Finite Group Databasebeta

← #13127295

Subgroups — #13127295

Order 1664.

344 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719340C211yesmaximal, characteristic
2#11719218C211yesmaximal, characteristic
3C13×#483C211yesmaximal, characteristic, complemented
4#11718712C211yesmaximal, characteristic, complemented
5C2×#88048C211yesmaximal, characteristic, complemented
6#11718523C211yesmaximal, characteristic, complemented
7#11718522C211yesmaximal, characteristic, complemented
8#11718517C211yesmaximal, characteristic, complemented
9#11718515C211yesmaximal, characteristic, complemented
10#11718477C211yesmaximal, characteristic, complemented
11#11718475C211yesmaximal, characteristic, complemented
12#11718457C211yesmaximal, characteristic, complemented
13#11718450C211yesmaximal, characteristic, complemented
14#11718391C211yesmaximal, characteristic
15#11718383C211yesmaximal, characteristic, complemented
16C13×C22⋊Q8C2211yescharacteristic
17C2×C13×C4⋊C4C2211yescharacteristic
18#88200C2211yescharacteristic
19Q8×Dic13C2211yescharacteristic
20C2×#6107C2211yescharacteristic
21#88183—21no—
22C4×C22⋊D13C2211yescharacteristic
23#88180—21no—
24C2×C4⋊Dic13C2211yescharacteristic
25#88178C2211yescharacteristic
26C22×#1055C2211yescharacteristic
27C2×#6094C2211yescharacteristic
28#88152—21no—
29#88151—21no—
30#88151C2211yescharacteristic
31#88146C2211yescharacteristic
32C4⋊C4×D13C2211yescharacteristic
33#88144C2211yescharacteristic
34#88143—21no—
35#88143—21no—
36#88142C2211yescharacteristic
37#88141C2211yescharacteristic
38#88135—21no—
39#88132—21no—
40C13×#106C2211yescharacteristic
41C13×#106C2211yescharacteristic
42C13×#103C2211yescharacteristic
43C13×#103C2211yescharacteristic
44C13×C22⋊C8C2211yescharacteristic
45#88075C2211yescharacteristic
46#88060C2211yescharacteristic
47#88058C2211yescharacteristic
48#88058C2211yescharacteristic
49#88056C2211yescharacteristic
50#88056C2211yescharacteristic
51#88055C2211yescharacteristic
52#88054C2211yescharacteristic
53#88050C2211yescharacteristic
54#88048C2211yescharacteristic
55#88048C2211yescharacteristic
56#88048C2211yescharacteristic
57#88048C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C22×C4×C13—21no—
61C22×C4×C13C2311yescharacteristic
62C2×C22⋊D13D411yescharacteristic
63C22×Dic13—21no—
64C2×C4×D13—21no—
65C2×C4×D13C2311yescharacteristic
66C2×Dic26—21no—
67C2×Dic26C2311yescharacteristic
68C2×C8×C13C2311yescharacteristic
69C2×C8×C13C2311yescharacteristic
70C13×C4⋊C4—21no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4C2311yescharacteristic
73C13×C4⋊C4C2311yescharacteristic
74C13×C4⋊C4C2311yescharacteristic
75C13×C22⋊C4—21no—
76C22⋊Dic13—21no—
77C22⋊Dic13D411yescharacteristic
78#6107—22no—
79#6103—21no—
80#6103—21no—
81#6103—21no—
82#6103D411yescharacteristic
83C4⋊Dic13—21no—
84C4⋊Dic13—21no—
85C4⋊Dic13—21no—
86C4⋊Dic13—21no—
87C4⋊Dic13C2311yescharacteristic
88C4⋊Dic13C2311yescharacteristic
89C4⋊Dic13C2311yescharacteristic
90#6101—21no—
91#6101—21no—
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101D411yescharacteristic
97C4×Dic13—21no—
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13C2311yescharacteristic
101C2×#1055—22no—
102C2×#1055C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104#6094—22no—
105#3344—131nomaximal, Sylow
106C23×C13C2×D411yescharacteristic
107C22×D13C2×D411yescharacteristic
108Q8×C13—21no—
109Q8×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—42no—
117C2×C4×C13C2×D411yescharacteristic
118C2×C4×C13C2411yescharacteristic
119C22⋊D13—22no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—81no—
125C2×Dic13C2×D411yescharacteristic
126C2×Dic13C2×D411yescharacteristic
127C2×Dic13C2×D411yescharacteristic
128C4×D13—21no—
129C4×D13—21no—
130C4×D13—81no—
131Dic26—21no—
132Dic26—21no—
133Dic26—81no—
134C8×C13—21no—
135C8×C13—21no—
136#1055—21no—
137#1055#4112yes—
138#554—131no—
139#552—131no—
140#501—131no—
141#485—131no—
142#484—131no—
143#483—131no—
