Finite Group Databasebeta

← #25017986

Subgroups — #25017986

Order 11008.

2782 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063281C212yesmaximal
2C23×Dic43⋊C4C211yesmaximal, characteristic
3Dic43⋊#95C218yesmaximal, complemented
4#19132818C211yesmaximal, characteristic
5#19132817C212yesmaximal
6C43×C22⋊#95C211yesmaximal, characteristic
7C24×Dic43C2211yescharacteristic
8C24×Dic43C2211yescharacteristic
9C2×#13063281—28no—
10C2×#13063281—28no—
11C2×#13063281C4116yescomplemented
12C22×Dic43⋊C4—28no—
13C22×Dic43⋊C4C418yescomplemented
14C22×Dic43⋊C4C2214yes—
15C22×Dic43⋊C4C2214yes—
16C22×C22⋊Dic43C2212yes—
17C22×C4×Dic43C2214yes—
18C2×C43⋊#95C2218yes—
19C2×C43⋊#95C2214yes—
20C24×C4×C43C2211yescharacteristic
21C22×C22⋊C4×C43C2212yes—
22C2×#95×C43C2214yes—
23C23×Dic43—24no—
24C23×Dic43—44no—
25C23×Dic43C2×C414yes—
26C23×Dic43C2×C414yes—
27C23×Dic43C2×C418yes—
28C23×Dic43D418yes—
29C23×Dic43D414yes—
30C23×Dic43Q814yes—
31C23×Dic43C2314yes—
32C23×Dic43C2312yes—
33C23×Dic43C2312yes—
34#13063281—264no—
35C2×Dic43⋊C4—232no—
36C2×Dic43⋊C4—28no—
37C2×Dic43⋊C4—28no—
38C2×Dic43⋊C4—28no—
39C2×Dic43⋊C4—28no—
40C2×Dic43⋊C4C2×C4116yes—
41C2×Dic43⋊C4C2×C4116yescomplemented
42C2×C22⋊Dic43—24no—
43C2×C22⋊Dic43—24no—
44C2×C22⋊Dic43C2×C418yes—
45C2×C4×Dic43—28no—
46C2×C4×Dic43—28no—
47C2×C4×Dic43C2×C4116yescomplemented
48C43⋊#95—44no—
49C43⋊#95—48no—
50C25×C43C2311yescharacteristic
51C23×C4×C43—24no—
52C23×C4×C43—44no—
53C23×C4×C43C2×C414yes—
54C23×C4×C43C2314yes—
55C23×C4×C43C2312yes—
56C2×C22⋊C4×C43—24no—
57C2×C22⋊C4×C43—24no—
58C2×C22⋊C4×C43C2×C418yes—
59#95×C43—44no—
60C24×C43—24no—
61C24×C43—24no—
62C24×C43C22×C414yes—
63C24×C43C22×C412yes—
64C24×C43C2×D412yes—
65C24×C43C2×D414yes—
66C24×C43C2×Q812yes—
67C24×C43C2411yescharacteristic
68C22×C4×C43—28no—
69C22×C4×C43—24no—
70C22×C4×C43—24no—
71C22×C4×C43—24no—
72C22×C4×C43—24no—
73C22×C4×C43—28no—
74C22×C4×C43—24no—
75C22×C4×C43—28no—
76C22×C4×C43—48no—
77C22×C4×C43—416no—
78C22×C4×C43C22×C418yes—
79C22×C4×C43C22×C414yes—
80C22×Dic43—28no—
81C22×Dic43—24no—
82C22×Dic43—24no—
83C22×Dic43—24no—
84C22×Dic43—28no—
85C22×Dic43—28no—
86C22×Dic43—28no—
87C22×Dic43—48no—
88C22×Dic43—416no—
89C22×Dic43C42116yes—
90C22×Dic43C22⋊C4116yes—
91C22×Dic43C22⋊C4132yes—
92C22×Dic43C4⋊C4116yes—
93C22×Dic43C4⋊C4132yes—
94C22×Dic43C22×C418yes—
95C22×Dic43C22×C414yes—
96C22×Dic43C22×C414yes—
97C22×Dic43C22×C414yes—
98C22×Dic43C22×C414yes—
99C22×Dic43C2×D414yes—
100C22×Dic43C2×D414yes—
101C22×Dic43C2×D414yes—
102C22×Dic43C2×Q814yes—
103C22⋊C4×C43—216no—
104C22⋊Dic43—216no—
105Dic43⋊C4—232no—
106Dic43⋊C4—232no—
107C4×Dic43—232no—
108C23×C43—24no—
109C23×C43—24no—
110C23×C43—216no—
111C23×C43—28no—
112C23×C43—28no—
113C23×C43—28no—
114C23×C43—28no—
115C23×C43C2×C4214yes—
116C23×C43C2×C22⋊C418yes—
117C23×C43C2×C22⋊C414yes—
118C23×C43C2×C4⋊C414yes—
119C23×C43C2×C4⋊C418yes—
