Finite Group Databasebeta

← #15761836

Subgroups — #15761836

Order 3328.

478 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#6095C211yesmaximal, characteristic
2#13113232C211yesmaximal, characteristic, complemented
3#13113228C211yesmaximal, characteristic
4#13113159C211yesmaximal, characteristic, complemented
5#13113156C211yesmaximal, characteristic
6#13113119C211yesmaximal, characteristic, complemented
7C13×#1564C211yesmaximal, characteristic, complemented
8C22×#6095C411yescharacteristic
9C2×C4×D52C2211yescharacteristic
10C2×C4×Dic26C2211yescharacteristic
11C13×#431C2211yescharacteristic
12C13×#431C2211yescharacteristic
13C2×C4×C8×C13C2211yescharacteristic
14C2×#88061C411yescharacteristic
15C2×#88057C411yescharacteristic
16C2×#88056C411yescharacteristic
17#11718586C2211yescharacteristic
18#11718586C2211yescharacteristic
19C4×#6095—21no—
20C4×#6095—21no—
21C4×#6095—21no—
22C4×#6095—21no—
23C13×#335—21no—
24C13×#334—21no—
25#11718061—22no—
26#11718060—22no—
27#11718051—22no—
28#11718048—22no—
29#11718047—21no—
30C8×#1055—21no—
31C22×D52C2×C411yescharacteristic
32C22×C4×D13—21no—
33C22×Dic26C2×C411yescharacteristic
34C22×C8×C13C2×C411yescharacteristic
35C22×C8×C13C2×C411yescharacteristic
36C2×C42×C13C2311yescharacteristic
37C2×#6103—21no—
38C2×C4⋊Dic13C2×C411yescharacteristic
39C2×C4⋊Dic13C2×C411yescharacteristic
40C2×#6101—21no—
41C2×C4×Dic13—21no—
42C2×#6095—21no—
43C2×#6095—21no—
44C2×#6095—22no—
45C2×#6095C814yescomplemented
46C4×D52—21no—
47C4×D52—21no—
48C4×D52—21no—
49C4×D52—21no—
50C4×Dic26—21no—
51C4×Dic26—21no—
52C4×Dic26—21no—
53C4×Dic26—21no—
54C13×C4⋊C8—21no—
55C13×C4⋊C8—21no—
56C13×C22⋊C8—21no—
57C13×C22⋊C8—21no—
58C4×C8×C13—21no—
59C4×C8×C13—21no—
60C4×C8×C13D411yescharacteristic
61C4×C8×C13D411yescharacteristic
62C4×C8×C13D411yescharacteristic
63C4×C8×C13D411yescharacteristic
64C22⋊#1055—21no—
65C22⋊#1055D412yes—
66#88061—21no—
67#88061—21no—
68#88057—21no—
69#88057—21no—
70#88056—21no—
71#88056—21no—
72C4⋊#1055—21no—
73C4⋊#1055D412yes—
74C4×#1055—21no—
75C4×#1055—21no—
76#9667—131nomaximal, Sylow
77C23×D13—21no—
78C22×C4×C13C22×C411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13#4111yescharacteristic
81C22×Dic13—21no—
82C22×Dic13—21no—
83C22×Dic13—21no—
84C2×D52—21no—
85C2×D52—21no—
86C2×D52—21no—
87C2×D52—21no—
88C2×D52—21no—
89C2×D52C2×C812yes—
90C2×C4×D13—41no—
91C2×C4×D13—41no—
92C2×C4×D13—82no—
93C2×Dic26—21no—
94C2×Dic26—21no—
95C2×Dic26—21no—
96C2×Dic26—21no—
97C2×Dic26—21no—
98C2×Dic26C2×C812yes—
99C2×C8×C13—21no—
100C2×C8×C13—21no—
101C2×C8×C13—41no—
102C2×C8×C13—41no—
103C2×C8×C13C22⋊C411yescharacteristic
104C2×C8×C13C22⋊C411yescharacteristic
105C2×C8×C13C22⋊C411yescharacteristic
106C2×C8×C13C22⋊C411yescharacteristic
107C2×C8×C13C2×C812yes—
108C2×C8×C13M1612yes—
109C42×C13C2×D411yescharacteristic
110C42×C13C2×D411yescharacteristic
111C42×C13C2×D411yescharacteristic
112C42×C13#4111yescharacteristic
113#6103—41no—
114#6103—41no—
115C4⋊Dic13—21no—
116C4⋊Dic13—21no—
117C4⋊Dic13—21no—
118C4⋊Dic13—21no—
119#6101—41no—
120#6101—41no—
121C4×Dic13—41no—
