Finite Group Databasebeta

← #13117827

Subgroups — #13117827

Order 1664.

652 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88146C211yesmaximal, characteristic, complemented
2C2×#88137C211yesmaximal, characteristic
3C2×#88135C211yesmaximal, characteristic
4C13×#388C211yesmaximal, characteristic, complemented
5#11718639C211yesmaximal, characteristic, complemented
6#11718617C211yesmaximal, characteristic
7#11718611C211yesmaximal, characteristic, complemented
8#11718605C211yesmaximal, characteristic, complemented
9C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
10C4×#6103C211yesmaximal, characteristic, complemented
11C4×C4⋊Dic13C211yesmaximal, characteristic, complemented
12#11718329C211yesmaximal, characteristic, complemented
13D13×#95C211yesmaximal, characteristic, complemented
14#11718315C211yesmaximal, characteristic, complemented
15#11718308C211yesmaximal, characteristic, complemented
16C22×C22⋊D13C2211yescharacteristic
17C23×Dic13C2211yescharacteristic
18C22×C4×D13C2211yescharacteristic
19C22×C4×D13C2211yescharacteristic
20C22×C4×D13C2211yescharacteristic
21C2×C13×C4⋊C4C2211yescharacteristic
22C2×C13×C22⋊C4C2211yescharacteristic
23C2×C13×C22⋊C4C2211yescharacteristic
24C2×C13×C22⋊C4C2211yescharacteristic
25C2×C42×C13C2211yescharacteristic
26C2×C22⋊Dic13C2211yescharacteristic
27C2×C22⋊Dic13C2211yescharacteristic
28C2×#6103C2211yescharacteristic
29C2×#6103C2211yescharacteristic
30C2×#6103C2211yescharacteristic
31C2×C4⋊Dic13C2211yescharacteristic
32C2×C4⋊Dic13C2211yescharacteristic
33C2×C4⋊Dic13C2211yescharacteristic
34C2×#6101C2211yescharacteristic
35C2×#6101C2211yescharacteristic
36C2×#6101C2211yescharacteristic
37C2×C4×Dic13C2211yescharacteristic
38C2×C4×Dic13C2211yescharacteristic
39C2×C4×Dic13C2211yescharacteristic
40C2×C4×Dic13C2211yescharacteristic
41#88146—24no—
42#88137C418yescomplemented
43#88135—24no—
44C13×#95C2211yescharacteristic
45C13×#95C2211yescharacteristic
46#88071C2211yescharacteristic
47#88071C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51#88071C2211yescharacteristic
52#88071C2211yescharacteristic
53#88071C2211yescharacteristic
54C24×C13C2311yescharacteristic
55C23×D13C2311yescharacteristic
56C22×C4×C13C2311yescharacteristic
57C22×C4×C13C2311yescharacteristic
58C22×C4×C13C2311yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C2×C22⋊D13—22no—
63C2×C22⋊D13—22no—
64C2×C22⋊D13C2×C414yes—
65C22×Dic13—22no—
66C22×Dic13—22no—
67C22×Dic13—41no—
68C22×Dic13C2311yescharacteristic
69C22×Dic13C2311yescharacteristic
70C22×Dic13C2311yescharacteristic
71C22×Dic13C2311yescharacteristic
72C22×Dic13C2311yescharacteristic
73C22×Dic13C2311yescharacteristic
74C22×Dic13C2311yescharacteristic
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—
83C2×C4×D13C2×C414yescomplemented
84C13×C4⋊C4—22no—
85C13×C22⋊C4—22no—
86C13×C22⋊C4—22no—
87C13×C22⋊C4C2×C414yescomplemented
88C42×C13—22no—
89C22⋊Dic13—41no—
90C22⋊Dic13C2×C414yescomplemented
91#6103—22no—
92#6103C2×C414yescomplemented
93#6103D414yes—
94C4⋊Dic13—22no—
95C4⋊Dic13—22no—
96C4⋊Dic13C2×C414yescomplemented
97#6101—22no—
98#6101—41no—
99#6101C2×C414yescomplemented
100C4×Dic13—22no—
101C4×Dic13—22no—
