Finite Group Databasebeta

← C2×#19140426 #25263665

Subgroups — C2×#19140426 #25263665

Order 11008.

2614 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063282C211yesmaximal, characteristic
2#19140426C2116yesmaximal, direct product factor
3C2×#14582832C214yesmaximal, complemented
4C2×#14582821C214yesmaximal
5C2×#14582795C212yesmaximal, complemented
6C2×#14582769C211yesmaximal, characteristic, complemented
7C2×#14582756C212yesmaximal
8C22×#125×C43C211yesmaximal, characteristic, complemented
9C23×C4×D43C2211yescharacteristic
10C2×#13063282—28no—
11C2×#13063282C2218yes—
12C22×C4⋊Dic43C2212yes—
13C22×C4⋊Dic43C2214yes—
14C22×Dic43⋊C4C2212yes—
15C22×Dic43⋊C4C2214yes—
16C22×(C2×D43)⋊C4C2212yes—
17C22×(C2×D43)⋊C4C2214yes—
18C22×C4×Dic43C2211yescharacteristic
19#14582832C22132yescomplemented
20#14582821C22132yes—
21#14582795C22116yescomplemented
22#14582769C2218yescomplemented
23#14582756C22116yes—
24C2×C43⋊#95C2214yes—
25C2×C43⋊#95C2214yes—
26C2×#125×C43—28no—
27C2×#125×C43C2218yescomplemented
28C22×C4⋊C4×C43C2212yes—
29C22×C4⋊C4×C43C2214yes—
30C22×C42×C43C2211yescharacteristic
31C24×D43C2311yescharacteristic
32C23×Dic43C2312yes—
33C23×Dic43C2314yes—
34C23×Dic43C2311yescharacteristic
35C22×C4×D43—24no—
36C22×C4×D43—24no—
37C22×C4×D43Q818yes—
38C22×C4×D43C2314yes—
39#13063282—232no—
40C2×C4⋊Dic43—28no—
41C2×C4⋊Dic43—48no—
42C2×C4⋊Dic43C2318yes—
43C2×C4⋊Dic43C23116yes—
44C2×Dic43⋊C4—28no—
45C2×Dic43⋊C4—48no—
46C2×Dic43⋊C4C2318yes—
47C2×Dic43⋊C4C23116yes—
48C2×(C2×D43)⋊C4—28no—
49C2×(C2×D43)⋊C4—48no—
50C2×(C2×D43)⋊C4C2318yes—
51C2×(C2×D43)⋊C4C23116yes—
52C2×C4×Dic43—24no—
53C2×C4×Dic43C2314yes—
54C43⋊#95C23116yes—
55C43⋊#95C23116yes—
56C23×C4×C43C2314yes—
57C23×C4×C43C2312yes—
58C23×C4×C43C2311yescharacteristic
59#125×C43—232no—
60C2×C4⋊C4×C43—216no—
61C2×C4⋊C4×C43—28no—
62C2×C4⋊C4×C43C2318yes—
63C2×C4⋊C4×C43C23116yes—
64C2×C42×C43D418yes—
65C2×C42×C43C2314yes—
66C24×C43C2411yescharacteristic
67C23×D43—22no—
68C23×D43—22no—
69C23×D43—24no—
70C23×D43—24no—
71C23×D43C2×Q814yes—
72C23×D43C2412yes—
73C22×C4×C43—28no—
74C22×C4×C43—24no—
75C22×C4×C43—28no—
76C22×C4×C43—24no—
77C22×C4×C43—28no—
78C22×C4×C43C2×D418yes—
79C22×C4×C43C2×D414yes—
80C22×C4×C43C2×Q814yes—
81C22×C4×C43#4114yes—
82C22×C4×C43C2418yes—
83C22×C4×C43C2414yes—
84C22×C4×C43C2412yes—
85C22×Dic43—22no—
86C22×Dic43—24no—
87C22×Dic43—22no—
88C22×Dic43—28no—
89C22×Dic43—28no—
90C22×Dic43—24no—
91C22×Dic43—28no—
92C22×Dic43—24no—
93C22×Dic43C2×Q814yes—
94C22×Dic43C2414yes—
95C22×Dic43C2418yes—
96C22×Dic43C2412yes—
97C2×C4×D43—232no—
98C2×C4×D43—28no—
99C2×C4×D43—28no—
100C2×C4×D43C2×Q8116yes—
101C4⋊C4×C43—232no—
102C4⋊C4×C43—216no—
103C42×C43C2×D4116yes—
104(C2×D43)⋊C4—216no—
105(C2×D43)⋊C4—416no—
106C4⋊Dic43—216no—
107C4⋊Dic43—416no—
108Dic43⋊C4—216no—
109Dic43⋊C4—416no—
110C4×Dic43—28no—
111C23×C43C22×D412yes—
112C23×C43C22×Q812yes—
113C23×C43C2×#4112yes—
114C23×C43H(5,𝔽2)14yes—
