Finite Group Databasebeta

← #13127681

Subgroups — #13127681

Order 1664.

332 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719390C211yesmaximal, characteristic, complemented
2#11719247C211yesmaximal, characteristic
3C13×#478C211yesmaximal, characteristic
4#11718730C211yesmaximal, characteristic, complemented
5#11718679C211yesmaximal, characteristic
6#11718536C211yesmaximal, characteristic, complemented
7#11718534C211yesmaximal, characteristic, complemented
8#11718518C211yesmaximal, characteristic, complemented
9#11718514C211yesmaximal, characteristic, complemented
10#11718510C211yesmaximal, characteristic, complemented
11#11718489C211yesmaximal, characteristic, complemented
12#11718429C211yesmaximal, characteristic
13#11718428C211yesmaximal, characteristic
14#11718428C211yesmaximal, characteristic
15#11718426C211yesmaximal, characteristic
16C13×#125C2211yescharacteristic
17C4×D4×C13C2211yescharacteristic
18#88190C2211yescharacteristic
19#88190C2211yescharacteristic
20C2×#6105C2211yescharacteristic
21#88180—21no—
22#88178—21no—
23C2×Dic52C2211yescharacteristic
24C2×Dic52C2211yescharacteristic
25#88144C2211yescharacteristic
26#88143—21no—
27#88143—21no—
28#88142—21no—
29#88142C2211yescharacteristic
30#88141—21no—
31#88141C2211yescharacteristic
32#88141C2211yescharacteristic
33#88141C2211yescharacteristic
34#88141C2211yescharacteristic
35#88133—21no—
36#88133—21no—
37#88123C2211yescharacteristic
38C4×Dic26C2211yescharacteristic
39C4×Dic26C2211yescharacteristic
40C13×#107C2211yescharacteristic
41C13×#106C2211yescharacteristic
42C13×C4⋊C8C2211yescharacteristic
43C13×#102C2211yescharacteristic
44C13×#102C2211yescharacteristic
45#88072C2211yescharacteristic
46#88056C2211yescharacteristic
47#88056C2211yescharacteristic
48#88055C2211yescharacteristic
49#88054C2211yescharacteristic
50#88054C2211yescharacteristic
51C8×Dic13C2211yescharacteristic
52#88050C2211yescharacteristic
53#88050C2211yescharacteristic
54#88050C2211yescharacteristic
55#88050C2211yescharacteristic
56#88050C2211yescharacteristic
57#88047C2211yescharacteristic
58#88043C2211yescharacteristic
59C2×D4×C13C2311yescharacteristic
60C22×C4×C13—21no—
61C2×Dic26—21no—
62C2×Dic26D411yescharacteristic
63C2×Dic26C2311yescharacteristic
64C2×Dic26C2311yescharacteristic
65C2×Dic26C2311yescharacteristic
66C2×C8×C13C2311yescharacteristic
67C2×C8×C13C2311yescharacteristic
68C13×C4⋊C4—21no—
69C13×C4⋊C4—21no—
70C13×C4⋊C4C2311yescharacteristic
71C13×C4⋊C4C2311yescharacteristic
72C13×C4⋊C4C2311yescharacteristic
73C13×C22⋊C4—21no—
74C42×C13C2311yescharacteristic
75C22⋊Dic13—21no—
76C22⋊Dic13—21no—
77C22⋊Dic13—21no—
78C22⋊Dic13—21no—
79#6105—22no—
80C4⋊Dic13—21no—
81C4⋊Dic13—21no—
82C4⋊Dic13—21no—
83C4⋊Dic13D411yescharacteristic
84C4⋊Dic13C2311yescharacteristic
85#6101—21no—
86#6101—21no—
87#6101—21no—
88#6101—21no—
89#6101—21no—
90#6101—21no—
91#6101—21no—
92#6101D411yescharacteristic
93#6101D411yescharacteristic
94C4×Dic13—21no—
95C4×Dic13—21no—
96C4×Dic13—21no—
97C4×Dic13—21no—
98C4×Dic13—21no—
99C4×Dic13C2311yescharacteristic
100C4×Dic13C2311yescharacteristic
101C2×#1055C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103Dic52—22no—
104Dic52—22no—
105#3377—131nomaximal, Sylow
106C23×C13—21no—
107D4×C13—21no—
108D4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—42no—
113C2×C4×C13C2×D411yescharacteristic
114C2×C4×C13C2×D411yescharacteristic
115C2×C4×C13C2411yescharacteristic
116C2×Dic13—21no—
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13C2×D411yescharacteristic
121C2×Dic13C2×D411yescharacteristic
122C2×Dic13C2×D411yescharacteristic
123C2×Dic13C2×D411yescharacteristic
124Dic26—21no—
125Dic26—21no—
126Dic26—21no—
127Dic26—21no—
128Dic26—21no—
129Dic26—41no—
130Dic26—42no—
131Dic26#4112yes—
132C8×C13—21no—
133C8×C13—21no—
134#1055—21no—
135#1055—21no—
