Finite Group Databasebeta

← #13127178

Subgroups — #13127178

Order 1664.

420 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719316C211yesmaximal, characteristic, complemented
2#11719212C211yesmaximal, characteristic, complemented
3C13×#480C211yesmaximal, characteristic, complemented
4#11718699C211yesmaximal, characteristic, complemented
5C2×#88047C211yesmaximal, characteristic, complemented
6#11718551C211yesmaximal, characteristic, complemented
7#11718543C211yesmaximal, characteristic, complemented
8D13×#107C211yesmaximal, characteristic, complemented
9#11718535C211yesmaximal, characteristic, complemented
10#11718436C211yesmaximal, characteristic, complemented
11#11718435C211yesmaximal, characteristic, complemented
12#11718420C211yesmaximal, characteristic, complemented
13#11718417C211yesmaximal, characteristic, complemented
14#11718397C211yesmaximal, characteristic, complemented
15#11718386C211yesmaximal, characteristic, complemented
16C2×#6129—21no—
17C2×#6127—21no—
18C13×#121C2211yescharacteristic
19C2×C13×C4⋊C4C2211yescharacteristic
20#88192C2211yescharacteristic
21#88189—21no—
22D4×Dic13C2211yescharacteristic
23C2×#6104C2211yescharacteristic
24#88184C2211yescharacteristic
25#88183—21no—
26C4×C22⋊D13C2211yescharacteristic
27C2×C4⋊Dic13C2211yescharacteristic
28C22×#1055C2211yescharacteristic
29C2×C8×D13C2211yescharacteristic
30#88150—21no—
31#88149C2211yescharacteristic
32#88148—21no—
33#88147C2211yescharacteristic
34C4⋊C4×D13C2211yescharacteristic
35C4⋊C4×D13C2211yescharacteristic
36#88142C2211yescharacteristic
37#88142C2211yescharacteristic
38#88137—21no—
39#88132—21no—
40C13×#107C2211yescharacteristic
41C13×#107C2211yescharacteristic
42C13×#102C2211yescharacteristic
43C13×#102C2211yescharacteristic
44C13×C22⋊C8C2211yescharacteristic
45#88072C2211yescharacteristic
46#88061C2211yescharacteristic
47#88061C2211yescharacteristic
48#88060C2211yescharacteristic
49#88058C2211yescharacteristic
50#88058C2211yescharacteristic
51#88054C2211yescharacteristic
52C8×Dic13C2211yescharacteristic
53#88049C2211yescharacteristic
54#88047C2211yescharacteristic
55#88047C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×D4×C13—21no—
60C2×D4×C13C2311yescharacteristic
61C22×C4×C13—21no—
62C22×C4×C13C2311yescharacteristic
63C2×C22⋊D13—21no—
64C2×C22⋊D13—21no—
65C2×C22⋊D13D411yescharacteristic
66C22×Dic13—21no—
67C22×Dic13—21no—
68#6129—44no—
69#6127—44no—
70C2×D52—21no—
71C2×D52C2311yescharacteristic
72C2×C4×D13—21no—
73C2×C4×D13—21no—
74C2×C4×D13—21no—
75C2×C4×D13C2311yescharacteristic
76C2×Dic26—21no—
77C2×Dic26—21no—
78C2×C8×C13C2311yescharacteristic
79C2×C8×C13C2311yescharacteristic
80C13×C4⋊C4—21no—
81C13×C4⋊C4C2311yescharacteristic
82C13×C4⋊C4C2311yescharacteristic
83C13×C4⋊C4C2311yescharacteristic
84C13×C22⋊C4—21no—
85C22⋊Dic13—21no—
86C22⋊Dic13—21no—
87C22⋊Dic13D411yescharacteristic
88#6104—22no—
89#6103—21no—
90#6103—21no—
91#6103—21no—
92#6103D411yescharacteristic
