Finite Group Databasebeta

← #15756036

Subgroups — #15756036

Order 3328.

418 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718685C211yesmaximal, characteristic
2#13114963C211yesmaximal, characteristic
3#13114841C211yesmaximal, characteristic
4C2×#11718072C211yesmaximal, characteristic
5#13112720C211yesmaximal, characteristic
6#13112719C211yesmaximal, characteristic
7C13×#1803C211yesmaximal, characteristic
8C2×C4×Q8×C13C2211yescharacteristic
9C2×C13×C4⋊C8C2211yescharacteristic
10C2×C13×#103—21no—
11C13×#384C2211yescharacteristic
12C2×#88075—21no—
13#11718685—22no—
14#11718685C414yescomplemented
15#11718596C2211yescharacteristic
16C2×C4⋊#1055—21no—
17C2×C4⋊#1055C2211yescharacteristic
18C2×C4⋊#1055C2211yescharacteristic
19C2×#88043—21no—
20C2×C4×#1055C2211yescharacteristic
21C13×#340—21no—
22#11718121—21no—
23#11718121—21no—
24#11718121—21no—
25#11718072—22no—
26C22×Q8×C13D411yescharacteristic
27C22×C8×C13—21no—
28C4×Q8×C13—21no—
29C4×Q8×C13—21no—
30C4×Q8×C13C2×C412yes—
31C4×Q8×C13Q812yes—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C42×C13—21no—
38C2×C42×C13C2311yescharacteristic
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13—21no—
42C22×#1055—21no—
43C22×#1055—21no—
44C22×#1055D411yescharacteristic
45C22×#1055D411yescharacteristic
46C13×C4⋊C8—21no—
47C13×C4⋊C8—21no—
48C13×#103—42no—
49#88075—42no—
50C4⋊#1055—21no—
51C4⋊#1055—24no—
52C4⋊#1055—21no—
53C4⋊#1055—21no—
54C4⋊#1055C2×C412yes—
55#88043—24no—
56C4×#1055C2×C412yes—
57C4×#1055D412yes—
58#8657—131nomaximal, Sylow
59C2×Q8×C13—21no—
60C2×Q8×C13—21no—
61C2×Q8×C13—21no—
62C2×Q8×C13—21no—
63C2×Q8×C13—21no—
64C2×Q8×C13C4⋊C412yes—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—41no—
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13#4111yescharacteristic
71C22×Dic13—41no—
72C2×C8×C13—41no—
73C2×C8×C13—41no—
74C2×C8×C13—41no—
75C13×C4⋊C4—22no—
76C13×C4⋊C4—21no—
77C13×C4⋊C4—22no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—81no—
83C13×C4⋊C4C4⋊C412yes—
84C42×C13—22no—
85C42×C13—22no—
86C42×C13C22×C411yescharacteristic
87C42×C13C2×D411yescharacteristic
88C42×C13C2×Q811yescharacteristic
89C42×C13#4111yescharacteristic
90C4⋊Dic13—41no—
91C4⋊Dic13—41no—
92C4⋊Dic13—41no—
93C4⋊Dic13—41no—
94C4⋊Dic13—81no—
95C2×#1055—21no—
96C2×#1055—21no—
97C2×#1055—21no—
98C2×#1055—21no—
99C2×#1055—22no—
100C2×#1055—41no—
101C2×#1055—41no—
102C2×#1055—41no—
103C2×#1055—41no—
104C2×#1055—41no—
105C2×#1055C22⋊C412yes—
106C2×#1055C22⋊C412yes—
107C2×#446—131no—
108#1834—131no—
109#1803—131no—
110#1803D1311yescharacteristic
111C2×#334—131no—
112#1296—131no—
113#1296—131no—
114C23×C13#12111yescharacteristic
115Q8×C13—22no—
116Q8×C13—22no—
117Q8×C13—41no—
118Q8×C13—41no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—22no—
122C2×C4×C13—22no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—81no—
128C2×C4×C13—81no—
129C2×C4×C13—81no—
130C2×C4×C13C2×C22⋊C411yescharacteristic
131C2×C4×C13C2×C4⋊C411yescharacteristic
132C2×C4×C13#11711yescharacteristic
133C2×C4×C13#12111yescharacteristic
134C2×C4×C13C22⋊Q811yescharacteristic
135C2×C4×C13C22⋊Q811yescharacteristic
136C2×C4×C13#13511yescharacteristic
137C2×C4×C13#13511yescharacteristic
138C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C13#13711yescharacteristic
141C2×C4×C13#13711yescharacteristic
142C2×C4×C13#13711yescharacteristic
143C2×C4×C13#13711yescharacteristic
144C2×Dic13—81no—
145C2×Dic13—81no—
146C2×Dic13—81no—
147C8×C13—81no—
148#1055—22no—
149#1055—22no—
150#1055—42no—
151#1055—81no—
152C2×C4×Q8C2×D1311yescharacteristic
153#446—134no—
154#446—262no—
155C2×C4⋊C8—131no—
156C2×C4⋊C8—131no—
157C2×C4⋊C8—261no—
158C2×C4⋊C8C2×D1311yescharacteristic
159C2×#103—21no—
160C2×#103—261no—
161C2×#97—261no—
162C2×C4×C8—131no—
163#384—131no—
164#384C2×D1311yescharacteristic
165#340—21no—
166#340—261no—
167#340—261no—
168#340—261no—
169#334—262no—
170C22×C13#38011yescharacteristic
171C22×C13#46411yescharacteristic
172C22×C13#46411yescharacteristic
173C22×C13#46911yescharacteristic
174C22×C13#47011yescharacteristic
175C22×C13#47111yescharacteristic
176C22×C13#47111yescharacteristic
177C4×C13—21no—
178C4×C13—21no—