122C4×Dic13—41no—
123C2×#1055—22no—
124C2×#1055—22no—
125#6095—24no—
126#6095—24no—
127C2×C4×SD16—131no—
128#1564D1311yescharacteristic, complemented
129#1479—131no—
130#1478—131no—
131#1461—131no—
132#1460—131no—
133#1450—131no—
134C23×C13C4×D411yescharacteristic
135C22×D13—22no—
136C22×D13—41no—
137C22×D13—41no—
138C22×D13—81no—
139C22×D13—81no—
140C2×C4×C13—22no—
141C2×C4×C13—41no—
142C2×C4×C13C2×C22⋊C411yescharacteristic
143C2×C4×C13C4×D411yescharacteristic
144C2×C4×C13#12111yescharacteristic
145C2×C4×C13#12111yescharacteristic
146C2×C4×C13#12411yescharacteristic
147C2×C4×C13#12711yescharacteristic
148C2×C4×C13C22×C811yescharacteristic
149C2×C4×C13C2×M1611yescharacteristic
150C2×C4×C13#13111yescharacteristic
151C2×C4×C13#13111yescharacteristic
152C2×Dic13—22no—
153C2×Dic13—41no—
154C2×Dic13—41no—
155C2×Dic13—41no—
156C2×Dic13—41no—
157C2×Dic13—81no—
158C2×Dic13—81no—
159D52—22no—
160D52—22no—
161D52—41no—
162D52—41no—
163C4×D13—82no—
164C4×D13—82no—
165Dic26—22no—
166Dic26—22no—
167Dic26—41no—
168Dic26—41no—
169C8×C13—21no—
170C8×C13—21no—
171C8×C13—81no—
172C8×C13—81no—
173C8×C13C22⋊C812yes—
174C8×C13C22⋊C812yes—
175#1055—42no—
176#1055—42no—
177C22×SD16—131no—
178C2×C4×Q8—131no—
179C2×C4×D4—131no—
180C4×SD16—261no—
181C4×SD16—261no—
182C4×SD16—261no—
183C4×SD16—261no—
184#431—131no—
185#431—131no—
186#431C2×D1311yescharacteristic
187#431C2×D1311yescharacteristic
188C2×#106—131no—
189C2×#103—131no—
190C2×#102—131no—
191C2×C4×C8C2×D1311yescharacteristic
192#335—21no—
193#334—21no—
194Q8⋊C8—262no—
195D4⋊C8—262no—
196#324—262no—
197#323—262no—
198#322—261no—
199C82—261no—
200C22×C13—21no—
201C22×C13—21no—
202C22×C13#39011yescharacteristic
203C22×C13C8×D411yescharacteristic
204C22×C13#43611yescharacteristic
205C2×D13—42no—
206C2×D13—82no—
207C2×D13—81no—
208C2×D13—81no—
209C2×D13—82no—
210C4×C13—21no—
211C4×C13—21no—
212C4×C13—21no—
213C4×C13C2×C22⋊C811yescharacteristic
214C4×C13#40811yescharacteristic
215C4×C13C8×D411yescharacteristic
216C4×C13#43611yescharacteristic
217C4×C13#47112yes—
218Dic13—42no—
219Dic13—81no—
220Dic13—81no—
221C22×Q8—131no—
222C22×D4—131no—
223C23×C4—261no—
224C2×SD16—134no—
225C2×SD16—262no—
226C2×SD16—261no—
227C2×SD16—261no—
228C22×C8C4×D1311yescharacteristic
229C22×C8C4×D1311yescharacteristic
230C4×Q8—261no—
231C4×Q8—261no—
232C4×Q8—261no—
233C4×Q8—261no—
234C4×D4—261no—
235C4×D4—261no—
236C4×D4—261no—
237C4×D4—261no—
238C2×C4⋊C4—131no—
239C2×C4⋊C4—131no—
240C2×C4⋊C4—261no—
241C2×C22⋊C4—261no—
242C2×C42—261no—
243C2×C42C22×D1311yescharacteristic
244#106—261no—
245#106—261no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—132no—
249C4⋊C8—261no—
250#103—261no—
251#103—261no—
252#102—261no—
253#102—261no—
254C22⋊C8—21no—
255C22⋊C8—21no—
256C22⋊C8—132no—
257C22⋊C8—261no—
258C4×C8—21no—
259C4×C8—21no—
260C4×C8—261no—
261C4×C8—261no—
262C4×C8D5211yescharacteristic
263C4×C8D5211yescharacteristic
264C4×C8C22⋊D1311yescharacteristic
265C4×C8C22⋊D1311yescharacteristic
266C2×C13—21no—
267C2×C13—21no—
268C2×C13#195411yescharacteristic
269C2×C13#197611yescharacteristic
