Finite Group Databasebeta

← #15761804

Subgroups — #15761804

Order 3328.

534 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#6095C211yesmaximal, characteristic
2#13115772C211yesmaximal, characteristic, complemented
3#13115630C211yesmaximal, characteristic
4C2×#11718049C211yesmaximal, characteristic, complemented
5C2×#11718048C211yesmaximal, characteristic, complemented
6C2×#11718051C211yesmaximal, characteristic
7C2×C13×#322C211yesmaximal, characteristic, complemented
8C22×#6095C411yescharacteristic
9C2×C4×D52C2211yescharacteristic
10C2×C4×Dic26C2211yescharacteristic
11C2×C4×C8×C13C2211yescharacteristic
12C2×C4×C8×C13C2211yescharacteristic
13C2×C4×C8×C13C2211yescharacteristic
14C2×#88061C411yescharacteristic
15C2×#88060—22no—
16C2×#88057C411yescharacteristic
17C2×#88056C411yescharacteristic
18C2×C4⋊#1055C2211yescharacteristic
19C2×C4⋊#1055C2211yescharacteristic
20C4×#6095—22no—
21C4×#6095—22no—
22C13×#322—22no—
23#11718142—22no—
24#11718051—22no—
25#11718049—22no—
26#11718048—22no—
27C22×D52C2×C411yescharacteristic
28C22×C4×D13—21no—
29C22×Dic26C2×C411yescharacteristic
30C22×C8×C13—21no—
31C22×C8×C13C2×C411yescharacteristic
32C22×C8×C13C2×C411yescharacteristic
33C22×C8×C13D412yes—
34C2×C42×C13C2311yescharacteristic
35C2×#6103—21no—
36C2×C4⋊Dic13C2×C411yescharacteristic
37C2×C4⋊Dic13C2×C411yescharacteristic
38C2×#6101—21no—
39C2×C4×Dic13—21no—
40C22×#1055—21no—
41C22×#1055—21no—
42C2×#6095—22no—
43C2×#6095—22no—
44C2×#6095—22no—
45C4×D52—21no—
46C4×D52—21no—
47C4×D52—21no—
48C4×D52—21no—
49C4×Dic26—21no—
50C4×Dic26—21no—
51C4×Dic26—21no—
52C4×Dic26—21no—
53C4×C8×C13—21no—
54C4×C8×C13—21no—
55C4×C8×C13—21no—
56C4×C8×C13D412yes—
57C4×C8×C13D412yes—
58C4×C8×C13D412yes—
59#88061—22no—
60#88060—44no—
61#88057—22no—
62#88056—22no—
63C4⋊#1055—21no—
64C4⋊#1055—21no—
65C4⋊#1055—21no—
66C4⋊#1055—21no—
67#9661—131nomaximal, Sylow
68C23×D13—21no—
69C22×C4×C13C22×C411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13#4111yescharacteristic
72C22×Dic13—21no—
73C22×Dic13—21no—
74C22×Dic13—21no—
75C2×D52—21no—
76C2×D52—21no—
77C2×D52—21no—
78C2×D52—21no—
79C2×D52—21no—
80C2×D52M1612yes—
81C2×C4×D13—41no—
82C2×C4×D13—41no—
83C2×C4×D13—42no—
84C2×C4×D13—42no—
85C2×Dic26—21no—
86C2×Dic26—21no—
87C2×Dic26—21no—
88C2×Dic26—21no—
89C2×Dic26—21no—
90C2×Dic26M1612yes—
91C2×C8×C13—22no—
92C2×C8×C13—21no—
93C2×C8×C13—21no—
94C2×C8×C13—21no—
95C2×C8×C13—21no—
96C2×C8×C13—22no—
97C2×C8×C13—22no—
98C2×C8×C13—42no—
99C2×C8×C13C22⋊C412yes—
100C2×C8×C13C22⋊C412yes—
101C2×C8×C13SD1614yescomplemented
102C42×C13C2×D411yescharacteristic
103C42×C13C2×D411yescharacteristic
104C42×C13C2×D411yescharacteristic
105C42×C13#4111yescharacteristic
106#6103—41no—
107#6103—41no—
108C4⋊Dic13—21no—
109C4⋊Dic13—21no—
110C4⋊Dic13—21no—
111C4⋊Dic13—21no—
112#6101—41no—
113#6101—41no—
114C4×Dic13—41no—
115C4×Dic13—41no—
116C2×#1055—41no—
117C2×#1055—41no—
118C2×#1055—42no—
119C2×#1055—42no—
120#6095—28no—
121C2×C4×SD16—131no—
122#1984—131no—
123#1954—131no—
124C2×#334—131no—
125C2×Q8⋊C8—131no—
