Finite Group Databasebeta

← C2×#19133928 #25077764

Subgroups — C2×#19133928 #25077764

Order 11008.

894 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583649C211yesmaximal, characteristic
2C2×#14583305C211yesmaximal, characteristic, complemented
3C2×#14583267C211yesmaximal, characteristic, complemented
4#19133928C218yesmaximal, direct product factor
5C2×#14582640C211yesmaximal, characteristic, complemented
6C2×#14582640C211yesmaximal, characteristic, complemented
7C2×#14582639C211yesmaximal, characteristic
8C2×C43×#489C211yesmaximal, characteristic
9#14583649—22no—
10#14583649—22no—
11#14583649—22no—
12#14583649C2214yes—
13C2×#13063323—21no—
14C2×#13063318—21no—
15C2×#13063318—21no—
16C2×#13063317C2211yescharacteristic
17C2×#13063317C2211yescharacteristic
18C2×#13063306—21no—
19C2×#13063302—21no—
20C2×#13063302—21no—
21#14583305—22no—
22#14583305C2214yescomplemented
23#14583267—22no—
24#14583267C2214yescomplemented
25C2×#13063258—21no—
26C2×#13063256—21no—
27C2×#13063249—21no—
28C2×#13063249—21no—
29C2×#13063236C2211yescharacteristic
30C2×#13063236C2211yescharacteristic
31#14582640C2214yescomplemented
32#14582640C2214yescomplemented
33#14582639C2214yes—
34C2×C4⋊Q8×C43C2211yescharacteristic
35C2×#124×C43C2211yescharacteristic
36C43×#489—22no—
37C43×#489C2214yes—
38C2×#103×C43—21no—
39C2×#102×C43—21no—
40C2×#97×C43C2211yescharacteristic
41C22×Dic86—21no—
42C23×Dic43—21no—
43C22×C43⋊C8—21no—
44C22×C43⋊C8—21no—
45#13063323—24no—
46#13063323—24no—
47#13063318—24no—
48#13063318—24no—
49#13063318—24no—
50#13063318—24no—
51#13063317—21no—
52#13063317—21no—
53#13063317—21no—
54#13063317—21no—
55#13063317D412yes—
56#13063317D412yes—
57#13063317C2312yes—
58#13063317C2312yes—
59#13063306—24no—
60#13063306—24no—
61#13063302—24no—
62#13063302—24no—
63#13063302—24no—
64#13063302—24no—
65C2×C4⋊Dic43D411yescharacteristic
66C2×C4⋊Dic43D411yescharacteristic
67C2×C4⋊Dic43D411yescharacteristic
68C2×C4⋊Dic43D411yescharacteristic
69C2×Dic43⋊C4—21no—
70C2×Dic43⋊C4—21no—
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×C22⋊Dic43—21no—
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43—21no—
78C2×C4×Dic43—21no—
79#13063258—24no—
80#13063256—24no—
81#13063249—24no—
82#13063249—24no—
83#13063236—21no—
84#13063236—21no—
85#13063236C2312yes—
86#13063236C2312yes—
87C22×Q8×C43—21no—
88C22×Q8×C43D411yescharacteristic
89C22×D4×C43D411yescharacteristic
90C22×C8×C43—21no—
91C4⋊Q8×C43—21no—
92C4⋊Q8×C43—21no—
93C4⋊Q8×C43—21no—
94C4⋊Q8×C43C2312yes—
95#124×C43—21no—
96#124×C43—21no—
97#124×C43D412yes—
