Finite Group Databasebeta

← C2×#19134133 #25079243

Subgroups — C2×#19134133 #25079243

Order 11008.

702 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583245C211yesmaximal, characteristic
2C2×#14583194C211yesmaximal, characteristic, complemented
3C2×#14583030C211yesmaximal, characteristic, complemented
4#19134133C218yesmaximal, direct product factor
5C2×#14582651C211yesmaximal, characteristic, complemented
6C2×#14582647C211yesmaximal, characteristic, complemented
7C2×#14582643C211yesmaximal, characteristic
8C2×C43×#460C211yesmaximal, characteristic
9C2×#13063325C2211yescharacteristic
10#14583245—22no—
11#14583245C2214yes—
12#14583194—22no—
13#14583194C2214yescomplemented
14#14583030—22no—
15#14583030C2214yescomplemented
16C2×#13063258—21no—
17C2×C4⋊(C43⋊C8)—21no—
18C2×C4⋊(C43⋊C8)C2211yescharacteristic
19C2×C4⋊(C43⋊C8)C2211yescharacteristic
20C2×#13063249—21no—
21C2×#13063246—21no—
22C2×#13063246—21no—
23C2×#13063236—21no—
24C2×C4×C43⋊C8C2211yescharacteristic
25#14582651C2214yescomplemented
26#14582647C2214yescomplemented
27#14582643C2214yes—
28C22×SD16×C43—21no—
29C2×#127×C43C2211yescharacteristic
30C2×C4×Q8×C43C2211yescharacteristic
31C43×#460—22no—
32C43×#460C2214yes—
33C2×C4⋊C8×C43C2211yescharacteristic
34C2×#102×C43—21no—
35C22×Dic86—21no—
36C22×C43⋊C8—21no—
37C22×C43⋊C8—21no—
38C22×C43⋊C8D411yescharacteristic
39C22×C43⋊C8D411yescharacteristic
40#13063325—21no—
41#13063325—21no—
42#13063325—21no—
43#13063325C2312yes—
44C2×C4⋊Dic43—21no—
45C2×C4⋊Dic43—21no—
46#13063258—24no—
47C4⋊(C43⋊C8)—21no—
48C4⋊(C43⋊C8)—21no—
49C4⋊(C43⋊C8)—24no—
50C4⋊(C43⋊C8)C2312yes—
51C4⋊(C43⋊C8)C2312yes—
52#13063249—24no—
53#13063246—24no—
54#13063246—24no—
55#13063236—24no—
56C4×C43⋊C8D412yes—
57C4×C43⋊C8C2312yes—
58C22×Q8×C43D411yescharacteristic
59C22×D4×C43—21no—
60C22×D4×C43—21no—
61C22×D4×C43—21no—
62C2×SD16×C43—24no—
63C2×SD16×C43—44no—
64C22×C8×C43—21no—
65#127×C43—21no—
66#127×C43—21no—
67#127×C43—21no—
68#127×C43C2312yes—
69C4×Q8×C43—21no—
70C4×Q8×C43—21no—
71C4×Q8×C43D412yes—
72C4×Q8×C43C2312yes—
73C2×C4⋊C4×C43—21no—
74C2×C4⋊C4×C43D411yescharacteristic
75C2×C42×C43—21no—
76C2×C42×C43C2311yescharacteristic
77C4⋊C8×C43—21no—
78C4⋊C8×C43C2312yes—
79#102×C43—24no—
80C24×C43—41no—
81C2×Q8×C43—21no—
82C2×Q8×C43—22no—
83C2×Q8×C43—22no—
84C2×Q8×C43C2×D412yes—
85C2×D4×C43—22no—
86C2×D4×C43—22no—
87C2×D4×C43—22no—
88C2×D4×C43—41no—
89C2×D4×C43—41no—
90C2×D4×C43—41no—
91C2×D4×C43—42no—
92C2×D4×C43—42no—
93C2×D4×C43—42no—
94C2×D4×C43—42no—
95C2×D4×C43—82no—
96C22×C4×C43—21no—
97C22×C4×C43—21no—
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43#4111yescharacteristic
101C22×Dic43—41no—
102C2×Dic86—22no—
103C2×Dic86—41no—
104C2×Dic86—82no—
105SD16×C43—48no—
106C2×C8×C43—22no—
107C2×C8×C43—42no—
108C4⋊C4×C43—22no—
109C4⋊C4×C43—21no—
110C4⋊C4×C43—22no—
111C4⋊C4×C43C2×D412yes—
112C42×C43—22no—
113C42×C43—22no—
114C42×C43C2×D411yescharacteristic
115C42×C43C2×D411yescharacteristic
116C42×C43#4111yescharacteristic
117C42×C43C2411yescharacteristic
118C4⋊Dic43—22no—
119C4⋊Dic43—22no—
120C4⋊Dic43—41no—
121C4⋊Dic43—41no—
122C2×C43⋊C8—22no—