126C2×D4⋊C8—131no—
127C2×#322D1311yescharacteristic, complemented
128C23×C13C4×D411yescharacteristic
129C22×D13—22no—
130C22×D13—41no—
131C22×D13—41no—
132C22×D13—42no—
133C22×D13—42no—
134C2×C4×C13—22no—
135C2×C4×C13C2×C22⋊C411yescharacteristic
136C2×C4×C13C4×D411yescharacteristic
137C2×C4×C13#12111yescharacteristic
138C2×C4×C13#12111yescharacteristic
139C2×C4×C13#12411yescharacteristic
140C2×C4×C13#12711yescharacteristic
141C2×C4×C13C2×M1611yescharacteristic
142C2×C4×C13C2×M1611yescharacteristic
143C2×C4×C13#13111yescharacteristic
144C2×C4×C13#13111yescharacteristic
145C2×C4×C13C2×SD1612yes—
146C2×C4×C13#13512yes—
147C2×Dic13—22no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—42no—
153C2×Dic13—42no—
154D52—22no—
155D52—22no—
156D52—41no—
157D52—41no—
158C4×D13—82no—
159C4×D13—81no—
160C4×D13—81no—
161Dic26—22no—
162Dic26—22no—
163Dic26—41no—
164Dic26—41no—
165C8×C13—22no—
166C8×C13—22no—
167C8×C13—24no—
168C8×C13—42no—
169#1055—81no—
170#1055—81no—
171C22×SD16—131no—
172C2×C4×Q8—131no—
173C2×C4×D4—131no—
174C4×SD16—262no—
175C4×SD16—262no—
176C2×#106—131no—
177C2×C4⋊C8—131no—
178C2×C4⋊C8—131no—
179C2×#103—131no—
180C2×#102—131no—
181C2×C22⋊C8—262no—
182C2×C4×C8C2×D1311yescharacteristic
183C2×C4×C8C2×D1311yescharacteristic
184C2×C4×C8C2×D1311yescharacteristic
185#336—262no—
186#334—262no—
187Q8⋊C8—262no—
188D4⋊C8—262no—
189#322—22no—
190C22×C13#39011yescharacteristic
191C22×C13#43511yescharacteristic
192C22×C13#43511yescharacteristic
193C22×C13C4×SD1612yes—
194C22×C13#44412yes—
195C2×D13—44no—
196C2×D13—42no—
197C2×D13—82no—
198C2×D13—81no—
199C2×D13—81no—
200C4×C13—21no—
201C4×C13—21no—
202C4×C13#40711yescharacteristic
203C4×C13#40811yescharacteristic
204C4×C13#43511yescharacteristic
205C4×C13#43511yescharacteristic
206C4×C13#46512yes—
207C4×C13#49211yescharacteristic
208C4×C13#49511yescharacteristic
209Dic13—42no—
210Dic13—81no—
211Dic13—81no—
212C22×Q8—131no—
213C22×D4—131no—
214C23×C4—261no—
215C2×SD16—262no—
216C2×SD16—262no—
217C2×SD16—262no—
218C22×C8—21no—
219C22×C8—261no—
220C22×C8—261no—
221C22×C8C4×D1311yescharacteristic
222C22×C8C4×D1311yescharacteristic
223C22×C8D5212yes—
224C4×Q8—261no—
225C4×Q8—261no—
226C4×Q8—261no—
227C4×Q8—261no—
228C4×D4—261no—
229C4×D4—261no—
230C4×D4—261no—
231C4×D4—261no—
232C2×C4⋊C4—131no—
233C2×C4⋊C4—131no—
234C2×C4⋊C4—261no—
235C2×C22⋊C4—261no—
236C2×C42—261no—
237C2×C42C22×D1311yescharacteristic
238#106—262no—
239C4⋊C8—261no—
240C4⋊C8—261no—
241C4⋊C8—261no—
242C4⋊C8—261no—
243#103—262no—
244#102—262no—
245C22⋊C8—524no—
246C4×C8—21no—
247C4×C8—21no—
248C4×C8—21no—
249C4×C8D5212yes—
250C4×C8D5212yes—
251C4×C8C22⋊D1312yes—
252C2×C13#158212yes—
253C2×C13#158312yes—
254C2×C13#195511yescharacteristic
255C2×C13#196811yescharacteristic
256C2×C13#197511yescharacteristic
257D13—82no—
258C24—261no—
259C2×Q8—132no—
260C2×Q8—261no—
261C2×Q8—261no—
262C2×Q8—261no—
263C2×Q8—261no—
264C2×Q8—261no—
265C2×D4—132no—
266C2×D4—261no—
267C2×D4—261no—
268C2×D4—261no—
269C2×D4—261no—
270C2×D4—261no—
271C22×C4—261no—
272C22×C4—261no—
273C22×C4—261no—
