Finite Group Databasebeta

← #13119554

Subgroups — #13119554

Order 1664.

428 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C13×C22⋊C4C211yesmaximal, characteristic
2#11718873C211yesmaximal, characteristic
3#11718871C211yesmaximal, characteristic
4#11718612C211yesmaximal, characteristic
5#11718612C211yesmaximal, characteristic
6#11718610C211yesmaximal, characteristic
7#11718609C211yesmaximal, characteristic
8C4×C4⋊Dic13C211yesmaximal, characteristic, complemented
9#11718594C211yesmaximal, characteristic, complemented
10#11718594C211yesmaximal, characteristic, complemented
11#11718589C211yesmaximal, characteristic, complemented
12#11718322C211yesmaximal, characteristic, complemented
13#11718322C211yesmaximal, characteristic, complemented
14#11718315C211yesmaximal, characteristic, complemented
15#11718308C211yesmaximal, characteristic, complemented
16C23×C4×C13C2211yescharacteristic
17C2×C13×C22⋊C4C2211yescharacteristic
18C2×C13×C22⋊C4C2211yescharacteristic
19C2×C42×C13C2211yescharacteristic
20C2×C42×C13C2211yescharacteristic
21C2×C22⋊Dic13C2211yescharacteristic
22C2×C22⋊Dic13C2211yescharacteristic
23C2×C22⋊Dic13C2211yescharacteristic
24C2×C22⋊Dic13C2211yescharacteristic
25C2×C4⋊Dic13C2211yescharacteristic
26C2×C4⋊Dic13C2211yescharacteristic
27C2×C4⋊Dic13C2211yescharacteristic
28C2×C4⋊Dic13C2211yescharacteristic
29C2×C4⋊Dic13C2211yescharacteristic
30C2×C4⋊Dic13C2211yescharacteristic
31C2×#6101C2211yescharacteristic
32C2×#6101C2211yescharacteristic
33C2×#6101C2211yescharacteristic
34C2×#6101C2211yescharacteristic
35C2×#6101C2211yescharacteristic
36C2×#6101C2211yescharacteristic
37C2×C4×Dic13C2211yescharacteristic
38C2×C4×Dic13C2211yescharacteristic
39C13×#95C2211yescharacteristic
40C13×#95C2211yescharacteristic
41#88071C2211yescharacteristic
42#88071C2211yescharacteristic
43#88071C2211yescharacteristic
44#88071C2211yescharacteristic
45#88071C2211yescharacteristic
46#88071C2211yescharacteristic
47#88071C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51C24×C13C2311yescharacteristic
52C22×C4×C13—22no—
53C22×C4×C13—22no—
54C22×C4×C13—41no—
55C22×C4×C13C2311yescharacteristic
56C22×C4×C13C2311yescharacteristic
57C22×C4×C13C2311yescharacteristic
58C22×C4×C13C2311yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×Dic13C2311yescharacteristic
62C22×Dic13C2311yescharacteristic
63C22×Dic13C2311yescharacteristic
64C22×Dic13C2311yescharacteristic
65C22×Dic13C2311yescharacteristic
66C22×Dic13C2311yescharacteristic
67C22×Dic13C2311yescharacteristic
68C22×Dic13C2311yescharacteristic
69C13×C22⋊C4—22no—
70C13×C22⋊C4Q814yes—
71C42×C13—22no—
72C42×C13—41no—
73C22⋊Dic13—22no—
74C22⋊Dic13—41no—
75C22⋊Dic13—41no—
76C22⋊Dic13—41no—
77C4⋊Dic13—22no—
78C4⋊Dic13—22no—
79C4⋊Dic13—22no—
80C4⋊Dic13—22no—
81C4⋊Dic13—41no—
82C4⋊Dic13—41no—
83#6101—22no—
84#6101—22no—
85#6101—22no—
86#6101—41no—
87#6101—41no—
88#6101—41no—
89C4×Dic13—41no—
90C4×Dic13—41no—
91#2522—131nomaximal, Sylow
92C23×C13—21no—
93C23×C13—21no—
94C23×C13—21no—
95C23×C13—21no—
96C23×C13—21no—
97C23×C13—21no—
98C23×C13C2×Q812yes—
99C23×C13C2411yescharacteristic
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—44no—
114C2×C4×C13C2×Q812yes—
115C2×C4×C13C2×Q812yes—
116C2×C4×C13#4112yes—
117C2×C4×C13#4112yes—
118C2×C4×C13#4112yes—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13#4112yes—
143#399—131no—
144#398—131no—
145#398—131no—
146#396—131no—
147#389—131no—
148#389—131no—
149#388—131no—
150#388—131no—
151#387—131no—
152#387—131no—
153#387—131no—
154#385—131no—
155#380—131no—
156C4×C4⋊C4—131no—
157C4×C22⋊C4D1311yescharacteristic
158C22×C13—22no—
159C22×C13—22no—
160C22×C13—22no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13—41no—
165C22×C13C22×Q811yescharacteristic
166C22×C13C2×#4111yescharacteristic
167C22×C13C2×#4111yescharacteristic
168C22×C13C2×#4111yescharacteristic
169C22×C13C2×#4111yescharacteristic
170C22×C13H(5,𝔽2)11yescharacteristic
171C22×C13H(5,𝔽2)11yescharacteristic
172C4×C13—22no—
173C4×C13—22no—
174C4×C13—22no—
175C4×C13—22no—
