Finite Group Databasebeta

← #15758794

Subgroups — #15758794

Order 3328.

432 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124645C211yesmaximal, characteristic
2#13123501C211yesmaximal, characteristic
3#13113521C211yesmaximal, characteristic, complemented
4#13113221C211yesmaximal, characteristic
5#13112733C211yesmaximal, characteristic, complemented
6#13112711C211yesmaximal, characteristic, complemented
7C2×C13×#333C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C4×#6127C2211yescharacteristic
10C2×C13×C4⋊C8C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12#11718771—21no—
13#11718762—21no—
14#11718755C412yes—
15#11718752—21no—
16#11718748C412yes—
17#11718745—21no—
18#11718627—21no—
19#11718625—21no—
20#11718586C2211yescharacteristic
21#11718585C2211yescharacteristic
22#11718585C2211yescharacteristic
23#11718501—22no—
24#11718496—21no—
25#11718494—21no—
26C13×#333—21no—
27C13×#333—21no—
28#11718139—22no—
29#11718076—21no—
30#11718075—21no—
31C22×Q8×C13—21no—
32C2×#6127D411yescharacteristic
33C22×C8×C13—21no—
34C22×C8×C13—21no—
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8—21no—
37C13×C4⋊Q8—21no—
38C13×C4⋊Q8C2×C412yes—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4—21no—
41C2×C42×C13C2311yescharacteristic
42C4×C22⋊D13—21no—
43C4×C22⋊D13—21no—
44#88180D411yescharacteristic
45C2×#6099—21no—
46C2×#6099—21no—
47C4×D52C2×C411yescharacteristic
48C4×D52D411yescharacteristic
49#88126—21no—
50C42×D13—21no—
51C4×Dic26C2×C411yescharacteristic
52C4×Dic26D411yescharacteristic
53C13×C4⋊C8—21no—
54C13×C4⋊C8—21no—
55C13×C4⋊C8—21no—
56C13×C4⋊C8D411yescharacteristic
57C13×C4⋊C8D411yescharacteristic
58C22⋊#1055—21no—
59#88060—22no—
60#88060—22no—
61#88055—22no—
62C8×Dic13—22no—
63#88050—22no—
64#88049—22no—
65#88048—22no—
66#88047—22no—
67C4⋊#1055—21no—
68C4⋊#1055—21no—
69C4⋊#1055—21no—
70C4⋊#1055C2×C412yes—
71C4⋊#1055D412yes—
72C4×#1055—21no—
73#9170—131nomaximal, Sylow
74C2×Q8×C13—22no—
75C2×Q8×C13—41no—
76C2×Q8×C13—82no—
77C22×C4×C13—41no—
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13#4111yescharacteristic
80C22×C4×C13#4111yescharacteristic
81C2×C22⋊D13—21no—
82#6127—21no—
83#6127—21no—
84#6127—21no—
85#6127—21no—
86C2×D52C22⋊C411yescharacteristic
87C2×C4×D13—21no—
88C2×C4×D13—21no—
89C2×C4×D13—21no—
90C2×Dic26C22⋊C411yescharacteristic
91C2×C8×C13—21no—
92C2×C8×C13—21no—
93C2×C8×C13—41no—
94C2×C8×C13—41no—
95C2×C8×C13—41no—
96C2×C8×C13—81no—
97C13×C4⋊C4—22no—
98C13×C4⋊C4—22no—
99C13×C4⋊C4—41no—
100C13×C4⋊C4—41no—
101C42×C13C22×C411yescharacteristic
102C42×C13C2×D411yescharacteristic
103C42×C13C2×D411yescharacteristic
104C42×C13C2×D411yescharacteristic
105C22⋊Dic13—21no—
106#6103—21no—
107#6103—21no—
108C4⋊Dic13C22⋊C411yescharacteristic
109C4⋊Dic13C22⋊C411yescharacteristic
110#6101—21no—
111#6101—21no—
112C4×Dic13—21no—
113C4×Dic13—21no—
114C4×Dic13—21no—
115#6099—41no—
