Finite Group Databasebeta

← C22×#14582667 #25094038

Subgroups — C22×#14582667 #25094038

Order 11008.

2494 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
1C23×#10621877C211yesmaximal, characteristic
2C23×C4⋊Dic43C211yesmaximal, characteristic
3C2×#14582667C2112yesmaximal, direct product factor
4C23×M16×C43C211yesmaximal, characteristic
5C24×Dic43C412yes—
6C22×#10621877—23no—
7C22×#10621877—24no—
8C22×#10621877C418yescomplemented
9C22×#10621877C2216yes—
10C23×C43⋊C8—21no—
11C22×C4⋊Dic43—21no—
12C22×C4⋊Dic43—23no—
13C22×C4⋊Dic43—21no—
14C22×C4⋊Dic43—23no—
15C22×C4⋊Dic43C416yes—
16C22×C4⋊Dic43C2216yes—
17#14582667C22116yesdirect product factor
18C24×C4×C43C2211yescharacteristic
19C22×M16×C43—24no—
20C22×M16×C43—23no—
21C22×M16×C43C418yescomplemented
22C22×M16×C43C2216yes—
23C23×C8×C43—21no—
24C23×Dic43—26no—
25C23×Dic43—22no—
26C23×Dic43—48no—
27C23×Dic43C2×C4112yes—
28C2×#10621877—224no—
29C2×#10621877—26no—
30C2×#10621877—212no—
31C2×#10621877C2×C4124yescomplemented
32C2×#10621877C2314yes—
33C22×C43⋊C8—28no—
34C22×C43⋊C8—26no—
35C2×C4⋊Dic43—212no—
36C2×C4⋊Dic43—26no—
37C2×C4⋊Dic43—26no—
38C2×C4⋊Dic43—26no—
39C2×C4⋊Dic43—26no—
40C2×C4⋊Dic43—26no—
41C2×C4⋊Dic43—26no—
42C2×C4⋊Dic43C2×C4112yes—
43C2×C4⋊Dic43C2314yes—
44C25×C43C2×C411yescharacteristic
45C23×C4×C43C2×C413yes—
46C23×C4×C43C2×C414yes—
47C23×C4×C43C2×C414yes—
48C23×C4×C43D411yescharacteristic
49C23×C4×C43D413yes—
50C23×C4×C43D414yes—
51C23×C4×C43D411yescharacteristic
52C23×C4×C43D413yes—
53C23×C4×C43Q814yes—
54C23×C4×C43C2313yes—
55C2×M16×C43—224no—
56C2×M16×C43—212no—
57C2×M16×C43—26no—
58C2×M16×C43C2×C4124yescomplemented
59C2×M16×C43C2314yes—
60C22×C8×C43—28no—
61C22×C8×C43—26no—
62C24×C43—24no—
63C24×C43—24no—
64C24×C43C4214yes—
65C24×C43C22⋊C413yes—
66C24×C43C22⋊C411yescharacteristic
67C24×C43C4⋊C414yes—
68C24×C43C22×C413yes—
69C22×C4×C43C42112yes—
70C22×C4×C43C22⋊C414yes—
71C22×C4×C43C22⋊C4112yes—
72C22×C4×C43C22⋊C414yes—
73C22×C4×C43C22⋊C4112yes—
74C22×C4×C43C22⋊C416yes—
75C22×C4×C43C22⋊C413yes—
76C22×C4×C43C22⋊C413yes—
77C22×C4×C43C4⋊C4112yes—
78C22×C4×C43C4⋊C414yes—
79C22×C4×C43C4⋊C4112yes—
80C22×C4×C43C4⋊C414yes—
81C22×C4×C43C4⋊C4112yes—
82C22×C4×C43C22×C416yes—
83C22×C4×C43C22×C416yes—
84C22×C4×C43C22×C413yes—
85C22×C4×C43C2×D413yes—
86C22×C4×C43C2×D413yes—
87C22×C4×C43C2×D413yes—
88C22×C4×C43C2×D413yes—
89C22×C4×C43C2×D416yes—
90C22×C4×C43C2×Q816yes—
91C22×C4×C43C2411yescharacteristic
92C22×Dic43—212no—
93C22×Dic43—212no—
