Finite Group Databasebeta

← C2×#19142771 #25302972

Subgroups — C2×#19142771 #25302972

Order 11008.

1718 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142771C2116yesmaximal, direct product factor
2C2×C43⋊#401C212yesmaximal
3C2×#14582841C212yesmaximal
4C2×#14582840C212yesmaximal
5C2×#14582838C211yesmaximal, characteristic
6C2×#14582833C212yesmaximal
7C2×#14582829C211yesmaximal, characteristic
8C2×#14582818C212yesmaximal
9C2×#14582783C212yesmaximal
10C2×C43×#391C211yesmaximal, characteristic
11C22×C4⋊Dic43C2211yescharacteristic
12C22×C4⋊Dic43C2211yescharacteristic
13C22×Dic43⋊C4C2212yes—
14C22×Dic43⋊C4C2212yes—
15C22×Dic43⋊C4C2212yes—
16C22×Dic43⋊C4C2212yes—
17C43⋊#401C22116yes—
18#14582841C22116yes—
19#14582840C22116yes—
20#14582838C2218yes—
21#14582833C22116yes—
22#14582829C2218yes—
23#14582818C22116yes—
24#14582783C22116yes—
25C2×C43⋊#95C2212yes—
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2211yescharacteristic
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2211yescharacteristic
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2212yes—
35C23×Q8×C43C2211yescharacteristic
36C22×C4⋊C4×C43C2211yescharacteristic
37C22×C42×C43C2211yescharacteristic
38C43×#391C2218yes—
39C2×#95×C43C2212yes—
40C2×#95×C43C2212yes—
41C23×Dic43C2312yes—
42C23×Dic43C2312yes—
43C23×Dic43C2312yes—
44C23×Dic43C2312yes—
45C2×C4⋊Dic43—42no—
46C2×C4⋊Dic43—42no—
47C2×C4⋊Dic43C2314yes—
48C2×C4⋊Dic43C2314yes—
49C2×Dic43⋊C4—28no—
50C2×Dic43⋊C4—44no—
51C2×Dic43⋊C4—44no—
52C2×Dic43⋊C4—44no—
53C2×Dic43⋊C4C2318yes—
54C2×Dic43⋊C4C2318yes—
55C2×Dic43⋊C4C2318yes—
56C2×Dic43⋊C4C2318yes—
57C43⋊#95C2318yes—
58C43⋊#95C2318yes—
59C43⋊#95C2318yes—
60C43⋊#95C2318yes—
61C43⋊#95C2314yes—
62C43⋊#95C2318yes—
63C43⋊#95C2318yes—
64C43⋊#95C2314yes—
65C43⋊#95C2318yes—
66C43⋊#95C2318yes—
67C22×Q8×C43—24no—
68C22×Q8×C43—42no—
69C22×Q8×C43—42no—
70C22×Q8×C43C2314yes—
71C23×C4×C43C2312yes—
72C23×C4×C43C2311yescharacteristic
73C23×C4×C43C2311yescharacteristic
74C23×C4×C43C2312yes—
75C23×C4×C43C2311yescharacteristic
76C2×C4⋊C4×C43—42no—
77C2×C4⋊C4×C43C2314yes—
78C2×C42×C43—42no—
79C2×C42×C43C2314yes—
80#95×C43C2318yes—
81#95×C43C2318yes—
82C24×C43C2411yescharacteristic
83C2×Q8×C43—28no—
84C2×Q8×C43—44no—
85C2×Q8×C43—44no—
86C2×Q8×C43—416no—
87C22×C4×C43—24no—
88C22×C4×C43—22no—
89C22×C4×C43—22no—
90C22×C4×C43—24no—
91C22×C4×C43—22no—
92C22×C4×C43—22no—
93C22×C4×C43—24no—
94C22×C4×C43—24no—
95C22×C4×C43—24no—
96C22×C4×C43—24no—
97C22×C4×C43—24no—
98C22×C4×C43—24no—
99C22×C4×C43#4114yes—
100C22×C4×C43C2414yes—
101C22×C4×C43C2412yes—
102C22×C4×C43C2412yes—
103C22×C4×C43C2414yes—
104C22×C4×C43C2412yes—
105C22×Dic43—24no—
106C22×Dic43—24no—
107C22×Dic43—24no—
108C22×Dic43—24no—
109C22×Dic43—24no—
110C22×Dic43—24no—
111C22×Dic43—24no—
112C22×Dic43—24no—
113C22×Dic43—24no—
114C22×Dic43—24no—
115C22×Dic43—28no—
116C22×Dic43C2414yes—
117C22×Dic43C2414yes—
118C22×Dic43C2414yes—
119C22×Dic43C2414yes—
120C4⋊C4×C43—44no—