93C4⋊Dic13—21no—
94C4⋊Dic13C2311yescharacteristic
95C4⋊Dic13C2311yescharacteristic
96C4⋊Dic13C2311yescharacteristic
97#6101—21no—
98#6101—21no—
99#6101—21no—
100#6101—21no—
101#6101D411yescharacteristic
102C4×Dic13C2311yescharacteristic
103C2×#1055—22no—
104C2×#1055C2311yescharacteristic
105C2×#1055C2311yescharacteristic
106C8×D13—22no—
107#3334—131nomaximal, Sylow
108C23×C13—21no—
109C23×C13C2×D411yescharacteristic
110C22×D13—21no—
111C22×D13C2×D411yescharacteristic
112D4×C13—21no—
113D4×C13—21no—
114D4×C13—42no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—42no—
121C2×C4×C13C2×D411yescharacteristic
122C2×C4×C13C2411yescharacteristic
123C22⋊D13—42no—
124C22⋊D13—42no—
125C22⋊D13D814yescomplemented
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—42no—
130C2×Dic13—42no—
131C2×Dic13C2×D411yescharacteristic
132C2×Dic13C2×D411yescharacteristic
133C2×Dic13C2×D411yescharacteristic
134D52—21no—
135D52—21no—
136D52—42no—
137C4×D13—21no—
138C4×D13—21no—
139C4×D13—42no—
140C4×D13—42no—
141C4×D13—42no—
142Dic26—42no—
143Dic26—42no—
144C8×C13—21no—
145C8×C13—21no—
146#1055—21no—
147#1055#4112yescomplemented
148#547—131no—
149#547—131no—
150#500—131no—
151#480—131no—
152#480—131no—
153#480—131no—
154#480D1311yescharacteristic, complemented
155#474—131no—
156#474—131no—
157#466—131no—
158#466—131no—
159C4×D8—131no—
160C8×D4—131no—
161C2×#107—131no—
162C2×#107—131no—
163C22×C13—21no—
164C22×C13—21no—
165C22×C13—41no—
166C22×C13—41no—
167C22×C13—41no—
168C22×C13C2×D812yes—
169C22×C13C22×D411yescharacteristic
170C2×D13—21no—
171C2×D13—21no—
172C2×D13—41no—
173C2×D13—41no—
174C2×D13—41no—
175C2×D13C2×D812yes—
176C4×C13—21no—
177C4×C13—41no—
178C4×C13—41no—
179C4×C13—41no—
180C4×C13C2×#4111yescharacteristic
181C4×C132−1+411yescharacteristic
182Dic13—21no—
183Dic13—21no—
184Dic13—41no—
185Dic13—41no—
186Dic13—41no—
187Dic13C2×D812yes—
188C2×#41—261no—
189C2×#41—261no—
190C2×D8—131no—
191C22×C8—131no—
192C22×C8—131no—
193C4⋊Q8—131no—
194C4⋊Q8—131no—
195#123—261no—
196#123—261no—
197#123—261no—
198#123—261no—
199C22⋊Q8—261no—
200C22⋊Q8—261no—
201#121—131no—
202#121—131no—
203#121—131no—
204#121C2×D1311yescharacteristic
205C4×D4—131no—
206C4×D4—131no—
207C4×D4—131no—
208C2×C4⋊C4—131no—
209C2×C4⋊C4—131no—
210C2×C4⋊C4—131no—
211C2×C4⋊C4C2×D1311yescharacteristic
212#107—131no—
213#107—131no—
214#107—131no—
215#107—131no—
216#107—131no—
217#107—131no—
218#107—131no—
219#107C2×D1311yescharacteristic
220#107C2×D1311yescharacteristic
221C4⋊C8—131no—
222#102—131no—
223#102—131no—
224#102—131no—
225#102—131no—
226#102C2×D1311yescharacteristic
227#102C2×D1311yescharacteristic
228C22⋊C8—131no—
229C22⋊C8C2×D1311yescharacteristic
230C4×C8—131no—
231C2×C13—22no—
232C2×C13—81no—
233C2×C13#54711yescharacteristic
234C2×C13C22×D811yescharacteristic
235C2×C13#57811yescharacteristic
236D13—22no—
237D13—81no—
238#41—524no—
239#41—524no—
240C2×Q8—261no—
241C2×Q8—261no—
242C2×D4—21no—
