Finite Group Databasebeta

← #15769199

Subgroups — #15769199

Order 3328.

1078 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88050C212yesmaximal
2C22×#88043C211yesmaximal, characteristic
3C2×#11718590C211yesmaximal, characteristic
4C2×#11718121C212yesmaximal
5C13×C4⋊#95C211yesmaximal, characteristic
6C23×Dic26C2211yescharacteristic
7C22×C13×C4⋊C4C2212yes—
8C22×C42×C13C2211yescharacteristic
9C22×C4⋊Dic13C2211yescharacteristic
10C23×#1055C2212yes—
11C2×C13×#95—22no—
12C2×#88071—22no—
13C2×#88050—24no—
14C2×#88050—24no—
15C2×#88050C418yescomplemented
16#11718590—22no—
17#11718590C414yescomplemented
18C2×#88043—22no—
19C2×#88043—24no—
20#11718121—24no—
21C23×C4×C13—22no—
22C23×C4×C13D412yes—
23C23×C4×C13C2311yescharacteristic
24C23×Dic13—21no—
25C23×Dic13—21no—
26C22×Dic26—22no—
27C22×Dic26—22no—
28C22×Dic26—22no—
29C22×Dic26—22no—
30C22×Dic26—21no—
31C22×Dic26—22no—
32C22×Dic26C2×C412yes—
33C22×Dic26C2×C414yes—
34C2×C13×C4⋊C4—22no—
35C2×C13×C4⋊C4—22no—
36C2×C13×C4⋊C4—22no—
37C2×C13×C4⋊C4—22no—
38C2×C13×C4⋊C4—22no—
39C2×C13×C4⋊C4C2×C414yes—
40C2×C42×C13—22no—
41C2×C42×C13—22no—
42C2×C42×C13C2×C412yes—
43C2×C42×C13D412yes—
44C2×C4⋊Dic13—22no—
45C2×C4⋊Dic13—22no—
46C2×C4⋊Dic13—21no—
47C2×C4⋊Dic13C2×C412yes—
48C22×#1055—22no—
49C22×#1055—22no—
50C22×#1055—22no—
51C22×#1055—22no—
52C22×#1055C2×C414yes—
53C22×#1055D414yes—
54C22×#1055D414yes—
55C13×#95—44no—
56#88071—28no—
57#88050—216no—
58#88043—28no—
59#10928—131nomaximal, Sylow
60C24×C13C2×D411yescharacteristic
61C22×C4×C13—24no—
62C22×C4×C13—22no—
63C22×C4×C13—22no—
64C22×C4×C13—24no—
65C22×C4×C13—24no—
66C22×C4×C13—42no—
67C22×C4×C13—42no—
68C22×C4×C13—44no—
69C22×C4×C13—44no—
70C22×C4×C13C22⋊C414yes—
71C22×C4×C13C22×C412yes—
72C22×C4×C13C22×C411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13C2×D412yes—
75C22×C4×C13C2×D412yes—
76C22×C4×C13#4112yes—
77C22×C4×C13#4112yes—
78C22×C4×C13#4112yes—
79C22×Dic13—22no—
80C22×Dic13—24no—
81C22×Dic13—22no—
82C22×Dic13—42no—
83C22×Dic13—41no—
84C22×Dic13—41no—
85C22×Dic13—41no—
86C22×Dic13—41no—
87C22×Dic13—42no—
88C22×Dic13—42no—
89C2×Dic26—24no—
90C2×Dic26—24no—
91C2×Dic26—24no—
92C2×Dic26—24no—
93C2×Dic26—24no—
94C2×Dic26—24no—
95C2×Dic26—22no—
96C2×Dic26—24no—
97C2×Dic26—41no—
98C2×Dic26—42no—
99C2×Dic26—42no—
100C2×Dic26—42no—
101C2×Dic26—41no—
102C2×Dic26—42no—
103C2×Dic26—42no—
104C2×Dic26C4214yes—
105C13×C4⋊C4—24no—
106C13×C4⋊C4—24no—
107C13×C4⋊C4—42no—
108C13×C4⋊C4—42no—
109C42×C13—24no—
110C42×C13—22no—
111C42×C13—22no—
112C4⋊Dic13—24no—
113C4⋊Dic13—42no—
114C2×#1055—24no—
115C2×#1055—24no—
116C2×#1055—24no—
117C2×#1055—24no—
118C2×#1055—24no—
119C2×#1055—24no—
120C2×#1055C22⋊C418yes—
121C22×#103—132no—
122C22×#97—131no—
123C2×#391—131no—
124C2×#340—132no—
125C4⋊#95D1311yescharacteristic
126C23×C13C2×C22⋊C411yescharacteristic
127C23×C13C4×D412yes—
128C23×C13#12112yes—
129C23×C13#12411yescharacteristic
130C23×C13#12711yescharacteristic
131C23×C13AGL(1,ℤ/8)12yes—
132C23×C13#13712yes—
133C23×C13#13714yes—
