Finite Group Databasebeta

← #15754522

Subgroups — #15754522

Order 3328.

788 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13114935C212yesmaximal, complemented
2C4×#88074C211yesmaximal, characteristic
3#13113356C212yesmaximal, complemented
4#13113174C211yesmaximal, characteristic
5C2×C13×#552C211yesmaximal, characteristic
6C13×#552—24no—
7C13×#552—24no—
8C2×C13×#126—21no—
9C2×C13×#125—21no—
10C2×C13×#125C411yescharacteristic, complemented
11C2×C13×#123—21no—
12C2×C13×C22⋊Q8C411yescharacteristic, complemented
13C2×C13×C22⋊Q8C2211yescharacteristic
14C2×C4×Q8×C13C411yescharacteristic, complemented
15C2×C4×D4×C13C2211yescharacteristic
16C2×C13×#117—21no—
17C2×C13×#117C2211yescharacteristic
18C22×C13×C4⋊C4C411yescharacteristic, complemented
19C2×#88074—21no—
20C4×C22⋊Dic13C2212yes—
21#11718868C2212yes—
22#11718130—24no—
23#11718124—24no—
24#11718120—21no—
25#11718118—21no—
26#11718117—21no—
27C22×Q8×C13C2×C411yescharacteristic
28C22×D4×C13D411yescharacteristic
29C23×C4×C13—21no—
30C23×C4×C13C2×C411yescharacteristic
31C23×C4×C13C2311yescharacteristic
32C13×#126—28no—
33C13×#125—28no—
34C13×#125—22no—
35C13×#125—22no—
36C13×#123—28no—
37C13×C22⋊Q8—22no—
38C13×C22⋊Q8—22no—
39C13×C22⋊Q8—22no—
40C13×C22⋊Q8D414yes—
41C4×Q8×C13—22no—
42C4×Q8×C13—22no—
43C4×D4×C13—22no—
44C4×D4×C13—22no—
45C13×#117—28no—
46C13×#117—22no—
47C13×#117D414yes—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4—22no—
55C2×C13×C4⋊C4—22no—
56C2×C13×C4⋊C4C2×C411yescharacteristic
57C2×C13×C4⋊C4C2×C411yescharacteristic
58C2×C13×C4⋊C4C2×C411yescharacteristic
59C2×C13×C4⋊C4D411yescharacteristic
60C2×C13×C22⋊C4—21no—
61C2×C13×C22⋊C4—21no—
62C2×C13×C22⋊C4—21no—
63C2×C13×C22⋊C4D411yescharacteristic
64C2×C13×C22⋊C4D411yescharacteristic
65C2×C42×C13—21no—
66C2×C42×C13—21no—
67C2×C42×C13C2×C411yescharacteristic
68C2×C22⋊Dic13—22no—
69C2×C4×Dic13—22no—
70C2×#6099—22no—
71#88074—24no—
72#88071—22no—
73C22⋊#1055—22no—
74C22⋊#1055—22no—
75#8363—131nomaximal, Sylow
76C24×C13C22⋊C411yescharacteristic
77C24×C13C2×D411yescharacteristic
78C2×Q8×C13—21no—
79C2×Q8×C13—42no—
80C2×Q8×C13C22⋊C412yes—
81C2×D4×C13—22no—
82C2×D4×C13—22no—
83C2×D4×C13—41no—
84C22×C4×C13—24no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13—21no—
89C22×C4×C13—21no—
90C22×C4×C13—21no—
91C22×C4×C13—42no—
92C22×C4×C13—42no—
93C22×C4×C13—42no—
94C22×C4×C13—42no—
95C22×C4×C13C22⋊C411yescharacteristic
96C22×C4×C13C22⋊C411yescharacteristic
97C22×C4×C13C22⋊C411yescharacteristic
98C22×C4×C13C22×C411yescharacteristic
99C22×C4×C13C2×D412yes—
100C22×C4×C13C2×D412yes—
101C22×C4×C13C2×D411yescharacteristic
102C22×Dic13—42no—
103C13×C4⋊C4—24no—
104C13×C4⋊C4—24no—
105C13×C4⋊C4—24no—
106C13×C4⋊C4—24no—
107C13×C4⋊C4—24no—
108C13×C4⋊C4—21no—
109C13×C4⋊C4—21no—
110C13×C4⋊C4—21no—
111C13×C4⋊C4—24no—
112C13×C4⋊C4—22no—
113C13×C4⋊C4C22⋊C412yes—
114C13×C4⋊C4C22⋊C412yes—
115C13×C4⋊C4C22⋊C412yes—
116C13×C22⋊C4—24no—
117C13×C22⋊C4—24no—
118C13×C22⋊C4—24no—
119C13×C22⋊C4—22no—
120C13×C22⋊C4—22no—
121C42×C13—24no—
