Finite Group Databasebeta

← #13127612

Subgroups — #13127612

Order 1664.

340 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719426C211yesmaximal, characteristic, complemented
2#11719244C211yesmaximal, characteristic
3C13×#461C211yesmaximal, characteristic
4#11718825C211yesmaximal, characteristic
5#11718823C211yesmaximal, characteristic
6#11718823C211yesmaximal, characteristic
7SD16×Dic13C211yesmaximal, characteristic
8#11718743C211yesmaximal, characteristic, complemented
9#11718679C211yesmaximal, characteristic
10#11718490C211yesmaximal, characteristic, complemented
11#11718489C211yesmaximal, characteristic, complemented
12#11718460C211yesmaximal, characteristic, complemented
13#11718458C211yesmaximal, characteristic, complemented
14#11718455C211yesmaximal, characteristic, complemented
15#11718453C211yesmaximal, characteristic, complemented
16C2×C13×SD16C2211yescharacteristic
17C2×C13×SD16C2211yescharacteristic
18C13×C4⋊Q8C2211yescharacteristic
19C4×D4×C13C2211yescharacteristic
20Q8×Dic13C2211yescharacteristic
21Q8×Dic13C2211yescharacteristic
22#88198C2211yescharacteristic
23#88198C2211yescharacteristic
24D4×Dic13C2211yescharacteristic
25D4×Dic13C2211yescharacteristic
26C2×#6105C2211yescharacteristic
27#88178—21no—
28C2×#6101—21no—
29#88144—21no—
30#88144C2211yescharacteristic
31#88143—21no—
32#88143—21no—
33#88142C2211yescharacteristic
34#88141—21no—
35#88132—21no—
36#88132—21no—
37#88124C2211yescharacteristic
38C4×Dic26C2211yescharacteristic
39C4×Dic26C2211yescharacteristic
40C13×C4⋊C8C2211yescharacteristic
41C13×#103C2211yescharacteristic
42C13×#103C2211yescharacteristic
43#88075C2211yescharacteristic
44#88075C2211yescharacteristic
45#88075C2211yescharacteristic
46#88075C2211yescharacteristic
47#88072C2211yescharacteristic
48#88058C2211yescharacteristic
49#88057C2211yescharacteristic
50#88056C2211yescharacteristic
51#88056C2211yescharacteristic
52#88055C2211yescharacteristic
53#88054C2211yescharacteristic
54#88054C2211yescharacteristic
55C8×Dic13C2211yescharacteristic
56#88050C2211yescharacteristic
57#88047C2211yescharacteristic
58#88043C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×Q8×C13C2311yescharacteristic
61C2×D4×C13C2311yescharacteristic
62C22×C4×C13—21no—
63C22×Dic13—21no—
64C22×Dic13—21no—
65C2×Dic26—21no—
66C2×Dic26D411yescharacteristic
67C2×Dic26C2311yescharacteristic
68C13×SD16—22no—
69C13×SD16—22no—
70C2×C8×C13C2311yescharacteristic
71C2×C8×C13C2311yescharacteristic
72C13×C4⋊C4—21no—
73C13×C4⋊C4—21no—
74C13×C4⋊C4C2311yescharacteristic
75C13×C22⋊C4—21no—
76C42×C13C2311yescharacteristic
77C22⋊Dic13—21no—
78C22⋊Dic13—21no—
79#6105—22no—
80C4⋊Dic13—21no—
81C4⋊Dic13—21no—
82C4⋊Dic13—21no—
83C4⋊Dic13D411yescharacteristic
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#6101—21no—
95#6101—21no—
96#6101D411yescharacteristic
97#6101D411yescharacteristic
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13—21no—
101C4×Dic13C2311yescharacteristic
102C4×Dic13C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105#3372—131nomaximal, Sylow
106C23×C13—21no—
107Q8×C13—21no—
108Q8×C13—21no—
109Q8×C13—21no—
110Q8×C13—21no—
111D4×C13—21no—
112D4×C13#4112yes—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—81no—
117C2×C4×C13C2×D411yescharacteristic
118C2×C4×C13C2×D411yescharacteristic
119C2×C4×C13C2411yescharacteristic
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—42no—
125C2×Dic13—81no—
126C2×Dic13C2×D411yescharacteristic
127C2×Dic13C2×D411yescharacteristic
128C2×Dic13C2×D411yescharacteristic
129C2×Dic13C2×D411yescharacteristic
130Dic26—22no—
131Dic26—21no—
132Dic26—21no—
133Dic26—81no—
134C8×C13—21no—
135C8×C13—21no—
136#1055—21no—
137#1055—21no—
138#557—131no—
139#554—131no—
140#491—131no—
141#491—131no—
142#487—131no—
143#479—131no—
144#479—131no—
145#477—131no—
146#461—131no—