134C2×C4×C13—24no—
135C2×C4×C13—24no—
136C2×C4×C13—24no—
137C2×C4×C13—44no—
138C2×C4×C13—44no—
139C2×C4×C13—44no—
140C2×C4×C13—48no—
141C2×C4×C13—84no—
142C2×C4×C13—82no—
143C2×C4×C13—82no—
144C2×C4×C13C2×C4211yescharacteristic
145C2×C4×C13C2×C22⋊C412yes—
146C2×C4×C13#11712yes—
147C2×C4×C13#11711yescharacteristic
148C2×C4×C13C4×D412yes—
149C2×C4×C13C4×D412yes—
150C2×C4×C13C4×D412yes—
151C2×C4×C13C4×D412yes—
152C2×C4×C13C4×D412yes—
153C2×C4×C13#12011yescharacteristic
154C2×C4×C13#12112yes—
155C2×C4×C13#12112yes—
156C2×C4×C13#12312yes—
157C2×C4×C13#12311yescharacteristic
158C2×C4×C13#12412yes—
159C2×C4×C13#12612yes—
160C2×Dic13—24no—
161C2×Dic13—42no—
162C2×Dic13—44no—
163C2×Dic13—44no—
164C2×Dic13—42no—
165C2×Dic13—42no—
166C2×Dic13—44no—
167C2×Dic13—82no—
168C2×Dic13—81no—
169C2×Dic13—81no—
170Dic26—28no—
171Dic26—44no—
172Dic26—44no—
173Dic26—44no—
174#1055—28no—
175C23×Q8—131no—
176C23×C8—132no—
177C22×C4⋊C4—131no—
178C22×C4⋊C4C2×D1312yes—
179C22×C42C2×D1311yescharacteristic
180C2×#103—138no—
181C2×#103—264no—
182C2×#103—264no—
183C2×#97—264no—
184C2×#97—262no—
185#391—134no—
186#391—262no—
187C2×#95—22no—
188C2×#95—262no—
189#340—264no—
190C22×C13C4×C22⋊C411yescharacteristic
191C22×C13#38611yescharacteristic
192C22×C13#38812yes—
193C22×C13#39012yes—
194C22×C13#39011yescharacteristic
195C22×C13#41712yes—
196C22×C13#41912yes—
197C22×C13#44014yes—
198C22×C13#44114yes—
199C22×C13#46814yes—
200C22×C13#47014yes—
201C22×C13#48912yes—
202C22×C13#49112yes—
203C22×C13#49611yescharacteristic
204C22×C13#49712yes—
205C22×C13#49711yescharacteristic
206C4×C13—44no—
207C4×C13—84no—
208C4×C13C4×C22⋊C412yes—
209C4×C13#38612yes—
210C4×C13#38812yes—
211C4×C13#38812yes—
212Dic13—44no—
213Dic13—82no—
214C22×Q8—132no—
215C22×Q8—134no—
216C22×Q8—261no—
217C22×Q8—262no—
218C22×Q8—262no—
219C22×Q8—262no—
220C22×Q8—262no—
221C22×Q8—262no—
222C23×C4—22no—
223C23×C4—261no—
224C23×C4—261no—
225C23×C4C22⋊D1312yes—
226C23×C4C22×D1311yescharacteristic
227C22×C8—134no—
228C22×C8—134no—
229C22×C8—134no—
230C22×C8—262no—
231C22×C8—262no—
232C22×C8—262no—
233C22×C8—262no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—132no—
240C2×C4⋊C4—262no—
241C2×C4⋊C4—262no—
242C2×C4⋊C4—261no—
243C2×C4⋊C4C4×D1314yes—
244C2×C42—22no—
245C2×C42—22no—
246C2×C42C4×D1312yes—
247C2×C42D5212yes—
248#103—2616no—
249#97—268no—
250#95—44no—
251#95—268no—
252C2×C13#143711yescharacteristic
253C2×C13#176312yes—
254C2×C13#189412yes—
255C2×C13#193514yes—
256C2×C13#195911yescharacteristic
257C2×C13#196011yescharacteristic
258C2×C13#197112yes—
259C2×C13#197312yes—
260C24C2×C22⋊D1311yescharacteristic
261C2×Q8—134no—
262C2×Q8—262no—
263C2×Q8—264no—
264C2×Q8—264no—
265C2×Q8—264no—
266C2×Q8—264no—
267C2×Q8—264no—
268C2×Q8—264no—
269C2×Q8—264no—
270C2×Q8—521no—
271C2×Q8—522no—
272C2×Q8—522no—
273C2×Q8—521no—
274C2×Q8—522no—
275C2×Q8—522no—
276C2×Q8—522no—
277C22×C4—22no—
278C22×C4—24no—
279C22×C4—22no—
280C22×C4—24no—
281C22×C4—24no—
282C22×C4—44no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—44no—
