Finite Group Databasebeta

← #15771185

Subgroups — #15771185

Order 3328.

798 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718121C212yesmaximal
2C2×#11718121C212yesmaximal
3C2×#11718116C211yesmaximal, characteristic
4#13113066C211yesmaximal, characteristic
5C2×C13×#382C211yesmaximal, characteristic
6C22×C13×C4⋊C4C2212yes—
7C22×C42×C13C2211yescharacteristic
8C22×C4⋊Dic13C2211yescharacteristic
9C22×C4⋊Dic13C2211yescharacteristic
10C23×#1055C2212yes—
11C13×#382—24no—
12C2×C13×#95—22no—
13C2×#88071—22no—
14#11718121—24no—
15#11718121—24no—
16#11718116C414yescomplemented
17C23×C4×C13—22no—
18C23×C4×C13D412yes—
19C23×C4×C13C2311yescharacteristic
20C23×Dic13—21no—
21C23×Dic13—21no—
22C2×C13×C4⋊C4—22no—
23C2×C13×C4⋊C4—22no—
24C2×C13×C4⋊C4—22no—
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4D414yes—
28C2×C42×C13—22no—
29C2×C42×C13—22no—
30C2×C42×C13C2×C412yes—
31C2×C42×C13Q812yes—
32C2×C4⋊Dic13—22no—
33C2×C4⋊Dic13—22no—
34C2×C4⋊Dic13—22no—
35C2×C4⋊Dic13—22no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13D412yes—
39C2×C4⋊Dic13Q812yes—
40C22×#1055—22no—
41C22×#1055—22no—
42C22×#1055—22no—
43C22×#1055—22no—
44C22×#1055—22no—
45C22×#1055—22no—
46C22×#1055C2×C414yes—
47C13×#95—28no—
48#88071—44no—
49#11268—131nomaximal, Sylow
50C24×C13C2×D411yescharacteristic
51C22×C4×C13—22no—
52C22×C4×C13—22no—
53C22×C4×C13—22no—
54C22×C4×C13—22no—
55C22×C4×C13—22no—
56C22×C4×C13—22no—
57C22×C4×C13—24no—
58C22×C4×C13—42no—
59C22×C4×C13—42no—
60C22×C4×C13—42no—
61C22×C4×C13—42no—
62C22×C4×C13—42no—
63C22×C4×C13—42no—
64C22×C4×C13C4⋊C414yes—
65C22×C4×C13C22×C411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C22×C4×C13C2×D412yes—
68C22×C4×C13C2×Q811yescharacteristic
69C22×C4×C13C2×Q811yescharacteristic
70C22×C4×C13#4112yes—
71C22×C4×C13#4112yes—
72C22×C4×C13#4111yescharacteristic
73C22×C4×C13#4112yes—
74C22×C4×C13#4111yescharacteristic
75C22×Dic13—22no—
76C22×Dic13—22no—
77C22×Dic13—41no—
78C22×Dic13—41no—
79C22×Dic13—41no—
80C22×Dic13—41no—
81C22×Dic13—42no—
82C22×Dic13—42no—
83C22×Dic13—42no—
84C22×Dic13—42no—
85C13×C4⋊C4—24no—
86C13×C4⋊C4—24no—
87C13×C4⋊C4—42no—
88C13×C4⋊C4—42no—
89C42×C13—24no—
90C42×C13—24no—
91C4⋊Dic13—24no—
92C4⋊Dic13—24no—
93C4⋊Dic13—42no—
94C4⋊Dic13—42no—
95C2×#1055—24no—
96C2×#1055—24no—
97C2×#1055—24no—
98C2×#1055—42no—
99C2×#1055—42no—
100C2×#1055—42no—
101C2×#1055—42no—
102C2×#382D1311yescharacteristic
103C2×#340—132no—
104C2×#340—132no—
105C2×#336—131no—
106C4⋊#95—131no—
107C23×C13C2×C4⋊C411yescharacteristic
108C23×C13#12011yescharacteristic
109C23×C13#12111yescharacteristic
110C23×C13C22⋊Q811yescharacteristic
111C23×C13#12311yescharacteristic
112C23×C13#12411yescharacteristic
113C23×C13#12411yescharacteristic
114C23×C13#13512yes—
115C23×C13#13512yes—
116C23×C13AGL(1,ℤ/8)12yes—
117C23×C13#13712yes—
118C2×C4×C13—24no—
119C2×C4×C13—24no—
120C2×C4×C13—24no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—44no—
126C2×C4×C13—44no—
127C2×C4×C13—44no—
128C2×C4×C13—82no—
129C2×C4×C13—82no—
130C2×C4×C13—82no—
131C2×C4×C13—82no—
132C2×C4×C13#11712yes—
133C2×C4×C13C4×D412yes—
