Finite Group Databasebeta

← #15754672

Subgroups — #15754672

Order 3328.

998 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 998 conjugacy classes of subgroups — too many to draw. Only its 159 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#13114828C211yesmaximal, characteristic, complemented
2#13113517C212yesmaximal, complemented
3#13113261C212yesmaximal, complemented
4#13113157C211yesmaximal, characteristic, complemented
5C2×C13×#547C211yesmaximal, characteristic
6C22×C13×#41C412yes—
7C13×#547—24no—
8C13×#547—24no—
9C2×C13×C4⋊Q8C2211yescharacteristic
10C2×C13×#123—22no—
11C2×C13×C22⋊Q8C412yes—
12C2×C13×#121—21no—
13C2×C4×D4×C13C2211yescharacteristic
14C2×C4×D4×C13C2211yescharacteristic
15C22×C13×C4⋊C4—21no—
16C2×#88073—21no—
17#11718586C2212yes—
18#11718585C2212yes—
19#11718138—24no—
20D4⋊#1055—24no—
21#11718122—21no—
22#11718117—22no—
23C2×C13×#41—24no—
24C2×C13×#41—24no—
25C2×C13×#41—48no—
26C22×Q8×C13C2×C412yes—
27C22×D4×C13—22no—
28C22×D4×C13C2×C411yescharacteristic
29C22×D4×C13D411yescharacteristic
30C23×C4×C13—22no—
31C23×C4×C13—21no—
32C23×C4×C13C2×C412yes—
33C13×C4⋊Q8—22no—
34C13×C4⋊Q8D414yes—
35C13×#123—216no—
36C13×C22⋊Q8—24no—
37C13×C22⋊Q8—24no—
38C13×#121—28no—
39C4×D4×C13—22no—
40C4×D4×C13—22no—
41C4×D4×C13—22no—
42C4×D4×C13D414yes—
43C2×C13×C4⋊C4—28no—
44C2×C13×C4⋊C4—22no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4C2×C411yescharacteristic
48C2×C13×C4⋊C4D411yescharacteristic
49C2×C13×C22⋊C4—22no—
50C2×C13×C22⋊C4—21no—
51C2×C13×C22⋊C4D412yes—
52C2×C42×C13C2311yescharacteristic
53C2×#6099—22no—
54#88073—42no—
55C22⋊#1055—22no—
56C4⋊#1055—22no—
57C4⋊#1055—22no—
58C4⋊#1055—22no—
59C4×#1055—22no—
60#8393—131nomaximal, Sylow
61C24×C13—21no—
62C24×C13C22⋊C412yes—
63C13×#41—416no—
64C13×#41—48no—
65C13×#41—48no—
66C2×Q8×C13—22no—
67C2×Q8×C13—44no—
68C2×Q8×C13C22⋊C414yes—
69C2×D4×C13—24no—
70C2×D4×C13—28no—
71C2×D4×C13—21no—
72C2×D4×C13—22no—
73C2×D4×C13—22no—
74C2×D4×C13—21no—
75C2×D4×C13—21no—
76C2×D4×C13—48no—
77C2×D4×C13C22⋊C412yes—
78C22×C4×C13—28no—
79C22×C4×C13—21no—
80C22×C4×C13—22no—
81C22×C4×C13—22no—
82C22×C4×C13—22no—
83C22×C4×C13—24no—
84C22×C4×C13—44no—
85C22×C4×C13—48no—
86C22×C4×C13—42no—
87C22×C4×C13—41no—
88C22×C4×C13—41no—
89C22×C4×C13C22⋊C412yes—
90C22×C4×C13C22×C411yescharacteristic
91C22×C4×C13C2×D411yescharacteristic
92C22×C4×C13C2×D411yescharacteristic
93C13×C4⋊C4—28no—
94C13×C4⋊C4—21no—
95C13×C4⋊C4—22no—
96C13×C4⋊C4—24no—
97C13×C4⋊C4—24no—
98C13×C4⋊C4C22⋊C412yes—
99C13×C22⋊C4—28no—
100C13×C22⋊C4—24no—
101C13×C22⋊C4—24no—
102C42×C13C2×D412yes—
103C42×C13C2×D412yes—
104#6099—42no—
105#6099—42no—
106C2×#1055—42no—
107C2×#1055—42no—
108C2×#547D1311yescharacteristic
109#1800—131no—
110#1548—132no—