147#461—131no—
148#461D1311yescharacteristic
149#446—131no—
150#440—131no—
151#440—131no—
152C4×SD16—131no—
153C22×C13—22no—
154C22×C13—41no—
155C22×C13—41no—
156C22×C13C22×D411yescharacteristic
157C4×C13—21no—
158C4×C13—21no—
159C4×C13—41no—
160C4×C13—41no—
161C4×C13—41no—
162C4×C13C2×#4111yescharacteristic
163C4×C132−1+411yescharacteristic
164Dic13—21no—
165Dic13—21no—
166Dic13—21no—
167Dic13—41no—
168Dic13—41no—
169Dic13—41no—
170Dic13—41no—
171Dic13#13712yes—
172C2×SD16—131no—
173C2×SD16C2×D1311yescharacteristic
174C2×SD16C2×D1311yescharacteristic
175C4⋊Q8—131no—
176C4⋊Q8—131no—
177C4⋊Q8—131no—
178C4⋊Q8C2×D1311yescharacteristic
179#125—131no—
180#125—131no—
181#125—261no—
182#125—261no—
183#125—261no—
184C22⋊Q8—261no—
185C22⋊Q8—261no—
186C22⋊Q8—261no—
187C4×Q8—131no—
188C4×Q8—131no—
189C4×Q8—131no—
190C4×Q8—131no—
191C4×Q8—261no—
192C4×D4—131no—
193C4×D4—131no—
194C4×D4C2×D1311yescharacteristic
195C2×C4⋊C4—261no—
196#107—131no—
197#107—131no—
198#106—131no—
199C4⋊C8—131no—
200C4⋊C8—131no—
201C4⋊C8C2×D1311yescharacteristic
202#103—131no—
203#103—131no—
204#103—131no—
205#103—131no—
206#103—131no—
207#103—131no—
208#103—131no—
209#103C2×D1311yescharacteristic
210#103C2×D1311yescharacteristic
211#102—131no—
212#97—131no—
213#97—131no—
214C4×C8—131no—
215C2×C13—42no—
216C2×C13#54811yescharacteristic
217C2×C13C2×#13711yescharacteristic
218C2×C13#57711yescharacteristic
219C2×Q8—131no—
220C2×Q8—131no—
221C2×Q8—261no—
222C2×Q8C22×D1311yescharacteristic
223C2×Q8C22×D1311yescharacteristic
224C2×D4C22×D1311yescharacteristic
225C22×C4—21no—
226C22×C4—261no—
227C22×C4—261no—
228SD16—22no—
229SD16—22no—
230SD16—262no—
231C2×C8—131no—
232C2×C8—131no—
233C2×C8C22×D1311yescharacteristic
234C2×C8C22×D1311yescharacteristic
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—131no—
238C4⋊C4—131no—
239C4⋊C4—131no—
240C4⋊C4—131no—
241C4⋊C4—131no—
242C4⋊C4—131no—
243C4⋊C4—261no—
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⋊C4—261no—
255C4⋊C4C22×D1311yescharacteristic
256C22⋊C4—21no—
257C22⋊C4—261no—
258C22⋊C4—261no—
259C42—131no—
260C42—131no—
261C42—261no—
262C42—261no—
263C42—261no—
264C42C22×D1311yescharacteristic
265C13#337211yescharacteristic, complemented, Sylow
266C23—21no—
267Q8—21no—
268Q8—21no—
269Q8—21no—
270Q8—21no—
271Q8—262no—
272Q8—261no—
273Q8—261no—
274Q8—1041no—
275D4—21no—
276D4#612912yes—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—81no—
281C2×C4—131no—
282C2×C4—131no—
283C2×C4—131no—
284C2×C4—131no—
285C2×C4—261no—
286C2×C4—261no—
287C2×C4—261no—
288C2×C4—261no—
289C2×C4—522no—
290C2×C4—1041no—
291C2×C4D4×D1311yescharacteristic
292C2×C4D4×D1311yescharacteristic
293C2×C4C23×D1311yescharacteristic
294C8—21no—
295C8—21no—
296C8—261no—
297C8—261no—
298C22—22no—
299C22—41no—
300C22—41no—
301C22C2×D4×D1311yescharacteristic
302C4—21no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—132no—
308C4—261no—
309C4—261no—
310C4—261no—
311C4—521no—
312C4—521no—
313C4—521no—
314C4—521no—
315C4C2×#612911yescharacteristic
316C4#8825711yescharacteristic
317C2—42no—
318C2#1171930311yescharacteristic
319C2#1171946711yescharacteristic
320C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#461C2
socleC22×C13C22×D4
prime radicalC2×D4×C13C23
hypercenter#461D13
hypocenterC13#3372
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #11719426C2semidirect
8. #11718743C2semidirect
10. #11718490C2semidirect
11. #11718489C2semidirect
12. #11718460C2semidirect
13. #11718458C2semidirect
14. #11718455C2semidirect
15. #11718453C2semidirect
265. C13#3372semidirect

Maximal subgroups

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

subgroupindex
#117194262
#117192442
C13×#4612
#117188252
#117188232
SD16×Dic132
#117187432
#117186792
#117184902
#117184892
#117184602
#117184582
#117184552
#117184532
#337213