Finite Group Databasebeta

← C2×#19134809 #25097405

Subgroups — C2×#19134809 #25097405

Order 11008.

1402 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
1C2×#14583377C211yesmaximal, characteristic
2C2×#14582939C212yesmaximal
3C22×#13063244C211yesmaximal, characteristic
4#19134809C218yesmaximal, direct product factor
5C2×#14582659C212yesmaximal
6C2×C43×#391C211yesmaximal, characteristic
7C22×#10621877C2212yes—
8#14583377—24no—
9#14583377—22no—
10#14583377C2214yes—
11C2×Q8×Dic43—22no—
12C2×Q8×Dic43—22no—
13C2×#13063284—22no—
14C2×#13063284C2212yes—
15#14582939—24no—
16#14582939C2218yes—
17C2×#13063258—22no—
18C2×#13063256—22no—
19C2×#13063244C418yescomplemented
20C2×#13063244C2214yes—
21#14582659C2218yes—
22C23×Q8×C43C2211yescharacteristic
23C22×C4⋊C4×C43C2211yescharacteristic
24C22×C42×C43C2211yescharacteristic
25C43×#391—22no—
26C43×#391C2214yes—
27C2×#95×C43—22no—
28C2×#10621877—22no—
29C2×#10621877—24no—
30C2×#10621877C2×C418yes—
31C2×#10621877C2314yes—
32C22×C43⋊C8—22no—
33Q8×Dic43—28no—
34Q8×Dic43—28no—
35Q8×Dic43—28no—
36Q8×Dic43—28no—
37#13063284—28no—
38#13063284—28no—
39#13063284—22no—
40#13063284—22no—
41#13063284D414yes—
42#13063284C2314yes—
43C2×C4⋊Dic43—22no—
44C2×C4⋊Dic43—22no—
45C2×C4⋊Dic43D412yes—
46C2×C4⋊Dic43D412yes—
47C2×C22⋊Dic43—22no—
48C2×C4×Dic43—24no—
49C2×C4×Dic43—22no—
50#13063258—28no—
51#13063256—28no—
52#13063244C2×C4116yescomplemented
53C22×Q8×C43—22no—
54C22×Q8×C43—22no—
55C22×Q8×C43—24no—
56C22×Q8×C43C2×C414yes—
57C22×Q8×C43D412yes—
58C22×Q8×C43Q814yes—
59C22×Q8×C43C2312yes—
60C23×C4×C43—21no—
61C23×C4×C43—21no—
62C23×C4×C43D412yes—
63C23×C4×C43C2311yescharacteristic
64C2×C4⋊C4×C43—22no—
65C2×C4⋊C4×C43—22no—
66C2×C4⋊C4×C43—21no—
67C2×C4⋊C4×C43C2312yes—
68C2×C42×C43—24no—
69C2×C42×C43—21no—
70C2×C42×C43C2312yes—
71#95×C43—28no—
72C24×C43C2×D411yescharacteristic
73C2×Q8×C43—28no—
74C2×Q8×C43—28no—
75C2×Q8×C43—24no—
76C2×Q8×C43—28no—
77C2×Q8×C43—28no—
78C2×Q8×C43—24no—
79C2×Q8×C43—24no—
80C2×Q8×C43—24no—
81C2×Q8×C43C4⋊C418yes—
82C2×Q8×C43C22×C414yes—
83C2×Q8×C43C2×Q814yes—
84C22×C4×C43—24no—
85C22×C4×C43—22no—
86C22×C4×C43—22no—
87C22×C4×C43—24no—
88C22×C4×C43—22no—
89C22×C4×C43—22no—
90C22×C4×C43—42no—
91C22×C4×C43—44no—
92C22×C4×C43—41no—
93C22×C4×C43—41no—
94C22×C4×C43—42no—
95C22×C4×C43C4⋊C418yes—
96C22×C4×C43C22×C412yes—
97C22×C4×C43C2×D412yes—
98C22×C4×C43C2×D412yes—
99C22×C4×C43C2×D414yes—
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43C2×Q812yes—
102C22×C4×C43#4114yes—
103C22×C4×C43C2411yescharacteristic
104C22×Dic43—22no—
105C22×Dic43—22no—
106C4⋊C4×C43—24no—
107C4⋊C4×C43—42no—
108C42×C43—24no—
109C42×C43—42no—
110C22⋊Dic43—24no—
111C22⋊Dic43—24no—
112C4⋊Dic43—28no—
113C4⋊Dic43—28no—
114C4⋊Dic43—22no—
115C4⋊Dic43—22no—
116C4⋊Dic43C2×D414yes—
117C4⋊Dic43C2×D414yes—
118C4×Dic43—216no—
119C4×Dic43—24no—
120C4×Dic43—24no—
121#10621877—28no—
122#10621877—24no—
123#10621877C22×C418yes—
124C2×C43⋊C8—28no—
125C2×C43⋊C8—24no—
126C23×C43—22no—
