Finite Group Databasebeta

← C2×#19133912 #25077730

Subgroups — C2×#19133912 #25077730

Order 11008.

1022 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583309C211yesmaximal, characteristic, complemented
2C2×#14583294C211yesmaximal, characteristic, complemented
3C2×#14583258C211yesmaximal, characteristic, complemented
4#19133912C218yesmaximal, direct product factor
5C2×#14582641C211yesmaximal, characteristic, complemented
6C2×#14582639C211yesmaximal, characteristic, complemented
7C2×#14582639C211yesmaximal, characteristic, complemented
8C2×C43×#562C211yesmaximal, characteristic
9C22×#10621885—21no—
10C22×#10621883—21no—
11C2×#13063325C2211yescharacteristic
12#14583309—22no—
13#14583309C2214yescomplemented
14#14583294—22no—
15#14583294C2214yescomplemented
16#14583258—22no—
17#14583258C2214yescomplemented
18C2×#13063258—21no—
19C2×#13063256—21no—
20C2×#13063249—21no—
21C2×#13063246—21no—
22C2×#13063236C2211yescharacteristic
23C2×#13063236C2211yescharacteristic
24C2×#13063236C2211yescharacteristic
25#14582641C2214yescomplemented
26#14582639C2214yescomplemented
27#14582639C2214yescomplemented
28C43×#562—22no—
29C43×#562—22no—
30C43×#562—22no—
31C43×#562C2214yes—
32C2×#125×C43C2211yescharacteristic
33C2×#124×C43C2211yescharacteristic
34C2×#124×C43C2211yescharacteristic
35C2×#123×C43—21no—
36C2×#123×C43—21no—
37C2×C22⋊Q8×C43—21no—
38C2×C22⋊Q8×C43—21no—
39C2×#121×C43—21no—
40C2×#121×C43—21no—
41C22×Dic86—21no—
42C2×#10621885—24no—
43C2×#10621885—44no—
44C2×#10621883—24no—
45C2×#10621883—44no—
46C22×C43⋊C8—21no—
47C22×C43⋊C8—21no—
48C22×C43⋊C8—21no—
49#13063325—21no—
50#13063325—21no—
51#13063325—21no—
52#13063325C2312yes—
53C2×C4⋊Dic43—21no—
54C2×C4⋊Dic43—21no—
55#13063258—24no—
56#13063256—24no—
57#13063249—24no—
58#13063246—24no—
59#13063236—21no—
60#13063236—21no—
61#13063236—21no—
62#13063236C2312yes—
63#13063236C2312yes—
64#13063236C2312yes—
65C22×Q8×C43D411yescharacteristic
66C22×Q8×C43D411yescharacteristic
67C22×D4×C43—21no—
68C22×D4×C43—21no—
69C22×D4×C43D411yescharacteristic
70C22×D4×C43D411yescharacteristic
71C23×C4×C43—21no—
72C23×C4×C43—21no—
73#125×C43—21no—
74#125×C43—21no—
75#125×C43D412yes—
76#125×C43C2312yes—
77#124×C43—21no—
78#124×C43—21no—
79#124×C43—21no—
80#124×C43—21no—
81#124×C43D412yes—
82#124×C43D412yes—
83#124×C43C2312yes—
84#124×C43C2312yes—
85#123×C43—24no—
86#123×C43—24no—
87#123×C43—24no—
88#123×C43—24no—
89C22⋊Q8×C43—24no—
90C22⋊Q8×C43—24no—
91C22⋊Q8×C43—24no—
92C22⋊Q8×C43—24no—
93#121×C43—24no—
94#121×C43—24no—
95#121×C43—24no—
96#121×C43—24no—
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43D411yescharacteristic
102C2×C4⋊C4×C43D411yescharacteristic
103C2×C22⋊C4×C43—21no—
104C2×C22⋊C4×C43—21no—
105C2×C22⋊C4×C43—21no—
106C2×C22⋊C4×C43—21no—
107C2×C22⋊C4×C43—21no—
108C2×C22⋊C4×C43—21no—
