Finite Group Databasebeta

← #13117964

Subgroups — #13117964

Order 1664.

552 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88137C211yesmaximal, characteristic
2C13×#388C211yesmaximal, characteristic, complemented
3#11718651C211yesmaximal, characteristic, complemented
4C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
5#11718619C211yesmaximal, characteristic
6#11718618C211yesmaximal, characteristic
7#11718605C211yesmaximal, characteristic, complemented
8C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
9C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
10C4×#6103C211yesmaximal, characteristic, complemented
11C4×#6101C211yesmaximal, characteristic, complemented
12#11718330C211yesmaximal, characteristic, complemented
13#11718327C211yesmaximal, characteristic, complemented
14#11718314C211yesmaximal, characteristic, complemented
15#11718313C211yesmaximal, characteristic, complemented
16C22×C22⋊D13C2211yescharacteristic
17C23×Dic13C2211yescharacteristic
18C22×C4×D13C2211yescharacteristic
19C2×C13×C4⋊C4C2211yescharacteristic
20C2×C13×C22⋊C4C2211yescharacteristic
21C2×C13×C22⋊C4C2211yescharacteristic
22C2×C13×C22⋊C4C2211yescharacteristic
23C2×C42×C13C2211yescharacteristic
24C2×C22⋊Dic13C2211yescharacteristic
25C2×C22⋊Dic13C2211yescharacteristic
26C2×#6103C2211yescharacteristic
27C2×#6103C2211yescharacteristic
28C2×#6103C2211yescharacteristic
29C2×#6103C2211yescharacteristic
30C2×#6103C2211yescharacteristic
31C2×C4⋊Dic13C2211yescharacteristic
32C2×#6101C2211yescharacteristic
33C2×#6101C2211yescharacteristic
34C2×#6101C2211yescharacteristic
35C2×C4×Dic13C2211yescharacteristic
36C2×C4×Dic13C2211yescharacteristic
37C2×C4×Dic13C2211yescharacteristic
38C2×C4×Dic13C2211yescharacteristic
39C2×C4×Dic13C2211yescharacteristic
40C2×C4×Dic13C2211yescharacteristic
41#88137C418yescomplemented
42C13×#95C2211yescharacteristic
43C13×#95C2211yescharacteristic
44#88071C2211yescharacteristic
45#88071C2211yescharacteristic
46#88071C2211yescharacteristic
47#88071C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51#88071C2211yescharacteristic
52C24×C13C2311yescharacteristic
53C23×D13C2311yescharacteristic
54C22×C4×C13C2311yescharacteristic
55C22×C4×C13C2311yescharacteristic
56C22×C4×C13C2311yescharacteristic
57C22×C4×C13C2311yescharacteristic
58C22×C4×C13C2311yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C2×C22⋊D13—41no—
61C2×C22⋊D13—41no—
62C2×C22⋊D13C2×C414yes—
63C22×Dic13—22no—
64C22×Dic13—22no—
65C22×Dic13—41no—
66C22×Dic13C2311yescharacteristic
67C22×Dic13C2311yescharacteristic
68C22×Dic13C2311yescharacteristic
69C22×Dic13C2311yescharacteristic
70C22×Dic13C2311yescharacteristic
71C22×Dic13C2311yescharacteristic
72C22×Dic13C2311yescharacteristic
73C2×C4×D13—41no—
74C2×C4×D13—41no—
75C2×C4×D13C2×C414yescomplemented
76C13×C4⋊C4—22no—
77C13×C22⋊C4—22no—
78C13×C22⋊C4—41no—
79C13×C22⋊C4C2×C414yes—
80C42×C13—41no—
81C22⋊Dic13—22no—
82C22⋊Dic13C2×C414yes—
83#6103—22no—
84#6103—22no—
85#6103—22no—
86#6103—22no—
87#6103C2×C414yescomplemented
88C4⋊Dic13C2×C414yescomplemented
