Finite Group Databasebeta

← #13127367

Subgroups — #13127367

Order 1664.

336 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719238C211yesmaximal, characteristic
2#11719218C211yesmaximal, characteristic
3C13×#428C211yesmaximal, characteristic, complemented
4#11718798C211yesmaximal, characteristic, complemented
5#11718788C211yesmaximal, characteristic
6#11718657C211yesmaximal, characteristic, complemented
7#11718631C211yesmaximal, characteristic, complemented
8#11718549C211yesmaximal, characteristic, complemented
9#11718548C211yesmaximal, characteristic, complemented
10#11718537C211yesmaximal, characteristic, complemented
11#11718536C211yesmaximal, characteristic, complemented
12#11718528C211yesmaximal, characteristic, complemented
13#11718521C211yesmaximal, characteristic, complemented
14#11718518C211yesmaximal, characteristic, complemented
15#11718514C211yesmaximal, characteristic, complemented
16C2×C13×M16C2211yescharacteristic
17C13×#117C2211yescharacteristic
18C2×C13×C4⋊C4C2211yescharacteristic
19#88183—21no—
20C4×C22⋊D13C2211yescharacteristic
21#88180—21no—
22#88178C2211yescharacteristic
23#88178C2211yescharacteristic
24C2×Dic52C2211yescharacteristic
25C2×C8×D13C2211yescharacteristic
26#88152—21no—
27#88151C2211yescharacteristic
28#88151C2211yescharacteristic
29#88146C2211yescharacteristic
30#88146C2211yescharacteristic
31#88144C2211yescharacteristic
32#88143—21no—
33#88142C2211yescharacteristic
34#88141C2211yescharacteristic
35#88141C2211yescharacteristic
36#88139—21no—
37#88133—21no—
38#88130—21no—
39C4×Dic26—21no—
40C13×#107C2211yescharacteristic
41C13×#107C2211yescharacteristic
42C13×#106C2211yescharacteristic
43C13×#106C2211yescharacteristic
44C22⋊#1055C2211yescharacteristic
45#88060C2211yescharacteristic
46#88057C2211yescharacteristic
47#88056C2211yescharacteristic
48#88056C2211yescharacteristic
49#88055C2211yescharacteristic
50#88054C2211yescharacteristic
51#88050C2211yescharacteristic
52#88050C2211yescharacteristic
53#88050C2211yescharacteristic
54#88050C2211yescharacteristic
55#88048C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58#88047C2211yescharacteristic
59C22×C4×C13—21no—
60C22×C4×C13C2311yescharacteristic
61C2×C22⋊D13D411yescharacteristic
62C2×C4×D13C2311yescharacteristic
63C2×Dic26—21no—
64C2×Dic26C2311yescharacteristic
65C2×Dic26C2311yescharacteristic
66C13×M16—22no—
67C2×C8×C13C2311yescharacteristic
68C2×C8×C13C2311yescharacteristic
69C13×C4⋊C4—21no—
70C13×C4⋊C4C2311yescharacteristic
71C13×C4⋊C4C2311yescharacteristic
72C13×C4⋊C4C2311yescharacteristic
73C13×C4⋊C4C2311yescharacteristic
74C13×C22⋊C4—21no—
75C42×C13—21no—
76C22⋊Dic13—21no—
77C22⋊Dic13—21no—
78C22⋊Dic13D411yescharacteristic
79#6103—21no—
80#6103—21no—
81#6103—21no—
82#6103—21no—
83#6103D411yescharacteristic
84C4⋊Dic13—21no—
85C4⋊Dic13—21no—
86C4⋊Dic13—21no—
87C4⋊Dic13C2311yescharacteristic
88C4⋊Dic13C2311yescharacteristic
89#6101—21no—
90#6101—21no—
91#6101—21no—
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101D411yescharacteristic
96C4×Dic13—21no—
97C4×Dic13—21no—
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13C2311yescharacteristic
101C2×#1055C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103Dic52—22no—
104C8×D13—22no—
105#3349—131nomaximal, Sylow
106C23×C13C2×D411yescharacteristic
107C22×D13C2×D411yescharacteristic
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—42no—
115C2×C4×C13C2×D411yescharacteristic
116C2×C4×C13C2411yescharacteristic
117C22⋊D13—41no—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13C2×D411yescharacteristic
123C2×Dic13C2×D411yescharacteristic
124C2×Dic13C2×D411yescharacteristic
125C4×D13—21no—
126C4×D13—21no—
127Dic26—21no—
128Dic26—21no—
129Dic26—21no—
130Dic26—21no—
131Dic26—42no—
132C8×C13—21no—
133C8×C13#4112yes—
134#1055—21no—
135#1055—21no—
136#556—131no—
137#552—131no—
138#501—131no—
139#485—131no—
140#485—131no—
141#485—131no—
142#484—131no—
143#479—131no—
144#477—131no—
145#470—131no—
146#467—131no—
147#441—131no—
148#435—131no—
