Finite Group Databasebeta

← C2×#19134116 #25079130

Subgroups — C2×#19134116 #25079130

Order 11008.

694 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583302C211yesmaximal, characteristic, complemented
2C2×#14583189C211yesmaximal, characteristic
3C2×#14582977C211yesmaximal, characteristic
4#19134116C218yesmaximal, direct product factor
5C2×#14582649C211yesmaximal, characteristic, complemented
6C2×#14582648C211yesmaximal, characteristic, complemented
7C2×#14582647C211yesmaximal, characteristic, complemented
8C2×C43×#476C211yesmaximal, characteristic
9C22×#10621877—21no—
10C2×#13063325C2211yescharacteristic
11#14583302—22no—
12#14583302C2214yescomplemented
13#14583189—22no—
14#14583189C2214yes—
15#14582977—22no—
16#14582977C2214yes—
17C2×#13063258—21no—
18C2×#13063258—21no—
19C2×#13063256—21no—
20C2×C4⋊(C43⋊C8)C2211yescharacteristic
21C2×C4⋊(C43⋊C8)C2211yescharacteristic
22C2×#13063246—21no—
23C2×C22⋊(C43⋊C8)—21no—
24C2×C4×C43⋊C8C2211yescharacteristic
25#14582649C2214yescomplemented
26#14582648C2214yescomplemented
27#14582647C2214yescomplemented
28C2×C4⋊Q8×C43C2211yescharacteristic
29C2×C4×D4×C43C2211yescharacteristic
30C43×#476—22no—
31C43×#476C2214yes—
32C2×#106×C43—21no—
33C2×C4⋊C8×C43C2211yescharacteristic
34C2×#102×C43—21no—
35C22×Dic86—21no—
36C2×#10621877—24no—
37C2×#10621877—44no—
38C22×C43⋊C8—21no—
39C22×C43⋊C8—21no—
40C22×C43⋊C8D411yescharacteristic
41C22×C43⋊C8D411yescharacteristic
42#13063325—21no—
43#13063325—21no—
44#13063325—21no—
45#13063325C2312yes—
46C2×C4⋊Dic43—21no—
47C2×C4⋊Dic43—21no—
48#13063258—24no—
49#13063258—24no—
50#13063256—24no—
51C4⋊(C43⋊C8)—21no—
52C4⋊(C43⋊C8)—21no—
53C4⋊(C43⋊C8)C2312yes—
54C4⋊(C43⋊C8)C2312yes—
55#13063246—24no—
56C22⋊(C43⋊C8)—24no—
57C4×C43⋊C8D412yes—
58C4×C43⋊C8C2312yes—
59C22×Q8×C43—21no—
60C22×D4×C43D411yescharacteristic
61C23×C4×C43—21no—
62C22×C8×C43—21no—
63C4⋊Q8×C43—21no—
64C4⋊Q8×C43—21no—
65C4⋊Q8×C43—21no—
66C4⋊Q8×C43C2312yes—
67C4×D4×C43—21no—
68C4×D4×C43—21no—
69C4×D4×C43D412yes—
70C4×D4×C43C2312yes—
71C2×C4⋊C4×C43—21no—
72C2×C4⋊C4×C43—21no—
73C2×C4⋊C4×C43D411yescharacteristic
74C2×C22⋊C4×C43—21no—
75C2×C42×C43C2311yescharacteristic
76#106×C43—24no—
77C4⋊C8×C43—21no—
78C4⋊C8×C43C2312yes—
79#102×C43—24no—
80C24×C43—21no—
81C2×Q8×C43—22no—
82C2×Q8×C43—41no—
83C2×Q8×C43—82no—
84C2×D4×C43—21no—
85C2×D4×C43—22no—
86C2×D4×C43—22no—
87C2×D4×C43C2×D412yes—
88C22×C4×C43—22no—
89C22×C4×C43—22no—
90C22×C4×C43—21no—
91C22×C4×C43—42no—
92C22×C4×C43—42no—
93C22×C4×C43—41no—
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43#4111yescharacteristic
97C22×Dic43—41no—
98C2×Dic86—22no—
99C2×Dic86—41no—
100C2×Dic86—82no—
101C2×C8×C43—22no—
102C2×C8×C43—42no—
103C4⋊C4×C43—21no—
104C4⋊C4×C43—22no—
105C4⋊C4×C43—22no—
106C4⋊C4×C43—41no—
107C4⋊C4×C43—41no—
108C4⋊C4×C43C2×D412yes—
109C22⋊C4×C43—22no—
110C22⋊C4×C43—22no—
111C42×C43C2×D411yescharacteristic
112C42×C43C2×D411yescharacteristic
113C42×C43#4111yescharacteristic
114C42×C43C2411yescharacteristic
115C4⋊Dic43—22no—
116C4⋊Dic43—22no—
117C4⋊Dic43—41no—
118C4⋊Dic43—41no—
