Finite Group Databasebeta

← C2×#19135603 #25123393

Subgroups — C2×#19135603 #25123393

Order 11008.

2182 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#10621885C211yesmaximal, characteristic, complemented
2C22×#13063304C211yesmaximal, characteristic
3C22×#13063249C211yesmaximal, characteristic, complemented
4C22×#13063248C211yesmaximal, characteristic, complemented
5C22×C22⋊(C43⋊C8)C211yesmaximal, characteristic
6#19135603C218yesmaximal, direct product factor
7C2×#14582661C211yesmaximal, characteristic, complemented
8C22×C22⋊Q8×C43C211yesmaximal, characteristic
9C23×Dic86C2211yescharacteristic
10C22×#10621885—24no—
11C22×#10621885—24no—
12C22×#10621885—24no—
13C22×#10621885C2214yescomplemented
14C23×C43⋊C8C2211yescharacteristic
15C23×C43⋊C8C2211yescharacteristic
16C2×#13063304—24no—
17C2×#13063304—24no—
18C2×#13063304—22no—
19C2×#13063304C2214yes—
20C22×C4⋊Dic43C2211yescharacteristic
21C22×Dic43⋊C4—21no—
22C22×C22⋊Dic43—21no—
23C2×#13063249—24no—
24C2×#13063249C2214yescomplemented
25C2×#13063248—24no—
26C2×#13063248C2214yescomplemented
27C2×C22⋊(C43⋊C8)—24no—
28C2×C22⋊(C43⋊C8)C2214yes—
29#14582661C2214yescomplemented
30C23×Q8×C43C2211yescharacteristic
31C24×C4×C43C2211yescharacteristic
32C2×C22⋊Q8×C43—24no—
33C2×C22⋊Q8×C43—22no—
34C2×C22⋊Q8×C43—24no—
35C2×C22⋊Q8×C43C2214yes—
36C22×C4⋊C4×C43—21no—
37C22×C4⋊C4×C43C2211yescharacteristic
38C22×C22⋊C4×C43—21no—
39C22×Dic86—22no—
40C22×Dic86—22no—
41C22×Dic86—22no—
42C22×Dic86—22no—
43C22×Dic86—22no—
44C22×Dic86—21no—
45C22×Dic86D414yes—
46C22×Dic86C2312yes—
47C23×Dic43—21no—
48C23×Dic43—21no—
49C2×#10621885—232no—
50C2×#10621885—28no—
51C2×#10621885—28no—
52C2×#10621885—28no—
53C22×C43⋊C8—22no—
54C22×C43⋊C8—22no—
55C22×C43⋊C8—22no—
56C22×C43⋊C8—22no—
57C22×C43⋊C8—22no—
58C22×C43⋊C8D414yes—
59C22×C43⋊C8C2312yes—
60C22×C43⋊C8C2312yes—
61#13063304—216no—
62#13063304—28no—
63#13063304—28no—
64C2×C4⋊Dic43—22no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43D414yes—
67C2×C4⋊Dic43C2312yes—
68C2×Dic43⋊C4—28no—
69C2×Dic43⋊C4—24no—
70C2×C22⋊Dic43—28no—
71C2×C22⋊Dic43—24no—
72#13063249—28no—
73#13063248—28no—
74C22⋊(C43⋊C8)—28no—
75C25×C43D411yescharacteristic
76C22×Q8×C43—22no—
77C22×Q8×C43—21no—
78C22×Q8×C43—22no—
79C22×Q8×C43—22no—
80C22×Q8×C43—22no—
81C22×Q8×C43—22no—
82C22×Q8×C43D414yes—
83C22×Q8×C43C2312yes—
84C23×C4×C43—21no—
85C23×C4×C43—21no—
86C23×C4×C43—22no—
87C23×C4×C43—22no—
88C23×C4×C43—22no—
89C23×C4×C43—22no—
90C23×C4×C43—22no—
91C23×C4×C43—22no—
92C23×C4×C43D411yescharacteristic
93C23×C4×C43D412yes—
94C23×C4×C43C2312yes—
95C23×C4×C43C2311yescharacteristic
96C22⋊Q8×C43—216no—
97C22⋊Q8×C43—28no—
98C22⋊Q8×C43—28no—
99C2×C4⋊C4×C43—28no—
100C2×C4⋊C4×C43—24no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—22no—
103C2×C4⋊C4×C43D414yes—
104C2×C4⋊C4×C43C2312yes—
