Finite Group Databasebeta

← #13126476

Subgroups — #13126476

Order 1664.

472 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#137C211yesmaximal, characteristic, complemented
2#11719529C211yesmaximal, characteristic
3Q8×C22⋊D13C211yesmaximal, characteristic, complemented
4C2×#88169C211yesmaximal, characteristic, complemented
5#11718900C211yesmaximal, characteristic, complemented
6#11718889C211yesmaximal, characteristic, complemented
7#11718850C211yesmaximal, characteristic, complemented
8#11718847C211yesmaximal, characteristic, complemented
9#11718843C211yesmaximal, characteristic, complemented
10#11718842C211yesmaximal, characteristic, complemented
11#11718834C211yesmaximal, characteristic, complemented
12#11718823C211yesmaximal, characteristic, complemented
13SD16×Dic13C211yesmaximal, characteristic, complemented
14#11718798C211yesmaximal, characteristic, complemented
15#11718789C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C22×Q8×C13C2211yescharacteristic
18C2×Q8×D13C2211yescharacteristic
19C2×#6129C2211yescharacteristic
20C13×#137—24no—
21C2×C13×Q16C2211yescharacteristic
22C2×C13×Q16C2211yescharacteristic
23C2×C13×SD16C2211yescharacteristic
24C2×C13×SD16C2211yescharacteristic
25C2×C13×M16C2211yescharacteristic
26#88200—21no—
27#88200C2211yescharacteristic
28#88200C2211yescharacteristic
29Q8×Dic13C2211yescharacteristic
30#88198—21no—
31#88198C2211yescharacteristic
32#88198C2211yescharacteristic
33C2×#6107C2211yescharacteristic
34C2×#6107C2211yescharacteristic
35C2×#6107C2211yescharacteristic
36#88193—21no—
37#88189—21no—
38D4×Dic13C2211yescharacteristic
39C2×#6105C2211yescharacteristic
40#88183—21no—
41C4×C22⋊D13—21no—
42C4×C22⋊D13C2211yescharacteristic
43#88178—21no—
44#88178C2211yescharacteristic
45#88178C2211yescharacteristic
46C2×#6101—21no—
47#88169—24no—
48C2×Dic52C2211yescharacteristic
49C2×#6094C2211yescharacteristic
50#88075C2211yescharacteristic
51#88075C2211yescharacteristic
52#88075C2211yescharacteristic
53#88072C2211yescharacteristic
54C22⋊#1055C2211yescharacteristic
55#88060C2211yescharacteristic
56#88057C2211yescharacteristic
57#88056C2211yescharacteristic
58#88056C2211yescharacteristic
59#88054C2211yescharacteristic
60C8×Dic13C2211yescharacteristic
61C13×#41—22no—
62C13×#41—41no—
63C2×Q8×C13—21no—
64C2×Q8×C13—22no—
65C2×Q8×C13—41no—
66C2×Q8×C13C2311yescharacteristic
67C2×Q8×C13C2311yescharacteristic
68C2×Q8×C13C2311yescharacteristic
69C2×D4×C13—21no—
70C2×D4×C13C2311yescharacteristic
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13C2311yescharacteristic
74C2×C22⋊D13—21no—
75C2×C22⋊D13D411yescharacteristic
76C22×Dic13—21no—
77C22×Dic13—21no—
78Q8×D13—22no—
79Q8×D13—41no—
80#6129—22no—
81#6129—41no—
82C2×C4×D13—21no—
83C2×C4×D13C2311yescharacteristic
84C2×Dic26—21no—
85C2×Dic26C2311yescharacteristic
86C2×Dic26C2311yescharacteristic
87C13×Q16—22no—
88C13×Q16—22no—
89C13×SD16—22no—
90C13×SD16D414yescomplemented
91C13×M16—22no—
92C2×C8×C13C2311yescharacteristic
93C2×C8×C13C2311yescharacteristic
94C22⋊Dic13—21no—
95C22⋊Dic13—21no—
96C22⋊Dic13—21no—
97C22⋊Dic13D411yescharacteristic
98#6107—22no—
99#6107—41no—
100#6107—41no—
101#6105—22no—