120C23×C43C23×C411yescharacteristic
121C23×C43C23×C412yes—
122C23×C43C22×D412yes—
123C23×C43C22×D411yescharacteristic
124C23×C43C22×Q811yescharacteristic
125C23×C43H(5,𝔽2)14yes—
126C23×C432−1+414yes—
127C2×C4×C43—28no—
128C2×C4×C43—24no—
129C2×C4×C43—24no—
130C2×C4×C43—24no—
131C2×C4×C43—216no—
132C2×C4×C43—416no—
133C2×C4×C43—44no—
134C2×C4×C43—48no—
135C2×C4×C43—44no—
136C2×C4×C43—48no—
137C2×Dic43—28no—
138C2×Dic43—24no—
139C2×Dic43—28no—
140C2×Dic43—216no—
141C2×Dic43—416no—
142C2×Dic43—44no—
143C2×Dic43—48no—
144C2×Dic43—44no—
145C2×Dic43—48no—
146C2×Dic43#95164yescomplemented
147C2×Dic43C2×C4218yes—
148C2×Dic43C2×C22⋊C418yes—
149C2×Dic43C2×C22⋊C418yes—
150C2×Dic43C2×C22⋊C418yes—
151C2×Dic43C2×C4⋊C418yes—
152C2×Dic43C2×C4⋊C418yes—
153C2×Dic43C2×C4⋊C418yes—
154#13795—431nomaximal, Sylow
155C22×C43—24no—
156C22×C43—24no—
157C22×C43—216no—
158C22×C43—28no—
159C22×C43—216no—
160C22×C43—28no—
161C22×C43C2×#9518yes—
162C22×C43C22×C4211yescharacteristic
163C22×C43C22×C22⋊C411yescharacteristic
164C22×C43C22×C22⋊C412yes—
165C22×C43C22×C4⋊C411yescharacteristic
166C22×C43C22×C4⋊C412yes—
167C22×C43#51812yes—
168C22×C43#51912yes—
169C22×C43#52018yes—
170C22×C43#53514yes—
171C22×C43#53614yes—
172C22×C43#53714yes—
173C22×C43#54414yes—
174C4×C43—44no—
175C4×C43—48no—
176Dic43—44no—
177Dic43—48no—
178Dic43C2×#95116yes—
179C22×#117—432no—
180C23×C4⋊C4—431no—
181C4⋊#95—438no—
182C22⋊#95—431no—
183C22⋊#95—432no—
184C22⋊#95D4311yescharacteristic
185C2×C43—28no—
186C2×C43C22×#9511yescharacteristic
187C2×C43#227412yes—
188C2×C43#230911yescharacteristic
189C2×C43#231011yescharacteristic
190C2×C43#231114yes—
191C2×C43#231612yes—
192C2×C43#231714yes—
193C24×C4—431no—
194C24×C4—431no—
195C24×C4C2×D4311yescharacteristic
196C2×#117—4316no—
197C2×#117—868no—
198C2×#117—868no—
199C22×C4⋊C4—434no—
200C22×C4⋊C4—434no—
201C22×C4⋊C4—438no—
202C22×C4⋊C4—868no—
203C22×C22⋊C4—432no—
204C22×C22⋊C4C2×D4312yes—
205C22×C42—434no—
206C2×#95—434no—
207C2×#95—438no—
208C2×#95C2×D4314yes—
209C43#1379511yescharacteristic, complemented, Sylow
210C25C22×D4311yescharacteristic
211C23×C4—24no—
212C23×C4—44no—
213C23×C4—434no—
214C23×C4—438no—
215C23×C4—438no—
216C23×C4—434no—
217C23×C4—434no—
218C23×C4—432no—
219C23×C4—434no—
220C23×C4—432no—
221C23×C4—434no—
222C23×C4—864no—
223C23×C4—1724no—
224C23×C4C4×D4314yes—
225C23×C4C22×D4314yes—
226C23×C4C22×D4312yes—
227#117—8664no—
228C2×C4⋊C4—4316no—
229C2×C4⋊C4—4316no—
230C2×C4⋊C4—8632no—
231C2×C4⋊C4—868no—
232C2×C4⋊C4—868no—
233C2×C4⋊C4—868no—
234C2×C4⋊C4—868no—
235C2×C22⋊C4—24no—
236C2×C22⋊C4—24no—
237C2×C22⋊C4—438no—
238C2×C22⋊C4—864no—
239C2×C22⋊C4—864no—
240C2×C22⋊C4C4×D4318yes—
241C2×C42—4316no—
242C2×C42—868no—
243C2×C42—868no—
244#95—44no—
245#95—1728no—
246#95—1724no—
247C24—24no—
248C24—24no—
249C24C2×C4×D4314yes—
250C24C2×C4×D4312yes—
251C24D4×D4312yes—
252C24D4×D4314yes—
253C24Q8×D4312yes—
