Finite Group Databasebeta

← #15778897

Subgroups — #15778897

Order 3328.

512 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718131C212yesmaximal
2#13114828C211yesmaximal, characteristic
3#13114824C211yesmaximal, characteristic
4#13112954C212yesmaximal
5C13×#2322C211yesmaximal, characteristic
6C2×C13×#123C2211yescharacteristic
7C2×C4×D4×C13C2211yescharacteristic
8C22×C13×C4⋊C4C411yescharacteristic, complemented
9C13×#389—21no—
10C13×#388—21no—
11C13×#387—21no—
12C13×#386C2211yescharacteristic
13C13×#385—21no—
14C13×#385C411yescharacteristic, complemented
15C13×#381C411yescharacteristic, complemented
16C4×C13×C22⋊C4C411yescharacteristic, complemented
17C2×#88074C2212yes—
18C2×#88073C2212yes—
19#11718873—21no—
20#11718585—21no—
21#11718131—24no—
22#11718122—21no—
23#11718118—21no—
24C22×D4×C13C2311yescharacteristic
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13C2×C411yescharacteristic
27C23×C4×C13C2×C411yescharacteristic
28C23×C4×C13D411yescharacteristic
29C13×#123—21no—
30C13×#123—21no—
31C13×#123D412yes—
32C13×#123Q812yes—
33C4×D4×C13—41no—
34C4×D4×C13—41no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4—41no—
40C2×C13×C4⋊C4—41no—
41C2×C13×C4⋊C4D411yescharacteristic
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4C2×C411yescharacteristic
45C2×C13×C22⋊C4C2×C411yescharacteristic
46C2×C13×C22⋊C4C2×C411yescharacteristic
47C2×C13×C22⋊C4D411yescharacteristic
48C2×C42×C13—21no—
49C2×C42×C13D411yescharacteristic
50C2×C22⋊Dic13—22no—
51C2×C4⋊Dic13—41no—
52C2×#6099—22no—
53C13×#95—21no—
54C13×#95—21no—
55C13×#95—21no—
56C13×#95—21no—
57C13×#95—21no—
58#88074—22no—
59#88074—22no—
60#88073—22no—
61#88073—22no—
62#88071—41no—
63C4⋊#1055—41no—
64C4⋊#1055—41no—
65#12796—131nomaximal, Sylow
66C24×C13C22×C411yescharacteristic
67C24×C13C2×D411yescharacteristic
68C2×D4×C13—41no—
69C2×D4×C13—41no—
70C2×D4×C13C2×D411yescharacteristic
71C2×D4×C13C2×Q811yescharacteristic
72C2×D4×C13#4111yescharacteristic
73C2×D4×C13#4111yescharacteristic
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13—21no—
80C22×C4×C13—21no—
81C22×C4×C13—21no—
82C22×C4×C13—21no—
83C22×C4×C13—41no—
84C22×C4×C13—41no—
85C22×C4×C13—41no—
86C22×C4×C13—81no—
87C22×C4×C13—81no—
88C22×C4×C13—81no—
89C22×C4×C13C22⋊C411yescharacteristic
90C22×C4×C13C22⋊C411yescharacteristic
91C22×C4×C13C22⋊C411yescharacteristic
92C22×C4×C13C22⋊C411yescharacteristic
93C22×C4×C13C4⋊C412yescomplemented
94C22×C4×C13C2×D411yescharacteristic
95C22×Dic13—42no—
96C13×C4⋊C4—22no—
97C13×C4⋊C4—22no—
98C13×C4⋊C4—41no—
99C13×C4⋊C4—42no—
100C13×C4⋊C4—41no—
101C13×C4⋊C4—41no—
102C13×C4⋊C4—81no—
103C13×C22⋊C4—21no—
104C13×C22⋊C4—22no—
105C13×C22⋊C4—22no—
106C13×C22⋊C4—41no—
107C13×C22⋊C4—41no—
108C13×C22⋊C4—41no—
109C13×C22⋊C4—81no—
110C13×C22⋊C4C4⋊C412yescomplemented
111C42×C13—21no—
112C42×C13—21no—
113C42×C13—81no—
114C22⋊Dic13—42no—
115C22⋊Dic13—42no—
116C4⋊Dic13—82no—
117#6099—42no—
118#6099—42no—
119C2×#1055—42no—
120#2322D1311yescharacteristic
121C2×#352—132no—
122#1800—131no—
123#1799—131no—
124#1390—132no—
