Finite Group Databasebeta

← #13126095

Subgroups — #13126095

Order 1664.

332 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719324C211yesmaximal, characteristic
2#11719224C211yesmaximal, characteristic, complemented
3C13×#482C211yesmaximal, characteristic, complemented
4#11718695C211yesmaximal, characteristic, complemented
5#11718664C211yesmaximal, characteristic, complemented
6#11718552C211yesmaximal, characteristic, complemented
7#11718539C211yesmaximal, characteristic, complemented
8#11718531C211yesmaximal, characteristic, complemented
9#11718517C211yesmaximal, characteristic, complemented
10#11718427C211yesmaximal, characteristic, complemented
11#11718425C211yesmaximal, characteristic, complemented
12#11718421C211yesmaximal, characteristic, complemented
13#11718420C211yesmaximal, characteristic, complemented
14#11718397C211yesmaximal, characteristic, complemented
15#11718381C211yesmaximal, characteristic, complemented
16C13×#121C2211yescharacteristic
17C13×#117C2211yescharacteristic
18#88194C2211yescharacteristic
19#88193—21no—
20#88192—21no—
21D4×Dic13C2211yescharacteristic
22#88184C2211yescharacteristic
23#88180C2211yescharacteristic
24C2×C4⋊Dic13C2211yescharacteristic
25#88147C2211yescharacteristic
26#88144C2211yescharacteristic
27#88144C2211yescharacteristic
28#88144C2211yescharacteristic
29#88142C2211yescharacteristic
30#88142C2211yescharacteristic
31#88140—21no—
32#88137—21no—
33#88132—21no—
34#88132—21no—
35#88124—21no—
36#88123—21no—
37C13×#107C2211yescharacteristic
38C13×#106C2211yescharacteristic
39C13×#102C2211yescharacteristic
40C13×#102C2211yescharacteristic
41C13×C22⋊C8C2211yescharacteristic
42#88072C2211yescharacteristic
43#88072C2211yescharacteristic
44C22⋊#1055C2211yescharacteristic
45#88061C2211yescharacteristic
46#88061C2211yescharacteristic
47#88058C2211yescharacteristic
48#88058C2211yescharacteristic
49#88055C2211yescharacteristic
50#88054C2211yescharacteristic
51#88054C2211yescharacteristic
52C8×Dic13C2211yescharacteristic
53#88049C2211yescharacteristic
54#88049C2211yescharacteristic
55#88048C2211yescharacteristic
56#88048C2211yescharacteristic
57#88048C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×D4×C13—21no—
60C2×D4×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C2×C22⋊D13—21no—
63C2×C22⋊D13—21no—
64C2×C22⋊D13—21no—
65C22×Dic13—21no—
66C22×Dic13—21no—
67C2×D52C2311yescharacteristic
68C2×C4×D13—21no—
69C2×Dic26—21no—
70C2×Dic26—21no—
71C2×C8×C13C2311yescharacteristic
72C2×C8×C13C2311yescharacteristic
73C13×C4⋊C4C2311yescharacteristic
74C13×C4⋊C4C2311yescharacteristic
75C13×C4⋊C4C2311yescharacteristic
76C13×C22⋊C4—21no—
77C13×C22⋊C4—21no—
78C42×C13—21no—
79C22⋊Dic13—21no—
80C22⋊Dic13D411yescharacteristic
81C22⋊Dic13D411yescharacteristic
82#6103—21no—
83#6103—21no—
84C4⋊Dic13—21no—
85C4⋊Dic13—21no—
86C4⋊Dic13—21no—
87C4⋊Dic13—21no—
88C4⋊Dic13D411yescharacteristic
89C4⋊Dic13D411yescharacteristic
90C4⋊Dic13C2311yescharacteristic
91C4⋊Dic13C2311yescharacteristic
92C4⋊Dic13C2311yescharacteristic
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101—21no—
98C4×Dic13C2311yescharacteristic
99C4×Dic13C2311yescharacteristic
100C2×#1055C2311yescharacteristic
101C2×#1055C2311yescharacteristic
102#3241—131nomaximal, Sylow
103C23×C13—21no—
104C23×C13C2×D411yescharacteristic
105C22×D13—21no—
106D4×C13—21no—
107D4×C13—21no—
108D4×C13—81no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13C2×D411yescharacteristic
115C2×C4×C13C2411yescharacteristic
116C22⋊D13—81no—
117C22⋊D13—81no—
118C22⋊D13—81no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—81no—
123C2×Dic13—81no—
124C2×Dic13C2×D411yescharacteristic
125C2×Dic13C2×D411yescharacteristic
126C2×Dic13C2×D411yescharacteristic
127C2×Dic13C2×D411yescharacteristic
128D52—21no—
129D52—21no—
130C4×D13—81no—
131Dic26—81no—
132Dic26—81no—
133C8×C13—21no—
134C8×C13—21no—
135#1055—21no—
136#1055—21no—
137#544—131no—
138#540—131no—
139#501—131no—
140#499—131no—
141#490—131no—
142#486—131no—
143#482—131no—
144#482D1311yescharacteristic, complemented
145#481—131no—
146#480—131no—
147#478—131no—
148#478—131no—
149#476—131no—