274C22×C4—521no—
275C22×C4—522no—
276C22×C4—522no—
277C22×C4—521no—
278C22×C4C2×C4×D1311yescharacteristic
279C22×C4C2×D5211yescharacteristic
280C22×C4#612711yescharacteristic
281SD16—268no—
282C2×C8—22no—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—21no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—42no—
290C2×C8—521no—
291C2×C8—521no—
292C2×C8—522no—
293C2×C8—522no—
294C2×C8#609514yescomplemented
295C2×C8#610312yes—
296C2×C8#610312yes—
297C4⋊C4—261no—
298C4⋊C4—261no—
299C4⋊C4—261no—
300C4⋊C4—261no—
301C4⋊C4—521no—
302C4⋊C4—521no—
303C22⋊C4—521no—
304C22⋊C4—521no—
305C42—521no—
306C42—521no—
307C42C2×D5211yescharacteristic
308C42C2×D5211yescharacteristic
309C42#612711yescharacteristic
310C42C2×C22⋊D1311yescharacteristic
311C13#966111yescharacteristic, complemented, Sylow
312C23—262no—
313C23—521no—
314C23—522no—
315C23—521no—
316C23—522no—
317C23C4×D5211yescharacteristic
318Q8—262no—
319Q8—262no—
320Q8—521no—
321Q8—521no—
322D4—262no—
323D4—262no—
324D4—521no—
325D4—521no—
326C2×C4—22no—
327C2×C4—262no—
328C2×C4—521no—
329C2×C4—521no—
330C2×C4—521no—
331C2×C4—521no—
332C2×C4—522no—
333C2×C4—522no—
334C2×C4—1042no—
335C2×C4—1041no—
336C2×C4—1041no—
337C2×C4C4×D5211yescharacteristic
338C2×C4#8812811yescharacteristic
339C2×C4#8812911yescharacteristic
340C2×C4C2×#609512yes—
341C2×C4#8815812yes—
342C2×C4M16×D1311yescharacteristic
343C2×C4M16×D1311yescharacteristic
344C2×C4#8816111yescharacteristic
345C2×C4#8816111yescharacteristic
346C2×C4C2×#610311yescharacteristic
347C2×C4#8818411yescharacteristic
348C2×C4#8818411yescharacteristic
349C8—24no—
350C8—22no—
351C8—22no—
352C8—42no—
353C8—1041no—
354C8—1041no—
355C22—524no—
356C22—522no—
357C22—1041no—
358C22—1042no—
359C22—1041no—
360C22C4×#609512yes—
361C22#1171836711yescharacteristic
362C22#1171836711yescharacteristic
363C22#1171837812yes—
364C22#1171860011yescharacteristic
365C4—21no—
366C4—21no—
367C4—522no—
368C4—1041no—
369C4—1041no—
370C4#1171835411yescharacteristic
371C4#1171835711yescharacteristic
372C4#1171836711yescharacteristic
373C4#1171836711yescharacteristic
374C4#1171877512yes—
375C4#1171878711yescharacteristic
376C4#1171879011yescharacteristic
377C2—1042no—
378C2#1311367412yes—
379C2#1311368112yes—
380C2#1311563411yescharacteristic
381C2#1311569011yescharacteristic
382C2#1311572911yescharacteristic
subgroupG/H
centerC22×C4C2×D52
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC2×C13×#322C2
socleC23×C13C4×D4
prime radicalC22×D52C2×C4
cosocleC2×C42×C13C23
hypercenterC2×#322D13
hypocenterC13#9661
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#322

Complements

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

NH ≅ G/Ntype
2. #13115772C2semidirect
4. C2×#11718049C2semidirect
5. C2×#11718048C2semidirect
7. C2×C13×#322C2semidirect
101. C2×C8×C13SD16semidirect
127. C2×#322D13semidirect
294. C2×C8#6095semidirect
311. C13#9661semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#60952
#131157722
#131156302
C2×#117180492
C2×#117180482
C2×#117180512
C2×C13×#3222
#966113