Finite Group Databasebeta

← C2×#19133587 #25068725

Subgroups — C2×#19133587 #25068725

Order 11008.

1136 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583524C211yesmaximal, characteristic
2C2×#14583230C211yesmaximal, characteristic, complemented
3C2×#14583227C211yesmaximal, characteristic, complemented
4C2×#14582826C211yesmaximal, characteristic
5#19133587C218yesmaximal, direct product factor
6C2×#14582635C211yesmaximal, characteristic, complemented
7C2×#14582622C211yesmaximal, characteristic
8C2×C43×#328C211yesmaximal, characteristic, complemented
9#14583524—22no—
10#14583524—22no—
11#14583524—22no—
12#14583524C2214yes—
13C2×#13063305—21no—
14C2×#13063304C2211yescharacteristic
15C2×#13063303—21no—
16C2×#13063303—21no—
17C2×#13063302—21no—
18C2×#13063301—21no—
19C22×C4⋊Dic43C2211yescharacteristic
20C22×(C2×D43)⋊C4—21no—
21C22×(C2×D43)⋊C4C2211yescharacteristic
22C2×C22⋊C4×D43—21no—
23#14583230—22no—
24#14583230C2214yescomplemented
25#14583227—22no—
26#14583227C2214yescomplemented
27C2×#13063257—21no—
28C2×#13063256—21no—
29C2×#13063250—21no—
30C2×#13063249—21no—
31C2×C22⋊(C43⋊C8)C2211yescharacteristic
32#14582826—22no—
33#14582826C2214yes—
34C2×C43⋊#95—21no—
35#14582635C2214yescomplemented
36#14582622C2214yes—
37C2×C22⋊Q8×C43C2211yescharacteristic
38C2×C22⋊C8×C43C2211yescharacteristic
39C2×#95×C43C2211yescharacteristic
40C43×#328C2214yescomplemented
41C24×D43D411yescharacteristic
42C22×Dic86—21no—
43C22×Dic86D411yescharacteristic
44C23×Dic43—21no—
45C23×Dic43D411yescharacteristic
46C22×C4×D43—21no—
47C22×C4×D43—21no—
48C22×C43⋊C8—21no—
49#13063305—24no—
50#13063305—24no—
51#13063304—21no—
52#13063304—21no—
53#13063304D412yes—
54#13063304C2312yes—
55#13063303—24no—
56#13063303—24no—
57#13063303—24no—
58#13063303—24no—
59#13063302—24no—
60#13063302—24no—
61#13063301—24no—
62#13063301—24no—
63C2×C4⋊Dic43—21no—
64C2×C4⋊Dic43—21no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43D411yescharacteristic
70C2×C4⋊Dic43C2312yes—
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×C22⋊Dic43—21no—
75C2×(C2×D43)⋊C4—21no—
76C2×(C2×D43)⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—24no—
82C2×(C2×D43)⋊C4—44no—
83C2×(C2×D43)⋊C4D412yes—
84C2×(C2×D43)⋊C4C2312yes—
85C22⋊C4×D43—24no—
86C22⋊C4×D43—24no—
87#13063257—24no—
88#13063256—24no—
89#13063250—24no—
90#13063249—24no—
91C22⋊(C43⋊C8)—21no—
92C22⋊(C43⋊C8)C2312yes—
93C43⋊#95—24no—
94C22×Q8×C43D411yescharacteristic
95C23×C4×C43—21no—
96C23×C4×C43C2311yescharacteristic
97C22×C8×C43—21no—
98C22⋊Q8×C43—21no—
99C22⋊Q8×C43—21no—
100C22⋊Q8×C43D412yes—
101C22⋊Q8×C43C2312yes—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43D411yescharacteristic
104C2×C22⋊C4×C43—21no—
105C22⋊C8×C43—21no—
106C22⋊C8×C43C2312yes—
107#95×C43—21no—
108#95×C43C2312yes—
109C24×C43C2×D411yescharacteristic
110C23×D43—21no—
111C23×D43—21no—
112C23×D43—22no—
113C23×D43—42no—
114C23×D43—42no—
115C23×D43SD1614yes—
116C23×D43C2×D412yes—
117C2×Q8×C43—21no—
118C2×Q8×C43—42no—
119C2×Q8×C43C2×D412yes—
