Finite Group Databasebeta

← #13125028

Subgroups — #13125028

Order 1664.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719532C211yesmaximal, characteristic, complemented
2#11719324C211yesmaximal, characteristic, complemented
3C13×#449C211yesmaximal, characteristic, complemented
4#11718899C211yesmaximal, characteristic, complemented
5#11718825C211yesmaximal, characteristic, complemented
6#11718824C211yesmaximal, characteristic, complemented
7#11718811C211yesmaximal, characteristic, complemented
8D8×Dic13C211yesmaximal, characteristic, complemented
9#11718695C211yesmaximal, characteristic, complemented
10#11718457C211yesmaximal, characteristic, complemented
11#11718449C211yesmaximal, characteristic, complemented
12#11718446C211yesmaximal, characteristic, complemented
13#11718427C211yesmaximal, characteristic, complemented
14#11718397C211yesmaximal, characteristic, complemented
15#11718381C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C2×C13×SD16C2211yescharacteristic
18C2×C13×D8C2211yescharacteristic
19C13×#121C2211yescharacteristic
20Q8×Dic13C2211yescharacteristic
21Q8×Dic13C2211yescharacteristic
22C2×#6106C2211yescharacteristic
23#88194C2211yescharacteristic
24#88193—21no—
25#88192—21no—
26D4×Dic13—21no—
27D4×Dic13—21no—
28D4×Dic13C2211yescharacteristic
29D4×Dic13C2211yescharacteristic
30D4×Dic13C2211yescharacteristic
31C2×#6104C2211yescharacteristic
32#88184C2211yescharacteristic
33#88180—21no—
34#88180C2211yescharacteristic
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13C2211yescharacteristic
37#88147C2211yescharacteristic
38#88144C2211yescharacteristic
39#88140—21no—
40#88137—21no—
41C13×#103C2211yescharacteristic
42C13×#102C2211yescharacteristic
43C13×C22⋊C8C2211yescharacteristic
44#88075C2211yescharacteristic
45#88072C2211yescharacteristic
46#88072C2211yescharacteristic
47#88072C2211yescharacteristic
48C22⋊#1055C2211yescharacteristic
49#88061C2211yescharacteristic
50#88061C2211yescharacteristic
51#88058C2211yescharacteristic
52#88058C2211yescharacteristic
53#88055C2211yescharacteristic
54#88054C2211yescharacteristic
55#88054C2211yescharacteristic
56C8×Dic13C2211yescharacteristic
57#88048C2211yescharacteristic
58#88048C2211yescharacteristic
59C13×#41—22no—
60C13×#41—22no—
61C2×Q8×C13C2311yescharacteristic
62C2×D4×C13—21no—
63C2×D4×C13—21no—
64C2×D4×C13C2311yescharacteristic
65C2×D4×C13C2311yescharacteristic
66C22×C4×C13—21no—
67C22×C4×C13C2311yescharacteristic
68C2×C22⋊D13—21no—
69C2×C22⋊D13—21no—
70C2×C22⋊D13—21no—
71C22×Dic13—21no—
72C22×Dic13—21no—
73C22×Dic13—21no—
74C22×Dic13—21no—
75C2×D52C2311yescharacteristic
76C2×C4×D13—21no—
77C13×SD16—22no—
78C13×D8—22no—
79C2×C8×C13C2311yescharacteristic
80C2×C8×C13C2311yescharacteristic
81C13×C4⋊C4C2311yescharacteristic
82C13×C22⋊C4—21no—
83C22⋊Dic13—21no—
84C22⋊Dic13—21no—
85C22⋊Dic13—21no—
86C22⋊Dic13D411yescharacteristic
87C22⋊Dic13D411yescharacteristic
88#6106—22no—
89#6104—22no—
90#6103—21no—
