Finite Group Databasebeta

← #15754692

Subgroups — #15754692

Order 3328.

802 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 802 conjugacy classes of subgroups — too many to draw. Only its 151 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#13113521C212yesmaximal, complemented
3#13113261C212yesmaximal, complemented
4#13113157C211yesmaximal, characteristic, complemented
5C2×C13×#555C211yesmaximal, characteristic
6C13×#555—24no—
7C13×#555—24no—
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C13×#124—22no—
10C2×C13×#121—21no—
11C2×C13×#121C412yes—
12C2×C4×D4×C13C2211yescharacteristic
13C2×C4×D4×C13C2211yescharacteristic
14C2×C13×#117—21no—
15C2×C13×#117C412yes—
16C2×#88073—21no—
17#11718586C2212yes—
18#11718585C2212yes—
19#11718139—24no—
20D4⋊#1055—24no—
21#11718122—21no—
22#11718117—22no—
23C22×Q8×C13—21no—
24C22×D4×C13—22no—
25C22×D4×C13C2×C411yescharacteristic
26C22×D4×C13D411yescharacteristic
27C23×C4×C13—21no—
28C23×C4×C13C2×C412yes—
29C13×C4⋊Q8—22no—
30C13×C4⋊Q8D414yes—
31C13×#124—216no—
32C13×#121—28no—
33C13×#121—24no—
34C13×#121—24no—
35C4×D4×C13—22no—
36C4×D4×C13—22no—
37C4×D4×C13—22no—
38C4×D4×C13D414yes—
39C13×#117—28no—
40C13×#117—24no—
41C13×#117—24no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4C2×C411yescharacteristic
44C2×C13×C4⋊C4C2×C412yes—
45C2×C13×C4⋊C4D411yescharacteristic
46C2×C13×C22⋊C4—22no—
47C2×C13×C22⋊C4—22no—
48C2×C13×C22⋊C4—21no—
49C2×C13×C22⋊C4D412yes—
50C2×C42×C13—22no—
51C2×C42×C13C2311yescharacteristic
52C2×#6099—22no—
53#88073—42no—
54C22⋊#1055—22no—
55C4⋊#1055—22no—
56C4⋊#1055—22no—
57C4⋊#1055—22no—
58C4×#1055—22no—
59#8397—131nomaximal, Sylow
60C24×C13—21no—
61C24×C13C22⋊C412yes—
62C2×Q8×C13—24no—
63C2×Q8×C13—82no—
64C2×D4×C13—28no—
65C2×D4×C13—21no—
66C2×D4×C13—22no—
67C2×D4×C13—22no—
68C2×D4×C13—21no—
69C2×D4×C13—21no—
70C2×D4×C13—42no—
71C2×D4×C13—84no—
72C2×D4×C13C22⋊C412yes—
73C22×C4×C13—21no—
74C22×C4×C13—22no—
75C22×C4×C13—22no—
76C22×C4×C13—22no—
77C22×C4×C13—24no—
78C22×C4×C13—44no—
79C22×C4×C13—42no—
80C22×C4×C13—41no—
81C22×C4×C13—41no—
82C22×C4×C13C22⋊C412yes—
83C22×C4×C13C22×C411yescharacteristic
84C22×C4×C13C2×D411yescharacteristic
85C22×C4×C13C2×D411yescharacteristic
86C13×C4⋊C4—21no—
87C13×C4⋊C4—22no—
88C13×C4⋊C4—24no—
89C13×C4⋊C4—22no—
90C13×C4⋊C4C22⋊C412yes—
91C13×C4⋊C4C22⋊C414yes—
92C13×C22⋊C4—28no—
93C13×C22⋊C4—28no—
94C13×C22⋊C4—24no—
95C13×C22⋊C4—24no—
96C42×C13—28no—
97C42×C13C2×D412yes—
98C42×C13C2×D412yes—
99#6099—42no—
100#6099—42no—
101C2×#1055—42no—
102C2×#1055—42no—
103C2×#555D1311yescharacteristic
104#1800—131no—
105#1549—132no—
106#1486—132no—
107#1460—131no—
108C23×C13—22no—
109C23×C13—22no—
110C23×C13—22no—
111C23×C13—22no—
112C23×C13—42no—
113C23×C13—42no—
114C23×C13—42no—
115C23×C13—42no—
116C23×C13—41no—
117C23×C13—41no—
118C23×C13C2×C22⋊C411yescharacteristic
119Q8×C13—84no—
120D4×C13—24no—
121D4×C13—42no—
122D4×C13—42no—
123D4×C13—42no—
124D4×C13—88no—
125C2×C4×C13—22no—
126C2×C4×C13—22no—
127C2×C4×C13—22no—
128C2×C4×C13—24no—
129C2×C4×C13—41no—
130C2×C4×C13—44no—
131C2×C4×C13—44no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—44no—
135C2×C4×C13—44no—
136C2×C4×C13—44no—
137C2×C4×C13—42no—
138C2×C4×C13C2×C22⋊C411yescharacteristic
139C2×C4×C13C2×C22⋊C411yescharacteristic
140C2×C4×C13#12012yes—
141C2×C4×C13#12012yes—
142C2×C4×C13#13512yes—
143C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C13#13711yescharacteristic
145#1055—82no—
146#1055—82no—
147#555—24no—
148#555—24no—
149C2×C4⋊Q8C2×D1311yescharacteristic
150C2×#124—22no—
151C2×#121—21no—
152C2×#121Dic1312yes—
153C2×C4×D4C2×D1311yescharacteristic
154C2×C4×D4C2×D1311yescharacteristic
155C2×#117—21no—
156C2×#117Dic1312yes—
157#431—132no—
158#423—132no—
159C2×#100—261no—
160#343—261no—
161#332—264no—
162D4⋊C8—264no—
163#323—262no—
164C22×C13—21no—
165C22×C13—21no—
166C22×C13—42no—
167C22×C13—42no—
168C22×C13—42no—
169C22×C13—42no—