94C22×Dic43—424no—
95C22×Dic43—424no—
96C22×Dic43—48no—
97C22×Dic43C22×C418yes—
98M16×C43—224no—
99M16×C43—24no—
100M16×C43C22×C418yescomplemented
101C2×C8×C43—224no—
102C2×C8×C43—24no—
103C4⋊Dic43—212no—
104C4⋊Dic43—212no—
105C4⋊Dic43—24no—
106C4⋊Dic43—24no—
107#10621877—224no—
108#10621877—24no—
109#10621877C22×C418yescomplemented
110C2×C43⋊C8—224no—
111C2×C43⋊C8—24no—
112C23×C43—216no—
113C23×C43—216no—
114C23×C43—26no—
115C23×C43—26no—
116C23×C43—26no—
117C23×C43—26no—
118C23×C43#95112yes—
119C23×C43#9514yes—
120C23×C43#10014yes—
121C23×C43#10114yes—
122C23×C43C2×C4216yes—
123C23×C43C2×C22⋊C413yes—
124C23×C43C2×C22⋊C413yes—
125C23×C43C2×C4⋊C416yes—
126C23×C43C23×C411yescharacteristic
127C2×C4×C43#95124yes—
128C2×C4×C43#95112yes—
129C2×C4×C43#95112yes—
130C2×C4×C43C2×C4216yes—
131C2×C4×C43C2×C22⋊C416yes—
132C2×C4×C43C2×C22⋊C416yes—
133C2×C4×C43C2×C22⋊C413yes—
134C2×C4×C43C2×C22⋊C413yes—
135C2×C4×C43C2×C22⋊C416yes—
136C2×C4×C43C2×C22⋊C416yes—
137C2×C4×C43C2×C4⋊C416yes—
138C2×C4×C43C2×C4⋊C416yes—
139C2×C4×C43C2×C4⋊C416yes—
140C2×C4×C43C2×C4⋊C416yes—
141C2×C4×C43C2×C4⋊C416yes—
142C2×C4×C43C23×C411yescharacteristic
143C2×C4×C43C23×C411yescharacteristic
144C2×C4×C43C22×D411yescharacteristic
145C2×C4×C43C22×D411yescharacteristic
146C2×C4×C43C22×D411yescharacteristic
147C2×C4×C43C22×Q811yescharacteristic
148C2×Dic43—28no—
149C2×Dic43—424no—
150C2×Dic43—424no—
151C2×Dic43—48no—
152C8×C43—28no—
153C43⋊C8—28no—
154C22×#343—431nomaximal, Sylow
155C22×C43—23no—
156C22×C43—21no—
157C22×C43—23no—
158C22×C43—21no—
159C22×C43—224no—
160C22×C43—212no—
161C22×C43—212no—
162C22×C43#343116yescomplemented
163C22×C43C2×#9516yes—
164C22×C43C2×#9516yes—
165C22×C43C2×#10016yes—
166C22×C43C2×#10116yes—
167C22×C43C22×C4211yescharacteristic
168C22×C43C22×C22⋊C411yescharacteristic
169C22×C43C22×C4⋊C411yescharacteristic
170C4×C43C2×#9516yes—
171C4×C43C2×#9516yes—
172C4×C43C22×C22⋊C411yescharacteristic
173C4×C43C22×C22⋊C411yescharacteristic
174C4×C43C22×C4⋊C411yescharacteristic
175C4×C43C22×C4⋊C411yescharacteristic
176Dic43—48no—
177C23×M16—431no—
178C23×M16D4311yescharacteristic
179C23×C4⋊C4—431no—
180C2×#343—4312no—
181C2×C43—21no—
182C2×C43—26no—
183C2×C43—21no—
184C2×C43C2×#343112yescomplemented
185C2×C43C22×#9511yescharacteristic
186C2×C43C22×#10011yescharacteristic
187C2×C43C22×#10111yescharacteristic
188C24×C4—432no—
189C24×C4C2×D4311yescharacteristic
190C22×M16—24no—
191C22×M16—23no—
192C22×M16—436no—
193C22×M16—438no—
194C22×M16—863no—
