Finite Group Databasebeta

← #13127593

Subgroups — #13127593

Order 1664.

358 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719386C211yesmaximal, characteristic, complemented
2#11719244C211yesmaximal, characteristic, complemented
3C13×#463C211yesmaximal, characteristic, complemented
4#11718826C211yesmaximal, characteristic, complemented
5#11718825C211yesmaximal, characteristic, complemented
6#11718813C211yesmaximal, characteristic, complemented
7#11718811C211yesmaximal, characteristic
8#11718717C211yesmaximal, characteristic, complemented
9C4×#6104C211yesmaximal, characteristic, complemented
10#11718508C211yesmaximal, characteristic, complemented
11#11718492C211yesmaximal, characteristic, complemented
12#11718460C211yesmaximal, characteristic, complemented
13#11718456C211yesmaximal, characteristic, complemented
14#11718425C211yesmaximal, characteristic, complemented
15#11718420C211yesmaximal, characteristic, complemented
16C2×C13×SD16C2211yescharacteristic
17C2×C13×D8C2211yescharacteristic
18C13×#124C2211yescharacteristic
19C4×D4×C13C2211yescharacteristic
20#88201C2211yescharacteristic
21Q8×Dic13C2211yescharacteristic
22#88194C2211yescharacteristic
23D4×Dic13C2211yescharacteristic
24D4×Dic13C2211yescharacteristic
25D4×Dic13C2211yescharacteristic
26C2×#6104C2211yescharacteristic
27#88178—21no—
28C2×#6101—21no—
29#88144C2211yescharacteristic
30#88142C2211yescharacteristic
31#88140—21no—
32#88139—21no—
33#88137—21no—
34#88135—21no—
35#88132—21no—
36#88132—21no—
37C4×D52C2211yescharacteristic
38#88124C2211yescharacteristic
39C4×Dic26C2211yescharacteristic
40C13×C4⋊C8C2211yescharacteristic
41C13×#103C2211yescharacteristic
42C13×#102C2211yescharacteristic
43#88075C2211yescharacteristic
44#88075C2211yescharacteristic
45#88072C2211yescharacteristic
46#88072C2211yescharacteristic
47#88072C2211yescharacteristic
48#88061C2211yescharacteristic
49#88061C2211yescharacteristic
50#88058C2211yescharacteristic
51#88057C2211yescharacteristic
52#88055C2211yescharacteristic
53#88055C2211yescharacteristic
54#88054C2211yescharacteristic
55#88054C2211yescharacteristic
56#88049C2211yescharacteristic
57#88047C2211yescharacteristic
58C4×#1055C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×D4×C13C2311yescharacteristic
61C2×D4×C13C2311yescharacteristic
62C22×C4×C13—21no—
63C2×C22⋊D13—21no—
64C2×C22⋊D13—21no—
65C22×Dic13—21no—
66C22×Dic13—21no—
67C22×Dic13—21no—
68C2×D52C2311yescharacteristic
69C2×C4×D13—21no—
70C2×Dic26—21no—
71C2×Dic26D411yescharacteristic
72C13×SD16—22no—
73C13×D8—22no—
74C2×C8×C13C2311yescharacteristic
75C2×C8×C13C2311yescharacteristic
76C13×C4⋊C4C2311yescharacteristic
77C13×C22⋊C4—21no—
78C13×C22⋊C4—21no—
79C13×C22⋊C4—21no—
80C42×C13C2311yescharacteristic
81C22⋊Dic13—21no—
82C22⋊Dic13—21no—
83C22⋊Dic13—21no—
84#6104—22no—
85#6103—21no—
86#6103—21no—
87#6103—21no—
88C4⋊Dic13—21no—
89C4⋊Dic13—21no—
90C4⋊Dic13D411yescharacteristic
91C4⋊Dic13C2311yescharacteristic
92C4⋊Dic13C2311yescharacteristic
93C4⋊Dic13C2311yescharacteristic
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101—21no—
98#6101D411yescharacteristic
99#6101D411yescharacteristic
100C4×Dic13—21no—
101C4×Dic13C2311yescharacteristic
102C4×Dic13C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105#3370—131nomaximal, Sylow
106C23×C13—21no—
107C23×C13—21no—
108C22×D13—21no—
109Q8×C13—21no—
110Q8×C13—21no—
111D4×C13—21no—
112D4×C13—21no—
113D4×C13—21no—
114D4×C13#4112yes—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—81no—
118C2×C4×C13C2×D411yescharacteristic
119C2×C4×C13C2×D411yescharacteristic
120C2×C4×C13C2411yescharacteristic
121C22⋊D13—42no—
122C22⋊D13—81no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—42no—
127C2×Dic13—81no—
128C2×Dic13—81no—
129C2×Dic13C2×D411yescharacteristic
130C2×Dic13C2×D411yescharacteristic
131C2×Dic13C2×D411yescharacteristic
132C2×Dic13C2×D411yescharacteristic
133D52—21no—
134D52—21no—
135C4×D13—81no—
136Dic26—41no—
137Dic26—81no—
138C8×C13—21no—
139C8×C13—21no—
140#1055—21no—
141#1055—21no—
142#559—131no—
143#554—131no—
144#490—131no—
145#489—131no—
146#488—131no—
147#479—131no—
148#478—131no—
149#474—131no—
150#463—131no—
151#463D1311yescharacteristic, complemented
152#459—131no—
153#446—131no—