102#6103—21no—
103#6103—21no—
104#6103D411yescharacteristic
105C4⋊Dic13—21no—
106C4⋊Dic13C2311yescharacteristic
107C4⋊Dic13C2311yescharacteristic
108#6101—21no—
109#6101—21no—
110#6101—21no—
111#6101—21no—
112#6101—21no—
113#6101—21no—
114#6101—21no—
115#6101—21no—
116#6101D411yescharacteristic
117C4×Dic13—21no—
118C4×Dic13C2311yescharacteristic
119C2×#1055C2311yescharacteristic
120C2×#1055C2311yescharacteristic
121Dic52—22no—
122#6094—22no—
123#3276—131nomaximal, Sylow
124C23×C13—21no—
125C23×C13C2×D411yescharacteristic
126C22×D13C2×D411yescharacteristic
127Q8×C13—21no—
128Q8×C13—21no—
129Q8×C13—21no—
130Q8×C13—21no—
131Q8×C13—21no—
132Q8×C13—42no—
133Q8×C13C2×D412yes—
134D4×C13—21no—
135D4×C13—42no—
136D4×C13C2×D412yes—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—42no—
143C2×C4×C13—42no—
144C2×C4×C13C2×D411yescharacteristic
145C2×C4×C13C2411yescharacteristic
146C22⋊D13—22no—
147C22⋊D13—42no—
148C2×Dic13—21no—
149C2×Dic13—21no—
150C2×Dic13—21no—
151C2×Dic13—21no—
152C2×Dic13—42no—
153C2×Dic13—42no—
154C2×Dic13C2×D411yescharacteristic
155C2×Dic13C2×D411yescharacteristic
156C2×Dic13C2×D411yescharacteristic
157C4×D13—21no—
158C4×D13—21no—
159C4×D13—42no—
160Dic26—21no—
161Dic26—21no—
162Dic26—21no—
163Dic26—21no—
164Dic26—42no—
165C8×C13—21no—
166C8×C13C2×D412yes—
167#1055—21no—
168#1055—21no—
169C2×#137—131no—
170C2×#137D1311yescharacteristic, complemented
171D4×Q8—131no—
172#547—131no—
173#494—131no—
174#470—131no—
175#470—131no—
176#462—131no—
177#461—131no—
178#452—131no—
179#452—131no—
180#451—131no—
181#451—131no—
182C4×SD16—131no—
183#436—131no—
184C22×C13—22no—
185C22×C13—21no—
186C22×C13—21no—
187C22×C13—21no—
188C22×C13—41no—
189C22×C13—41no—
190C22×C13C22×D411yescharacteristic
191C2×D13—21no—
192C2×D13—21no—
193C2×D13—21no—
194C4×C13—22no—
195C4×C13—21no—
196C4×C13—41no—
197C4×C13—41no—
198C4×C13C22×D411yescharacteristic
199C4×C13H(5,𝔽2)11yescharacteristic
200Dic13—21no—
201Dic13—21no—
202Dic13—41no—
203Dic13—41no—
204Dic13—41no—
205Dic13—41no—
206Dic13#13712yescomplemented
207C2×#41—131no—
208C2×#41C2×D1311yescharacteristic
209C22×Q8—131no—
210C22×Q8C2×D1311yescharacteristic
211#137—24no—
212#137—264no—
213C2×Q16—131no—
214C2×Q16—131no—
215C2×Q16—131no—
216C2×Q16—131no—
217C2×Q16C2×D1311yescharacteristic
218C2×Q16C2×D1311yescharacteristic
219C2×SD16—131no—
220C2×SD16C2×D1311yescharacteristic
221C2×SD16C2×D1311yescharacteristic
222C2×M16—131no—
223C2×M16C2×D1311yescharacteristic
224C4⋊Q8—131no—
225C4⋊Q8—131no—
226C4⋊Q8—261no—
227#123—261no—
228#123—261no—
229C22⋊Q8—131no—
230C22⋊Q8—131no—
231C22⋊Q8—131no—
232C22⋊Q8—131no—
233C22⋊Q8—261no—
234C22⋊Q8—261no—
235#121—261no—
236C4×Q8—131no—
237C4×D4—131no—
238C4×D4—131no—
239C4×D4—261no—
240C2×C4⋊C4—261no—
241#106—131no—
242C4⋊C8—131no—
243#103—131no—
244#103—131no—
245#103—131no—
246#103—131no—
247#103—131no—
248#102—131no—
249C22⋊C8—131no—
250C22⋊C8—131no—
251C4×C8—131no—
252C2×C13—41no—
253C2×C13—42no—
254C2×C13D4211yescharacteristic
255C2×C13C2×#13711yescharacteristic
256C2×C13#57811yescharacteristic
257D13—41no—
258#41—22no—
259#41—41no—
260#41—262no—
261#41—521no—
262C2×Q8—21no—
263C2×Q8—22no—
264C2×Q8—41no—
