Finite Group Databasebeta

← #16782139

Subgroups — #16782139

Order 3328.

592 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13130690C211yesmaximal, characteristic
2C4×C22⋊#1057C211yesmaximal, characteristic
3#13129672C212yesmaximal, complemented
4#13129672C212yesmaximal, complemented
5#117×Dic13C211yesmaximal, characteristic
6C2×C13×#117C411yescharacteristic
7C2×#88180C411yescharacteristic
8C22×C4×Dic13C2211yescharacteristic
9C2×C22⋊#1057—21no—
10C2×C22⋊#1057—21no—
11C2×C4⋊#1057C2212yes—
12C2×C4×#1057C2212yes—
13C4⋊C4×Dic13C411yescharacteristic
14C4⋊C4×Dic13C411yescharacteristic
15C4⋊C4×Dic13C2211yescharacteristic
16C4⋊C4×Dic13C2211yescharacteristic
17C22⋊C4×Dic13—21no—
18C22⋊C4×Dic13—21no—
19#11718593—21no—
20C42×Dic13—21no—
21#11718290—21no—
22#11718290—21no—
23C23×C4×C13C2×C411yescharacteristic
24C23×Dic13D411yescharacteristic
25C23×Dic13D411yescharacteristic
26C22×#1057—22no—
27C22×#1057—22no—
28C13×#117—22no—
29C13×#117C814yescomplemented
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C22⋊C4—21no—
33C2×C42×C13—21no—
34C2×C22⋊Dic13—21no—
35#88180—22no—
36#88180—22no—
37C2×C4⋊Dic13C2×C411yescharacteristic
38C2×C4⋊Dic13C2×C411yescharacteristic
39C2×C4×Dic13—21no—
40C2×C4×Dic13—22no—
41C2×C4×Dic13—22no—
42C2×C4×Dic13—21no—
43C2×C4×Dic13—21no—
44C2×C4×Dic13—21no—
45C2×C4×Dic13—21no—
46C2×C4×Dic13C2×C411yescharacteristic
47C2×C4×Dic13D411yescharacteristic
48C2×C4×Dic13D411yescharacteristic
49C2×C4×Dic13C2311yescharacteristic
50C22⋊#1057—24no—
51C22⋊#1057—42no—
52C4⋊#1057—22no—
53C4⋊#1057—22no—
54C4×#1057—22no—
55C4×#1057—22no—
56#88071—21no—
57#88071—21no—
58#88071—21no—
59#88071—21no—
60#8708—131nomaximal, Sylow
61C24×C13C22⋊C411yescharacteristic
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C2×C812yes—
70C22×C4×C13M1612yes—
71C22×C4×C13C22×C411yescharacteristic
72C22×Dic13—21no—
73C22×Dic13—21no—
74C22×Dic13—22no—
75C22×Dic13—22no—
76C22×Dic13—22no—
77C22×Dic13—22no—
78C22×Dic13—21no—
79C22×Dic13—21no—
80C22×Dic13—41no—
81C22×Dic13C22⋊C411yescharacteristic
82C22×Dic13C22⋊C411yescharacteristic
83C22×Dic13C2×D411yescharacteristic
84C22×Dic13C2×D411yescharacteristic
85C2×#1057—24no—
86C2×#1057—42no—
87C2×#1057—42no—
88C2×#1057—42no—
89C2×#1057—42no—
90C2×#1057—42no—
91C13×C4⋊C4—21no—
92C13×C4⋊C4—21no—
93C13×C4⋊C4C2×C812yes—
94C13×C4⋊C4C2×C812yes—
95C13×C22⋊C4—24no—
96C42×C13—24no—
97C22⋊Dic13—24no—
98C4⋊Dic13—21no—
99C4⋊Dic13—21no—
100C4⋊Dic13M1612yes—
101C4⋊Dic13M1612yes—
102C4×Dic13—24no—
103C4×Dic13—21no—
104C4×Dic13—21no—
105C4×Dic13—22no—
106C4×Dic13—22no—
107C4×Dic13—42no—
108C4×Dic13—42no—
109C4×Dic13—42no—
110C4×Dic13—41no—
111C4×Dic13—41no—
112C4×Dic13#4112yes—
113C4×Dic13#4112yes—
114C4×#117—131no—
115#1797—131no—
116C4×C22⋊C8—131no—
117#1279—132no—
118#1279—132no—
119C23×C13—21no—
120C23×C13—21no—
121C23×C13—21no—
122C23×C13—21no—
123C23×C13—21no—
124C23×C13—21no—
125C23×C13C22⋊C812yes—
126C23×C13C2×C22⋊C411yescharacteristic
