Finite Group Databasebeta

← #13124671

Subgroups — #13124671

Order 1664.

362 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719434C211yesmaximal, characteristic
2#11719277C211yesmaximal, characteristic
3C13×#475C211yesmaximal, characteristic, complemented
4#11718752C211yesmaximal, characteristic, complemented
5#11718683C211yesmaximal, characteristic, complemented
6#11718522C211yesmaximal, characteristic
7#11718521C211yesmaximal, characteristic
8#11718518C211yesmaximal, characteristic, complemented
9#11718515C211yesmaximal, characteristic, complemented
10#11718500C211yesmaximal, characteristic
11#11718490C211yesmaximal, characteristic, complemented
12#11718463C211yesmaximal, characteristic
13D13×#103C211yesmaximal, characteristic
14#11718460C211yesmaximal, characteristic, complemented
15#11718455C211yesmaximal, characteristic, complemented
16C2×Q8×D13C2211yescharacteristic
17C13×C4⋊Q8C2211yescharacteristic
18C4×Q8×C13C2211yescharacteristic
19#88200—21no—
20Q8×Dic13C2211yescharacteristic
21#88198—21no—
22C2×#6094C2211yescharacteristic
23C2×C8×D13C2211yescharacteristic
24#88150—21no—
25#88146—21no—
26#88146C2211yescharacteristic
27#88146C2211yescharacteristic
28C4⋊C4×D13C2211yescharacteristic
29#88144C2211yescharacteristic
30#88143—21no—
31#88142C2211yescharacteristic
32#88141—21no—
33#88141C2211yescharacteristic
34#88126—21no—
35#88126C2211yescharacteristic
36#88124C2211yescharacteristic
37C4×Dic26—21no—
38C4×Dic26C2211yescharacteristic
39C13×#106C2211yescharacteristic
40C13×#106C2211yescharacteristic
41C13×C4⋊C8C2211yescharacteristic
42C13×#103C2211yescharacteristic
43C13×#103C2211yescharacteristic
44#88075C2211yescharacteristic
45#88075C2211yescharacteristic
46#88058C2211yescharacteristic
47#88057C2211yescharacteristic
48#88056C2211yescharacteristic
49#88056C2211yescharacteristic
50#88054C2211yescharacteristic
51#88054C2211yescharacteristic
52#88050C2211yescharacteristic
53#88050C2211yescharacteristic
54#88048C2211yescharacteristic
55#88047C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×Q8×C13C2311yescharacteristic
61Q8×D13—22no—
62Q8×D13Q814yescomplemented
63C2×C4×D13—21no—
64C2×C4×D13—21no—
65C2×C4×D13C2311yescharacteristic
66C2×Dic26—21no—
67C2×Dic26—21no—
68C2×Dic26C2311yescharacteristic
69C2×C8×C13C2311yescharacteristic
70C2×C8×C13C2311yescharacteristic
71C13×C4⋊C4—21no—
72C13×C4⋊C4—21no—
73C13×C4⋊C4C2311yescharacteristic
74C13×C4⋊C4C2311yescharacteristic
75C13×C4⋊C4C2311yescharacteristic
76C42×C13—21no—
77C42×C13C2311yescharacteristic
78#6103—21no—
79#6103—21no—
80#6103D411yescharacteristic
81#6103D411yescharacteristic
82C4⋊Dic13—21no—
83C4⋊Dic13—21no—
84C4⋊Dic13C2311yescharacteristic
85C4⋊Dic13C2311yescharacteristic
86C4⋊Dic13C2311yescharacteristic
87#6101—21no—
88#6101—21no—
89#6101—21no—
90#6101—21no—
91#6101—21no—
92#6101—21no—
93#6101—21no—
94#6101D411yescharacteristic
95#6101D411yescharacteristic
96C4×Dic13—21no—
97C4×Dic13—21no—
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13—21no—
101C4×Dic13C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104#6094—22no—
105C8×D13—22no—
106#3082—131nomaximal, Sylow
107C22×D13C2×D411yescharacteristic
108Q8×C13—21no—
109Q8×C13—81no—
110Q8×C13C2×Q812yes—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13C2×D411yescharacteristic
116C2×C4×C13C2×D411yescharacteristic
117C2×C4×C13C2411yescharacteristic
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13C2×D411yescharacteristic
123C2×Dic13C2×D411yescharacteristic
124C2×Dic13C2×D411yescharacteristic
125C4×D13—24no—
126C4×D13—81no—
127C4×D13C2×Q812yes—
128C4×D13#4112yes—
129Dic26—21no—
130Dic26—24no—
131Dic26—81no—
132Dic26C2×Q812yes—
133C8×C13—21no—
134C8×C13—21no—
135#1055—21no—
136#1055—21no—
137#544—131no—
138#519—131no—
139#479—131no—
140#479—131no—
141#479—131no—
142#479—131no—
143#477—131no—
144#477—131no—
145#475—131no—
146#475D1311yescharacteristic, complemented
147#428—131no—
