Finite Group Databasebeta

← #13119814

Subgroups — #13119814

Order 1664.

576 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×#88142C211yesmaximal, characteristic, complemented
2C2×#88139C211yesmaximal, characteristic
3C2×#88139C211yesmaximal, characteristic
4C2×C4×Dic26C211yesmaximal, characteristic, complemented
5C13×#388C211yesmaximal, characteristic, complemented
6#11718655C211yesmaximal, characteristic, complemented
7#11718618C211yesmaximal, characteristic
8#11718609C211yesmaximal, characteristic, complemented
9#11718609C211yesmaximal, characteristic, complemented
10#11718605C211yesmaximal, characteristic, complemented
11#11718601C211yesmaximal, characteristic, complemented
12#11718337C211yesmaximal, characteristic, complemented
13#11718331C211yesmaximal, characteristic, complemented
14#11718310C211yesmaximal, characteristic, complemented
15#11718307C211yesmaximal, characteristic, complemented
16C22×C22⋊D13C2211yescharacteristic
17C22×Dic26C2211yescharacteristic
18C22×Dic26C2211yescharacteristic
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×C22⋊Dic13C2211yescharacteristic
27C2×#6103C2211yescharacteristic
28C2×#6103C2211yescharacteristic
29C2×#6103C2211yescharacteristic
30C2×#6103C2211yescharacteristic
31C2×#6103C2211yescharacteristic
32C2×#6103C2211yescharacteristic
33C2×C4⋊Dic13C2211yescharacteristic
34C2×C4⋊Dic13C2211yescharacteristic
35C2×#6101C2211yescharacteristic
36C2×#6101C2211yescharacteristic
37C2×#6101C2211yescharacteristic
38C2×#6101C2211yescharacteristic
39C2×#6101C2211yescharacteristic
40C2×#6101C2211yescharacteristic
41C2×C4×Dic13C2211yescharacteristic
42C2×C4×Dic13C2211yescharacteristic
43C2×C4×Dic13C2211yescharacteristic
44C2×C4×Dic13C2211yescharacteristic
45#88142—24no—
46#88139—24no—
47#88139—24no—
48C4×Dic26—24no—
49C13×#95C2211yescharacteristic
50C13×#95C2211yescharacteristic
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—22no—
66C22×Dic13C2311yescharacteristic
67C22×Dic13C2311yescharacteristic
68C22×Dic13C2311yescharacteristic
69C22×Dic13C2311yescharacteristic
70C22×Dic13C2311yescharacteristic
71C22×Dic13C2311yescharacteristic
72C22×Dic13C2311yescharacteristic
73C2×Dic26—22no—
74C2×Dic26—22no—
75C2×Dic26—22no—
76C2×Dic26—22no—
77C2×Dic26—22no—
78C2×Dic26D414yes—
79C13×C4⋊C4—22no—
80C13×C22⋊C4—22no—
81C13×C22⋊C4—22no—
82C13×C22⋊C4—22no—
83C42×C13—22no—
84C22⋊Dic13—22no—
85C22⋊Dic13—22no—
86C22⋊Dic13—22no—
87#6103—22no—
88#6103—22no—
89#6103—22no—
90#6103—22no—
91#6103—22no—
92#6103—22no—
93C4⋊Dic13—22no—
94C4⋊Dic13—22no—
95#6101—22no—
96#6101—22no—
97#6101—22no—
98#6101—22no—
99#6101—22no—
100#6101—22no—
101C4×Dic13—22no—
102C4×Dic13—22no—
103C4×Dic13—22no—
104C4×Dic13D414yes—
105#2545—131nomaximal, Sylow
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—21no—
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×C13C2×D412yes—
137C2×C4×C13C2×D412yes—
138C2×C4×C13#4112yes—
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×Dic13C2×D412yes—
156C2×Dic13C2×D412yes—
157C2×Dic13C2×D412yes—
158C2×Dic13C2×D412yes—
159C2×Dic13#4112yes—
160C2×Dic13#4112yes—
161Dic26—28no—
162Dic26—44no—
163C2×C4⋊Q8—131no—
164C2×#124—131no—
165C2×#124—131no—
166C2×C4×Q8—131no—
167#396—131no—
168#396—131no—
169#396—131no—
170#396—131no—
171#391—131no—
172#390—131no—
173#388—131no—
174#388—131no—
175#388—131no—
176#388D1311yescharacteristic, complemented
177C4×C4⋊C4—131no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13C22×D411yescharacteristic
186C22×C13C22×D411yescharacteristic
187C22×C13C2×#4111yescharacteristic
188C22×C13C2×#4111yescharacteristic
189C22×C13C2×#4111yescharacteristic
190C22×C132−1+411yescharacteristic
191C22×C132−1+411yescharacteristic
192C2×D13—41no—
193C2×D13—41no—
194C2×D13—41no—
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—41no—
209Dic13—41no—
210Dic13—41no—
