Finite Group Databasebeta

← #13126255

Subgroups — #13126255

Order 1664.

334 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719330C211yesmaximal, characteristic, complemented
2#11719308C211yesmaximal, characteristic
3C13×#465C211yesmaximal, characteristic
4#11718827C211yesmaximal, characteristic, complemented
5#11718823C211yesmaximal, characteristic, complemented
6#11718777C211yesmaximal, characteristic, complemented
7#11718763C211yesmaximal, characteristic, complemented
8#11718713C211yesmaximal, characteristic, complemented
9#11718703C211yesmaximal, characteristic
10#11718518C211yesmaximal, characteristic, complemented
11#11718515C211yesmaximal, characteristic, complemented
12#11718455C211yesmaximal, characteristic, complemented
13#11718454C211yesmaximal, characteristic, complemented
14#11718428C211yesmaximal, characteristic, complemented
15#11718427C211yesmaximal, characteristic, complemented
16C2×C13×SD16C2211yescharacteristic
17C22×C8×C13C2211yescharacteristic
18C13×C22⋊Q8C2211yescharacteristic
19C13×#121C2211yescharacteristic
20Q8×Dic13C2211yescharacteristic
21#88198C2211yescharacteristic
22C2×#6107C2211yescharacteristic
23#88190—21no—
24#88190C2211yescharacteristic
25#88189—21no—
26D4×Dic13C2211yescharacteristic
27C2×#6105C2211yescharacteristic
28#88180C2211yescharacteristic
29#88178C2211yescharacteristic
30#88178C2211yescharacteristic
31C2×#6099C2211yescharacteristic
32C2×Dic52C2211yescharacteristic
33#88144—21no—
34#88144C2211yescharacteristic
35#88143—21no—
36#88142C2211yescharacteristic
37#88141C2211yescharacteristic
38#88141C2211yescharacteristic
39#88133—21no—
40#88133—21no—
41#88133—21no—
42#88132—21no—
43C13×#106C2211yescharacteristic
44C13×#103C2211yescharacteristic
45C13×#102C2211yescharacteristic
46#88075C2211yescharacteristic
47#88072C2211yescharacteristic
48#88058C2211yescharacteristic
49#88056C2211yescharacteristic
50#88056C2211yescharacteristic
51#88054C2211yescharacteristic
52#88054C2211yescharacteristic
53#88054C2211yescharacteristic
54#88054C2211yescharacteristic
55#88050C2211yescharacteristic
56#88050C2211yescharacteristic
57#88048C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×D4×C13—21no—
61C2×D4×C13C2311yescharacteristic
62C22×C4×C13C2311yescharacteristic
63C22×Dic13—21no—
64C2×Dic26—21no—
65C2×Dic26C2311yescharacteristic
66C2×Dic26C2311yescharacteristic
67C13×SD16—41no—
68C2×C8×C13—41no—
69C2×C8×C13C2311yescharacteristic
70C2×C8×C13C2311yescharacteristic
71C13×C4⋊C4—21no—
72C13×C4⋊C4C2311yescharacteristic
73C13×C4⋊C4C2311yescharacteristic
74C13×C22⋊C4—21no—
75C13×C22⋊C4—21no—
76C22⋊Dic13—21no—
77C22⋊Dic13—21no—
78C22⋊Dic13—21no—
79C22⋊Dic13—21no—
80C22⋊Dic13—21no—
81C22⋊Dic13D411yescharacteristic
82C22⋊Dic13D411yescharacteristic
83#6107—41no—
84#6105—41no—
85C4⋊Dic13—21no—
86C4⋊Dic13—21no—
87C4⋊Dic13D411yescharacteristic
88C4⋊Dic13D411yescharacteristic
89C4⋊Dic13C2311yescharacteristic
90C4⋊Dic13C2311yescharacteristic
91#6101—21no—
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101—21no—
98#6101—21no—
99C4×Dic13—21no—
100C4×Dic13—21no—
101C4×Dic13—21no—
102C4×Dic13C2311yescharacteristic
103C4×Dic13C2311yescharacteristic
104#6099—41no—
105C2×#1055C2311yescharacteristic
106C2×#1055C2311yescharacteristic
107Dic52—41no—
108#3258—131nomaximal, Sylow
109C23×C13—21no—
110C23×C13C2×D411yescharacteristic
111Q8×C13—21no—
112Q8×C13—21no—
113D4×C13—21no—
114D4×C13—21no—
115D4×C13—81no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13C2×D411yescharacteristic
122C2×C4×C13C2411yescharacteristic
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—81no—
128C2×Dic13C2×D411yescharacteristic
129C2×Dic13C2×D411yescharacteristic
130C2×Dic13C2×D411yescharacteristic
131C2×Dic13C2×D411yescharacteristic
132Dic26—21no—
133Dic26—21no—
134Dic26—21no—
135Dic26—21no—
136Dic26—81no—
137C8×C13—21no—
138C8×C13—21no—
139#1055—21no—
140#1055—21no—
141#542—131no—
142#541—131no—
143#479—131no—
144#478—131no—
145#477—131no—
146#475—131no—
147#470—131no—
148#468—131no—
149#467—131no—
150#465D1311yescharacteristic