123C2×C43⋊C8—22no—
124C2×C43⋊C8—22no—
125C2×C43⋊C8—22no—
126C2×C43⋊C8—42no—
127C2×C43⋊C8—42no—
128C2×C43⋊C8C2×D412yes—
129C2×C43⋊C8C2×D412yes—
130C23×C43—42no—
131C23×C43—82no—
132C23×C43—82no—
133C23×C43—82no—
134C23×C43#12111yescharacteristic
135Q8×C43—22no—
136Q8×C43—22no—
137Q8×C43—42no—
138D4×C43—42no—
139D4×C43—42no—
140D4×C43—42no—
141D4×C43—42no—
142D4×C43—82no—
143D4×C43—82no—
144D4×C43—82no—
145D4×C43—82no—
146C2×C4×C43—22no—
147C2×C4×C43—22no—
148C2×C4×C43—22no—
149C2×C4×C43—42no—
150C2×C4×C43—42no—
151C2×C4×C43#12111yescharacteristic
152C2×C4×C43#12111yescharacteristic
153C2×C4×C43#12111yescharacteristic
154C2×C4×C43#13512yes—
155C2×C4×C43AGL(1,ℤ/8)12yes—
156C2×C4×C43#13712yes—
157C2×C4×C43#13712yes—
158C2×C4×C43C22×D411yescharacteristic
159C2×C4×C43C22×D411yescharacteristic
160C2×C4×C43C2×#4111yescharacteristic
161C2×Dic43—42no—
162C2×Dic43—82no—
163Dic86—82no—
164Dic86—82no—
165C8×C43—42no—
166C43⋊C8—22no—
167C43⋊C8—22no—
168C43⋊C8—42no—
169C43⋊C8—42no—
170C2×#1698—431nomaximal, Sylow
171C22×C43—82no—
172C22×C43—82no—
173C22×C43—82no—
174C22×C43—164no—
175C22×C43#46412yes—
176C22×C43#46812yes—
177C22×C43#47212yes—
178C22×C43C2×#12111yescharacteristic
179C4×C43—21no—
180C4×C43—21no—
181C4×C43—42no—
182C4×C43—42no—
183C4×C43#46412yes—
184C4×C43#46812yes—
185C4×C43C2×#13511yescharacteristic
186C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
187C4×C43C2×#13711yescharacteristic
188C4×C43C2×#13711yescharacteristic
189Dic43—82no—
190C2×#486—431no—
191C2×#477—431no—
192C2×#460D4311yescharacteristic
193C2×#446—431no—
194#1698—438no—
195C2×#335—431no—
196C2×#333—431no—
197C2×#331—431no—
198C2×C43—162no—
199C2×C43#169814yescomplemented
200C2×C43C2×#46411yescharacteristic
201C2×C43C2×#46811yescharacteristic
202C2×C43C2×#47211yescharacteristic
203C22×SD16—21no—
204C2×C4⋊Q8—431no—
205C2×#127C2×D4311yescharacteristic
206C2×C4×Q8C2×D4311yescharacteristic
207#486—434no—
208#486—862no—
209#477—434no—
210#477—862no—
211#460—22no—
212#460C2×D4314yes—
213#446—434no—
214#446—862no—
215C2×#107—861no—
216C2×C4⋊C8—431no—
217C2×C4⋊C8—431no—
218C2×C4⋊C8—861no—
219C2×C4⋊C8C2×D4311yescharacteristic
220C2×#103—861no—
221C2×#102—21no—
222C2×#102—861no—
223C2×#102—861no—
224C2×#97—861no—
225C2×C4×C8—431no—
226#335—434no—
227#333—434no—
228#331—434no—
229C43C2×#169811yescharacteristic, complemented, Sylow
230C22×Q8—861no—
231C22×Q8C22⋊D4311yescharacteristic
232C22×D4—21no—
233C22×D4—21no—
234C22×D4—21no—
235C2×SD16—24no—
236C2×SD16—44no—
237C22×C8—21no—
238C22×C8—431no—
239C22×C8—431no—
240C22×C8—861no—
241C22×C8—861no—
242C4⋊Q8—432no—
243C4⋊Q8—861no—
244C4⋊Q8—861no—
245C4⋊Q8—861no—
246#127—21no—
247#127—21no—
248#127—21no—
249#127C22×D4312yes—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×Q8C22⋊D4312yes—
253C4×Q8C22×D4312yes—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—861no—
256C2×C4⋊C4—861no—
257C2×C4⋊C4C22⋊D4311yescharacteristic
258C2×C42—21no—
259C2×C42C22×D4311yescharacteristic
260#107—864no—
261C4⋊C8—21no—
262C4⋊C8—432no—
263C4⋊C8—432no—
264C4⋊C8—864no—
265C4⋊C8—861no—
266C4⋊C8—861no—
