Finite Group Databasebeta

← #15759746

Subgroups — #15759746

Order 3328.

428 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123487C211yesmaximal, characteristic, complemented
2#13113447C211yesmaximal, characteristic, complemented
3#13113270C211yesmaximal, characteristic, complemented
4#13113253C211yesmaximal, characteristic, complemented
5#13112734C211yesmaximal, characteristic, complemented
6#13112707C211yesmaximal, characteristic, complemented
7C13×#3115C211yesmaximal, characteristic
8C13×#532C2211yescharacteristic
9C4×C13×#41C2211yescharacteristic
10C13×#482—21no—
11C13×#475C411yescharacteristic
12C13×#474C411yescharacteristic
13C13×#460C411yescharacteristic
14C13×#459C411yescharacteristic
15C13×#449—21no—
16C13×#442—21no—
17C13×#440—21no—
18C13×#432C2211yescharacteristic
19#11718895—21no—
20#11718661—22no—
21#11718660—21no—
22#11718587—22no—
23#11718587C2211yescharacteristic
24#11718586C2211yescharacteristic
25C4×#6099C2211yescharacteristic
26C2×#88043C2211yescharacteristic
27#11718132—22no—
28Q8⋊#1055—21no—
29D4⋊#1055—22no—
30D4⋊#1055—21no—
31C2×C13×#41—21no—
32C2×C13×#41D411yescharacteristic
33C2×C13×SD16—21no—
34C2×C13×D8—21no—
35C13×C4⋊Q8C2×C411yescharacteristic
36C13×#127C2×C411yescharacteristic
37C13×#124—21no—
38C13×#121—21no—
39C13×#121—21no—
40C4×Q8×C13C2×C411yescharacteristic
41C4×Q8×C13D411yescharacteristic
42C4×D4×C13—21no—
43C4×D4×C13—21no—
44C4×D4×C13—21no—
45C4×D4×C13—21no—
46C4×D4×C13C2×C411yescharacteristic
47C4×D4×C13D411yescharacteristic
48C13×#117—21no—
49C13×#117D411yescharacteristic
50C2×C42×C13—21no—
51C2×C42×C13C2311yescharacteristic
52C2×#6099—21no—
53C22×#1055—21no—
54C13×#107—21no—
55C13×#106—21no—
56C13×C4⋊C8C2×C411yescharacteristic
57C13×C4⋊C8C2×C411yescharacteristic
58C13×#103—21no—
59C13×#102—21no—
60C13×#102—21no—
61C13×#102—21no—
62C13×C22⋊C8—21no—
63C13×#97—21no—
64C22⋊#1055—24no—
65C22⋊#1055—21no—
66C22⋊#1055—21no—
67C4⋊#1055—24no—
68C4⋊#1055—21no—
69C4⋊#1055—21no—
70#88043—21no—
71#88043—21no—
72#88043—21no—
73#88043D412yes—
74C4×#1055—21no—
75C4×#1055D412yes—
76#9313—131nomaximal, Sylow
77C13×#41—41no—
78C13×#41—41no—
79C13×#41—82no—
80C2×Q8×C13—21no—
81C2×Q8×C13C22⋊C411yescharacteristic
82C2×D4×C13—21no—
83C2×D4×C13—21no—
84C2×D4×C13—21no—
85C2×D4×C13—21no—
86C2×D4×C13—41no—
87C2×D4×C13C22⋊C411yescharacteristic
88C22×C4×C13—21no—
89C22×C4×C13—21no—
90C22×C4×C13—21no—
91C22×C4×C13—41no—
92C22×C4×C13C2×D411yescharacteristic
93C22×C4×C13#4111yescharacteristic
94C22×C4×C13#4111yescharacteristic
95C13×SD16—42no—
96C13×D8—42no—
97C2×C8×C13—21no—
98C2×C8×C13—21no—
99C13×C4⋊C4—21no—
100C13×C4⋊C4—21no—
101C13×C4⋊C4—21no—
102C13×C4⋊C4—21no—
103C13×C4⋊C4C22⋊C411yescharacteristic
104C13×C4⋊C4C22⋊C411yescharacteristic
105C13×C22⋊C4—21no—
106C13×C22⋊C4—21no—
107C13×C22⋊C4—21no—
108C13×C22⋊C4—41no—
109C13×C22⋊C4—41no—