270C2×C13#197711yescharacteristic
271D13—82no—
272C24—261no—
273C2×Q8—132no—
274C2×Q8—261no—
275C2×Q8—261no—
276C2×Q8—261no—
277C2×Q8—261no—
278C2×Q8—261no—
279C2×D4—132no—
280C2×D4—261no—
281C2×D4—261no—
282C2×D4—261no—
283C2×D4—261no—
284C2×D4—261no—
285C22×C4—261no—
286C22×C4—261no—
287C22×C4—261no—
288C22×C4—521no—
289C22×C4—521no—
290C22×C4—1042no—
291C22×C4C2×C4×D1311yescharacteristic
292C22×C4D4×D1311yescharacteristic
293C22×C4#613111yescharacteristic
294SD16—264no—
295SD16—264no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—262no—
301C2×C8—262no—
302C2×C8C8×D1312yes—
303C2×C8#609412yes—
304C2×C8#610311yescharacteristic
305C2×C8#610311yescharacteristic
306C2×C8#610311yescharacteristic
307C2×C8#610311yescharacteristic
308C4⋊C4—261no—
309C4⋊C4—261no—
310C4⋊C4—261no—
311C4⋊C4—261no—
312C4⋊C4—521no—
313C4⋊C4—521no—
314C22⋊C4—521no—
315C22⋊C4—521no—
316C42—521no—
317C42—521no—
318C42C2×D5211yescharacteristic
319C42D4×D1311yescharacteristic
320C42#613111yescharacteristic
321C42C2×C22⋊D1311yescharacteristic
322C13#966711yescharacteristic, complemented, Sylow
323C23—262no—
324C23—521no—
325C23—521no—
326C23—1041no—
327C23—1041no—
328C23#8814711yescharacteristic
329Q8—262no—
330Q8—262no—
331Q8—521no—
332Q8—521no—
333D4—262no—
334D4—262no—
335D4—521no—
336D4—521no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—262no—
340C2×C4—521no—
341C2×C4—521no—
342C2×C4—521no—
343C2×C4—521no—
344C2×C4—1042no—
345C2×C4—1042no—
346C2×C4—1041no—
347C2×C4—1041no—
348C2×C4#8814711yescharacteristic
349C2×C4#8814911yescharacteristic
350C2×C4#8814911yescharacteristic
351C2×C4C2×C8×D1311yescharacteristic
352C2×C4C2×#609411yescharacteristic
353C2×C4#8816111yescharacteristic
354C2×C4#8816111yescharacteristic
355C2×C4C2×#610311yescharacteristic
356C2×C4#8819411yescharacteristic
357C2×C4#8820111yescharacteristic
358C8—21no—
359C8—21no—
360C8—81no—
361C8—81no—
362C8—522no—
363C8—522no—
364C8#8806012yes—
365C8#8806012yes—
366C22—21no—
367C22—21no—
368C22—522no—
369C22—1042no—
370C22—1042no—
371C22—1041no—
372C22—1041no—
373C22#1171849511yescharacteristic
374C22#1171849911yescharacteristic
375C22#1171864911yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—522no—
380C4—1041no—
381C4—1041no—
382C4#1171849511yescharacteristic
383C4#1171849911yescharacteristic
384C4#1171855912yes—
385C4C2×#8806011yescharacteristic
386C4#1171879011yescharacteristic
387C2—21no—
388C2—21no—
389C2—1042no—
390C2#1311562911yescharacteristic
391C2#1311573211yescharacteristic
392C2#1311573711yescharacteristic
subgroupG/H
centerC2×C4#88149
commutatorC2×C4×C13C22×C8
FrattiniC2×C42C22×D13
FittingC13×#1564C2
socleC22×C13#390
prime radicalC22×D52C2×C4
cosocleC2×C42×C13C23
hypercenter#1564D13
hypocenterC13#9667
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. #13113232C2semidirect
4. #13113159C2semidirect
6. #13113119C2semidirect
7. C13×#1564C2semidirect
45. C2×#6095C8semidirect
128. #1564D13semidirect
322. C13#9667semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#60952
#131132322
#131132282
#131131592
#131131562
#131131192
C13×#15642
#966713