Finite Group Databasebeta

← #16785058

Subgroups — #16785058

Order 3328.

490 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13130753C211yesmaximal, characteristic
2#13130550C211yesmaximal, characteristic
3#13129672C212yesmaximal
4#13129672C212yesmaximal
5#13117407C211yesmaximal, characteristic
6C2×#88142C411yescharacteristic
7C2×#88141—21no—
8C2×C4⋊#1057C2212yes—
9C2×C4×#1057C2212yes—
10C13×#389C411yescharacteristic
11#11718637C411yescharacteristic
12C4⋊C4×Dic13C2211yescharacteristic
13C4⋊C4×Dic13C2211yescharacteristic
14#11718633—21no—
15C42×Dic13C2211yescharacteristic
16#11718589C411yescharacteristic
17#11718310—21no—
18#11718307—21no—
19#11718290—21no—
20#11718290—21no—
21#11718290—21no—
22#11718290—21no—
23C22×Dic26—21no—
24C22×#1057—22no—
25C22×#1057—22no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C13×C4⋊C4C2×C411yescharacteristic
29C2×C42×C13C2×C411yescharacteristic
30C2×C4⋊Dic13C2×C411yescharacteristic
31C2×C4⋊Dic13C2×C411yescharacteristic
32C2×#6101—21no—
33C2×#6101—21no—
34C2×#6101—21no—
35C2×#6101—21no—
36C2×C4×Dic13—21no—
37C2×C4×Dic13—21no—
38C2×C4×Dic13C2×C411yescharacteristic
39C2×C4×Dic13D411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13C2311yescharacteristic
44#88142—22no—
45#88142C814yescomplemented
46#88141—44no—
47C4⋊#1057—24no—
48C4×#1057—22no—
49C4×#1057Q814yescomplemented
50C13×#95—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#9873—131nomaximal, Sylow
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22×C411yescharacteristic
60C22×Dic13—21no—
61C22×Dic13—21no—
62C22×Dic13C22⋊C411yescharacteristic
63C22×Dic13C22⋊C411yescharacteristic
64C22×Dic13C2×D411yescharacteristic
65C22×Dic13C2×D411yescharacteristic
66C2×Dic26—24no—
67C2×Dic26—42no—
68C2×Dic26—42no—
69C2×#1057—24no—
70C2×#1057—42no—
71C2×#1057—42no—
72C2×#1057—42no—
73C2×#1057—42no—
74C2×#1057—42no—
75C13×C4⋊C4—21no—
76C13×C4⋊C4—22no—
77C13×C4⋊C4—42no—
78C13×C4⋊C4C2×C812yes—
79C42×C13—22no—
80C4⋊Dic13—21no—
81C4⋊Dic13—22no—
82C4⋊Dic13C2×C812yes—
83#6101—24no—
84#6101—42no—
85#6101—42no—
86#6101—42no—
87C4×Dic13—22no—
88C4×Dic13—22no—
89C4×Dic13—41no—
90C4×Dic13—41no—
91C4×Dic13—42no—
92C4×Dic13—42no—
93C4×Dic13C2×C812yes—
94C4×Dic13M1612yes—
95C4×Dic13C2×Q812yes—
96C4×Dic13#4112yes—
97C4×C4⋊Q8—131no—
98#1831—131no—
99#1744—131no—
100#1279—132no—
101#1279—132no—
102C23×C13C2×C22⋊C411yescharacteristic
103C2×C4×C13—22no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—41no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13C4×Q812yes—
116C2×C4×C13C22×C811yescharacteristic
117C2×C4×C13C2×M1611yescharacteristic
118C2×C4×C13#13112yes—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—22no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13C22⋊C812yes—
132C2×Dic13C22⋊C812yes—
133C2×Dic13C22⋊Q812yes—
134C2×Dic13#12411yescharacteristic
135C2×Dic13C4⋊Q811yescharacteristic
136C2×Dic13AGL(1,ℤ/8)12yes—
137C2×Dic13#13712yes—
138Dic26—48no—
139#1057—44no—
140#1057—82no—
141C2×C4⋊Q8—131no—
142C2×C4×Q8—261no—
143C2×C4⋊C8—132no—
144C2×C4×C8—132no—
145#391—261no—
146#389—131no—
147#389—261no—
148#389#26111yescharacteristic
149#384—131no—
150C4×C4⋊C4—131no—
151C4×C4⋊C4—131no—
152C4×C4⋊C4—261no—
153C43—131no—
154#336—261no—
155#336—261no—
156#336—261no—
157#336—261no—
158C22×C13#39111yescharacteristic
159C22×C13C2×C22⋊C811yescharacteristic
160C22×C13#40811yescharacteristic
161C22×C13#41811yescharacteristic
162C22×C13#41911yescharacteristic
163C22×C13#42111yescharacteristic
164C22×C13#42111yescharacteristic