170C22×C13—42no—
171C22×C13—42no—
172C22×C13—82no—
173C22×C13—82no—
174C22×C13—82no—
175C22×C13—82no—
176C22×C13#37911yescharacteristic
177C22×C13#41611yescharacteristic
178C22×C13#41711yescharacteristic
179C4×C13—22no—
180C4×C13—21no—
181C4×C13—44no—
182C4×C13—42no—
183C4×C13—42no—
184C4×C13#41312yes—
185C4×C13#44912yes—
186C4×C13#45212yes—
187C22×Q8—21no—
188C22×D4—22no—
189C22×D4C2×Dic1311yescharacteristic
190C22×D4C22⋊D1311yescharacteristic
191C23×C4—21no—
192C23×C4C2×Dic1312yes—
193C2×M16—262no—
194C4⋊Q8—22no—
195C4⋊Q8C22⋊D1314yes—
196#124—216no—
197#121—28no—
198#121—24no—
199#121—24no—
200C4×D4—22no—
201C4×D4—22no—
202C4×D4—22no—
203C4×D4C22⋊D1314yes—
204#117—28no—
205#117—24no—
206#117—24no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4C2×Dic1311yescharacteristic
209C2×C4⋊C4C2×Dic1312yes—
210C2×C4⋊C4C22⋊D1311yescharacteristic
211C2×C22⋊C4—22no—
212C2×C22⋊C4—22no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4C22⋊D1312yes—
215C2×C42—22no—
216C2×C42C22×D1311yescharacteristic
217C4⋊C8—262no—
218C4⋊C8—262no—
219C4⋊C8—262no—
220#100—522no—
221C22⋊C8—262no—
222C4×C8—262no—
223C2×C13—21no—
224C2×C13—21no—
225C2×C13—82no—
226C2×C13—82no—
227C2×C13#178511yescharacteristic
228C2×C13#178811yescharacteristic
229C2×C13#179511yescharacteristic
230C24—21no—
231C24C22⋊Dic1312yes—
232C2×Q8—24no—
233C2×Q8—82no—
234C2×D4—28no—
235C2×D4—21no—
236C2×D4—22no—
237C2×D4—21no—
238C2×D4—21no—
239C2×D4—22no—
240C2×D4—42no—
241C2×D4—84no—
242C2×D4C22⋊Dic1312yes—
243C22×C4—21no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—24no—
248C22×C4—44no—
249C22×C4—41no—
250C22×C4—42no—
251C22×C4—41no—
252C22×C4C22⋊Dic1312yes—
253C22×C4C22×Dic1311yescharacteristic
254C22×C4C2×C22⋊D1311yescharacteristic
255C22×C4C2×C22⋊D1311yescharacteristic
256M16—522no—
257M16—522no—
258C2×C8—522no—
259C2×C8—522no—
260C4⋊C4—21no—
261C4⋊C4—22no—
262C4⋊C4—24no—
263C4⋊C4—22no—
264C4⋊C4C22⋊Dic1312yes—
265C4⋊C4C22⋊Dic1314yes—
266C22⋊C4—28no—
267C22⋊C4—28no—
268C22⋊C4—24no—
269C22⋊C4—24no—
270C42—28no—
271C42C2×C22⋊D1312yes—
272C42C2×C22⋊D1312yes—
273C13#839711yescharacteristic, complemented, Sylow
274C23—22no—
275C23—22no—
276C23—22no—
277C23—22no—
278C23—42no—
279C23—42no—
280C23—42no—
281C23—42no—
282C23—41no—
283C23—41no—
284C23C2×C22⋊Dic1311yescharacteristic
285Q8—84no—
286D4—24no—
287D4—42no—
288D4—42no—
289D4—42no—
290D4—88no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—24no—
295C2×C4—41no—
296C2×C4—44no—
297C2×C4—44no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—44no—
301C2×C4—44no—
302C2×C4—44no—
303C2×C4—42no—
304C2×C4#8820311yescharacteristic
305C2×C4#8820412yes—
306C2×C4#8820511yescharacteristic
307C2×C4C2×C22⋊Dic1311yescharacteristic
308C2×C4C2×C22⋊Dic1311yescharacteristic
309C2×C4#8820712yes—
310C2×C4#8820712yes—
311C8—1042no—
312C8—1042no—
313C22—21no—
314C22—21no—
315C22—42no—
316C22—42no—
317C22—42no—
318C22—42no—
319C22—42no—
320C22—42no—
321C22—82no—
322C22—82no—
323C22—82no—
324C22—82no—
325C22#1171889311yescharacteristic
326C22#1171889411yescharacteristic
327C22#1171890811yescharacteristic
328C4—21no—
329C4—22no—
330C4—42no—
331C4—42no—
332C4—44no—
333C4#1171889812yes—
334C4#1171889912yes—
335C4#1171890012yes—
336C2—21no—
337C2—21no—
338C2—82no—
339C2—82no—
340C2#1311476411yescharacteristic
341C2#1311477611yescharacteristic
342C2#1311480611yescharacteristic
subgroupG/H
centerC22#11718908
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
Fitting, prime radicalC2×C13×#555C2
socleC22×C13#379
cosocleC2×C42×C13C23
hypercenterC2×#555D13
hypocenterC13#8397
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. #13114828C2semidirect
2. #13113521C2semidirect
3. #13113261C2semidirect
4. #13113157C2semidirect
273. C13#8397semidirect

Maximal subgroups

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

subgroupindex
#131148282
#131135212
#131132612
#131131572
C2×C13×#5552
#839713