111#1486—132no—
112#1460—131no—
113C23×C13—24no—
114C23×C13—22no—
115C23×C13—22no—
116C23×C13—22no—
117C23×C13—22no—
118C23×C13—42no—
119C23×C13—42no—
120C23×C13—42no—
121C23×C13—41no—
122C23×C13—41no—
123C23×C13C2×C22⋊C411yescharacteristic
124Q8×C13—44no—
125Q8×C13—44no—
126D4×C13—24no—
127D4×C13—22no—
128D4×C13—416no—
129D4×C13—42no—
130D4×C13—42no—
131D4×C13#10014yescomplemented
132C2×C4×C13—22no—
133C2×C4×C13—22no—
134C2×C4×C13—22no—
135C2×C4×C13—24no—
136C2×C4×C13—41no—
137C2×C4×C13—44no—
138C2×C4×C13—44no—
139C2×C4×C13—416no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—44no—
143C2×C4×C13—44no—
144C2×C4×C13—44no—
145C2×C4×C13—42no—
146C2×C4×C13C2×C22⋊C411yescharacteristic
147C2×C4×C13C2×C22⋊C411yescharacteristic
148C2×C4×C13#12012yes—
149C2×C4×C13#12012yes—
150C2×C4×C13#13512yes—
151C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C13#13711yescharacteristic
153#1055—82no—
154#1055—82no—
155C22×#41Dic1312yes—
156#547—24no—
157#547—24no—
158C2×C4⋊Q8C2×D1311yescharacteristic
159C2×#123—22no—
160C2×C22⋊Q8Dic1312yes—
161C2×#121—21no—
162C2×C4×D4C2×D1311yescharacteristic
163C2×C4×D4C2×D1311yescharacteristic
164C22×C4⋊C4—21no—
165#431—132no—
166#423—132no—
167C2×#100—261no—
168#343—261no—
169#333—264no—
170D4⋊C8—264no—
171#323—262no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—24no—
175C22×C13—44no—
176C22×C13—44no—
177C22×C13—42no—
178C22×C13—42no—
179C22×C13—42no—
180C22×C13—42no—
181C22×C13—42no—
182C22×C13—82no—
183C22×C13—82no—
184C22×C13#37911yescharacteristic
185C22×C13#41611yescharacteristic
186C22×C13#41711yescharacteristic
187C4×C13—22no—
188C4×C13—21no—
189C4×C13—42no—
190C4×C13—44no—
191C4×C13—42no—
192C4×C13C2×#10012yes—
193C4×C13#44912yes—
194C4×C13#45212yes—
195C2×#41—24no—
196C2×#41—24no—
197C2×#41—48no—
198C22×Q8C2×Dic1312yes—
199C22×D4—22no—
200C22×D4C2×Dic1311yescharacteristic
201C22×D4C22⋊D1311yescharacteristic
202C23×C4—22no—
203C23×C4—21no—
204C23×C4C2×Dic1312yes—
205C2×M16—262no—
206C4⋊Q8—22no—
207C4⋊Q8C22⋊D1314yes—
208#123—216no—
209C22⋊Q8—24no—
210C22⋊Q8—24no—
211#121—28no—
212C4×D4—22no—
213C4×D4—22no—
214C4×D4—22no—
215C4×D4C22⋊D1314yes—
216C2×C4⋊C4—28no—
217C2×C4⋊C4—22no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4C2×Dic1311yescharacteristic
221C2×C4⋊C4C22⋊D1311yescharacteristic
222C2×C22⋊C4—22no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4C22⋊D1312yes—
225C2×C42C22×D1311yescharacteristic
226C4⋊C8—262no—
227C4⋊C8—262no—
228C4⋊C8—262no—
229#100—522no—
230C22⋊C8—262no—
231C4×C8—262no—
232C2×C13—21no—
233C2×C13—21no—
234C2×C13—44no—
235C2×C13—82no—
236C2×C13#178311yescharacteristic
237C2×C13#178811yescharacteristic
238C2×C13#179611yescharacteristic
239C24—21no—
240C24C22⋊Dic1312yes—
241#41—416no—