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—22no—
123C22×C4×C43—42no—
124C22×C4×C43—42no—
125C22×C4×C43—42no—
126C22×C4×C43—42no—
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2411yescharacteristic
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—22no—
138C22×Dic43—42no—
139C22×Dic43—41no—
140C22×Dic43—41no—
141C22×Dic43—42no—
142C22×Dic43—42no—
143C22×Dic43C2×D412yes—
144C2×C4×D43—24no—
145C2×C4×D43—24no—
146C2×C4×D43—82no—
147C2×C4×D43—82no—
148C2×Dic86—24no—
149C2×Dic86—21no—
150C2×Dic86—42no—
151C2×Dic86—82no—
152C2×Dic86C2×D412yes—
153C2×C8×C43—22no—
154C2×C8×C43—42no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—22no—
158C4⋊C4×C43C2×D412yes—
159C22⋊C4×C43—22no—
160C22⋊C4×C43—22no—
161C22⋊Dic43—22no—
162C22⋊Dic43—22no—
163(C2×D43)⋊C4—24no—
164(C2×D43)⋊C4—24no—
165(C2×D43)⋊C4—22no—
166(C2×D43)⋊C4—22no—
167(C2×D43)⋊C4—22no—
168(C2×D43)⋊C4—22no—
169(C2×D43)⋊C4—48no—
170C4⋊Dic43—24no—
171C4⋊Dic43—21no—
172C4⋊Dic43—22no—
173C4⋊Dic43—22no—
174C4⋊Dic43—41no—
175C4⋊Dic43—41no—
176C4⋊Dic43C2×D412yes—
177Dic43⋊C4—24no—
178Dic43⋊C4—24no—
179Dic43⋊C4—22no—
180Dic43⋊C4—22no—
181C2×C43⋊C8—22no—
182C2×C43⋊C8—42no—
183C23×C43—22no—
184C23×C43—22no—
185C23×C43#12011yescharacteristic
186C23×C43#12011yescharacteristic
187C23×C43C2×SD1612yes—
188C23×C43#13712yes—
189C23×C43C22×D411yescharacteristic
190C22×D43—22no—
191C22×D43—24no—
192C22×D43—22no—
193C22×D43—24no—
194C22×D43—42no—
195C22×D43—42no—
196C22×D43—48no—
197C22×D43—42no—
198C22×D43—42no—
199C22×D43—84no—
200C22×D43—81no—
201C22×D43—81no—
202C22×D43C2×SD1614yes—
203Q8×C43—42no—
204Q8×C43—81no—
205C2×C4×C43—22no—
206C2×C4×C43—22no—
207C2×C4×C43—22no—
208C2×C4×C43—22no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—42no—
214C2×C4×C43—42no—
215C2×C4×C43—42no—
216C2×C4×C43—42no—
217C2×C4×C43—42no—
218C2×C4×C43—84no—
219C2×C4×C43#12011yescharacteristic
220C2×C4×C43#12011yescharacteristic
221C2×C4×C43C22×D411yescharacteristic
222C2×C4×C43C22×D411yescharacteristic
223C2×Dic43—22no—
224C2×Dic43—22no—
225C2×Dic43—22no—
226C2×Dic43—42no—
227C2×Dic43—42no—
228C2×Dic43—42no—
229C2×Dic43—42no—
230C2×Dic43—42no—
231C2×Dic43—42no—
232C2×Dic43—42no—
233C2×Dic43—81no—
234C2×Dic43—82no—
235C2×Dic43—82no—
236C4×D43—84no—
237C4×D43—84no—
238Dic86—42no—
239Dic86—81no—
240Dic86—84no—
241C8×C43—42no—
242C43⋊C8—42no—
243C2×#1608—431nomaximal, Sylow
244C22×C43—24no—
245C22×C43—24no—
246C22×C43—21no—
247C22×C43—21no—
248C22×C43—21no—
249C22×C43—21no—
250C22×C43#44812yes—
251C22×C43#44812yes—
252C22×C43#45512yes—
253C22×C43#45812yes—
254C22×C43C2×#12011yescharacteristic
255C22×C43C22×SD1611yescharacteristic
256C22×C43C2×#13711yescharacteristic
257C2×D43—24no—
258C2×D43—48no—
259C2×D43—42no—
260C2×D43—42no—
261C2×D43—44no—
262C2×D43—82no—
263C2×D43—84no—
264C4×C43—21no—
265C4×C43—21no—
266C4×C43—21no—
267C4×C43—21no—
268C4×C43—42no—
269C4×C43—42no—
270C4×C43—82no—
271Dic43—42no—
272Dic43—42no—
273Dic43—42no—
274Dic43—82no—
275C2×#543—431no—
276C2×#483—431no—
277C2×#483—431no—
