Finite Group Databasebeta

← #35310239

Subgroups — #35310239

Order 21248.

1338 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127561C212yesmaximal
2C2×#19127468C214yesmaximal
3C2×C4×C22⋊C4×C83C211yesmaximal, characteristic
4C22×C4⋊Dic83—22no—
5C22×C22⋊Dic83C2214yes—
6#19127561—24no—
7#19127561C418yescomplemented
8C2×C83⋊#95—22no—
9#19127468—28no—
10C24×C4×C83C2211yescharacteristic
11C22×C22⋊C4×C83C2212yes—
12C22×C42×C83C412yescomplemented
13C4×C22⋊C4×C83—22no—
14C4×C22⋊C4×C83—22no—
15C2×#95×C83C412yescomplemented
16C23×Dic83—24no—
17C2×C4⋊Dic83—28no—
18C2×C4⋊Dic83—48no—
19C2×C22⋊Dic83—28no—
20C2×C22⋊Dic83—24no—
21C2×C22⋊Dic83—28no—
22C2×C22⋊Dic83C2×C418yes—
23C83⋊#95—28no—
24C25×C83C2311yescharacteristic
25C23×C4×C83—44no—
26C23×C4×C83C2×C414yes—
27C23×C4×C83C2×C411yescharacteristic
28C23×C4×C83C2×C414yes—
29C23×C4×C83C2×C411yescharacteristic
30C23×C4×C83D412yes—
31C23×C4×C83D412yes—
32C23×C4×C83D412yes—
33C23×C4×C83Q812yes—
34C2×C22⋊C4×C83—24no—
35C2×C22⋊C4×C83—24no—
36C2×C22⋊C4×C83D414yes—
37C2×C22⋊C4×C83Q814yes—
38C2×C42×C83—22no—
39C2×C42×C83—22no—
40C2×C42×C83—44no—
41#95×C83—24no—
42C22×Dic83—28no—
43C22×Dic83—48no—
44C22×Dic83—48no—
45C22×Dic83—48no—
46C4⋊Dic83—416no—
47C22⋊Dic83—216no—
48C22⋊Dic83—44no—
49C22⋊Dic83—44no—
50C24×C83—42no—
51C24×C83—42no—
52C24×C83C22×C412yes—
53C24×C83C22×C411yescharacteristic
54C24×C83C2×D412yes—
55C24×C83C2×D411yescharacteristic
56C24×C83C2×D412yes—
57C24×C83C2×Q811yescharacteristic
58C24×C83C2×Q812yes—
59C24×C83#4114yes—
60C22×C4×C83—24no—
61C22×C4×C83—28no—
62C22×C4×C83—24no—
63C22×C4×C83—24no—
64C22×C4×C83—48no—
65C22×C4×C83—44no—
66C22×C4×C83—44no—
67C22×C4×C83—42no—
68C22×C4×C83—44no—
69C22×C4×C83—44no—
70C22×C4×C83—44no—
71C22×C4×C83C4212yes—
72C22×C4×C83C4212yes—
73C22×C4×C83C22⋊C414yes—
74C22×C4×C83C22⋊C414yes—
75C22×C4×C83C22⋊C412yes—
76C22×C4×C83C22⋊C411yescharacteristic
77C22×C4×C83C22⋊C411yescharacteristic
78C22×C4×C83C4⋊C414yes—
79C22×C4×C83C4⋊C414yes—
80C22×C4×C83C4⋊C412yes—
81C22×C4×C83C4⋊C412yes—
82C22×C4×C83C4⋊C418yescomplemented
83C22⋊C4×C83—28no—
84C22⋊C4×C83—28no—
85C42×C83—44no—
86C42×C83—44no—
87C23×C83—22no—
88C23×C83—24no—
89C23×C83—22no—
90C23×C83—24no—
91C23×C83—42no—
92C23×C83—41no—
93C23×C83—41no—
94C23×C83—42no—
95C23×C83—44no—
96C23×C83—41no—
97C23×C83—44no—
98C23×C83—41no—
99C23×C83—48no—
100C23×C83C2×C4211yescharacteristic
101C23×C83C2×C22⋊C412yes—
102C23×C83C2×C22⋊C411yescharacteristic
103C23×C83C2×C4⋊C412yes—
104C23×C83C2×C4⋊C411yescharacteristic
105C23×C83C2×C4⋊C412yes—
106C23×C83#11712yes—
107C23×C83C4×D414yes—
108C23×C83C4×Q814yes—
109C23×C83#12114yes—
110C23×C83C22⋊Q814yes—
111C23×C83#12412yes—
112C23×C83#12512yes—
113C23×C83#12711yescharacteristic
114C23×C83C4⋊Q812yes—
115C23×C83C4⋊Q811yescharacteristic
116C2×C4×C83—22no—
117C2×C4×C83—24no—
118C2×C4×C83—24no—
119C2×C4×C83—28no—
120C2×C4×C83—28no—