91#6103—21no—
92C4⋊Dic13—21no—
93C4⋊Dic13—21no—
94C4⋊Dic13—21no—
95C4⋊Dic13—21no—
96C4⋊Dic13D411yescharacteristic
97C4⋊Dic13D411yescharacteristic
98C4⋊Dic13C2311yescharacteristic
99C4⋊Dic13C2311yescharacteristic
100C4⋊Dic13C2311yescharacteristic
101#6101—21no—
102C4×Dic13—21no—
103C4×Dic13—21no—
104C4×Dic13C2311yescharacteristic
105C4×Dic13C2311yescharacteristic
106C2×#1055C2311yescharacteristic
107C2×#1055C2311yescharacteristic
108#3119—131nomaximal, Sylow
109C23×C13—21no—
110C23×C13—21no—
111C23×C13C2×D411yescharacteristic
112C22×D13—21no—
113Q8×C13—21no—
114Q8×C13#4112yes—
115D4×C13—24no—
116D4×C13—21no—
117D4×C13—21no—
118D4×C13—21no—
119D4×C13—81no—
120D4×C13#4112yes—
121C2×C4×C13—24no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13C2×D411yescharacteristic
127C2×C4×C13C2411yescharacteristic
128C22⋊D13—81no—
129C22⋊D13—81no—
130C22⋊D13—81no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—81no—
135C2×Dic13—81no—
136C2×Dic13—81no—
137C2×Dic13—81no—
138C2×Dic13C2×D411yescharacteristic
139C2×Dic13C2×D411yescharacteristic
140C2×Dic13C2×D411yescharacteristic
141C2×Dic13C2×D411yescharacteristic
142D52—21no—
143D52—21no—
144C4×D13—81no—
145C8×C13—21no—
146C8×C13—21no—
147#1055—21no—
148#1055—21no—
149#540—131no—
150#520—131no—
151#481—131no—
152#480—131no—
153#479—131no—
154#478—131no—
155#460—131no—
156#459—131no—
157#449—131no—
158#449D1311yescharacteristic, complemented
159#442—131no—
160#440—131no—
161C4×SD16—131no—
162C4×D8—131no—
163#433—131no—
164C22×C13—21no—
165C22×C13—22no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13—41no—
169C22×C13—41no—
170C22×C13—41no—
171C22×C13—41no—
172C22×C13—41no—
173C22×C13C22×D411yescharacteristic
174C2×D13—41no—
175C2×D13—41no—
176C2×D13—41no—
177C4×C13—21no—
178C4×C13—22no—
179C4×C13—41no—
180C4×C13C2×#4111yescharacteristic
181C4×C13C2×#4111yescharacteristic
182Dic13—21no—
183Dic13—21no—
184Dic13—21no—
185Dic13—21no—
186Dic13—41no—
187Dic13—41no—
188Dic13—41no—
189C2×#41C2×D1311yescharacteristic
190C2×SD16—131no—
191C2×SD16C2×D1311yescharacteristic
192C2×D8—131no—
193C2×D8C2×D1311yescharacteristic
194#127—131no—
195#125—131no—
196#123—261no—
197#123—261no—
198#121—131no—
199#121—261no—
200#121—261no—
201#121C2×D1311yescharacteristic
202C4×Q8—131no—
203C4×Q8—131no—
204C4×D4—131no—
205C4×D4—131no—
206C4×D4—131no—
207C4×D4—131no—
208C4×D4—261no—
209C4×D4—261no—
210#117—131no—
211#117—261no—
212C2×C4⋊C4—131no—
213C2×C4⋊C4—261no—
214#107—131no—
215#107—131no—
216#106—131no—
217#106—131no—
218C4⋊C8—131no—
219C4⋊C8—131no—
220#103—131no—
221#103C2×D1311yescharacteristic
222#102—131no—
223#102—131no—
224#102—131no—
225#102—131no—
226#102—131no—
227#102C2×D1311yescharacteristic
228C22⋊C8—131no—
229C22⋊C8C2×D1311yescharacteristic
230#97—131no—
231C4×C8—131no—
232C2×C13—41no—
233C2×C13—42no—
234C2×C13—81no—
235C2×C13#52511yescharacteristic
236C2×C13#57611yescharacteristic
237C2×C13#57711yescharacteristic
238D13—81no—
239#41—22no—
240#41—22no—