148#427—131no—
149#424—131no—
150#419—131no—
151C2×#103—131no—
152C22×C13C22×D411yescharacteristic
153C2×D13—21no—
154C2×D13—21no—
155C2×D13C22⋊Q812yes—
156C4×C13—22no—
157C4×C13—21no—
158C4×C13—21no—
159C4×C13—41no—
160C4×C13—41no—
161C4×C13—41no—
162C4×C13C22×Q811yescharacteristic
163C4×C13C2×#4111yescharacteristic
164Dic13—22no—
165Dic13—21no—
166Dic13—21no—
167Dic13—41no—
168Dic13—41no—
169Dic13—41no—
170Dic13C22⋊Q812yes—
171C22×Q8—131no—
172C2×M16—131no—
173C22×C8—131no—
174C4⋊Q8—131no—
175C4⋊Q8—261no—
176C4⋊Q8C2×D1311yescharacteristic
177#125—131no—
178#125—131no—
179#125—261no—
180C22⋊Q8—261no—
181C22⋊Q8—261no—
182C4×Q8—131no—
183C4×Q8—131no—
184C4×Q8—131no—
185C4×Q8—261no—
186C4×Q8—261no—
187C4×Q8C2×D1311yescharacteristic
188#117—131no—
189#117—131no—
190#117—131no—
191#117—261no—
192#117—261no—
193C2×C4⋊C4—131no—
194#107—131no—
195#107—131no—
196#107—131no—
197#107—131no—
198#106—131no—
199#106—131no—
200#106C2×D1311yescharacteristic
201#106C2×D1311yescharacteristic
202C4⋊C8—131no—
203C4⋊C8—131no—
204C4⋊C8—131no—
205C4⋊C8C2×D1311yescharacteristic
206#103—131no—
207#103—131no—
208#103—131no—
209#103—131no—
210#103—131no—
211#103—131no—
212#103C2×D1311yescharacteristic
213#103C2×D1311yescharacteristic
214C2×C13C2×C22⋊Q811yescharacteristic
215C2×C13#57711yescharacteristic
216C2×C13#57811yescharacteristic
217D13—22no—
218C2×Q8—21no—
219C2×Q8—134no—
220C2×Q8—131no—
221C2×Q8—261no—
222C2×Q8—261no—
223C2×Q8—262no—
224C2×Q8C22×D1311yescharacteristic
225C22×C4—131no—
226C22×C4—261no—
227C22×C4—261no—
228M16—262no—
229C2×C8—131no—
230C2×C8—131no—
231C2×C8—262no—
232C2×C8C22×D1311yescharacteristic
233C2×C8C22×D1311yescharacteristic
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—131no—
237C4⋊C4—131no—
238C4⋊C4—131no—
239C4⋊C4—131no—
240C4⋊C4—131no—
241C4⋊C4—261no—
242C4⋊C4—261no—
243C4⋊C4—261no—
244C4⋊C4—261no—
245C4⋊C4—261no—
246C4⋊C4—261no—
247C4⋊C4—261no—
248C4⋊C4—261no—
249C4⋊C4—261no—
250C4⋊C4C22×D1311yescharacteristic
251C4⋊C4C22×D1311yescharacteristic
252C4⋊C4C22×D1311yescharacteristic
253C22⋊C4—131no—
254C22⋊C4—131no—
255C22⋊C4—261no—
256C22⋊C4—261no—
257C42—21no—
258C42—131no—
259C42—261no—
260C42—261no—
261C42—261no—
262C42—261no—
263C42—261no—
264C42C22×D1311yescharacteristic
265C13#308211yescharacteristic, complemented, Sylow
266C23—131no—
267Q8—21no—
268Q8—81no—
269Q8—132no—
270Q8—264no—
271Q8—261no—
272Q8—1041no—
273Q8Q8×D1312yes—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—131no—
279C2×C4—132no—
280C2×C4—132no—
281C2×C4—131no—
282C2×C4—131no—
283C2×C4—264no—
284C2×C4—261no—
285C2×C4—261no—
286C2×C4—261no—
287C2×C4—261no—
288C2×C4—1041no—
289C2×C4D4×D1311yescharacteristic
290C2×C4D4×D1311yescharacteristic
291C2×C4C23×D1311yescharacteristic
292C8—21no—
293C8—21no—
294C8—261no—
295C8—261no—
296C22—132no—
297C22—261no—
298C22—261no—
299C22C2×D4×D1311yescharacteristic
300C4—21no—
301C4—21no—
302C4—22no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—132no—
307C4—261no—
308C4—261no—
309C4—262no—
310C4—521no—
311C4—521no—
312C4—521no—
313C4C2×Q8×D1311yescharacteristic
314C4#41×D1311yescharacteristic
315C2—262no—
316C2D13×C22⋊Q811yescharacteristic
317C2#1171946711yescharacteristic
318C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#475C2
socleC22×C13C22×D4
prime radicalC22×D13C2×D4
hypercenter#475D13
hypocenterC13#3082
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
3. C13×#475C2semidirect
4. #11718752C2semidirect
5. #11718683C2semidirect
8. #11718518C2semidirect
9. #11718515C2semidirect
11. #11718490C2semidirect
14. #11718460C2semidirect
15. #11718455C2semidirect
62. Q8×D13Q8semidirect
146. #475D13semidirect
265. C13#3082semidirect

Maximal subgroups

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

subgroupindex
#117194342
#117192772
C13×#4752
#117187522
#117186832
#117185222
#117185212
#117185182
#117185152
#117185002
#117184902
#117184632
D13×#1032
#117184602
#117184552
#308213