121C42×C43—44no—
122C4⋊Dic43—44no—
123C4⋊Dic43—44no—
124Dic43⋊C4—216no—
125Dic43⋊C4—48no—
126Dic43⋊C4—48no—
127Dic43⋊C4—48no—
128C23×C43C2×#4112yes—
129C23×C43H(5,𝔽2)12yes—
130C23×C43H(5,𝔽2)12yes—
131C23×C432−1+414yes—
132C23×C432−1+414yes—
133C23×C43C2511yescharacteristic
134Q8×C43—416no—
135C2×C4×C43—28no—
136C2×C4×C43—22no—
137C2×C4×C43—22no—
138C2×C4×C43—24no—
139C2×C4×C43—24no—
140C2×C4×C43—24no—
141C2×C4×C43—24no—
142C2×C4×C43—22no—
143C2×C4×C43—22no—
144C2×C4×C43—24no—
145C2×C4×C43—24no—
146C2×C4×C43—24no—
147C2×C4×C43—24no—
148C2×C4×C43—48no—
149C2×C4×C43—44no—
150C2×C4×C43—44no—
151C2×C4×C43—48no—
152C2×C4×C43C2×#4114yes—
153C2×Dic43—24no—
154C2×Dic43—24no—
155C2×Dic43—24no—
156C2×Dic43—24no—
157C2×Dic43—24no—
158C2×Dic43—24no—
159C2×Dic43—24no—
160C2×Dic43—24no—
161C2×Dic43—24no—
162C2×Dic43—24no—
163C2×Dic43—28no—
164C2×Dic43—48no—
165C2×Dic43—48no—
166C2×Dic43—48no—
167C2×Dic43—48no—
168C2×#2833—431nomaximal, Sylow
169C22×C43#53814yes—
170C22×C43#54118yes—
171C22×C43#56314yes—
172C22×C43#56314yes—
173C22×C43#56318yes—
174C22×C43C22×#4111yescharacteristic
175C22×C43C2×H(5,𝔽2)11yescharacteristic
176C22×C43C2×H(5,𝔽2)11yescharacteristic
177C22×C43C2×2−1+412yes—
178C22×C43C2×2−1+412yes—
179C4×C43—24no—
180C4×C43—44no—
181C4×C43—42no—
182C4×C43—42no—
183C4×C43—44no—
184Dic43—44no—
185Dic43—44no—
186Dic43—44no—
187Dic43—44no—
188#2833—4316no—
189C2×#401—432no—
190C2×#400—432no—
191C2×#400—432no—
192C2×#400—431no—
193C2×#398—432no—
194C2×#398—431no—
195C2×#395—432no—
196C2×#391D4311yescharacteristic
197C2×#387—432no—
198C2×C43#283318yescomplemented
199C2×C43C2×#53811yescharacteristic
200C2×C43C2×#54112yes—
201C2×C43C2×#56311yescharacteristic
202C2×C43C2×#56311yescharacteristic
203C2×C43C2×#56312yes—
204C23×Q8C2×D4311yescharacteristic
205C22×C4⋊C4—432no—
206C22×C4⋊C4—432no—
207C22×C4⋊C4—432no—
208C22×C4⋊C4—432no—
209C22×C4⋊C4—431no—
210C22×C4⋊C4—431no—
211C22×C4⋊C4C2×D4311yescharacteristic
212C22×C42C2×D4311yescharacteristic
213#401—4316no—
214#400—438no—
215#400—4316no—
216#400—4316no—
217#398—438no—
218#398—4316no—
219#395—4316no—
220#391C2×D4318yes—
221#387—4316no—
222C2×#95—432no—
223C2×#95—432no—
224C2×#95—432no—
225C2×#95—432no—
226C2×#95—432no—
227C2×#95—432no—
228C2×#95—431no—
229C2×#95—431no—
230C2×#95—432no—
231C2×#95—432no—
232C2×#95C2×D4312yes—
233C2×#95C2×D4312yes—
234C43C2×#283311yescharacteristic, complemented, Sylow
235C22×Q8—24no—
236C22×Q8—42no—
237C22×Q8—42no—
238C22×Q8C22×D4314yes—
239C23×C4—432no—
240C23×C4—432no—
241C23×C4—432no—
242C23×C4—432no—
243C23×C4C22×D4312yes—
244C23×C4C22×D4311yescharacteristic
245C23×C4C22×D4311yescharacteristic
246C23×C4C22×D4312yes—
247C23×C4C22×D4311yescharacteristic
248C2×C4⋊C4—42no—
249C2×C4⋊C4—438no—
250C2×C4⋊C4—438no—
251C2×C4⋊C4—438no—
252C2×C4⋊C4—438no—
253C2×C4⋊C4—434no—
254C2×C4⋊C4—434no—
255C2×C4⋊C4—868no—
256C2×C4⋊C4—1724no—
257C2×C4⋊C4—1724no—
258C2×C4⋊C4—1724no—
259C2×C4⋊C4—1722no—
260C2×C4⋊C4—1722no—
