Finite Group Databasebeta

← #13127331

Subgroups — #13127331

Order 1664.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719323C211yesmaximal, characteristic, complemented
2#11719321C211yesmaximal, characteristic, complemented
3C13×#469C211yesmaximal, characteristic, complemented
4#11718818C211yesmaximal, characteristic, complemented
5#11718813C211yesmaximal, characteristic, complemented
6#11718788C211yesmaximal, characteristic, complemented
7#11718782C211yesmaximal, characteristic, complemented
8#11718696C211yesmaximal, characteristic, complemented
9#11718694C211yesmaximal, characteristic, complemented
10#11718521C211yesmaximal, characteristic, complemented
11#11718517C211yesmaximal, characteristic, complemented
12#11718445C211yesmaximal, characteristic, complemented
13#11718440C211yesmaximal, characteristic, complemented
14#11718424C211yesmaximal, characteristic, complemented
15#11718420C211yesmaximal, characteristic, complemented
16C2×C13×D8C2211yescharacteristic
17C2×C13×M16C2211yescharacteristic
18C13×#121C2211yescharacteristic
19C13×#121C2211yescharacteristic
20#88193—21no—
21#88193—21no—
22#88192C2211yescharacteristic
23#88192C2211yescharacteristic
24#88190—21no—
25D4×Dic13—21no—
26D4×Dic13C2211yescharacteristic
27D4×Dic13C2211yescharacteristic
28C4×C22⋊D13C2211yescharacteristic
29#88180C2211yescharacteristic
30C2×C4⋊Dic13C2211yescharacteristic
31C2×C8×D13C2211yescharacteristic
32#88146C2211yescharacteristic
33#88146C2211yescharacteristic
34#88144C2211yescharacteristic
35#88142C2211yescharacteristic
36#88140—21no—
37#88139—21no—
38#88133—21no—
39#88131—21no—
40C13×#106C2211yescharacteristic
41C13×#102C2211yescharacteristic
42C13×#102C2211yescharacteristic
43#88072C2211yescharacteristic
44#88072C2211yescharacteristic
45#88072C2211yescharacteristic
46#88072C2211yescharacteristic
47C22⋊#1055C2211yescharacteristic
48#88060C2211yescharacteristic
49#88058C2211yescharacteristic
50#88058C2211yescharacteristic
51#88057C2211yescharacteristic
52#88057C2211yescharacteristic
53#88055C2211yescharacteristic
54#88054C2211yescharacteristic
55#88048C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×D4×C13—21no—
60C2×D4×C13—21no—
61C2×D4×C13C2311yescharacteristic
62C2×D4×C13C2311yescharacteristic
63C22×C4×C13C2311yescharacteristic
64C2×C22⋊D13—21no—
65C2×C22⋊D13—21no—
66C2×C22⋊D13D411yescharacteristic
67C22×Dic13—21no—
68C22×Dic13—21no—
69C22×Dic13—21no—
70C2×C4×D13C2311yescharacteristic
71C2×Dic26—21no—
72C13×D8—22no—
73C13×M16—22no—
74C2×C8×C13C2311yescharacteristic
75C2×C8×C13C2311yescharacteristic
76C13×C4⋊C4C2311yescharacteristic
77C13×C4⋊C4C2311yescharacteristic
78C13×C22⋊C4—21no—
79C13×C22⋊C4—21no—
80C22⋊Dic13—21no—
81C22⋊Dic13—21no—
82C22⋊Dic13—21no—
83C22⋊Dic13—21no—
84C22⋊Dic13—21no—
85C22⋊Dic13D411yescharacteristic
86#6103—21no—
87#6103—21no—
88#6103D411yescharacteristic
89C4⋊Dic13—21no—
90C4⋊Dic13—21no—
91C4⋊Dic13C2311yescharacteristic
92C4⋊Dic13C2311yescharacteristic
93C4⋊Dic13C2311yescharacteristic
94C4⋊Dic13C2311yescharacteristic
95#6101—21no—
96#6101—21no—
97#6101D411yescharacteristic
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13—21no—
101C4×Dic13C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104C8×D13—22no—
105#3347—131nomaximal, Sylow
106C23×C13—21no—
107C23×C13—21no—
108C23×C13C2×D411yescharacteristic
109C22×D13C2×D411yescharacteristic
110D4×C13—21no—
111D4×C13—21no—
112D4×C13—21no—
113D4×C13—21no—
114D4×C13—42no—
115D4×C13—81no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13C2×D411yescharacteristic
121C2×C4×C13C2411yescharacteristic
122C22⋊D13—41no—
123C22⋊D13—81no—
124C22⋊D13—81no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—42no—
130C2×Dic13—81no—
131C2×Dic13—81no—
132C2×Dic13C2×D411yescharacteristic
133C2×Dic13C2×D411yescharacteristic
134C2×Dic13C2×D411yescharacteristic
135C4×D13—21no—
136C4×D13—21no—
137Dic26—81no—
138C8×C13—21no—
139C8×C13#4112yes—
140#1055—21no—
141#1055—21no—
142#555—131no—
143#553—131no—
144#501—131no—
145#482—131no—
146#482—131no—
147#482—131no—
148#480—131no—
149#478—131no—
150#474—131no—
151#469D1311yescharacteristic, complemented
152#466—131no—
153#442—131no—
154#435—131no—
155#428—131no—