286C22×C4—262no—
287C22×C4—264no—
288C22×C4—262no—
289C22×C4—522no—
290C22×C4—521no—
291C22×C4—521no—
292C22×C4—522no—
293C22×C4—521no—
294C22×C4—522no—
295C22×C4—521no—
296C22×C4#610314yes—
297C22×C4C2×C4×D1311yescharacteristic
298C22×C4C2×C4×D1312yes—
299C22×C4C2×D5211yescharacteristic
300C22×C4#612712yes—
301C22×C4D4×D1312yes—
302C22×C4D4×D1312yes—
303C22×C4#612912yes—
304C22×C4#613112yes—
305C2×C8—138no—
306C2×C8—264no—
307C2×C8—264no—
308C2×C8—264no—
309C2×C8—264no—
310C2×C8—264no—
311C2×C8—264no—
312C4⋊C4—24no—
313C4⋊C4—24no—
314C4⋊C4—42no—
315C4⋊C4—42no—
316C4⋊C4—264no—
317C4⋊C4—522no—
318C42—24no—
319C42—22no—
320C42—22no—
321C13#1092811yescharacteristic, complemented, Sylow
322C23C2×#610311yescharacteristic
323C23C4×C22⋊D1312yes—
324C23#8818612yes—
325C23#8819312yes—
326C23#8819411yescharacteristic
327C23#8819612yes—
328C23#8820111yescharacteristic
329C23#8820514yes—
330Q8—268no—
331Q8—524no—
332Q8—524no—
333Q8—524no—
334C2×C4—24no—
335C2×C4—24no—
336C2×C4—24no—
337C2×C4—44no—
338C2×C4—44no—
339C2×C4—48no—
340C2×C4—44no—
341C2×C4—84no—
342C2×C4—82no—
343C2×C4—82no—
344C2×C4—264no—
345C2×C4—524no—
346C2×C4—522no—
347C2×C4—522no—
348C2×C4—524no—
349C2×C4—524no—
350C2×C4—522no—
351C2×C4—1041no—
352C2×C4—1041no—
353C2×C4—1042no—
354C2×C4C42×D1311yescharacteristic
355C2×C4#8812611yescharacteristic
356C2×C4C4×D5212yes—
357C2×C4C22⋊C4×D1312yes—
358C2×C4#8813512yes—
359C2×C4#8813512yes—
360C2×C4#8813611yescharacteristic
361C2×C4#8813812yes—
362C2×C4#8813912yes—
363C2×C4#8814011yescharacteristic
364C2×C4#8814612yes—
365C2×C4#8814712yes—
366C2×C4#8814712yes—
367C2×C4#8814812yes—
368C2×C4#8814912yes—
369C2×C4#8815212yes—
370C8—268no—
371C22C4×#610311yescharacteristic
372C22#1171861812yes—
373C22#1171861911yescharacteristic
374C22#1171862712yes—
375C22#1171864911yescharacteristic
376C22#1171865112yes—
377C22#1171866512yes—
378C22#1171867914yes—
379C22#1171869114yes—
380C22#1171870314yes—
381C22#1171871314yes—
382C22#1171872112yes—
383C22#1171873012yes—
384C22#1171873511yescharacteristic
385C22#1171874711yescharacteristic
386C22#1171875012yes—
387C4—44no—
388C4—84no—
389C4—524no—
390C4—1042no—
391C4#1171832612yes—
392C4#1171832712yes—
393C4#1171833012yes—
394C4#1171833112yes—
395C2#1311307211yescharacteristic
396C2#1311466912yes—
397C2#1311526712yes—
398C2#1311552514yes—
399C2#1311565011yescharacteristic
400C2#1311565511yescharacteristic
401C2#1311570612yes—
402C2#1311571612yes—
subgroupG/H
centerC24C2×C22⋊D13
commutatorC2×C4×C13C2×C42
FrattiniC23×C4C22×D13
FittingC13×C4⋊#95C2
socle, prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenterC4⋊#95D13
hypocenterC13#10928
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C42 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
15. C2×#88050C4semidirect
17. #11718590C4semidirect
321. C13#10928semidirect

Maximal subgroups

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

subgroupindex
C22×#880502
C22×#880432
C2×#117185902
C2×#117181212
C13×C4⋊#952
#1092813