Finite Group Databasebeta

← #13117902

Subgroups — #13117902

Order 1664.

632 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88141C211yesmaximal, characteristic, complemented
2C2×#88139C211yesmaximal, characteristic
3C2×#88135C211yesmaximal, characteristic
4C13×#388C211yesmaximal, characteristic, complemented
5#11718650C211yesmaximal, characteristic, complemented
6#11718618C211yesmaximal, characteristic
7#11718607C211yesmaximal, characteristic, complemented
8#11718605C211yesmaximal, characteristic, complemented
9C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
10C4×#6103C211yesmaximal, characteristic, complemented
11C4×#6101C211yesmaximal, characteristic, complemented
12#11718330C211yesmaximal, characteristic, complemented
13#11718330C211yesmaximal, characteristic, complemented
14#11718310C211yesmaximal, characteristic, complemented
15#11718307C211yesmaximal, characteristic, complemented
16C22×C22⋊D13C2211yescharacteristic
17C23×Dic13C2211yescharacteristic
18C22×C4×D13C2211yescharacteristic
19C22×Dic26C2211yescharacteristic
20C2×C13×C4⋊C4C2211yescharacteristic
21C2×C13×C22⋊C4C2211yescharacteristic
22C2×C13×C22⋊C4C2211yescharacteristic
23C2×C13×C22⋊C4C2211yescharacteristic
24C2×C42×C13C2211yescharacteristic
25C2×C22⋊Dic13C2211yescharacteristic
26C2×C22⋊Dic13C2211yescharacteristic
27C2×#6103C2211yescharacteristic
28C2×#6103C2211yescharacteristic
29C2×#6103C2211yescharacteristic
30C2×#6103C2211yescharacteristic
31C2×#6103C2211yescharacteristic
32C2×#6101C2211yescharacteristic
33C2×#6101C2211yescharacteristic
34C2×#6101C2211yescharacteristic
35C2×#6101C2211yescharacteristic
36C2×#6101C2211yescharacteristic
37C2×C4×Dic13C2211yescharacteristic
38C2×C4×Dic13C2211yescharacteristic
39C2×C4×Dic13C2211yescharacteristic
40C2×C4×Dic13C2211yescharacteristic
41C2×C4×Dic13C2211yescharacteristic
42C2×C4×Dic13C2211yescharacteristic
43#88141—24no—
44#88139C418yescomplemented
45#88135—24no—
46C13×#95C2211yescharacteristic
47C13×#95C2211yescharacteristic
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—41no—
78C2×Dic26—22no—
79C2×Dic26—22no—
80C2×Dic26C2×C414yescomplemented
81C13×C4⋊C4—22no—
82C13×C22⋊C4—22no—
83C13×C22⋊C4—41no—
84C13×C22⋊C4C2×C414yescomplemented
85C42×C13—41no—
86C22⋊Dic13—22no—
87C22⋊Dic13C2×C414yescomplemented
88#6103—22no—
89#6103—22no—
90#6103—41no—
91#6103C2×C414yescomplemented
92#6103C2×C414yescomplemented
93#6101—22no—
94#6101—22no—
95#6101—22no—
96#6101—22no—
97#6101D414yes—
98C4×Dic13—22no—
99C4×Dic13—22no—
100C4×Dic13—22no—
101C4×Dic13—22no—
102C4×Dic13—41no—
103C4×Dic13C2×C414yescomplemented
104#2367—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×D13—21no—
118C22×D13—21no—
119C22×D13C22×C412yes—
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×C13—21no—
135C2×C4×C13C22×C412yes—
136C2×C4×C13C22×C412yes—
137C2×C4×C13C2×D412yes—