243C2×D4—131no—
244C2×D4—131no—
245C2×D4—261no—
246C2×D4—261no—
247C2×D4—261no—
248C2×D4C22×D1311yescharacteristic
249C22×C4—21no—
250C22×C4—131no—
251C22×C4—261no—
252C22×C4—261no—
253C22×C4—261no—
254C22×C4—261no—
255C22×C4—261no—
256C22×C4C22×D1311yescharacteristic
257D8—262no—
258C2×C8—131no—
259C2×C8—131no—
260C2×C8—262no—
261C2×C8—262no—
262C2×C8C22×D1311yescharacteristic
263C2×C8C22×D1311yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—131no—
266C4⋊C4—131no—
267C4⋊C4—131no—
268C4⋊C4—131no—
269C4⋊C4—261no—
270C4⋊C4—261no—
271C4⋊C4—261no—
272C4⋊C4—261no—
273C4⋊C4—261no—
274C4⋊C4C22×D1311yescharacteristic
275C4⋊C4C22×D1311yescharacteristic
276C4⋊C4C22×D1311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—131no—
279C22⋊C4—131no—
280C22⋊C4—261no—
281C22⋊C4—261no—
282C22⋊C4—261no—
283C22⋊C4—261no—
284C22⋊C4—261no—
285C42—131no—
286C13#333411yescharacteristic, complemented, Sylow
287C23—21no—
288C23—131no—
289C23—261no—
290C23D4×D1311yescharacteristic
291Q8—522no—
292Q8—522no—
293D4—21no—
294D4—21no—
295D4—42no—
296D4—134no—
297D4—261no—
298D4—261no—
299D4—522no—
300D4—522no—
301D4—522no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—131no—
309C2×C4—131no—
310C2×C4—131no—
311C2×C4—261no—
312C2×C4—261no—
313C2×C4—261no—
314C2×C4—261no—
315C2×C4—261no—
316C2×C4—522no—
317C2×C4—522no—
318C2×C4—522no—
319C2×C4—522no—
320C2×C4—522no—
321C2×C4D4×D1311yescharacteristic
322C2×C4C23×D1311yescharacteristic
323C8—21no—
324C8—21no—
325C8—132no—
326C8—261no—
327C22—21no—
328C22—21no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—132no—
333C22—261no—
334C22—261no—
335C22—521no—
336C22—521no—
337C22—521no—
338C22D8×D1312yes—
339C22C2×D4×D1311yescharacteristic
340C4—21no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—132no—
345C4—261no—
346C4—261no—
347C4—521no—
348C4—521no—
349C4—521no—
350C4#41×D1311yescharacteristic
351C4#8825711yescharacteristic
352C2—22no—
353C2—81no—
354C2—262no—
355C2—1041no—
356C2#1171936011yescharacteristic
357C2C2×D8×D1311yescharacteristic
358C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#480C2
socleC22×C13C22×D4
hypercenter#480D13
hypocenterC13#3334
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #11719316C2semidirect
2. #11719212C2semidirect
3. C13×#480C2semidirect
4. #11718699C2semidirect
5. C2×#88047C2semidirect
6. #11718551C2semidirect
7. #11718543C2semidirect
8. D13×#107C2semidirect
9. #11718535C2semidirect
10. #11718436C2semidirect
11. #11718435C2semidirect
12. #11718420C2semidirect
13. #11718417C2semidirect
14. #11718397C2semidirect
15. #11718386C2semidirect
125. C22⋊D13D8semidirect
147. #1055#41semidirect
154. #480D13semidirect
286. C13#3334semidirect

Maximal subgroups

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

subgroupindex
#117193162
#117192122
C13×#4802
#117186992
C2×#880472
#117185512
#117185432
D13×#1072
#117185352
#117184362
#117184352
#117184202
#117184172
#117183972
#117183862
#333413