Finite Group Databasebeta

← #13126823

Subgroups — #13126823

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#11719522C211yesmaximal, characteristic, complemented
2#11719212C211yesmaximal, characteristic, complemented
3C2×C13×#103C211yesmaximal, characteristic, complemented
4#11718888C211yesmaximal, characteristic, complemented
5#11718776C211yesmaximal, characteristic, complemented
6#11718772C211yesmaximal, characteristic, complemented
7#11718628C211yesmaximal, characteristic, complemented
8#11718480C211yesmaximal, characteristic, complemented
9#11718478C211yesmaximal, characteristic, complemented
10#11718473C211yesmaximal, characteristic, complemented
11#11718472C211yesmaximal, characteristic, complemented
12#11718470C211yesmaximal, characteristic, complemented
13#11718464C211yesmaximal, characteristic, complemented
14#11718456C211yesmaximal, characteristic, complemented
15#11718455C211yesmaximal, characteristic, complemented
16C22×Q8×C13C2211yescharacteristic
17C2×#6131C2211yescharacteristic
18C2×#6127—21no—
19C22×C8×C13C2211yescharacteristic
20C2×C13×C4⋊C4C2211yescharacteristic
21#88201—21no—
22#88201C2211yescharacteristic
23#88200—21no—
24#88200C2211yescharacteristic
25Q8×Dic13C2211yescharacteristic
26C2×#6106C2211yescharacteristic
27C2×#6106C2211yescharacteristic
28#88184—21no—
29#88184C2211yescharacteristic
30#88184C2211yescharacteristic
31#88183—21no—
32C4×C22⋊D13—21no—
33C4×C22⋊D13C2211yescharacteristic
34C2×D104C2211yescharacteristic
35C2×#6094C2211yescharacteristic
36#88150—21no—
37#88149C2211yescharacteristic
38#88148—21no—
39#88147C2211yescharacteristic
40C4⋊C4×D13C2211yescharacteristic
41#88142C2211yescharacteristic
42C13×#103C2211yescharacteristic
43C13×#103C2211yescharacteristic
44C13×#103C2211yescharacteristic
45C13×#103C2211yescharacteristic
46#88075C2211yescharacteristic
47#88075C2211yescharacteristic
48C22⋊#1055C2211yescharacteristic
49#88061C2211yescharacteristic
50#88061C2211yescharacteristic
51#88060C2211yescharacteristic
52#88058C2211yescharacteristic
53#88055C2211yescharacteristic
54#88054C2211yescharacteristic
55#88049C2211yescharacteristic
56#88049C2211yescharacteristic
57#88047C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×Q8×C13—22no—
61C2×Q8×C13—41no—
62C2×Q8×C13C2311yescharacteristic
63C2×Q8×C13C2311yescharacteristic
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13C2311yescharacteristic
67C2×C22⋊D13—21no—
68C2×C22⋊D13—21no—
69C2×C22⋊D13D411yescharacteristic
70#6131—22no—
71#6131—41no—
72#6127—44no—
73C2×D52—21no—
74C2×D52—21no—
75C2×D52C2311yescharacteristic
76C2×D52C2311yescharacteristic
77C2×C4×D13—21no—
78C2×C4×D13—21no—
79C2×C4×D13—21no—
80C2×C4×D13C2311yescharacteristic
81C2×Dic26—21no—
82C2×C8×C13—41no—
83C2×C8×C13C2311yescharacteristic
84C2×C8×C13C2311yescharacteristic
85C13×C4⋊C4—21no—
86C13×C4⋊C4C2311yescharacteristic
87C13×C4⋊C4C2311yescharacteristic
88C22⋊Dic13D411yescharacteristic
89#6106—22no—
90#6106—41no—
91#6103—21no—
92#6103—21no—
93#6103—21no—
94#6103—21no—
95#6103—21no—
96#6103—21no—
97#6103—21no—
98#6103D411yescharacteristic
99C4⋊Dic13—21no—
100C4⋊Dic13C2311yescharacteristic
101C4⋊Dic13C2311yescharacteristic
102#6101—21no—
103#6101—21no—
104#6101—21no—
105#6101D411yescharacteristic
106C4×Dic13—21no—
107C4×Dic13C2311yescharacteristic
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110D104—41no—
111#6094—41no—
112#3308—131nomaximal, Sylow
113C23×C13C2×D411yescharacteristic
114C22×D13—21no—
115C22×D13—21no—
116C22×D13C2×D411yescharacteristic
117Q8×C13—21no—
118Q8×C13—21no—
119Q8×C13—21no—
120Q8×C13—42no—
121Q8×C13#4112yescomplemented
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—42no—
129C2×C4×C13—42no—
130C2×C4×C13C2×D411yescharacteristic
131C2×C4×C13C2411yescharacteristic
132C22⋊D13—22no—
133C22⋊D13—42no—
134C22⋊D13—42no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13C2×D411yescharacteristic
138C2×Dic13C2×D411yescharacteristic
139C2×Dic13C2×D411yescharacteristic
140D52—21no—
141D52—21no—
142D52—21no—
143D52—21no—
144D52—42no—
145D52—42no—
146C4×D13—21no—
147C4×D13—21no—
148C4×D13—42no—
149C4×D13—42no—
150C4×D13—42no—
151Dic26—42no—
152C8×C13—21no—
153C8×C13—21no—
154#1055—21no—
155#1055—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#435—131no—
169#417—131no—
170C2×#103D1311yescharacteristic, complemented