115C23×C432−1+414yes—
116C23×C43C2511yescharacteristic
117C22×D43—28no—
118C22×D43—216no—
119C22×D43—22no—
120C22×D43—22no—
121C22×D43—24no—
122C22×D43—24no—
123C22×D43—48no—
124C22×D43—44no—
125C22×D43—44no—
126C22×D43C22×Q814yes—
127C2×C4×C43—216no—
128C2×C4×C43—24no—
129C2×C4×C43—24no—
130C2×C4×C43—28no—
131C2×C4×C43—28no—
132C2×C4×C43—28no—
133C2×C4×C43—416no—
134C2×C4×C43C22⋊Q8116yes—
135C2×C4×C43C22×D418yes—
136C2×C4×C43C22×D414yes—
137C2×C4×C43C22×Q814yes—
138C2×C4×C43C2×#4114yes—
139C2×Dic43—28no—
140C2×Dic43—22no—
141C2×Dic43—22no—
142C2×Dic43—24no—
143C2×Dic43—28no—
144C2×Dic43—24no—
145C2×Dic43—28no—
146C2×Dic43—28no—
147C2×Dic43—24no—
148C2×Dic43—48no—
149C2×Dic43—416no—
150C2×Dic43C22×Q814yes—
151C4×D43—232no—
152C2×#2629—431nomaximal, Sylow
153C22×C43C2×C22⋊Q814yes—
154C22×C43#53718yes—
155C22×C43#54014yes—
156C22×C43#54114yes—
157C22×C43#54418yes—
158C22×C43C23×D411yescharacteristic
159C22×C43C23×Q811yescharacteristic
160C22×C43C22×#4111yescharacteristic
161C22×C43C2×H(5,𝔽2)12yes—
162C22×C43C2×2−1+412yes—
163C2×D43—24no—
164C2×D43—28no—
165C2×D43—416no—
166C2×D43—44no—
167C2×D43—42no—
168C2×D43—42no—
169C4×C43—28no—
170C4×C43—48no—
171C4×C43C2×C22⋊Q818yes—
172Dic43—24no—
173Dic43—44no—
174Dic43—48no—
175C22×#125D4311yescharacteristic, complemented
176C22×#117—431no—
177#2629—4316no—
178C2×#398—434no—
179C2×#396—434no—
180C2×#389—432no—
181C2×#384—431no—
182C2×#380—432no—
183C2×C43#262918yescomplemented
184C2×C43C22×C22⋊Q811yescharacteristic
185C2×C43C2×#53712yes—
186C2×C43C2×#54011yescharacteristic
187C2×C43C2×#54111yescharacteristic
188C2×C43C2×#54412yes—
189D43—44no—
190C24×C4—431no—
191C2×#125—28no—
192C2×#125C2×D4318yescomplemented
193C2×#117—438no—
194C2×#117—868no—
195C22×C4⋊C4—432no—
196C22×C4⋊C4—432no—
197C22×C4⋊C4—434no—
198C22×C4⋊C4—434no—
199C22×C4⋊C4C2×D4314yes—
200C22×C4⋊C4C2×D4312yes—
201C22×C22⋊C4—432no—
202C22×C22⋊C4—434no—
203C22×C42—431no—
204C22×C42C2×D4311yescharacteristic
205#398—4332no—
206#396—4332no—
207#389—4316no—
208#384—438no—
209#380—4316no—
210C2×#95—434no—
211C2×#95—434no—
212C43C2×#262911yescharacteristic, complemented, Sylow
213C25—431no—
214C23×C4—431no—
215C23×C4—438no—
216C23×C4—434no—
217C23×C4—434no—
218C23×C4—432no—
219C23×C4—864no—
220C23×C4—864no—
221C23×C4C22×D4314yes—
222C23×C4C22×D4312yes—
223C23×C4C22×D4311yescharacteristic
224#125—232no—
225#117—8632no—
226C2×C4⋊C4—216no—
227C2×C4⋊C4—28no—
228C2×C4⋊C4—438no—
229C2×C4⋊C4—438no—
230C2×C4⋊C4—4316no—
231C2×C4⋊C4—4316no—
232C2×C4⋊C4—868no—
233C2×C4⋊C4—868no—
234C2×C4⋊C4—1728no—
235C2×C4⋊C4—1728no—
236C2×C4⋊C4C22×D4318yes—
237C2×C4⋊C4C22×D43116yes—
238C2×C22⋊C4—438no—
239C2×C22⋊C4—4316no—
240C2×C22⋊C4—868no—
241C2×C22⋊C4—1728no—
242C2×C42—434no—
243C2×C42—864no—
244C2×C42C22⋊D4318yes—
245C2×C42C22×D4314yes—
246#95—4316no—
247#95—4316no—
248C24—434no—
249C24—432no—
250C24—862no—
251C24—862no—
252C24—864no—
253C24—864no—
