Finite Group Databasebeta

← C2×#19133618 #25068728

Subgroups — C2×#19133618 #25068728

Order 11008.

1180 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583524C211yesmaximal, characteristic
2C2×#14583234C211yesmaximal, characteristic, complemented
3C2×#14582834C211yesmaximal, characteristic
4#19133618C218yesmaximal, direct product factor
5C2×#14582637C211yesmaximal, characteristic, complemented
6C2×#14582636C211yesmaximal, characteristic, complemented
7C2×#14582622C211yesmaximal, characteristic
8C2×C43×#484C211yesmaximal, 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×Dic43⋊C4—21no—
20C22×(C2×D43)⋊C4—21no—
21C22×(C2×D43)⋊C4C2211yescharacteristic
22C2×C22⋊C4×D43—21no—
23#14583234—22no—
24#14583234C2214yescomplemented
25C2×#13063258—21no—
26C2×#13063248—21no—
27C2×C22⋊(C43⋊C8)C2211yescharacteristic
28#14582834—22no—
29#14582834C2214yes—
30C2×C43⋊#95C2211yescharacteristic
31#14582637C2214yescomplemented
32#14582636C2214yescomplemented
33#14582622C2214yes—
34C2×C22⋊Q8×C43C2211yescharacteristic
35C22×C4⋊C4×C43C2211yescharacteristic
36C43×#484—22no—
37C43×#484C2214yescomplemented
38C2×#107×C43—21no—
39C2×#103×C43—21no—
40C2×C22⋊C8×C43C2211yescharacteristic
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⋊Dic43D411yescharacteristic
65C2×Dic43⋊C4—21no—
66C2×Dic43⋊C4—21no—
67C2×Dic43⋊C4—21no—
68C2×Dic43⋊C4—24no—
69C2×Dic43⋊C4—44no—
70C2×C22⋊Dic43—21no—
71C2×(C2×D43)⋊C4—21no—
72C2×(C2×D43)⋊C4—21no—
73C2×(C2×D43)⋊C4—21no—
74C2×(C2×D43)⋊C4—21no—
75C2×(C2×D43)⋊C4—21no—
76C2×(C2×D43)⋊C4—21no—
77C2×(C2×D43)⋊C4—24no—
78C2×(C2×D43)⋊C4—44no—
79C2×(C2×D43)⋊C4D412yes—
80C2×(C2×D43)⋊C4C2312yes—
81C22⋊C4×D43—24no—
82C22⋊C4×D43—24no—
83#13063258—24no—
84#13063248—24no—
85C22⋊(C43⋊C8)—21no—
86C22⋊(C43⋊C8)C2312yes—
87C43⋊#95—21no—
88C43⋊#95C2312yes—
89C22×Q8×C43D411yescharacteristic
90C23×C4×C43—21no—
91C23×C4×C43C2311yescharacteristic
92C22×C8×C43—21no—
93C22⋊Q8×C43—21no—
94C22⋊Q8×C43—21no—
95C22⋊Q8×C43D412yes—
96C22⋊Q8×C43C2312yes—
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43D411yescharacteristic
104C2×C4⋊C4×C43C2312yes—
105C2×C22⋊C4×C43—21no—
106#107×C43—24no—
107#103×C43—24no—
108C22⋊C8×C43—21no—
109C22⋊C8×C43C2312yes—
110C24×C43C2×D411yescharacteristic
111C23×D43—21no—
112C23×D43—21no—
113C23×D43—22no—
114C23×D43—42no—
115C23×D43—42no—
116C23×D43Q1614yes—
117C23×D43C2×D412yes—
118C2×Q8×C43—21no—
119C2×Q8×C43—42no—
120C2×Q8×C43C2×D412yes—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—22no—
124C22×C4×C43—42no—
125C22×C4×C43—42no—
126C22×C4×C43—42no—
127C22×C4×C43—41no—
128C22×C4×C43—41no—
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2411yescharacteristic
135C22×Dic43—24no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—22no—
141C22×Dic43—42no—
142C22×Dic43—42no—
143C22×Dic43—42no—
144C22×Dic43C2×D412yes—
145C2×C4×D43—24no—
146C2×C4×D43—24no—