176C4×C13—22no—
177C4×C13—41no—
178Dic13—22no—
179Dic13—41no—
180Dic13—41no—
181Dic13—41no—
182Dic13—41no—
183Dic13—41no—
184Dic13—41no—
185Dic13—41no—
186C23×C4C2×D1311yescharacteristic
187C2×C4⋊C4—131no—
188C2×C4⋊C4—131no—
189C2×C4⋊C4—131no—
190C2×C4⋊C4—131no—
191C2×C4⋊C4—131no—
192C2×C4⋊C4—131no—
193C2×C4⋊C4—131no—
194C2×C4⋊C4—131no—
195C2×C4⋊C4—131no—
196C2×C4⋊C4—131no—
197C2×C4⋊C4—131no—
198C2×C4⋊C4—131no—
199C2×C22⋊C4—131no—
200C2×C22⋊C4—131no—
201C2×C22⋊C4—131no—
202C2×C22⋊C4—131no—
203C2×C22⋊C4C2×D1311yescharacteristic
204C2×C22⋊C4C2×D1311yescharacteristic
205C2×C42—131no—
206C2×C42—131no—
207C2×C42C2×D1311yescharacteristic
208C2×C42C2×D1311yescharacteristic
209#95—131no—
210#95—131no—
211#95—131no—
212#95—131no—
213#95—131no—
214#95—131no—
215#95—131no—
216#95—131no—
217#95—131no—
218#95—131no—
219#95C2×D1311yescharacteristic
220#95C2×D1311yescharacteristic
221C2×C13—42no—
222C2×C13#52911yescharacteristic
223C2×C13#53311yescharacteristic
224C2×C13#54011yescharacteristic
225C2×C13#55111yescharacteristic
226C2×C13#55311yescharacteristic
227C2×C13#55411yescharacteristic
228C2×C13#55411yescharacteristic
229C24C22×D1311yescharacteristic
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—41no—
233C22×C4—131no—
234C22×C4—131no—
235C22×C4—131no—
236C22×C4—131no—
237C22×C4—131no—
238C22×C4—131no—
239C22×C4—131no—
240C22×C4—131no—
241C22×C4C22×D1311yescharacteristic
242C22×C4C22×D1311yescharacteristic
243C22×C4C22×D1311yescharacteristic
244C22×C4C22×D1311yescharacteristic
245C22×C4C22×D1311yescharacteristic
246C22×C4C22×D1311yescharacteristic
247C4⋊C4—262no—
248C4⋊C4—262no—
249C4⋊C4—262no—
250C4⋊C4—262no—
251C4⋊C4—262no—
252C4⋊C4—262no—
253C4⋊C4—262no—
254C4⋊C4—521no—
255C4⋊C4—521no—
256C4⋊C4—521no—
257C4⋊C4—521no—
258C4⋊C4—521no—
259C22⋊C4—22no—
260C22⋊C4—262no—
261C22⋊C4—521no—
262C22⋊C4—521no—
263C22⋊C4—521no—
264C22⋊C4Dic2614yes—
265C42—22no—
266C42—41no—
267C42—521no—
268C42—521no—
269C13#252211yescharacteristic, complemented, Sylow
270C23—21no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23C2×Dic2612yes—
277C23C23×D1311yescharacteristic
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—44no—
292C2×C4—132no—
293C2×C4—261no—
294C2×C4—261no—
295C2×C4—261no—
296C2×C4—261no—
297C2×C4—261no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4—261no—
305C2×C4—261no—
306C2×C4—261no—
307C2×C4—261no—
308C2×C4—261no—
309C2×C4—261no—
310C2×C4—261no—
311C2×C4—261no—
312C2×C4—261no—
313C2×C4—261no—
314C2×C4—261no—
315C2×C4—261no—
316C2×C4C2×Dic2612yes—
317C2×C4C2×Dic2612yes—
318C2×C4#612712yes—
319C2×C4#612712yes—
320C2×C4#612912yes—
321C22—22no—
322C22—22no—
323C22—22no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22C22×Dic2611yescharacteristic
329C22C2×#612711yescharacteristic
330C22C2×#612711yescharacteristic
331C22C2×#612911yescharacteristic
332C22#8825111yescharacteristic
333C22#41×D1311yescharacteristic
334C22#8825611yescharacteristic
335C4—22no—
336C4—22no—
337C4—22no—
338C4—22no—
339C4—22no—
340C4—41no—
341C4—262no—
342C4—521no—
343C4—521no—
344C4—521no—
345C4—521no—
346C4—521no—
347C4—521no—
348C4—521no—
349C2—42no—
350C2#1171917511yescharacteristic
351C2#1171920011yescharacteristic
352C2#1171923511yescharacteristic
353C2#1171924311yescharacteristic
354C2#1171924411yescharacteristic
355C2#1171924811yescharacteristic
356C2#1171926711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC4×C13×C22⋊C4C2
prime radicalC24×C13C23
hypercenterC4×C22⋊C4D13
hypocenterC13#2522
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
8. C4×C4⋊Dic13C2semidirect
9. #11718594C2semidirect
10. #11718594C2semidirect
11. #11718589C2semidirect
12. #11718322C2semidirect
13. #11718322C2semidirect
14. #11718315C2semidirect
15. #11718308C2semidirect
269. C13#2522semidirect

Maximal subgroups

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

subgroupindex
C4×C13×C22⋊C42
#117188732
#117188712
#117186122
#117186102
#117186092
C4×C4⋊Dic132
#117185942
#117185892
#117183222
#117183152
#117183082
#252213