278C2×#397—431no—
279#1608—438no—
280C2×#328—431no—
281C2×#328D4311yescharacteristic, complemented
282C2×#323—431no—
283C2×C43—21no—
284C2×C43—21no—
285C2×C43—22no—
286C2×C43#160814yescomplemented
287C2×C43C2×#44811yescharacteristic
288C2×C43C2×#45511yescharacteristic
289C2×C43C2×#45811yescharacteristic
290D43—44no—
291#543—434no—
292#543—862no—
293#543—862no—
294#543—862no—
295C2×C22⋊Q8—431no—
296C2×C22⋊Q8—861no—
297C2×C22⋊Q8—861no—
298C2×C22⋊Q8—861no—
299C2×C22⋊Q8—861no—
300C2×C22⋊Q8—861no—
301C2×C22⋊Q8C2×D4311yescharacteristic
302C22×C4⋊C4—431no—
303C22×C22⋊C4—431no—
304C22×C22⋊C4—861no—
305C22×C22⋊C4—861no—
306#483—434no—
307#483—434no—
308#483—862no—
309#483—862no—
310C2×#106—861no—
311C2×#106—861no—
312C2×#103—861no—
313C2×#103—861no—
314C2×C22⋊C8—431no—
315C2×C22⋊C8C2×D4311yescharacteristic
316#397—434no—
317#397—862no—
318C2×#95—861no—
319C2×#95C2×D4311yescharacteristic
320#328—434no—
321#328C2×D4314yescomplemented
322#323—434no—
323C43C2×#160811yescharacteristic, complemented, Sylow
324C25—431no—
325C22×Q8—431no—
326C22×Q8—861no—
327C22×Q8D17211yescharacteristic
328C23×C4—21no—
329C23×C4—431no—
330C23×C4—861no—
331C23×C4—861no—
332C23×C4—861no—
333C23×C4C22×D4311yescharacteristic
334C22×C8—21no—
335C22×C8—861no—
336C22⋊Q8—21no—
337C22⋊Q8—21no—
338C22⋊Q8—432no—
339C22⋊Q8—432no—
340C22⋊Q8—864no—
341C22⋊Q8—864no—
342C22⋊Q8—864no—
343C22⋊Q8—864no—
344C22⋊Q8—864no—
345C22⋊Q8—864no—
346C22⋊Q8—864no—
347C22⋊Q8—864no—
348C22⋊Q8—864no—
349C22⋊Q8—861no—
350C22⋊Q8—861no—
351C22⋊Q8—864no—
352C22⋊Q8D17212yes—
353C22⋊Q8C22×D4312yes—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—431no—
356C2×C4⋊C4—432no—
357C2×C4⋊C4—861no—
358C2×C4⋊C4—861no—
359C2×C4⋊C4—861no—
360C2×C4⋊C4—861no—
361C2×C4⋊C4—861no—
362C2×C4⋊C4—861no—
363C2×C4⋊C4—861no—
364C2×C4⋊C4—861no—
365C2×C4⋊C4—861no—
366C2×C4⋊C4D17211yescharacteristic
367C2×C22⋊C4—21no—
368C2×C22⋊C4—432no—
369C2×C22⋊C4—432no—
370C2×C22⋊C4—864no—
371C2×C22⋊C4—864no—
372C2×C22⋊C4—861no—
373C2×C22⋊C4—861no—
374C2×C22⋊C4—861no—
375C2×C22⋊C4—861no—
376C2×C22⋊C4—861no—
377C2×C22⋊C4—861no—
378C2×C22⋊C4—861no—
379C2×C22⋊C4—864no—
380C2×C22⋊C4—1724no—
381#106—864no—
382#106—864no—
383#103—864no—
384#103—864no—
385C22⋊C8—21no—
386C22⋊C8—432no—
387C22⋊C8—861no—
388C22⋊C8C22×D4312yes—
389#95—21no—
390#95—864no—
391#95C22×D4312yes—
392C24—434no—
393C24—432no—
394C24—861no—
395C24—862no—
396C24—861no—
397C24—1722no—
398C24—1722no—
399C24D4×D4311yescharacteristic
400C2×Q8—21no—
401C2×Q8—42no—
402C2×Q8—432no—
403C2×Q8—864no—
404C2×Q8—861no—
405C2×Q8—3442no—
406C2×Q8—1722no—
407C2×Q8C2×D17212yes—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4—42no—
414C22×C4—42no—
415C22×C4—432no—
416C22×C4—864no—
417C22×C4—864no—
418C22×C4—861no—
419C22×C4—861no—
420C22×C4—861no—
421C22×C4—861no—
422C22×C4—862no—
423C22×C4—3442no—
424C22×C4—3442no—
425C22×C4—1721no—
426C22×C4—1721no—
427C22×C4—1722no—
428C22×C4—1722no—
429C22×C4—1722no—
430C22×C4C2×D17211yescharacteristic
431C22×C4C2×D17211yescharacteristic
