Finite Group Databasebeta

← #13119893

Subgroups — #13119893

Order 1664.

560 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88140C211yesmaximal, characteristic, complemented
2C2×#88133C211yesmaximal, characteristic, complemented
3C13×#390C211yesmaximal, characteristic, complemented
4#11718884C211yesmaximal, characteristic
5#11718881C211yesmaximal, characteristic, complemented
6#11718651C211yesmaximal, characteristic, complemented
7#11718645C211yesmaximal, characteristic, complemented
8#11718622C211yesmaximal, characteristic, complemented
9#11718618C211yesmaximal, characteristic, complemented
10#11718618C211yesmaximal, characteristic, complemented
11#11718612C211yesmaximal, characteristic, complemented
12#11718609C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
14#11718601C211yesmaximal, characteristic, complemented
15C4×C4⋊Dic13C211yesmaximal, characteristic, complemented
16C22×D4×C13C2211yescharacteristic
17C22×C22⋊D13C2211yescharacteristic
18C22×C22⋊D13C2211yescharacteristic
19C23×Dic13C2211yescharacteristic
20C2×C13×C4⋊C4C2211yescharacteristic
21C2×C13×C22⋊C4C2211yescharacteristic
22C2×C13×C22⋊C4C2211yescharacteristic
23C2×C13×C22⋊C4C2211yescharacteristic
24C2×C13×C22⋊C4C2211yescharacteristic
25C2×C42×C13C2211yescharacteristic
26C2×C22⋊Dic13C2211yescharacteristic
27C2×C22⋊Dic13C2211yescharacteristic
28C2×C22⋊Dic13C2211yescharacteristic
29C2×C22⋊Dic13C2211yescharacteristic
30C2×C22⋊Dic13C2211yescharacteristic
31C2×#6103C2211yescharacteristic
32C2×#6103C2211yescharacteristic
33C2×#6103C2211yescharacteristic
34C2×#6103C2211yescharacteristic
35C2×#6103C2211yescharacteristic
36C2×C4⋊Dic13C2211yescharacteristic
37C2×C4⋊Dic13C2211yescharacteristic
38C2×C4⋊Dic13C2211yescharacteristic
39C2×#6101C2211yescharacteristic
40C2×#6101C2211yescharacteristic
41C2×#6101C2211yescharacteristic
42C2×C4×Dic13C2211yescharacteristic
43C2×C4×Dic13C2211yescharacteristic
44C2×C4×Dic13C2211yescharacteristic
45#88140—24no—
46#88133—24no—
47#88071C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51#88071C2211yescharacteristic
52#88071C2211yescharacteristic
53C24×C13C2311yescharacteristic
54C24×C13C2311yescharacteristic
55C23×D13C2311yescharacteristic
56C2×D4×C13—22no—
57C2×D4×C13—22no—
58C2×D4×C13—41no—
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—
67C2×C22⋊D13—41no—
68C2×C22⋊D13—41no—
69C2×C22⋊D13—41no—
70C22×Dic13—22no—
71C22×Dic13—22no—
72C22×Dic13—41no—
73C22×Dic13C2311yescharacteristic
74C22×Dic13C2311yescharacteristic
75C22×Dic13C2311yescharacteristic
76C22×Dic13C2311yescharacteristic
77C22×Dic13C2311yescharacteristic
78C22×Dic13C2311yescharacteristic
79C22×Dic13C2311yescharacteristic
80C13×C4⋊C4—41no—
81C13×C22⋊C4—22no—
82C13×C22⋊C4—22no—
83C13×C22⋊C4—22no—
84C13×C22⋊C4—22no—
85C42×C13—22no—
86C22⋊Dic13—22no—
87C22⋊Dic13—22no—
88C22⋊Dic13—22no—
89C22⋊Dic13—41no—
90C22⋊Dic13—41no—
91#6103—22no—
92#6103—22no—
93#6103—22no—
94#6103—22no—
95#6103—41no—
96C4⋊Dic13—22no—
97C4⋊Dic13—22no—
98C4⋊Dic13D414yescomplemented
99#6101—22no—
100#6101—22no—
101#6101—41no—
102C4×Dic13—22no—
103C4×Dic13—41no—
104C4×Dic13—41no—
105#2554—131nomaximal, Sylow
