Finite Group Databasebeta

← #13121123

Subgroups — #13121123

Order 1664.

562 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×#88142C211yesmaximal, characteristic, complemented
2C2×#88140C211yesmaximal, characteristic
3C2×#88139C211yesmaximal, characteristic
4C2×#88132C211yesmaximal, characteristic, complemented
5C13×#397C211yesmaximal, characteristic, complemented
6#11718653C211yesmaximal, characteristic, complemented
7#11718620C211yesmaximal, characteristic
8#11718607C211yesmaximal, characteristic, complemented
9#11718605C211yesmaximal, characteristic, complemented
10#11718337C211yesmaximal, characteristic, complemented
11#11718334C211yesmaximal, characteristic, complemented
12#11718331C211yesmaximal, characteristic, complemented
13#11718317C211yesmaximal, characteristic, complemented
14#11718315C211yesmaximal, characteristic, complemented
15#11718308C211yesmaximal, characteristic, complemented
16C22×C22⋊D13C2211yescharacteristic
17C23×Dic13C2211yescharacteristic
18C22×Dic26C2211yescharacteristic
19C22×Dic26C2211yescharacteristic
20C2×C13×C4⋊C4C2211yescharacteristic
21C2×C13×C22⋊C4C2211yescharacteristic
22C2×C13×C22⋊C4C2211yescharacteristic
23C2×C13×C22⋊C4C2211yescharacteristic
24C2×C22⋊Dic13C2211yescharacteristic
25C2×C22⋊Dic13C2211yescharacteristic
26C2×#6103C2211yescharacteristic
27C2×#6103C2211yescharacteristic
28C2×#6103C2211yescharacteristic
29C2×#6103C2211yescharacteristic
30C2×#6103C2211yescharacteristic
31C2×#6103C2211yescharacteristic
32C2×C4⋊Dic13C2211yescharacteristic
33C2×C4⋊Dic13C2211yescharacteristic
34C2×C4⋊Dic13C2211yescharacteristic
35C2×#6101C2211yescharacteristic
36C2×#6101C2211yescharacteristic
37C2×#6101C2211yescharacteristic
38C2×#6101C2211yescharacteristic
39C2×#6101C2211yescharacteristic
40C2×#6101C2211yescharacteristic
41C2×C4×Dic13C2211yescharacteristic
42C2×C4×Dic13C2211yescharacteristic
43#88142—24no—
44#88140—24no—
45#88139—24no—
46#88132—24no—
47C13×#95C2211yescharacteristic
48C13×#95C2211yescharacteristic
49C13×#95C2211yescharacteristic
50#88071C2211yescharacteristic
51#88071C2211yescharacteristic
52#88071C2211yescharacteristic
53#88071C2211yescharacteristic
54#88071C2211yescharacteristic
55C24×C13C2311yescharacteristic
56C23×D13C2311yescharacteristic
57C22×C4×C13C2311yescharacteristic
58C22×C4×C13C2311yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C22×C4×C13C2311yescharacteristic
63C2×C22⋊D13—22no—
64C2×C22⋊D13—22no—
65C2×C22⋊D13—41no—
66C22×Dic13—22no—
67C22×Dic13—22no—
68C22×Dic13—41no—
69C22×Dic13C2311yescharacteristic
70C22×Dic13C2311yescharacteristic
71C22×Dic13C2311yescharacteristic
72C22×Dic13C2311yescharacteristic
73C22×Dic13C2311yescharacteristic
74C22×Dic13C2311yescharacteristic
75C22×Dic13C2311yescharacteristic
76C2×Dic26—22no—
77C2×Dic26—22no—
78C2×Dic26—22no—
79C2×Dic26—22no—
80C2×Dic26—41no—
81C2×Dic26—41no—
82C13×C4⋊C4—22no—
83C13×C22⋊C4—22no—
84C13×C22⋊C4—22no—
85C13×C22⋊C4—22no—
86C22⋊Dic13—22no—
87C22⋊Dic13D414yes—
88#6103—22no—
