Finite Group Databasebeta

← #15772175

Subgroups — #15772175

Order 3328.

488 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 107 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
1C4×#88189C211yesmaximal, characteristic
2#13113154C211yesmaximal, characteristic
3#13112783C212yesmaximal, complemented
4#13112765C212yesmaximal, complemented
5C13×#1460C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88189C411yescharacteristic
8C22×C4×Dic13C411yescharacteristic
9C13×#431—21no—
10#11718881C411yescharacteristic
11C4×C22⋊Dic13—21no—
12C4×C22⋊Dic13C411yescharacteristic
13C2×C22⋊#1055—21no—
14#11718639—21no—
15#11718607C2211yescharacteristic
16#11718605—21no—
17#11718604C2211yescharacteristic
18C4×#6101—21no—
19C13×#323—21no—
20C13×#323C2212yes—
21#11718120—21no—
22#11718117C2212yes—
23C22×D4×C13C2×C411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C23×Dic13C2×C411yescharacteristic
27C23×Dic13C2×C411yescharacteristic
28C4×D4×C13—41no—
29C4×D4×C13—41no—
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C13×C22⋊C4D411yescharacteristic
32C2×C13×C22⋊C4C2311yescharacteristic
33C2×C42×C13D411yescharacteristic
34C2×C22⋊Dic13—21no—
35C2×C22⋊Dic13—21no—
36C2×C22⋊Dic13C2×C411yescharacteristic
37C2×C22⋊Dic13C2×C411yescharacteristic
38#88189—22no—
39#88189C814yescomplemented
40C2×#6101—21no—
41C2×#6101—21no—
42C2×C4×Dic13—21no—
43C2×C4×Dic13—21no—
44C2×C4×Dic13—21no—
45C2×C4×Dic13—41no—
46C2×C4×Dic13—41no—
47C22×#1055—41no—
48C13×C4⋊C8—41no—
49C13×C22⋊C8—22no—
50C4×C8×C13—41no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56C22⋊#1055—22no—
57C22⋊#1055—41no—
58#11472—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—42no—
70C22×C4×C13—42no—
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—42no—
82C22×Dic13—41no—
83C22×Dic13—41no—
84C22×Dic13—41no—
85C22×Dic13C2×C812yescomplemented
86C2×C8×C13—42no—
87C13×C4⋊C4—41no—
88C13×C22⋊C4—41no—
89C13×C22⋊C4—41no—
90C42×C13—21no—
91C42×C13—21no—
92C22⋊Dic13—24no—
93C22⋊Dic13—21no—
94C22⋊Dic13—42no—
95C22⋊Dic13—41no—
96C22⋊Dic13C2×C812yescomplemented
97#6101—24no—
98#6101—42no—
99C4×Dic13—42no—
100C4×Dic13—42no—
101C4×Dic13—41no—
102C4×Dic13—41no—
103C2×#1055—42no—
104C2×#1055—82no—
105C4×#123—131no—
106#1460D1311yescharacteristic
107#1459—131no—
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—22no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—42no—
131C2×C4×C13—42no—
132C2×C4×C13—42no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—81no—
137C2×C4×C13C22⋊C812yes—
138C2×C4×C13#9911yescharacteristic
139C2×C4×C13#9911yescharacteristic
140C2×Dic13—22no—
141C2×Dic13—22no—
142C2×Dic13—22no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—42no—
147C2×Dic13—42no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—42no—
152C2×Dic13—42no—
153C2×Dic13—41no—
154C2×Dic13—41no—
155C2×Dic13—41no—
156C8×C13—82no—
157#1055—82no—
158C2×#123—131no—
159C2×C4×D4C2×D1311yescharacteristic
160C22×C42—131no—
161#431—21no—
162C2×C22⋊C8—261no—
163#388—261no—
164#387—261no—
165#386—131no—
166#385—131no—
167#381—131no—
168C4×C4⋊C4—261no—
169C4×C22⋊C4—131no—
170C4×C22⋊C4—261no—
171#324—261no—
172#323—21no—
173#323—132no—
174#323C2×D1312yes—
175C22×C13—21no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13—21no—
179C22×C13—22no—
180C22×C13—42no—
181C22×C13—41no—
182C22×C13—41no—
183C22×C13—42no—
184C22×C13—41no—
185C22×C13—41no—
186C22×C13—41no—
187C22×C13—41no—
188C22×C13—81no—
189C22×C13C2×C22⋊C811yescharacteristic
190C22×C13C2×#9911yescharacteristic
191C22×C13#41311yescharacteristic
192C4×C13—21no—
193C4×C13—22no—
194C4×C13—41no—
195C4×C13—41no—
196C4×C13—41no—
197C4×C13#35212yes—
198Dic13—42no—
199Dic13—42no—
200Dic13—42no—
201Dic13—81no—
202C22×D4C4×D1311yescharacteristic