102C4×Dic13—22no—
103C4×Dic13—41no—
104#2359—131nomaximal, Sylow
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13C22×C412yes—
112C23×C13C2411yescharacteristic
113C22×D13—21no—
114C22×D13—21no—
115C22×D13—21no—
116C22×D13—21no—
117C22×D13C22×C412yes—
118C22×D13C2×D412yes—
119C22×D13#4112yes—
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×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13C22×C412yes—
135C2×C4×C13C22×C412yes—
136C2×C4×C13C2×D412yes—
137C2×C4×C13#4112yes—
138C22⋊D13—28no—
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×Dic13—21no—
155C2×Dic13—44no—
156C2×Dic13C22×C412yes—
157C2×Dic13C22×C412yes—
158C2×Dic13C22×C412yes—
159C2×Dic13C2×D412yes—
160C2×Dic13#4112yes—
161C4×D13—28no—
162C4×D13—44no—
163C4×D13—44no—
164C2×#123—131no—
165C2×C4×D4—131no—
166C2×#117—131no—
167#389—131no—
168#388—131no—
169#388D1311yescharacteristic, complemented
170#387—131no—
171#387—131no—
172#386—131no—
173#385—131no—
174#385—131no—
175C4×C4⋊C4—131no—
176C4×C22⋊C4—131no—
177C4×C22⋊C4—131no—
178C2×#95—131no—
179C22×C13—22no—
180C22×C13—22no—
181C22×C13—22no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13—41no—
186C22×C13C23×C411yescharacteristic
187C22×C13C22×D411yescharacteristic
188C22×C13C2×#4111yescharacteristic
189C22×C13C2×#4111yescharacteristic
190C22×C13C2×#4111yescharacteristic
191C22×C13H(5,𝔽2)11yescharacteristic
192C22×C132−1+411yescharacteristic
193C2×D13—22no—
194C2×D13—22no—
195C2×D13—22no—
196C2×D13—22no—
197C2×D13—22no—
198C2×D13—22no—
199C2×D13C4×D414yes—
200C4×C13—22no—
201C4×C13—22no—
202C4×C13—22no—
203C4×C13—22no—
204C4×C13—41no—
205C4×C13—41no—
206Dic13—22no—
207Dic13—22no—
208Dic13—22no—
209Dic13—22no—
210Dic13—22no—
211Dic13—41no—
212Dic13—41no—
213C22×D4—131no—
214C23×C4—131no—
215C23×C4—131no—
216C23×C4—131no—
217C23×C4—131no—
218#123—138no—
219C4×D4—264no—
220#117—264no—
221C2×C4⋊C4—131no—
222C2×C4⋊C4—131no—
223C2×C4⋊C4—131no—
224C2×C4⋊C4—131no—
225C2×C4⋊C4—131no—
226C2×C4⋊C4—131no—
227C2×C4⋊C4C2×D1311yescharacteristic
228C2×C22⋊C4—131no—
229C2×C22⋊C4—131no—
230C2×C22⋊C4—131no—
231C2×C22⋊C4—131no—
232C2×C22⋊C4—131no—
233C2×C22⋊C4C2×D1311yescharacteristic
234C2×C22⋊C4C2×D1311yescharacteristic
235C2×C22⋊C4C2×D1311yescharacteristic
236C2×C42—131no—
237C2×C42—131no—
238C2×C42—131no—
239C2×C42—131no—
240C2×C42C2×D1311yescharacteristic
241#95—131no—
242#95—131no—
243#95—131no—
244#95—131no—
245#95—131no—
246#95—131no—
247#95—131no—
248#95—131no—
249#95C2×D1311yescharacteristic
250#95C2×D1311yescharacteristic
251C2×C13—42no—
252C2×C13C2×C4×D411yescharacteristic
253C2×C13C4×#4111yescharacteristic
254C2×C13#52011yescharacteristic
255C2×C13#54611yescharacteristic
256C2×C13#54711yescharacteristic
257C2×C13#55111yescharacteristic
258C2×C13#55211yescharacteristic
259D13—24no—
260C24—131no—
261C24C22×D1311yescharacteristic
262C2×D4—134no—
263C2×D4—262no—
264C2×D4—262no—
265C22×C4—131no—
266C22×C4—131no—
267C22×C4—131no—
268C22×C4—131no—
269C22×C4—131no—
270C22×C4—134no—
271C22×C4—131no—
272C22×C4—131no—
273C22×C4—262no—
274C22×C4—262no—
275C22×C4—262no—
276C22×C4—262no—
277C22×C4—262no—
278C22×C4—262no—
279C22×C4—262no—
280C22×C4—262no—
281C22×C4—521no—