122C42×C13—21no—
123C42×C13—21no—
124C42×C13—24no—
125C22⋊Dic13—24no—
126C22⋊Dic13—42no—
127C4×Dic13—44no—
128#6099—44no—
129C2×#1055—42no—
130C2×#552D1311yescharacteristic
131#1826—132no—
132C4×#99—131no—
133#1508—132no—
134#1465—131no—
135C23×C13—21no—
136C23×C13—21no—
137C23×C13—21no—
138C23×C13—21no—
139C23×C13—41no—
140C23×C13—41no—
141C23×C13—41no—
142C23×C13—41no—
143C23×C13#10412yes—
144C23×C13C2×C22⋊C411yescharacteristic
145C23×C13#12012yes—
146Q8×C13—42no—
147Q8×C13—42no—
148D4×C13—44no—
149C2×C4×C13—24no—
150C2×C4×C13—22no—
151C2×C4×C13—21no—
152C2×C4×C13—22no—
153C2×C4×C13—22no—
154C2×C4×C13—22no—
155C2×C4×C13—21no—
156C2×C4×C13—21no—
157C2×C4×C13—22no—
158C2×C4×C13—21no—
159C2×C4×C13—21no—
160C2×C4×C13—41no—
161C2×C4×C13—42no—
162C2×C4×C13—42no—
163C2×C4×C13—42no—
164C2×C4×C13—48no—
165C2×C4×C13—42no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—42no—
171C2×C4×C13—41no—
172C2×C4×C13—41no—
173C2×C4×C13C2×C22⋊C411yescharacteristic
174C2×C4×C13C2×C22⋊C411yescharacteristic
175C2×C4×C13#12012yes—
176C2×Dic13—44no—
177C2×Dic13—82no—
178C2×Dic13—82no—
179#1055—82no—
180#552—24no—
181#552—24no—
182C2×#126—21no—
183C2×#125—21no—
184C2×#125Dic1311yescharacteristic, complemented
185C2×#123—21no—
186C2×C22⋊Q8Dic1311yescharacteristic, complemented
187C2×C22⋊Q8C2×D1311yescharacteristic
188C2×C4×Q8Dic1311yescharacteristic, complemented
189C2×C4×D4C2×D1311yescharacteristic
190C2×#117—21no—
191C2×#117C2×D1311yescharacteristic
192C22×C4⋊C4Dic1311yescharacteristic, complemented
193C2×#99—261no—
194#407—132no—
195C4×C22⋊C4—132no—
196#342—261no—
197#339—264no—
198#328—264no—
199#324—261no—
200#323—261no—
201C22×C13—21no—
202C22×C13—21no—
203C22×C13—22no—
204C22×C13—22no—
205C22×C13—22no—
206C22×C13—22no—
207C22×C13—42no—
208C22×C13—42no—
209C22×C13—41no—
210C22×C13—41no—
211C22×C13—81no—
212C22×C13—81no—
213C22×C13#37911yescharacteristic
214C22×C13C2×#10411yescharacteristic
215C22×C13#42111yescharacteristic
216C4×C13—22no—
217C4×C13—21no—
218C4×C13—41no—
219C4×C13—42no—
220C4×C13—41no—
221C4×C13—42no—
222C4×C13—41no—
223C4×C13—42no—
224C4×C13—42no—
225C4×C13#41012yes—
226Dic13—84no—
227C22×Q8C2×Dic1311yescharacteristic
228C22×D4C22⋊D1311yescharacteristic
229C23×C4—21no—
230C23×C4C2×Dic1311yescharacteristic
231C23×C4C22×D1311yescharacteristic
232C2×M16—262no—
233#126—28no—
234#125—28no—
235#125—22no—
236#125—22no—
237#123—28no—
238C22⋊Q8—22no—
239C22⋊Q8—22no—
240C22⋊Q8—22no—
241C22⋊Q8C22⋊D1314yes—
242C4×Q8—22no—
243C4×Q8—22no—
244C4×D4—22no—
245C4×D4—22no—
246#117—28no—
247#117—22no—
248#117C22⋊D1314yes—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4C2×Dic1311yescharacteristic
258C2×C4⋊C4C2×Dic1311yescharacteristic
259C2×C4⋊C4C2×Dic1311yescharacteristic
260C2×C4⋊C4C22⋊D1311yescharacteristic
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—262no—
265C2×C22⋊C4C22⋊D1311yescharacteristic
266C2×C22⋊C4C22⋊D1311yescharacteristic
267C2×C42—21no—
268C2×C42—21no—
269C2×C42—262no—
270C2×C42C2×Dic1311yescharacteristic
271#99—264no—