109C2×C42×C43C2311yescharacteristic
110C24×C43—21no—
111C24×C43—21no—
112C2×Q8×C43—21no—
113C2×Q8×C43—21no—
114C2×Q8×C43—42no—
115C2×Q8×C43—42no—
116C2×Q8×C43C2×D412yes—
117C2×Q8×C43C2×D412yes—
118C2×D4×C43—24no—
119C2×D4×C43—24no—
120C2×D4×C43—21no—
121C2×D4×C43—21no—
122C2×D4×C43—42no—
123C2×D4×C43—42no—
124C2×D4×C43—82no—
125C2×D4×C43—82no—
126C2×D4×C43C2×D412yes—
127C2×D4×C43C2×D412yes—
128C22×C4×C43—24no—
129C22×C4×C43—24no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—82no—
135C22×C4×C43—82no—
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×Dic43—41no—
140C2×Dic86—22no—
141C2×Dic86—42no—
142C2×Dic86—42no—
143C2×Dic86—41no—
144C4⋊C4×C43—24no—
145C4⋊C4×C43—24no—
146C4⋊C4×C43—22no—
147C4⋊C4×C43—22no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—22no—
151C4⋊C4×C43—22no—
152C4⋊C4×C43C2×D412yes—
153C4⋊C4×C43C2×D412yes—
154C22⋊C4×C43—24no—
155C22⋊C4×C43—24no—
156C22⋊C4×C43—22no—
157C22⋊C4×C43—22no—
158C22⋊C4×C43—22no—
159C22⋊C4×C43—22no—
160C22⋊C4×C43—22no—
161C22⋊C4×C43—22no—
162C22⋊C4×C43—22no—
163C22⋊C4×C43—22no—
164C42×C43C2×D411yescharacteristic
165C42×C43C2×D411yescharacteristic
166C42×C43C2×D411yescharacteristic
167C42×C43C2411yescharacteristic
168#10621885—48no—
169#10621883—48no—
170C4⋊Dic43—22no—
171C4⋊Dic43—22no—
172C4⋊Dic43—41no—
173C4⋊Dic43—41no—
174C2×C43⋊C8—24no—
175C2×C43⋊C8—24no—
176C2×C43⋊C8—22no—
177C2×C43⋊C8—22no—
178C2×C43⋊C8—22no—
179C2×C43⋊C8—42no—
180C23×C43—22no—
181C23×C43—22no—
182C23×C43—42no—
183C23×C43—42no—
184C23×C43—42no—
185C23×C43—42no—
186C23×C43—42no—
187C23×C43—42no—
188C23×C43#12011yescharacteristic
189Q8×C43—42no—
190Q8×C43—42no—
191Q8×C43—81no—
192Q8×C43—81no—
193D4×C43—42no—
194D4×C43—42no—
195D4×C43—81no—
196D4×C43—81no—
197D4×C43—84no—
198D4×C43—84no—
199C2×C4×C43—22no—
200C2×C4×C43—22no—
201C2×C4×C43—22no—
202C2×C4×C43—22no—
203C2×C4×C43—22no—
204C2×C4×C43—22no—
205C2×C4×C43—22no—
206C2×C4×C43—42no—
207C2×C4×C43—42no—
208C2×C4×C43—42no—
209C2×C4×C43—42no—
210C2×C4×C43—84no—
211C2×C4×C43—84no—
212C2×C4×C43#12011yescharacteristic
213C2×C4×C43#12011yescharacteristic
214C2×C4×C43#12011yescharacteristic
215C2×C4×C43C22×D411yescharacteristic
216C2×C4×C43C22×D411yescharacteristic
217C2×C4×C43C22×D411yescharacteristic
218C2×Dic43—42no—
219C2×Dic43—82no—
220Dic86—42no—
221Dic86—42no—
222Dic86—82no—
223C43⋊C8—24no—
224C43⋊C8—24no—
225C43⋊C8—42no—
226C2×#1661—431nomaximal, Sylow
227C22×C43—42no—
228C22×C43—42no—
229C22×C43—42no—
230C22×C43—42no—
231C22×C43—42no—
232C22×C43—42no—
233C22×C43—84no—
234C22×C43—84no—
235C22×C43#45312yes—
236C22×C43#45512yes—
237C22×C43#45612yes—
238C22×C43C2×#12011yescharacteristic
239C4×C43—21no—
240C4×C43—21no—
241C4×C43—21no—
242C4×C43—21no—
243C4×C43—21no—
244C4×C43—21no—
245C4×C43—42no—
246C4×C43—42no—
247C4×C43—42no—