125C23×C13—21no—
126C23×C13—21no—
127C23×C13—21no—
128C23×C13—21no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13—41no—
132C23×C13—41no—
133C23×C13C2×C22⋊C411yescharacteristic
134C23×C13C2×C4⋊C411yescharacteristic
135C23×C13#11711yescharacteristic
136C23×C13#12111yescharacteristic
137C23×C13C22⋊Q811yescharacteristic
138D4×C13—41no—
139D4×C13—41no—
140D4×C13—41no—
141D4×C13—41no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—22no—
145C2×C4×C13—22no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—41no—
150C2×C4×C13—42no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—42no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—42no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—81no—
167C2×C4×C13—81no—
168C2×C4×C13—81no—
169C2×C4×C13—82no—
170C2×C4×C13#9911yescharacteristic
171C2×C4×C13#9911yescharacteristic
172C2×C4×C13#12111yescharacteristic
173C2×C4×C13C22⋊Q811yescharacteristic
174C2×Dic13—82no—
175C2×Dic13—82no—
176C2×Dic13—82no—
177#1055—82no—
178C2×#123C2×D1311yescharacteristic
179C2×C4×D4C2×D1311yescharacteristic
180C22×C4⋊C4Dic1311yescharacteristic, complemented
181#423—261no—
182C2×#100—132no—
183C2×#99—132no—
184#389—21no—
185#388—21no—
186#387—21no—
187#386C2×D1311yescharacteristic
188#385—21no—
189#385Dic1311yescharacteristic, complemented
190#381Dic1311yescharacteristic, complemented
191#380—261no—
192C4×C22⋊C4Dic1311yescharacteristic, complemented
193#352—264no—
194#343—261no—
195#342—261no—
196C22×C13—21no—
197C22×C13—21no—
198C22×C13—21no—
199C22×C13—21no—
200C22×C13—21no—
201C22×C13—21no—
202C22×C13—41no—
203C22×C13—41no—
204C22×C13—41no—
205C22×C13—41no—
206C22×C13—42no—
207C22×C13—41no—
208C22×C13—41no—
209C22×C13—41no—
210C22×C13—41no—
211C22×C13—81no—
212C22×C13#38011yescharacteristic
213C22×C13C2×#9911yescharacteristic
214C22×C13#41011yescharacteristic
215C4×C13—21no—
216C4×C13—21no—
217C4×C13—21no—
218C4×C13—21no—
219C4×C13—42no—
220C4×C13—42no—
221C4×C13—41no—
222C4×C13—41no—
223C4×C13—41no—
224C4×C13—81no—
225C4×C13—81no—
226Dic13—162no—
227C22×D4C22×D1311yescharacteristic
228C23×C4C2×Dic1311yescharacteristic
229C23×C4C2×Dic1311yescharacteristic
230C23×C4C2×Dic1311yescharacteristic
231C23×C4C22⋊D1311yescharacteristic
232C2×M16—262no—
233#123—21no—
234#123—21no—
235#123Dic2612yes—
236#123D5212yes—
237C4×D4—41no—
238C4×D4—41no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—41no—
244C2×C4⋊C4—41no—
245C2×C4⋊C4—521no—
246C2×C4⋊C4C22⋊D1311yescharacteristic
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—262no—
250C2×C22⋊C4C2×Dic1311yescharacteristic
251C2×C22⋊C4C2×Dic1311yescharacteristic
252C2×C22⋊C4C2×Dic1311yescharacteristic
253C2×C22⋊C4C22⋊D1311yescharacteristic
254C2×C42—21no—
255C2×C42C22⋊D1311yescharacteristic
256C4⋊C8—521no—
257C4⋊C8—521no—
258#100—262no—
259#100—262no—
260#99—262no—
261#99—262no—
262#95—21no—
263#95—21no—
264#95—21no—
265#95—21no—
266#95—21no—
267#95—521no—
268C2×C13—21no—
269C2×C13—21no—
270C2×C13—41no—
271C2×C13—41no—
272C2×C13—41no—
273C2×C13—41no—