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—44no—
153C2×Dic13C22×C412yes—
154C2×Dic13C22×C412yes—
155C2×Dic13C22×C412yes—
156C2×Dic13C2×D412yes—
157C2×Dic13C2×D412yes—
158C2×Dic13#4112yes—
159C2×Dic13#4112yes—
160C2×Dic13#4112yes—
161C4×D13—44no—
162Dic26—28no—
163C2×#124—131no—
164C2×C4×Q8—131no—
165C2×C4×D4—131no—
166#391—131no—
167#390—131no—
168#388—131no—
169#388—131no—
170#388—131no—
171#388D1311yescharacteristic, complemented
172#385—131no—
173#385—131no—
174C4×C4⋊C4—131no—
175C4×C4⋊C4—131no—
176C4×C22⋊C4—131no—
177C4×C22⋊C4—131no—
178C22×C13—22no—
179C22×C13—22no—
180C22×C13—22no—
181C22×C13—41no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13C23×C411yescharacteristic
186C22×C13C22×D411yescharacteristic
187C22×C13C2×#4111yescharacteristic
188C22×C13C2×#4111yescharacteristic
189C22×C13C2×#4111yescharacteristic
190C22×C13H(5,𝔽2)11yescharacteristic
191C22×C132−1+411yescharacteristic
192C2×D13—22no—
193C2×D13—22no—
194C2×D13—22no—
195C2×D13—41no—
196C2×D13—41no—
197C2×D13—41no—
198C2×D13—41no—
199C4×C13—22no—
200C4×C13—22no—
201C4×C13—22no—
202C4×C13—41no—
203C4×C13—41no—
204C4×C13—41no—
205Dic13—22no—
206Dic13—22no—
207Dic13—22no—
208Dic13—22no—
209Dic13—22no—
210Dic13—41no—
211Dic13C4×D414yes—
212C22×Q8—131no—
213C22×D4—131no—
214C23×C4—131no—
215C23×C4—131no—
216#124—138no—
217C4×Q8—264no—
218C4×D4—264no—
219C2×C4⋊C4—131no—
220C2×C4⋊C4—131no—
221C2×C4⋊C4—131no—
222C2×C4⋊C4—131no—
223C2×C4⋊C4—131no—
224C2×C4⋊C4C2×D1311yescharacteristic
225C2×C22⋊C4—131no—
226C2×C22⋊C4—131no—
227C2×C22⋊C4—131no—
228C2×C22⋊C4—131no—
229C2×C22⋊C4—131no—
230C2×C22⋊C4—131no—
231C2×C22⋊C4—131no—
232C2×C22⋊C4C2×D1311yescharacteristic
233C2×C22⋊C4C2×D1311yescharacteristic
234C2×C22⋊C4C2×D1311yescharacteristic
235C2×C42—131no—
236C2×C42—131no—
237C2×C42—131no—
238C2×C42—131no—
239C2×C42—131no—
240C2×C42—131no—
241C2×C42C2×D1311yescharacteristic
242#95—131no—
243#95—131no—
244#95—131no—
245#95—131no—
246#95—131no—
247#95—131no—
248#95C2×D1311yescharacteristic
249#95C2×D1311yescharacteristic
250C2×C13—42no—
251C2×C13C2×C4×D411yescharacteristic
252C2×C13C4×#4111yescharacteristic
253C2×C13#52011yescharacteristic
254C2×C13#54611yescharacteristic
255C2×C13#54811yescharacteristic
256C2×C13#55611yescharacteristic
257C2×C13#55911yescharacteristic
258D13—42no—
259C24—131no—
260C24C22×D1311yescharacteristic
261C2×Q8—134no—
262C2×Q8—262no—
263C2×Q8—262no—
264C2×D4—134no—
265C2×D4—262no—
266C2×D4—262no—
267C22×C4—131no—
268C22×C4—131no—
269C22×C4—131no—
270C22×C4—131no—
271C22×C4—131no—
272C22×C4—131no—
273C22×C4—131no—
274C22×C4—262no—
275C22×C4—262no—
276C22×C4—262no—
277C22×C4—262no—
278C22×C4—521no—
279C22×C4—521no—
280C22×C4C22×D1311yescharacteristic
281C22×C4C22×D1311yescharacteristic
282C22×C4C22×D1311yescharacteristic
283C22×C4C22×D1311yescharacteristic
284C22×C4C22×D1311yescharacteristic
285C22×C4C22×D1311yescharacteristic