89#6103—22no—
90#6103—22no—
91#6103—22no—
92#6103—22no—
93#6103—41no—
94C4⋊Dic13—22no—
95C4⋊Dic13—22no—
96C4⋊Dic13D414yes—
97#6101—22no—
98#6101—22no—
99#6101—22no—
100#6101—22no—
101#6101—22no—
102#6101—41no—
103C4×Dic13—22no—
104C4×Dic13—22no—
105#2674—131nomaximal, Sylow
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13C2×D412yes—
113C23×C13C2411yescharacteristic
114C22×D13—21no—
115C22×D13—21no—
116C22×D13—21no—
117C22×D13—21no—
118C22×D13—21no—
119C22×D13—21no—
120C22×D13—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×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13C2×D412yes—
139C22⋊D13—44no—
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—21no—
156C2×Dic13—44no—
157C2×Dic13C2×D412yes—
158C2×Dic13C2×D412yes—
159C2×Dic13C2×D412yes—
160C2×Dic13C2×D412yes—
161C2×Dic13#4112yes—
162Dic26—44no—
163Dic26—44no—
164C2×C4⋊Q8—131no—
165C2×#124—131no—
166C2×#123—131no—
167C2×C22⋊Q8—131no—
168#399—131no—
169#397D1311yescharacteristic, complemented
170#396—131no—
171#395—131no—
172#394—131no—
173#393—131no—
174#389—131no—
175#388—131no—
176#388—131no—
177#387—131no—
178#385—131no—
179C22×C13—22no—
180C22×C13—22no—
181C22×C13—22no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13—41no—
186C22×C13C22×D411yescharacteristic
187C22×C13C22×D411yescharacteristic
188C22×C13C2×#4111yescharacteristic
189C22×C13H(5,𝔽2)11yescharacteristic
190C22×C132−1+411yescharacteristic
191C22×C132−1+411yescharacteristic
192C22×C132−1+411yescharacteristic
193C2×D13—41no—
194C2×D13—41no—
195C2×D13—41no—
196C2×D13—41no—
197C2×D13—41no—
198C2×D13—41no—
199C2×D13—41no—
200C4×C13—22no—
201C4×C13—41no—
202C4×C13—41no—
203C4×C13—41no—
204C4×C13—41no—
205C4×C13—41no—
206Dic13—22no—
207Dic13—22no—
208Dic13—22no—
209Dic13—22no—
210Dic13—22no—
211Dic13—41no—
212Dic13—41no—
213C22×Q8—131no—
214C22×Q8—131no—
215C22×D4—131no—
216C23×C4—131no—
217C4⋊Q8—264no—
218#124—264no—
219#123—264no—
220C22⋊Q8—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⋊C4—131no—
228C2×C4⋊C4—131no—
229C2×C4⋊C4—131no—
230C2×C4⋊C4C2×D1311yescharacteristic
231C2×C22⋊C4—131no—
232C2×C22⋊C4—131no—
233C2×C22⋊C4—131no—
234C2×C22⋊C4—131no—
235C2×C22⋊C4—131no—
236C2×C22⋊C4—131no—
237C2×C22⋊C4—131no—
238C2×C22⋊C4—131no—
239C2×C22⋊C4C2×D1311yescharacteristic
240C2×C22⋊C4C2×D1311yescharacteristic
241C2×C22⋊C4C2×D1311yescharacteristic
242C2×C42—131no—
243C2×C42—131no—
244#95—131no—
245#95—131no—
246#95—131no—
247#95—131no—
248#95—131no—
249#95C2×D1311yescharacteristic
250#95C2×D1311yescharacteristic
251#95C2×D1311yescharacteristic
252C2×C13—42no—
253C2×C13#53611yescharacteristic
254C2×C13#53611yescharacteristic
255C2×C13#54211yescharacteristic
256C2×C13D4211yescharacteristic
257C2×C13#54711yescharacteristic
258C2×C13#54811yescharacteristic
259C2×C13#56311yescharacteristic
260D13—81no—
261C24—131no—
262C24C22×D1311yescharacteristic
263C2×Q8—262no—
264C2×Q8—262no—
265C2×Q8—262no—
266C2×Q8—262no—
267C2×Q8—521no—
268C2×Q8—521no—
269C2×D4—262no—
270C2×D4—262no—
