Finite Group Databasebeta

← C2×#19138899 #25265645

Subgroups — C2×#19138899 #25265645

Order 11008.

3678 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063307C212yesmaximal
2C22×C4×C22⋊D43C211yesmaximal, characteristic
3C22×C4⋊C4×D43C211yesmaximal, characteristic, complemented
4#19138899C2116yesmaximal, direct product factor
5C2×#14582833C212yesmaximal, complemented
6C2×#14582827C212yesmaximal, complemented
7C2×#14582798C211yesmaximal, characteristic, complemented
8C2×#14582795C211yesmaximal, characteristic, complemented
9C2×#14582761C212yesmaximal, complemented
10C2×#14582759C211yesmaximal, characteristic, complemented
11C2×#14582756C211yesmaximal, characteristic, complemented
12C2×C43×#380C211yesmaximal, characteristic, complemented
13C23×C22⋊D43C2211yescharacteristic
14C23×C4×D43C2212yes—
15C23×C4×D43C2211yescharacteristic
16C2×#13063307—216no—
17C2×#13063307C22116yes—
18C2×C4×C22⋊D43—28no—
19C2×C4×C22⋊D43C2218yes—
20C22×C4⋊Dic43C2211yescharacteristic
21C22×C4⋊Dic43C2212yes—
22C22×C4⋊Dic43C2211yescharacteristic
23C22×Dic43⋊C4C2212yes—
24C22×Dic43⋊C4C2212yes—
25C22×Dic43⋊C4C2211yescharacteristic
26C2×C4⋊C4×D43—28no—
27C2×C4⋊C4×D43C2218yescomplemented
28C22×C22⋊Dic43C2211yescharacteristic
29C22×C22⋊Dic43C2212yes—
30C22×(C2×D43)⋊C4C2212yes—
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×C4×Dic43C2211yescharacteristic
33#14582833C22116yescomplemented
34#14582827C22116yescomplemented
35#14582798C2218yescomplemented
36#14582795C2218yescomplemented
37#14582761C22116yescomplemented
38#14582759C2218yescomplemented
39#14582756C2218yescomplemented
40C2×C43⋊#95C2212yes—
41C2×C43⋊#95C2212yes—
42C2×C43⋊#95C2212yes—
43C2×C43⋊#95C2212yes—
44C24×C4×C43C2211yescharacteristic
45C22×C4⋊C4×C43C2211yescharacteristic
46C22×C4⋊C4×C43C2211yescharacteristic
47C22×C22⋊C4×C43C2212yes—
48C43×#380C2218yescomplemented
49C2×#95×C43C2212yes—
50C24×D43C2311yescharacteristic
51C22×C22⋊D43—24no—
52C22×C22⋊D43—24no—
53C22×C22⋊D43D418yes—
54C22×C22⋊D43C2314yes—
55C23×Dic43C2311yescharacteristic
56C23×Dic43C2312yes—
57C23×Dic43C2312yes—
58C23×Dic43C2311yescharacteristic
59C23×Dic43C2311yescharacteristic
60C22×C4×D43—24no—
61C22×C4×D43—24no—
62C22×C4×D43—28no—
63C22×C4×D43—28no—
64C22×C4×D43—28no—
65C22×C4×D43D418yes—
66C22×C4×D43C2318yes—
67C22×C4×D43C2314yes—
68#13063307—264no—
69C4×C22⋊D43—232no—
70C2×C4⋊Dic43—24no—