105C2×C22⋊C4×C43—28no—
106C2×C22⋊C4×C43—24no—
107C24×C43—22no—
108C24×C43—22no—
109C24×C43—22no—
110C24×C43—22no—
111C24×C43—22no—
112C24×C43—22no—
113C24×C43Q1614yescomplemented
114C24×C43C2×D412yes—
115C24×C43C2×D411yescharacteristic
116C2×Q8×C43—24no—
117C2×Q8×C43—22no—
118C2×Q8×C43—28no—
119C2×Q8×C43—28no—
120C2×Q8×C43—22no—
121C2×Q8×C43—22no—
122C2×Q8×C43—22no—
123C2×Q8×C43—22no—
124C2×Q8×C43—42no—
125C2×Q8×C43—44no—
126C2×Q8×C43—42no—
127C2×Q8×C43—44no—
128C2×Q8×C43C2×D414yes—
129C22×C4×C43—24no—
130C22×C4×C43—24no—
131C22×C4×C43—24no—
132C22×C4×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43—22no—
135C22×C4×C43—22no—
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43—24no—
139C22×C4×C43—24no—
140C22×C4×C43—22no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—22no—
144C22×C4×C43—22no—
145C22×C4×C43—44no—
146C22×C4×C43—44no—
147C22×C4×C43—44no—
148C22×C4×C43—44no—
149C22×C4×C43—42no—
150C22×C4×C43—42no—
151C22×C4×C43—42no—
152C22×C4×C43—42no—
153C22×C4×C43C2×D412yes—
154C22×C4×C43C2×D412yes—
155C22×C4×C43C2×D412yes—
156C22×C4×C43C2×D412yes—
157C22×C4×C43C2×D412yes—
158C22×C4×C43C2×D412yes—
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43#4112yes—
161C22×C4×C43C2411yescharacteristic
162C22×Dic43—24no—
163C22×Dic43—24no—
164C22×Dic43—22no—
165C22×Dic43—22no—
166C22×Dic43—42no—
167C22×Dic43—42no—
168C22×Dic43—42no—
169C22×Dic43—42no—
170C2×Dic86—28no—
171C2×Dic86—28no—
172C2×Dic86—22no—
173C2×Dic86—22no—
174C2×Dic86—22no—
175C2×Dic86—22no—
176C2×Dic86—24no—
177C2×Dic86—22no—
178C2×Dic86—42no—
179C2×Dic86—44no—
180C2×Dic86—42no—
181C2×Dic86—44no—
182C2×Dic86C2×D414yes—
183C4⋊C4×C43—216no—
184C4⋊C4×C43—24no—
185C4⋊C4×C43—22no—
186C4⋊C4×C43C2×D414yes—
187C22⋊C4×C43—216no—
188C22⋊Dic43—216no—
189#10621885—232no—
190C4⋊Dic43—24no—
191C4⋊Dic43—22no—
192C4⋊Dic43C2×D414yes—
193Dic43⋊C4—216no—
194C2×C43⋊C8—28no—
195C2×C43⋊C8—22no—
196C2×C43⋊C8—22no—
197C2×C43⋊C8—22no—
198C2×C43⋊C8—22no—
199C2×C43⋊C8—22no—
200C2×C43⋊C8—44no—
201C2×C43⋊C8C2×D414yes—
202C23×C43—22no—
203C23×C43—22no—
204C23×C43—22no—
205C23×C43—22no—
206C23×C43—22no—
207C23×C43—22no—
208C23×C43—28no—
209C23×C43—28no—
210C23×C43—28no—
211C23×C43—44no—
212C23×C43—44no—
213C23×C43—44no—
214C23×C43—44no—
215C23×C43#12012yes—
216C23×C43#12012yes—
217C23×C43#12112yes—
218C23×C43C2×Q1612yes—
219C23×C43C2×Q1614yescomplemented
220C23×C43#13512yes—
221C23×C43#13712yes—
222C23×C43#13712yes—
223C23×C43C22×D411yescharacteristic
224Q8×C43—24no—
225Q8×C43—24no—
226Q8×C43—42no—
227Q8×C43—42no—
228Q8×C43—48no—
229C2×C4×C43—22no—
230C2×C4×C43—24no—
231C2×C4×C43—24no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43—42no—
238C2×C4×C43—44no—
239C2×C4×C43—48no—
240C2×C4×C43—48no—
241C2×C4×C43—42no—
242C2×C4×C43—42no—
243C2×C4×C43—42no—
244C2×C4×C43—42no—
245C2×C4×C43—48no—