241C2×Q8C22×D1311yescharacteristic
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—131no—
245C2×D4—261no—
246C2×D4—261no—
247C2×D4—261no—
248C2×D4C22×D1311yescharacteristic
249C2×D4C22×D1311yescharacteristic
250C22×C4—21no—
251C22×C4—261no—
252C22×C4—261no—
253C22×C4—261no—
254C22×C4—261no—
255C22×C4—261no—
256C22×C4C22×D1311yescharacteristic
257SD16—22no—
258SD16—262no—
259D8—22no—
260D8—262no—
261C2×C8—131no—
262C2×C8—131no—
263C2×C8C22×D1311yescharacteristic
264C2×C8C22×D1311yescharacteristic
265C4⋊C4—131no—
266C4⋊C4—131no—
267C4⋊C4—131no—
268C4⋊C4—131no—
269C4⋊C4—131no—
270C4⋊C4—261no—
271C4⋊C4—261no—
272C4⋊C4—261no—
273C4⋊C4—261no—
274C4⋊C4—261no—
275C4⋊C4C22×D1311yescharacteristic
276C22⋊C4—21no—
277C22⋊C4—131no—
278C22⋊C4—131no—
279C22⋊C4—261no—
280C22⋊C4—261no—
281C22⋊C4—261no—
282C22⋊C4—261no—
283C22⋊C4—261no—
284C42—131no—
285C42—131no—
286C42—261no—
287C42—261no—
288C13#311911yescharacteristic, complemented, Sylow
289C23—21no—
290C23—21no—
291C23—261no—
292C23D4×D1311yescharacteristic
293Q8—21no—
294Q8#612912yes—
295D4—24no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—261no—
301D4—261no—
302D4—1041no—
303D4—1041no—
304D4—1041no—
305D4#612912yes—
306C2×C4—24no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—131no—
312C2×C4—131no—
313C2×C4—131no—
314C2×C4—131no—
315C2×C4—261no—
316C2×C4—261no—
317C2×C4—261no—
318C2×C4—1041no—
319C2×C4—1041no—
320C2×C4—1041no—
321C2×C4—1041no—
322C2×C4—1041no—
323C2×C4D4×D1311yescharacteristic
324C2×C4C23×D1311yescharacteristic
325C8—21no—
326C8—21no—
327C8—261no—
328C8—261no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—22no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—521no—
339C22—521no—
340C22—521no—
341C22C2×D4×D1311yescharacteristic
342C4—21no—
343C4—22no—
344C4—41no—
345C4—261no—
346C4—261no—
347C4—261no—
348C4—261no—
349C4—521no—
350C4—521no—
351C4—521no—
352C4C2×#612911yescharacteristic
353C4C2×#612911yescharacteristic
354C2—41no—
355C2—42no—
356C2—81no—
357C2—1041no—
358C2#1171929111yescharacteristic
359C2#1171947411yescharacteristic
360C2#1171948011yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#449C2
socleC22×C13C22×D4
hypercenter#449D13
hypocenterC13#3119
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #11719532C2semidirect
2. #11719324C2semidirect
3. C13×#449C2semidirect
4. #11718899C2semidirect
5. #11718825C2semidirect
6. #11718824C2semidirect
7. #11718811C2semidirect
8. D8×Dic13C2semidirect
9. #11718695C2semidirect
10. #11718457C2semidirect
11. #11718449C2semidirect
12. #11718446C2semidirect
13. #11718427C2semidirect
14. #11718397C2semidirect
15. #11718381C2semidirect
158. #449D13semidirect
288. C13#3119semidirect

Maximal subgroups

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

subgroupindex
#117195322
#117193242
C13×#4492
#117188992
#117188252
#117188242
#117188112
D8×Dic132
#117186952
#117184572
#117184492
#117184462
#117184272
#117183972
#117183812
#311913