Finite Group Databasebeta

← #15760600

Subgroups — #15760600

Order 3328.

468 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 95 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#13123920C211yesmaximal, characteristic
2#13119825C211yesmaximal, characteristic
3#13113562C211yesmaximal, characteristic
4#13113179C211yesmaximal, characteristic
5#13112693C211yesmaximal, characteristic
6#13112691C211yesmaximal, characteristic
7C13×#1558C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×#88198C412yes—
10C2×C4×Dic26C2211yescharacteristic
11C13×#432C2211yescharacteristic
12C13×#432C2211yescharacteristic
13#11718891C412yes—
14#11718641—21no—
15#11718641—21no—
16#11718634—21no—
17#11718634—21no—
18C4×C4⋊Dic13C2211yescharacteristic
19#11718587C2211yescharacteristic
20#11718587C2211yescharacteristic
21#11718489—22no—
22#11718380—21no—
23#11718379—21no—
24#11718362—22no—
25C13×#333—22no—
26#11718138—22no—
27#11718061—21no—
28#11718061—21no—
29C22×Q8×C13C2×C412yes—
30C22×Dic26C2×C411yescharacteristic
31C13×C4⋊Q8—21no—
32C13×C4⋊Q8—21no—
33C13×C4⋊Q8—21no—
34C13×C4⋊Q8—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—21no—
37C2×C42×C13C2311yescharacteristic
38#88198—44no—
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13C2×C411yescharacteristic
41C2×#6101—22no—
42C2×#6101—22no—
43C2×#6101D411yescharacteristic
44C2×#6101D411yescharacteristic
45C2×C4×Dic13C2×C412yes—
46C2×C4×Dic13D411yescharacteristic
47C2×C4×Dic13D411yescharacteristic
48C4×Dic26—21no—
49C4×Dic26—21no—
50C4×Dic26—21no—
51C4×Dic26—21no—
52C13×C4⋊C8—21no—
53C13×C4⋊C8D412yes—
54C13×C22⋊C8—21no—
55C13×C22⋊C8—21no—
56C13×#97—21no—
57C13×#97—21no—
58#88071—21no—
59#88071—22no—
60#88071—22no—
61C22⋊#1055—21no—
62C22⋊#1055—21no—
63#88055—22no—
64#88054—22no—
65#88054—22no—
66C8×Dic13—22no—
67C4⋊#1055—21no—
68C4⋊#1055D412yes—
69#88043—21no—
70#88043—21no—
71#9452—131nomaximal, Sylow
72C2×Q8×C13—22no—
73C2×Q8×C13—22no—
74C2×Q8×C13—42no—
75C2×Q8×C13—42no—
76C22×C4×C13—22no—
77C22×C4×C13C22×C411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C22×Dic13—22no—
81C22×Dic13C22⋊C411yescharacteristic
82C22×Dic13C22⋊C411yescharacteristic
83C22×Dic13C22⋊C411yescharacteristic
84C22×Dic13C22⋊C411yescharacteristic
85C2×Dic26—21no—
86C2×Dic26—21no—
87C2×Dic26—22no—
88C2×Dic26—41no—
89C2×C8×C13—22no—
90C2×C8×C13—41no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—41no—
95C42×C13C2×D411yescharacteristic
96C42×C13C2×D411yescharacteristic
97C42×C13#4111yescharacteristic
98C42×C13#4111yescharacteristic
99C4⋊Dic13—24no—
100C4⋊Dic13—21no—
101C4⋊Dic13—21no—
102#6101—21no—
103#6101—21no—
104#6101—21no—
105#6101—21no—
106#6101—44no—
107#6101—44no—
108C4×Dic13—21no—
109C4×Dic13—21no—
110C4×Dic13—21no—
111C4×Dic13—21no—
112C4×Dic13—42no—
113C2×#1055—22no—
114C2×#1055—41no—
115#2983—131no—
116#2546—131no—
117#1558—131no—
118#1558D1311yescharacteristic
119#1467—131no—
120#1285—131no—
121#1285—131no—
122C23×C13C2×C22⋊C411yescharacteristic
123Q8×C13—82no—
124Q8×C13—82no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—22no—
128C2×C4×C13—41no—
129C2×C4×C13—42no—
130C2×C4×C13—42no—
131C2×C4×C13—42no—
132C2×C4×C13C4×D411yescharacteristic
133C2×C4×C13C4×D411yescharacteristic
134C2×C4×C13#12011yescharacteristic
135C2×C4×C13#12111yescharacteristic
136C2×C4×C13#12111yescharacteristic
137C2×C4×C13#12311yescharacteristic
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13—24no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143C2×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13—21no—
146C2×Dic13—42no—
147C2×Dic13—42no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13#10012yes—
151Dic26—42no—
152Dic26—42no—
153C8×C13—42no—
154C8×C13—81no—
155#1055—42no—
156#1055—81no—
157C2×C4⋊Q8—132no—
158C2×C4⋊Q8C2×D1311yescharacteristic
159C2×C4×Q8—131no—
160#446—262no—
161#446—262no—
162#432—131no—