272C22⋊C8—262no—
273C22⋊C8—262no—
274#95—262no—
275C2×C13—21no—
276C2×C13—21no—
277C2×C13—42no—
278C2×C13—42no—
279C2×C13#178211yescharacteristic
280C2×C13#178911yescharacteristic
281C2×C13#179611yescharacteristic
282C24C22⋊Dic1311yescharacteristic
283C24C2×C22⋊D1311yescharacteristic
284C2×Q8—21no—
285C2×Q8—42no—
286C2×Q8C22⋊Dic1312yes—
287C2×D4—22no—
288C2×D4—22no—
289C2×D4—41no—
290C22×C4—24no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—42no—
301C22×C4—522no—
302C22×C4C22⋊Dic1311yescharacteristic
303C22×C4C22⋊Dic1311yescharacteristic
304C22×C4C22⋊Dic1311yescharacteristic
305C22×C4C22×Dic1311yescharacteristic
306C22×C4C2×C22⋊D1312yes—
307C22×C4C2×C22⋊D1312yes—
308C22×C4C2×C22⋊D1311yescharacteristic
309M16—524no—
310C2×C8—522no—
311C4⋊C4—24no—
312C4⋊C4—24no—
313C4⋊C4—24no—
314C4⋊C4—24no—
315C4⋊C4—24no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—24no—
320C4⋊C4—22no—
321C4⋊C4C22⋊Dic1312yes—
322C4⋊C4C22⋊Dic1312yes—
323C4⋊C4C22⋊Dic1312yes—
324C22⋊C4—24no—
325C22⋊C4—24no—
326C22⋊C4—24no—
327C22⋊C4—22no—
328C22⋊C4—22no—
329C22⋊C4—264no—
330C22⋊C4—522no—
331C42—24no—
332C42—21no—
333C42—21no—
334C42—24no—
335C42—524no—
336C13#836311yescharacteristic, complemented, Sylow
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23#8807712yes—
346C23C2×C22⋊Dic1311yescharacteristic
347C23#8820712yes—
348Q8—42no—
349Q8—42no—
350D4—44no—
351C2×C4—24no—
352C2×C4—22no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—22no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—48no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—524no—
376C2×C4—1042no—
377C2×C4—1042no—
378C2×C4C2×C22⋊Dic1311yescharacteristic
379C2×C4C2×C22⋊Dic1311yescharacteristic
380C2×C4#8820712yes—
381C8—1042no—
382C22—21no—
383C22—21no—
384C22—22no—
385C22—22no—
386C22—22no—
387C22—22no—
388C22—42no—
389C22—42no—
390C22—41no—
391C22—41no—
392C22—81no—
393C22—81no—
394C22C2×#8807711yescharacteristic
395C22#1171889711yescharacteristic
396C22#1171890811yescharacteristic
397C4—22no—
398C4—21no—
399C4—41no—
400C4—42no—
401C4—41no—
402C4—42no—
403C4—42no—
404C4—41no—
405C4—42no—
406C4—1044no—
407C4#1171890112yes—
408C2—21no—
409C2—21no—
410C2—42no—
411C2—42no—
412C2#1311475411yescharacteristic
413C2#1311478011yescharacteristic
414C2#1311481111yescharacteristic
subgroupG/H
centerC22#11718908
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#552C2
socleC22×C13#379
prime radicalC22×D4×C13D4
cosocleC23×C4×C13C23
hypercenterC2×#552D13
hypocenterC13#8363
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
1. #13114935C2semidirect
3. #13113356C2semidirect
10. C2×C13×#125C4semidirect
12. C2×C13×C22⋊Q8C4semidirect
14. C2×C4×Q8×C13C4semidirect
18. C22×C13×C4⋊C4C4semidirect
184. C2×#125Dic13semidirect
186. C2×C22⋊Q8Dic13semidirect
188. C2×C4×Q8Dic13semidirect
192. C22×C4⋊C4Dic13semidirect
336. C13#8363semidirect

Maximal subgroups

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

subgroupindex
#131149352
C4×#880742
#131133562
#131131742
C2×C13×#5522
#836313