Finite Group Databasebeta

← #13119155

Subgroups — #13119155

Order 1664.

546 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88200C211yesmaximal, characteristic, complemented
2C2×#88137C211yesmaximal, characteristic
3C13×#393C211yesmaximal, characteristic, complemented
4#11718891C211yesmaximal, characteristic, complemented
5#11718617C211yesmaximal, characteristic
6#11718617C211yesmaximal, characteristic
7#11718613C211yesmaximal, characteristic, complemented
8#11718612C211yesmaximal, characteristic, complemented
9#11718606C211yesmaximal, characteristic, complemented
10#11718327C211yesmaximal, characteristic, complemented
11#11718325C211yesmaximal, characteristic, complemented
12D13×#95C211yesmaximal, characteristic, complemented
13#11718321C211yesmaximal, characteristic, complemented
14#11718320C211yesmaximal, characteristic, complemented
15#11718311C211yesmaximal, characteristic, complemented
16C22×Q8×C13C2211yescharacteristic
17C22×C22⋊D13C2211yescharacteristic
18C22×C4×D13C2211yescharacteristic
19C22×C4×D13C2211yescharacteristic
20C22×C4×D13C2211yescharacteristic
21C2×C13×C22⋊C4C2211yescharacteristic
22C2×C13×C22⋊C4C2211yescharacteristic
23C2×C13×C22⋊C4C2211yescharacteristic
24C2×C22⋊Dic13C2211yescharacteristic
25C2×C22⋊Dic13C2211yescharacteristic
26C2×C22⋊Dic13C2211yescharacteristic
27#88200—24no—
28C2×#6103C2211yescharacteristic
29C2×#6103C2211yescharacteristic
30C2×#6103C2211yescharacteristic
31C2×C4⋊Dic13C2211yescharacteristic
32C2×C4⋊Dic13C2211yescharacteristic
33C2×#6101C2211yescharacteristic
34C2×#6101C2211yescharacteristic
35C2×#6101C2211yescharacteristic
36C2×C4×Dic13C2211yescharacteristic
37C2×C4×Dic13C2211yescharacteristic
38#88137—24no—
39C13×#95C2211yescharacteristic
40C13×#95C2211yescharacteristic
41C13×#95C2211yescharacteristic
42#88071C2211yescharacteristic
43#88071C2211yescharacteristic
44#88071C2211yescharacteristic
45#88071C2211yescharacteristic
46#88071C2211yescharacteristic
47#88071C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51#88071C2211yescharacteristic
52#88071C2211yescharacteristic
53C24×C13C2311yescharacteristic
54C23×D13C2311yescharacteristic
55C2×Q8×C13—22no—
56C2×Q8×C13—22no—
57C2×Q8×C13—41no—
58C22×C4×C13C2311yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C22×C4×C13C2311yescharacteristic
63C22×C4×C13C2311yescharacteristic
64C2×C22⋊D13—22no—
65C2×C22⋊D13—22no—
66C2×C22⋊D13—22no—
67C22×Dic13C2311yescharacteristic
68C22×Dic13C2311yescharacteristic
69C22×Dic13C2311yescharacteristic
70C22×Dic13C2311yescharacteristic
71C22×Dic13C2311yescharacteristic
72C22×Dic13C2311yescharacteristic
73C22×Dic13C2311yescharacteristic
74C2×C4×D13—22no—
75C2×C4×D13—22no—
76C2×C4×D13—22no—
77C2×C4×D13—22no—
78C2×C4×D13—22no—
79C2×C4×D13—22no—
80C2×C4×D13—22no—
81C2×C4×D13—41no—
82C2×C4×D13—41no—
83C13×C22⋊C4—22no—
84C13×C22⋊C4—22no—
85C13×C22⋊C4—41no—
86C22⋊Dic13—22no—
87C22⋊Dic13—22no—
88C22⋊Dic13—41no—
89#6103—22no—
90#6103—22no—
91#6103D414yes—