246C2×C4×C43#12014yes—
247C2×C4×C43#12012yes—
248C2×C4×C43#12012yes—
249C2×C4×C43#12114yes—
250C2×C4×C43#12114yes—
251C2×C4×C43#12112yes—
252C2×C4×C43#12714yes—
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C22×D411yescharacteristic
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43C22×D411yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×Dic43—24no—
260C2×Dic43—24no—
261C2×Dic43—42no—
262C2×Dic43—42no—
263C2×Dic43—42no—
264C2×Dic43—42no—
265C2×Dic43—48no—
266C2×Dic43—48no—
267Dic86—24no—
268Dic86—24no—
269Dic86—42no—
270Dic86—42no—
271Dic86—48no—
272C43⋊C8—24no—
273C43⋊C8—42no—
274C2×#2001—431nomaximal, Sylow
275C22×C43—24no—
276C22×C43—24no—
277C22×C43—24no—
278C22×C43—42no—
279C22×C43—42no—
280C22×C43—42no—
281C22×C43—416no—
282C22×C43—42no—
283C22×C43#39214yes—
284C22×C43#45114yes—
285C22×C43#45114yes—
286C22×C43#45214yes—
287C22×C43#45214yes—
288C22×C43#46714yes—
289C22×C43#47014yes—
290C22×C43C2×#12011yescharacteristic
291C22×C43C2×#12011yescharacteristic
292C22×C43C2×#12111yescharacteristic
293C22×C43C22×Q1611yescharacteristic
294C22×C43C2×#13511yescharacteristic
295C22×C43C2×#13711yescharacteristic
296C22×C43C2×#13711yescharacteristic
297C4×C43—42no—
298C4×C43—44no—
299C4×C43—44no—
300C4×C43#39214yes—
301C4×C43C2×#12011yescharacteristic
302C4×C43C2×#12111yescharacteristic
303C4×C43C2×#12111yescharacteristic
304C4×C43C2×#12711yescharacteristic
305Dic43—44no—
306Dic43—44no—
307C23×Q16—431no—
308C22×C22⋊Q8—431no—
309C22×C22⋊Q8D4311yescharacteristic
310C22×#103—431no—
311C22×#103—431no—
312C22×C22⋊C8—431no—
313#2001—438no—
314C2×#340—431no—
315C2×C43—44no—
316C2×C43#200118yescomplemented
317C2×C43C2×#39211yescharacteristic
318C2×C43C2×#45111yescharacteristic
319C2×C43C2×#45111yescharacteristic
320C2×C43C2×#45211yescharacteristic
321C2×C43C2×#45211yescharacteristic
322C2×C43C2×#46711yescharacteristic
323C2×C43C2×#47011yescharacteristic
324C23×Q8—431no—
325C23×Q8C2×D4311yescharacteristic
326C24×C4C2×D4311yescharacteristic
327C22×Q16—434no—
328C22×Q16—864no—
329C22×Q16—864no—
330C22×Q16—864no—
331C23×C8—431no—
332C23×C8—431no—
333C2×C22⋊Q8—24no—
334C2×C22⋊Q8—22no—
335C2×C22⋊Q8—24no—
336C2×C22⋊Q8—434no—
337C2×C22⋊Q8—864no—
338C2×C22⋊Q8—864no—
339C2×C22⋊Q8—862no—
340C2×C22⋊Q8C2×D4314yes—
341C22×C4⋊C4—21no—
342C22×C4⋊C4—431no—
343C22×C4⋊C4—861no—
344C22×C4⋊C4C2×D4311yescharacteristic
345C22×C22⋊C4—21no—
346C22×C22⋊C4—861no—
347C2×#103—434no—
348C2×#103—434no—
349C2×#103—864no—
350C2×#103—864no—
351C2×C22⋊C8—434no—
352C2×C22⋊C8—864no—
353#340—434no—
354C43C2×#200111yescharacteristic, complemented, Sylow
355C25C22⋊D4311yescharacteristic
356C22×Q8—22no—
357C22×Q8—21no—
358C22×Q8—22no—
359C22×Q8—22no—
360C22×Q8—22no—
361C22×Q8—22no—
362C22×Q8—434no—
363C22×Q8—432no—
364C22×Q8—862no—
365C22×Q8—861no—
366C22×Q8—862no—
367C22×Q8—862no—