267C4⋊C8C22×D4312yes—
268#103—864no—
269#102—24no—
270#102—864no—
271#102—864no—
272#97—864no—
273C4×C8—432no—
274C4×C8—432no—
275C24—41no—
276C2×Q8—21no—
277C2×Q8—22no—
278C2×Q8—22no—
279C2×Q8—862no—
280C2×Q8—3442no—
281C2×Q8—1721no—
282C2×Q8C2×C22⋊D4312yes—
283C2×D4—22no—
284C2×D4—22no—
285C2×D4—22no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—42no—
290C2×D4—42no—
291C2×D4—42no—
292C2×D4—42no—
293C2×D4—82no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—1721no—
297C22×C4D4×D4311yescharacteristic
298C22×C4#1062190011yescharacteristic
299C22×C4C2×C22⋊D4311yescharacteristic
300SD16—48no—
301C2×C8—22no—
302C2×C8—42no—
303C2×C8—432no—
304C2×C8—432no—
305C2×C8—862no—
306C2×C8—862no—
307C2×C8—862no—
308C2×C8—862no—
309C2×C8—1722no—
310C2×C8—1722no—
311C4⋊C4—22no—
312C4⋊C4—21no—
313C4⋊C4—22no—
314C4⋊C4—862no—
315C4⋊C4—862no—
316C4⋊C4—1721no—
317C4⋊C4—1721no—
318C4⋊C4C2×C22⋊D4312yes—
319C42—22no—
320C42—22no—
321C42D4×D4311yescharacteristic
322C42#1062190011yescharacteristic
323C42C2×C22⋊D4311yescharacteristic
324C42C23×D4311yescharacteristic
325C23—42no—
326C23—82no—
327C23—82no—
328C23—82no—
329C23#1306329711yescharacteristic
330Q8—22no—
331Q8—22no—
332Q8—42no—
333Q8—3442no—
334Q8—3442no—
335D4—42no—
336D4—42no—
337D4—42no—
338D4—42no—
339D4—82no—
340D4—82no—
341D4—82no—
342D4—82no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—3442no—
349C2×C4—1722no—
350C2×C4#1306329711yescharacteristic
351C2×C4#1306329711yescharacteristic
352C2×C4#1306329711yescharacteristic
353C2×C4#1306334612yes—
354C2×C4#1306335112yes—
355C2×C4#1306335412yes—
356C2×C4#1306335512yes—
357C2×C4C2×D4×D4311yescharacteristic
358C2×C4C22×C22⋊D4311yescharacteristic
359C2×C4C2×#1062190011yescharacteristic
360C8—42no—
361C8—862no—
362C8—862no—
363C8—1722no—
364C8—1722no—
365C22—82no—
366C22—82no—
367C22—82no—
368C22—164no—
369C22#1458311912yes—
370C22#1458314312yes—
371C22#1458316712yes—
372C22C2×#1306329711yescharacteristic
373C4—21no—
374C4—21no—
375C4—42no—
376C4—42no—
377C4—3442no—
378C4#1458311912yes—
379C4#1458314312yes—
380C4C2×#1306334611yescharacteristic
381C4C2×#1306335111yescharacteristic
382C4C2×#1306335411yescharacteristic
383C4C2×#1306335511yescharacteristic
384C2—162no—
385C2#1913413314yesdirect product factor
386C2C2×#1458311911yescharacteristic
387C2C2×#1458314311yescharacteristic
388C2C2×#1458316711yescharacteristic
subgroupG/H
centerC23#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#460C2
socleC23×C43#121
prime radicalC2×#127×C43C22
hypercenterC2×#460D43
hypocenterC43C2×#1698
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
2. C2×#14583194C2semidirect
3. C2×#14583030C2semidirect
4. #19134133C2direct (N × H)
5. C2×#14582651C2semidirect
6. C2×#14582647C2semidirect
13. #14583194C22semidirect
15. #14583030C22semidirect
25. #14582651C22semidirect
26. #14582647C22semidirect
199. C2×C43#1698semidirect
229. C43C2×#1698semidirect
385. C2#19134133direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145832452
C2×#145831942
C2×#145830302
#191341332
C2×#145826512
C2×#145826472
C2×#145826432
C2×C43×#4602
C2×#169843