282C22×C4—521no—
283C22×C4—521no—
284C22×C4C22×D1311yescharacteristic
285C22×C4C22×D1311yescharacteristic
286C22×C4C22×D1311yescharacteristic
287C22×C4C22×D1311yescharacteristic
288C22×C4C22×D1311yescharacteristic
289C22×C4C22×D1311yescharacteristic
290C4⋊C4—22no—
291C4⋊C4—134no—
292C4⋊C4—134no—
293C4⋊C4—262no—
294C4⋊C4—262no—
295C4⋊C4—262no—
296C4⋊C4—521no—
297C22⋊C4—22no—
298C22⋊C4—22no—
299C22⋊C4—134no—
300C22⋊C4—134no—
301C22⋊C4—134no—
302C22⋊C4—262no—
303C22⋊C4—521no—
304C22⋊C4C4×D1314yescomplemented
305C42—22no—
306C42—262no—
307C42—262no—
308C42—262no—
309C42—521no—
310C13#235911yescharacteristic, complemented, Sylow
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—132no—
318C23—132no—
319C23—132no—
320C23—261no—
321C23—261no—
322C23—261no—
323C23—261no—
324C23C2×C4×D1312yes—
325C23C23×D1311yescharacteristic
326D4—268no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—132no—
342C2×C4—132no—
343C2×C4—132no—
344C2×C4—132no—
345C2×C4—132no—
346C2×C4—268no—
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—261no—
356C2×C4—261no—
357C2×C4—261no—
358C2×C4—261no—
359C2×C4—261no—
360C2×C4—261no—
361C2×C4—261no—
362C2×C4—261no—
363C2×C4—524no—
364C2×C4—524no—
365C2×C4—524no—
366C2×C4C2×C4×D1312yes—
367C2×C4C2×C4×D1312yes—
368C2×C4D4×D1312yes—
369C2×C4#612912yes—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—134no—
378C22—262no—
379C22—262no—
380C22—262no—
381C22—262no—
382C22—262no—
383C22—262no—
384C22C22×C4×D1311yescharacteristic
385C22C2×D4×D1311yescharacteristic
386C22C2×#612911yescharacteristic
387C22#41×D1311yescharacteristic
388C22#41×D1311yescharacteristic
389C22#8825611yescharacteristic
390C22#8825711yescharacteristic
391C4—22no—
392C4—22no—
393C4—22no—
394C4—22no—
395C4—41no—
396C4—41no—
397C4—262no—
398C4—262no—
399C4—262no—
400C4—262no—
401C4—262no—
402C4—521no—
403C4—521no—
404C2—42no—
405C2—264no—
406C2#1171922811yescharacteristic
407C2C4×#612911yescharacteristic
408C2C4×D4×D1311yescharacteristic
409C2#1171931611yescharacteristic
410C2#1171936311yescharacteristic
411C2#1171938111yescharacteristic
412C2#1171941311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutatorC22×C13C23×C4
FittingC13×#388C2
socle, cosocleC23×C13C24
prime radicalC22×C22⋊D13C22
hypercenter#388D13
hypocenterC13#2359
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#88146C2semidirect
4. C13×#388C2semidirect
5. #11718639C2semidirect
7. #11718611C2semidirect
8. #11718605C2semidirect
9. C22⋊C4×Dic13C2semidirect
10. C4×#6103C2semidirect
11. C4×C4⋊Dic13C2semidirect
12. #11718329C2semidirect
13. D13×#95C2semidirect
14. #11718315C2semidirect
15. #11718308C2semidirect
42. #88137C4semidirect
83. C2×C4×D13C2×C4semidirect
87. C13×C22⋊C4C2×C4semidirect
90. C22⋊Dic13C2×C4semidirect
92. #6103C2×C4semidirect
96. C4⋊Dic13C2×C4semidirect
99. #6101C2×C4semidirect
169. #388D13semidirect
304. C22⋊C4C4×D13semidirect
310. C13#2359semidirect

Maximal subgroups

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

subgroupindex
C2×#881462
C2×#881372
C2×#881352
C13×#3882
#117186392
#117186172
#117186112
#117186052
C22⋊C4×Dic132
C4×#61032
C4×C4⋊Dic132
#117183292
D13×#952
#117183152
#117183082
#235913