Finite Group Databasebeta

← #15772182

Subgroups — #15772182

Order 3328.

460 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 103 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#13117501C211yesmaximal, characteristic
2#13113157C211yesmaximal, characteristic
3#13112783C212yesmaximal, complemented
4#13112765C212yesmaximal, complemented
5C13×#1459C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88189C411yescharacteristic
8C22×#6101C411yescharacteristic
9C2×C13×C22⋊C8—21no—
10#11718881C411yescharacteristic
11#11718871—21no—
12C4×C22⋊Dic13C411yescharacteristic
13#11718633—21no—
14#11718607C2211yescharacteristic
15#11718606—21no—
16#11718604C2211yescharacteristic
17#11718594—21no—
18#11718586—21no—
19C13×#324—21no—
20C13×#323C2212yes—
21#11718117—21no—
22#11718117C2212yes—
23C22×D4×C13C2×C411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C23×Dic13C2×C411yescharacteristic
27C23×Dic13C2×C411yescharacteristic
28C22×C8×C13—41no—
29C4×D4×C13—41no—
30C4×D4×C13—41no—
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C13×C22⋊C4D411yescharacteristic
33C2×C13×C22⋊C4C2311yescharacteristic
34C2×C42×C13D411yescharacteristic
35C2×C22⋊Dic13—21no—
36C2×C22⋊Dic13—21no—
37C2×C22⋊Dic13C2×C411yescharacteristic
38C2×C22⋊Dic13C2×C411yescharacteristic
39#88189—22no—
40#88189C814yescomplemented
41C2×#6101—21no—
42C2×#6101—21no—
43C2×#6101—21no—
44C2×#6101—21no—
45C2×#6101—41no—
46C2×#6101—41no—
47C2×C4×Dic13—21no—
48C13×C22⋊C8—22no—
49C13×C22⋊C8—41no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55C22⋊#1055—22no—
56C4⋊#1055—41no—
57C4×#1055—41no—
58#11474—131nomaximal, Sylow
59C24×C13C22⋊C411yescharacteristic
60C24×C13C22×C411yescharacteristic
61C2×D4×C13—41no—
62C2×D4×C13—41no—
63C2×D4×C13C2×C812yes—
64C2×D4×C13M1612yes—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—81no—
70C22×C4×C13—81no—
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×Dic13—21no—
77C22×Dic13—21no—
78C22×Dic13—21no—
79C22×Dic13—21no—
80C22×Dic13—21no—
81C22×Dic13—41no—
82C22×Dic13—41no—
83C22×Dic13—41no—
84C22×Dic13—81no—
85C22×Dic13C2×C812yescomplemented
86C2×C8×C13—42no—
87C2×C8×C13—82no—
88C13×C4⋊C4—41no—
89C13×C22⋊C4—41no—
90C13×C22⋊C4—41no—
91C42×C13—21no—
92C42×C13—21no—
93C22⋊Dic13—24no—
94C22⋊Dic13—21no—
95C22⋊Dic13—41no—
96C22⋊Dic13—81no—
97C22⋊Dic13C2×C812yescomplemented
98#6101—24no—
99#6101—42no—
100#6101—41no—
101#6101—41no—
102#6101—81no—
103C4×Dic13—81no—
104C2×#1055—42no—
105#2322—131no—
106#1460—131no—
107#1459D1311yescharacteristic
108#1326—132no—
109#1317—132no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—41no—
115C23×C13—41no—
116C23×C13—41no—
117C23×C13—41no—
118C23×C13C22⋊C812yes—
119C23×C13C2×C22⋊C411yescharacteristic
120C23×C13C22×C811yescharacteristic
121C23×C13C2×M1611yescharacteristic
122D4×C13—42no—
123D4×C13—42no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—41no—
130C2×C4×C13—42no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—81no—
135C2×C4×C13—81no—
136C2×C4×C13—81no—
137C2×C4×C13C22⋊C812yes—
138C2×C4×C13#9911yescharacteristic
139C2×C4×C13#9911yescharacteristic
140C2×Dic13—22no—
141C2×Dic13—22no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—42no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—42no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13—82no—
155C8×C13—82no—
156#1055—82no—
157C2×#123—131no—
158C2×C4×D4C2×D1311yescharacteristic
159C22×C4⋊C4—131no—
160#431—261no—
161C2×C22⋊C8—21no—
162#389—261no—
163#388—261no—
164#387—261no—
165#386—131no—
166#385—131no—
167#385—261no—
168#381—131no—
169C4×C22⋊C4—131no—
170#324—21no—
171#323—132no—
172#323—261no—
173#323C2×D1312yes—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13—22no—
179C22×C13—42no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13—42no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13—41no—
186C22×C13—41no—
187C22×C13—81no—
188C22×C13C2×C22⋊C811yescharacteristic