156#427—131no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—21no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13—41no—
165C22×C13—41no—
166C22×C13C22×D411yescharacteristic
167C2×D13—21no—
168C2×D13—21no—
169C2×D13—21no—
170C4×C13—21no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13C2×#4111yescharacteristic
174C4×C132−1+411yescharacteristic
175Dic13—21no—
176Dic13—21no—
177Dic13—21no—
178Dic13—41no—
179Dic13—41no—
180Dic13—41no—
181Dic13—41no—
182C2×D8C2×D1311yescharacteristic
183C2×M16C2×D1311yescharacteristic
184C22×C8—131no—
185C4⋊Q8—131no—
186#126—261no—
187#125—131no—
188#124—261no—
189#124—261no—
190#123—261no—
191#121—131no—
192#121—131no—
193#121—261no—
194#121—261no—
195#121C2×D1311yescharacteristic
196#121C2×D1311yescharacteristic
197C4×D4—131no—
198C4×D4—131no—
199C4×D4—131no—
200C4×D4—261no—
201#117—131no—
202#117—131no—
203#117—131no—
204#117—261no—
205C2×C4⋊C4—131no—
206#107—131no—
207#107—131no—
208#107—131no—
209#107—131no—
210#107—131no—
211#106—131no—
212#106—131no—
213#106—131no—
214#106C2×D1311yescharacteristic
215C4⋊C8—131no—
216#102—131no—
217#102—131no—
218#102—131no—
219#102—131no—
220#102C2×D1311yescharacteristic
221#102C2×D1311yescharacteristic
222C22⋊C8—131no—
223C22⋊C8—131no—
224#97—131no—
225C2×C13—41no—
226C2×C13—81no—
227C2×C13—81no—
228C2×C13#54711yescharacteristic
229C2×C13#57511yescharacteristic
230C2×C13#57611yescharacteristic
231D13—41no—
232C2×Q8—261no—
233C2×D4—21no—
234C2×D4—21no—
235C2×D4—131no—
236C2×D4—261no—
237C2×D4—261no—
238C2×D4C22×D1311yescharacteristic
239C2×D4C22×D1311yescharacteristic
240C22×C4—131no—
241C22×C4—261no—
242C22×C4—261no—
243C22×C4—261no—
244C22×C4C22×D1311yescharacteristic
245D8—22no—
246M16—22no—
247C2×C8—131no—
248C2×C8—131no—
249C2×C8—262no—
250C2×C8C22×D1311yescharacteristic
251C2×C8C22×D1311yescharacteristic
252C4⋊C4—131no—
253C4⋊C4—131no—
254C4⋊C4—131no—
255C4⋊C4—131no—
256C4⋊C4—131no—
257C4⋊C4—261no—
258C4⋊C4—261no—
259C4⋊C4—261no—
260C4⋊C4—261no—
261C4⋊C4C22×D1311yescharacteristic
262C4⋊C4C22×D1311yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—131no—
266C22⋊C4—131no—
267C22⋊C4—261no—
268C22⋊C4—261no—
269C22⋊C4—261no—
270C22⋊C4—261no—
271C22⋊C4—261no—
272C22⋊C4—261no—
273C22⋊C4—261no—
274C42—131no—
275C42—261no—
276C42—261no—
277C42—261no—
278C13#334711yescharacteristic, complemented, Sylow
279C23—21no—
280C23—21no—
281C23—131no—
282C23D4×D1311yescharacteristic
283Q8—1041no—
284D4—21no—
285D4—21no—
286D4—21no—
287D4—21no—
288D4—42no—
289D4—81no—
290D4—521no—
291D4—1041no—
292D4—1041no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—131no—
298C2×C4—131no—
299C2×C4—131no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4—261no—
305C2×C4—261no—
306C2×C4—522no—
307C2×C4—1041no—
308C2×C4—1041no—
309C2×C4D4×D1311yescharacteristic
310C2×C4C23×D1311yescharacteristic
311C8—21no—
312C8—261no—
313C8—261no—
314C8#612912yes—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—261no—
325C22—261no—
326C22—261no—
327C22C2×D4×D1311yescharacteristic
328C4—21no—
329C4—41no—
330C4—41no—
331C4—261no—
332C4—261no—
333C4—261no—
334C4—521no—
335C4—521no—
336C4—521no—
337C4—521no—
338C4C2×#612911yescharacteristic
339C4#8825711yescharacteristic
340C2—41no—
341C2—81no—
342C2—81no—
343C2—521no—
344C2#1171931611yescharacteristic
345C2#1171947811yescharacteristic
346C2#1171947911yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#469C2
socleC22×C13C22×D4
hypercenter#469D13
hypocenterC13#3347
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #11719323C2semidirect
2. #11719321C2semidirect
3. C13×#469C2semidirect
4. #11718818C2semidirect
5. #11718813C2semidirect
6. #11718788C2semidirect
7. #11718782C2semidirect
8. #11718696C2semidirect
9. #11718694C2semidirect
10. #11718521C2semidirect
11. #11718517C2semidirect
12. #11718445C2semidirect
13. #11718440C2semidirect
14. #11718424C2semidirect
15. #11718420C2semidirect
151. #469D13semidirect
278. C13#3347semidirect

Maximal subgroups

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

subgroupindex
#117193232
#117193212
C13×#4692
#117188182
#117188132
#117187882
#117187822
#117186962
#117186942
#117185212
#117185172
#117184452
#117184402
#117184242
#117184202
#334713