71C2×C4⋊Dic43—24no—
72C2×C4⋊Dic43—28no—
73C2×C4⋊Dic43C2314yes—
74C2×C4⋊Dic43C2318yes—
75C2×C4⋊Dic43C2314yes—
76C2×Dic43⋊C4—28no—
77C2×Dic43⋊C4—24no—
78C2×Dic43⋊C4—28no—
79C2×Dic43⋊C4C2318yes—
80C2×Dic43⋊C4C2318yes—
81C2×Dic43⋊C4C2314yes—
82C4⋊C4×D43—232no—
83C2×C22⋊Dic43—28no—
84C2×C22⋊Dic43—24no—
85C2×C22⋊Dic43C2314yes—
86C2×C22⋊Dic43C2318yes—
87C2×(C2×D43)⋊C4—24no—
88C2×(C2×D43)⋊C4—28no—
89C2×(C2×D43)⋊C4C2314yes—
90C2×(C2×D43)⋊C4C2318yes—
91C2×C4×Dic43—24no—
92C2×C4×Dic43C2314yes—
93C43⋊#95C2318yes—
94C43⋊#95C2318yes—
95C43⋊#95C2318yes—
96C43⋊#95C2318yes—
97C25×C43C2311yescharacteristic
98C23×C4×C43—24no—
99C23×C4×C43—24no—
100C23×C4×C43—24no—
101C23×C4×C43C2312yes—
102C23×C4×C43C2312yes—
103C23×C4×C43C2311yescharacteristic
104C23×C4×C43C2314yes—
105C23×C4×C43C2311yescharacteristic
106C2×C4⋊C4×C43—24no—
107C2×C4⋊C4×C43—24no—
108C2×C4⋊C4×C43C2314yes—
109C2×C4⋊C4×C43C2314yes—
110C2×C22⋊C4×C43—28no—
111C2×C22⋊C4×C43C2318yes—
112#95×C43C2318yes—
113C24×C43—22no—
114C24×C43—22no—
115C24×C43—22no—
116C24×C43—22no—
117C24×C43—22no—
118C24×C43—22no—
119C24×C43C2×D414yes—
120C24×C43C2412yes—
121C24×C43C2411yescharacteristic
122C23×D43—22no—
123C23×D43—22no—
124C23×D43—22no—
125C23×D43—22no—
126C23×D43C2×D414yes—
127C23×D43C2×D414yes—
128C23×D43#4114yes—
129C23×D43C2412yes—
130C22×C4×C43—28no—
131C22×C4×C43—28no—
132C22×C4×C43—28no—
133C22×C4×C43—24no—
134C22×C4×C43—24no—
135C22×C4×C43—24no—
136C22×C4×C43—22no—
137C22×C4×C43—24no—
138C22×C4×C43—22no—
139C22×C4×C43—22no—
140C22×C4×C43—24no—
141C22×C4×C43—24no—
142C22×C4×C43—416no—
143C22×C4×C43C2×D414yes—
144C22×C4×C43#4114yes—
145C22×C4×C43#4114yes—
146C22×C4×C43C2412yes—
147C22×C4×C43C2414yes—
148C22×C4×C43C2414yes—
149C22×C4×C43C2412yes—
150C2×C22⋊D43—232no—
151C2×C22⋊D43—28no—
152C2×C22⋊D43—28no—
153C2×C22⋊D43C2×D4116yes—
154C22×Dic43—22no—
155C22×Dic43—22no—
156C22×Dic43—24no—
157C22×Dic43—24no—
158C22×Dic43—24no—
159C22×Dic43—22no—
160C22×Dic43—22no—
161C22×Dic43—22no—
162C22×Dic43—24no—
163C22×Dic43—24no—
164C22×Dic43—22no—
165C22×Dic43—22no—
166C22×Dic43—24no—
167C22×Dic43C2×D414yes—
168C22×Dic43C2×D414yes—
169C22×Dic43C2412yes—
170C22×Dic43C2414yes—
171C22×Dic43C2414yes—
172C22×Dic43C2412yes—
173C22×Dic43C2412yes—
174C2×C4×D43—232no—
175C2×C4×D43—28no—
176C2×C4×D43—28no—
177C2×C4×D43—216no—
178C2×C4×D43—216no—
179C2×C4×D43—216no—
180C2×C4×D43—432no—
