Finite Group Databasebeta

← #13126805

Subgroups — #13126805

Order 1664.

394 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719529C211yesmaximal, characteristic, complemented
2#11719323C211yesmaximal, characteristic, complemented
3C13×#449C211yesmaximal, characteristic, complemented
4#11718893C211yesmaximal, characteristic, complemented
5#11718832C211yesmaximal, characteristic, complemented
6#11718823C211yesmaximal, characteristic, complemented
7#11718819C211yesmaximal, characteristic, complemented
8#11718813C211yesmaximal, characteristic, complemented
9#11718703C211yesmaximal, characteristic, complemented
10#11718476C211yesmaximal, characteristic, complemented
11#11718458C211yesmaximal, characteristic, complemented
12#11718433C211yesmaximal, characteristic, complemented
13#11718424C211yesmaximal, characteristic, complemented
14#11718389C211yesmaximal, characteristic, complemented
15#11718382C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C2×#6129C2211yescharacteristic
18C2×C13×SD16C2211yescharacteristic
19C2×C13×D8C2211yescharacteristic
20C13×#121C2211yescharacteristic
21#88200C2211yescharacteristic
22#88198C2211yescharacteristic
23#88193—21no—
24#88193—21no—
25#88192C2211yescharacteristic
26#88189—21no—
27D4×Dic13—21no—
28D4×Dic13C2211yescharacteristic
29D4×Dic13C2211yescharacteristic
30C2×#6105C2211yescharacteristic
31#88183—21no—
32C4×C22⋊D13C2211yescharacteristic
33C2×C4⋊Dic13C2211yescharacteristic
34#88178C2211yescharacteristic
35C2×#6101—21no—
36C2×#6099C2211yescharacteristic
37C2×C8×D13C2211yescharacteristic
38#88146C2211yescharacteristic
39#88144C2211yescharacteristic
40#88140—21no—
41#88133—21no—
42C13×#103C2211yescharacteristic
43C13×#102C2211yescharacteristic
44C13×C22⋊C8C2211yescharacteristic
45#88075C2211yescharacteristic
46#88075C2211yescharacteristic
47#88072C2211yescharacteristic
48#88072C2211yescharacteristic
49#88072C2211yescharacteristic
50#88060C2211yescharacteristic
51#88057C2211yescharacteristic
52#88057C2211yescharacteristic
53#88056C2211yescharacteristic
54#88056C2211yescharacteristic
55#88055C2211yescharacteristic
56#88054C2211yescharacteristic
57#88050C2211yescharacteristic
58#88047C2211yescharacteristic
59C13×#41—22no—
60C13×#41—41no—
61C2×Q8×C13C2311yescharacteristic
62C2×D4×C13—21no—
63C2×D4×C13—21no—
64C2×D4×C13C2311yescharacteristic
65C2×D4×C13C2311yescharacteristic
66C22×C4×C13—21no—
67C22×C4×C13C2311yescharacteristic
68C2×C22⋊D13—21no—
69C2×C22⋊D13—21no—
70C2×C22⋊D13D411yescharacteristic
71C22×Dic13—21no—
72C22×Dic13—21no—
73C22×Dic13—21no—
74C22×Dic13—21no—
75#6129—22no—
76#6129—41no—
77C2×C4×D13C2311yescharacteristic
78C2×Dic26C2311yescharacteristic
79C13×SD16—41no—
80C13×D8—22no—
81C2×C8×C13C2311yescharacteristic
82C2×C8×C13C2311yescharacteristic
83C13×C4⋊C4C2311yescharacteristic
84C13×C22⋊C4—21no—
85C22⋊Dic13—21no—
86C22⋊Dic13—21no—
87C22⋊Dic13—21no—
88C22⋊Dic13—21no—
89C22⋊Dic13D411yescharacteristic
90#6105—41no—
91#6103—21no—
92#6103—21no—
93#6103D411yescharacteristic
94C4⋊Dic13—21no—
95C4⋊Dic13—21no—
96C4⋊Dic13C2311yescharacteristic
97C4⋊Dic13C2311yescharacteristic
98C4⋊Dic13C2311yescharacteristic
99#6101—21no—
100#6101—21no—
101#6101—21no—
102#6101—21no—
103#6101—21no—
104#6101D411yescharacteristic
105C4×Dic13—21no—
106C4×Dic13C2311yescharacteristic
107#6099—41no—
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110C8×D13—41no—
111#3307—131nomaximal, Sylow
112C23×C13—21no—
113C23×C13—21no—
114C23×C13C2×D411yescharacteristic
115C22×D13C2×D411yescharacteristic
116Q8×C13—21no—
117Q8×C13—21no—
118D4×C13—21no—
119D4×C13—21no—
120D4×C13—21no—
121D4×C13—42no—
122D4×C13—42no—
123D4×C13#4112yes—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—42no—
129C2×C4×C13C2×D411yescharacteristic
130C2×C4×C13C2411yescharacteristic
131C22⋊D13—41no—
132C22⋊D13—42no—
133C22⋊D13—81no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—42no—
139C2×Dic13—42no—
140C2×Dic13—81no—
141C2×Dic13—81no—
142C2×Dic13C2×D411yescharacteristic
143C2×Dic13C2×D411yescharacteristic
144C2×Dic13C2×D411yescharacteristic
145C4×D13—21no—
146C4×D13—21no—
147Dic26—21no—
148Dic26—21no—
149C8×C13—21no—
150C8×C13—21no—
151#1055—21no—
152#1055—21no—
153#553—131no—
154#547—131no—
155#491—131no—
156#485—131no—
157#483—131no—
158#478—131no—
159#468—131no—
160#465—131no—
161#461—131no—
162#449—131no—
163#449D1311yescharacteristic, complemented
164#442—131no—