134C2×C4×C13C4×D411yescharacteristic
135C2×C4×C13C4×Q811yescharacteristic
136C2×C4×C13#12112yes—
137C2×C4×C13C22⋊Q812yes—
138C2×C4×C13C22⋊Q812yes—
139C2×C4×C13#12312yes—
140C2×C4×C13#12312yes—
141C2×C4×C13#12412yes—
142C2×C4×C13#12512yes—
143C2×C4×C13#12512yes—
144C2×C4×C13#12511yescharacteristic
145C2×C4×C13#12612yes—
146C2×C4×C13#12612yes—
147C2×C4×C13C4⋊Q811yescharacteristic
148C2×Dic13—42no—
149C2×Dic13—42no—
150C2×Dic13—44no—
151C2×Dic13—44no—
152C2×Dic13—82no—
153C2×Dic13—82no—
154C2×Dic13—81no—
155C2×Dic13—81no—
156C2×Dic13—81no—
157C2×Dic13—81no—
158#1055—44no—
159C23×C8—132no—
160C22×C4⋊C4—131no—
161C22×C4⋊C4—131no—
162C22×C4⋊C4C2×D1312yes—
163C22×C42C2×D1311yescharacteristic
164#382—24no—
165C2×#95—22no—
166C2×#95—262no—
167#340—264no—
168#340—264no—
169#336—134no—
170C22×C13#38211yescharacteristic
171C22×C13#38511yescharacteristic
172C22×C13#38911yescharacteristic
173C22×C13#39311yescharacteristic
174C22×C13#39411yescharacteristic
175C22×C13#39711yescharacteristic
176C22×C13#40011yescharacteristic
177C22×C13#42712yes—
178C22×C13#42812yes—
179C22×C13#44912yes—
180C22×C13#45212yes—
181C22×C13#46312yes—
182C22×C13#46412yes—
183C22×C13#47812yes—
184C22×C13#47912yes—
185C22×C13#48212yes—
186C22×C13#48512yes—
187C22×C13#48812yes—
188C22×C13#48811yescharacteristic
189C22×C13#48811yescharacteristic
190C22×C13#48912yes—
191C22×C13#49011yescharacteristic
192C22×C13#49111yescharacteristic
193C4×C13—44no—
194C4×C13—84no—
195C4×C13#38712yes—
196C4×C13#38812yes—
197C4×C13#39812yes—
198C4×C13#40012yes—
199Dic13—82no—
200Dic13—82no—
201C23×C4—22no—
202C23×C4—261no—
203C23×C4—261no—
204C23×C4C22⋊D1312yes—
205C23×C4C22×D1311yescharacteristic
206C22×C8—134no—
207C22×C8—262no—
208C22×C8—262no—
209C22×C8—262no—
210C22×C8—262no—
211C22×C8—262no—
212C22×C8—262no—
213C2×C4⋊C4—22no—
214C2×C4⋊C4—22no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—22no—
217C2×C4⋊C4—22no—
218C2×C4⋊C4—132no—
219C2×C4⋊C4—132no—
220C2×C4⋊C4—262no—
221C2×C4⋊C4—262no—
222C2×C4⋊C4—262no—
223C2×C4⋊C4—262no—
224C2×C4⋊C4—261no—
225C2×C4⋊C4—261no—
226C2×C4⋊C4C22⋊D1314yes—
227C2×C42—22no—
228C2×C42—22no—
229C2×C42Dic2612yes—
230C2×C42C4×D1312yes—
231#95—28no—
232#95—524no—
233C2×C13#144211yescharacteristic
234C2×C13#183511yescharacteristic
235C2×C13#183611yescharacteristic
236C2×C13#185412yes—
237C2×C13#194912yes—
238C2×C13#202511yescharacteristic
239C2×C13#202611yescharacteristic
240C2×C13#204212yes—
241C2×C13#207311yescharacteristic
242C2×C13#207411yescharacteristic
243C2×C13#210112yes—
244C24C2×C22⋊D1311yescharacteristic
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—24no—
252C22×C4—42no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—42no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—262no—
259C22×C4—262no—
260C22×C4—521no—
261C22×C4—521no—
262C22×C4—521no—
263C22×C4—522no—
264C22×C4—522no—
265C22×C4—522no—
266C22×C4—522no—
267C22×C4—521no—
268C22×C4#610114yes—
269C22×C4C2×Dic2611yescharacteristic
270C22×C4C2×C4×D1311yescharacteristic
271C22×C4#612712yes—
272C22×C4D4×D1311yescharacteristic
273C22×C4#612911yescharacteristic