211Dic13#12114yes—
212C22×Q8—131no—
213C22×Q8—131no—
214C22×D4—131no—
215C4⋊Q8—264no—
216#124—264no—
217#124—264no—
218C4×Q8—264no—
219C2×C4⋊C4—131no—
220C2×C4⋊C4—131no—
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⋊C4—131no—
234C2×C22⋊C4—131no—
235C2×C22⋊C4—131no—
236C2×C22⋊C4—131no—
237C2×C22⋊C4C2×D1311yescharacteristic
238C2×C22⋊C4C2×D1311yescharacteristic
239C2×C22⋊C4C2×D1311yescharacteristic
240C2×C42—131no—
241C2×C42—131no—
242C2×C42—131no—
243C2×C42—131no—
244C2×C42C2×D1311yescharacteristic
245#95—131no—
246#95—131no—
247#95—131no—
248#95—131no—
249#95C2×D1311yescharacteristic
250#95C2×D1311yescharacteristic
251C2×C13—81no—
252C2×C13C2×#12111yescharacteristic
253C2×C13#53211yescharacteristic
254C2×C13#53611yescharacteristic
255C2×C13#54811yescharacteristic
256C2×C13#54811yescharacteristic
257C2×C13#55611yescharacteristic
258C2×C13#55611yescharacteristic
259D13—81no—
260C24—131no—
261C24C22×D1311yescharacteristic
262C2×Q8—134no—
263C2×Q8—262no—
264C2×Q8—262no—
265C2×Q8—262no—
266C2×Q8—262no—
267C2×Q8—262no—
268C2×D4—262no—
269C2×D4—262no—
270C2×D4—262no—
271C22×C4—131no—
272C22×C4—131no—
273C22×C4—131no—
274C22×C4—131no—
275C22×C4—131no—
276C22×C4—131no—
277C22×C4—131no—
278C22×C4C22×D1311yescharacteristic
279C22×C4C22×D1311yescharacteristic
280C22×C4C22×D1311yescharacteristic
281C22×C4C22×D1311yescharacteristic
282C22×C4C22×D1311yescharacteristic
283C22×C4C22×D1311yescharacteristic
284C4⋊C4—22no—
285C4⋊C4—262no—
286C4⋊C4—262no—
287C4⋊C4—262no—
288C4⋊C4—262no—
289C4⋊C4—262no—
290C4⋊C4—262no—
291C4⋊C4—262no—
292C4⋊C4—262no—
293C22⋊C4—22no—
294C22⋊C4—22no—
295C22⋊C4—22no—
296C22⋊C4—262no—
297C22⋊C4—262no—
298C22⋊C4—262no—
299C22⋊C4—262no—
300C22⋊C4—262no—
301C22⋊C4—262no—
302C22⋊C4—262no—
303C22⋊C4—262no—
304C22⋊C4—262no—
305C42—22no—
306C42—134no—
307C42—262no—
308C42—262no—
309C42—262no—
310C13#254511yescharacteristic, complemented, Sylow
311C23—21no—
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—
325C23C23×D1311yescharacteristic
326Q8—268no—
327Q8—524no—
328D4—524no—
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—21no—
343C2×C4—21no—
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—261no—
364C2×C4—261no—
365C2×C4#612712yes—
366C2×C4D4×D1312yes—
367C2×C4D4×D1312yes—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—521no—
376C22—521no—
377C22—521no—
378C22—521no—
379C22—521no—
380C22—521no—
381C22—521no—
382C22C2×#612711yescharacteristic
383C22C2×D4×D1311yescharacteristic
384C22C2×D4×D1311yescharacteristic
385C22#41×D1311yescharacteristic
386C22#41×D1311yescharacteristic
387C22#8825711yescharacteristic
388C22#8825711yescharacteristic
389C4—22no—
390C4—22no—
391C4—22no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—134no—
396C4—262no—
397C4—262no—
398C4—262no—
399C4—521no—
400C4—521no—
401C4—521no—
402C2—81no—
403C2—1041no—
404C2#1171923811yescharacteristic
405C2#1171925311yescharacteristic
406C2#1171925711yescharacteristic
407C2D13×#12111yescharacteristic
408C2#1171935311yescharacteristic
409C2#1171938211yescharacteristic
410C2#1171940711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#388C2
prime radicalC22×C22⋊D13C22
hypercenter#388D13
hypocenterC13#2545
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#88142C2semidirect
4. C2×C4×Dic26C2semidirect
5. C13×#388C2semidirect
6. #11718655C2semidirect
8. #11718609C2semidirect
9. #11718609C2semidirect
10. #11718605C2semidirect
11. #11718601C2semidirect
12. #11718337C2semidirect
13. #11718331C2semidirect
14. #11718310C2semidirect
15. #11718307C2semidirect
176. #388D13semidirect
310. C13#2545semidirect

Maximal subgroups

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

subgroupindex
C2×#881422
C2×#881392
C2×C4×Dic262
C13×#3882
#117186552
#117186182
#117186092
#117186052
#117186012
#117183372
#117183312
#117183102
#117183072
#254513