Finite Group Databasebeta

← #13126829

Subgroups — #13126829

Order 1664.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719260C211yesmaximal, characteristic, complemented
2#11719257C211yesmaximal, characteristic, complemented
3C13×#435C211yesmaximal, characteristic, complemented
4#11718795C211yesmaximal, characteristic, complemented
5#11718794C211yesmaximal, characteristic, complemented
6#11718776C211yesmaximal, characteristic, complemented
7C2×#88056C211yesmaximal, characteristic, complemented
8#11718511C211yesmaximal, characteristic, complemented
9#11718505C211yesmaximal, characteristic, complemented
10#11718399C211yesmaximal, characteristic, complemented
11#11718397C211yesmaximal, characteristic, complemented
12#11718395C211yesmaximal, characteristic, complemented
13#11718383C211yesmaximal, characteristic, complemented
14#11718375C211yesmaximal, characteristic, complemented
15#11718371C211yesmaximal, characteristic, complemented
16C2×#6129—21no—
17C2×#6127C2211yescharacteristic
18C22×Dic26C2211yescharacteristic
19C2×C13×M16C2211yescharacteristic
20C22×C8×C13C2211yescharacteristic
21C4×D4×C13C2211yescharacteristic
22#88193—21no—
23#88184C2211yescharacteristic
24#88184C2211yescharacteristic
25#88184C2211yescharacteristic
26C2×C4⋊Dic13C2211yescharacteristic
27C2×C4⋊Dic13C2211yescharacteristic
28#88178C2211yescharacteristic
29C2×D104C2211yescharacteristic
30C2×#6095C2211yescharacteristic
31C2×#6095C2211yescharacteristic
32#88151—21no—
33#88150—21no—
34#88140—21no—
35#88140—21no—
36#88139—21no—
37#88135—21no—
38#88129C2211yescharacteristic
39C4×D52C2211yescharacteristic
40#88123C2211yescharacteristic
41C4×Dic26C2211yescharacteristic
42C13×C4⋊C8C2211yescharacteristic
43C13×C22⋊C8C2211yescharacteristic
44C13×C22⋊C8C2211yescharacteristic
45C13×#97C2211yescharacteristic
46#88061C2211yescharacteristic
47#88061C2211yescharacteristic
48#88061C2211yescharacteristic
49#88061C2211yescharacteristic
50#88058C2211yescharacteristic
51#88058C2211yescharacteristic
52#88058C2211yescharacteristic
53#88056C2211yescharacteristic
54#88056C2211yescharacteristic
55#88056C2211yescharacteristic
56#88056C2211yescharacteristic
57#88056C2211yescharacteristic
58#88056C2211yescharacteristic
59C2×D4×C13D411yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C2×C22⋊D13—21no—
63C2×C22⋊D13—21no—
64C2×C22⋊D13—21no—
65C2×C22⋊D13—21no—
66C22×Dic13—21no—
67C22×Dic13—21no—
68C22×Dic13—21no—
69#6129—44no—
70#6127—22no—
71#6127—41no—
72C2×D52C2311yescharacteristic
73C2×D52C2311yescharacteristic
74C2×C4×D13—21no—
75C2×C4×D13—21no—
76C2×Dic26—22no—
77C2×Dic26—21no—
78C2×Dic26—21no—
79C2×Dic26—41no—
80C2×Dic26C2311yescharacteristic
81C2×Dic26C2311yescharacteristic
82C13×M16—41no—
83C2×C8×C13—41no—
84C2×C8×C13C2311yescharacteristic
85C2×C8×C13C2311yescharacteristic
86C2×C8×C13C2311yescharacteristic
87C2×C8×C13C2311yescharacteristic
88C13×C4⋊C4D411yescharacteristic
89C13×C22⋊C4D411yescharacteristic
90C13×C22⋊C4D411yescharacteristic
91C42×C13C2311yescharacteristic
92C22⋊Dic13—21no—
93#6103—21no—