92C4⋊Dic13—22no—
93C4⋊Dic13—22no—
94#6101—22no—
95#6101—22no—
96#6101—22no—
97C4×Dic13—22no—
98C4×Dic13—41no—
99#2488—131nomaximal, Sylow
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13C2411yescharacteristic
108C22×D13—21no—
109C22×D13—21no—
110C22×D13—21no—
111C22×D13—21no—
112C22×D13C2×D412yes—
113C22×D13#4112yes—
114C22×D13#4112yes—
115Q8×C13—44no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13C2×D412yes—
133C2×C4×C13#4112yes—
134C22⋊D13—44no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143C2×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13—21no—
146C2×Dic13—21no—
147C2×Dic13—21no—
148C2×Dic13—21no—
149C2×Dic13—21no—
150C2×Dic13—21no—
151C2×Dic13—21no—
152C2×Dic13—21no—
153C2×Dic13—21no—
154C2×Dic13C2×D412yes—
155C2×Dic13#4112yes—
156C4×D13—44no—
157C4×D13—44no—
158C4×D13—44no—
159C2×#123—131no—
160C2×C22⋊Q8—131no—
161#400—131no—
162#400—131no—
163#397—131no—
164#393D1311yescharacteristic, complemented
165#391—131no—
166#388—131no—
167#388—131no—
168#386—131no—
169#386—131no—
170#382—131no—
171#381—131no—
172C4×C22⋊C4—131no—
173C2×#95—131no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13C22×D411yescharacteristic
182C22×C13C2×#4111yescharacteristic
183C22×C13C2×#4111yescharacteristic
184C22×C13C2×#4111yescharacteristic
185C22×C13C2×#4111yescharacteristic
186C22×C13H(5,𝔽2)11yescharacteristic
187C22×C132−1+411yescharacteristic
188C2×D13—22no—
189C2×D13—22no—
190C2×D13—22no—
191C2×D13—22no—
192C2×D13—22no—
193C2×D13—22no—
194C2×D13#12414yes—
195C4×C13—22no—
196C4×C13—22no—
197C4×C13—41no—
198C4×C13—41no—
199C4×C13—41no—
200C4×C13—41no—
201Dic13—22no—
202Dic13—22no—
203Dic13—41no—
204Dic13—41no—
205Dic13—41no—
206Dic13—41no—
207Dic13—41no—
208C22×Q8C2×D1311yescharacteristic
209C22×D4—131no—
210C23×C4—131no—
211C23×C4—131no—
212C23×C4—131no—
213#123—264no—
214C22⋊Q8—264no—
215C2×C4⋊C4—131no—
216C2×C4⋊C4—131no—
217C2×C4⋊C4—131no—
218C2×C4⋊C4—131no—
219C2×C4⋊C4—131no—
220C2×C22⋊C4—131no—
221C2×C22⋊C4—131no—
222C2×C22⋊C4—131no—
223C2×C22⋊C4—131no—
224C2×C22⋊C4—131no—
225C2×C22⋊C4—131no—
226C2×C22⋊C4C2×D1311yescharacteristic
227C2×C22⋊C4C2×D1311yescharacteristic
228C2×C22⋊C4C2×D1311yescharacteristic
229C2×C42—131no—
230C2×C42—131no—
231#95—131no—
232#95—131no—
233#95—131no—
234#95—131no—
235#95—131no—
236#95—131no—
237#95—131no—
238#95—131no—
239#95—131no—
240#95—131no—
241#95—131no—
242#95C2×D1311yescharacteristic
243#95C2×D1311yescharacteristic
244#95C2×D1311yescharacteristic
245C2×C13—81no—
246C2×C13C2×#12411yescharacteristic
247C2×C13#52911yescharacteristic
248C2×C13#53911yescharacteristic
249C2×C13#54611yescharacteristic
250C2×C13#54711yescharacteristic
251C2×C13#55111yescharacteristic
252C2×C13#55211yescharacteristic
253D13—24no—
254C24—131no—
255C24C22×D1311yescharacteristic
256C2×Q8—22no—
257C2×Q8—22no—
258C2×Q8—41no—
259C2×D4—262no—
260C2×D4—262no—
261C2×D4—262no—
262C22×C4—131no—
263C22×C4—131no—
264C22×C4—131no—
265C22×C4—131no—
266C22×C4—131no—