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—22no—
130C2×C4×C13—22no—
131C2×C4×C13—22no—
132C2×C4×C13—22no—
133C2×C4×C13—22no—
134C2×C4×C13—22no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13C22⋊C812yes—
140C2×C4×C13#11711yescharacteristic
141C2×C4×C13#11711yescharacteristic
142C2×C4×C13C22×C811yescharacteristic
143C2×C4×C13C2×M1611yescharacteristic
144C2×C4×C13C2×M1611yescharacteristic
145C2×C4×C13C2×M1611yescharacteristic
146C2×Dic13—21no—
147C2×Dic13—21no—
148C2×Dic13—21no—
149C2×Dic13—21no—
150C2×Dic13—21no—
151C2×Dic13—22no—
152C2×Dic13—22no—
153C2×Dic13—21no—
154C2×Dic13—21no—
155C2×Dic13—44no—
156C2×Dic13—41no—
157C2×Dic13—41no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160C2×Dic13—42no—
161C2×Dic13—42no—
162C2×Dic13#10412yes—
163C2×Dic13#12312yes—
164C2×Dic13#12312yes—
165C2×Dic13#13512yes—
166C2×Dic13AGL(1,ℤ/8)11yescharacteristic
167C2×Dic13#13711yescharacteristic
168#1057—44no—
169#1057—82no—
170C2×#117—131no—
171C2×#117#26111yescharacteristic
172C22×C42—131no—
173C2×C4⋊C8—132no—
174C2×C22⋊C8—261no—
175C2×C22⋊C8—261no—
176C2×C4×C8—132no—
177C4×C4⋊C4—131no—
178C4×C4⋊C4—131no—
179C4×C4⋊C4—131no—
180C4×C4⋊C4—131no—
181C4×C22⋊C4—261no—
182C4×C22⋊C4—261no—
183#376—261no—
184C43—261no—
185#336—261no—
186#336—261no—
187C22×C13—22no—
188C22×C13—22no—
189C22×C13—22no—
190C22×C13—41no—
191C22×C13—41no—
192C22×C13—41no—
193C22×C13—41no—
194C22×C13#38111yescharacteristic
195C22×C13C2×C22⋊C811yescharacteristic
196C22×C13#40711yescharacteristic
197C22×C13#41611yescharacteristic
198C22×C13#41711yescharacteristic
199C22×C13C2×#10411yescharacteristic
200C22×C13#42111yescharacteristic
201C4×C13—22no—
202C4×C13—42no—
203C4×C13—42no—
204C4×C13#43111yescharacteristic
205C4×C13#43111yescharacteristic
206C4×C13#43211yescharacteristic
207C4×C13#43211yescharacteristic
208Dic13—22no—
209Dic13—22no—
210Dic13—41no—
211Dic13—42no—
212Dic13—42no—
213Dic13#48212yes—
214Dic13#48512yes—
215C23×C4—131no—
216C23×C4—131no—
217C23×C4C2×#26111yescharacteristic
218C22×C8—262no—
219C22×C8—262no—
220#117—22no—
221#117—262no—
222#117—262no—
223#117#105714yescomplemented
224C2×C4⋊C4—131no—
225C2×C4⋊C4—131no—
226C2×C4⋊C4C2×#26111yescharacteristic
227C2×C4⋊C4C2×#26111yescharacteristic
228C2×C22⋊C4—21no—
229C2×C22⋊C4—261no—
230C2×C42—21no—
231C2×C42—131no—
232C2×C42—131no—
233C2×C42—131no—
234C2×C42—131no—
235C2×C42—262no—
236C2×C42—262no—
237C2×C42—261no—
238C2×C42—261no—
239C2×C42—261no—
240C2×C42—261no—
241C2×C42—261no—
242C4⋊C8—262no—
243C4⋊C8—262no—
244C22⋊C8—264no—
245C22⋊C8—522no—
246C4×C8—262no—
247C4×C8—262no—
248#95—261no—
249#95—261no—
250#95—261no—
251#95—261no—
252C2×C13—42no—
253C2×C13#147611yescharacteristic
254C2×C13#147711yescharacteristic
255C2×C13#148811yescharacteristic
256C2×C13#148911yescharacteristic
257C2×C13#181711yescharacteristic
258C2×C13#182511yescharacteristic
259C2×C13#182611yescharacteristic
260C24C22⋊#26111yescharacteristic
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—131no—
