Finite Group Databasebeta

← #15755790

Subgroups — #15755790

Order 3328.

462 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
1C4×#88155C211yesmaximal, characteristic
2C2×#11718049C211yesmaximal, characteristic, complemented
3#13113224C212yesmaximal
4#13112685C212yesmaximal, complemented
5C13×#1564C211yesmaximal, characteristic, complemented
6C2×#88155C411yescharacteristic
7C2×#88155C411yescharacteristic
8C4×#6127C2211yescharacteristic
9C13×#431C2212yes—
10C2×C4×C8×C13C2211yescharacteristic
11#11718762C411yescharacteristic
12#11718762C411yescharacteristic
13C2×C4⋊#1055C2212yes—
14C4×#6099C2211yescharacteristic
15#11718350—21no—
16#11718350—21no—
17C4×#6094—21no—
18C4×C8×D13—21no—
19C13×#335—21no—
20C13×#334—21no—
21#11718051—22no—
22#11718049—21no—
23#11718049—21no—
24#11718048—22no—
25C2×#6127C2×C411yescharacteristic
26C22×C8×C13C2×C411yescharacteristic
27C22×C8×C13C2×C411yescharacteristic
28C2×C42×C13C2311yescharacteristic
29C4×C22⋊D13—21no—
30C4×C22⋊D13—21no—
31#88180C2×C411yescharacteristic
32C2×#6099C2×C411yescharacteristic
33C2×#6099C2×C411yescharacteristic
34C22×#1055—22no—
35#88155—22no—
36#88155—22no—
37#88155—22no—
38#88155C814yescomplemented
39C2×#6094—21no—
40C2×#6094—21no—
41C2×C8×D13—21no—
42C2×C8×D13—21no—
43C4×D52D411yescharacteristic
44C4×D52Q811yescharacteristic
45#88126—21no—
46C42×D13—21no—
47C4×Dic26D411yescharacteristic
48C4×Dic26Q811yescharacteristic
49C13×C4⋊C8—22no—
50C13×C22⋊C8—22no—
51C4×C8×C13—22no—
52C4×C8×C13D411yescharacteristic
53C4×C8×C13D411yescharacteristic
54C4×C8×C13D411yescharacteristic
55C4×C8×C13D411yescharacteristic
56#88055—21no—
57#88055—21no—
58C8×Dic13—21no—
59C8×Dic13—21no—
60C4⋊#1055—22no—
61C4⋊#1055—22no—
62#88043—21no—
63C4×#1055—21no—
64#8604—131nomaximal, Sylow
65C22×C4×C13C22×C411yescharacteristic
66C22×C4×C13#4111yescharacteristic
67C22×C4×C13#4111yescharacteristic
68C2×C22⋊D13—21no—
69#6127—21no—
70#6127—21no—
71#6127C2×C812yes—
72#6127M1612yes—
73C2×D52C4⋊C411yescharacteristic
74C2×C4×D13—21no—
75C2×C4×D13—21no—
76C2×C4×D13—21no—
77C2×Dic26C4⋊C411yescharacteristic
78C2×C8×C13—21no—
79C2×C8×C13—21no—
80C2×C8×C13—42no—
81C2×C8×C13C22⋊C411yescharacteristic
82C2×C8×C13C22⋊C411yescharacteristic
83C2×C8×C13C22⋊C411yescharacteristic
84C2×C8×C13C22⋊C411yescharacteristic
85C2×C8×C13C2×C812yes—
86C2×C8×C13M1612yes—
87C42×C13C2×D411yescharacteristic
88C42×C13C2×D411yescharacteristic
89C42×C13C2×D411yescharacteristic
90C42×C13C2×Q811yescharacteristic
91C22⋊Dic13—21no—
92#6103—21no—
93#6103—21no—
94C4⋊Dic13C4⋊C411yescharacteristic
95C4⋊Dic13C4⋊C411yescharacteristic
96#6101—21no—
97#6101—21no—
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13—21no—
101#6099—21no—
102#6099—21no—
103#6099C2×C812yes—
104#6099M1612yes—
105C2×#1055—21no—
106C2×#1055—21no—
107C2×#1055—42no—
108C2×#1055—82no—
109#6094—24no—