149#428D1311yescharacteristic, complemented
150#427—131no—
151C22×C13—21no—
152C22×C13—21no—
153C22×C13—21no—
154C22×C13C22×D411yescharacteristic
155C2×D13—21no—
156C2×D13—21no—
157C2×D13—21no—
158C4×C13—21no—
159C4×C13—41no—
160C4×C13—41no—
161C4×C13—41no—
162C4×C13—41no—
163C4×C13C2×#4111yescharacteristic
164C4×C132−1+411yescharacteristic
165Dic13—21no—
166Dic13—21no—
167Dic13—21no—
168Dic13—41no—
169Dic13—41no—
170Dic13—41no—
171Dic13—41no—
172C2×Q16—131no—
173C2×M16C2×D1311yescharacteristic
174C22×C8—131no—
175C4⋊Q8—131no—
176#126—261no—
177#126—261no—
178#126—261no—
179#125—131no—
180#125—261no—
181#124—261no—
182#123—261no—
183C22⋊Q8—131no—
184C22⋊Q8—131no—
185C22⋊Q8—131no—
186C22⋊Q8—131no—
187C4×Q8—131no—
188C4×Q8—131no—
189C4×Q8—261no—
190C4×D4—131no—
191#117—131no—
192#117—131no—
193#117—261no—
194#117C2×D1311yescharacteristic
195C2×C4⋊C4C2×D1311yescharacteristic
196#107—131no—
197#107—131no—
198#107—131no—
199#107C2×D1311yescharacteristic
200#107C2×D1311yescharacteristic
201#106—131no—
202#106—131no—
203#106C2×D1311yescharacteristic
204#106C2×D1311yescharacteristic
205C4⋊C8—131no—
206#103—131no—
207#103—131no—
208#103—131no—
209#103—131no—
210#103—131no—
211#103—131no—
212C22⋊C8—131no—
213C22⋊C8—131no—
214#97—131no—
215C2×C13—41no—
216C2×C13#54711yescharacteristic
217C2×C13#57511yescharacteristic
218C2×C13#57811yescharacteristic
219D13—41no—
220C2×Q8—131no—
221C2×Q8—131no—
222C2×Q8—261no—
223C2×D4—131no—
224C22×C4—21no—
225C22×C4—131no—
226C22×C4C22×D1311yescharacteristic
227Q16—262no—
228M16—22no—
229C2×C8—131no—
230C2×C8—131no—
231C2×C8—262no—
232C2×C8C22×D1311yescharacteristic
233C2×C8C22×D1311yescharacteristic
234C4⋊C4—21no—
235C4⋊C4—131no—
236C4⋊C4—131no—
237C4⋊C4—131no—
238C4⋊C4—261no—
239C4⋊C4—261no—
240C4⋊C4—261no—
241C4⋊C4—261no—
242C4⋊C4—261no—
243C4⋊C4—261no—
244C4⋊C4—261no—
245C4⋊C4—261no—
246C4⋊C4—261no—
247C4⋊C4C22×D1311yescharacteristic
248C4⋊C4C22×D1311yescharacteristic
249C4⋊C4C22×D1311yescharacteristic
250C4⋊C4C22×D1311yescharacteristic
251C22⋊C4—21no—
252C22⋊C4—131no—
253C22⋊C4—131no—
254C22⋊C4—261no—
255C22⋊C4—261no—
256C22⋊C4—261no—
257C22⋊C4—261no—
258C22⋊C4—261no—
259C22⋊C4—261no—
260C42—21no—
261C42—131no—
262C42—261no—
263C42—261no—
264C42—261no—
265C42—261no—
266C13#334911yescharacteristic, complemented, Sylow
267C23—131no—
268C23D4×D1311yescharacteristic
269Q8—261no—
270Q8—261no—
271Q8—261no—
272Q8—261no—
273Q8—522no—
274D4—521no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—42no—
282C2×C4—131no—
283C2×C4—131no—
284C2×C4—131no—
285C2×C4—261no—
286C2×C4—261no—
287C2×C4—261no—
288C2×C4—261no—
289C2×C4—261no—
290C2×C4—261no—
291C2×C4D4×D1311yescharacteristic
292C2×C4C23×D1311yescharacteristic
293C8—21no—
294C8—261no—
295C8—261no—
296C8#612712yes—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—261no—
301C22—261no—
302C22—261no—
303C22C2×D4×D1311yescharacteristic
304C4—21no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—261no—
310C4—261no—
311C4—261no—
312C4—521no—
313C4—521no—
314C4—521no—
315C4—521no—
316C4C2×#612711yescharacteristic
317C4#8825411yescharacteristic
318C2—41no—
319C2—521no—
320C2#1171921211yescharacteristic
321C2#1171947811yescharacteristic
322C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#428C2
socleC22×C13C22×D4
prime radicalC2×C22⋊D13D4
hypercenter#428D13
hypocenterC13#3349
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
3. C13×#428C2semidirect
4. #11718798C2semidirect
6. #11718657C2semidirect
7. #11718631C2semidirect
8. #11718549C2semidirect
9. #11718548C2semidirect
10. #11718537C2semidirect
11. #11718536C2semidirect
12. #11718528C2semidirect
13. #11718521C2semidirect
14. #11718518C2semidirect
15. #11718514C2semidirect
149. #428D13semidirect
266. C13#3349semidirect

Maximal subgroups

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

subgroupindex
#117192382
#117192182
C13×#4282
#117187982
#117187882
#117186572
#117186312
#117185492
#117185482
#117185372
#117185362
#117185282
#117185212
#117185182
#117185142
#334913