248C4×C43—42no—
249Dic43—82no—
250C2×#562D4311yescharacteristic
251C2×#501—431no—
252C2×#497—431no—
253C2×#489—431no—
254#1661—438no—
255C2×#330—431no—
256C2×#329—431no—
257C2×#329—431no—
258C2×C43—82no—
259C2×C43—82no—
260C2×C43#166114yescomplemented
261C2×C43C2×#45311yescharacteristic
262C2×C43C2×#45511yescharacteristic
263C2×C43C2×#45611yescharacteristic
264C22×Q16—861no—
265C22×SD16—861no—
266#562—22no—
267#562—22no—
268#562—22no—
269#562C2×D4314yes—
270C2×C4⋊Q8—431no—
271C2×#125C2×D4311yescharacteristic
272C2×#124C2×D4311yescharacteristic
273C2×#124C2×D4311yescharacteristic
274C2×#123—21no—
275C2×#123—21no—
276C2×C22⋊Q8—21no—
277C2×C22⋊Q8—21no—
278C2×#121—21no—
279C2×#121—21no—
280#501—434no—
281#501—862no—
282#497—434no—
283#497—862no—
284#489—434no—
285#489—862no—
286C2×#107—861no—
287C2×#106—861no—
288C2×#103—861no—
289C2×#102—861no—
290C2×#97—431no—
291C2×#97—431no—
292C2×#97—431no—
293#330—434no—
294#329—434no—
295#329—434no—
296C43C2×#166111yescharacteristic, complemented, Sylow
297C22×Q8—861no—
298C22×Q8C22⋊D4311yescharacteristic
299C22×Q8C22⋊D4311yescharacteristic
300C22×D4—21no—
301C22×D4—21no—
302C22×D4C22⋊D4311yescharacteristic
303C22×D4C22⋊D4311yescharacteristic
304C23×C4—21no—
305C23×C4—21no—
306C2×Q16—864no—
307C2×Q16—1724no—
308C2×SD16—864no—
309C2×SD16—1724no—
310C22×C8—861no—
311C22×C8—861no—
312C22×C8—861no—
313C4⋊Q8—432no—
314C4⋊Q8—861no—
315C4⋊Q8—861no—
316C4⋊Q8—861no—
317#125—21no—
318#125—21no—
319#125C22⋊D4312yes—
320#125C22×D4312yes—
321#124—21no—
322#124—21no—
323#124—21no—
324#124—21no—
325#124C22⋊D4312yes—
326#124C22⋊D4312yes—
327#124C22×D4312yes—
328#124C22×D4312yes—
329#123—24no—
330#123—24no—
331#123—24no—
332#123—24no—
333C22⋊Q8—24no—
334C22⋊Q8—24no—
335C22⋊Q8—24no—
336C22⋊Q8—24no—
337#121—24no—
338#121—24no—
339#121—24no—
340#121—24no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—861no—
346C2×C4⋊C4—861no—
347C2×C4⋊C4C22⋊D4311yescharacteristic
348C2×C4⋊C4C22⋊D4311yescharacteristic
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C42C22×D4311yescharacteristic
356#107—864no—
357#106—864no—
358#103—864no—
359#102—864no—
360#97—432no—
361#97—432no—
362#97—432no—
363#97—861no—
364#97—861no—
365#97—861no—
366C24—21no—
367C24—21no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8—42no—
371C2×Q8—42no—
372C2×Q8—862no—
373C2×Q8—1722no—
374C2×Q8—1722no—
375C2×Q8—1721no—
376C2×Q8C2×C22⋊D4312yes—
377C2×Q8C2×C22⋊D4312yes—
378C2×D4—24no—
379C2×D4—24no—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—42no—
383C2×D4—42no—
384C2×D4—82no—
385C2×D4—82no—
386C2×D4C2×C22⋊D4312yes—
387C2×D4C2×C22⋊D4312yes—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—24no—
393C22×C4—24no—
394C22×C4—82no—
395C22×C4—82no—
396C22×C4—1721no—
397C22×C4C2×C22⋊D4311yescharacteristic