265C2×Q8—131no—
266C2×Q8—131no—
267C2×Q8—261no—
268C2×Q8—262no—
269C2×Q8—521no—
270C2×Q8C22×D1311yescharacteristic
271C2×Q8C22×D1311yescharacteristic
272C2×Q8C22×D1311yescharacteristic
273C2×D4—21no—
274C2×D4—131no—
275C2×D4—261no—
276C2×D4C22×D1311yescharacteristic
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—131no—
280C22×C4—261no—
281C22×C4—261no—
282C22×C4—261no—
283C22×C4C22×D1311yescharacteristic
284Q16—22no—
285Q16—22no—
286Q16—262no—
287Q16—262no—
288Q16—521no—
289Q16—521no—
290SD16—22no—
291SD16—262no—
292SD16C22⋊D1314yescomplemented
293M16—22no—
294M16—262no—
295C2×C8—131no—
296C2×C8—131no—
297C2×C8C22×D1311yescharacteristic
298C2×C8C22×D1311yescharacteristic
299C4⋊C4—131no—
300C4⋊C4—131no—
301C4⋊C4—131no—
302C4⋊C4—261no—
303C4⋊C4—261no—
304C4⋊C4—261no—
305C4⋊C4—261no—
306C4⋊C4—261no—
307C4⋊C4—261no—
308C4⋊C4—261no—
309C4⋊C4—261no—
310C4⋊C4—261no—
311C22⋊C4—131no—
312C22⋊C4—131no—
313C22⋊C4—261no—
314C22⋊C4—261no—
315C22⋊C4—261no—
316C22⋊C4—261no—
317C22⋊C4—261no—
318C42—131no—
319C42—261no—
320C13#327611yescharacteristic, complemented, Sylow
321C23—21no—
322C23—131no—
323C23D4×D1311yescharacteristic
324Q8—21no—
325Q8—21no—
326Q8—21no—
327Q8—21no—
328Q8—21no—
329Q8—42no—
330Q8—261no—
331Q8—261no—
332Q8—261no—
333Q8—261no—
334Q8—522no—
335Q8C2×C22⋊D1312yes—
336D4—21no—
337D4—42no—
338D4—262no—
339D4—522no—
340D4C2×C22⋊D1312yes—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—131no—
349C2×C4—131no—
350C2×C4—131no—
351C2×C4—261no—
352C2×C4—261no—
353C2×C4—261no—
354C2×C4—261no—
355C2×C4—261no—
356C2×C4—261no—
357C2×C4—522no—
358C2×C4—522no—
359C2×C4—522no—
360C2×C4D4×D1311yescharacteristic
361C2×C4C23×D1311yescharacteristic
362C8—21no—
363C8—261no—
364C8—261no—
365C8C2×C22⋊D1312yes—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—22no—
370C22—41no—
371C22—41no—
372C22—261no—
373C22—261no—
374C22—261no—
375C22C2×D4×D1311yescharacteristic
376C4—21no—
377C4—22no—
378C4—41no—
379C4—41no—
380C4—132no—
381C4—261no—
382C4—261no—
383C4—521no—
384C4—521no—
385C4—521no—
386C4—521no—
387C4#8825111yescharacteristic
388C4C22×C22⋊D1311yescharacteristic
389C2—41no—
390C2—42no—
391C2—521no—
392C2D13×#13711yescharacteristic
393C2#1171948411yescharacteristic
394C2D4×C22⋊D1311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC2×C13×#137C2
socleC22×C13C22×D4
prime radical#11719529C2
hypercenterC2×#137D13
hypocenterC13#3276
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×C13×#137C2semidirect
3. Q8×C22⋊D13C2semidirect
4. C2×#88169C2semidirect
5. #11718900C2semidirect
6. #11718889C2semidirect
7. #11718850C2semidirect
8. #11718847C2semidirect
9. #11718843C2semidirect
10. #11718842C2semidirect
11. #11718834C2semidirect
12. #11718823C2semidirect
13. SD16×Dic13C2semidirect
14. #11718798C2semidirect
15. #11718789C2semidirect
90. C13×SD16D4semidirect
170. C2×#137D13semidirect
206. Dic13#137semidirect
292. SD16C22⋊D13semidirect
320. C13#3276semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1372
#117195292
Q8×C22⋊D132
C2×#881692
#117189002
#117188892
#117188502
#117188472
#117188432
#117188422
#117188342
#117188232
SD16×Dic132
#117187982
#117187892
#327613