110C42×C13—21no—
111C42×C13—21no—
112C42×C13—21no—
113C42×C13C22×C411yescharacteristic
114C42×C13C2×D411yescharacteristic
115C42×C13C2×D411yescharacteristic
116C42×C13C2×D411yescharacteristic
117#6099—41no—
118#6099—41no—
119C2×#1055—22no—
120C2×#1055—22no—
121C2×#1055—41no—
122C2×#1055—41no—
123C2×#1055—41no—
124C2×#1055—41no—
125#3115D1311yescharacteristic
126#2923—131no—
127#1530—131no—
128#1488—131no—
129#1484—131no—
130#1302—131no—
131#1291—131no—
132C23×C13—21no—
133C23×C13—41no—
134C23×C13#12311yescharacteristic
135Q8×C13—21no—
136Q8×C13—21no—
137Q8×C13—81no—
138D4×C13—21no—
139D4×C13—21no—
140D4×C13—42no—
141D4×C13—42no—
142D4×C13—41no—
143D4×C13—41no—
144D4×C13—81no—
145D4×C13—82no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—21no—
150C2×C4×C13—21no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—42no—
154C2×C4×C13—41no—
155C2×C4×C13—81no—
156C2×C4×C13—81no—
157C2×C4×C13—82no—
158C2×C4×C13C2×C22⋊C411yescharacteristic
159C2×C4×C13C4×D411yescharacteristic
160C2×C4×C13C4×D411yescharacteristic
161C2×C4×C13#12011yescharacteristic
162C2×C4×C13#12111yescharacteristic
163C2×C4×C13#12111yescharacteristic
164C8×C13—41no—
165C8×C13—41no—
166#1055—42no—
167#1055—42no—
168#1055—81no—
169#1055—81no—
170#532C2×D1311yescharacteristic
171C4×#41C2×D1311yescharacteristic
172#482—21no—
173#475Dic1311yescharacteristic
174#474Dic1311yescharacteristic
175#460Dic1311yescharacteristic
176#459Dic1311yescharacteristic
177#449—21no—
178#442—21no—
179#440—21no—
180#433—262no—
181#432—131no—
182#432—262no—
183#432C2×D1311yescharacteristic
184#431—131no—
185#424—261no—
186#408—261no—
187C4×M16—131no—
188C2×#97—131no—
189#329—262no—
190Q8⋊C8—261no—
191D4⋊C8—262no—
192D4⋊C8—261no—
193C22×C13—21no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13—41no—
197C22×C13—41no—
198C22×C13—41no—
199C22×C13—81no—
200C22×C13—81no—
201C22×C13—81no—
202C22×C13#38611yescharacteristic
203C4×C13—21no—
204C4×C13—21no—
205C4×C13—21no—
206C4×C13—21no—
207C4×C13—21no—
208C4×C13—41no—
209C4×C13—41no—
210C4×C13—41no—
211C4×C13—81no—
212C4×C13#42111yescharacteristic
213C4×C13#42111yescharacteristic
214C2×#41—21no—
215C2×#41C22⋊D1311yescharacteristic
216C2×SD16—21no—
217C2×D8—21no—
218C2×M16—261no—
219C22×C8—261no—
220C4⋊Q8C2×Dic1311yescharacteristic
221#127C2×Dic1311yescharacteristic
222#124—21no—
223#121—21no—
224#121—21no—
225C4×Q8C2×Dic1311yescharacteristic
226C4×Q8C22⋊D1311yescharacteristic
227C4×D4—21no—
228C4×D4—21no—
229C4×D4—21no—
230C4×D4—21no—
231C4×D4C2×Dic1311yescharacteristic
232C4×D4C22⋊D1311yescharacteristic
233#117—21no—
234#117C22⋊D1311yescharacteristic
235C2×C42—21no—
236C2×C42C22×D1311yescharacteristic
237#107—21no—
238#106—21no—
239C4⋊C8—264no—
240C4⋊C8—261no—
241C4⋊C8—261no—
242C4⋊C8C2×Dic1311yescharacteristic
243C4⋊C8C2×Dic1311yescharacteristic
244#103—21no—
245#102—21no—