147C2×C4×D43—82no—
148C2×C4×D43—82no—
149C2×Dic86—24no—
150C2×Dic86—21no—
151C2×Dic86—42no—
152C2×Dic86—82no—
153C2×Dic86C2×D412yes—
154C2×C8×C43—22no—
155C2×C8×C43—42no—
156C4⋊C4×C43—22no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—22no—
159C4⋊C4×C43—22no—
160C4⋊C4×C43—22no—
161C4⋊C4×C43—41no—
162C4⋊C4×C43—41no—
163C4⋊C4×C43C2×D412yes—
164C22⋊C4×C43—22no—
165C22⋊C4×C43—22no—
166C22⋊Dic43—22no—
167C22⋊Dic43—22no—
168(C2×D43)⋊C4—24no—
169(C2×D43)⋊C4—24no—
170(C2×D43)⋊C4—22no—
171(C2×D43)⋊C4—22no—
172(C2×D43)⋊C4—22no—
173(C2×D43)⋊C4—22no—
174(C2×D43)⋊C4—48no—
175C4⋊Dic43—24no—
176C4⋊Dic43—21no—
177C4⋊Dic43C2×D412yes—
178Dic43⋊C4—24no—
179Dic43⋊C4—24no—
180Dic43⋊C4—22no—
181Dic43⋊C4—22no—
182Dic43⋊C4—48no—
183C2×C43⋊C8—22no—
184C2×C43⋊C8—42no—
185C23×C43—22no—
186C23×C43—22no—
187C23×C43#12011yescharacteristic
188C23×C43#12011yescharacteristic
189C23×C43C2×Q1612yes—
190C23×C43#13712yes—
191C23×C43C22×D411yescharacteristic
192C22×D43—22no—
193C22×D43—24no—
194C22×D43—22no—
195C22×D43—24no—
196C22×D43—42no—
197C22×D43—42no—
198C22×D43—42no—
199C22×D43—48no—
200C22×D43—42no—
201C22×D43—84no—
202C22×D43—81no—
203C22×D43—81no—
204C22×D43C2×Q1614yes—
205Q8×C43—42no—
206Q8×C43—81no—
207C2×C4×C43—22no—
208C2×C4×C43—22no—
209C2×C4×C43—22no—
210C2×C4×C43—22no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—42no—
216C2×C4×C43—42no—
217C2×C4×C43—42no—
218C2×C4×C43—42no—
219C2×C4×C43—42no—
220C2×C4×C43—82no—
221C2×C4×C43—82no—
222C2×C4×C43#12011yescharacteristic
223C2×C4×C43#12011yescharacteristic
224C2×C4×C43C22×D411yescharacteristic
225C2×C4×C43C22×D411yescharacteristic
226C2×Dic43—24no—
227C2×Dic43—22no—
228C2×Dic43—22no—
229C2×Dic43—22no—
230C2×Dic43—48no—
231C2×Dic43—42no—
232C2×Dic43—42no—
233C2×Dic43—42no—
234C2×Dic43—42no—
235C2×Dic43—42no—
236C2×Dic43—42no—
237C2×Dic43—81no—
238C4×D43—84no—
239C4×D43—84no—
240Dic86—42no—
241Dic86—81no—
242Dic86—84no—
243C8×C43—42no—
244C43⋊C8—42no—
245C2×#1614—431nomaximal, Sylow
246C22×C43—24no—
247C22×C43—24no—
248C22×C43—21no—
249C22×C43—21no—
250C22×C43—21no—
251C22×C43—21no—
252C22×C43#45112yes—
253C22×C43#45112yes—
254C22×C43#45312yes—
255C22×C43#45812yes—
256C22×C43C2×#12011yescharacteristic
257C22×C43C22×Q1611yescharacteristic
258C22×C43C2×#13711yescharacteristic
259C2×D43—24no—
260C2×D43—48no—
261C2×D43—42no—
262C2×D43—42no—
263C2×D43—44no—
264C2×D43—82no—
265C2×D43—84no—
266C4×C43—21no—
267C4×C43—21no—
268C4×C43—21no—
269C4×C43—21no—
270C4×C43—42no—
271C4×C43—42no—
272C4×C43—82no—
273Dic43—44no—
274Dic43—42no—
275Dic43—42no—
276Dic43—42no—
277C2×#543—431no—
278C2×#484—431no—
279C2×#484D4311yescharacteristic, complemented
280C2×#399—431no—
281#1614—438no—
282C2×#328—431no—
283C2×#328—431no—
284C2×#323—431no—
285C2×C43—21no—
286C2×C43—21no—
287C2×C43—22no—
288C2×C43#161414yescomplemented
289C2×C43C2×#45111yescharacteristic