432C22×C4D4×D4311yescharacteristic
433C22×C4D4×D4311yescharacteristic
434C22×C4D4×D4311yescharacteristic
435C22×C4C23×D4311yescharacteristic
436C2×C8—22no—
437C2×C8—42no—
438C2×C8—862no—
439C2×C8—1722no—
440C4⋊C4—22no—
441C4⋊C4—21no—
442C4⋊C4—22no—
443C4⋊C4—432no—
444C4⋊C4—864no—
445C4⋊C4—864no—
446C4⋊C4—864no—
447C4⋊C4—861no—
448C4⋊C4—862no—
449C4⋊C4—862no—
450C4⋊C4—862no—
451C4⋊C4—862no—
452C4⋊C4—1721no—
453C4⋊C4—1721no—
454C4⋊C4C2×D17212yes—
455C22⋊C4—22no—
456C22⋊C4—22no—
457C22⋊C4—864no—
458C22⋊C4—864no—
459C22⋊C4—862no—
460C22⋊C4—862no—
461C22⋊C4—862no—
462C22⋊C4—862no—
463C22⋊C4—862no—
464C22⋊C4—862no—
465C22⋊C4—1728no—
466C23—22no—
467C23—22no—
468C23—434no—
469C23—862no—
470C23—864no—
471C23—862no—
472C23—864no—
473C23—3441no—
474C23—3444no—
475C23—3441no—
476C23—1722no—
477C23—1728no—
478C23—1722no—
479C23—1722no—
480C23—1722no—
481C23#1306329511yescharacteristic
482C23#1306329511yescharacteristic
483C23SD16×D4312yes—
484C23#1306335712yes—
485C23C2×D4×D4311yescharacteristic
486Q8—42no—
487Q8—81no—
488Q8—3441no—
489Q8—3444no—
490Q8—1722no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—84no—
505C2×C4—862no—
506C2×C4—862no—
507C2×C4—862no—
508C2×C4—3444no—
509C2×C4—3444no—
510C2×C4—3442no—
511C2×C4—3442no—
512C2×C4—3441no—
513C2×C4—1722no—
514C2×C4—1722no—
515C2×C4—1722no—
516C2×C4—1722no—
517C2×C4—1722no—
518C2×C4—1722no—
519C2×C4—1722no—
520C2×C4#1306329511yescharacteristic
521C2×C4#1306329511yescharacteristic
522C2×C4C2×D4×D4311yescharacteristic
523C2×C4C22×D17211yescharacteristic
524C8—42no—
525C8—1722no—
526C22—21no—
527C22—21no—
528C22—24no—
529C22—24no—
530C22—21no—
531C22—21no—
532C22—864no—
533C22—3442no—
534C22—3444no—
535C22—1724no—
536C22—1722no—
537C22—1728no—
538C22—1722no—
539C22#1458303912yes—
540C22#1458303912yes—
541C22#1458307812yes—
542C22#1458309012yes—
543C22C2×#1306329511yescharacteristic
544C22C2×SD16×D4311yescharacteristic
545C22C2×#1306335711yescharacteristic
546C4—21no—
547C4—21no—
548C4—21no—
549C4—21no—
550C4—42no—
551C4—42no—
552C4—82no—
553C4—3442no—
554C4—1722no—
555C4—1722no—
556C4—1722no—
557C2—21no—
558C2—21no—
559C2—22no—
560C2—1724no—
561C2#1913358714yesdirect product factor
562C2C2×#1458303911yescharacteristic
563C2C2×#1458307811yescharacteristic
564C2C2×#1458309011yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#328C2
socleC23×C43#120
prime radicalC24×D43D4
hypercenterC2×#328D43
hypocenterC43C2×#1608
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
2. C2×#14583230C2semidirect
3. C2×#14583227C2semidirect
5. #19133587C2direct (N × H)
6. C2×#14582635C2semidirect
8. C2×C43×#328C2semidirect
24. #14583230C22semidirect
26. #14583227C22semidirect
35. #14582635C22semidirect
40. C43×#328C22semidirect
281. C2×#328D43semidirect
286. C2×C43#1608semidirect
321. #328C2×D43semidirect
323. C43C2×#1608semidirect
561. C2#19133587direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835242
C2×#145832302
C2×#145832272
C2×#145828262
#191335872
C2×#145826352
C2×#145826222
C2×C43×#3282
C2×#160843