110#6094—24no—
111C8×D13—24no—
112C8×D13—24no—
113C4×#131—131no—
114#1564D1311yescharacteristic, complemented
115C2×#334—131no—
116#1477—132no—
117#1283—132no—
118C23×C13#11711yescharacteristic
119C22×D13—21no—
120C2×C4×C13—22no—
121C2×C4×C13—41no—
122C2×C4×C13C2×C22⋊C411yescharacteristic
123C2×C4×C13C2×C4⋊C411yescharacteristic
124C2×C4×C13#12111yescharacteristic
125C2×C4×C13#12111yescharacteristic
126C2×C4×C13C22⋊Q811yescharacteristic
127C2×C4×C13C22⋊Q811yescharacteristic
128C2×C4×C13C22×C811yescharacteristic
129C2×C4×C13C2×M1611yescharacteristic
130C2×C4×C13C2×M1611yescharacteristic
131C2×C4×C13C2×M1611yescharacteristic
132C22⋊D13—22no—
133C22⋊D13—22no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137D52—21no—
138D52C4⋊C812yes—
139C4×D13—22no—
140C4×D13—22no—
141C4×D13—42no—
142C4×D13—42no—
143Dic26—21no—
144Dic26C4⋊C812yes—
145C8×C13—21no—
146C8×C13—21no—
147C8×C13—82no—
148C8×C13C22⋊C812yes—
149C8×C13C22⋊C812yes—
150#1055—22no—
151#1055—22no—
152#1055—82no—
153C2×#131—131no—
154C2×#131—131no—
155C4×#41—131no—
156#431C2×D1312yes—
157C2×C4⋊C8—132no—
158#405—131no—
159#405—131no—
160#405—261no—
161#405—261no—
162C4×M16—131no—
163C4×M16—261no—
164C2×C4×C8—261no—
165C2×C4×C8C2×D1311yescharacteristic
166#335—21no—
167#334—21no—
168#334—261no—
169#334—261no—
170Q8⋊C8—262no—
171D4⋊C8—262no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13#38011yescharacteristic
175C22×C13#43111yescharacteristic
176C22×C13#43211yescharacteristic
177C2×D13—22no—
178C2×D13—41no—
179C2×D13—41no—
180C4×C13—21no—
181C4×C13—21no—
182C4×C13—21no—
183C4×C13C2×C22⋊C811yescharacteristic
184C4×C13#40711yescharacteristic
185C4×C13C2×C4⋊C811yescharacteristic
186C4×C13#42311yescharacteristic
187C4×C13#47112yes—
188Dic13—22no—
189Dic13—41no—
190Dic13—41no—
191C2×#41—131no—
192#131—134no—
193#131—262no—
194#131—262no—
195#131—262no—
196C2×M16—131no—
197C2×M16—131no—
198C2×M16—261no—
199C2×M16—261no—
200C22×C8—261no—
201C22×C8—261no—
202C22×C8—262no—
203C22×C8C4×D1311yescharacteristic
204C22×C8C4×D1311yescharacteristic
205C4×Q8—131no—
206C4×Q8—131no—
207C4×D4—131no—
208C4×D4—131no—
209C4×D4—261no—
210C4×D4—261no—
211#117—131no—
212#117—261no—
213C2×C42—261no—
214C2×C42C22×D1311yescharacteristic
215C4⋊C8—22no—
216C4⋊C8—262no—
217C4⋊C8—262no—
218C22⋊C8—22no—
219#97—261no—
220#97—261no—
221#97—261no—
222C4×C8—22no—
223C4×C8—261no—
224C4×C8—261no—
225C4×C8—261no—
226C4×C8D5211yescharacteristic
227C4×C8D5211yescharacteristic
228C4×C8C22⋊D1311yescharacteristic
229C4×C8C22⋊D1311yescharacteristic
230C2×C13—21no—
231C2×C13—21no—
232C2×C13#179711yescharacteristic
233C2×C13#181411yescharacteristic
234C2×C13#181511yescharacteristic
235D13—42no—
236#41—132no—
237#41—132no—
238#41—261no—
239#41—261no—
240C2×Q8—131no—
241C2×D4—131no—
242C2×D4—261no—
243C22×C4—261no—
244C22×C4—261no—