203C23×C4—131no—
204C23×C4—131no—
205C23×C4C4×D1311yescharacteristic
206C23×C4D5211yescharacteristic
207C22×C8—521no—
208#123—134no—
209#123—262no—
210C4×D4—41no—
211C4×D4—41no—
212C2×C4⋊C4—261no—
213C2×C4⋊C4—261no—
214C2×C4⋊C4D5211yescharacteristic
215C2×C22⋊C4—131no—
216C2×C22⋊C4—131no—
217C2×C22⋊C4—261no—
218C2×C22⋊C4—261no—
219C2×C22⋊C4C22⋊D1311yescharacteristic
220C2×C22⋊C4C22×D1311yescharacteristic
221C2×C42—261no—
222C2×C42—261no—
223C2×C42—261no—
224C2×C42—521no—
225C2×C42—521no—
226C2×C42C22⋊D1311yescharacteristic
227C4⋊C8—41no—
228C22⋊C8—22no—
229C22⋊C8—262no—
230C22⋊C8—521no—
231C4×C8—41no—
232#95—261no—
233#95—261no—
234#95—261no—
235#95—261no—
236#95—261no—
237C2×C13—21no—
238C2×C13—21no—
239C2×C13—41no—
240C2×C13—41no—
241C2×C13—42no—
242C2×C13#145911yescharacteristic
243C2×C13C2×#35211yescharacteristic
244C2×C13#212011yescharacteristic
245C24#610311yescharacteristic
246C24C2×C4×D1311yescharacteristic
247C2×D4—41no—
248C2×D4—41no—
249C2×D4C8×D1312yes—
250C2×D4#609412yes—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—42no—
256C22×C4—42no—
257C22×C4—132no—
258C22×C4—261no—
259C22×C4—261no—
260C22×C4—261no—
261C22×C4—261no—
262C22×C4—261no—
263C22×C4—522no—
264C22×C4—521no—
265C22×C4—521no—
266C22×C4—521no—
267C22×C4#610311yescharacteristic
268C22×C4#610311yescharacteristic
269C22×C4#610311yescharacteristic
270C22×C4C2×D5211yescharacteristic
271C22×C4C2×C22⋊D1311yescharacteristic
272C2×C8—42no—
273C2×C8—522no—
274C2×C8—1042no—
275C4⋊C4—41no—
276C4⋊C4—264no—
277C4⋊C4—522no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—132no—
281C22⋊C4—261no—
282C22⋊C4—264no—
283C22⋊C4—522no—
284C22⋊C4—521no—
285C42—21no—
286C42—21no—
287C42—522no—
288C42—522no—
289C42—521no—
290C42—521no—
291C13#1147211yescharacteristic, complemented, Sylow
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23#8806012yes—
301C23C2×C8×D1311yescharacteristic
302C23C2×#609411yescharacteristic
303C23C2×#610311yescharacteristic
304D4—42no—
305D4—42no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—22no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—81no—
319C2×C4—262no—
320C2×C4—262no—
321C2×C4—262no—
322C2×C4—521no—
323C2×C4—521no—
324C2×C4—521no—
325C2×C4—522no—
326C2×C4—522no—
327C2×C4—521no—
328C2×C4—521no—
329C2×C4—521no—
330C2×C4—522no—
331C2×C4—522no—
332C2×C4—521no—
333C2×C4—521no—
334C2×C4—521no—
335C2×C4#8804611yescharacteristic
336C2×C4#8804611yescharacteristic
337C2×C4#8806012yes—
338C8—82no—
339C8—1042no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—22no—
345C22—41no—
346C22—41no—
347C22—42no—
348C22—42no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—81no—
354C22C2×#8804611yescharacteristic
355C22C2×#8806011yescharacteristic
356C22#1171879311yescharacteristic
357C4—21no—
358C4—22no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—522no—
363C4—522no—
364C4—522no—
365C4—1041no—
366C4#1171806812yes—
367C2—21no—
368C2—21no—
369C2—41no—
370C2—41no—
371C2—42no—
372C2#1311315211yescharacteristic
373C2C2×#1171806811yescharacteristic
374C2#1311647511yescharacteristic
subgroupG/H
centerC2×C4#88046
commutatorC23×C13C22×C8
FrattiniC2×C22⋊C4C22×D13
FittingC13×#1460C2
socleC22×C13C2×#99
prime radicalC22×D4×C13C2×C4
cosocleC2×C13×C22⋊C4C23
hypercenter#1460D13
hypocenterC13#11472
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1460

Complements

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

NH ≅ G/Ntype
3. #13112783C2semidirect
4. #13112765C2semidirect
39. #88189C8semidirect
85. C22×Dic13C2×C8semidirect
96. C22⋊Dic13C2×C8semidirect
291. C13#11472semidirect

Maximal subgroups

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

subgroupindex
C4×#881892
#131131542
#131127832
#131127652
C13×#14602
#1147213