Finite Group Databasebeta

← #15760782

Subgroups — #15760782

Order 3328.

454 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123919C211yesmaximal, characteristic
2#13120203C211yesmaximal, characteristic
3#13114829C211yesmaximal, characteristic
4#13113266C211yesmaximal, characteristic
5#13113264C211yesmaximal, characteristic
6#13112694C211yesmaximal, characteristic
7C13×#1286C211yesmaximal, characteristic
8C2×C4×Dic26C2211yescharacteristic
9C2×C4×Dic26C2211yescharacteristic
10C13×#431C2211yescharacteristic
11C13×#423C2211yescharacteristic
12C13×#382C2211yescharacteristic
13C2×#88064—21no—
14#11718646—21no—
15#11718635—21no—
16#11718586C2211yescharacteristic
17#11718585C2211yescharacteristic
18#11718492—22no—
19#11718380—22no—
20#11718340—22no—
21#11718320C412yes—
22#11718317C412yes—
23#11718314—22no—
24#11718146—21no—
25#11718076—22no—
26#11718048—22no—
27C22×Dic26C2×C411yescharacteristic
28C22×Dic26D411yescharacteristic
29C2×C13×M16—21no—
30C2×C13×C4⋊C4—21no—
31C2×C42×C13C2311yescharacteristic
32C2×C4⋊Dic13—22no—
33C2×C4⋊Dic13C2×C411yescharacteristic
34C2×C4⋊Dic13D411yescharacteristic
35C2×#6101—21no—
36C2×#6101C2×C412yes—
37C2×C4×Dic13—21no—
38C2×C4×Dic13D412yes—
39C2×#6099—21no—
40C4×Dic26—21no—
41C4×Dic26—21no—
42C4×Dic26—21no—
43C4×Dic26—21no—
44C4×Dic26—21no—
45C4×Dic26—21no—
46C4×Dic26—21no—
47C4×Dic26—21no—
48C13×C4⋊C8—21no—
49C13×C4⋊C8—21no—
50C13×C4⋊C8—21no—
51C13×C22⋊C8—21no—
52C4×C8×C13D412yes—
53C13×#95—21no—
54C13×#95C2×C412yes—
55#88071—22no—
56#88071—22no—
57#88071—22no—
58C22⋊#1055—21no—
59#88064—42no—
60#88055—24no—
61#88054—24no—
62C4⋊#1055—21no—
63C4⋊#1055—21no—
64C4⋊#1055—21no—
65C4×#1055D412yes—
66#9488—131nomaximal, Sylow
67C22×C4×C13—22no—
68C22×C4×C13C22×C411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×Dic13—21no—
72C22×Dic13—21no—
73C22×Dic13C22⋊C412yes—
74C22×Dic13C22⋊C412yes—
75C2×Dic26—21no—
76C2×Dic26—21no—
77C2×Dic26—21no—
78C2×Dic26—21no—
79C2×Dic26—21no—
80C2×Dic26—21no—
81C2×Dic26—21no—
82C2×Dic26—21no—
83C2×Dic26—42no—
84C13×M16—41no—
85C13×M16—41no—
86C2×C8×C13—22no—
87C2×C8×C13—41no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—41no—
90C42×C13C2×D411yescharacteristic
91C42×C13C2×D411yescharacteristic
92C42×C13#4111yescharacteristic
93C42×C13#4111yescharacteristic
94C4⋊Dic13—21no—
95C4⋊Dic13—21no—
96C4⋊Dic13—21no—
97C4⋊Dic13—21no—
98C4⋊Dic13—44no—
99#6101—22no—
100#6101—22no—
101#6101—41no—
102#6101—41no—
103C4×Dic13—22no—
104C4×Dic13—22no—
105C4×Dic13—41no—
106C4×Dic13—41no—
107#6099—41no—
108#6099—41no—
109C2×#1055—22no—
110C2×#1055—41no—
111#2983—131no—
112#2581—131no—
113#1801—131no—
114#1487—131no—
115#1487—131no—
116#1286—131no—
117#1286D1311yescharacteristic
118C23×C13C2×C22⋊C411yescharacteristic
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13C4×D411yescharacteristic
125C2×C4×C13C4×D411yescharacteristic
126C2×C4×C13#12011yescharacteristic
127C2×C4×C13#12111yescharacteristic
128C2×C4×C13#12111yescharacteristic
129C2×C4×C13#12311yescharacteristic
130C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C13#13711yescharacteristic
132C2×C4×C13#13711yescharacteristic
133C2×C4×C13#13711yescharacteristic
134C2×Dic13—22no—
135C2×Dic13—22no—
136C2×Dic13—22no—
137C2×Dic13—22no—
138C2×Dic13—22no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—42no—
142C2×Dic13—42no—
143C2×Dic13—41no—
144Dic26—22no—
145Dic26—22no—
146Dic26—41no—
147Dic26—41no—
148Dic26—41no—
149Dic26—41no—
150Dic26—41no—
151Dic26—41no—
152C8×C13—42no—
153C8×C13—81no—
154#1055—42no—
155#1055—81no—
156C2×C4×Q8—131no—
157C2×C4×Q8—131no—
158#446—262no—
159#446—262no—
160#432—262no—
161#431—131no—
162#431C2×D1311yescharacteristic
163#423—131no—
164#423C2×D1311yescharacteristic
165C2×#101—261no—
166#400—132no—
167#395—132no—
168#391—261no—
169#389—261no—
170#387—262no—
171#382C2×D1311yescharacteristic
172#343—261no—
173Q8⋊C8—262no—
174Q8⋊C8—262no—