121C2×C4×C83—24no—
122C2×C4×C83—28no—
123C2×C4×C83—42no—
124C2×C4×C83—44no—
125C2×C4×C83—44no—
126C2×C4×C83—42no—
127C2×C4×C83—48no—
128C2×C4×C83—44no—
129C2×C4×C83—44no—
130C2×C4×C83—48no—
131C2×C4×C83#9512yes—
132C2×C4×C83#9514yes—
133C2×C4×C83#9512yes—
134C2×C4×C83#9914yes—
135C2×Dic83—48no—
136C2×Dic83—48no—
137C2×Dic83—48no—
138C2×Dic83—816no—
139C22×C83—28no—
140C22×C83—24no—
141C22×C83—24no—
142C22×C83—28no—
143C22×C83—22no—
144C22×C83—21no—
145C22×C83—22no—
146C22×C83—21no—
147C22×C83—22no—
148C22×C83—21no—
149C22×C83—22no—
150C22×C83—21no—
151C22×C83—44no—
152C22×C83—44no—
153C22×C83—42no—
154C22×C83—42no—
155C22×C83—41no—
156C22×C83—42no—
157C22×C83—41no—
158C22×C83C2×#9511yescharacteristic
159C22×C83C4×C4⋊C412yes—
160C22×C83#38012yes—
161C22×C83#38211yescharacteristic
162C22×C83#38411yescharacteristic
163C22×C83#38914yes—
164C22×C83#39012yes—
165C22×C83#39112yes—
166C22×C83C2×#9912yes—
167C22×C83#41012yes—
168C4×C83—22no—
169C4×C83—24no—
170C4×C83—48no—
171C4×C83#34214yescomplemented
172Dic83—88no—
173#10846—831nomaximal, Sylow
174C2×C83—22no—
175C2×C83—22no—
176C2×C83—21no—
177C2×C83—21no—
178C2×C83—24no—
179C2×C83—22no—
180C2×C83C4⋊#9511yescharacteristic
181C2×C83C2×#34211yescharacteristic
182C2×C83#174011yescharacteristic
183C2×C83#179914yes—
184C2×#380—832no—
185C2×C4×C22⋊C4D8311yescharacteristic
186C2×#342—834no—
187C83#1084611yescharacteristic, complemented, Sylow
188C24×C4C2×D8311yescharacteristic
189C22×C4⋊C4—1662no—
190C22×C22⋊C4—834no—
191C22×C22⋊C4C2×D8312yes—
192C22×C42Dic8312yescomplemented
193#380—838no—
194#380—1664no—
195C4×C22⋊C4—22no—
196C4×C22⋊C4—22no—
197C2×#95—1662no—
198C2×#95Dic8312yescomplemented
199#342—1668no—
200C25C22×D8311yescharacteristic
201C23×C4—44no—
202C23×C4—1664no—
203C23×C4Dic16612yes—
204C23×C4C4×D8314yes—
205C23×C4D33212yes—
206C23×C4C2×Dic8311yescharacteristic
207C23×C4C2×Dic8314yes—
208C23×C4C2×Dic8311yescharacteristic
209C23×C4C22⋊D8312yes—
210C23×C4C22⋊D8312yes—
211C2×C4⋊C4—3328no—
212C2×C4⋊C4—1668no—
213C2×C22⋊C4—24no—
214C2×C22⋊C4—24no—
215C2×C22⋊C4—838no—
216C2×C22⋊C4—1664no—
217C2×C22⋊C4—1668no—
218C2×C22⋊C4—1668no—
219C2×C22⋊C4Dic16614yes—
220C2×C22⋊C4D33214yes—
221C2×C42—22no—
222C2×C42—22no—
223C2×C42—44no—
224#95—24no—
225#95—1668no—
226C24—42no—
227C24—42no—
228C24C2×C4×D8312yes—
229C24C22×Dic8311yescharacteristic
230C24C2×C22⋊D8312yes—
231C24C2×D33212yes—
232C24C2×D33211yescharacteristic
233C24C2×Dic16612yes—
234C24C2×Dic16611yescharacteristic
235C24#1305059014yes—
236C22×C4—24no—
237C22×C4—28no—
238C22×C4—24no—
239C22×C4—24no—
240C22×C4—44no—
241C22×C4—48no—
242C22×C4—44no—
243C22×C4—42no—
244C22×C4—44no—
245C22×C4—44no—
246C22×C4—44no—
247C22×C4—3328no—
248C22×C4—3328no—
249C22×C4—3328no—
250C22×C4—1668no—
251C22×C4C4×Dic8312yes—
252C22×C4C4×Dic8312yes—
253C22×C4(C2×D83)⋊C414yes—
254C22×C4(C2×D83)⋊C414yes—
