Finite Group Databasebeta

← C2×#19138027 #25265014

Subgroups — C2×#19138027 #25265014

Order 11008.

3526 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063301C211yesmaximal, characteristic, complemented
2C22×#13063301C211yesmaximal, characteristic, complemented
3C22×C4×D172C211yesmaximal, characteristic
4C22×#13063283C211yesmaximal, characteristic, complemented
5#19138027C2116yesmaximal, direct product factor
6C2×#14582828C212yesmaximal, complemented
7C2×#14582817C212yesmaximal
8C2×#14582797C211yesmaximal, characteristic, complemented
9C2×#14582796C212yesmaximal, complemented
10C2×#14582788C212yesmaximal, complemented
11C2×#14582756C211yesmaximal, characteristic, complemented
12C2×C43×#391C211yesmaximal, characteristic, complemented
13C23×D172C2211yescharacteristic
14C23×C4×D43C2211yescharacteristic
15C23×C4×D43C2211yescharacteristic
16C2×#13063301—28no—
17C2×#13063301—28no—
18C2×#13063301C2218yescomplemented
19C2×#13063301C2218yescomplemented
20C2×C4×D172—28no—
21C2×C4×D172C2218yes—
22C2×#13063283—28no—
23C2×#13063283C2218yescomplemented
24C22×C4⋊Dic43C2211yescharacteristic
25C22×C4⋊Dic43C2211yescharacteristic
26C22×C4⋊Dic43C2211yescharacteristic
27C22×Dic43⋊C4C2212yes—
28C22×Dic43⋊C4C2212yes—
29C22×Dic43⋊C4C2212yes—
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2212yes—
32C22×(C2×D43)⋊C4C2212yes—
33C22×(C2×D43)⋊C4C2212yes—
34C22×(C2×D43)⋊C4C2212yes—
35C22×(C2×D43)⋊C4C2211yescharacteristic
36C22×C4×Dic43C2212yes—
37#14582828C22116yescomplemented
38#14582817C22116yes—
39#14582797C2218yescomplemented
40#14582796C22116yescomplemented
41#14582788C22116yescomplemented
42#14582756C2218yescomplemented
43C2×C43⋊#95C2212yes—
44C2×C43⋊#95C2212yes—
45C23×Q8×C43C2211yescharacteristic
46C22×C4⋊C4×C43C2211yescharacteristic
47C22×C42×C43C2211yescharacteristic
48C43×#391C2218yescomplemented
49C2×#95×C43C2212yes—
50C2×#95×C43C2212yes—
51C24×D43C2311yescharacteristic
52C24×D43C2311yescharacteristic
53C22×D172—24no—
54C22×D172—24no—
55C22×D172—24no—
56C22×D172C2314yes—
57C23×Dic43C2312yes—
58C23×Dic43C2311yescharacteristic
59C23×Dic43C2311yescharacteristic
60C23×Dic43C2312yes—
61C22×C4×D43—24no—
62C22×C4×D43—24no—
63C22×C4×D43—24no—
64C22×C4×D43—24no—
65C22×C4×D43—24no—
66C22×C4×D43D418yes—
67C22×C4×D43C2314yes—
68C22×C4×D43C2314yes—
69#13063301—232no—
70#13063301—232no—
71C4×D172—232no—
72#13063283—232no—
73C2×C4⋊Dic43—24no—
74C2×C4⋊Dic43—24no—
75C2×C4⋊Dic43D418yescomplemented
76C2×C4⋊Dic43C2314yes—