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—21no—
118C23×C13—21no—
119C23×C13#4112yes—
120C23×C13C2411yescharacteristic
121C22×D13—21no—
122C22×D13—21no—
123C22×D13—21no—
124C22×D13—21no—
125C22×D13—21no—
126C22×D13—21no—
127C22×D13—21no—
128D4×C13—44no—
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×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13C2×D412yes—
142C2×C4×C13#4112yes—
143C2×C4×C13#4112yes—
144C22⋊D13—44no—
145C22⋊D13—44no—
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—21no—
157C2×Dic13—21no—
158C2×Dic13—21no—
159C2×Dic13—21no—
160C2×Dic13—21no—
161C2×Dic13—21no—
162C2×Dic13—21no—
163C2×Dic13—21no—
164C2×Dic13—44no—
165C2×Dic13C2×D412yes—
166C2×Dic13C2×D412yes—
167C2×Dic13#4112yes—
168C2×#126—131no—
169C2×#123—131no—
170#398—131no—
171#396—131no—
172#394—131no—
173#392—131no—
174#390—131no—
175#390—131no—
176#390D1311yescharacteristic, complemented
177#388—131no—
178#388—131no—
179#388—131no—
180#386—131no—
181C4×C4⋊C4—131no—
182C4×C22⋊C4—131no—
183C22×C13—22no—
184C22×C13—22no—
185C22×C13—22no—
186C22×C13—41no—
187C22×C13—41no—
188C22×C13—41no—
189C22×C13—41no—
190C22×C13—41no—
191C22×C13—41no—
192C22×C13—41no—
193C22×C13—41no—
194C22×C13—41no—
195C22×C13—41no—
196C22×C13—41no—
197C22×C13C22×D411yescharacteristic
198C22×C13C2×#4111yescharacteristic
199C22×C13C2×#4111yescharacteristic
200C22×C13C2×#4111yescharacteristic
201C22×C13C2×#4111yescharacteristic
202C22×C13H(5,𝔽2)11yescharacteristic
203C22×C13H(5,𝔽2)11yescharacteristic
204C2×D13—41no—
205C2×D13—41no—
206C2×D13—41no—
207C2×D13—41no—
208C2×D13—41no—
209C2×D13—41no—
210C2×D13—41no—
211C4×C13—22no—
212C4×C13—22no—
213C4×C13—22no—
214C4×C13—41no—
215C4×C13—41no—
216Dic13—22no—
217Dic13—22no—
218Dic13—22no—
219Dic13—41no—
220Dic13—41no—
221Dic13—41no—
222Dic13—41no—
223C22×D4—131no—
224C22×D4—131no—
225C22×D4C2×D1311yescharacteristic
226C23×C4—131no—
227#126—264no—
228#123—264no—
229C2×C4⋊C4—131no—
230C2×C4⋊C4—131no—
231C2×C4⋊C4—131no—
232C2×C4⋊C4—131no—
233C2×C4⋊C4—131no—
234C2×C4⋊C4—131no—
235C2×C4⋊C4C2×D1311yescharacteristic
236C2×C22⋊C4—131no—
237C2×C22⋊C4—131no—
238C2×C22⋊C4—131no—
239C2×C22⋊C4—131no—
240C2×C22⋊C4—131no—
241C2×C22⋊C4—131no—
242C2×C22⋊C4—131no—
243C2×C22⋊C4—131no—
244C2×C22⋊C4—131no—
245C2×C22⋊C4—131no—
246C2×C22⋊C4C2×D1311yescharacteristic
247C2×C22⋊C4C2×D1311yescharacteristic
248C2×C22⋊C4C2×D1311yescharacteristic
249C2×C22⋊C4C2×D1311yescharacteristic
250C2×C42—131no—
251C2×C42—131no—
252C2×C42—131no—
253C2×C42C2×D1311yescharacteristic
254#95—131no—
255#95—131no—
256#95—131no—
257#95—131no—
258#95—131no—
259#95—131no—
260C2×C13—42no—
261C2×C13—81no—
262C2×C13#52911yescharacteristic
263C2×C13#53211yescharacteristic
264C2×C13#53811yescharacteristic
265C2×C13#54611yescharacteristic
266C2×C13#55011yescharacteristic
267C2×C13#55111yescharacteristic
268C2×C13#55311yescharacteristic
269D13—81no—
270C24—131no—
271C24C22×D1311yescharacteristic
272C24C22×D1311yescharacteristic
273C2×D4—22no—
274C2×D4—22no—
275C2×D4—41no—
276C2×D4—262no—
277C2×D4—262no—
278C2×D4—262no—
279C2×D4—521no—
280C2×D4—521no—
281C2×D4—521no—
282C22×C4—131no—
283C22×C4—131no—
284C22×C4—131no—