98#124×C43C2312yes—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—21no—
101C2×C22⋊C4×C43—21no—
102C2×C22⋊C4×C43—21no—
103C2×C42×C43C2311yescharacteristic
104#103×C43—24no—
105#102×C43—24no—
106#97×C43—21no—
107#97×C43C2312yes—
108C24×C43—21no—
109C2×Q8×C43—21no—
110C2×Q8×C43—22no—
111C2×Q8×C43—42no—
112C2×Q8×C43—44no—
113C2×Q8×C43—41no—
114C2×Q8×C43C2×D412yes—
115C2×D4×C43—21no—
116C2×D4×C43—42no—
117C2×D4×C43C2×D412yes—
118C22×C4×C43—21no—
119C22×C4×C43—41no—
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C22×Dic43—24no—
124C22×Dic43—21no—
125C22×Dic43—21no—
126C22×Dic43—21no—
127C22×Dic43—21no—
128C22×Dic43—82no—
129C2×Dic86—24no—
130C2×Dic86—82no—
131C2×C8×C43—22no—
132C2×C8×C43—42no—
133C4⋊C4×C43—22no—
134C4⋊C4×C43—22no—
135C4⋊C4×C43—41no—
136C4⋊C4×C43—41no—
137C22⋊C4×C43—22no—
138C22⋊C4×C43—22no—
139C22⋊C4×C43—22no—
140C22⋊C4×C43—22no—
141C42×C43C2×D411yescharacteristic
142C42×C43C2×D411yescharacteristic
143C42×C43C2×D411yescharacteristic
144C42×C43C2411yescharacteristic
145C22⋊Dic43—24no—
146C22⋊Dic43—24no—
147C22⋊Dic43—24no—
148C4⋊Dic43—21no—
149C4⋊Dic43—21no—
150C4⋊Dic43—21no—
151C4⋊Dic43—21no—
152C4⋊Dic43C2×D412yes—
153C4⋊Dic43C2×D412yes—
154C4⋊Dic43C2×D412yes—
155C4⋊Dic43C2×D412yes—
156Dic43⋊C4—24no—
157Dic43⋊C4—24no—
158Dic43⋊C4—22no—
159Dic43⋊C4—22no—
160Dic43⋊C4—22no—
161Dic43⋊C4—22no—
162Dic43⋊C4—22no—
163Dic43⋊C4—22no—
164Dic43⋊C4—22no—
165Dic43⋊C4—22no—
166C4×Dic43—24no—
167C2×C43⋊C8—24no—
168C2×C43⋊C8—22no—
169C2×C43⋊C8—22no—
170C2×C43⋊C8—42no—
171C23×C43—22no—
172C23×C43—42no—
173C23×C43—42no—
174C23×C43—42no—
175C23×C43#12011yescharacteristic
176Q8×C43—42no—
177Q8×C43—44no—
178Q8×C43—81no—
179Q8×C43—82no—
180D4×C43—42no—
181D4×C43—81no—
182C2×C4×C43—22no—
183C2×C4×C43—22no—
184C2×C4×C43—22no—
185C2×C4×C43—22no—
186C2×C4×C43—42no—
187C2×C4×C43—42no—
188C2×C4×C43—82no—
189C2×C4×C43#12011yescharacteristic
190C2×C4×C43#12011yescharacteristic
191C2×C4×C43#12011yescharacteristic
192C2×C4×C43C22×D411yescharacteristic
193C2×C4×C43C22×D411yescharacteristic
194C2×C4×C43C22×D411yescharacteristic
195C2×Dic43—22no—
196C2×Dic43—22no—
197C2×Dic43—22no—
198C2×Dic43—22no—
199C2×Dic43—42no—
200C2×Dic43—42no—
201C2×Dic43—42no—
202C2×Dic43—42no—
203C2×Dic43—84no—
204Dic86—84no—
205C8×C43—42no—
206C43⋊C8—24no—
207C43⋊C8—42no—
208C2×#1664—431nomaximal, Sylow
209C22×C43—42no—
210C22×C43—42no—
211C22×C43—42no—
212C22×C43—84no—
213C22×C43#45412yes—
214C22×C43#45512yes—
215C22×C43#45612yes—
216C22×C43C2×#12011yescharacteristic
217C4×C43—21no—
218C4×C43—21no—
219C4×C43—21no—
220C4×C43—21no—
221C4×C43—21no—
222C4×C43—21no—
223C4×C43—42no—