94#6103—21no—
95#6103—21no—
96#6103—21no—
97#6103—21no—
98#6103—21no—
99C4⋊Dic13—21no—
100C4⋊Dic13—21no—
101C4⋊Dic13—21no—
102C4⋊Dic13C2311yescharacteristic
103C4⋊Dic13C2311yescharacteristic
104C4⋊Dic13C2311yescharacteristic
105C4⋊Dic13C2311yescharacteristic
106#6101—21no—
107#6101—21no—
108C4×Dic13—21no—
109D104—41no—
110#6095—22no—
111#6095—41no—
112#3308—131nomaximal, Sylow
113C23×C13C2×D411yescharacteristic
114C23×C13C2×D411yescharacteristic
115C22×D13—21no—
116C22×D13—21no—
117D4×C13—22no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13C2×D411yescharacteristic
123C2×C4×C13C2×D411yescharacteristic
124C2×C4×C13C2×D411yescharacteristic
125C2×C4×C13C2×D411yescharacteristic
126C2×C4×C13C2411yescharacteristic
127C22⋊D13—42no—
128C22⋊D13—42no—
129C22⋊D13—42no—
130C22⋊D13—42no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—42no—
138C2×Dic13—42no—
139C2×Dic13—42no—
140D52—21no—
141D52—21no—
142D52—21no—
143D52—21no—
144C4×D13—42no—
145C4×D13—42no—
146Dic26—21no—
147Dic26—21no—
148Dic26—21no—
149Dic26—42no—
150Dic26—42no—
151Dic26#4112yescomplemented
152C8×C13—21no—
153C8×C13—21no—
154C8×C13—21no—
155C8×C13—21no—
156#548—131no—
157#547—131no—
158#489—131no—
159#484—131no—
160#480—131no—
161#477—131no—
162#468—131no—
163#466—131no—
164#463—131no—
165#449—131no—
166#448—131no—
167#440—131no—
168#435D1311yescharacteristic, complemented
169#417—131no—
170C2×#103—131no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13AGL(1,ℤ/8)12yes—
177C22×C13C22×D411yescharacteristic
178C2×D13—41no—
179C2×D13—41no—
180C2×D13—41no—
181C2×D13—41no—
182C2×D13—41no—
183C2×D13—41no—
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—21no—
187C4×C13—21no—
188C4×C13C2×#4111yescharacteristic
189C4×C13H(5,𝔽2)11yescharacteristic
190Dic13—22no—
191Dic13—41no—
192Dic13—41no—
193Dic13—41no—
194Dic13—41no—
195Dic13—41no—
196C2×#41—131no—
197C2×#41—261no—
198C22×Q8—131no—
199C2×SD16—131no—
200C2×SD16—131no—
201C2×D8—131no—
202C2×M16C2×D1311yescharacteristic
203C22×C8C2×D1311yescharacteristic
204C4⋊Q8—131no—
205#124—131no—
206#124—261no—
207#123—261no—
208#123—261no—
209C22⋊Q8—131no—
210C22⋊Q8—261no—
211C22⋊Q8—261no—
212#121—131no—
213#121—131no—
214#121—131no—
215#121—261no—
216C4×Q8—131no—
217C4×D4—131no—
218C4×D4—261no—
219C4×D4C2×D1311yescharacteristic
220C2×C4⋊C4—131no—
221C2×C4⋊C4—131no—
222#107—131no—
223#107—131no—
224#107—131no—
225C4⋊C8C2×D1311yescharacteristic
226#103—131no—
227#103—131no—
228#103—131no—
229#103—131no—
230#103—131no—
231#103—131no—
232#102—131no—
233#102—131no—
234#102—131no—
235#102—131no—
236C22⋊C8C2×D1311yescharacteristic
237C22⋊C8C2×D1311yescharacteristic
238#97C2×D1311yescharacteristic
239C2×C13—22no—
240C2×C13—41no—
241C2×C13#54611yescharacteristic
242C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
243C2×C13#57811yescharacteristic
244D13—81no—
245D13—81no—
246#41—262no—
247#41—521no—
248#41—524no—
249C2×Q8—131no—
250C2×Q8—131no—
251C2×Q8—262no—
252C2×Q8—261no—
253C2×Q8—261no—
254C2×Q8—521no—
255C2×D4—131no—
256C2×D4—131no—