271C2×D4—521no—
272C22×C4—131no—
273C22×C4—131no—
274C22×C4—131no—
275C22×C4—131no—
276C22×C4—131no—
277C22×C4—131no—
278C22×C4—131no—
279C22×C4—262no—
280C22×C4—262no—
281C22×C4—521no—
282C22×C4C22×D1311yescharacteristic
283C22×C4C22×D1311yescharacteristic
284C22×C4C22×D1311yescharacteristic
285C22×C4C22×D1311yescharacteristic
286C22×C4C22×D1311yescharacteristic
287C22×C4C22×D1311yescharacteristic
288C4⋊C4—22no—
289C4⋊C4—134no—
290C4⋊C4—262no—
291C4⋊C4—262no—
292C4⋊C4—262no—
293C4⋊C4—262no—
294C4⋊C4—262no—
295C4⋊C4—262no—
296C4⋊C4—262no—
297C4⋊C4—521no—
298C22⋊C4—22no—
299C22⋊C4—22no—
300C22⋊C4—22no—
301C22⋊C4—134no—
302C22⋊C4—262no—
303C22⋊C4—262no—
304C22⋊C4—262no—
305C22⋊C4—262no—
306C22⋊C4—262no—
307C22⋊C4—262no—
308C22⋊C4—521no—
309C42—262no—
310C42—262no—
311C13#267411yescharacteristic, complemented, Sylow
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—261no—
319C23—261no—
320C23—261no—
321C23—261no—
322C23—261no—
323C23—261no—
324C23—261no—
325C23D4×D1312yes—
326C23C23×D1311yescharacteristic
327Q8—524no—
328Q8—524no—
329D4—524no—
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—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—132no—
348C2×C4—132no—
349C2×C4—132no—
350C2×C4—132no—
351C2×C4—132no—
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—261no—
364C2×C4—261no—
365C2×C4—261no—
366C2×C4—261no—
367C2×C4—261no—
368C2×C4—524no—
369C2×C4D4×D1312yes—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—521no—
378C22—521no—
379C22—521no—
380C22—521no—
381C22—521no—
382C22—521no—
383C22—521no—
384C22C2×D4×D1311yescharacteristic
385C22C2×D4×D1311yescharacteristic
386C22#41×D1311yescharacteristic
387C22#8825611yescharacteristic
388C22#8825711yescharacteristic
389C22#8825711yescharacteristic
390C22#8825711yescharacteristic
391C4—22no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—262no—
398C4—262no—
399C4—262no—
400C4—262no—
401C4—262no—
402C4—521no—
403C4—521no—
404C2—42no—
405C2—1041no—
406C2#1171931411yescharacteristic
407C2#1171935311yescharacteristic
408C2#1171935311yescharacteristic
409C2#1171936011yescharacteristic
410C2#1171938211yescharacteristic
411C2#1171941511yescharacteristic
412C2#1171941711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#397C2
prime radicalC22×C22⋊D13C22
hypercenter#397D13
hypocenterC13#2674
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#88142C2semidirect
4. C2×#88132C2semidirect
5. C13×#397C2semidirect
6. #11718653C2semidirect
8. #11718607C2semidirect
9. #11718605C2semidirect
10. #11718337C2semidirect
11. #11718334C2semidirect
12. #11718331C2semidirect
13. #11718317C2semidirect
14. #11718315C2semidirect
15. #11718308C2semidirect
169. #397D13semidirect
311. C13#2674semidirect

Maximal subgroups

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

subgroupindex
C2×#881422
C2×#881402
C2×#881392
C2×#881322
C13×#3972
#117186532
#117186202
#117186072
#117186052
#117183372
#117183342
#117183312
#117183172
#117183152
#117183082
#267413