242#41—48no—
243#41—48no—
244C2×Q8—22no—
245C2×Q8—44no—
246C2×Q8C22⋊Dic1314yes—
247C2×D4—24no—
248C2×D4—28no—
249C2×D4—21no—
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—22no—
254C2×D4—48no—
255C2×D4C22⋊Dic1312yes—
256C22×C4—28no—
257C22×C4—21no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—24no—
262C22×C4—44no—
263C22×C4—48no—
264C22×C4—41no—
265C22×C4—42no—
266C22×C4—41no—
267C22×C4C22⋊Dic1312yes—
268C22×C4C22×Dic1311yescharacteristic
269C22×C4C2×C22⋊D1311yescharacteristic
270C22×C4C2×C22⋊D1311yescharacteristic
271M16—522no—
272M16—522no—
273C2×C8—522no—
274C2×C8—522no—
275C4⋊C4—28no—
276C4⋊C4—21no—
277C4⋊C4—22no—
278C4⋊C4—24no—
279C4⋊C4—24no—
280C4⋊C4C22⋊Dic1312yes—
281C22⋊C4—28no—
282C22⋊C4—24no—
283C22⋊C4—24no—
284C42C2×C22⋊D1312yes—
285C42C2×C22⋊D1312yes—
286C13#839311yescharacteristic, complemented, Sylow
287C23—24no—
288C23—22no—
289C23—22no—
290C23—22no—
291C23—22no—
292C23—42no—
293C23—42no—
294C23—42no—
295C23—41no—
296C23—41no—
297C23C2×C22⋊Dic1311yescharacteristic
298Q8—44no—
299Q8—44no—
300D4—24no—
301D4—22no—
302D4—416no—
303D4—42no—
304D4—42no—
305D4#8807314yescomplemented
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—24no—
310C2×C4—41no—
311C2×C4—44no—
312C2×C4—44no—
313C2×C4—416no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—44no—
317C2×C4—44no—
318C2×C4—44no—
319C2×C4—42no—
320C2×C4#8820311yescharacteristic
321C2×C4#8820412yes—
322C2×C4#8820511yescharacteristic
323C2×C4C2×C22⋊Dic1311yescharacteristic
324C2×C4C2×C22⋊Dic1311yescharacteristic
325C2×C4#8820712yes—
326C2×C4#8820712yes—
327C8—1042no—
328C8—1042no—
329C22—21no—
330C22—21no—
331C22—24no—
332C22—44no—
333C22—44no—
334C22—42no—
335C22—42no—
336C22—42no—
337C22—42no—
338C22—42no—
339C22—82no—
340C22—82no—
341C22#1171889311yescharacteristic
342C22#1171889411yescharacteristic
343C22#1171890811yescharacteristic
344C4—21no—
345C4—22no—
346C4—42no—
347C4—44no—
348C4—42no—
349C4C2×#8807312yes—
350C4#1171889912yes—
351C4#1171890012yes—
352C2—21no—
353C2—21no—
354C2—44no—
355C2—82no—
356C2#1311475711yescharacteristic
357C2#1311477611yescharacteristic
358C2#1311481111yescharacteristic
subgroupG/H
centerC22#11718908
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
Fitting, prime radicalC2×C13×#547C2
socleC22×C13#379
cosocleC2×C42×C13C23
hypercenterC2×#547D13
hypocenterC13#8393
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. #13114828C2semidirect
2. #13113517C2semidirect
3. #13113261C2semidirect
4. #13113157C2semidirect
131. D4×C13#100semidirect
286. C13#8393semidirect
305. D4#88073semidirect

Maximal subgroups

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

subgroupindex
#131148282
#131135172
#131132612
#131131572
C2×C13×#5472
#839313