257C2×D4—261no—
258C2×D4—261no—
259C2×D4—261no—
260C2×D4—261no—
261C2×D4D5211yescharacteristic
262C22×C4—261no—
263C22×C4—261no—
264C22×C4—261no—
265C22×C4—261no—
266C22×C4—261no—
267C22×C4C22×D1311yescharacteristic
268C22×C4C22×D1311yescharacteristic
269SD16—262no—
270SD16—521no—
271D8—521no—
272M16—41no—
273C2×C8—41no—
274C2×C8C22×D1311yescharacteristic
275C2×C8C22×D1311yescharacteristic
276C2×C8C22×D1311yescharacteristic
277C2×C8C22×D1311yescharacteristic
278C4⋊C4—131no—
279C4⋊C4—131no—
280C4⋊C4—131no—
281C4⋊C4—131no—
282C4⋊C4—261no—
283C4⋊C4—261no—
284C4⋊C4—261no—
285C4⋊C4—261no—
286C4⋊C4—261no—
287C4⋊C4D5211yescharacteristic
288C22⋊C4—261no—
289C22⋊C4—261no—
290C22⋊C4—261no—
291C22⋊C4—261no—
292C22⋊C4—261no—
293C22⋊C4—261no—
294C22⋊C4—261no—
295C22⋊C4D5211yescharacteristic
296C22⋊C4D5211yescharacteristic
297C42—261no—
298C42C22×D1311yescharacteristic
299C13#330811yescharacteristic, complemented, Sylow
300C23—261no—
301C23—261no—
302C23C2×D5211yescharacteristic
303C23C2×D5211yescharacteristic
304Q8—132no—
305Q8—261no—
306Q8—261no—
307Q8—261no—
308Q8—522no—
309Q8—522no—
310D4—22no—
311D4—261no—
312D4—261no—
313D4—261no—
314D4—261no—
315D4—522no—
316D4—522no—
317D4—522no—
318D4—522no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—261no—
324C2×C4—261no—
325C2×C4—261no—
326C2×C4—261no—
327C2×C4—261no—
328C2×C4—261no—
329C2×C4—522no—
330C2×C4—522no—
331C2×C4—522no—
332C2×C4—522no—
333C2×C4—522no—
334C2×C4C2×D5211yescharacteristic
335C2×C4C2×D5211yescharacteristic
336C2×C4C2×D5211yescharacteristic
337C2×C4C2×D5211yescharacteristic
338C2×C4C23×D1311yescharacteristic
339C8—21no—
340C8—21no—
341C8—21no—
342C8—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—521no—
349C22—521no—
350C22—521no—
351C22—521no—
352C22—521no—
353C22—521no—
354C22#8816212yes—
355C22C22×D5211yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—262no—
361C4—521no—
362C4—521no—
363C4—521no—
364C4—521no—
365C4—521no—
366C4#8825111yescharacteristic
367C4#41×D1311yescharacteristic
368C2—22no—
369C2—41no—
370C2—1041no—
371C2—1041no—
372C2#1171925911yescharacteristic
373C2C2×#8816211yescharacteristic
374C2#1171945811yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#435C2
socleC22×C13C22×D4
hypercenter#435D13
hypocenterC13#3308
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #11719260C2semidirect
2. #11719257C2semidirect
3. C13×#435C2semidirect
4. #11718795C2semidirect
5. #11718794C2semidirect
6. #11718776C2semidirect
7. C2×#88056C2semidirect
8. #11718511C2semidirect
9. #11718505C2semidirect
10. #11718399C2semidirect
11. #11718397C2semidirect
12. #11718395C2semidirect
13. #11718383C2semidirect
14. #11718375C2semidirect
15. #11718371C2semidirect
151. Dic26#41semidirect
168. #435D13semidirect
299. C13#3308semidirect

Maximal subgroups

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

subgroupindex
#117192602
#117192572
C13×#4352
#117187952
#117187942
#117187762
C2×#880562
#117185112
#117185052
#117183992
#117183972
#117183952
#117183832
#117183752
#117183712
#330813