151#464—131no—
152#464—131no—
153#462—131no—
154#461—131no—
155#424—131no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13C22×D411yescharacteristic
163C4×C13—21no—
164C4×C13—41no—
165C4×C13—41no—
166C4×C13—41no—
167C4×C13H(5,𝔽2)11yescharacteristic
168C4×C132−1+411yescharacteristic
169Dic13—21no—
170Dic13—21no—
171Dic13—21no—
172Dic13—21no—
173Dic13—41no—
174Dic13—41no—
175Dic13—41no—
176Dic13—41no—
177C2×Q16—131no—
178C2×Q16—131no—
179C2×SD16—131no—
180C2×SD16C2×D1311yescharacteristic
181C2×M16—131no—
182C22×C8C2×D1311yescharacteristic
183C4⋊Q8—131no—
184C4⋊Q8—131no—
185#126—261no—
186#126—261no—
187#126—261no—
188#125—131no—
189#125—261no—
190#125—261no—
191#124—131no—
192#124—261no—
193#123—261no—
194C22⋊Q8—131no—
195C22⋊Q8—131no—
196C22⋊Q8—261no—
197C22⋊Q8C2×D1311yescharacteristic
198#121C2×D1311yescharacteristic
199C4×Q8—131no—
200C4×Q8—131no—
201C4×Q8—131no—
202C4×D4—131no—
203#117—131no—
204#107—131no—
205#107—131no—
206#106—131no—
207#106C2×D1311yescharacteristic
208C4⋊C8—131no—
209C4⋊C8—131no—
210C4⋊C8—131no—
211C4⋊C8—131no—
212#103—131no—
213#103—131no—
214#103—131no—
215#103—131no—
216#103—131no—
217#103C2×D1311yescharacteristic
218#102—131no—
219#102C2×D1311yescharacteristic
220C2×C13—41no—
221C2×C13—81no—
222C2×C13#53711yescharacteristic
223C2×C13#57711yescharacteristic
224C2×C13#57811yescharacteristic
225C2×Q8—131no—
226C2×Q8—131no—
227C2×Q8—261no—
228C2×Q8C22×D1311yescharacteristic
229C2×D4—21no—
230C2×D4C22×D1311yescharacteristic
231C22×C4—261no—
232C22×C4C22×D1311yescharacteristic
233Q16—521no—
234Q16—521no—
235SD16—41no—
236SD16—521no—
237M16—521no—
238C2×C8—41no—
239C2×C8—131no—
240C2×C8—131no—
241C2×C8C22×D1311yescharacteristic
242C2×C8C22×D1311yescharacteristic
243C4⋊C4—21no—
244C4⋊C4—131no—
245C4⋊C4—131no—
246C4⋊C4—131no—
247C4⋊C4—131no—
248C4⋊C4—261no—
249C4⋊C4—261no—
250C4⋊C4—261no—
251C4⋊C4—261no—
252C4⋊C4—261no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4—261no—
258C4⋊C4C22×D1311yescharacteristic
259C4⋊C4C22×D1311yescharacteristic
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—131no—
263C22⋊C4—131no—
264C22⋊C4—261no—
265C22⋊C4—261no—
266C22⋊C4—261no—
267C22⋊C4—261no—
268C22⋊C4—261no—
269C42—131no—
270C42—131no—
271C42—261no—
272C42—261no—
273C42—261no—
274C13#325811yescharacteristic, complemented, Sylow
275C23—21no—
276C23D4×D1311yescharacteristic
277Q8—21no—
278Q8—21no—
279Q8—261no—
280Q8—261no—
281Q8—261no—
282Q8—261no—
283Q8—1041no—
284D4—21no—
285D4—21no—
286D4—81no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—131no—
293C2×C4—131no—
294C2×C4—131no—
295C2×C4—131no—
296C2×C4—261no—
297C2×C4—261no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—1041no—
301C2×C4D4×D1311yescharacteristic
302C2×C4C23×D1311yescharacteristic
303C8—21no—
304C8—21no—
305C8—261no—
306C8—261no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—41no—
311C22—41no—
312C22—41no—
313C22C2×D4×D1311yescharacteristic
314C4—21no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—261no—
319C4—261no—
320C4—261no—
321C4—261no—
322C4—521no—
323C4—521no—
324C4—521no—
325C4—521no—
326C4#8825111yescharacteristic
327C4#8825711yescharacteristic
328C2—41no—
329C2—81no—
330C2#1171930211yescharacteristic
331C2#1171946711yescharacteristic
332C2#1171947611yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#465C2
socleC22×C13C22×D4
prime radicalC13×#121C22
hypercenter#465D13
hypocenterC13#3258
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #11719330C2semidirect
4. #11718827C2semidirect
5. #11718823C2semidirect
6. #11718777C2semidirect
7. #11718763C2semidirect
8. #11718713C2semidirect
10. #11718518C2semidirect
11. #11718515C2semidirect
12. #11718455C2semidirect
13. #11718454C2semidirect
14. #11718428C2semidirect
15. #11718427C2semidirect
274. C13#3258semidirect

Maximal subgroups

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

subgroupindex
#117193302
#117193082
C13×#4652
#117188272
#117188232
#117187772
#117187632
#117187132
#117187032
#117185182
#117185152
#117184552
#117184542
#117184282
#117184272
#325813