267C22×C4—131no—
268C22×C4—131no—
269C22×C4—262no—
270C22×C4—262no—
271C22×C4—262no—
272C22×C4—262no—
273C22×C4—262no—
274C22×C4—262no—
275C22×C4—262no—
276C22×C4—521no—
277C22×C4—521no—
278C22×C4C22×D1311yescharacteristic
279C22×C4C22×D1311yescharacteristic
280C22×C4C22×D1311yescharacteristic
281C22×C4C22×D1311yescharacteristic
282C22×C4C22×D1311yescharacteristic
283C22×C4C22×D1311yescharacteristic
284C4⋊C4—262no—
285C4⋊C4—262no—
286C4⋊C4—262no—
287C4⋊C4—262no—
288C4⋊C4—262no—
289C22⋊C4—22no—
290C22⋊C4—22no—
291C22⋊C4—41no—
292C22⋊C4—134no—
293C22⋊C4—262no—
294C22⋊C4—262no—
295C22⋊C4—262no—
296C22⋊C4—262no—
297C22⋊C4—521no—
298C42—262no—
299C42—521no—
300C13#248811yescharacteristic, complemented, Sylow
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—132no—
309C23—132no—
310C23—132no—
311C23—261no—
312C23—261no—
313C23—261no—
314C23—261no—
315C23C23×D1311yescharacteristic
316Q8—44no—
317D4—524no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—132no—
335C2×C4—132no—
336C2×C4—261no—
337C2×C4—261no—
338C2×C4—261no—
339C2×C4—261no—
340C2×C4—261no—
341C2×C4—261no—
342C2×C4—261no—
343C2×C4—261no—
344C2×C4—261no—
345C2×C4—261no—
346C2×C4—261no—
347C2×C4—261no—
348C2×C4—261no—
349C2×C4—261no—
350C2×C4—261no—
351C2×C4—261no—
352C2×C4—261no—
353C2×C4—261no—
354C2×C4—261no—
355C2×C4—524no—
356C2×C4—524no—
357C2×C4—524no—
358C2×C4D4×D1312yes—
359C2×C4#612912yes—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—134no—
368C22—262no—
369C22—262no—
370C22—262no—
371C22—262no—
372C22—262no—
373C22—262no—
374C22C2×D4×D1311yescharacteristic
375C22C2×#612911yescharacteristic
376C22#8825111yescharacteristic
377C22#8825411yescharacteristic
378C22#41×D1311yescharacteristic
379C22#41×D1311yescharacteristic
380C22#41×D1311yescharacteristic
381C4—22no—
382C4—22no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—262no—
388C4—262no—
389C4—521no—
390C4—521no—
391C4—521no—
392C4—521no—
393C4—521no—
394C2—81no—
395C2—264no—
396C2#1171929611yescharacteristic
397C2#1171933611yescharacteristic
398C2#1171934311yescharacteristic
399C2#1171934411yescharacteristic
400C2D13×#12411yescharacteristic
401C2#1171938411yescharacteristic
402C2#1171938511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#393C2
prime radicalC22×C22⋊D13C22
hypercenter#393D13
hypocenterC13#2488
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#88200C2semidirect
3. C13×#393C2semidirect
4. #11718891C2semidirect
7. #11718613C2semidirect
8. #11718612C2semidirect
9. #11718606C2semidirect
10. #11718327C2semidirect
11. #11718325C2semidirect
12. D13×#95C2semidirect
13. #11718321C2semidirect
14. #11718320C2semidirect
15. #11718311C2semidirect
164. #393D13semidirect
300. C13#2488semidirect

Maximal subgroups

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

subgroupindex
C2×#882002
C2×#881372
C13×#3932
#117188912
#117186172
#117186132
#117186122
#117186062
#117183272
#117183252
D13×#952
#117183212
#117183202
#117183112
#248813