144#483D1311yescharacteristic, complemented
145#479—131no—
146#475—131no—
147#470—131no—
148#467—131no—
149#441—131no—
150#435—131no—
151#428—131no—
152C2×#106—131no—
153C22×C13—21no—
154C22×C13—21no—
155C22×C13#13712yes—
156C22×C13C22×D411yescharacteristic
157C2×D13—21no—
158C2×D13—21no—
159C2×D13—21no—
160C4×C13—21no—
161C4×C13—41no—
162C4×C13—41no—
163C4×C13—41no—
164C4×C13—41no—
165C4×C13C2×#4111yescharacteristic
166C4×C132−1+411yescharacteristic
167Dic13—21no—
168Dic13—21no—
169Dic13—21no—
170Dic13—41no—
171Dic13—41no—
172Dic13—41no—
173Dic13—41no—
174C2×Q16—131no—
175C2×M16—131no—
176C22×C8—131no—
177C4⋊Q8—131no—
178#126—261no—
179#125—131no—
180#125—261no—
181#125—261no—
182#123—261no—
183C22⋊Q8—131no—
184C22⋊Q8—131no—
185C22⋊Q8—131no—
186C22⋊Q8—261no—
187C22⋊Q8—261no—
188C22⋊Q8C2×D1311yescharacteristic
189C4×Q8—131no—
190C4×Q8—131no—
191C4×D4—131no—
192C4×D4—261no—
193#117—131no—
194#117—261no—
195C2×C4⋊C4—131no—
196C2×C4⋊C4—131no—
197C2×C4⋊C4C2×D1311yescharacteristic
198#107—131no—
199#107—131no—
200#107—131no—
201#106—131no—
202#106—131no—
203#106—131no—
204#106—131no—
205#106C2×D1311yescharacteristic
206#106C2×D1311yescharacteristic
207C4⋊C8—131no—
208#103—131no—
209#103—131no—
210#103—131no—
211#103—131no—
212#103C2×D1311yescharacteristic
213#103C2×D1311yescharacteristic
214C22⋊C8—131no—
215C22⋊C8C2×D1311yescharacteristic
216#97—131no—
217C2×C13—22no—
218C2×C13#54711yescharacteristic
219C2×C13C2×#13711yescharacteristic
220C2×C13#57711yescharacteristic
221D13—41no—
222C2×Q8—131no—
223C2×Q8—261no—
224C2×Q8C22×D1311yescharacteristic
225C2×D4—131no—
226C22×C4—21no—
227C22×C4—131no—
228C22×C4—261no—
229C22×C4—261no—
230C22×C4C22×D1311yescharacteristic
231Q16—262no—
232M16—262no—
233C2×C8—131no—
234C2×C8—131no—
235C2×C8—262no—
236C2×C8C22×D1311yescharacteristic
237C2×C8C22×D1311yescharacteristic
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—131no—
241C4⋊C4—131no—
242C4⋊C4—131no—
243C4⋊C4—131no—
244C4⋊C4—261no—
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—131no—
259C22⋊C4—131no—
260C22⋊C4—261no—
261C22⋊C4—261no—
262C22⋊C4—261no—
263C22⋊C4—261no—
264C42—131no—
265C42—261no—
266C42—261no—
267C42—261no—
268C13#334411yescharacteristic, complemented, Sylow
269C23—131no—
270C23D4×D1311yescharacteristic
271Q8—21no—
272Q8—21no—
273Q8—261no—
274Q8—261no—
275Q8—1041no—
276D4—262no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—42no—
284C2×C4—131no—
285C2×C4—131no—
286C2×C4—131no—
287C2×C4—261no—
288C2×C4—261no—
289C2×C4—261no—
290C2×C4—261no—
291C2×C4—261no—
292C2×C4—261no—
293C2×C4—1041no—
294C2×C4—1041no—
295C2×C4D4×D1311yescharacteristic
296C2×C4C23×D1311yescharacteristic
297C8—21no—
298C8—21no—
299C8—132no—
300C8—261no—
301C22—21no—
302C22—21no—
303C22—261no—
304C22—261no—
305C22—261no—
306C22#8816912yes—
307C22C2×D4×D1311yescharacteristic
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—261no—
314C4—261no—
315C4—261no—
316C4—521no—
317C4—521no—
318C4—521no—
319C4—521no—
320C4#41×D1311yescharacteristic
321C4#8825711yescharacteristic
322C2—22no—
323C2—521no—
324C2#1171936011yescharacteristic
325C2C2×#8816911yescharacteristic
326C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#483C2
socleC22×C13C22×D4
prime radicalC2×C22⋊D13D4
hypercenter#483D13
hypocenterC13#3344
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
3. C13×#483C2semidirect
4. #11718712C2semidirect
5. C2×#88048C2semidirect
6. #11718523C2semidirect
7. #11718522C2semidirect
8. #11718517C2semidirect
9. #11718515C2semidirect
10. #11718477C2semidirect
11. #11718475C2semidirect
12. #11718457C2semidirect
13. #11718450C2semidirect
15. #11718383C2semidirect
144. #483D13semidirect
268. C13#3344semidirect

Maximal subgroups

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

subgroupindex
#117193402
#117192182
C13×#4832
#117187122
C2×#880482
#117185232
#117185222
#117185172
#117185152
#117184772
#117184752
#117184572
#117184502
#117183912
#117183832
#334413