254C24C23×D4311yescharacteristic
255C22×C4—24no—
256C22×C4—24no—
257C22×C4—28no—
258C22×C4—28no—
259C22×C4—28no—
260C22×C4—434no—
261C22×C4—432no—
262C22×C4—4316no—
263C22×C4—434no—
264C22×C4—438no—
265C22×C4—862no—
266C22×C4—862no—
267C22×C4—8632no—
268C22×C4—868no—
269C22×C4—868no—
270C22×C4—864no—
271C22×C4—868no—
272C22×C4—868no—
273C22×C4—864no—
274C22×C4—868no—
275C22×C4—864no—
276C22×C4Q8×D4314yes—
277C22×C4#1062190214yes—
278C22×C4C2×C22⋊D4318yes—
279C22×C4C2×C22⋊D4314yes—
280C22×C4C23×D4318yes—
281C22×C4C23×D4314yes—
282C22×C4C23×D4312yes—
283C4⋊C4—232no—
284C4⋊C4—216no—
285C4⋊C4—8616no—
286C4⋊C4—8616no—
287C4⋊C4—17216no—
288C4⋊C4—17216no—
289C22⋊C4—8616no—
290C22⋊C4—17216no—
291C42—868no—
292C42C2×C22⋊D43116yes—
293C23—434no—
294C23—868no—
295C23—862no—
296C23—862no—
297C23—864no—
298C23—864no—
299C23—8616no—
300C23—1728no—
301C23—1724no—
302C23—1724no—
303C23C22×C22⋊D4312yes—
304C23C2×Q8×D4312yes—
305C23C2×#1062190212yes—
306C23#1306337114yes—
307C23#1306337214yes—
308C23C24×D4311yescharacteristic
309C2×C4—24no—
310C2×C4—24no—
311C2×C4—216no—
312C2×C4—28no—
313C2×C4—28no—
314C2×C4—28no—
315C2×C4—416no—
316C2×C4—434no—
317C2×C4—868no—
318C2×C4—862no—
319C2×C4—862no—
320C2×C4—8632no—
321C2×C4—864no—
322C2×C4—868no—
323C2×C4—868no—
324C2×C4—864no—
325C2×C4—868no—
326C2×C4—864no—
327C2×C4—1728no—
328C2×C4—17216no—
329C2×C4#13063301116yes—
330C2×C4C22×C22⋊D4318yes—
331C2×C4C22×C22⋊D4314yes—
332C2×C4C2×Q8×D4314yes—
333C2×C4C2×#1062190214yes—
334C22—864no—
335C22—868no—
336C22—17216no—
337C22—1724no—
338C22—1722no—
339C22—1722no—
340C22C2×#1306330114yes—
341C22#1458347718yes—
342C22#1458350514yes—
343C22#1458351214yes—
344C22#1458352918yes—
345C22C23×C22⋊D4311yescharacteristic
346C22C22×Q8×D4311yescharacteristic
347C22C22×#1062190211yescharacteristic
348C22C2×#1306337112yes—
349C22C2×#1306337212yes—
350C4—28no—
351C4—48no—
352C4—864no—
353C4—1724no—
354C4—1728no—
355C4C2×#1306330118yes—
356C2—1724no—
357C2#1914042618yesdirect product factor
358C2C22×#1306330111yescharacteristic
359C2C2×#1458347712yes—
360C2C2×#1458350511yescharacteristic
361C2C2×#1458351211yescharacteristic
362C2C2×#1458352912yes—
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC22×#125×C43C2
socleC24×C43C24
prime radicalC24×D43C23
hypercenterC22×#125D43
hypocenterC43C2×#2629
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
2. #19140426C2direct (N × H)
3. C2×#14582832C2semidirect
5. C2×#14582795C2semidirect
6. C2×#14582769C2semidirect
8. C22×#125×C43C2semidirect
19. #14582832C22semidirect
21. #14582795C22semidirect
22. #14582769C22semidirect
27. C2×#125×C43C22semidirect
175. C22×#125D43semidirect
183. C2×C43#2629semidirect
192. C2×#125C2×D43semidirect
212. C43C2×#2629semidirect
357. C2#19140426direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130632822
#191404262
C2×#145828322
C2×#145828212
C2×#145827952
C2×#145827692
C2×#145827562
C22×#125×C432
C2×#262943