77C2×C4⋊Dic43C2314yes—
78C2×C4⋊Dic43C2314yes—
79C2×Dic43⋊C4—28no—
80C2×Dic43⋊C4—28no—
81C2×Dic43⋊C4—28no—
82C2×Dic43⋊C4C2318yes—
83C2×Dic43⋊C4C2318yes—
84C2×Dic43⋊C4C2318yes—
85C2×(C2×D43)⋊C4—24no—
86C2×(C2×D43)⋊C4—28no—
87C2×(C2×D43)⋊C4—28no—
88C2×(C2×D43)⋊C4—28no—
89C2×(C2×D43)⋊C4—24no—
90C2×(C2×D43)⋊C4—28no—
91C2×(C2×D43)⋊C4C2314yes—
92C2×(C2×D43)⋊C4C2318yes—
93C2×(C2×D43)⋊C4C2318yes—
94C2×(C2×D43)⋊C4C2318yes—
95C2×(C2×D43)⋊C4C2318yes—
96C2×(C2×D43)⋊C4C2314yes—
97C2×C4×Dic43—28no—
98C2×C4×Dic43C2318yes—
99C43⋊#95C2318yes—
100C43⋊#95C2318yes—
101C22×Q8×C43—24no—
102C22×Q8×C43—24no—
103C22×Q8×C43—24no—
104C22×Q8×C43C2314yes—
105C23×C4×C43C2311yescharacteristic
106C23×C4×C43C2312yes—
107C23×C4×C43C2312yes—
108C23×C4×C43C2311yescharacteristic
109C23×C4×C43C2311yescharacteristic
110C2×C4⋊C4×C43—24no—
111C2×C4⋊C4×C43C2314yes—
112C2×C42×C43—24no—
113C2×C42×C43C2314yes—
114#95×C43C2318yes—
115#95×C43C2318yes—
116C24×C43C2411yescharacteristic
117C23×D43—22no—
118C23×D43—22no—
119C23×D43—22no—
120C23×D43—22no—
121C23×D43—22no—
122C23×D43—22no—
123C23×D43—22no—
124C23×D43—22no—
125C23×D43—22no—
126C23×D43—22no—
127C23×D43—22no—
128C23×D43—22no—
129C23×D43C2×D414yes—
130C23×D43#4114yes—
131C23×D43C2412yes—
132C23×D43C2412yes—
133C2×Q8×C43—28no—
134C2×Q8×C43—28no—
135C2×Q8×C43—28no—
136C2×Q8×C43—416no—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—24no—
140C22×C4×C43—24no—
141C22×C4×C43—24no—
142C22×C4×C43—22no—
143C22×C4×C43—24no—
144C22×C4×C43—24no—
145C22×C4×C43—22no—
146C22×C4×C43—24no—
147C22×C4×C43—22no—
148C22×C4×C43C2×D414yes—
149C22×C4×C43C2×D414yes—
150C22×C4×C43#4114yes—
151C22×C4×C43#4114yes—
152C22×C4×C43C2412yes—
153C22×C4×C43C2414yes—
154C22×C4×C43C2414yes—
155C22×C4×C43C2412yes—
156C22×C4×C43C2412yes—
157C22×Dic43—22no—
158C22×Dic43—24no—
159C22×Dic43—22no—
160C22×Dic43—22no—
161C22×Dic43—24no—
162C22×Dic43—22no—
163C22×Dic43—24no—
164C22×Dic43—24no—
165C22×Dic43—22no—
166C22×Dic43—24no—
167C22×Dic43C2×D418yes—
168C22×Dic43C2×D414yes—
169C22×Dic43C2414yes—
170C22×Dic43C2412yes—
171C22×Dic43C2414yes—
172C22×Dic43C2412yes—
173C2×D172—232no—
174C2×D172—28no—
175C2×D172—28no—
176C2×D172—28no—
177C2×C4×D43—232no—
178C2×C4×D43—28no—
179C2×C4×D43—28no—
180C2×C4×D43—28no—
181C2×C4×D43—28no—
182C2×C4×D43—28no—
183C2×C4×D43—416no—
184C2×C4×D43C2×D4116yes—
185C4⋊C4×C43—28no—
186C42×C43—28no—
187(C2×D43)⋊C4—216no—
188(C2×D43)⋊C4—28no—
189(C2×D43)⋊C4—216no—
190(C2×D43)⋊C4—28no—
191(C2×D43)⋊C4—216no—