116#6099—41no—
117#6099—41no—
118#6099—41no—
119C2×#1055—22no—
120C2×#1055—22no—
121C2×#1055—41no—
122#3079—131no—
123#2925—131no—
124#1549—131no—
125C2×#333D1311yescharacteristic, complemented
126#1477—131no—
127#1301—131no—
128#1292—131no—
129C23×C13#12311yescharacteristic
130C22×D13—21no—
131Q8×C13—82no—
132Q8×C13—82no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—41no—
136C2×C4×C13—42no—
137C2×C4×C13—82no—
138C2×C4×C13C2×C22⋊C411yescharacteristic
139C2×C4×C13C4×D411yescharacteristic
140C2×C4×C13C4×D411yescharacteristic
141C2×C4×C13#12011yescharacteristic
142C2×C4×C13#12111yescharacteristic
143C2×C4×C13#12111yescharacteristic
144C2×C4×C13#13511yescharacteristic
145C2×C4×C13#13511yescharacteristic
146C2×C4×C13#13711yescharacteristic
147C2×C4×C13#13711yescharacteristic
148C22⋊D13—41no—
149C22⋊D13—41no—
150C2×Dic13—21no—
151C2×Dic13—21no—
152C2×Dic13—21no—
153D52—21no—
154D52—21no—
155C4×D13—41no—
156C4×D13—41no—
157C4×D13—41no—
158C4×D13—41no—
159C4×D13—81no—
160Dic26—21no—
161Dic26—21no—
162C8×C13—41no—
163C8×C13—41no—
164C8×C13—81no—
165#1055—42no—
166#1055—42no—
167#1055—81no—
168C2×C4⋊Q8C2×D1311yescharacteristic
169C4×#41—131no—
170#477—261no—
171#476—261no—
172#475—132no—
173#474—132no—
174#433—262no—
175#432—261no—
176#431—131no—
177#431—261no—
178#428—261no—
179#423—131no—
180#423—131no—
181C2×C4⋊C8C2×D1311yescharacteristic
182C2×C4⋊C8C2×D1311yescharacteristic
183#417—261no—
184#408—261no—
185#405—261no—
186#333—21no—
187#333—21no—
188#332—262no—
189Q8⋊C8—261no—
190D4⋊C8—261no—
191C22×C13—21no—
192C22×C13—21no—
193C22×C13#38611yescharacteristic
194C22×C13#48511yescharacteristic
195C22×C13#48511yescharacteristic
196C2×D13—41no—
197C2×D13—41no—
198C2×D13—41no—
199C4×C13—21no—
200C4×C13—21no—
201C4×C13—21no—
202C4×C13—82no—
203C4×C13#41611yescharacteristic
204C4×C13#41911yescharacteristic
205C4×C13#45211yescharacteristic
206C4×C13#45211yescharacteristic
207C4×C13#47111yescharacteristic
208C4×C13#47311yescharacteristic
209Dic13—41no—
210Dic13—41no—
211Dic13—41no—
212C2×#41—131no—
213C22×Q8—21no—
214C2×M16—261no—
215C2×M16—261no—
216C22×C8—21no—
217C22×C8—21no—
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8C4×D1312yes—
222C4×Q8—131no—
223C4×Q8—131no—
224C4×D4—131no—
225C4×D4—131no—
226C4×D4—261no—
227C4×D4—261no—
228#117—131no—
229#117—261no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C42—261no—
233C2×C42C22×D1311yescharacteristic
234#107—262no—
235#106—262no—
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—132no—
240C4⋊C8—132no—
241C4⋊C8—261no—
242C4⋊C8—261no—
243C4⋊C8—261no—
244C4⋊C8C22⋊D1311yescharacteristic
245C4⋊C8C22⋊D1311yescharacteristic
246#103—262no—
247#102—262no—
248C22⋊C8—262no—
249C22⋊C8—262no—
250C22⋊C8—261no—
251#97—262no—
252C4×C8—262no—
253C4×C8—261no—
254C2×C13—21no—
255C2×C13—21no—
256C2×C13#187311yescharacteristic
257C2×C13#190311yescharacteristic