89#6101—22no—
90#6101—41no—
91#6101C2×C414yescomplemented
92C4×Dic13—22no—
93C4×Dic13—22no—
94C4×Dic13—41no—
95C4×Dic13—41no—
96C4×Dic13—41no—
97C4×Dic13—41no—
98#2374—131nomaximal, Sylow
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—21no—
105C23×C13C22×C412yes—
106C23×C13C2411yescharacteristic
107C22×D13—21no—
108C22×D13—21no—
109C22×D13—21no—
110C22×D13—21no—
111C22×D13—21no—
112C22×D13—21no—
113C22×D13C22×C412yes—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
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×C13C22×C412yes—
130C2×C4×C13C22×C412yes—
131C2×C4×C13#4112yes—
132C22⋊D13—44no—
133C2×Dic13—21no—
134C2×Dic13—21no—
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—44no—
149C2×Dic13C22×C412yes—
150C2×Dic13C22×C412yes—
151C2×Dic13C22×C412yes—
152C2×Dic13#4112yes—
153C2×Dic13#4112yes—
154C2×Dic13#4112yes—
155C4×D13—44no—
156C2×#123—131no—
157#390—131no—
158#388—131no—
159#388—131no—
160#388—131no—
161#388D1311yescharacteristic, complemented
162#387—131no—
163#387—131no—
164#386—131no—
165C4×C4⋊C4—131no—
166C4×C4⋊C4—131no—
167C4×C22⋊C4—131no—
168C4×C22⋊C4—131no—
169C4×C22⋊C4—131no—
170C4×C22⋊C4—131no—
171C22×C13—22no—
172C22×C13—22no—
173C22×C13—22no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13C23×C411yescharacteristic
179C22×C13C2×#4111yescharacteristic
180C22×C13C2×#4111yescharacteristic
181C22×C13C2×#4111yescharacteristic
182C22×C13C2×#4111yescharacteristic
183C22×C13H(5,𝔽2)11yescharacteristic
184C22×C13H(5,𝔽2)11yescharacteristic
185C2×D13—22no—
186C2×D13—22no—
187C2×D13—22no—
188C2×D13—41no—
189C2×D13—41no—
190C2×D13—41no—
191C2×D13—41no—
192C4×C13—22no—
193C4×C13—22no—
194C4×C13—22no—
195C4×C13—41no—
196C4×C13—41no—
197C4×C13—41no—
198Dic13—22no—
199Dic13—22no—
200Dic13—22no—
201Dic13—22no—
202Dic13—22no—
203Dic13—22no—
204Dic13—41no—
205C22×D4—131no—
206C23×C4—131no—
207C23×C4—131no—
208#123—138no—
209C2×C4⋊C4—131no—
210C2×C4⋊C4—131no—
211C2×C4⋊C4—131no—
212C2×C4⋊C4—131no—
213C2×C4⋊C4C2×D1311yescharacteristic
214C2×C22⋊C4—131no—
215C2×C22⋊C4—131no—
216C2×C22⋊C4—131no—
217C2×C22⋊C4—131no—
218C2×C22⋊C4—131no—
219C2×C22⋊C4—131no—
220C2×C22⋊C4—131no—
221C2×C22⋊C4C2×D1311yescharacteristic
222C2×C22⋊C4C2×D1311yescharacteristic
223C2×C22⋊C4C2×D1311yescharacteristic
224C2×C42—131no—
225C2×C42—131no—
226C2×C42—131no—
227C2×C42—131no—
228C2×C42—131no—
229C2×C42—131no—
230C2×C42C2×D1311yescharacteristic
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#95C2×D1311yescharacteristic
240#95C2×D1311yescharacteristic
241C2×C13—42no—
242C2×C13C4×#4111yescharacteristic
243C2×C13C4×#4111yescharacteristic
244C2×C13#51811yescharacteristic
245C2×C13#55111yescharacteristic
246C2×C13#55311yescharacteristic
247C2×C13#55311yescharacteristic
248C2×C13#55911yescharacteristic
249D13—42no—
250C24—131no—
251C24C22×D1311yescharacteristic
252C2×D4—134no—
253C2×D4—521no—
254C2×D4—521no—
255C22×C4—131no—
256C22×C4—131no—
257C22×C4—131no—
258C22×C4—131no—
259C22×C4—131no—
260C22×C4—131no—
261C22×C4—134no—
262C22×C4—131no—
263C22×C4—262no—
264C22×C4—262no—