171C22×C13—21no—
172C22×C13—21no—
173C22×C13AGL(1,ℤ/8)12yes—
174C22×C13C22×D411yescharacteristic
175C2×D13—21no—
176C2×D13—21no—
177C2×D13—21no—
178C2×D13—41no—
179C2×D13—41no—
180C2×D13—41no—
181C2×D13—41no—
182C2×D13—41no—
183C2×D13—41no—
184C4×C13—22no—
185C4×C13—21no—
186C4×C13—41no—
187C4×C13—41no—
188C4×C13—41no—
189C4×C13C2×#4111yescharacteristic
190C4×C13H(5,𝔽2)11yescharacteristic
191Dic13—21no—
192Dic13—21no—
193Dic13—21no—
194Dic13—41no—
195Dic13—41no—
196C2×#41—131no—
197C2×#41—261no—
198C22×Q8C2×D1311yescharacteristic
199C2×SD16—131no—
200C2×SD16—131no—
201C2×D8—131no—
202C2×M16—131no—
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—131no—
219C4×D4—261no—
220C2×C4⋊C4—131no—
221C2×C4⋊C4C2×D1311yescharacteristic
222#107—131no—
223#107—131no—
224#107—131no—
225C4⋊C8—131no—
226#103—131no—
227#103—131no—
228#103C2×D1311yescharacteristic
229#103C2×D1311yescharacteristic
230#103C2×D1311yescharacteristic
231#103C2×D1311yescharacteristic
232#102—131no—
233#102—131no—
234#102—131no—
235#102—131no—
236C22⋊C8—131no—
237C22⋊C8—131no—
238#97—131no—
239C2×C13—22no—
240C2×C13#54611yescharacteristic
241C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
242C2×C13#57811yescharacteristic
243D13—41no—
244D13—81no—
245D13—81no—
246#41—262no—
247#41—524no—
248#41—521no—
249C2×Q8—21no—
250C2×Q8—22no—
251C2×Q8—41no—
252C2×Q8—261no—
253C2×Q8C22×D1311yescharacteristic
254C2×Q8C22×D1311yescharacteristic
255C2×D4—131no—
256C2×D4—131no—
257C2×D4—131no—
258C2×D4—261no—
259C2×D4—261no—
260C2×D4—261no—
261C2×D4—261no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—131no—
265C22×C4—261no—
266C22×C4—261no—
267C22×C4—261no—
268C22×C4C22×D1311yescharacteristic
269SD16—262no—
270SD16—521no—
271D8—521no—
272M16—521no—
273C2×C8—41no—
274C2×C8—131no—
275C2×C8—131no—
276C2×C8C22×D1311yescharacteristic
277C2×C8C22×D1311yescharacteristic
278C4⋊C4—21no—
279C4⋊C4—131no—
280C4⋊C4—131no—
281C4⋊C4—131no—
282C4⋊C4—261no—
283C4⋊C4—261no—
284C4⋊C4—261no—
285C4⋊C4—261no—
286C4⋊C4C22×D1311yescharacteristic
287C4⋊C4C22×D1311yescharacteristic
288C22⋊C4—131no—
289C22⋊C4—131no—
290C22⋊C4—261no—
291C22⋊C4—261no—
292C22⋊C4—261no—
293C22⋊C4—261no—
294C22⋊C4—261no—
295C22⋊C4—261no—
296C22⋊C4—261no—
297C42—131no—
298C42—261no—
299C13#330811yescharacteristic, complemented, Sylow
300C23—131no—
301C23—261no—
302C23—261no—
303C23D4×D1311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—42no—
308Q8—522no—
309Q8#612712yescomplemented
310D4—262no—
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—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—131no—
328C2×C4—131no—
329C2×C4—131no—
330C2×C4—261no—
331C2×C4—261no—
332C2×C4—261no—
333C2×C4—261no—
334C2×C4—522no—
335C2×C4—522no—
336C2×C4—522no—
337C2×C4D4×D1311yescharacteristic
338C2×C4C23×D1311yescharacteristic
339C8—21no—
340C8—21no—
341C8—261no—
342C8—261no—
343C22—21no—
344C22—21no—
345C22—261no—
346C22—261no—
347C22—261no—
348C22—521no—
349C22—521no—
350C22—521no—
351C22—521no—
352C22—521no—
353C22—521no—
354C22#8816812yes—
355C22C2×D4×D1311yescharacteristic
356C4—21no—
357C4—22no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—261no—
362C4—261no—
363C4—261no—
364C4—521no—
365C4—521no—
366C4C2×#612711yescharacteristic
367C4#8825111yescharacteristic
368C2—22no—
369C2—521no—
370C2—1041no—
371C2—1041no—
372C2#1171919511yescharacteristic
373C2C2×#8816811yescharacteristic
374C2#1171947111yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC2×C13×#103C2
socleC22×C13C22×D4
hypercenterC2×#103D13
hypocenterC13#3308
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. #11719522C2semidirect
2. #11719212C2semidirect
3. C2×C13×#103C2semidirect
4. #11718888C2semidirect
5. #11718776C2semidirect
6. #11718772C2semidirect
7. #11718628C2semidirect
8. #11718480C2semidirect
9. #11718478C2semidirect
10. #11718473C2semidirect
11. #11718472C2semidirect
12. #11718470C2semidirect
13. #11718464C2semidirect
14. #11718456C2semidirect
15. #11718455C2semidirect
121. Q8×C13#41semidirect
170. C2×#103D13semidirect
299. C13#3308semidirect
309. Q8#6127semidirect

Maximal subgroups

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

subgroupindex
#117195222
#117192122
C2×C13×#1032
#117188882
#117187762
#117187722
#117186282
#117184802
#117184782
#117184732
#117184722
#117184702
#117184642
#117184562
#117184552
#330813