285C22×C4—131no—
286C22×C4—131no—
287C22×C4—131no—
288C22×C4—131no—
289C22×C4—262no—
290C22×C4—262no—
291C22×C4—521no—
292C22×C4C22×D1311yescharacteristic
293C22×C4C22×D1311yescharacteristic
294C22×C4C22×D1311yescharacteristic
295C22×C4C22×D1311yescharacteristic
296C22×C4C22×D1311yescharacteristic
297C4⋊C4—41no—
298C4⋊C4—134no—
299C4⋊C4—262no—
300C4⋊C4—262no—
301C4⋊C4—262no—
302C4⋊C4—262no—
303C4⋊C4—521no—
304C22⋊C4—22no—
305C22⋊C4—22no—
306C22⋊C4—22no—
307C22⋊C4—22no—
308C22⋊C4—262no—
309C22⋊C4—262no—
310C22⋊C4—262no—
311C22⋊C4—262no—
312C22⋊C4—262no—
313C22⋊C4—262no—
314C22⋊C4—262no—
315C22⋊C4—521no—
316C22⋊C4—521no—
317C22⋊C4—521no—
318C42—22no—
319C42—262no—
320C42—521no—
321C42—521no—
322C13#255411yescharacteristic, complemented, Sylow
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—261no—
337C23—261no—
338C23—261no—
339C23—261no—
340C23—261no—
341C23—261no—
342C23—261no—
343C23#612712yes—
344C23C23×D1311yescharacteristic
345D4—44no—
346D4—524no—
347D4—524no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—132no—
361C2×C4—132no—
362C2×C4—132no—
363C2×C4—261no—
364C2×C4—261no—
365C2×C4—261no—
366C2×C4—261no—
367C2×C4—261no—
368C2×C4—261no—
369C2×C4—261no—
370C2×C4—261no—
371C2×C4—261no—
372C2×C4—261no—
373C2×C4—261no—
374C2×C4—261no—
375C2×C4—261no—
376C2×C4—261no—
377C2×C4—261no—
378C2×C4—261no—
379C2×C4—261no—
380C2×C4—261no—
381C2×C4—524no—
382C2×C4D4×D1312yes—
383C2×C4#612912yes—
384C2×C4#612912yes—
385C22—22no—
386C22—22no—
387C22—22no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—521no—
400C22—521no—
401C22—521no—
402C22—521no—
403C22—521no—
404C22—521no—
405C22—521no—
406C22C2×#612711yescharacteristic
407C22C2×D4×D1311yescharacteristic
408C22C2×#612911yescharacteristic
409C22C2×#612911yescharacteristic
410C22#8825111yescharacteristic
411C22#41×D1311yescharacteristic
412C22#8825611yescharacteristic
413C4—22no—
414C4—22no—
415C4—22no—
416C4—41no—
417C4—41no—
418C4—262no—
419C4—262no—
420C4—262no—
421C4—521no—
422C4—521no—
423C4—521no—
424C4—521no—
425C2—42no—
426C2—81no—
427C2—1041no—
428C2#1171920011yescharacteristic
429C2#1171924311yescharacteristic
430C2#1171925511yescharacteristic
431C2#1171930111yescharacteristic
432C2#1171932311yescharacteristic
433C2#1171938311yescharacteristic
434C2#1171942311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#390C2
prime radical#11718884C2
hypercenter#390D13
hypocenterC13#2554
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#88140C2semidirect
2. C2×#88133C2semidirect
3. C13×#390C2semidirect
5. #11718881C2semidirect
6. #11718651C2semidirect
7. #11718645C2semidirect
8. #11718622C2semidirect
9. #11718618C2semidirect
10. #11718618C2semidirect
11. #11718612C2semidirect
12. #11718609C2semidirect
13. C22⋊C4×Dic13C2semidirect
14. #11718601C2semidirect
15. C4×C4⋊Dic13C2semidirect
98. C4⋊Dic13D4semidirect
176. #390D13semidirect
322. C13#2554semidirect

Maximal subgroups

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

subgroupindex
C2×#881402
C2×#881332
C13×#3902
#117188842
#117188812
#117186512
#117186452
#117186222
#117186182
#117186122
#117186092
C22⋊C4×Dic132
#117186012
C4×C4⋊Dic132
#255413