179C4×C13—42no—
180C4×C13—42no—
181C4×C13—161no—
182C4×C13#41611yescharacteristic
183C4×C13#41911yescharacteristic
184C4×C13#42811yescharacteristic
185C4×C13#42811yescharacteristic
186C4×C13#46811yescharacteristic
187C4×C13#46811yescharacteristic
188C4×C13#47911yescharacteristic
189C4×C13#47911yescharacteristic
190Dic13—161no—
191C22×Q8C22⋊D1311yescharacteristic
192C22×C8—21no—
193C22×C8—131no—
194C22×C8—131no—
195C22×C8—261no—
196C22×C8—261no—
197C4×Q8—21no—
198C4×Q8—21no—
199C4×Q8Dic2612yes—
200C4×Q8C4×D1312yes—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—261no—
206C2×C4⋊C4—261no—
207C2×C4⋊C4—261no—
208C2×C4⋊C4C22⋊D1311yescharacteristic
209C2×C42—21no—
210C2×C42C22×D1311yescharacteristic
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—132no—
214C4⋊C8—264no—
215C4⋊C8—261no—
216C4⋊C8—261no—
217C4⋊C8—261no—
218#103—42no—
219#103—522no—
220#97—264no—
221C4×C8—132no—
222C4×C8—132no—
223C2×C13#170211yescharacteristic
224C2×C13#170211yescharacteristic
225C2×C13#170411yescharacteristic
226C2×C13#170411yescharacteristic
227C2×C13#180511yescharacteristic
228C2×C13#180911yescharacteristic
229C2×C13#181511yescharacteristic
230C2×Q8—21no—
231C2×Q8—21no—
232C2×Q8—21no—
233C2×Q8—21no—
234C2×Q8—21no—
235C2×Q8#610112yes—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—41no—
239C22×C4—521no—
240C22×C4D4×D1311yescharacteristic
241C22×C4#612911yescharacteristic
242C22×C4C2×C22⋊D1311yescharacteristic
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—132no—
247C2×C8—132no—
248C2×C8—261no—
249C2×C8—261no—
250C2×C8—261no—
251C2×C8—261no—
252C2×C8—262no—
253C2×C8—521no—
254C2×C8—521no—
255C2×C8—521no—
256C2×C8—521no—
257C2×C8—521no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—21no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—81no—
266C4⋊C4—521no—
267C4⋊C4—521no—
268C4⋊C4—521no—
269C4⋊C4—521no—
270C4⋊C4—1041no—
271C4⋊C4#610112yes—
272C42—22no—
273C42—22no—
274C42C2×Dic2611yescharacteristic
275C42C2×C4×D1311yescharacteristic
276C42D4×D1311yescharacteristic
277C42#612911yescharacteristic
278C13#865711yescharacteristic, complemented, Sylow
279C23#8819311yescharacteristic
280Q8—22no—
281Q8—22no—
282Q8—41no—
283Q8—41no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—1041no—
296C2×C4—1041no—
297C2×C4—1041no—
298C2×C4#8813111yescharacteristic
299C2×C4#8813211yescharacteristic
300C2×C4#8813211yescharacteristic
301C2×C4C22⋊C4×D1311yescharacteristic
302C2×C4#8816911yescharacteristic
303C2×C4#8817011yescharacteristic
304C2×C4#8817211yescharacteristic
305C2×C4#8817311yescharacteristic
306C2×C4C2×#610111yescharacteristic
307C2×C4#8818611yescharacteristic
308C2×C4#8819311yescharacteristic
309C2×C4#8819611yescharacteristic
310C2×C4#8820311yescharacteristic
311C2×C4#8820511yescharacteristic
312C8—81no—
313C8—262no—
314C8—262no—
315C8—522no—
316C8—1041no—
317C22#1171860311yescharacteristic
318C22#1171870011yescharacteristic
319C22#1171871311yescharacteristic
320C22#1171882711yescharacteristic
321C22#1171884611yescharacteristic
322C22#1171886111yescharacteristic
323C22#1171886411yescharacteristic
324C4—21no—
325C4—21no—
326C4—42no—
327C4—42no—
328C4—161no—
329C4—2081no—
330C4#1171845711yescharacteristic
331C4#1171846011yescharacteristic
332C4#1171846311yescharacteristic
333C4#1171846511yescharacteristic
334C4#1171862511yescharacteristic
335C4#1171865611yescharacteristic
336C4#1171870311yescharacteristic
337C4#1171871011yescharacteristic
338C2#1311440211yescharacteristic
339C2#1311440611yescharacteristic
340C2#1311441611yescharacteristic
341C2#1311442011yescharacteristic
342C2#1311484911yescharacteristic
343C2#1311486711yescharacteristic
344C2#1311489311yescharacteristic
subgroupG/H
centerC23#88193
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1803C2
socle, prime radicalC23×C13#121
cosocleC2×C42×C13C23
hypercenter#1803D13
hypocenterC13#8657
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
14. #11718685C4semidirect
278. C13#8657semidirect

Maximal subgroups

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

subgroupindex
C2×#117186852
#131149632
#131148412
C2×#117180722
#131127202
#131127192
C13×#18032
#865713