165#435—131no—
166#417—131no—
167#416—131no—
168C22×C13—22no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13C22×D411yescharacteristic
178C2×D13—21no—
179C2×D13—21no—
180C2×D13—21no—
181C4×C13—21no—
182C4×C13—41no—
183C4×C13—41no—
184C4×C13C2×#4111yescharacteristic
185C4×C13H(5,𝔽2)11yescharacteristic
186Dic13—21no—
187Dic13—21no—
188Dic13—21no—
189Dic13—41no—
190Dic13—41no—
191Dic13—41no—
192Dic13—41no—
193C2×#41—131no—
194C2×#41C2×D1311yescharacteristic
195C2×SD16—131no—
196C2×SD16C2×D1311yescharacteristic
197C2×D8C2×D1311yescharacteristic
198C2×M16—131no—
199C22×C8—131no—
200C4⋊Q8—131no—
201#126—261no—
202#125—131no—
203#123—261no—
204#123—261no—
205#123—261no—
206C22⋊Q8—131no—
207C22⋊Q8—131no—
208#121—131no—
209#121—261no—
210#121—261no—
211#121C2×D1311yescharacteristic
212C4×D4—131no—
213C4×D4—131no—
214C4×D4—131no—
215C4×D4—261no—
216#117—131no—
217C2×C4⋊C4—131no—
218C2×C4⋊C4—261no—
219#107—131no—
220#106—131no—
221#106—131no—
222C4⋊C8—131no—
223#103—131no—
224#103—131no—
225#103—131no—
226#103—131no—
227#103—131no—
228#103C2×D1311yescharacteristic
229#102—131no—
230#102—131no—
231#102—131no—
232#102C2×D1311yescharacteristic
233C22⋊C8—131no—
234C22⋊C8C2×D1311yescharacteristic
235#97—131no—
236C2×C13—41no—
237C2×C13—42no—
238C2×C13—81no—
239C2×C13#54611yescharacteristic
240C2×C13#57511yescharacteristic
241C2×C13#57711yescharacteristic
242D13—41no—
243#41—22no—
244#41—41no—
245#41—262no—
246#41—521no—
247C2×Q8—131no—
248C2×Q8C22×D1311yescharacteristic
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—131no—
252C2×D4—261no—
253C2×D4—261no—
254C2×D4C22×D1311yescharacteristic
255C2×D4C22×D1311yescharacteristic
256C22×C4—21no—
257C22×C4—131no—
258C22×C4—261no—
259C22×C4—261no—
260C22×C4—261no—
261C22×C4—261no—
262C22×C4C22×D1311yescharacteristic
263SD16—41no—
264SD16—521no—
265D8—22no—
266M16—521no—
267C2×C8—131no—
268C2×C8—131no—
269C2×C8—521no—
270C2×C8C22×D1311yescharacteristic
271C2×C8C22×D1311yescharacteristic
272C4⋊C4—131no—
273C4⋊C4—131no—
274C4⋊C4—131no—
275C4⋊C4—131no—
276C4⋊C4—261no—
277C4⋊C4—261no—
278C4⋊C4—261no—
279C4⋊C4—261no—
280C4⋊C4—261no—
281C4⋊C4—261no—
282C4⋊C4—261no—
283C4⋊C4C22×D1311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—131no—
286C22⋊C4—131no—
287C22⋊C4—261no—
288C22⋊C4—261no—
289C22⋊C4—261no—
290C22⋊C4—261no—
291C22⋊C4—261no—
292C22⋊C4—261no—
293C42—131no—
294C42—261no—
295C13#330711yescharacteristic, complemented, Sylow
296C23—21no—
297C23—21no—
298C23—131no—
299C23D4×D1311yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—261no—
303Q8—261no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—42no—
308D4—42no—
309D4—521no—
310D4—522no—
311D4—1041no—
312D4#612912yes—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—42no—
318C2×C4—131no—
319C2×C4—131no—
320C2×C4—131no—
321C2×C4—261no—
322C2×C4—261no—
323C2×C4—261no—
324C2×C4—261no—
325C2×C4—261no—
326C2×C4—261no—
327C2×C4—522no—
328C2×C4—522no—
329C2×C4—1041no—
330C2×C4—1041no—
331C2×C4D4×D1311yescharacteristic
332C2×C4C23×D1311yescharacteristic
333C8—21no—
334C8—21no—
335C8—261no—
336C8—261no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—261no—
347C22—261no—
348C22—261no—
349C22C2×D4×D1311yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—261no—
354C4—261no—
355C4—261no—
356C4—521no—
357C4—521no—
358C4—521no—
359C4—521no—
360C4C2×#612911yescharacteristic
361C4#8825111yescharacteristic
362C2—41no—
363C2—42no—
364C2—81no—
365C2—521no—
366C2#1171929611yescharacteristic
367C2#1171947511yescharacteristic
368C2#1171947811yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#449C2
socleC22×C13C22×D4
hypercenter#449D13
hypocenterC13#3307
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #11719529C2semidirect
2. #11719323C2semidirect
3. C13×#449C2semidirect
4. #11718893C2semidirect
5. #11718832C2semidirect
6. #11718823C2semidirect
7. #11718819C2semidirect
8. #11718813C2semidirect
9. #11718703C2semidirect
10. #11718476C2semidirect
11. #11718458C2semidirect
12. #11718433C2semidirect
13. #11718424C2semidirect
14. #11718389C2semidirect
15. #11718382C2semidirect
163. #449D13semidirect
295. C13#3307semidirect

Maximal subgroups

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

subgroupindex
#117195292
#117193232
C13×#4492
#117188932
#117188322
#117188232
#117188192
#117188132
#117187032
#117184762
#117184582
#117184332
#117184242
#117183892
#117183822
#330713