119#10621877—48no—
120C2×C43⋊C8—22no—
121C2×C43⋊C8—22no—
122C2×C43⋊C8—22no—
123C2×C43⋊C8—42no—
124C2×C43⋊C8—42no—
125C2×C43⋊C8SD1614yes—
126C2×C43⋊C8C2×D412yes—
127C2×C43⋊C8C2×D412yes—
128C23×C43—22no—
129C23×C43—42no—
130C23×C43—42no—
131C23×C43—42no—
132C23×C43#12111yescharacteristic
133Q8×C43—82no—
134Q8×C43—82no—
135D4×C43—22no—
136D4×C43—22no—
137D4×C43—42no—
138C2×C4×C43—22no—
139C2×C4×C43—22no—
140C2×C4×C43—42no—
141C2×C4×C43—42no—
142C2×C4×C43—42no—
143C2×C4×C43—44no—
144C2×C4×C43—42no—
145C2×C4×C43—82no—
146C2×C4×C43#12111yescharacteristic
147C2×C4×C43#12111yescharacteristic
148C2×C4×C43#12111yescharacteristic
149C2×C4×C43C2×SD1612yes—
150C2×C4×C43#13712yes—
151C2×C4×C43#13712yes—
152C2×C4×C43#13712yes—
153C2×C4×C43C22×D411yescharacteristic
154C2×C4×C43C22×D411yescharacteristic
155C2×C4×C43C2×#4111yescharacteristic
156C2×Dic43—42no—
157C2×Dic43—82no—
158Dic86—82no—
159Dic86—82no—
160C8×C43—42no—
161C43⋊C8—22no—
162C43⋊C8—42no—
163C43⋊C8—42no—
164C43⋊C8C2×SD1614yes—
165C2×#1695—431nomaximal, Sylow
166C22×C43—42no—
167C22×C43—42no—
168C22×C43—42no—
169C22×C43—84no—
170C22×C43#46112yes—
171C22×C43#47012yes—
172C22×C43#47212yes—
173C22×C43C2×#12111yescharacteristic
174C4×C43—21no—
175C4×C43—21no—
176C4×C43—42no—
177C4×C43—82no—
178C4×C43#46112yes—
179C4×C43#47012yes—
180C4×C43C22×SD1611yescharacteristic
181C4×C43C2×#13711yescharacteristic
182C4×C43C2×#13711yescharacteristic
183C4×C43C2×#13711yescharacteristic
184Dic43—82no—
185C2×#500—431no—
186C2×#476—431no—
187C2×#476D4311yescharacteristic
188C2×#436—431no—
189#1695—438no—
190C2×#334—431no—
191C2×#333—431no—
192C2×#333—431no—
193C2×C43—82no—
194C2×C43#169514yescomplemented
195C2×C43C2×#46111yescharacteristic
196C2×C43C2×#47011yescharacteristic
197C2×C43C2×#47211yescharacteristic
198C22×M16—861no—
199C2×C4⋊Q8—431no—
200C2×C4⋊Q8C2×D4311yescharacteristic
201C2×C4×D4C2×D4311yescharacteristic
202#500—434no—
203#500—862no—
204#476—22no—
205#476—434no—
206#476—862no—
207#476C2×D4314yes—
208#436—434no—
209#436—862no—
210C2×#107—861no—
211C2×#107—861no—
212C2×#106—21no—
213C2×#106—861no—
214C2×C4⋊C8—431no—
215C2×C4⋊C8—431no—
216C2×C4⋊C8C2×D4311yescharacteristic
217C2×#102—21no—
218C2×#102—861no—
219C2×C22⋊C8—861no—
220C2×C4×C8—431no—
221#334—434no—
222#333—434no—
223#333—434no—
224C43C2×#169511yescharacteristic, complemented, Sylow
225C22×Q8—21no—
226C22×Q8—861no—
227C22×D4C22⋊D4311yescharacteristic
228C23×C4—21no—
229C2×M16—864no—
230C2×M16—1724no—
231C22×C8—21no—
232C22×C8—431no—
233C22×C8—431no—
234C22×C8—861no—
235C22×C8—861no—
236C4⋊Q8—21no—
237C4⋊Q8—21no—
238C4⋊Q8—21no—
239C4⋊Q8—432no—
240C4⋊Q8—861no—
241C4⋊Q8—861no—
242C4⋊Q8—861no—
243C4⋊Q8C22×D4312yes—
244C4×D4—21no—
245C4×D4—21no—
246C4×D4C22⋊D4312yes—
247C4×D4C22×D4312yes—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—861no—
251C2×C4⋊C4—861no—
252C2×C4⋊C4C22⋊D4311yescharacteristic
253C2×C22⋊C4—21no—
254C2×C42C22×D4311yescharacteristic
255#107—864no—
256#107—864no—
257#106—24no—
258#106—864no—
259C4⋊C8—21no—
260C4⋊C8—432no—
261C4⋊C8—432no—
262C4⋊C8—861no—