246#102—21no—
247#102—21no—
248C22⋊C8—21no—
249C22⋊C8—264no—
250C22⋊C8—261no—
251C22⋊C8—261no—
252#97—21no—
253#97—132no—
254#97—261no—
255#97—261no—
256#97—261no—
257C4×C8—132no—
258C4×C8—261no—
259C2×C13—41no—
260C2×C13—81no—
261C2×C13—161no—
262C2×C13#188111yescharacteristic
263C2×C13#189711yescharacteristic
264C2×C13#190311yescharacteristic
265#41—41no—
266#41—41no—
267#41—82no—
268C2×Q8—21no—
269C2×Q8C22⋊Dic1311yescharacteristic
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—41no—
275C2×D4C22⋊Dic1311yescharacteristic
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—41no—
280C22×C4#612911yescharacteristic
281C22×C4#612911yescharacteristic
282C22×C4C2×C22⋊D1311yescharacteristic
283SD16—42no—
284D8—42no—
285M16—521no—
286M16—521no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—262no—
290C2×C8—262no—
291C2×C8—521no—
292C2×C8—521no—
293C2×C8—521no—
294C2×C8—521no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4C22⋊Dic1311yescharacteristic
300C4⋊C4C22⋊Dic1311yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C42—21no—
307C42—21no—
308C42—21no—
309C42D4×D1311yescharacteristic
310C42D4×D1311yescharacteristic
311C42C22×Dic1311yescharacteristic
312C42C2×C22⋊D1311yescharacteristic
313C13#931311yescharacteristic, complemented, Sylow
314C23—21no—
315C23—41no—
316C23#8818911yescharacteristic
317Q8—21no—
318Q8—21no—
319Q8—81no—
320D4—21no—
321D4—21no—
322D4—42no—
323D4—42no—
324D4—41no—
325D4—41no—
326D4—81no—
327D4—82no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—82no—
340C2×C4D4×Dic1311yescharacteristic
341C2×C4D4×Dic1311yescharacteristic
342C2×C4#8819111yescharacteristic
343C2×C4#8819311yescharacteristic
344C2×C4#8819311yescharacteristic
345C2×C4C2×C22⋊Dic1311yescharacteristic
346C8—41no—
347C8—41no—
348C8—522no—
349C8—522no—
350C8—1041no—
351C8—1041no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—81no—
359C22—81no—
360C22—81no—
361C22#1171888111yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—81no—
371C4#1171889711yescharacteristic
372C4#1171889711yescharacteristic
373C2—41no—
374C2—81no—
375C2—161no—
376C2#1311520011yescharacteristic
377C2#1311528511yescharacteristic
378C2#1311531811yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
Fitting, prime radicalC13×#3115C2
socleC22×C13#386
cosocleC2×C42×C13C23
hypercenter#3115D13
hypocenterC13#9313
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3115

Complements

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

NH ≅ G/Ntype
1. #13123487C2semidirect
2. #13113447C2semidirect
3. #13113270C2semidirect
4. #13113253C2semidirect
5. #13112734C2semidirect
6. #13112707C2semidirect
313. C13#9313semidirect

Maximal subgroups

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

subgroupindex
#131234872
#131134472
#131132702
#131132532
#131127342
#131127072
C13×#31152
#931313