290C2×C43C2×#45311yescharacteristic
291C2×C43C2×#45811yescharacteristic
292D43—44no—
293#543—434no—
294#543—862no—
295#543—862no—
296#543—862no—
297C2×C22⋊Q8—431no—
298C2×C22⋊Q8—861no—
299C2×C22⋊Q8—861no—
300C2×C22⋊Q8—861no—
301C2×C22⋊Q8—861no—
302C2×C22⋊Q8—861no—
303C2×C22⋊Q8C2×D4311yescharacteristic
304C22×C4⋊C4—861no—
305C22×C4⋊C4C2×D4311yescharacteristic
306C22×C22⋊C4—431no—
307C22×C22⋊C4—861no—
308C22×C22⋊C4—861no—
309#484—22no—
310#484—434no—
311#484—862no—
312#484C2×D4314yescomplemented
313C2×#107—21no—
314C2×#107—861no—
315C2×#103—21no—
316C2×#103—861no—
317C2×C22⋊C8—431no—
318C2×C22⋊C8C2×D4311yescharacteristic
319#399—434no—
320#399—862no—
321C2×#95—431no—
322#328—434no—
323#328—434no—
324#323—434no—
325C43C2×#161411yescharacteristic, complemented, Sylow
326C25—431no—
327C22×Q8—431no—
328C22×Q8—861no—
329C22×Q8C22⋊D4311yescharacteristic
330C23×C4—21no—
331C23×C4—431no—
332C23×C4—861no—
333C23×C4—861no—
334C23×C4—861no—
335C23×C4C22×D4311yescharacteristic
336C22×C8—21no—
337C22×C8—861no—
338C22⋊Q8—21no—
339C22⋊Q8—21no—
340C22⋊Q8—432no—
341C22⋊Q8—432no—
342C22⋊Q8—864no—
343C22⋊Q8—864no—
344C22⋊Q8—864no—
345C22⋊Q8—864no—
346C22⋊Q8—864no—
347C22⋊Q8—864no—
348C22⋊Q8—864no—
349C22⋊Q8—864no—
350C22⋊Q8—864no—
351C22⋊Q8—861no—
352C22⋊Q8—861no—
353C22⋊Q8—864no—
354C22⋊Q8C22⋊D4312yes—
355C22⋊Q8C22×D4312yes—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—431no—
363C2×C4⋊C4—861no—
364C2×C4⋊C4—861no—
365C2×C4⋊C4—861no—
366C2×C4⋊C4—861no—
367C2×C4⋊C4—864no—
368C2×C4⋊C4—1724no—
369C2×C4⋊C4C22⋊D4311yescharacteristic
370C2×C4⋊C4C22×D4312yes—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—432no—
373C2×C22⋊C4—432no—
374C2×C22⋊C4—864no—
375C2×C22⋊C4—864no—
376C2×C22⋊C4—861no—
377C2×C22⋊C4—861no—
378C2×C22⋊C4—861no—
379C2×C22⋊C4—861no—
380C2×C22⋊C4—861no—
381C2×C22⋊C4—861no—
382C2×C22⋊C4—861no—
383C2×C22⋊C4—864no—
384C2×C22⋊C4—1724no—
385#107—24no—
386#107—864no—
387#103—24no—
388#103—864no—
389C22⋊C8—21no—
390C22⋊C8—432no—
391C22⋊C8—861no—
392C22⋊C8C22×D4312yes—
393#95—432no—
394#95—861no—
395C24—434no—
396C24—432no—
397C24—861no—
398C24—862no—
399C24—861no—
400C24—1722no—
401C24—1722no—
402C24D4×D4311yescharacteristic
403C2×Q8—21no—
404C2×Q8—42no—
405C2×Q8—432no—
406C2×Q8—864no—
407C2×Q8—861no—
408C2×Q8—3442no—
409C2×Q8—1722no—
410C2×Q8C2×C22⋊D4312yes—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4—432no—
420C22×C4—864no—
421C22×C4—864no—
422C22×C4—861no—
423C22×C4—864no—
424C22×C4—861no—
425C22×C4—861no—
426C22×C4—861no—
427C22×C4—862no—
428C22×C4—3442no—
429C22×C4—3442no—
430C22×C4—1722no—
431C22×C4—1722no—
432C22×C4—1722no—
433C22×C4D4×D4311yescharacteristic
434C22×C4D4×D4311yescharacteristic
435C22×C4D4×D4311yescharacteristic
436C22×C4C2×C22⋊D4311yescharacteristic
437C22×C4C2×C22⋊D4311yescharacteristic
438C22×C4C23×D4311yescharacteristic
439C2×C8—22no—
440C2×C8—42no—