274C2×C13#179911yescharacteristic
275C2×C13#212111yescharacteristic
276C2×C13#212311yescharacteristic
277C24C22×Dic1311yescharacteristic
278C24C2×C22⋊D1311yescharacteristic
279C2×D4—41no—
280C2×D4—41no—
281C2×D4C2×Dic2611yescharacteristic
282C2×D4C2×D5211yescharacteristic
283C2×D4#612711yescharacteristic
284C2×D4#612711yescharacteristic
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—81no—
298C22×C4—81no—
299C22×C4—81no—
300C22×C4—522no—
301C22×C4C4⋊Dic1312yescomplemented
302C22×C4C22⋊Dic1311yescharacteristic
303C22×C4C22⋊Dic1311yescharacteristic
304C22×C4C22⋊Dic1311yescharacteristic
305C22×C4C22⋊Dic1311yescharacteristic
306C22×C4C2×C22⋊D1311yescharacteristic
307M16—522no—
308M16—522no—
309C2×C8—522no—
310C4⋊C4—22no—
311C4⋊C4—22no—
312C4⋊C4—41no—
313C4⋊C4—42no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—81no—
317C4⋊C4—1042no—
318C22⋊C4—22no—
319C22⋊C4—21no—
320C22⋊C4—22no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—81no—
325C22⋊C4—522no—
326C22⋊C4—522no—
327C22⋊C4C4⋊Dic1312yescomplemented
328C42—21no—
329C42—21no—
330C42—81no—
331C13#1279611yescharacteristic, complemented, Sylow
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23#8817811yescharacteristic
341C23C2×C4⋊Dic1311yescharacteristic
342C23#8818011yescharacteristic
343C23#8818411yescharacteristic
344C23C2×C22⋊Dic1311yescharacteristic
345D4—41no—
346D4—41no—
347D4—41no—
348D4—41no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4—82no—
377C2×C4—1042no—
378C2×C4—1042no—
379C2×C4—1042no—
380C2×C4#8807411yescharacteristic
381C2×C4#8807411yescharacteristic
382C2×C4#8817811yescharacteristic
383C2×C4#8818411yescharacteristic
384C8—1042no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—42no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—81no—
401C22#1171887311yescharacteristic
402C22C2×#8807411yescharacteristic
403C22#1171890111yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—42no—
409C4—41no—
410C4—41no—
411C4—41no—
412C4—42no—
413C4—81no—
414C4—81no—
415C4—2082no—
416C2—21no—
417C2—21no—
418C2—41no—
419C2—41no—
420C2—41no—
421C2—41no—
422C2#1311482411yescharacteristic
423C2#1311648211yescharacteristic
424C2#1311649011yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC24×C13C22×C4
FrattiniC22×D4C22×D13
FittingC13×#2322C2
socleC22×C13C2×#99
prime radical, cosocleC22×D4×C13C23
hypercenter#2322D13
hypocenterC13#12796
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2322

Complements

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

NH ≅ G/Ntype
8. C22×C13×C4⋊C4C4semidirect
14. C13×#385C4semidirect
15. C13×#381C4semidirect
16. C4×C13×C22⋊C4C4semidirect
93. C22×C4×C13C4⋊C4semidirect
110. C13×C22⋊C4C4⋊C4semidirect
180. C22×C4⋊C4Dic13semidirect
189. #385Dic13semidirect
190. #381Dic13semidirect
192. C4×C22⋊C4Dic13semidirect
301. C22×C4C4⋊Dic13semidirect
327. C22⋊C4C4⋊Dic13semidirect
331. C13#12796semidirect

Maximal subgroups

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

subgroupindex
C2×#117181312
#131148282
#131148242
#131129542
C13×#23222
#1279613