368C22×Q8—862no—
369C22×Q8—862no—
370C22×Q8C22⋊D4314yes—
371C22×Q8C22×D4312yes—
372C23×C4—21no—
373C23×C4—21no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—861no—
381C23×C4—861no—
382C23×C4C22⋊D4312yes—
383C23×C4C22⋊D4311yescharacteristic
384C23×C4C22×D4312yes—
385C23×C4C22×D4311yescharacteristic
386C2×Q16—868no—
387C2×Q16—868no—
388C2×Q16—8632no—
389C2×Q16—868no—
390C22×C8—434no—
391C22×C8—432no—
392C22×C8—432no—
393C22×C8—862no—
394C22×C8—862no—
395C22×C8—862no—
396C22×C8—862no—
397C22×C8—862no—
398C22⋊Q8—216no—
399C22⋊Q8—28no—
400C22⋊Q8—28no—
401C22⋊Q8—868no—
402C22⋊Q8—868no—
403C22⋊Q8—8616no—
404C2×C4⋊C4—28no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—434no—
409C2×C4⋊C4—432no—
410C2×C4⋊C4—868no—
411C2×C4⋊C4—862no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4—864no—
414C2×C4⋊C4C22⋊D4314yes—
415C2×C4⋊C4C22×D4312yes—
416C2×C22⋊C4—28no—
417C2×C22⋊C4—24no—
418C2×C22⋊C4—868no—
419C2×C22⋊C4—864no—
420#103—868no—
421#103—868no—
422C22⋊C8—868no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24#1062188514yescomplemented
430C24C2×C22⋊D4312yes—
431C24C2×C22⋊D4311yescharacteristic
432C2×Q8—24no—
433C2×Q8—22no—
434C2×Q8—28no—
435C2×Q8—28no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—22no—
439C2×Q8—22no—
440C2×Q8—42no—
441C2×Q8—44no—
442C2×Q8—42no—
443C2×Q8—44no—
444C2×Q8—434no—
445C2×Q8—864no—
446C2×Q8—862no—
447C2×Q8—868no—
448C2×Q8—868no—
449C2×Q8—862no—
450C2×Q8—862no—
451C2×Q8—862no—
452C2×Q8—862no—
453C2×Q8—1722no—
454C2×Q8—1724no—
455C2×Q8—1722no—
456C2×Q8—1724no—
457C2×Q8C2×C22⋊D4314yes—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—44no—
479C22×C4—44no—
480C22×C4—44no—
481C22×C4—44no—
482C22×C4—864no—
483C22×C4—864no—
484C22×C4—862no—
485C22×C4—862no—
486C22×C4—1722no—
487C22×C4—1722no—
488C22×C4—1722no—
489C22×C4—1722no—
490C22×C4D4×D4312yes—
491C22×C4D4×D4312yes—
492C22×C4D4×D4312yes—
493C22×C4#1062190012yes—
494C22×C4C2×C22⋊D4312yes—
495C22×C4C2×C22⋊D4311yescharacteristic
496C22×C4C2×C22⋊D4312yes—
497C22×C4C2×C22⋊D4312yes—
498C22×C4C23×D4311yescharacteristic
499Q16—8632no—
500C2×C8—434no—
501C2×C8—868no—
502C2×C8—862no—
503C2×C8—862no—
504C2×C8—862no—
505C2×C8—862no—
506C2×C8—862no—
507C2×C8—1724no—
508C4⋊C4—216no—
509C4⋊C4—24no—
510C4⋊C4—22no—
511C4⋊C4—434no—
512C4⋊C4—8616no—
513C4⋊C4—864no—
514C4⋊C4—862no—
515C4⋊C4C2×C22⋊D4314yes—
516C22⋊C4—216no—
517C22⋊C4—8616no—
518C23—28no—
519C23—28no—
520C23—22no—
521C23—22no—
522C23—22no—
523C23—28no—
524C23—22no—
525C23—22no—
526C23—22no—
527C23—44no—
528C23—44no—
529C23—44no—
530C23—44no—
531C23#1306329312yes—
532C23#1306329412yes—
533C23#1306329712yes—
534C23C2×#1062188512yes—
535C23C2×#1062188514yescomplemented
536C23#1306334512yes—
537C23#1306335512yes—
538C23#1306335612yes—
539C23C22×C22⋊D4311yescharacteristic
540Q8—24no—
541Q8—24no—