286C4⋊C4—22no—
287C4⋊C4—134no—
288C4⋊C4—262no—
289C4⋊C4—262no—
290C4⋊C4—262no—
291C4⋊C4—262no—
292C22⋊C4—22no—
293C22⋊C4—41no—
294C22⋊C4—134no—
295C22⋊C4—134no—
296C22⋊C4—134no—
297C22⋊C4—262no—
298C22⋊C4—262no—
299C22⋊C4—262no—
300C22⋊C4—521no—
301C22⋊C4C4×D1314yescomplemented
302C42—41no—
303C42—134no—
304C42—262no—
305C42—262no—
306C42—262no—
307C42—262no—
308C42—521no—
309C13#236711yescharacteristic, complemented, Sylow
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—132no—
317C23—261no—
318C23—261no—
319C23—261no—
320C23—261no—
321C23—261no—
322C23—261no—
323C23C2×C4×D1312yes—
324C23C23×D1311yescharacteristic
325Q8—268no—
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—21no—
342C2×C4—132no—
343C2×C4—132no—
344C2×C4—132no—
345C2×C4—132no—
346C2×C4—132no—
347C2×C4—132no—
348C2×C4—132no—
349C2×C4—132no—
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×C4C2×C4×D1312yes—
366C2×C4C2×C4×D1312yes—
367C2×C4D4×D1312yes—
368C22—22no—
369C22—22no—
370C22—22no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—262no—
376C22—262no—
377C22—262no—
378C22—521no—
379C22—521no—
380C22—521no—
381C22—521no—
382C22C22×C4×D1311yescharacteristic
383C22C2×D4×D1311yescharacteristic
384C22#8825111yescharacteristic
385C22#41×D1311yescharacteristic
386C22#41×D1311yescharacteristic
387C22#41×D1311yescharacteristic
388C22#8825711yescharacteristic
389C4—22no—
390C4—22no—
391C4—22no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—134no—
396C4—262no—
397C4—262no—
398C4—262no—
399C4—262no—
400C4—262no—
401C4—521no—
402C2—42no—
403C2—522no—
404C2#1171922711yescharacteristic
405C2C4×D4×D1311yescharacteristic
406C2#1171925111yescharacteristic
407C2#1171931511yescharacteristic
408C2#1171936911yescharacteristic
409C2#1171938211yescharacteristic
410C2#1171940711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutatorC22×C13C23×C4
FittingC13×#388C2
socle, cosocleC23×C13C24
prime radicalC22×C22⋊D13C22
hypercenter#388D13
hypocenterC13#2367
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#88141C2semidirect
4. C13×#388C2semidirect
5. #11718650C2semidirect
7. #11718607C2semidirect
8. #11718605C2semidirect
9. C22⋊C4×Dic13C2semidirect
10. C4×#6103C2semidirect
11. C4×#6101C2semidirect
12. #11718330C2semidirect
13. #11718330C2semidirect
14. #11718310C2semidirect
15. #11718307C2semidirect
44. #88139C4semidirect
80. C2×Dic26C2×C4semidirect
84. C13×C22⋊C4C2×C4semidirect
87. C22⋊Dic13C2×C4semidirect
91. #6103C2×C4semidirect
92. #6103C2×C4semidirect
103. C4×Dic13C2×C4semidirect
171. #388D13semidirect
301. C22⋊C4C4×D13semidirect
309. C13#2367semidirect

Maximal subgroups

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

subgroupindex
C2×#881412
C2×#881392
C2×#881352
C13×#3882
#117186502
#117186182
#117186072
#117186052
C22⋊C4×Dic132
C4×#61032
C4×#61012
#117183302
#117183102
#117183072
#236713