265C22×C4—521no—
266C22×C4—521no—
267C22×C4—521no—
268C22×C4C22×D1311yescharacteristic
269C22×C4C22×D1311yescharacteristic
270C22×C4C22×D1311yescharacteristic
271C22×C4C22×D1311yescharacteristic
272C22×C4C22×D1311yescharacteristic
273C22×C4C22×D1311yescharacteristic
274C4⋊C4—22no—
275C4⋊C4—134no—
276C4⋊C4—134no—
277C4⋊C4—262no—
278C4⋊C4—521no—
279C22⋊C4—22no—
280C22⋊C4—41no—
281C22⋊C4—134no—
282C22⋊C4—134no—
283C22⋊C4—262no—
284C22⋊C4—262no—
285C22⋊C4—262no—
286C22⋊C4—262no—
287C22⋊C4—262no—
288C22⋊C4C4×D1314yes—
289C42—41no—
290C42—262no—
291C42—262no—
292C42—521no—
293C42—521no—
294C42—521no—
295C42—521no—
296C13#237411yescharacteristic, complemented, Sylow
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—132no—
304C23—261no—
305C23—261no—
306C23—261no—
307C23—261no—
308C23—261no—
309C23—261no—
310C23C2×C4×D1312yes—
311C23C23×D1311yescharacteristic
312D4—524no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
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—132no—
329C2×C4—132no—
330C2×C4—132no—
331C2×C4—132no—
332C2×C4—132no—
333C2×C4—132no—
334C2×C4—261no—
335C2×C4—261no—
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—524no—
350C2×C4—524no—
351C2×C4C2×C4×D1312yes—
352C2×C4C2×C4×D1312yes—
353C2×C4#612912yes—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—262no—
362C22—262no—
363C22—262no—
364C22—521no—
365C22—521no—
366C22—521no—
367C22—521no—
368C22C22×C4×D1311yescharacteristic
369C22C2×#612911yescharacteristic
370C22#8825111yescharacteristic
371C22#41×D1311yescharacteristic
372C22#41×D1311yescharacteristic
373C22#41×D1311yescharacteristic
374C22#8825611yescharacteristic
375C4—22no—
376C4—22no—
377C4—22no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—262no—
382C4—262no—
383C4—262no—
384C4—262no—
385C4—262no—
386C4—262no—
387C4—521no—
388C2—42no—
389C2—522no—
390C2#1171922711yescharacteristic
391C2C4×#612911yescharacteristic
392C2#1171925011yescharacteristic
393C2#1171930611yescharacteristic
394C2#1171936611yescharacteristic
395C2#1171938611yescharacteristic
396C2#1171941011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutatorC22×C13C23×C4
FittingC13×#388C2
socle, cosocleC23×C13C24
prime radicalC22×C22⋊D13C22
hypercenter#388D13
hypocenterC13#2374
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C13×#388C2semidirect
3. #11718651C2semidirect
4. C4⋊C4×Dic13C2semidirect
7. #11718605C2semidirect
8. C22⋊C4×Dic13C2semidirect
9. C22⋊C4×Dic13C2semidirect
10. C4×#6103C2semidirect
11. C4×#6101C2semidirect
12. #11718330C2semidirect
13. #11718327C2semidirect
14. #11718314C2semidirect
15. #11718313C2semidirect
41. #88137C4semidirect
75. C2×C4×D13C2×C4semidirect
87. #6103C2×C4semidirect
88. C4⋊Dic13C2×C4semidirect
91. #6101C2×C4semidirect
161. #388D13semidirect
296. C13#2374semidirect

Maximal subgroups

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

subgroupindex
C2×#881372
C13×#3882
#117186512
C4⋊C4×Dic132
#117186192
#117186182
#117186052
C22⋊C4×Dic132
C4×#61032
C4×#61012
#117183302
#117183272
#117183142
#117183132
#237413