Finite Group Databasebeta

← #13126757

Subgroups — #13126757

Order 1664.

398 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#11719321C211yesmaximal, characteristic, complemented
3C13×#449C211yesmaximal, characteristic, complemented
4#11718894C211yesmaximal, characteristic, complemented
5#11718832C211yesmaximal, characteristic, complemented
6#11718823C211yesmaximal, characteristic, complemented
7#11718819C211yesmaximal, characteristic, complemented
8D8×Dic13C211yesmaximal, characteristic, complemented
9#11718702C211yesmaximal, characteristic, complemented
10#11718475C211yesmaximal, characteristic, complemented
11#11718453C211yesmaximal, characteristic, complemented
12#11718433C211yesmaximal, characteristic, complemented
13#11718422C211yesmaximal, characteristic, complemented
14#11718386C211yesmaximal, characteristic, complemented
15#11718384C211yesmaximal, 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#88190—21no—
27#88189—21no—
28D4×Dic13C2211yescharacteristic
29D4×Dic13C2211yescharacteristic
30C2×#6105C2211yescharacteristic
31#88183—21no—
32C4×C22⋊D13C2211yescharacteristic
33#88180C2211yescharacteristic
34#88178C2211yescharacteristic
35C2×#6101—21no—
36C22×#1055C2211yescharacteristic
37C2×C8×D13C2211yescharacteristic
38#88146C2211yescharacteristic
39#88142C2211yescharacteristic
40#88139—21no—
41#88131—21no—
42C13×#103C2211yescharacteristic
43C13×#102C2211yescharacteristic
44C13×C22⋊C8C2211yescharacteristic
45#88075C2211yescharacteristic
46#88075C2211yescharacteristic
47#88072C2211yescharacteristic
48#88072C2211yescharacteristic
49#88072C2211yescharacteristic
50#88060C2211yescharacteristic
51#88058C2211yescharacteristic
52#88057C2211yescharacteristic
53#88056C2211yescharacteristic
54#88056C2211yescharacteristic
55#88054C2211yescharacteristic
56C8×Dic13C2211yescharacteristic
57#88050C2211yescharacteristic
58#88048C2211yescharacteristic
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—
74#6129—22no—
75#6129—41no—
76C2×C4×D13C2311yescharacteristic
77C2×Dic26—21no—
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⋊Dic13—21no—
90C22⋊Dic13D411yescharacteristic
91#6105—41no—
92#6103—21no—
93#6103—21no—
94#6103D411yescharacteristic
95C4⋊Dic13C2311yescharacteristic
96C4⋊Dic13C2311yescharacteristic
97C4⋊Dic13C2311yescharacteristic
98#6101—21no—
99#6101—21no—
100#6101—21no—
101#6101—21no—
102#6101—21no—
103#6101D411yescharacteristic
104C4×Dic13—21no—
105C4×Dic13—21no—
106C4×Dic13C2311yescharacteristic
107C2×#1055—41no—
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110C8×D13—41no—
111#3303—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—81no—
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—22no—
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—42no—
141C2×Dic13C2×D411yescharacteristic
142C2×Dic13C2×D411yescharacteristic
143C2×Dic13C2×D411yescharacteristic
144C4×D13—21no—
145C4×D13—21no—
146Dic26—21no—
147Dic26—21no—
148Dic26—81no—
149C8×C13—21no—
150C8×C13—21no—
151#1055—21no—
152#1055—21no—
153#555—131no—
154#547—131no—
155#487—131no—
156#485—131no—
157#485—131no—
158#476—131no—
159#465—131no—
160#465—131no—
161#461—131no—
162#449—131no—
163#449D1311yescharacteristic, complemented
164C4×D8—131no—
165C8×D4—131no—
166#416—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—41no—
189Dic13—41no—
190Dic13—41no—
191Dic13—41no—
192Dic13#13512yes—
193C2×#41—131no—
194C2×#41C2×D1311yescharacteristic
195C2×SD16—131no—
196C2×SD16C2×D1311yescharacteristic
197C2×D8C2×D1311yescharacteristic
198C22×C8—131no—
199C22×C8—131no—
200C4⋊Q8—131no—
201C4⋊Q8—131no—
202#124—261no—
203#124—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—
215#117—131no—
216#117—131no—
217#117—261no—
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
235C4×C8—131no—
236C2×C13—41no—
237C2×C13—42no—
238C2×C13—81no—
239C2×C13#54611yescharacteristic
240C2×C13C2×#13511yescharacteristic
241C2×C13#57711yescharacteristic
242D13—41no—
243#41—22no—
244#41—41no—
245#41—262no—
246#41—521no—
247C2×Q8—131no—
248C2×Q8—261no—
249C2×Q8C22×D1311yescharacteristic
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—131no—
253C2×D4—261no—
254C2×D4—261no—
255C2×D4C22×D1311yescharacteristic
256C2×D4C22×D1311yescharacteristic
257C22×C4—21no—
258C22×C4—131no—
259C22×C4—261no—
260C22×C4—261no—
261C22×C4—261no—
262C22×C4C22×D1311yescharacteristic
263SD16—41no—
264SD16—521no—
265D8—22no—
266C2×C8—131no—
267C2×C8—131no—
268C2×C8—521no—
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⋊C4C22×D1311yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—131no—
284C22⋊C4—131no—
285C22⋊C4—261no—
286C22⋊C4—261no—
287C22⋊C4—261no—
288C22⋊C4—261no—
289C22⋊C4—261no—
290C22⋊C4—261no—
291C22⋊C4—261no—
292C42—131no—
293C42—261no—
294C42—261no—
295C13#330311yescharacteristic, complemented, Sylow
296C23—21no—
297C23—21no—
298C23—131no—
299C23D4×D1311yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—261no—
303Q8—261no—
304Q8—1041no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—81no—
310D4—262no—
311D4—522no—
312D4—1041no—
313D4#612912yes—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—42no—
319C2×C4—131no—
320C2×C4—131no—
321C2×C4—131no—
322C2×C4—261no—
323C2×C4—261no—
324C2×C4—261no—
325C2×C4—261no—
326C2×C4—261no—
327C2×C4—261no—
328C2×C4—522no—
329C2×C4—522no—
330C2×C4—522no—
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—132no—
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
367C2D13×#13511yescharacteristic
368C2#1171948011yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#449C2
socleC22×C13C22×D4
hypercenter#449D13
hypocenterC13#3303
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. #11719321C2semidirect
3. C13×#449C2semidirect
4. #11718894C2semidirect
5. #11718832C2semidirect
6. #11718823C2semidirect
7. #11718819C2semidirect
8. D8×Dic13C2semidirect
9. #11718702C2semidirect
10. #11718475C2semidirect
11. #11718453C2semidirect
12. #11718433C2semidirect
13. #11718422C2semidirect
14. #11718386C2semidirect
15. #11718384C2semidirect
163. #449D13semidirect
295. C13#3303semidirect

Maximal subgroups

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

subgroupindex
#117195292
#117193212
C13×#4492
#117188942
#117188322
#117188232
#117188192
D8×Dic132
#117187022
#117184752
#117184532
#117184332
#117184222
#117183862
#117183842
#330313