192(C2×D43)⋊C4—216no—
193C4⋊Dic43—28no—
194C4⋊Dic43—28no—
195C4⋊Dic43C2×D4116yescomplemented
196Dic43⋊C4—216no—
197Dic43⋊C4—216no—
198Dic43⋊C4—216no—
199C4×Dic43—216no—
200C23×C43C22×D412yes—
201C23×C43C22×D412yes—
202C23×C43C2×#4112yes—
203C23×C43C2×#4112yes—
204C23×C43C2×#4112yes—
205C23×C432−1+412yes—
206C23×C432−1+412yes—
207C23×C43C2511yescharacteristic
208C22×D43—28no—
209C22×D43—28no—
210C22×D43—28no—
211C22×D43—28no—
212C22×D43—28no—
213C22×D43—28no—
214C22×D43—22no—
215C22×D43—22no—
216C22×D43—22no—
217C22×D43—22no—
218C22×D43—22no—
219C22×D43—22no—
220C22×D43—22no—
221C22×D43—22no—
222C22×D43—22no—
223C22×D43—22no—
224C22×D43—22no—
225C22×D43—22no—
226C22×D43—44no—
227C22×D43—44no—
228C22×D43—44no—
229C22×D43—44no—
230C22×D43—44no—
231C22×D43—44no—
232C22×D43—44no—
233C22×D43—44no—
234C22×D43C22×D414yes—
235C22×D43C2×#4114yes—
236Q8×C43—416no—
237C2×C4×C43—28no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—24no—
241C2×C4×C43—24no—
242C2×C4×C43—24no—
243C2×C4×C43—22no—
244C2×C4×C43—24no—
245C2×C4×C43—24no—
246C2×C4×C43—22no—
247C2×C4×C43—24no—
248C2×C4×C43—22no—
249C2×C4×C43—48no—
250C2×C4×C43—44no—
251C2×C4×C43—48no—
252C2×C4×C43#121116yes—
253C2×C4×C43C22×D414yes—
254C2×C4×C43C22×D414yes—
255C2×C4×C43C2×#4114yes—
256C2×C4×C43C2×#4114yes—
257C2×Dic43—28no—
258C2×Dic43—216no—
259C2×Dic43—22no—
260C2×Dic43—24no—
261C2×Dic43—22no—
262C2×Dic43—24no—
263C2×Dic43—22no—
264C2×Dic43—24no—
265C2×Dic43—22no—
266C2×Dic43—24no—
267C2×Dic43—24no—
268C2×Dic43—22no—
269C2×Dic43—44no—
270C2×Dic43—48no—
271C2×Dic43C22×D418yes—
272C2×Dic43C22×D414yes—
273D172—232no—
274C4×D43—232no—
275C4×D43—416no—
276C2×#2415—431nomaximal, Sylow
277C22×C43C2×#12114yes—
278C22×C43#52514yes—
279C22×C43#53614yes—
280C22×C43#54714yes—
281C22×C43#54814yes—
282C22×C43#55214yes—
283C22×C43#55614yes—
284C22×C43C23×D411yescharacteristic
285C22×C43C23×D411yescharacteristic
286C22×C43C22×#4111yescharacteristic
287C22×C43C22×#4111yescharacteristic
288C22×C43C22×#4111yescharacteristic
289C22×C43C2×2−1+411yescharacteristic
290C22×C43C2×2−1+411yescharacteristic
291C2×D43—24no—
292C2×D43—24no—
293C2×D43—24no—
294C2×D43—24no—
295C2×D43—24no—
296C2×D43—24no—
297C2×D43—42no—
298C2×D43—416no—
299C2×D43—416no—
300C2×D43—42no—
301C2×D43—42no—
302C2×D43—42no—
303C2×D43—42no—
304C2×D43—42no—
305C2×D43—42no—
306C2×D43—42no—
307C4×C43—24no—
308C4×C43—44no—
309C4×C43—42no—
310C4×C43—44no—
311C4×C43C2×#12118yes—
312Dic43—24no—
313Dic43—28no—
314Dic43—42no—
