Finite Group Databasebeta

← #13127677

Subgroups — #13127677

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#11719426C211yesmaximal, characteristic, complemented
2#11719376C211yesmaximal, characteristic
3C13×#489C211yesmaximal, characteristic
4#11718752C211yesmaximal, characteristic, complemented
5#11718715C211yesmaximal, characteristic
6#11718460C211yesmaximal, characteristic, complemented
7#11718458C211yesmaximal, characteristic, complemented
8#11718454C211yesmaximal, characteristic, complemented
9#11718451C211yesmaximal, characteristic, complemented
10#11718429C211yesmaximal, characteristic
11#11718428C211yesmaximal, characteristic
12#11718424C211yesmaximal, characteristic
13#11718418C211yesmaximal, characteristic
14#11718377C211yesmaximal, characteristic, complemented
15#11718362C211yesmaximal, characteristic, complemented
16C13×C4⋊Q8C2211yescharacteristic
17C13×#124C2211yescharacteristic
18Q8×Dic13—21no—
19Q8×Dic13C2211yescharacteristic
20#88198—21no—
21#88198C2211yescharacteristic
22C2×#6107C2211yescharacteristic
23#88190C2211yescharacteristic
24D4×Dic13C2211yescharacteristic
25C2×#6105C2211yescharacteristic
26C2×Dic52C2211yescharacteristic
27#88144C2211yescharacteristic
28#88144C2211yescharacteristic
29#88143—21no—
30#88143—21no—
31#88141C2211yescharacteristic
32#88141C2211yescharacteristic
33#88133—21no—
34#88133—21no—
35#88132—21no—
36#88131—21no—
37C4×Dic26C2211yescharacteristic
38C4×Dic26C2211yescharacteristic
39C4×Dic26C2211yescharacteristic
40C13×#103C2211yescharacteristic
41C13×#103C2211yescharacteristic
42C13×#102C2211yescharacteristic
43C13×#102C2211yescharacteristic
44C13×#97C2211yescharacteristic
45#88075C2211yescharacteristic
46#88072C2211yescharacteristic
47#88057C2211yescharacteristic
48#88056C2211yescharacteristic
49#88056C2211yescharacteristic
50#88055C2211yescharacteristic
51#88054C2211yescharacteristic
52#88054C2211yescharacteristic
53C8×Dic13C2211yescharacteristic
54#88050C2211yescharacteristic
55#88050C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×Q8×C13C2311yescharacteristic
61C2×D4×C13C2311yescharacteristic
62C22×Dic13—21no—
63C2×Dic26D411yescharacteristic
64C2×Dic26C2311yescharacteristic
65C2×Dic26C2311yescharacteristic
66C2×C8×C13C2311yescharacteristic
67C2×C8×C13C2311yescharacteristic
68C13×C4⋊C4—21no—
69C13×C4⋊C4C2311yescharacteristic
70C13×C4⋊C4C2311yescharacteristic
71C13×C22⋊C4—21no—
72C13×C22⋊C4—21no—
73C42×C13C2311yescharacteristic
74C22⋊Dic13—21no—
75C22⋊Dic13—21no—
76C22⋊Dic13—21no—
77#6107—22no—
78#6105—22no—
79C4⋊Dic13—21no—
80C4⋊Dic13—21no—
81C4⋊Dic13—21no—
82C4⋊Dic13D411yescharacteristic
83C4⋊Dic13C2311yescharacteristic
84C4⋊Dic13C2311yescharacteristic
85#6101—21no—
86#6101—21no—
87#6101—21no—
88#6101—21no—
89#6101—21no—
90#6101—21no—
91#6101—21no—
92#6101—21no—
93#6101D411yescharacteristic
94#6101D411yescharacteristic
95C4×Dic13—21no—
96C4×Dic13—21no—
97C4×Dic13—21no—
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13C2311yescharacteristic
101C4×Dic13C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104Dic52—22no—
105#3377—131nomaximal, Sylow