165C4×C13—42no—
166C4×C13—41no—
167C4×C13—41no—
168C4×C13—81no—
169C4×C13C8×Q812yes—
170C4×C13#44612yes—
171Dic13—22no—
172Dic13—22no—
173Dic13—22no—
174Dic13—42no—
175Dic13—81no—
176Dic13#48912yes—
177Dic13#50112yes—
178C22×Q8—261no—
179C22×C8—262no—
180C22×C8—262no—
181C4⋊Q8—134no—
182C4⋊Q8—262no—
183C4×Q8—524no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—131no—
186C2×C4⋊C4—131no—
187C2×C4⋊C4—261no—
188C2×C4⋊C4—261no—
189C2×C4⋊C4—261no—
190C2×C4⋊C4—261no—
191C2×C4⋊C4C2×#26111yescharacteristic
192C2×C4⋊C4C2×#26111yescharacteristic
193C2×C42—131no—
194C2×C42—131no—
195C2×C42—131no—
196C2×C42—131no—
197C2×C42—131no—
198C2×C42—131no—
199C2×C42—261no—
200C2×C42—261no—
201C2×C42C2×#26111yescharacteristic
202C4⋊C8—264no—
203C4×C8—134no—
204C4×C8—262no—
205#95—21no—
206#95—261no—
207#95—261no—
208#95—261no—
209C2×C13#147811yescharacteristic
210C2×C13#147911yescharacteristic
211C2×C13#149611yescharacteristic
212C2×C13#149711yescharacteristic
213C2×C13#198411yescharacteristic
214C2×C13#199311yescharacteristic
215C2×C13#199511yescharacteristic
216C2×Q8—264no—
217C2×Q8—522no—
218C2×Q8—522no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—131no—
222C22×C4—131no—
223C22×C4—131no—
224C22×C4—131no—
225C22×C4—261no—
226C22×C4—261no—
227C22×C4C22⋊#26111yescharacteristic
228C22×C4C22⋊#26111yescharacteristic
229C22×C4C22×#26111yescharacteristic
230C2×C8—264no—
231C2×C8—522no—
232C2×C8—522no—
233C2×C8—522no—
234C2×C8—522no—
235C2×C8—522no—
236C4⋊C4—21no—
237C4⋊C4—22no—
238C4⋊C4—42no—
239C4⋊C4—132no—
240C4⋊C4—264no—
241C4⋊C4—261no—
242C4⋊C4—262no—
243C4⋊C4—522no—
244C4⋊C4—522no—
245C4⋊C4—522no—
246C4⋊C4D13⋊C812yes—
247C42—22no—
248C42—132no—
249C42—132no—
250C42—132no—
251C42—132no—
252C42—262no—
253C42—262no—
254C42—521no—
255C42—521no—
256C42—522no—
257C42—522no—
258C13#987311yescharacteristic, complemented, Sylow
259C23C2×C22⋊#26111yescharacteristic
260Q8—528no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—132no—
274C2×C4—132no—
275C2×C4—131no—
276C2×C4—131no—
277C2×C4—132no—
278C2×C4—132no—
279C2×C4—132no—
280C2×C4—261no—
281C2×C4—261no—
282C2×C4—261no—
283C2×C4—261no—
284C2×C4—261no—
285C2×C4—261no—
286C2×C4—262no—
287C2×C4—521no—
288C2×C4—521no—
289C2×C4—521no—
290C2×C4—521no—
291C2×C4—521no—
292C2×C4C2×D13⋊C811yescharacteristic
293C2×C4D13⋊M1611yescharacteristic
294C2×C4#8823812yes—
295C2×C4Q8×#26112yes—
296C8—524no—
297C8—1042no—
298C22D13⋊(C22⋊C8)11yescharacteristic
299C22#1171913811yescharacteristic
300C22#1171914611yescharacteristic
301C22#1171915311yescharacteristic
302C22(C2×#261)⋊Q811yescharacteristic
303C22#1171916611yescharacteristic
304C22#1171916611yescharacteristic
305C4—42no—
306C4—41no—
307C4—41no—
308C4—81no—
309C4—132no—
310C4—132no—
311C4—262no—
312C4—262no—
313C4—262no—
314C4—522no—
315C4—1041no—
316C4#1171907412yes—
317C4#1171907812yes—
318C2#1313013611yescharacteristic
319C2#1313013911yescharacteristic
320C2#1313019511yescharacteristic
321C2#1313019811yescharacteristic
322C2#1313100711yescharacteristic
323C2#1313102011yescharacteristic
324C2#1313102311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC13×#389C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#389#261
hypocenterC13#9873
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
45. #88142C8semidirect
49. C4×#1057Q8semidirect
258. C13#9873semidirect

Maximal subgroups

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

subgroupindex
#131307532
#131305502
#131296722
#131174072
#987313