Finite Group Databasebeta

← #15778904

Subgroups — #15778904

Order 3328.

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

normal subgroups only

This group has 544 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#124×Dic13C211yesmaximal, characteristic
2C2×#11718133C211yesmaximal, characteristic
3#13114822C212yesmaximal
4#13112960C212yesmaximal
5C2×C13×#354C211yesmaximal, characteristic
6C2×C13×#124C2211yescharacteristic
7C2×Q8×Dic13C411yescharacteristic, complemented
8C2×D4×Dic13C2211yescharacteristic
9C2×C13×#99C2212yes—
10#11718891C411yescharacteristic, complemented
11#11718882C2211yescharacteristic
12C2×#88074C2212yes—
13#11718612—22no—
14#11718603—22no—
15C22⋊C4×Dic13—22no—
16#11718597C411yescharacteristic, complemented
17C42×Dic13C411yescharacteristic, complemented
18C13×#354—22no—
19#11718133—22no—
20#11718119—22no—
21C22×Q8×C13C2×C411yescharacteristic
22C22×D4×C13C2311yescharacteristic
23C23×Dic13D412yes—
24C13×#124—22no—
25C13×#124D412yes—
26C13×#124Q812yes—
27C2×C13×C22⋊C4—22no—
28C2×C13×C22⋊C4—22no—
29C2×C42×C13C2×C411yescharacteristic
30C2×C22⋊Dic13—22no—
31C2×C22⋊Dic13—22no—
32C2×C22⋊Dic13D412yes—
33Q8×Dic13—41no—
34Q8×Dic13—41no—
35D4×Dic13—41no—
36D4×Dic13—41no—
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13C2×C411yescharacteristic
39C2×C4⋊Dic13C2×C411yescharacteristic
40C2×#6101—42no—
41C2×C4×Dic13—21no—
42C2×C4×Dic13—21no—
43C2×C4×Dic13—21no—
44C2×C4×Dic13C2×C411yescharacteristic
45C2×C4×Dic13C2×C411yescharacteristic
46C13×#99—22no—
47C13×#99—22no—
48#88074—22no—
49#88074—22no—
50#88071—22no—
51#88071—22no—
52#88071—42no—
53#12798—131nomaximal, Sylow
54C24×C13C2×D412yes—
55C2×Q8×C13—21no—
56C2×Q8×C13—41no—
57C2×Q8×C13—41no—
58C2×Q8×C13C4⋊C412yescomplemented
59C2×D4×C13—41no—
60C2×D4×C13—41no—
61C2×D4×C13C2×D411yescharacteristic
62C2×D4×C13C2×Q811yescharacteristic
63C2×D4×C13#4112yes—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—42no—
67C22×C4×C13C22×C411yescharacteristic
68C22×Dic13—21no—
69C22×Dic13—22no—
70C22×Dic13—22no—
71C22×Dic13—21no—
72C22×Dic13—44no—
73C22×Dic13—42no—
74C22×Dic13C22⋊C411yescharacteristic
75C22×Dic13C22⋊C412yes—
76C22×Dic13C22⋊C411yescharacteristic
77C13×C22⋊C4—24no—
78C13×C22⋊C4—24no—
79C13×C22⋊C4—42no—
80C13×C22⋊C4—42no—
81C42×C13—21no—
82C42×C13C4⋊C412yescomplemented
83C22⋊Dic13—42no—
84C22⋊Dic13—44no—
85C22⋊Dic13—42no—
86C22⋊Dic13—42no—
87C4⋊Dic13—41no—
88C4⋊Dic13—42no—
89C4⋊Dic13—41no—
90#6101—84no—
91C4×Dic13—21no—
92C4×Dic13—21no—
93C4×Dic13—42no—
94C4×Dic13—42no—
95C4×Dic13—41no—
96C4×Dic13—41no—
97C4×Dic13—41no—
98C4×#124—131no—
99C2×#354—131no—
100C2×#354D1311yescharacteristic
101#1799—132no—
102#1393—132no—
103C23×C13—22no—
104C23×C13—22no—
105C23×C13—42no—
106C23×C13—42no—
107C23×C13C2×C22⋊C411yescharacteristic
108C23×C13#12112yes—
109C23×C13C22⋊Q812yes—
110Q8×C13—42no—
111Q8×C13—42no—
112D4×C13—41no—
113D4×C13—41no—
114D4×C13—42no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—22no—
118C2×C4×C13—22no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—82no—
124C2×C4×C13—82no—
125C2×C4×C13—82no—
126C2×C4×C13C2×C4⋊C411yescharacteristic
127C2×C4×C13#11711yescharacteristic
128C2×Dic13—22no—
129C2×Dic13—22no—
130C2×Dic13—21no—
131C2×Dic13—22no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C2×Dic13—44no—
135C2×Dic13—41no—
136C2×Dic13—42no—
137C2×Dic13—42no—
138C2×Dic13—41no—
139C2×Dic13—82no—
140C2×Dic13—82no—
141C2×Dic13—82no—
142C2×Dic13—82no—
143C2×Dic13#9911yescharacteristic
144C2×Dic13#9911yescharacteristic
145C2×#124C2×D1311yescharacteristic
146C2×C4×Q8—131no—
147C2×C4×D4—131no—
148C2×#99—132no—
149C2×#99C2×D1312yes—
150#391—131no—
151#390—131no—
152#388—262no—
153#382—131no—
154#380—262no—
155C4×C22⋊C4—262no—
156C43—131no—
157#354—22no—
158#354—262no—
159#342—262no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13—22no—
163C22×C13—22no—
164C22×C13—42no—
165C22×C13—42no—
166C22×C13—42no—