274C22×C4#612912yes—
275C22×C4Q8×D1311yescharacteristic
276C22×C4#613112yes—
277C22×C4#613111yescharacteristic
278C22×C4C2×C22⋊D1312yes—
279C2×C8—264no—
280C2×C8—264no—
281C2×C8—264no—
282C2×C8—522no—
283C2×C8—522no—
284C2×C8—522no—
285C2×C8—522no—
286C4⋊C4—24no—
287C4⋊C4—24no—
288C4⋊C4—42no—
289C4⋊C4—42no—
290C4⋊C4—264no—
291C4⋊C4—264no—
292C4⋊C4—522no—
293C4⋊C4—522no—
294C42—24no—
295C42—24no—
296C13#1126811yescharacteristic, complemented, Sylow
297C23C2×#610111yescharacteristic
298C23#8818311yescharacteristic
299C23#8819011yescharacteristic
300C23#8819211yescharacteristic
301C23#8820011yescharacteristic
302C23#8820111yescharacteristic
303C23#8820312yes—
304C23#8820412yes—
305C23#8820412yes—
306C23#8820512yes—
307C23#8820711yescharacteristic
308C2×C4—24no—
309C2×C4—24no—
310C2×C4—24no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—44no—
316C2×C4—44no—
317C2×C4—44no—
318C2×C4—82no—
319C2×C4—82no—
320C2×C4—82no—
321C2×C4—82no—
322C2×C4—524no—
323C2×C4—524no—
324C2×C4—522no—
325C2×C4—522no—
326C2×C4—1042no—
327C2×C4—1041no—
328C2×C4—1041no—
329C2×C4—1041no—
330C2×C4—1041no—
331C2×C4—1042no—
332C2×C4#8814111yescharacteristic
333C2×C4#8814211yescharacteristic
334C2×C4#8814312yes—
335C2×C4#8814412yes—
336C2×C4#8814411yescharacteristic
337C2×C4#8814612yes—
338C2×C4#8814711yescharacteristic
339C2×C4#8814812yes—
340C2×C4#8815212yes—
341C2×C4#8815212yes—
342C2×C4#8817812yes—
343C2×C4C4×C22⋊D1312yes—
344C2×C4#8818912yes—
345C2×C4#8819312yes—
346C2×C4#8820012yes—
347C2×C4#8820112yes—
348C8—524no—
349C22#1171863411yescharacteristic
350C22#1171863811yescharacteristic
351C22#1171864311yescharacteristic
352C22#1171865411yescharacteristic
353C22#1171865612yes—
354C22#1171865712yes—
355C22#1171865912yes—
356C22#1171866412yes—
357C22#1171871512yes—
358C22#1171871612yes—
359C22#1171871712yes—
360C22#1171871812yes—
361C22#1171872412yes—
362C22#1171872712yes—
363C22#1171872811yescharacteristic
364C22#1171872911yescharacteristic
365C22#1171872911yescharacteristic
366C22#1171873011yescharacteristic
367C22#1171887111yescharacteristic
368C22#1171888311yescharacteristic
369C22#1171889211yescharacteristic
370C22#1171889912yes—
371C22#1171890012yes—
372C4—44no—
373C4—84no—
374C4—1042no—
375C4—1042no—
376C4#1171863912yes—
377C4#1171864512yes—
378C4#1171864712yes—
379C4#1171865112yes—
380C2#1311309511yescharacteristic
381C2#1311496611yescharacteristic
382C2#1311496911yescharacteristic
383C2#1311503512yes—
384C2#1311560212yes—
385C2#1311597911yescharacteristic
386C2#1311598411yescharacteristic
387C2#1311607212yes—
388C2#1311625011yescharacteristic
389C2#1311625511yescharacteristic
390C2#1311640312yes—
subgroupG/H
centerC24C2×C22⋊D13
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#382C2
socle, prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenterC2×#382D13
hypocenterC13#11268
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
16. #11718116C4semidirect
296. C13#11268semidirect

Maximal subgroups

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

subgroupindex
C2×#117181212
C2×#117181162
#131130662
C2×C13×#3822
#1126813