189C22×C13C2×#9911yescharacteristic
190C22×C13#41311yescharacteristic
191C4×C13—21no—
192C4×C13—21no—
193C4×C13—22no—
194C4×C13—41no—
195C4×C13—41no—
196C4×C13—41no—
197Dic13—42no—
198Dic13—42no—
199Dic13—81no—
200Dic13—81no—
201C22×D4C4×D1311yescharacteristic
202C23×C4—131no—
203C23×C4—131no—
204C23×C4C4×D1311yescharacteristic
205C23×C4C22⋊D1311yescharacteristic
206C22×C8—41no—
207#123—134no—
208#123—262no—
209C4×D4—41no—
210C4×D4—41no—
211C2×C4⋊C4—261no—
212C2×C4⋊C4—261no—
213C2×C4⋊C4—261no—
214C2×C4⋊C4—261no—
215C2×C4⋊C4—521no—
216C2×C4⋊C4—521no—
217C2×C4⋊C4C22⋊D1311yescharacteristic
218C2×C22⋊C4—131no—
219C2×C22⋊C4—131no—
220C2×C22⋊C4—261no—
221C2×C22⋊C4—261no—
222C2×C22⋊C4D5211yescharacteristic
223C2×C22⋊C4C22×D1311yescharacteristic
224C2×C42—261no—
225C2×C42D5211yescharacteristic
226C4⋊C8—521no—
227C22⋊C8—22no—
228C22⋊C8—41no—
229C22⋊C8—262no—
230C4×C8—521no—
231#95—261no—
232#95—261no—
233#95—261no—
234#95—261no—
235#95—261no—
236C2×C13—21no—
237C2×C13—21no—
238C2×C13—41no—
239C2×C13—41no—
240C2×C13—42no—
241C2×C13#145911yescharacteristic
242C2×C13#212111yescharacteristic
243C2×C13#212311yescharacteristic
244C24#610311yescharacteristic
245C24C2×C4×D1311yescharacteristic
246C2×D4—41no—
247C2×D4—41no—
248C2×D4C8×D1312yes—
249C2×D4#609412yes—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—81no—
255C22×C4—81no—
256C22×C4—132no—
257C22×C4—261no—
258C22×C4—261no—
259C22×C4—261no—
260C22×C4—261no—
261C22×C4—261no—
262C22×C4—521no—
263C22×C4—521no—
264C22×C4—521no—
265C22×C4—1041no—
266C22×C4#610311yescharacteristic
267C22×C4#610311yescharacteristic
268C22×C4#610311yescharacteristic
269C22×C4C2×D5211yescharacteristic
270C22×C4C2×C22⋊D1311yescharacteristic
271C2×C8—42no—
272C2×C8—82no—
273C2×C8—522no—
274C4⋊C4—41no—
275C4⋊C4—264no—
276C4⋊C4—522no—
277C4⋊C4—521no—
278C4⋊C4—521no—
279C4⋊C4—1041no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C22⋊C4—132no—
283C22⋊C4—261no—
284C22⋊C4—264no—
285C22⋊C4—521no—
286C22⋊C4—1041no—
287C42—21no—
288C42—21no—
289C42—1041no—
290C13#1147411yescharacteristic, complemented, Sylow
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23#8806012yes—
300C23C2×C8×D1311yescharacteristic
301C23C2×#609411yescharacteristic
302C23C2×#610311yescharacteristic
303D4—42no—
304D4—42no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—262no—
319C2×C4—262no—
320C2×C4—521no—
321C2×C4—521no—
322C2×C4—522no—
323C2×C4—521no—
324C2×C4—521no—
325C2×C4—522no—
326C2×C4—521no—
327C2×C4—521no—
328C2×C4—521no—
329C2×C4—521no—
330C2×C4—521no—
331C2×C4—521no—
332C2×C4—1042no—
333C2×C4#8804611yescharacteristic
334C2×C4#8804611yescharacteristic
335C2×C4#8806012yes—
336C8—82no—
337C8—1042no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—22no—
343C22—41no—
344C22—41no—
345C22—42no—
346C22—42no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—81no—
352C22C2×#8804611yescharacteristic
353C22C2×#8806011yescharacteristic
354C22#1171879311yescharacteristic
355C4—22no—
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—522no—
362C4—522no—
363C4—1041no—
364C4—1041no—
365C2—21no—
366C2—21no—
367C2—41no—
368C2—41no—
369C2—42no—
370C2#1311315211yescharacteristic
371C2#1311648011yescharacteristic
372C2#1311649111yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC23×C13C22×C8
FrattiniC2×C22⋊C4C22×D13
FittingC13×#1459C2
socleC22×C13C2×#99
prime radicalC22×D4×C13C2×C4
cosocleC2×C13×C22⋊C4C23
hypercenter#1459D13
hypocenterC13#11474
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1459

Complements

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

NH ≅ G/Ntype
3. #13112783C2semidirect
4. #13112765C2semidirect
40. #88189C8semidirect
85. C22×Dic13C2×C8semidirect
97. C22⋊Dic13C2×C8semidirect
290. C13#11474semidirect

Maximal subgroups

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

subgroupindex
#131175012
#131131572
#131127832
#131127652
C13×#14592
#1147413