150#474—131no—
151#433—131no—
152C22×C13—21no—
153C22×C13—21no—
154C22×C13—21no—
155C22×C13—41no—
156C22×C13—41no—
157C22×C13—41no—
158C22×C13C22×D411yescharacteristic
159C2×D13—41no—
160C2×D13—41no—
161C2×D13—41no—
162C4×C13—21no—
163C4×C13—41no—
164C4×C13—41no—
165C4×C13—41no—
166C4×C132−1+411yescharacteristic
167C4×C132−1+411yescharacteristic
168Dic13—21no—
169Dic13—21no—
170Dic13—21no—
171Dic13—21no—
172Dic13—41no—
173Dic13—41no—
174Dic13—41no—
175C4⋊Q8—131no—
176C4⋊Q8—131no—
177C4⋊Q8—261no—
178#127—131no—
179#125—131no—
180#125—131no—
181#125—131no—
182#125—261no—
183#123—261no—
184#123—261no—
185C22⋊Q8—261no—
186C22⋊Q8—261no—
187#121—131no—
188#121—261no—
189#121—261no—
190#121C2×D1311yescharacteristic
191C4×D4—131no—
192C4×D4—131no—
193#117—131no—
194#117C2×D1311yescharacteristic
195C2×C4⋊C4—131no—
196#107—131no—
197#107—131no—
198#107—131no—
199#107C2×D1311yescharacteristic
200#106—131no—
201#106—131no—
202#106—131no—
203#106C2×D1311yescharacteristic
204C4⋊C8—131no—
205C4⋊C8—131no—
206#102—131no—
207#102—131no—
208#102—131no—
209#102—131no—
210#102—131no—
211#102—131no—
212#102C2×D1311yescharacteristic
213#102C2×D1311yescharacteristic
214C22⋊C8—131no—
215C22⋊C8C2×D1311yescharacteristic
216#97—131no—
217C4×C8—131no—
218C2×C13—41no—
219C2×C13—81no—
220C2×C13#53611yescharacteristic
221C2×C13#57611yescharacteristic
222C2×C13#57711yescharacteristic
223D13—81no—
224C2×Q8—261no—
225C2×Q8—261no—
226C2×D4—21no—
227C2×D4—131no—
228C2×D4—261no—
229C2×D4—261no—
230C2×D4—261no—
231C2×D4C22×D1311yescharacteristic
232C22×C4—261no—
233C22×C4—261no—
234C22×C4—261no—
235C22×C4C22×D1311yescharacteristic
236C2×C8—131no—
237C2×C8—131no—
238C2×C8C22×D1311yescharacteristic
239C2×C8C22×D1311yescharacteristic
240C4⋊C4—131no—
241C4⋊C4—131no—
242C4⋊C4—131no—
243C4⋊C4—131no—
244C4⋊C4—131no—
245C4⋊C4—261no—
246C4⋊C4—261no—
247C4⋊C4—261no—
248C4⋊C4—261no—
249C4⋊C4—261no—
250C4⋊C4—261no—
251C4⋊C4—261no—
252C4⋊C4—261no—
253C4⋊C4—261no—
254C4⋊C4C22×D1311yescharacteristic
255C4⋊C4C22×D1311yescharacteristic
256C4⋊C4C22×D1311yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—131no—
260C22⋊C4—131no—
261C22⋊C4—261no—
262C22⋊C4—261no—
263C22⋊C4—261no—
264C42—21no—
265C42—131no—
266C42—131no—
267C13#324111yescharacteristic, complemented, Sylow
268C23—21no—
269C23—261no—
270C23D4×D1311yescharacteristic
271Q8—1041no—
272Q8—1041no—
273D4—21no—
274D4—21no—
275D4—81no—
276D4—261no—
277D4—261no—
278D4—1041no—
279D4—1041no—
280D4—1041no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—131no—
287C2×C4—131no—
288C2×C4—131no—
289C2×C4—131no—
290C2×C4—261no—
291C2×C4—261no—
292C2×C4—261no—
293C2×C4—1041no—
294C2×C4—1041no—
295C2×C4—1041no—
296C2×C4D4×D1311yescharacteristic
297C2×C4C23×D1311yescharacteristic
298C8—21no—
299C8—21no—
300C8—261no—
301C8—261no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—521no—
309C22—521no—
310C22—521no—
311C22C2×D4×D1311yescharacteristic
312C4—21no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—261no—
317C4—261no—
318C4—261no—
319C4—261no—
320C4—521no—
321C4—521no—
322C4—521no—
323C4#8825711yescharacteristic
324C4#8825711yescharacteristic
325C2—41no—
326C2—81no—
327C2—1041no—
328C2#1171935311yescharacteristic
329C2#1171947411yescharacteristic
330C2#1171948011yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#482C2
socleC22×C13C22×D4
prime radical#11719324C2
hypercenter#482D13
hypocenterC13#3241
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #11719224C2semidirect
3. C13×#482C2semidirect
4. #11718695C2semidirect
5. #11718664C2semidirect
6. #11718552C2semidirect
7. #11718539C2semidirect
8. #11718531C2semidirect
9. #11718517C2semidirect
10. #11718427C2semidirect
11. #11718425C2semidirect
12. #11718421C2semidirect
13. #11718420C2semidirect
14. #11718397C2semidirect
15. #11718381C2semidirect
144. #482D13semidirect
267. C13#3241semidirect

Maximal subgroups

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

subgroupindex
#117193242
#117192242
C13×#4822
#117186952
#117186642
#117185522
#117185392
#117185312
#117185172
#117184272
#117184252
#117184212
#117184202
#117183972
#117183812
#324113