—
283C2×Q8—132no—
284C2×Q8—134no—
285C2×Q8—132no—
286C2×Q8—131no—
287C2×Q8—522no—
288C2×Q8—524no—
289C2×Q8C22×D1312yes—
290C2×Q8C22×D1312yes—
291C2×Q8C22×D1311yescharacteristic
292C2×D4—132no—
293C2×D4—132no—
294C2×D4—132no—
295C2×D4—131no—
296C2×D4C22×D1311yescharacteristic
297C2×D4C22×D1311yescharacteristic
298C2×D4C22×D1311yescharacteristic
299C22×C4—132no—
300C22×C4—132no—
301C22×C4—132no—
302C22×C4—134no—
303C22×C4C22×D1311yescharacteristic
304C22×C4C22×D1311yescharacteristic
305C22×C4C22×D1311yescharacteristic
306C22×C4C22×D1312yes—
307C4⋊C4—132no—
308C4⋊C4—134no—
309C4⋊C4—134no—
310C4⋊C4—134no—
311C4⋊C4—132no—
312C4⋊C4—132no—
313C4⋊C4—134no—
314C4⋊C4—134no—
315C4⋊C4—134no—
316C4⋊C4—134no—
317C4⋊C4—134no—
318C4⋊C4—134no—
319C4⋊C4C22×D1312yes—
320C4⋊C4C22×D1314yes—
321C4⋊C4C22×D1314yes—
322C22⋊C4—134no—
323C22⋊C4—132no—
324C22⋊C4—132no—
325C22⋊C4—132no—
326C22⋊C4—134no—
327C22⋊C4—134no—
328C22⋊C4—132no—
329C22⋊C4—132no—
330C22⋊C4—134no—
331C22⋊C4—134no—
332C22⋊C4C22×D1314yes—
333C22⋊C4C22×D1312yes—
334C22⋊C4C22×D1314yes—
335C42—132no—
336C42—131no—
337C42—131no—
338C42—134no—
339C42—134no—
340C42—132no—
341C42—134no—
342C42C22×D1312yes—
343C13#355011yescharacteristic, complemented, Sylow
344C23—132no—
345C23C23×D1311yescharacteristic
346C23C23×D1311yescharacteristic
347C23C23×D1311yescharacteristic
348Q8—24no—
349Q8—42no—
350Q8—41no—
351Q8—268no—
352Q8—264no—
353Q8—522no—
354Q8—524no—
355Q8—521no—
356D4—41no—
357D4—41no—
358D4—41no—
359D4—264no—
360D4—264no—
361D4—521no—
362D4—522no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—42no—
367C2×C4—132no—
368C2×C4—134no—
369C2×C4—132no—
370C2×C4—132no—
371C2×C4—134no—
372C2×C4—264no—
373C2×C4—264no—
374C2×C4—524no—
375C2×C4—522no—
376C2×C4C23×D1314yes—
377C2×C4C23×D1311yescharacteristic
378C2×C4C23×D1311yescharacteristic
379C2×C4C23×D1314yes—
380C2×C4C23×D1311yescharacteristic
381C2×C4C23×D1311yescharacteristic
382C22—21no—
383C22—21no—
384C22—21no—
385C22—22no—
386C22—22no—
387C22—22no—
388C22—262no—
389C22—262no—
390C22—262no—
391C22C24×D1311yescharacteristic
392C4—21no—
393C4—21no—
394C4—21no—
395C4—24no—
396C4—24no—
397C4—134no—
398C4—262no—
399C4—264no—
400C4—262no—
401C4—264no—
402C4#8825112yes—
403C2—41no—
404C2—41no—
405C2—41no—
406C2—522no—
407C2C2×#8825111yescharacteristic
408C2D13×2−1+412yes—
subgroupG/H
center, FrattiniC22C24×D13
commutator, socle, cosocleC22×C13C25
FittingC13×#536C2
prime radical#11719537C2
hypercenter#536D13
hypocenterC13#3550
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C13×#536C2semidirect
3. #11719530C2semidirect
4. Q8×C22⋊D13C2semidirect
5. #11719440C2semidirect
6. #11719427C2semidirect
7. #11719374C2semidirect
8. #11719369C2semidirect
9. #11719367C2semidirect
10. #11719356C2semidirect
11. #11719346C2semidirect
12. #11719337C2semidirect
13. #11719333C2semidirect
14. #11719327C2semidirect
15. #11719238C2semidirect
190. #536D13semidirect
343. C13#3550semidirect

Maximal subgroups

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

subgroupindex
C13×#5362
#117195372
#117195302
Q8×C22⋊D132
#117194402
#117194272
#117193742
#117193692
#117193672
#117193562
#117193462
#117193372
#117193332
#117193272
#117192382
#355013