263C4⋊C8—861no—
264C4⋊C8C22×D4312yes—
265#102—24no—
266#102—864no—
267C22⋊C8—864no—
268C4×C8—432no—
269C4×C8—432no—
270C24—21no—
271C2×Q8—22no—
272C2×Q8—41no—
273C2×Q8—82no—
274C2×Q8—862no—
275C2×Q8—3442no—
276C2×Q8—1721no—
277C2×D4—21no—
278C2×D4—22no—
279C2×D4—22no—
280C2×D4C2×C22⋊D4312yes—
281C22×C4—21no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—41no—
287C22×C4—1721no—
288C22×C4D4×D4311yescharacteristic
289C22×C4#1062190011yescharacteristic
290C22×C4C2×C22⋊D4311yescharacteristic
291M16—1728no—
292C2×C8—22no—
293C2×C8—42no—
294C2×C8—434no—
295C2×C8—432no—
296C2×C8—432no—
297C2×C8—862no—
298C2×C8—862no—
299C2×C8—862no—
300C2×C8—1722no—
301C2×C8—1722no—
302C4⋊C4—21no—
303C4⋊C4—22no—
304C4⋊C4—22no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—862no—
308C4⋊C4—862no—
309C4⋊C4—1721no—
310C4⋊C4—1721no—
311C4⋊C4C2×C22⋊D4312yes—
312C22⋊C4—22no—
313C22⋊C4—22no—
314C42D4×D4311yescharacteristic
315C42#1062190011yescharacteristic
316C42C2×C22⋊D4311yescharacteristic
317C42C23×D4311yescharacteristic
318C23—22no—
319C23—42no—
320C23—42no—
321C23—42no—
322C23#1306329711yescharacteristic
323Q8—82no—
324Q8—82no—
325Q8—3442no—
326Q8—3442no—
327D4—22no—
328D4—22no—
329D4—42no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—42no—
333C2×C4—44no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—82no—
338C2×C4—3442no—
339C2×C4—1722no—
340C2×C4#1306329711yescharacteristic
341C2×C4#1306329711yescharacteristic
342C2×C4#1306329711yescharacteristic
343C2×C4SD16×D4312yes—
344C2×C4#1306335412yes—
345C2×C4#1306335512yes—
346C2×C4#1306335612yes—
347C2×C4C2×D4×D4311yescharacteristic
348C2×C4C22×C22⋊D4311yescharacteristic
349C2×C4C2×#1062190011yescharacteristic
350C8—42no—
351C8—434no—
352C8—862no—
353C8—1722no—
354C8—1722no—
355C22—42no—
356C22—42no—
357C22—42no—
358C22—84no—
359C22#1458310212yes—
360C22#1458315512yes—
361C22#1458316712yes—
362C22C2×#1306329711yescharacteristic
363C4—21no—
364C4—21no—
365C4—42no—
366C4—82no—
367C4—3442no—
368C4#1458310212yes—
369C4#1458315512yes—
370C4C2×SD16×D4311yescharacteristic
371C4C2×#1306335411yescharacteristic
372C4C2×#1306335511yescharacteristic
373C4C2×#1306335611yescharacteristic
374C2—82no—
375C2#1913411614yesdirect product factor
376C2C2×#1458310211yescharacteristic
377C2C2×#1458315511yescharacteristic
378C2C2×#1458316711yescharacteristic
subgroupG/H
centerC23#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#476C2
socleC23×C43#121
prime radicalC22×D4×C43D4
hypercenterC2×#476D43
hypocenterC43C2×#1695
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#14583302C2semidirect
4. #19134116C2direct (N × H)
5. C2×#14582649C2semidirect
6. C2×#14582648C2semidirect
7. C2×#14582647C2semidirect
12. #14583302C22semidirect
25. #14582649C22semidirect
26. #14582648C22semidirect
27. #14582647C22semidirect
194. C2×C43#1695semidirect
224. C43C2×#1695semidirect
375. C2#19134116direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145833022
C2×#145831892
C2×#145829772
#191341162
C2×#145826492
C2×#145826482
C2×#145826472
C2×C43×#4762
C2×#169543