127C23×C43—22no—
128C23×C43C2×C4⋊C412yes—
129C23×C43#12011yescharacteristic
130C23×C43#12011yescharacteristic
131C23×C43#12312yes—
132C23×C43C22×D411yescharacteristic
133Q8×C43—28no—
134Q8×C43—28no—
135Q8×C43—216no—
136C2×C4×C43—24no—
137C2×C4×C43—24no—
138C2×C4×C43—28no—
139C2×C4×C43—28no—
140C2×C4×C43—24no—
141C2×C4×C43—48no—
142C2×C4×C43—42no—
143C2×C4×C43—42no—
144C2×C4×C43—44no—
145C2×C4×C43—42no—
146C2×C4×C43—82no—
147C2×C4×C43—82no—
148C2×C4×C43C2×C4⋊C418yes—
149C2×C4×C43C2×C4⋊C412yes—
150C2×C4×C43C4×D414yes—
151C2×C4×C43C4×D414yes—
152C2×C4×C43#12012yes—
153C2×C4×C43C22⋊Q814yes—
154C2×C4×C43C22⋊Q814yes—
155C2×C4×C43#12312yes—
156C2×C4×C43C23×C411yescharacteristic
157C2×C4×C43C22×D412yes—
158C2×C4×C43C22×Q811yescharacteristic
159C2×C4×C43C2×#4112yes—
160C2×Dic43—24no—
161C2×Dic43—24no—
162C2×Dic43—44no—
163C2×Dic43—44no—
164C43⋊C8—28no—
165C2×#1857—431nomaximal, Sylow
166C22×C43—24no—
167C22×C43—24no—
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—21no—
172C22×C43#38512yes—
173C22×C43#38512yes—
174C22×C43#45412yes—
175C22×C43#45612yes—
176C22×C43C22×C4⋊C411yescharacteristic
177C22×C43C2×#12011yescharacteristic
178C22×C43C2×#12311yescharacteristic
179C4×C43—28no—
180C4×C43—44no—
181C4×C43—82no—
182C4×C43#38514yes—
183C4×C43C2×C4×D412yes—
184C4×C43C2×C22⋊Q812yes—
185Dic43—44no—
186Dic43—44no—
187C2×#519—431no—
188C2×#428—432no—
189C22×#101—431no—
190C2×#391D4311yescharacteristic
191#1857—438no—
192C2×#339—432no—
193C2×C43—21no—
194C2×C43—21no—
195C2×C43—22no—
196C2×C43#185714yescomplemented
197C2×C43C2×#38511yescharacteristic
198C2×C43C2×#45411yescharacteristic
199C2×C43C2×#45611yescharacteristic
200C23×Q8C2×D4311yescharacteristic
201C22×M16—432no—
202#519—434no—
203#519—864no—
204#519—862no—
205C2×C4×Q8—862no—
206C2×C4×Q8—862no—
207C2×#117—432no—
208C2×#117—862no—
209C22×C4⋊C4C2×D4311yescharacteristic
210C22×C42C2×D4311yescharacteristic
211#428—438no—
212#428—864no—
213C2×#107—862no—
214C2×#106—862no—
215C2×#101—434no—
216C2×#101—438no—
217#391—22no—
218#391C2×D4314yes—
219C2×#95—22no—
220#339—438no—
221C43C2×#185711yescharacteristic, complemented, Sylow
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8—24no—
225C22×Q8Dic8614yes—
226C22×Q8C4×D4314yes—
227C22×Q8C22⋊D4312yes—
228C22×Q8C22×D4312yes—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4C22⋊D4312yes—
232C23×C4C22×D4311yescharacteristic
233C2×M16—438no—
234C2×M16—434no—
235C2×M16—862no—
236C2×M16—864no—
237C22×C8—862no—
238C4×Q8—868no—
239C4×Q8—868no—
240C4×Q8—868no—
241C4×Q8—868no—
242#117—434no—
243#117—434no—
244#117—868no—
245#117—862no—
246#117—862no—
247#117—868no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—432no—
252C2×C4⋊C4—432no—
253C2×C4⋊C4—862no—
254C2×C4⋊C4—862no—
255C2×C4⋊C4C22×D4312yes—
256C2×C22⋊C4—862no—
257C2×C42—24no—
258C2×C42—21no—
259C2×C42—864no—
260C2×C42—862no—
261C2×C42C22×D4312yes—
262#107—868no—
263#106—868no—
264#101—4316no—
265#95—28no—
266C24C2×C22⋊D4311yescharacteristic