441C2×C8—862no—
442C2×C8—1722no—
443C4⋊C4—22no—
444C4⋊C4—21no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—41no—
449C4⋊C4—41no—
450C4⋊C4—432no—
451C4⋊C4—864no—
452C4⋊C4—864no—
453C4⋊C4—864no—
454C4⋊C4—861no—
455C4⋊C4—862no—
456C4⋊C4—862no—
457C4⋊C4—1728no—
458C4⋊C4C2×C22⋊D4312yes—
459C22⋊C4—22no—
460C22⋊C4—22no—
461C22⋊C4—864no—
462C22⋊C4—864no—
463C22⋊C4—862no—
464C22⋊C4—862no—
465C22⋊C4—862no—
466C22⋊C4—862no—
467C22⋊C4—862no—
468C22⋊C4—862no—
469C22⋊C4—1728no—
470C23—22no—
471C23—22no—
472C23—434no—
473C23—864no—
474C23—862no—
475C23—864no—
476C23—862no—
477C23—3441no—
478C23—3444no—
479C23—3441no—
480C23—1722no—
481C23—1722no—
482C23—1728no—
483C23—1722no—
484C23—1722no—
485C23#1306329311yescharacteristic
486C23#1306329311yescharacteristic
487C23Q16×D4312yes—
488C23#1306335712yes—
489C23C2×D4×D4311yescharacteristic
490Q8—42no—
491Q8—81no—
492Q8—3441no—
493Q8—3444no—
494Q8—1722no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—82no—
509C2×C4—82no—
510C2×C4—864no—
511C2×C4—862no—
512C2×C4—862no—
513C2×C4—862no—
514C2×C4—3444no—
515C2×C4—3444no—
516C2×C4—3441no—
517C2×C4—1722no—
518C2×C4—1728no—
519C2×C4—1722no—
520C2×C4—1722no—
521C2×C4—1722no—
522C2×C4—1722no—
523C2×C4—1722no—
524C2×C4#1306329311yescharacteristic
525C2×C4#1306329311yescharacteristic
526C2×C4C2×D4×D4311yescharacteristic
527C2×C4C22×C22⋊D4311yescharacteristic
528C8—42no—
529C8—1722no—
530C22—21no—
531C22—21no—
532C22—24no—
533C22—24no—
534C22—21no—
535C22—21no—
536C22—864no—
537C22—3442no—
538C22—3444no—
539C22—1724no—
540C22—1722no—
541C22—1728no—
542C22—1722no—
543C22#1458305312yes—
544C22#1458305312yes—
545C22#1458306512yes—
546C22#1458308812yes—
547C22C2×#1306329311yescharacteristic
548C22C2×Q16×D4311yescharacteristic
549C22C2×#1306335711yescharacteristic
550C4—21no—
551C4—21no—
552C4—21no—
553C4—21no—
554C4—42no—
555C4—42no—
556C4—82no—
557C4—1724no—
558C4—1722no—
559C4—1722no—
560C4—1722no—
561C2—21no—
562C2—22no—
563C2—21no—
564C2—1724no—
565C2#1913361814yesdirect product factor
566C2C2×#1458305311yescharacteristic
567C2C2×#1458306511yescharacteristic
568C2C2×#1458308811yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#484C2
socleC23×C43#120
prime radicalC24×D43D4
hypercenterC2×#484D43
hypocenterC43C2×#1614
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
2. C2×#14583234C2semidirect
4. #19133618C2direct (N × H)
5. C2×#14582637C2semidirect
6. C2×#14582636C2semidirect
8. C2×C43×#484C2semidirect
24. #14583234C22semidirect
31. #14582637C22semidirect
32. #14582636C22semidirect
37. C43×#484C22semidirect
279. C2×#484D43semidirect
288. C2×C43#1614semidirect
312. #484C2×D43semidirect
325. C43C2×#1614semidirect
565. C2#19133618direct (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×#145832342
C2×#145828342
#191336182
C2×#145826372
C2×#145826362
C2×#145826222
C2×C43×#4842
C2×#161443