Finite Group Databasebeta

← #15758232

Subgroups — #15758232

Order 3328.

404 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 97 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#13125346C211yesmaximal, characteristic
2#13123937C211yesmaximal, characteristic
3#13113430C211yesmaximal, characteristic
4#13113257C211yesmaximal, characteristic
5#13112674C211yesmaximal, characteristic
6#13112672C211yesmaximal, characteristic
7C13×#1485C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9#11719175C2211yescharacteristic
10C13×#431C2211yescharacteristic
11C4×C13×M16C2211yescharacteristic
12#11718740C411yescharacteristic
13#11718740C411yescharacteristic
14#11718739C411yescharacteristic
15#11718739C411yescharacteristic
16#11718725—22no—
17#11718659—22no—
18#11718586C2211yescharacteristic
19C4×#6099C2211yescharacteristic
20C2×C4×#1055C2211yescharacteristic
21#11718492—21no—
22#11718491—21no—
23#11718381—22no—
24#11718340—21no—
25C8×Dic26—21no—
26C13×Q8⋊C8—21no—
27C13×Q8⋊C8—21no—
28Q8⋊#1055—21no—
29Q8⋊#1055—21no—
30#11718057—22no—
31C2×C13×M16—21no—
32C13×C4⋊Q8C2×C411yescharacteristic
33C13×C4⋊Q8C2×C411yescharacteristic
34C13×#125—21no—
35C13×C22⋊Q8—21no—
36C13×C22⋊Q8—21no—
37C4×Q8×C13—21no—
38C4×Q8×C13—21no—
39C13×#117—21no—
40C2×C42×C13C2311yescharacteristic
41#88180D412yes—
42#88178—21no—
43#88178—21no—
44C2×#6099—21no—
45C22×#1055—21no—
46#88124D412yes—
47#88123C2×C411yescharacteristic
48#88123C2×C411yescharacteristic
49C4×Dic26—21no—
50C4×Dic26—21no—
51C13×C4⋊C8D411yescharacteristic
52C13×C4⋊C8D411yescharacteristic
53C13×C22⋊C8—21no—
54C13×#97—21no—
55C4×C8×C13—21no—
56C4×C8×C13—21no—
57C22⋊#1055—21no—
58#88055—22no—
59#88054—22no—
60#88054—22no—
61C8×Dic13—22no—
62#88048—22no—
63#88048—22no—
64#88047—22no—
65#88047—22no—
66C4⋊#1055D411yescharacteristic
67C4⋊#1055D411yescharacteristic
68#88043—21no—
69C4×#1055—21no—
70C4×#1055—21no—
71C4×#1055—21no—
72C4×#1055C2×C411yescharacteristic
73C4×#1055C2×C411yescharacteristic
74#9068—131nomaximal, Sylow
75C2×Q8×C13—21no—
76C2×Q8×C13—21no—
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13#4111yescharacteristic
79C22×C4×C13#4111yescharacteristic
80C2×Dic26—21no—
81C2×Dic26—21no—
82C13×M16—22no—
83C13×M16—41no—
84C2×C8×C13—21no—
85C2×C8×C13—21no—
86C2×C8×C13—41no—
87C13×C4⋊C4—21no—
88C13×C4⋊C4—21no—
89C13×C4⋊C4—21no—
90C13×C4⋊C4—21no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C22⋊C4—41no—
94C42×C13—41no—
95C42×C13C22×C411yescharacteristic
96C42×C13C2×D411yescharacteristic
97C42×C13C2×D411yescharacteristic
98C42×C13C2×D411yescharacteristic
99C22⋊Dic13—22no—
100C4⋊Dic13—21no—
101C4⋊Dic13—21no—
102C4⋊Dic13C22⋊C412yes—
103C4⋊Dic13C22⋊C412yes—
104#6101—22no—
105#6101—22no—
106C4×Dic13—22no—
107#6099—22no—
108#6099—41no—
109C2×#1055—22no—
110C2×#1055—22no—
111C2×#1055—21no—
112C2×#1055—21no—
113C2×#1055—21no—
114C2×#1055—21no—
115C2×#1055—41no—
116#3160—131no—
117#2986—131no—
118#1526—131no—
119#1485—131no—
120#1485D1311yescharacteristic
121#1278—131no—
122#1278—131no—
123C23×C13#12311yescharacteristic
124Q8×C13—41no—
125Q8×C13—41no—
126Q8×C13—41no—
127Q8×C13—41no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13C2×C22⋊C411yescharacteristic
137C2×C4×C13C4×D411yescharacteristic
138C2×C4×C13C4×D411yescharacteristic
139C2×C4×C13#12011yescharacteristic
140C2×C4×C13#12111yescharacteristic
141C2×C4×C13#12111yescharacteristic
142C2×Dic13—22no—
143C2×Dic13—22no—
144Dic26—41no—
145Dic26—41no—
146Dic26—41no—
147Dic26—41no—
148C8×C13—42no—
149C8×C13—41no—
150C8×C13—41no—
151#1055—22no—
152#1055—22no—
153#1055—42no—
154#1055—41no—
155#1055—41no—
156#533—131no—
157#533C2×D1311yescharacteristic
158#500—131no—
159#500—131no—
160#499—262no—
161#498—131no—
162#498—131no—
163#446—261no—
164#446—261no—
165C8×Q8—261no—
166C8×Q8—261no—
167#433—262no—
168#431—131no—