398C22×C4C2×C22⋊D4311yescharacteristic
399C22×C4C2×C22⋊D4311yescharacteristic
400Q16—1728no—
401SD16—1728no—
402C2×C8—864no—
403C2×C8—864no—
404C2×C8—862no—
405C2×C8—862no—
406C2×C8—862no—
407C2×C8—1722no—
408C4⋊C4—24no—
409C4⋊C4—24no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—862no—
417C4⋊C4—862no—
418C4⋊C4—1721no—
419C4⋊C4—1721no—
420C4⋊C4C2×C22⋊D4312yes—
421C4⋊C4C2×C22⋊D4312yes—
422C22⋊C4—24no—
423C22⋊C4—24no—
424C22⋊C4—22no—
425C22⋊C4—22no—
426C22⋊C4—22no—
427C22⋊C4—22no—
428C22⋊C4—22no—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C42C2×C22⋊D4311yescharacteristic
433C42C2×C22⋊D4311yescharacteristic
434C42C2×C22⋊D4311yescharacteristic
435C42C23×D4311yescharacteristic
436C23—22no—
437C23—22no—
438C23—42no—
439C23—42no—
440C23—42no—
441C23—42no—
442C23—42no—
443C23—42no—
444C23#1306329411yescharacteristic
445Q8—42no—
446Q8—42no—
447Q8—81no—
448Q8—81no—
449Q8—3442no—
450Q8—1722no—
451Q8—1722no—
452D4—42no—
453D4—42no—
454D4—81no—
455D4—81no—
456D4—84no—
457D4—84no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—84no—
470C2×C4—84no—
471C2×C4—3442no—
472C2×C4—1722no—
473C2×C4#1306329411yescharacteristic
474C2×C4#1306329411yescharacteristic
475C2×C4#1306329411yescharacteristic
476C2×C4C22×C22⋊D4311yescharacteristic
477C2×C4C22×C22⋊D4311yescharacteristic
478C2×C4C22×C22⋊D4311yescharacteristic
479C8—864no—
480C8—864no—
481C8—1722no—
482C22—42no—
483C22—42no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22—42no—
488C22—84no—
489C22—84no—
490C22#1458306712yes—
491C22#1458307712yes—
492C22#1458308212yes—
493C22C2×#1306329411yescharacteristic
494C4—21no—
495C4—21no—
496C4—21no—
497C4—21no—
498C4—21no—
499C4—21no—
500C4—42no—
501C4—42no—
502C4—42no—
503C4—42no—
504C4—3442no—
505C2—82no—
506C2—82no—
507C2#1913391214yesdirect product factor
508C2C2×#1458306711yescharacteristic
509C2C2×#1458307711yescharacteristic
510C2C2×#1458308211yescharacteristic
subgroupG/H
centerC23#13063294
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC2×C43×#562C2
socleC23×C43#120
hypercenterC2×#562D43
hypocenterC43C2×#1661
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#562

Complements

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

NH ≅ G/Ntype
1. C2×#14583309C2semidirect
2. C2×#14583294C2semidirect
3. C2×#14583258C2semidirect
4. #19133912C2direct (N × H)
5. C2×#14582641C2semidirect
6. C2×#14582639C2semidirect
7. C2×#14582639C2semidirect
13. #14583309C22semidirect
15. #14583294C22semidirect
17. #14583258C22semidirect
25. #14582641C22semidirect
26. #14582639C22semidirect
27. #14582639C22semidirect
260. C2×C43#1661semidirect
296. C43C2×#1661semidirect
507. C2#19133912direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145833092
C2×#145832942
C2×#145832582
#191339122
C2×#145826412
C2×#145826392
C2×C43×#5622
C2×#166143