175C22×C13—21no—
176C22×C13—21no—
177C22×C13#38611yescharacteristic
178C22×C13#41711yescharacteristic
179C22×C13#41911yescharacteristic
180C4×C13—21no—
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—21no—
184C4×C13—82no—
185C4×C13#46811yescharacteristic
186C4×C13#46811yescharacteristic
187C4×C13#47011yescharacteristic
188C4×C13#47011yescharacteristic
189Dic13—42no—
190Dic13—42no—
191Dic13—42no—
192Dic13—81no—
193C22×Q8—131no—
194C22×Q8—131no—
195C2×M16—21no—
196C2×M16—261no—
197C4×Q8—261no—
198C4×Q8—261no—
199C4×Q8—261no—
200C4×Q8—261no—
201C4×Q8—261no—
202C4×Q8—261no—
203C4×Q8—261no—
204C4×Q8—261no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—132no—
207C2×C4⋊C4—131no—
208C2×C4⋊C4—131no—
209C2×C4⋊C4—262no—
210C2×C4⋊C4—261no—
211C2×C42—132no—
212C2×C42—261no—
213C2×C42C22×D1311yescharacteristic
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—264no—
218C4⋊C8—261no—
219C4⋊C8—261no—
220C4⋊C8—261no—
221#101—522no—
222C22⋊C8—21no—
223C22⋊C8—261no—
224#97—264no—
225C4×C8—132no—
226C4×C8D5212yes—
227#95—21no—
228#95—262no—
229#95—262no—
230#95—262no—
231#95C4×D1312yes—
232C2×C13—21no—
233C2×C13—21no—
234C2×C13#189111yescharacteristic
235C2×C13#189411yescharacteristic
236C2×C13#191211yescharacteristic
237C2×Q8—261no—
238C2×Q8—261no—
239C2×Q8—261no—
240C2×Q8—261no—
241C2×Q8—261no—
242C2×Q8—261no—
243C2×Q8—261no—
244C2×Q8—261no—
245C2×Q8—522no—
246C22×C4—22no—
247C22×C4—132no—
248C22×C4—132no—
249C22×C4—261no—
250C22×C4—261no—
251C22×C4C2×C4×D1311yescharacteristic
252C22×C4D4×D1311yescharacteristic
253C22×C4D4×D1311yescharacteristic
254M16—41no—
255M16—41no—
256M16—521no—
257M16—521no—
258C2×C8—22no—
259C2×C8—41no—
260C2×C8—262no—
261C2×C8—521no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—262no—
265C4⋊C4—261no—
266C4⋊C4—262no—
267C4⋊C4—261no—
268C4⋊C4—261no—
269C4⋊C4—261no—
270C4⋊C4—524no—
271C4⋊C4—521no—
272C4⋊C4—521no—
273C42—262no—
274C42—262no—
275C42—521no—
276C42—521no—
277C42C2×D5211yescharacteristic
278C42#612711yescharacteristic
279C42D4×D1311yescharacteristic
280C42#613111yescharacteristic
281C13#948811yescharacteristic, complemented, Sylow
282C23C22⋊C4×D1311yescharacteristic
283Q8—262no—
284Q8—262no—
285Q8—521no—
286Q8—521no—
287Q8—521no—
288Q8—521no—
289Q8—521no—
290Q8—521no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—262no—
297C2×C4—262no—
298C2×C4—262no—
299C2×C4—262no—
300C2×C4—262no—
301C2×C4—521no—
302C2×C4—521no—
303C2×C4—522no—
304C2×C4—522no—
305C2×C4—521no—
306C2×C4C4×D5211yescharacteristic
307C2×C4#8813611yescharacteristic
308C2×C4#8813811yescharacteristic
309C2×C4#8814711yescharacteristic
310C2×C4#8814811yescharacteristic
311C2×C4#8814911yescharacteristic
312C2×C4#8816511yescharacteristic
313C2×C4#8816911yescharacteristic
314C2×C4#8816911yescharacteristic
315C2×C4#8817211yescharacteristic
316C8—42no—
317C8—81no—
318C8—522no—
319C8—1041no—
320C22—21no—
321C22—21no—
322C22#1171832611yescharacteristic
323C22#1171843211yescharacteristic
324C22#1171846311yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—82no—
330C4—522no—
331C4—522no—
332C4—522no—
333C4—1041no—
334C4#1171844111yescharacteristic
335C4#1171847711yescharacteristic
336C4#1171852911yescharacteristic
337C4#1171854711yescharacteristic
338C2—21no—
339C2—21no—
340C2#1311525311yescharacteristic
341C2#1311526811yescharacteristic
342C2#1311537211yescharacteristic
subgroupG/H
centerC22#11718326
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1286C2
socleC22×C13#386
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1286D13
hypocenterC13#9488
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1286

Complements

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

NH ≅ G/Ntype
281. C13#9488semidirect

Maximal subgroups

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

subgroupindex
#131239192
#131202032
#131148292
#131132662
#131132642
#131126942
C13×#12862
#948813