169#431C2×D1311yescharacteristic
170#427—262no—
171C4×M16—131no—
172C4×M16C2×D1311yescharacteristic
173C2×C4×C8—131no—
174#330—262no—
175Q8⋊C8—21no—
176Q8⋊C8—21no—
177Q8⋊C8—261no—
178Q8⋊C8—261no—
179C22×C13—21no—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13#38611yescharacteristic
183C4×C13—21no—
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—81no—
187C4×C13—81no—
188C4×C13#44311yescharacteristic
189C4×C13#44311yescharacteristic
190C4×C13#44411yescharacteristic
191C4×C13#44411yescharacteristic
192C4×C13#45611yescharacteristic
193C4×C13#45611yescharacteristic
194Dic13—42no—
195Dic13—42no—
196C2×M16—21no—
197C2×M16—261no—
198C22×C8—261no—
199C4⋊Q8—131no—
200C4⋊Q8—131no—
201C4⋊Q8C4×D1311yescharacteristic
202C4⋊Q8C4×D1311yescharacteristic
203#125—21no—
204#125—132no—
205C22⋊Q8—21no—
206C22⋊Q8—21no—
207C22⋊Q8—261no—
208C22⋊Q8—261no—
209C4×Q8—21no—
210C4×Q8—21no—
211C4×Q8—261no—
212C4×Q8—261no—
213#117—21no—
214#117—132no—
215C2×C42C22×D1311yescharacteristic
216#107—262no—
217#107—262no—
218#106—262no—
219#106—262no—
220C4⋊C8—131no—
221C4⋊C8—131no—
222C4⋊C8—262no—
223C4⋊C8—262no—
224C4⋊C8C22⋊D1311yescharacteristic
225C4⋊C8C22⋊D1311yescharacteristic
226C22⋊C8—21no—
227C22⋊C8—261no—
228#97—21no—
229#97—262no—
230#97—261no—
231C4×C8—21no—
232C4×C8—21no—
233C4×C8—131no—
234C4×C8—131no—
235C4×C8—262no—
236C4×C8—261no—
237C4×C8—261no—
238C4×C8—261no—
239C2×C13—41no—
240C2×C13#187611yescharacteristic
241C2×C13#187611yescharacteristic
242C2×C13#188611yescharacteristic
243C2×Q8—21no—
244C2×Q8—21no—
245C2×Q8—261no—
246C2×Q8—261no—
247C22×C4#612711yescharacteristic
248C22×C4D4×D1311yescharacteristic
249C22×C4#612911yescharacteristic
250M16—22no—
251M16—41no—
252M16—262no—
253M16—521no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—41no—
257C2×C8—262no—
258C2×C8—262no—
259C2×C8—261no—
260C2×C8—261no—
261C2×C8—261no—
262C2×C8—261no—
263C2×C8—521no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—132no—
271C4⋊C4—132no—
272C4⋊C4—261no—
273C4⋊C4—262no—
274C4⋊C4—261no—
275C4⋊C4—262no—
276C22⋊C4—41no—
277C22⋊C4—262no—
278C42—41no—
279C42—262no—
280C42C2×C4×D1311yescharacteristic
281C42D4×D1311yescharacteristic
282C42D4×D1311yescharacteristic
283C42C2×C22⋊D1311yescharacteristic
284C13#906811yescharacteristic, complemented, Sylow
285C23#8813711yescharacteristic
286Q8—41no—
287Q8—41no—
288Q8—41no—
289Q8—41no—
290Q8—521no—
291Q8—521no—
292Q8—521no—
293Q8—521no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—262no—
303C2×C4—262no—
304C2×C4C22⋊C4×D1311yescharacteristic
305C2×C4#8813511yescharacteristic
306C2×C4#8813811yescharacteristic
307C2×C4C4×C22⋊D1311yescharacteristic
308C2×C4#8819111yescharacteristic
309C2×C4#8819211yescharacteristic
310C8—42no—
311C8—41no—
312C8—41no—
313C8—262no—
314C8—262no—
315C8—522no—
316C8—521no—
317C8—521no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22#1171861711yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—81no—
326C4—81no—
327C4—522no—
328C4—522no—
329C4#1171848411yescharacteristic
330C4#1171848511yescharacteristic
331C4#1171880511yescharacteristic
332C4#1171880611yescharacteristic
333C4#1171886611yescharacteristic
334C4#1171886611yescharacteristic
335C2—41no—
336C2#1311516011yescharacteristic
337C2#1311516611yescharacteristic
338C2#1311522611yescharacteristic
subgroupG/H
centerC2×C4#88191
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1485C2
socleC22×C13#386
prime radicalC23×C13#123
cosocleC2×C42×C13C23
hypercenter#1485D13
hypocenterC13#9068
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1485

Complements

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

NH ≅ G/Ntype
284. C13#9068semidirect

Maximal subgroups

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

subgroupindex
#131253462
#131239372
#131134302
#131132572
#131126742
#131126722
C13×#14852
#906813