315Dic43—44no—
316C22×C22⋊Q8—431no—
317C22×C22⋊Q8—431no—
318C22×C4×D4—431no—
319C22×#117—431no—
320#2415—4316no—
321C2×#397—432no—
322C2×#394—432no—
323C2×#391D4311yescharacteristic, complemented
324C2×#389—431no—
325C2×#389—432no—
326C2×#388—432no—
327C2×#380—431no—
328C2×C43#241518yescomplemented
329C2×C43C22×#12111yescharacteristic
330C2×C43C2×#52511yescharacteristic
331C2×C43C2×#53611yescharacteristic
332C2×C43C2×#54711yescharacteristic
333C2×C43C2×#54811yescharacteristic
334C2×C43C2×#55211yescharacteristic
335C2×C43C2×#55611yescharacteristic
336D43—44no—
337D43—44no—
338C23×Q8C2×D4311yescharacteristic
339C23×D4—431no—
340C24×C4—431no—
341C24×C4—431no—
342C2×C22⋊Q8—438no—
343C2×C22⋊Q8—438no—
344C2×C22⋊Q8—868no—
345C2×C22⋊Q8—868no—
346C2×C4×D4—438no—
347C2×C4×D4—868no—
348C2×#117—438no—
349C2×#117—868no—
350C22×C4⋊C4—431no—
351C22×C4⋊C4—432no—
352C22×C4⋊C4—432no—
353C22×C4⋊C4—432no—
354C22×C4⋊C4—431no—
355C22×C4⋊C4—431no—
356C22×C4⋊C4C2×D4311yescharacteristic
357C22×C22⋊C4—432no—
358C22×C22⋊C4—432no—
359C22×C22⋊C4—432no—
360C22×C22⋊C4—432no—
361C22×C22⋊C4—431no—
362C22×C22⋊C4—431no—
363C22×C42—432no—
364C22×C42C2×D4311yescharacteristic
365#397—4316no—
366#394—4316no—
367#391C2×D4318yescomplemented
368#389—438no—
369#389—4316no—
370#388—4316no—
371#380—438no—
372C2×#95—432no—
373C2×#95—432no—
374C2×#95C2×D4312yes—
375C2×#95C2×D4312yes—
376C43C2×#241511yescharacteristic, complemented, Sylow
377C25—431no—
378C25—431no—
379C22×Q8—24no—
380C22×Q8—24no—
381C22×Q8—24no—
382C22×Q8C22×D4314yes—
383C22×D4—434no—
384C22×D4—864no—
385C22×D4—864no—
386C22×D4—864no—
387C23×C4—432no—
388C23×C4—431no—
389C23×C4—438no—
390C23×C4—434no—
391C23×C4—432no—
392C23×C4—431no—
393C23×C4—434no—
394C23×C4—864no—
395C23×C4—864no—
396C23×C4—864no—
397C23×C4—864no—
398C23×C4—864no—
399C23×C4C22×D4312yes—
400C23×C4C22×D4312yes—
401C23×C4C22×D4311yescharacteristic
402C23×C4C22×D4311yescharacteristic
403C23×C4C22×D4311yescharacteristic
404C22⋊Q8—8632no—
405C22⋊Q8—8632no—
406C4×D4—8632no—
407#117—8632no—
408C2×C4⋊C4—24no—
409C2×C4⋊C4—438no—
410C2×C4⋊C4—434no—
411C2×C4⋊C4—434no—
412C2×C4⋊C4—438no—
413C2×C4⋊C4—438no—
414C2×C4⋊C4—434no—
415C2×C4⋊C4—438no—
416C2×C4⋊C4—864no—
417C2×C4⋊C4—868no—
418C2×C4⋊C4—868no—
419C2×C4⋊C4—864no—
420C2×C4⋊C4—868no—
421C2×C4⋊C4C22×D4314yes—
422C2×C22⋊C4—438no—
423C2×C22⋊C4—434no—
424C2×C22⋊C4—434no—
425C2×C22⋊C4—438no—
426C2×C22⋊C4—438no—
427C2×C22⋊C4—438no—
428C2×C22⋊C4—868no—
429C2×C22⋊C4—864no—