258C2×C13#190811yescharacteristic
259D13—81no—
260#41—261no—
261#41—261no—
262#41—261no—
263#41—261no—
264C2×Q8—22no—
265C2×Q8—41no—
266C2×Q8—82no—
267C2×Q8—131no—
268C2×D4—131no—
269C2×D4—261no—
270C22×C4—41no—
271C22×C4—261no—
272C22×C4—261no—
273C22×C4—261no—
274C22×C4#612711yescharacteristic
275C22×C4D4×D1311yescharacteristic
276C22×C4#612911yescharacteristic
277M16—521no—
278M16—521no—
279M16—521no—
280M16—521no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—81no—
287C2×C8—262no—
288C2×C8—262no—
289C2×C8—521no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—131no—
295C4⋊C4—131no—
296C4⋊C4—261no—
297C4⋊C4—261no—
298C22⋊C4—261no—
299C22⋊C4—261no—
300C22⋊C4—261no—
301C42—261no—
302C42—261no—
303C42—261no—
304C42C2×C4×D1311yescharacteristic
305C42D4×D1311yescharacteristic
306C42D4×D1311yescharacteristic
307C42C2×C22⋊D1311yescharacteristic
308C13#917011yescharacteristic, complemented, Sylow
309C23—261no—
310C23#8813711yescharacteristic
311Q8—82no—
312Q8—82no—
313Q8—261no—
314Q8—261no—
315D4—261no—
316D4—261no—
317D4—521no—
318D4—521no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—82no—
324C2×C4—261no—
325C2×C4—261no—
326C2×C4—261no—
327C2×C4—521no—
328C2×C4—521no—
329C2×C4—521no—
330C2×C4—521no—
331C2×C4—1041no—
332C2×C4C22⋊C4×D1311yescharacteristic
333C2×C4#8813511yescharacteristic
334C2×C4#8813811yescharacteristic
335C2×C4#8816911yescharacteristic
336C2×C4#8817011yescharacteristic
337C2×C4#8817211yescharacteristic
338C2×C4#8817311yescharacteristic
339C2×C4C4×C22⋊D1311yescharacteristic
340C2×C4#8819111yescharacteristic
341C2×C4#8819211yescharacteristic
342C8—41no—
343C8—41no—
344C8—81no—
345C8—522no—
346C8—522no—
347C8—1041no—
348C22—21no—
349C22—21no—
350C22—521no—
351C22—521no—
352C22—521no—
353C22#1171847511yescharacteristic
354C22#1171847611yescharacteristic
355C22#1171861711yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—82no—
360C4—521no—
361C4—521no—
362C4—521no—
363C4#1171846311yescharacteristic
364C4#1171846511yescharacteristic
365C4#1171883411yescharacteristic
366C4#1171883811yescharacteristic
367C4#1171884811yescharacteristic
368C4#1171885311yescharacteristic
369C2—21no—
370C2—21no—
371C2—1041no—
372C2#1311514511yescharacteristic
373C2#1311531911yescharacteristic
374C2#1311535411yescharacteristic
subgroupG/H
centerC22#11718617
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC2×C13×#333C2
socleC22×C13#386
prime radicalC2×#6127D4
cosocleC2×C42×C13C23
hypercenterC2×#333D13
hypocenterC13#9170
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
3. #13113521C2semidirect
5. #13112733C2semidirect
6. #13112711C2semidirect
7. C2×C13×#333C2semidirect
125. C2×#333D13semidirect
308. C13#9170semidirect

Maximal subgroups

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

subgroupindex
#131246452
#131235012
#131135212
#131132212
#131127332
#131127112
C2×C13×#3332
#917013