163#432—131no—
164#432—261no—
165#432C2×D1311yescharacteristic
166#432C2×D1311yescharacteristic
167#431—261no—
168#398—261no—
169#398—261no—
170#391—132no—
171#389—261no—
172#389—261no—
173C4×C4⋊C4—131no—
174#333—22no—
175#333—262no—
176#324—261no—
177#324—261no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13#38611yescharacteristic
181C22×C13C2×#10011yescharacteristic
182C22×C13#41311yescharacteristic
183C4×C13—21no—
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—21no—
187C4×C13—21no—
188C4×C13—82no—
189C4×C13#45612yes—
190Dic13—22no—
191Dic13—44no—
192Dic13—41no—
193Dic13—41no—
194Dic13—41no—
195C22×Q8—131no—
196C22×Q8C4×D1312yes—
197C4⋊Q8—21no—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—524no—
202C4×Q8—261no—
203C4×Q8—261no—
204C4×Q8—261no—
205C4×Q8—261no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—131no—
209C2×C4⋊C4—131no—
210C2×C4⋊C4—131no—
211C2×C4⋊C4—261no—
212C2×C4⋊C4—262no—
213C2×C4⋊C4—262no—
214C2×C42—131no—
215C2×C42—131no—
216C2×C42—132no—
217C2×C42C22×D1311yescharacteristic
218C4⋊C8—21no—
219C4⋊C8—132no—
220C4⋊C8—262no—
221C4⋊C8—262no—
222C4⋊C8—261no—
223C4⋊C8C22⋊D1312yes—
224C22⋊C8—21no—
225C22⋊C8—21no—
226C22⋊C8—261no—
227C22⋊C8—261no—
228#97—21no—
229#97—21no—
230#97—262no—
231#97—261no—
232#97—261no—
233C4×C8—262no—
234#95—262no—
235#95—262no—
236#95—261no—
237C2×C13—21no—
238C2×C13—21no—
239C2×C13#188611yescharacteristic
240C2×C13#190011yescharacteristic
241C2×C13#190911yescharacteristic
242C2×Q8—22no—
243C2×Q8—22no—
244C2×Q8—42no—
245C2×Q8—42no—
246C2×Q8—262no—
247C2×Q8—261no—
248C2×Q8—261no—
249C2×Q8—521no—
250C22×C4—22no—
251C22×C4—131no—
252C22×C4—131no—
253C22×C4—131no—
254C22×C4—131no—
255C22×C4—262no—
256C22×C4C2×C4×D1311yescharacteristic
257C22×C4D4×D1311yescharacteristic
258C22×C4D4×D1311yescharacteristic
259C2×C8—22no—
260C2×C8—41no—
261C2×C8—262no—
262C2×C8—521no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—264no—
268C4⋊C4—261no—
269C4⋊C4—261no—
270C4⋊C4—261no—
271C4⋊C4—261no—
272C4⋊C4—261no—
273C4⋊C4—261no—
274C4⋊C4—524no—
275C4⋊C4—524no—
276C42—261no—
277C42—261no—
278C42—261no—
279C42—261no—
280C42—522no—
281C42#612711yescharacteristic
282C42D4×D1311yescharacteristic
283C42#612911yescharacteristic
284C42C2×C22⋊D1311yescharacteristic
285C13#945211yescharacteristic, complemented, Sylow
286C23C22⋊C4×D1311yescharacteristic
287Q8—82no—
288Q8—82no—
289Q8—522no—
290Q8—522no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—132no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4—264no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4—261no—
305C2×C4—261no—
306C2×C4—261no—
307C2×C4—522no—
308C2×C4—522no—
309C2×C4—521no—
310C2×C4—521no—
311C2×C4#8813511yescharacteristic
312C2×C4#8813711yescharacteristic
313C2×C4#8813811yescharacteristic
314C2×C4C4×C22⋊D1311yescharacteristic
315C2×C4#8819111yescharacteristic
316C2×C4#8819211yescharacteristic
317C8—42no—
318C8—81no—
319C8—522no—
320C8—1041no—
321C22—21no—
322C22—21no—
323C22D13×#10011yescharacteristic
324C22#1171840611yescharacteristic
325C22#1171861711yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—82no—
332C4—262no—
333C4—524no—
334C4—521no—
335C4—521no—
336C4—521no—
337C4#1171886612yes—
338C2—21no—
339C2—21no—
340C2#1311522611yescharacteristic
341C2#1311529611yescharacteristic
342C2#1311535511yescharacteristic
subgroupG/H
centerC22#11718617
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1558C2
socleC22×C13#386
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1558D13
hypocenterC13#9452
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1558

Complements

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

NH ≅ G/Ntype
285. C13#9452semidirect

Maximal subgroups

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

subgroupindex
#131239202
#131198252
#131135622
#131131792
#131126932
#131126912
C13×#15582
#945213