542Q8—48no—
543Q8—42no—
544Q8—42no—
545Q8—864no—
546Q8—864no—
547Q8—1728no—
548Q8—1722no—
549Q8—1722no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—48no—
556C2×C4—44no—
557C2×C4—48no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—48no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—864no—
568C2×C4—864no—
569C2×C4—1728no—
570C2×C4—1728no—
571C2×C4—1722no—
572C2×C4—1722no—
573C2×C4—1722no—
574C2×C4—1722no—
575C2×C4#1306329312yes—
576C2×C4#1306329314yes—
577C2×C4#1306329412yes—
578C2×C4#1306329614yes—
579C2×C4#1306329712yes—
580C2×C4#1306329714yes—
581C2×C4#1306332114yes—
582C2×C4C2×D4×D4311yescharacteristic
583C2×C4C2×D4×D4311yescharacteristic
584C2×C4C2×D4×D4311yescharacteristic
585C2×C4C22×C22⋊D4311yescharacteristic
586C2×C4C22×C22⋊D4311yescharacteristic
587C2×C4C2×#1062190011yescharacteristic
588C8—864no—
589C8—1722no—
590C22—24no—
591C22—24no—
592C22—24no—
593C22—42no—
594C22—416no—
595C22—42no—
596C22—42no—
597C22—42no—
598C22#1458280714yes—
599C22#1458305414yes—
600C22#1458305514yes—
601C22#1458305914yes—
602C22#1458306114yes—
603C22#1458313814yes—
604C22#1458315514yes—
605C22C2×#1306329311yescharacteristic
606C22C2×#1306329411yescharacteristic
607C22C2×#1306329711yescharacteristic
608C22C22×#1062188511yescharacteristic
609C22C2×#1306334511yescharacteristic
610C22C2×#1306335511yescharacteristic
611C22C2×#1306335611yescharacteristic
612C4—44no—
613C4—42no—
614C4—44no—
615C4—1724no—
616C4—1724no—
617C4#1458280714yes—
618C4C2×#1306329311yescharacteristic
619C4C2×#1306329611yescharacteristic
620C4C2×#1306329711yescharacteristic
621C4C2×#1306332111yescharacteristic
622C2—44no—
623C2#1913560318yesdirect product factor
624C2C2×#1458280711yescharacteristic
625C2C2×#1458305411yescharacteristic
626C2C2×#1458305511yescharacteristic
627C2C2×#1458305911yescharacteristic
628C2C2×#1458306111yescharacteristic
629C2C2×#1458313811yescharacteristic
630C2C2×#1458315511yescharacteristic
subgroupG/H
centerC24C2×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC22×C22⋊Q8×C43C2
socleC24×C43C2×D4
prime radicalC25×C43D4
hypercenterC22×C22⋊Q8D43
hypocenterC43C2×#2001
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C23×#10621885C2semidirect
3. C22×#13063249C2semidirect
4. C22×#13063248C2semidirect
6. #19135603C2direct (N × H)
7. C2×#14582661C2semidirect
13. C22×#10621885C22semidirect
24. C2×#13063249C22semidirect
26. C2×#13063248C22semidirect
29. #14582661C22semidirect
113. C24×C43Q16semidirect
219. C23×C43C2×Q16semidirect
316. C2×C43#2001semidirect
354. C43C2×#2001semidirect
429. C24#10621885semidirect
535. C23C2×#10621885semidirect
623. C2#19135603direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#106218852
C22×#130633042
C22×#130632492
C22×#130632482
C22×C22⋊(C43⋊C8)2
#191356032
C2×#145826612
C22×C22⋊Q8×C432
C2×#200143