267C2×Q8—28no—
268C2×Q8—28no—
269C2×Q8—24no—
270C2×Q8—28no—
271C2×Q8—28no—
272C2×Q8—24no—
273C2×Q8—24no—
274C2×Q8—24no—
275C2×Q8Dic43⋊C418yes—
276C2×Q8C2×Dic8614yes—
277C2×Q8C2×C4×D4314yes—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—24no—
281C22×C4—24no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—44no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—862no—
290C22×C4—862no—
291C22×C4Dic43⋊C418yes—
292C22×C4C2×Dic8612yes—
293C22×C4C2×C4×D4312yes—
294C22×C4D4×D4312yes—
295C22×C4D4×D4312yes—
296C22×C4#1062190014yes—
297C22×C4C2×C22⋊D4314yes—
298C22×C4C2×C22⋊D4311yescharacteristic
299C22×C4C23×D4311yescharacteristic
300M16—438no—
301M16—868no—
302M16—864no—
303C2×C8—868no—
304C2×C8—864no—
305C4⋊C4—24no—
306C4⋊C4—42no—
307C4⋊C4—434no—
308C4⋊C4—434no—
309C4⋊C4—868no—
310C4⋊C4—868no—
311C4⋊C4—862no—
312C4⋊C4—862no—
313C22⋊C4—864no—
314C22⋊C4—864no—
315C42—24no—
316C42—42no—
317C42—8616no—
318C42—864no—
319C42—864no—
320C23—22no—
321C23—22no—
322C23C2×Dic43⋊C412yes—
323C23#1306329311yescharacteristic
324C23#1306329311yescharacteristic
325C23#1306330612yes—
326C23C22×C22⋊D4311yescharacteristic
327Q8—28no—
328Q8—28no—
329Q8—216no—
330C2×C4—24no—
331C2×C4—24no—
332C2×C4—28no—
333C2×C4—28no—
334C2×C4—24no—
335C2×C4—48no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—44no—
339C2×C4—42no—
340C2×C4—82no—
341C2×C4—82no—
342C2×C4—864no—
343C2×C4—864no—
344C2×C4—1724no—
345C2×C4—1724no—
346C2×C4C2×Dic43⋊C418yes—
347C2×C4C2×Dic43⋊C412yes—
348C2×C4(C22⋊D43)⋊C414yes—
349C2×C4(C22⋊D43)⋊C414yes—
350C2×C4#1306329312yes—
351C2×C4#1306330214yes—
352C2×C4#1306330214yes—
353C2×C4#1306330612yes—
354C2×C4C22×C4×D4311yescharacteristic
355C2×C4C2×D4×D4312yes—
356C2×C4C22×Dic8611yescharacteristic
357C2×C4C2×#1062190012yes—
358C8—868no—
359C22—21no—
360C22—21no—
361C22—24no—
362C22—24no—
363C22—21no—
364C22—21no—
365C22#1458277112yes—
366C22#1458277112yes—
367C22#1458307112yes—
368C22#1458308112yes—
369C22C22×Dic43⋊C411yescharacteristic
370C22C2×#1306329311yescharacteristic
371C22C2×#1306330611yescharacteristic
372C4—28no—
373C4—44no—
374C4—82no—
375C4—1724no—
376C4—1724no—
377C4#1458277114yes—
378C4C2×(C22⋊D43)⋊C412yes—
379C4C2×#1306330212yes—
380C2—21no—
381C2—21no—
382C2—22no—
383C2#1913480914yesdirect product factor
384C2C2×#1458277111yescharacteristic
385C2C2×#1458307111yescharacteristic
386C2C2×#1458308111yescharacteristic
subgroupG/H
centerC23#13063293
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#391C2
socleC23×C43#120
prime radicalC24×C43C2×D4
cosocleC22×C4×C43C24
hypercenterC2×#391D43
hypocenterC43C2×#1857
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
4. #19134809C2direct (N × H)
19. C2×#13063244C4semidirect
52. #13063244C2×C4semidirect
196. C2×C43#1857semidirect
221. C43C2×#1857semidirect
383. C2#19134809direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145833772
C2×#145829392
C22×#130632442
#191348092
C2×#145826592
C2×C43×#3912
C2×#185743