167C22×C13—42no—
168C22×C13—82no—
169C22×C13#38011yescharacteristic
170C22×C13C2×#9911yescharacteristic
171C22×C13#41011yescharacteristic
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—42no—
175C4×C13—42no—
176C4×C13—162no—
177Dic13—21no—
178Dic13—42no—
179Dic13—42no—
180Dic13—41no—
181Dic13—81no—
182Dic13—162no—
183Dic13#35412yescomplemented
184C22×Q8C4×D1311yescharacteristic
185C22×D4C22×D1311yescharacteristic
186C23×C4—132no—
187#124—22no—
188#124Dic2612yes—
189#124C22⋊D1312yes—
190C4×Q8—521no—
191C4×Q8—521no—
192C4×D4—521no—
193C4×D4—521no—
194C2×C4⋊C4—131no—
195C2×C4⋊C4—131no—
196C2×C4⋊C4—261no—
197C2×C4⋊C4—522no—
198C2×C22⋊C4—22no—
199C2×C22⋊C4—22no—
200C2×C22⋊C4—132no—
201C2×C22⋊C4—262no—
202C2×C22⋊C4—262no—
203C2×C42—131no—
204C2×C42—131no—
205C2×C42—261no—
206C2×C42—261no—
207C2×C42—261no—
208C2×C42C4×D1311yescharacteristic
209#99—22no—
210#99—22no—
211#99—262no—
212#99—262no—
213#95—262no—
214#95—262no—
215#95—522no—
216C2×C13—21no—
217C2×C13—21no—
218C2×C13—42no—
219C2×C13—42no—
220C2×C13#179911yescharacteristic
221C2×C13C2×#35411yescharacteristic
222C2×C13#212611yescharacteristic
223C24D4×D1312yes—
224C2×Q8—21no—
225C2×Q8—41no—
226C2×Q8—41no—
227C2×Q8#610112yescomplemented
228C2×D4—41no—
229C2×D4—41no—
230C2×D4C2×Dic2611yescharacteristic
231C2×D4#612912yes—
232C2×D4C2×C22⋊D1311yescharacteristic
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—42no—
236C22×C4—131no—
237C22×C4—132no—
238C22×C4—131no—
239C22×C4—262no—
240C22×C4—262no—
241C22×C4—261no—
242C22×C4—261no—
243C22×C4—524no—
244C22×C4—522no—
245C22×C4C2×C4×D1311yescharacteristic
246C4⋊C4—521no—
247C4⋊C4—521no—
248C4⋊C4—522no—
249C4⋊C4—1044no—
250C22⋊C4—24no—
251C22⋊C4—24no—
252C22⋊C4—42no—
253C22⋊C4—42no—
254C22⋊C4—522no—
255C22⋊C4—524no—
256C22⋊C4—522no—
257C22⋊C4—522no—
258C42—21no—
259C42—261no—
260C42—261no—
261C42—521no—
262C42—521no—
263C42—521no—
264C42—522no—
265C42—522no—
266C42#610112yescomplemented
267C13#1279811yescharacteristic, complemented, Sylow
268C23—22no—
269C23—22no—
270C23—42no—
271C23—42no—
272C23#8813212yes—
273C23C22⋊C4×D1311yescharacteristic
274C23#8819312yes—
275Q8—42no—
276Q8—42no—
277D4—41no—
278D4—42no—
279D4—41no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—82no—
289C2×C4—82no—
290C2×C4—82no—
291C2×C4—131no—
292C2×C4—131no—
293C2×C4—262no—
294C2×C4—262no—
295C2×C4—261no—
296C2×C4—262no—
297C2×C4—524no—
298C2×C4—521no—
299C2×C4—521no—
300C2×C4—521no—
301C2×C4—522no—
302C2×C4—522no—
303C2×C4—521no—
304C2×C4—1042no—
305C2×C4—1042no—
306C2×C4—1042no—
307C2×C4—1042no—
308C2×C4#8813111yescharacteristic
309C2×C4C2×#610111yescharacteristic
310C22—21no—
311C22—21no—
312C22—22no—
313C22—22no—
314C22—42no—
315C22—42no—
316C22—42no—
317C22—42no—
318C22—82no—
319C22#1171840111yescharacteristic
320C22D13×#9911yescharacteristic
321C22#1171860311yescharacteristic
322C4—21no—
323C4—21no—
324C4—42no—
325C4—42no—
326C4—132no—
327C4—162no—
328C4—261no—
329C4—522no—
330C4—522no—
331C4—521no—
332C4—1041no—
333C4—2082no—
334C2—21no—
335C2—21no—
336C2—42no—
337C2—42no—
338C2#1311482211yescharacteristic
339C2D13×#35411yescharacteristic
340C2#1311650011yescharacteristic
subgroupG/H
centerC22D13×#99
commutatorC22×C4×C13C22×C4
FrattiniC22×D4C22×D13
FittingC2×C13×#354C2
socleC22×C13C2×#99
prime radical, cosocleC22×D4×C13C23
hypercenterC2×#354D13
hypocenterC13#12798
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#354

Complements

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

NH ≅ G/Ntype
7. C2×Q8×Dic13C4semidirect
10. #11718891C4semidirect
16. #11718597C4semidirect
17. C42×Dic13C4semidirect
58. C2×Q8×C13C4⋊C4semidirect
82. C42×C13C4⋊C4semidirect
183. Dic13#354semidirect
227. C2×Q8#6101semidirect
266. C42#6101semidirect
267. C13#12798semidirect

Maximal subgroups

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

subgroupindex
#124×Dic132
C2×#117181332
#131148222
#131129602
C2×C13×#3542
#1279813