224C4×C43—82no—
225Dic43—42no—
226Dic43—42no—
227Dic43—42no—
228Dic43—42no—
229C2×#563—431no—
230C2×#501—431no—
231C2×#491—431no—
232C2×#489D4311yescharacteristic
233#1664—438no—
234C2×#330—431no—
235C2×#330—431no—
236C2×#329—431no—
237C2×C43—82no—
238C2×C43#166414yescomplemented
239C2×C43C2×#45511yescharacteristic
240C2×C43C2×#45411yescharacteristic
241C2×C43C2×#45611yescharacteristic
242#563—434no—
243#563—862no—
244#563—862no—
245#563—862no—
246C2×C4⋊Q8—861no—
247C2×C4⋊Q8C2×D4311yescharacteristic
248C2×#126—861no—
249C2×#126—861no—
250C2×#125—431no—
251C2×#125—431no—
252C2×#124C2×D4311yescharacteristic
253C2×#123—861no—
254C2×C22⋊Q8—861no—
255C2×C22⋊Q8—861no—
256#501—434no—
257#501—862no—
258#491—434no—
259#491—862no—
260#489—22no—
261#489C2×D4314yes—
262C2×#107—861no—
263C2×#106—861no—
264C2×#103—21no—
265C2×#103—861no—
266C2×#103—861no—
267C2×#102—21no—
268C2×#97—431no—
269C2×#97—431no—
270C2×#97C2×D4311yescharacteristic
271#330—434no—
272#330—434no—
273#329—434no—
274C43C2×#166411yescharacteristic, complemented, Sylow
275C22×Q8—21no—
276C22×Q8—861no—
277C22×Q8C22⋊D4311yescharacteristic
278C22×D4C22⋊D4311yescharacteristic
279C23×C4—861no—
280C22×C8—21no—
281C22×C8—861no—
282C22×C8—861no—
283C4⋊Q8—21no—
284C4⋊Q8—21no—
285C4⋊Q8—21no—
286C4⋊Q8—864no—
287C4⋊Q8—864no—
288C4⋊Q8C22×D4312yes—
289#126—864no—
290#126—864no—
291#126—864no—
292#126—864no—
293#125—432no—
294#125—432no—
295#125—432no—
296#125—432no—
297#125—861no—
298#125—861no—
299#125—861no—
300#125—861no—
301#124—21no—
302#124—21no—
303#124C22⋊D4312yes—
304#124C22×D4312yes—
305#123—864no—
306#123—864no—
307C22⋊Q8—864no—
308C22⋊Q8—864no—
309C22⋊Q8—864no—
310C22⋊Q8—864no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—431no—
314C2×C4⋊C4—431no—
315C2×C4⋊C4—431no—
316C2×C4⋊C4—431no—
317C2×C4⋊C4—861no—
318C2×C4⋊C4—861no—
319C2×C4⋊C4—861no—
320C2×C4⋊C4—861no—
321C2×C4⋊C4—861no—
322C2×C4⋊C4—861no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—861no—
326C2×C22⋊C4—861no—
327C2×C22⋊C4—861no—
328C2×C42—861no—
329C2×C42C22×D4311yescharacteristic
330#107—864no—
331#106—864no—
332#103—24no—
333#103—864no—
334#103—864no—
335#102—24no—
336#97—21no—
337#97—432no—
338#97—432no—
339#97—861no—
340#97—861no—
341#97C22×D4312yes—
342C24—21no—
343C2×Q8—21no—
344C2×Q8—22no—
345C2×Q8—42no—
346C2×Q8—44no—
347C2×Q8—41no—
348C2×Q8—864no—
349C2×Q8—3442no—
350C2×Q8C2×C22⋊D4312yes—
351C2×D4—21no—
352C2×D4—42no—
353C2×D4C2×C22⋊D4312yes—
354C22×C4—21no—
355C22×C4—41no—
356C22×C4—864no—
357C22×C4—861no—
358C22×C4—861no—
359C22×C4—861no—
360C22×C4—861no—
361C22×C4—3442no—