245C22×C4—261no—
246C22×C4C2×C4×D1311yescharacteristic
247C22×C4#612911yescharacteristic
248C22×C4#613111yescharacteristic
249M16—132no—
250M16—132no—
251M16—264no—
252M16—261no—
253M16—261no—
254M16—264no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—42no—
258C2×C8—264no—
259C2×C8—261no—
260C2×C8—261no—
261C2×C8—264no—
262C2×C8—522no—
263C2×C8—1042no—
264C2×C8C8×D1312yes—
265C2×C8#609412yes—
266C2×C8#610311yescharacteristic
267C2×C8#610311yescharacteristic
268C2×C8#610311yescharacteristic
269C2×C8#610311yescharacteristic
270C4⋊C4—131no—
271C4⋊C4—131no—
272C4⋊C4—261no—
273C4⋊C4—261no—
274C22⋊C4—261no—
275C22⋊C4—261no—
276C22⋊C4—261no—
277C42—261no—
278C42—261no—
279C42—261no—
280C42C2×D5211yescharacteristic
281C42D4×D1311yescharacteristic
282C42Q8×D1311yescharacteristic
283C42C2×C22⋊D1311yescharacteristic
284C13#860411yescharacteristic, complemented, Sylow
285C23—261no—
286C23#8814611yescharacteristic
287Q8—132no—
288Q8—261no—
289D4—132no—
290D4—262no—
291D4—262no—
292D4—261no—
293C2×C4—22no—
294C2×C4—41no—
295C2×C4—261no—
296C2×C4—262no—
297C2×C4—262no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—522no—
301C2×C4—522no—
302C2×C4C4⋊C4×D1311yescharacteristic
303C2×C4#8814911yescharacteristic
304C2×C4#8815111yescharacteristic
305C2×C4C2×C8×D1311yescharacteristic
306C2×C4C2×#609411yescharacteristic
307C2×C4M16×D1311yescharacteristic
308C2×C4M16×D1311yescharacteristic
309C2×C4C2×#610311yescharacteristic
310C2×C4#8819211yescharacteristic
311C2×C4#8820011yescharacteristic
312C8—21no—
313C8—21no—
314C8—82no—
315C8—262no—
316C8—262no—
317C8—1042no—
318C8#8806012yes—
319C8#8806012yes—
320C22—21no—
321C22—21no—
322C22—262no—
323C22—521no—
324C22—521no—
325C22#1171849411yescharacteristic
326C22#1171849611yescharacteristic
327C22#1171864811yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—262no—
332C4—521no—
333C4—521no—
334C4D13×C4⋊C811yescharacteristic
335C4#1171849811yescharacteristic
336C4#1171855912yes—
337C4C2×#8806011yescharacteristic
338C4#1171878711yescharacteristic
339C2—21no—
340C2—21no—
341C2—522no—
342C2#1311481311yescharacteristic
343C2#1311488711yescharacteristic
344C2#1311489211yescharacteristic
subgroupG/H
centerC2×C4#88149
commutatorC2×C4×C13C22×C8
FrattiniC2×C42C22×D13
FittingC13×#1564C2
socleC22×C13#380
prime radicalC2×#6127C2×C4
cosocleC2×C42×C13C23
hypercenter#1564D13
hypocenterC13#8604
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1564

Complements

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

NH ≅ G/Ntype
2. C2×#11718049C2semidirect
4. #13112685C2semidirect
5. C13×#1564C2semidirect
38. #88155C8semidirect
114. #1564D13semidirect
284. C13#8604semidirect

Maximal subgroups

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

subgroupindex
C4×#881552
C2×#117180492
#131132242
#131126852
C13×#15642
#860413