255C22×C4C22⋊Dic8312yes—
256C22×C4C22⋊Dic8311yescharacteristic
257C22×C4C22⋊Dic8311yescharacteristic
258C22×C4Dic83⋊C414yes—
259C22×C4Dic83⋊C414yes—
260C22×C4C4⋊Dic8312yes—
261C22×C4C4⋊Dic8312yes—
262C22×C4C4⋊Dic8318yescomplemented
263C4⋊C4—33216no—
264C22⋊C4—28no—
265C22⋊C4—28no—
266C22⋊C4—3324no—
267C22⋊C4—3324no—
268C22⋊C4—16616no—
269C42—44no—
270C42—44no—
271C23—22no—
272C23—24no—
273C23—22no—
274C23—24no—
275C23—42no—
276C23—41no—
277C23—41no—
278C23—42no—
279C23—44no—
280C23—41no—
281C23—44no—
282C23—41no—
283C23—48no—
284C23C2×C4×Dic8311yescharacteristic
285C23C2×(C2×D83)⋊C412yes—
286C23C2×C22⋊Dic8311yescharacteristic
287C23C2×Dic83⋊C412yes—
288C23C2×C4⋊Dic8312yes—
289C23C2×C4⋊Dic8311yescharacteristic
290C23#1458175112yes—
291C23C4×D33214yes—
292C23C4×Dic16614yes—
293C23#1458176614yes—
294C23#1458177114yes—
295C23#1458178012yes—
296C23#1458178412yes—
297C23#1458178911yescharacteristic
298C23#1458179212yes—
299C23#1458179211yescharacteristic
300C2×C4—22no—
301C2×C4—24no—
302C2×C4—28no—
303C2×C4—24no—
304C2×C4—28no—
305C2×C4—24no—
306C2×C4—28no—
307C2×C4—42no—
308C2×C4—44no—
309C2×C4—44no—
310C2×C4—42no—
311C2×C4—48no—
312C2×C4—44no—
313C2×C4—44no—
314C2×C4—48no—
315C2×C4—3328no—
316C2×C4—3328no—
317C2×C4—3328no—
318C2×C4—66416no—
319C2×C4C83⋊#9512yes—
320C2×C4C83⋊#9514yes—
321C2×C4C83⋊#9512yes—
322C2×C4#1458170714yes—
323C22—22no—
324C22—21no—
325C22—22no—
326C22—21no—
327C22—24no—
328C22—24no—
329C22—28no—
330C22—28no—
331C22—22no—
332C22—21no—
333C22—22no—
334C22—21no—
335C22—42no—
336C22—42no—
337C22—41no—
338C22—42no—
339C22—41no—
340C22—44no—
341C22—44no—
342C22C2×C83⋊#9511yescharacteristic
343C22C4×C4⋊Dic8312yes—
344C22#1912756112yes—
345C22#1912756711yescharacteristic
346C22#1912757111yescharacteristic
347C22#1912759914yes—
348C22#1912760312yes—
349C22#1912760712yes—
350C22C2×#1458170712yes—
351C22#1912767512yes—
352C4—22no—
353C4—24no—
354C4—48no—
355C4—6648no—
356C4#1912746814yescomplemented
357C2—22no—
358C2—22no—
359C2—21no—
360C2—21no—
361C2—24no—
362C2—22no—
363C2#2490569311yescharacteristic
364C2C2×#1912746811yescharacteristic
365C2#2490719611yescharacteristic
366C2#2490745114yes—
subgroupG/H
centerC23C2×C22⋊Dic83
commutatorC23×C83C2×C42
FrattiniC25C22×D83
FittingC2×C4×C22⋊C4×C83C2
socleC23×C83C2×C22⋊C4
prime radical, cosocleC25×C83C23
hypercenterC2×C4×C22⋊C4D83
hypocenterC83#10846
LCSG ▷ C23×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
7. #19127561C4semidirect
12. C22×C42×C83C4semidirect
15. C2×#95×C83C4semidirect
82. C22×C4×C83C4⋊C4semidirect
171. C4×C83#342semidirect
187. C83#10846semidirect
192. C22×C42Dic83semidirect
198. C2×#95Dic83semidirect
262. C22×C4C4⋊Dic83semidirect
356. C4#19127468semidirect

Maximal subgroups

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

subgroupindex
C2×#191275612
C2×#191274682
C2×C4×C22⋊C4×C832
#1084683