362C22×C4D4×D4311yescharacteristic
363C22×C4D4×D4311yescharacteristic
364C22×C4C2×C22⋊D4311yescharacteristic
365C2×C8—22no—
366C2×C8—42no—
367C2×C8—864no—
368C2×C8—862no—
369C2×C8—862no—
370C2×C8—1722no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—432no—
376C4⋊C4—432no—
377C4⋊C4—432no—
378C4⋊C4—432no—
379C4⋊C4—864no—
380C4⋊C4—864no—
381C4⋊C4—861no—
382C4⋊C4—861no—
383C4⋊C4—861no—
384C4⋊C4—861no—
385C4⋊C4—862no—
386C4⋊C4—862no—
387C4⋊C4—862no—
388C4⋊C4—862no—
389C4⋊C4—862no—
390C4⋊C4—862no—
391C4⋊C4—862no—
392C4⋊C4—862no—
393C22⋊C4—22no—
394C22⋊C4—22no—
395C22⋊C4—22no—
396C22⋊C4—22no—
397C22⋊C4—864no—
398C22⋊C4—864no—
399C22⋊C4—864no—
400C42—864no—
401C42D4×D4311yescharacteristic
402C42D4×D4311yescharacteristic
403C42C2×C22⋊D4311yescharacteristic
404C42C23×D4311yescharacteristic
405C23—22no—
406C23—42no—
407C23—42no—
408C23—42no—
409C23#1306329311yescharacteristic
410Q8—42no—
411Q8—44no—
412Q8—81no—
413Q8—82no—
414Q8—3444no—
415D4—42no—
416D4—81no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—82no—
424C2×C4—862no—
425C2×C4—862no—
426C2×C4—862no—
427C2×C4—862no—
428C2×C4—3444no—
429C2×C4—1722no—
430C2×C4—1722no—
431C2×C4—1722no—
432C2×C4—1722no—
433C2×C4#1306329311yescharacteristic
434C2×C4#1306329311yescharacteristic
435C2×C4#1306329311yescharacteristic
436C2×C4C2×D4×D4311yescharacteristic
437C2×C4C2×D4×D4311yescharacteristic
438C2×C4C22×C22⋊D4311yescharacteristic
439C8—42no—
440C8—864no—
441C8—1722no—
442C22—42no—
443C22—42no—
444C22—42no—
445C22—84no—
446C22#1458307012yes—
447C22#1458307612yes—
448C22#1458308012yes—
449C22C2×#1306329311yescharacteristic
450C4—21no—
451C4—21no—
452C4—21no—
453C4—21no—
454C4—21no—
455C4—21no—
456C4—42no—
457C4—82no—
458C4—1722no—
459C4—1722no—
460C4—1722no—
461C4—1722no—
462C2—82no—
463C2#1913392814yesdirect product factor
464C2C2×#1458307611yescharacteristic
465C2C2×#1458307011yescharacteristic
466C2C2×#1458308011yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#489C2
socleC23×C43#120
prime radicalC22×D4×C43D4
hypercenterC2×#489D43
hypocenterC43C2×#1664
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
2. C2×#14583305C2semidirect
3. C2×#14583267C2semidirect
4. #19133928C2direct (N × H)
5. C2×#14582640C2semidirect
6. C2×#14582640C2semidirect
22. #14583305C22semidirect
24. #14583267C22semidirect
31. #14582640C22semidirect
32. #14582640C22semidirect
238. C2×C43#1664semidirect
274. C43C2×#1664semidirect
463. C2#19133928direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836492
C2×#145833052
C2×#145832672
#191339282
C2×#145826402
C2×#145826392
C2×C43×#4892
C2×#166443