195C22×M16—864no—
196C22×M16Dic4318yescomplemented
197C22×M16C2×D4316yes—
198C23×C8—21no—
199C23×C8—861no—
200C22×C4⋊C4—436no—
201C22×C4⋊C4—436no—
202C22×C4⋊C4—863no—
203C22×C4⋊C4—861no—
204C22×C4⋊C4—863no—
205C22×C4⋊C4—861no—
206#343—4316no—
207C43C22×#34311yescharacteristic, complemented, Sylow
208C25C4×D4311yescharacteristic
209C23×C4—4312no—
210C23×C4—866no—
211C23×C4—862no—
212C23×C4—1728no—
213C23×C4Dic8614yes—
214C23×C4C4×D4313yes—
215C23×C4C4×D4314yes—
216C23×C4D17213yes—
217C23×C4D17211yescharacteristic
218C23×C4C2×Dic4314yes—
219C23×C4C22⋊D4313yes—
220C23×C4C22⋊D4311yescharacteristic
221C23×C4C22⋊D4314yes—
222C23×C4C22×D4313yes—
223C2×M16—224no—
224C2×M16—212no—
225C2×M16—26no—
226C2×M16—4324no—
227C2×M16—434no—
228C2×M16—8624no—
229C2×M16—866no—
230C2×M16—8612no—
231C2×M16C2×Dic43124yescomplemented
232C2×M16C22×D4314yes—
233C22×C8—28no—
234C22×C8—26no—
235C22×C8—868no—
236C22×C8—866no—
237C2×C4⋊C4—4312no—
238C2×C4⋊C4—434no—
239C2×C4⋊C4—8612no—
240C2×C4⋊C4—866no—
241C2×C4⋊C4—866no—
242C2×C4⋊C4—866no—
243C2×C4⋊C4—866no—
244C2×C4⋊C4—866no—
245C2×C4⋊C4—866no—
246C24—24no—
247C24—24no—
248C24C4×Dic4314yes—
249C24Dic43⋊C414yes—
250C24(C2×D43)⋊C413yes—
251C24(C2×D43)⋊C411yescharacteristic
252C24C2×C4×D4313yes—
253C22×C4—438no—
254C22×C4—8612no—
255C22×C4—8612no—
256C22×C4—17224no—
257C22×C4—1728no—
258C22×C4—17224no—
259C22×C4C4×Dic43112yes—
260C22×C4Dic43⋊C4112yes—
261C22×C4Dic43⋊C4112yes—
262C22×C4Dic43⋊C414yes—
263C22×C4C4⋊Dic43112yes—
264C22×C4C4⋊Dic4314yes—
265C22×C4(C2×D43)⋊C416yes—
266C22×C4(C2×D43)⋊C413yes—
267C22×C4(C2×D43)⋊C413yes—
268C22×C4(C2×D43)⋊C414yes—
269C22×C4(C2×D43)⋊C4112yes—
270C22×C4C22⋊Dic4314yes—
271C22×C4C22⋊Dic43112yes—
272C22×C4C2×Dic8616yes—
273C22×C4C2×C4×D4313yes—
274C22×C4C2×C4×D4316yes—
275C22×C4C2×D17213yes—
276C22×C4C2×D17213yes—
277C22×C4C22×Dic4316yes—
278C22×C4C2×C22⋊D4316yes—
279C22×C4C2×C22⋊D4313yes—
280C22×C4C2×C22⋊D4313yes—
281C22×C4C23×D4311yescharacteristic
282M16—224no—
283M16—24no—
284M16—438no—
285M16—8624no—
286M16—864no—
287M16C22×Dic4318yescomplemented
288C2×C8—224no—
289C2×C8—24no—
290C2×C8—8624no—
291C2×C8—864no—
292C4⋊C4—8612no—
293C4⋊C4—8612no—
294C4⋊C4—864no—
295C4⋊C4—864no—
296C23—26no—
297C23—26no—
298C23—26no—
299C23—26no—
300C23—216no—
301C23—216no—
302C23C43⋊#95112yes—
303C23C43⋊#9514yes—
304C23#1306324114yes—
305C23#1306324314yes—
306C23C2×C4×Dic4316yes—
307C23C2×(C2×D43)⋊C413yes—
308C23C2×(C2×D43)⋊C413yes—
309C23C2×Dic43⋊C416yes—