430C2×C22⋊C4—868no—
431C2×C22⋊C4—864no—
432C2×C22⋊C4—868no—
433C2×C22⋊C4—868no—
434C2×C42—24no—
435C2×C42—438no—
436C2×C42—868no—
437C2×C42C22×D4314yes—
438#95—438no—
439#95—438no—
440#95C22×D4318yes—
441#95C22×D4318yes—
442C24—434no—
443C24—434no—
444C24—432no—
445C24—432no—
446C24—862no—
447C24—862no—
448C24—862no—
449C24—862no—
450C24—862no—
451C24—862no—
452C24—862no—
453C24—862no—
454C24—862no—
455C24—862no—
456C24—862no—
457C24—862no—
458C24C23×D4311yescharacteristic
459C2×Q8—28no—
460C2×Q8—28no—
461C2×Q8—28no—
462C2×Q8—416no—
463C2×D4—868no—
464C2×D4—868no—
465C2×D4—8632no—
466C2×D4—868no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—438no—
479C22×C4—434no—
480C22×C4—434no—
481C22×C4—432no—
482C22×C4—4316no—
483C22×C4—434no—
484C22×C4—432no—
485C22×C4—862no—
486C22×C4—862no—
487C22×C4—864no—
488C22×C4—864no—
489C22×C4—8632no—
490C22×C4—868no—
491C22×C4—868no—
492C22×C4—864no—
493C22×C4—862no—
494C22×C4—862no—
495C22×C4—864no—
496C22×C4—862no—
497C22×C4—864no—
498C22×C4—868no—
499C22×C4—868no—
500C22×C4—868no—
501C22×C4—17216no—
502C22×C4#1062189814yes—
503C22×C4D4×D4314yes—
504C22×C4D4×D4314yes—
505C22×C4#1062190214yes—
506C22×C4C23×D4312yes—
507C22×C4C23×D4314yes—
508C22×C4C23×D4314yes—
509C22×C4C23×D4312yes—
510C22×C4C23×D4312yes—
511C4⋊C4—28no—
512C4⋊C4—4316no—
513C4⋊C4—868no—
514C4⋊C4—8616no—
515C4⋊C4—8616no—
516C4⋊C4—868no—
517C4⋊C4—8616no—
518C22⋊C4—8616no—
519C22⋊C4—868no—
520C22⋊C4—8616no—
521C22⋊C4—868no—
522C22⋊C4—8616no—
523C22⋊C4—8616no—
524C42—28no—
525C42—8616no—
526C23—434no—
527C23—434no—
528C23—868no—
529C23—868no—
530C23—868no—
531C23—868no—
532C23—868no—
533C23—862no—
534C23—862no—
535C23—862no—
536C23—862no—
537C23—862no—
538C23—862no—
539C23—862no—
540C23—862no—
541C23—868no—
542C23—862no—
543C23—862no—
544C23—862no—
545C23—862no—
546C23—1724no—
547C23—1724no—
548C23—1724no—
549C23—1724no—
550C23—1724no—
551C23—1724no—
552C23—1724no—
553C23—1724no—
554C23C2×D4×D4312yes—
555C23C2×D4×D4312yes—
556C23#41×D4312yes—
557C23C2×#1062189812yes—
558C23C2×#1062190212yes—
559C23#1306337212yes—
560C23#1306337312yes—
561C23C24×D4311yescharacteristic
562Q8—416no—
563D4—8632no—
564C2×C4—28no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—48no—
577C2×C4—48no—
578C2×C4—44no—
579C2×C4—438no—
580C2×C4—434no—
581C2×C4—8616no—
582C2×C4—868no—
583C2×C4—862no—
584C2×C4—862no—
585C2×C4—864no—
586C2×C4—864no—
587C2×C4—8632no—
588C2×C4—864no—
589C2×C4—862no—
590C2×C4—862no—
591C2×C4—864no—