254C24C23×D4311yescharacteristic
255C22×C4—28no—
256C22×C4—24no—
257C22×C4—24no—
258C22×C4—24no—
259C22×C4—28no—
260C22×C4—24no—
261C22×C4—24no—
262C22×C4—28no—
263C22×C4—48no—
264C22×C4—416no—
265C22×C4—4316no—
266C22×C4—4316no—
267C22×C4—4332no—
268C22×C4—4316no—
269C22×C4—4332no—
270C22×C4—434no—
271C22×C4—434no—
272C22×C4—434no—
273C22×C4—434no—
274C22×C4—434no—
275C22×C4—434no—
276C22×C4—434no—
277C22×C4—438no—
278C22×C4—434no—
279C22×C4—868no—
280C22×C4—864no—
281C22×C4—864no—
282C22×C4—864no—
283C22×C4—868no—
284C22×C4—868no—
285C22×C4—868no—
286C22×C4—1728no—
287C22×C4—17216no—
288C22×C4C2×C4×D4318yes—
289C22×C4C2×C4×D4314yes—
290C4⋊C4—8632no—
291C4⋊C4—8632no—
292C22⋊C4—216no—
293C22⋊C4—8616no—
294C42—8632no—
295C23—24no—
296C23—24no—
297C23—216no—
298C23—28no—
299C23—28no—
300C23—28no—
301C23—28no—
302C23C42×D4314yes—
303C23C22⋊C4×D4318yes—
304C23C22⋊C4×D4314yes—
305C23C4⋊C4×D4314yes—
306C23C4⋊C4×D4318yes—
307C23C22×C4×D4311yescharacteristic
308C23C22×C4×D4312yes—
309C23C2×D4×D4312yes—
310C23C2×D4×D4311yescharacteristic
311C23C2×Q8×D4311yescharacteristic
312C23#1306337014yes—
313C23#1306337214yes—
314C2×C4—28no—
315C2×C4—24no—
316C2×C4—24no—
317C2×C4—24no—
318C2×C4—216no—
319C2×C4—416no—
320C2×C4—48no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4—48no—
324C2×C4—438no—
325C2×C4—438no—
326C2×C4—438no—
327C2×C4—438no—
328C2×C4—438no—
329C2×C4—438no—
330C2×C4—438no—
331C2×C4—4364no—
332C2×C4—868no—
333C2×C4—864no—
334C2×C4—868no—
335C2×C4—8616no—
336C2×C4—17216no—
337C2×C4—1728no—
338C2×C4—1724no—
339C2×C4—1724no—
340C2×C4—1728no—
341C22—24no—
342C22—24no—
343C22—216no—
344C22—28no—
345C22—28no—
346C22—216no—
347C22#95×D4318yes—
348C22C2×C42×D4311yescharacteristic
349C22C2×C22⋊C4×D4311yescharacteristic
350C22C2×C22⋊C4×D4312yes—
351C22C2×C4⋊C4×D4311yescharacteristic
352C22C2×C4⋊C4×D4312yes—
353C22#1458337212yes—
354C22#1458337612yes—
355C22#1458337818yes—
356C22#1458346414yes—
357C22#1458347114yes—
358C22#1458347614yes—
359C22#1458352814yes—
360C4—44no—
361C4—48no—
362C4—4316no—
363C4—1724no—
364C4—1728no—
365C2—28no—
366C2C2×#95×D4311yescharacteristic
367C2#1913695012yes—
368C2#1913717611yescharacteristic
369C2#1913718011yescharacteristic
370C2#1913718214yes—
371C2#1913721212yes—
372C2#1913721414yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC22×C43C22×C42
FittingC43×C22⋊#95C2
socle, cosocleC24×C43C24
prime radicalC25×C43C23
hypercenterC22⋊#95D43
hypocenterC43#13795
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. Dic43⋊#95C2semidirect
11. C2×#13063281C4semidirect
13. C22×Dic43⋊C4C4semidirect
41. C2×Dic43⋊C4C2×C4semidirect
47. C2×C4×Dic43C2×C4semidirect
146. C2×Dic43#95semidirect
209. C43#13795semidirect

Maximal subgroups

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

subgroupindex
C22×#130632812
C23×Dic43⋊C42
Dic43⋊#952
#191328182
#191328172
C43×C22⋊#952
#1379543