310C23C22×C4×D4311yescharacteristic
311C2×C4—868no—
312C2×C4—17224no—
313C2×C4—17224no—
314C2×C4—1728no—
315C2×C4C43⋊#95124yes—
316C2×C4C43⋊#95112yes—
317C2×C4C43⋊#95112yes—
318C2×C4C2×C4×Dic4316yes—
319C2×C4C2×(C2×D43)⋊C416yes—
320C2×C4C2×(C2×D43)⋊C416yes—
321C2×C4C2×(C2×D43)⋊C413yes—
322C2×C4C2×(C2×D43)⋊C413yes—
323C2×C4C2×C22⋊Dic4316yes—
324C2×C4C2×C22⋊Dic4316yes—
325C2×C4C2×Dic43⋊C416yes—
326C2×C4C2×Dic43⋊C416yes—
327C2×C4C2×Dic43⋊C416yes—
328C2×C4C2×C4⋊Dic4316yes—
329C2×C4C2×C4⋊Dic4316yes—
330C2×C4C22×C4×D4311yescharacteristic
331C2×C4C23×Dic4311yescharacteristic
332C2×C4C22×C22⋊D4311yescharacteristic
333C2×C4C22×C22⋊D4311yescharacteristic
334C2×C4C22×D17211yescharacteristic
335C2×C4C22×Dic8611yescharacteristic
336C8—28no—
337C8—868no—
338C22—224no—
339C22—212no—
340C22—212no—
341C22—23no—
342C22—21no—
343C22—23no—
344C22—21no—
345C22#14582667116yesdirect product factor
346C22C2×C43⋊#9516yes—
347C22C2×C43⋊#9516yes—
348C22C2×#1306324116yes—
349C22C2×#1306324316yes—
350C22C22×C4×Dic4311yescharacteristic
351C22C22×(C2×D43)⋊C411yescharacteristic
352C22C22×Dic43⋊C411yescharacteristic
353C4—1728no—
354C4C2×C43⋊#9516yes—
355C4C2×C43⋊#9516yes—
356C4C22×(C2×D43)⋊C411yescharacteristic
357C4C22×C22⋊Dic4311yescharacteristic
358C4C22×Dic43⋊C411yescharacteristic
359C4C22×C4⋊Dic4311yescharacteristic
360C2—21no—
361C2—21no—
362C2—26no—
363C2C2×#14582667112yesdirect product factor
364C2C22×C43⋊#9511yescharacteristic
365C2C22×#1306324111yescharacteristic
366C2C22×#1306324311yescharacteristic
subgroupG/H
centerC24(C2×D43)⋊C4
commutatorC22×C43C22×C42
FrattiniC22×C4C23×D43
FittingC23×M16×C43C2
socleC24×C43C22⋊C4
prime radicalC25×C43C2×C4
cosocleC22×C4×C43C24
hypercenterC23×M16D43
hypocenterC43C22×#343
LCSG ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C24×C4 ◁ C23×M16

Complements

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

NH ≅ G/Ntype
3. C2×#14582667C2direct (N × H)
8. C22×#10621877C4semidirect
17. #14582667C22direct (N × H)
21. C22×M16×C43C4semidirect
31. C2×#10621877C2×C4semidirect
58. C2×M16×C43C2×C4semidirect
100. M16×C43C22×C4semidirect
109. #10621877C22×C4semidirect
162. C22×C43#343semidirect
184. C2×C43C2×#343semidirect
196. C22×M16Dic43semidirect
207. C43C22×#343semidirect
231. C2×M16C2×Dic43semidirect
287. M16C22×Dic43semidirect
345. C22#14582667direct (N × H)
363. C2C2×#14582667direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#106218772
C23×C4⋊Dic432
C2×#145826672
C23×M16×C432
C22×#34343