592C2×C4—862no—
593C2×C4—864no—
594C2×C4—1724no—
595C2×C4—1728no—
596C2×C4—17216no—
597C2×C4#13063298116yes—
598C2×C4C2×D4×D4314yes—
599C2×C4C2×D4×D4314yes—
600C2×C4C2×#1062189814yes—
601C2×C4C2×#1062190214yes—
602C22—864no—
603C22—864no—
604C22—864no—
605C22—864no—
606C22—864no—
607C22—864no—
608C22—1722no—
609C22—1722no—
610C22—1722no—
611C22—1722no—
612C22—1722no—
613C22—1722no—
614C22—1722no—
615C22—1722no—
616C22—17216no—
617C22—17216no—
618C22C2×#1306329814yes—
619C22#1458341214yes—
620C22#1458347214yes—
621C22#1458355214yes—
622C22#1458355714yes—
623C22#1458359014yes—
624C22#1458362214yes—
625C22C22×D4×D4311yescharacteristic
626C22C22×D4×D4311yescharacteristic
627C22C2×#41×D4311yescharacteristic
628C22C22×#1062189811yescharacteristic
629C22C22×#1062190211yescharacteristic
630C22C2×#1306337211yescharacteristic
631C22C2×#1306337311yescharacteristic
632C4—24no—
633C4—44no—
634C4—44no—
635C4—42no—
636C4—868no—
637C4—864no—
638C4—1722no—
639C4—1724no—
640C4C2×#1306329818yes—
641C2—1724no—
642C2—1724no—
643C2#1913802718yesdirect product factor
644C2C22×#1306329811yescharacteristic
645C2C2×#1458341211yescharacteristic
646C2C2×#1458347211yescharacteristic
647C2C2×#1458355211yescharacteristic
648C2C2×#1458355711yescharacteristic
649C2C2×#1458359011yescharacteristic
650C2C2×#1458362211yescharacteristic
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×#391C2
socleC24×C43C24
prime radicalC23×D172C22
hypercenterC2×#391D43
hypocenterC43C2×#2415
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
1. C22×#13063301C2semidirect
2. C22×#13063301C2semidirect
4. C22×#13063283C2semidirect
5. #19138027C2direct (N × H)
6. C2×#14582828C2semidirect
8. C2×#14582797C2semidirect
9. C2×#14582796C2semidirect
10. C2×#14582788C2semidirect
11. C2×#14582756C2semidirect
12. C2×C43×#391C2semidirect
18. C2×#13063301C22semidirect
19. C2×#13063301C22semidirect
23. C2×#13063283C22semidirect
37. #14582828C22semidirect
39. #14582797C22semidirect
40. #14582796C22semidirect
41. #14582788C22semidirect
42. #14582756C22semidirect
48. C43×#391C22semidirect
75. C2×C4⋊Dic43D4semidirect
195. C4⋊Dic43C2×D4semidirect
323. C2×#391D43semidirect
328. C2×C43#2415semidirect
367. #391C2×D43semidirect
376. C43C2×#2415semidirect
643. C2#19138027direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633012
C22×C4×D1722
C22×#130632832
#191380272
C2×#145828282
C2×#145828172
C2×#145827972
C2×#145827962
C2×#145827882
C2×#145827562
C2×C43×#3912
C2×#241543