154#442—131no—
155#440—131no—
156C4×D8—131no—
157C22×C13—22no—
158C22×C13—41no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13C22×D411yescharacteristic
164C2×D13—41no—
165C2×D13—41no—
166C2×D13—41no—
167C4×C13—21no—
168C4×C13—21no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13C2×#4111yescharacteristic
172C4×C132−1+411yescharacteristic
173Dic13—21no—
174Dic13—21no—
175Dic13—21no—
176Dic13—21no—
177Dic13—41no—
178Dic13—41no—
179Dic13—41no—
180C2×SD16C2×D1311yescharacteristic
181C2×D8—131no—
182C2×D8C2×D1311yescharacteristic
183C4⋊Q8—131no—
184#127—131no—
185#125—131no—
186#125—131no—
187#124—131no—
188#124—261no—
189#124C2×D1311yescharacteristic
190#123—261no—
191#123—261no—
192C22⋊Q8—261no—
193C22⋊Q8—261no—
194C22⋊Q8—261no—
195C4×Q8—131no—
196C4×Q8—131no—
197C4×D4—131no—
198C4×D4—131no—
199C4×D4—131no—
200C4×D4—131no—
201C4×D4—261no—
202C4×D4C2×D1311yescharacteristic
203C2×C4⋊C4—261no—
204#107—131no—
205#107—131no—
206#106—131no—
207C4⋊C8—131no—
208C4⋊C8—131no—
209C4⋊C8C2×D1311yescharacteristic
210#103—131no—
211#103—131no—
212#103C2×D1311yescharacteristic
213#102—131no—
214#102—131no—
215#102—131no—
216#102—131no—
217#102—131no—
218#102—131no—
219#102C2×D1311yescharacteristic
220#97—131no—
221#97—131no—
222C4×C8—131no—
223C2×C13—42no—
224C2×C13—81no—
225C2×C13#54811yescharacteristic
226C2×C13#57511yescharacteristic
227C2×C13#57611yescharacteristic
228D13—81no—
229C2×Q8—131no—
230C2×Q8—261no—
231C2×Q8C22×D1311yescharacteristic
232C2×D4—131no—
233C2×D4—261no—
234C2×D4—261no—
235C2×D4C22×D1311yescharacteristic
236C2×D4C22×D1311yescharacteristic
237C22×C4—21no—
238C22×C4—261no—
239C22×C4—261no—
240C22×C4—261no—
241C22×C4—261no—
242SD16—22no—
243D8—22no—
244D8—262no—
245C2×C8—131no—
246C2×C8—131no—
247C2×C8C22×D1311yescharacteristic
248C2×C8C22×D1311yescharacteristic
249C4⋊C4—131no—
250C4⋊C4—131no—
251C4⋊C4—131no—
252C4⋊C4—131no—
253C4⋊C4—131no—
254C4⋊C4—131no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4—261no—
258C4⋊C4—261no—
259C4⋊C4—261no—
260C4⋊C4—261no—
261C4⋊C4C22×D1311yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—261no—
266C22⋊C4—261no—
267C22⋊C4—261no—
268C22⋊C4—261no—
269C22⋊C4—261no—
270C22⋊C4—261no—
271C42—131no—
272C42—131no—
273C42—261no—
274C42C22×D1311yescharacteristic
275C13#337011yescharacteristic, complemented, Sylow
276C23—21no—
277C23—21no—
278C23—261no—
279Q8—21no—
280Q8—21no—
281Q8—521no—
282Q8—1041no—
283D4—21no—
284D4—21no—
285D4—21no—
286D4—261no—
287D4—261no—
288D4—522no—
289D4—1041no—
290D4#612912yes—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—81no—
294C2×C4—131no—
295C2×C4—131no—
296C2×C4—131no—
297C2×C4—131no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4—522no—
302C2×C4—1041no—
303C2×C4—1041no—
304C2×C4—1041no—
305C2×C4D4×D1311yescharacteristic
306C2×C4D4×D1311yescharacteristic
307C2×C4C23×D1311yescharacteristic
308C8—21no—
309C8—21no—
310C8—261no—
311C8—261no—
312C22—22no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—521no—
319C22—521no—
320C22—521no—
321C22C2×D4×D1311yescharacteristic
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—261no—
327C4—261no—
328C4—261no—
329C4—261no—
330C4—521no—
331C4—521no—
332C4—521no—
333C4C2×#612911yescharacteristic
334C4#8825711yescharacteristic
335C2—42no—
336C2—81no—
337C2—1041no—
338C2#1171930311yescharacteristic
339C2#1171947311yescharacteristic
340C2#1171947911yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#463C2
socleC22×C13C22×D4
prime radical#11718811C2
hypercenter#463D13
hypocenterC13#3370
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #11719386C2semidirect
2. #11719244C2semidirect
3. C13×#463C2semidirect
4. #11718826C2semidirect
5. #11718825C2semidirect
6. #11718813C2semidirect
8. #11718717C2semidirect
9. C4×#6104C2semidirect
10. #11718508C2semidirect
11. #11718492C2semidirect
12. #11718460C2semidirect
13. #11718456C2semidirect
14. #11718425C2semidirect
15. #11718420C2semidirect
151. #463D13semidirect
275. C13#3370semidirect

Maximal subgroups

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

subgroupindex
#117193862
#117192442
C13×#4632
#117188262
#117188252
#117188132
#117188112
#117187172
C4×#61042
#117185082
#117184922
#117184602
#117184562
#117184252
#117184202
#337013