106C23×C13—21no—
107Q8×C13—21no—
108Q8×C13—21no—
109Q8×C13—42no—
110D4×C13—21no—
111D4×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×Dic13—42no—
123C2×Dic13C2×D411yescharacteristic
124C2×Dic13C2×D411yescharacteristic
125C2×Dic13C2×D411yescharacteristic
126C2×Dic13C2×D411yescharacteristic
127Dic26—21no—
128Dic26—21no—
129Dic26—21no—
130Dic26—41no—
131Dic26#4112yes—
132C8×C13—21no—
133C8×C13—21no—
134#1055—21no—
135#1055—21no—
136#557—131no—
137#556—131no—
138#491—131no—
139#489D1311yescharacteristic
140#488—131no—
141#479—131no—
142#478—131no—
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—261no—
175C4⋊Q8C2×D1311yescharacteristic
176#126—261no—
177#126—261no—
178#125—131no—
179#125—131no—
180#125—261no—
181#125—261no—
182#124—131no—
183#124C2×D1311yescharacteristic
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×D4—131no—
193#117—261no—
194#107—131no—
195#107—131no—
196#106—131no—
197C4⋊C8—131no—
198C4⋊C8—131no—
199C4⋊C8—131no—
200#103—131no—
201#103—131no—
202#103—131no—
203#103—131no—
204#103—131no—
205#103C2×D1311yescharacteristic
206#103C2×D1311yescharacteristic
207#102—131no—
208#102C2×D1311yescharacteristic
209#102C2×D1311yescharacteristic
210#97—131no—
211#97C2×D1311yescharacteristic
212C4×C8—131no—
213C2×C13—81no—
214C2×C13#54811yescharacteristic
215C2×C13#57511yescharacteristic
216C2×C13#57811yescharacteristic
217C2×Q8—21no—
218C2×Q8—131no—
219C2×Q8—131no—
220C2×Q8—131no—
221C2×Q8C22×D1311yescharacteristic
222C2×D4C22×D1311yescharacteristic
223C22×C4—261no—
224Q16—262no—
225Q16—262no—
226SD16—262no—
227C2×C8—131no—
228C2×C8—131no—
229C2×C8C22×D1311yescharacteristic
230C2×C8C22×D1311yescharacteristic
231C4⋊C4—21no—
232C4⋊C4—131no—
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⋊C4—261no—
248C4⋊C4C22×D1311yescharacteristic
249C4⋊C4C22×D1311yescharacteristic
250C22⋊C4—21no—
251C22⋊C4—21no—
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—21no—
266Q8—21no—
267Q8—42no—
268Q8—132no—
269Q8—261no—
270Q8—261no—
271Q8—261no—
272Q8—521no—
273D4—21no—
274D4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—131no—
279C2×C4—131no—
280C2×C4—131no—
281C2×C4—131no—
282C2×C4—261no—
283C2×C4—261no—
284C2×C4—261no—
285C2×C4—261no—
286C2×C4—522no—
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#41×D1311yescharacteristic
312C4#8825711yescharacteristic
313C2—81no—
314C2#1171938211yescharacteristic
315C2#1171947811yescharacteristic
316C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#489C2
socleC22×C13C22×D4
prime radicalC2×D4×C13C23
hypercenter#489D13
hypocenterC13#3377
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #11719426C2semidirect
4. #11718752C2semidirect
6. #11718460C2semidirect
7. #11718458C2semidirect
8. #11718454C2semidirect
9. #11718451C2semidirect
14. #11718377C2semidirect
15. #11718362C2semidirect
263. C13#3377semidirect

Maximal subgroups

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

subgroupindex
#117194262
#117193762
C13×#4892
#117187522
#117187152
#117184602
#117184582
#117184542
#117184512
#117184292
#117184282
#117184242
#117184182
#117183772
#117183622
#337713