261C2×C4⋊C4C22×D4314yes—
262C2×C42—42no—
263C2×C42C22×D4314yes—
264#95—438no—
265#95—438no—
266#95—438no—
267#95—438no—
268#95—438no—
269#95—438no—
270#95—438no—
271#95—438no—
272#95—434no—
273#95—434no—
274#95C22×D4318yes—
275#95C22×D4318yes—
276C24C23×D4311yescharacteristic
277C2×Q8—28no—
278C2×Q8—44no—
279C2×Q8—44no—
280C2×Q8—416no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—24no—
284C22×C4—24no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—24no—
288C22×C4—24no—
289C22×C4—24no—
290C22×C4—24no—
291C22×C4—24no—
292C22×C4—24no—
293C22×C4—434no—
294C22×C4—434no—
295C22×C4—434no—
296C22×C4—434no—
297C22×C4—864no—
298C22×C4—864no—
299C22×C4—864no—
300C22×C4—864no—
301C22×C4—864no—
302C22×C4—864no—
303C22×C4—864no—
304C22×C4—864no—
305C22×C4—868no—
306C22×C4—864no—
307C22×C4—864no—
308C22×C4#1062189814yes—
309C22×C4C23×D4314yes—
310C22×C4C23×D4312yes—
311C22×C4C23×D4312yes—
312C22×C4C23×D4314yes—
313C22×C4C23×D4312yes—
314C4⋊C4—44no—
315C4⋊C4—8616no—
316C4⋊C4—1728no—
317C4⋊C4—1728no—
318C4⋊C4—1728no—
319C4⋊C4—1724no—
320C4⋊C4—1724no—
321C42—44no—
322C23C2×#1062189812yes—
323C23#1306337012yes—
324C23#1306337012yes—
325C23#1306337214yes—
326C23#1306337314yes—
327C23C24×D4311yescharacteristic
328Q8—416no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—28no—
332C2×C4—24no—
333C2×C4—24no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—24no—
337C2×C4—24no—
338C2×C4—24no—
339C2×C4—24no—
340C2×C4—24no—
341C2×C4—24no—
342C2×C4—44no—
343C2×C4—44no—
344C2×C4—48no—
345C2×C4—48no—
346C2×C4—864no—
347C2×C4—864no—
348C2×C4—864no—
349C2×C4—864no—
350C2×C4—864no—
351C2×C4—864no—
352C2×C4—864no—
353C2×C4—864no—
354C2×C4—868no—
355C2×C4—864no—
356C2×C4—864no—
357C2×C4—1728no—
358C2×C4—1728no—
359C2×C4—1728no—
360C2×C4—1728no—
361C2×C4C2×#1062189814yes—
362C22#1458348714yes—
363C22#1458350718yes—
364C22#1458364814yes—
365C22#1458364914yes—
366C22#1458365018yes—
367C22C22×#1062189811yescharacteristic
368C22C2×#1306337011yescharacteristic
369C22C2×#1306337011yescharacteristic
370C22C2×#1306337212yes—
371C22C2×#1306337312yes—
372C4—24no—
373C4—44no—
374C4—42no—
375C4—42no—
376C4—44no—
377C4—1724no—
378C4—1724no—
379C4—1724no—
380C4—1724no—
381C2#1914277118yesdirect product factor
382C2C2×#1458348711yescharacteristic
383C2C2×#1458350712yes—
384C2C2×#1458364811yescharacteristic
385C2C2×#1458364911yescharacteristic
386C2C2×#1458365012yes—
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×#391C2
socle, prime radicalC24×C43C24
hypercenterC2×#391D43
hypocenterC43C2×#2833
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
1. #19142771C2direct (N × H)
198. C2×C43#2833semidirect
234. C43C2×#2833semidirect
381. C2#19142771direct (N × H)

Maximal subgroups

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

subgroupindex
#191427712
C2×C43⋊#4012
C2×#145828412
C2×#145828402
C2×#145828382
C2×#145828332
C2×#145828292
C2×#145828182
C2×#145827832
C2×C43×#3912
C2×#283343