136#557—131no—
137#556—131no—
138#491—131no—
139#489—131no—
140#488—131no—
141#479—131no—
142#478D1311yescharacteristic
143#477—131no—
144#464—131no—
145#464—131no—
146#462—131no—
147#446—131no—
148#441—131no—
149#440—131no—
150C4×Q16—131no—
151C22×C13—41no—
152C22×C13—41no—
153C22×C13—41no—
154C22×C13C22×D411yescharacteristic
155C4×C13—21no—
156C4×C13—21no—
157C4×C13—41no—
158C4×C13—41no—
159C4×C13—41no—
160C4×C13C2×#4111yescharacteristic
161C4×C132−1+411yescharacteristic
162Dic13—22no—
163Dic13—21no—
164Dic13—21no—
165Dic13—21no—
166Dic13—21no—
167Dic13—41no—
168Dic13—41no—
169Dic13—41no—
170C2×Q16—131no—
171C2×Q16—131no—
172C2×SD16—131no—
173C4⋊Q8—131no—
174C4⋊Q8—131no—
175C4⋊Q8—261no—
176#126—261no—
177#126—261no—
178#125—131no—
179#125—261no—
180#125—261no—
181#125C2×D1311yescharacteristic
182#124—131no—
183#124—131no—
184C22⋊Q8—261no—
185C4×Q8—131no—
186C4×Q8—131no—
187C4×Q8—131no—
188C4×Q8—131no—
189C4×Q8—131no—
190C4×Q8—131no—
191C4×Q8—261no—
192C4×D4C2×D1311yescharacteristic
193#117—261no—
194#107—131no—
195#107C2×D1311yescharacteristic
196#106C2×D1311yescharacteristic
197C4⋊C8—131no—
198C4⋊C8—131no—
199C4⋊C8C2×D1311yescharacteristic
200#103—131no—
201#103—131no—
202#103—131no—
203#103—131no—
204#103—131no—
205#103—131no—
206#103—131no—
207#102—131no—
208#102C2×D1311yescharacteristic
209#102C2×D1311yescharacteristic
210#97—131no—
211#97—131no—
212C4×C8—131no—
213C2×C13—81no—
214C2×C13#54811yescharacteristic
215C2×C13#57511yescharacteristic
216C2×C13#57811yescharacteristic
217C2×Q8—131no—
218C2×Q8—131no—
219C2×Q8—131no—
220C2×Q8—131no—
221C2×Q8—261no—
222C2×D4C22×D1311yescharacteristic
223C22×C4—21no—
224Q16—262no—
225Q16—262no—
226SD16—262no—
227C2×C8—131no—
228C2×C8—131no—
229C2×C8C22×D1311yescharacteristic
230C2×C8C22×D1311yescharacteristic
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4—131no—
234C4⋊C4—131no—
235C4⋊C4—131no—
236C4⋊C4—131no—
237C4⋊C4—261no—
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
250C22⋊C4—21no—
251C22⋊C4—261no—
252C22⋊C4—261no—
253C22⋊C4—261no—
254C22⋊C4—261no—
255C42—131no—
256C42—131no—
257C42—261no—
258C42—261no—
259C42—261no—
260C42—261no—
261C42—261no—
262C42C22×D1311yescharacteristic
263C13#337711yescharacteristic, complemented, Sylow
264C23—21no—
265Q8—132no—
266Q8—261no—
267Q8—261no—
268Q8—261no—
269Q8—261no—
270Q8—261no—
271Q8—521no—
272Q8—522no—
273D4—21no—
274D4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—42no—
279C2×C4—131no—
280C2×C4—131no—
281C2×C4—131no—
282C2×C4—131no—
283C2×C4—261no—
284C2×C4—261no—
285C2×C4—261no—
286C2×C4—261no—
287C2×C4D4×D1311yescharacteristic
288C2×C4D4×D1311yescharacteristic
289C2×C4C23×D1311yescharacteristic
290C8—21no—
291C8—21no—
292C8—261no—
293C8—261no—
294C22—41no—
295C22—41no—
296C22—41no—
297C22C2×D4×D1311yescharacteristic
298C4—21no—
299C4—21no—
300C4—41no—
301C4—41no—
302C4—41no—
303C4—261no—
304C4—261no—
305C4—261no—
306C4—261no—
307C4—262no—
308C4—521no—
309C4—521no—
310C4—521no—
311C4#8825411yescharacteristic
312C4#41×D1311yescharacteristic
313C2—81no—
314C2#1171933811yescharacteristic
315C2#1171947611yescharacteristic
316C2#1171947811yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#478C2
socleC22×C13C22×D4
prime radicalC2×D4×C13C23
hypercenter#478D13
hypocenterC13#3377
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #11719390C2semidirect
4. #11718730C2semidirect
6. #11718536C2semidirect
7. #11718534C2semidirect
8. #11718518C2semidirect
9. #11718514C2semidirect
10. #11718510C2semidirect
11. #11718489C2semidirect
263. C13#3377semidirect

Maximal subgroups

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

subgroupindex
#117193902
#117192472
C13×#4782
#117187302
#117186792
#117185362
#117185342
#117185182
#117185142
#117185102
#117184892
#117184292
#117184282
#117184262
#337713