268C22×C4—131no—
269C22×C4—131no—
270C22×C4—131no—
271C22×C4—262no—
272C22×C4—261no—
273C22×C4—262no—
274C22×C4—262no—
275C22×C4—261no—
276C22×C4—262no—
277C22×C4—261no—
278C22×C4—261no—
279C22×C4—521no—
280C22×C4C2×#105712yes—
281C22×C4#612212yes—
282C22×C4C22⋊#26111yescharacteristic
283C22×C4C22×#26111yescharacteristic
284C2×C8—264no—
285C2×C8—522no—
286C2×C8—522no—
287C2×C8—522no—
288C2×C8—522no—
289C2×C8—522no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—132no—
293C4⋊C4—132no—
294C4⋊C4—261no—
295C4⋊C4—261no—
296C4⋊C4C2×#105712yes—
297C4⋊C4C2×#105712yes—
298C22⋊C4—24no—
299C22⋊C4—264no—
300C42—24no—
301C42—132no—
302C42—132no—
303C42—262no—
304C42—262no—
305C42—264no—
306C42—261no—
307C42—261no—
308C42—522no—
309C42—521no—
310C42—521no—
311C42—522no—
312C42—522no—
313C13#870811yescharacteristic, complemented, Sylow
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23C22⋊#105712yes—
321C23C2×C22⋊#26111yescharacteristic
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—132no—
335C2×C4—131no—
336C2×C4—131no—
337C2×C4—132no—
338C2×C4—132no—
339C2×C4—132no—
340C2×C4—261no—
341C2×C4—261no—
342C2×C4—261no—
343C2×C4—261no—
344C2×C4—262no—
345C2×C4—262no—
346C2×C4—261no—
347C2×C4—261no—
348C2×C4—261no—
349C2×C4—522no—
350C2×C4—522no—
351C2×C4—524no—
352C2×C4—521no—
353C2×C4—521no—
354C2×C4—521no—
355C2×C4—521no—
356C2×C4C22⋊#105712yes—
357C2×C4D13⋊M1611yescharacteristic
358C2×C4D13⋊M1611yescharacteristic
359C2×C4#8823711yescharacteristic
360C2×C4#8823711yescharacteristic
361C2×C4C22×#105711yescharacteristic
362C2×C4C2×#612211yescharacteristic
363C8—524no—
364C8—1042no—
365C22—22no—
366C22—22no—
367C22—22no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22#1171912611yescharacteristic
373C22#1171913511yescharacteristic
374C22D13⋊#10411yescharacteristic
375C22#1171916411yescharacteristic
376C22#1171916511yescharacteristic
377C22#1171916611yescharacteristic
378C22C2×C22⋊#105711yescharacteristic
379C4—22no—
380C4—42no—
381C4—42no—
382C4—132no—
383C4—132no—
384C4—262no—
385C4—262no—
386C4—522no—
387C4—522no—
388C4—521no—
389C4#1171911911yescharacteristic
390C4#1171911911yescharacteristic
391C4#1171912811yescharacteristic
392C4#1171912811yescharacteristic
393C2—42no—
394C2#1313012711yescharacteristic
395C2#1313013111yescharacteristic
396C2#1313016911yescharacteristic
397C2#1313017311yescharacteristic
398C2#1313072611yescharacteristic
399C2#1313074111yescharacteristic
400C2#1313074411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC2×C13×#117C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×#117#261
hypocenterC13#8708
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
3. #13129672C2semidirect
4. #13129672C2semidirect
29. C13×#117C8semidirect
223. #117#1057semidirect
313. C13#8708semidirect

Maximal subgroups

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

subgroupindex
#131306902
C4×C22⋊#10572
#131296722
#117×Dic132
#870813