181C2×C4×D43C2×D4116yes—
182C4⋊C4×C43—28no—
183C4⋊C4×C43—28no—
184C22⋊C4×C43—216no—
185C22⋊Dic43—28no—
186C22⋊Dic43—216no—
187(C2×D43)⋊C4—28no—
188(C2×D43)⋊C4—216no—
189C4⋊Dic43—28no—
190C4⋊Dic43—28no—
191C4⋊Dic43—216no—
192Dic43⋊C4—216no—
193Dic43⋊C4—28no—
194Dic43⋊C4—216no—
195C4×Dic43—28no—
196C23×C43—28no—
197C23×C43—28no—
198C23×C43—28no—
199C23×C43—22no—
200C23×C43—22no—
201C23×C43—22no—
202C23×C43—22no—
203C23×C43—22no—
204C23×C43—22no—
205C23×C43—44no—
206C23×C43—44no—
207C23×C43—44no—
208C23×C43—44no—
209C23×C43C22×D414yes—
210C23×C43C22×D412yes—
211C23×C43C22×D412yes—
212C23×C43C2×#4112yes—
213C23×C43C2×#4112yes—
214C23×C43C2×#4112yes—
215C23×C432−1+412yes—
216C23×C432−1+412yes—
217C23×C43C2511yescharacteristic
218C22×D43—28no—
219C22×D43—28no—
220C22×D43—28no—
221C22×D43—28no—
222C22×D43—28no—
223C22×D43—28no—
224C22×D43—22no—
225C22×D43—22no—
226C22×D43—22no—
227C22×D43—22no—
228C22×D43#121116yes—
229C22×D43C22×D414yes—
230C22×D43C22×D414yes—
231C22×D43C2×#4114yes—
232C2×C4×C43—22no—
233C2×C4×C43—24no—
234C2×C4×C43—24no—
235C2×C4×C43—24no—
236C2×C4×C43—24no—
237C2×C4×C43—24no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—24no—
241C2×C4×C43—48no—
242C2×C4×C43—44no—
243C2×C4×C43—48no—
244C2×C4×C43—416no—
245C2×C4×C43#123116yescomplemented
246C2×C4×C43C22×D414yes—
247C2×C4×C43C2×#4114yes—
248C2×C4×C43C2×#4114yes—
249C22⋊D43—232no—
250C2×Dic43—28no—
251C2×Dic43—28no—
252C2×Dic43—22no—
253C2×Dic43—22no—
254C2×Dic43—22no—
255C2×Dic43—22no—
256C2×Dic43—22no—
257C2×Dic43—24no—
258C2×Dic43—24no—
259C2×Dic43—24no—
260C2×Dic43—24no—
261C2×Dic43—24no—
262C2×Dic43—22no—
263C2×Dic43—22no—
264C2×Dic43—24no—
265C2×Dic43—48no—
266C2×Dic43—44no—
267C2×Dic43—48no—
268C2×Dic43C22×D414yes—
269C2×Dic43C22×D414yes—
270C4×D43—232no—
271C4×D43—432no—
272C2×#2486—431nomaximal, Sylow
273C22×C43—24no—
274C22×C43—24no—
275C22×C43—24no—
276C22×C43—42no—
277C22×C43—42no—
278C22×C43—42no—
279C22×C43—42no—
280C22×C43—416no—
281C22×C43C2×#12114yes—
282C22×C43C2×#12314yes—
283C22×C43#53614yes—
284C22×C43#54714yes—
285C22×C43#54714yes—
286C22×C43#55214yes—
287C22×C43#55214yes—
288C22×C43C23×D411yescharacteristic
289C22×C43C23×D411yescharacteristic
290C22×C43C22×#4111yescharacteristic
291C22×C43C22×#4111yescharacteristic
292C22×C43C22×#4111yescharacteristic
293C22×C43C2×2−1+411yescharacteristic
294C22×C43C2×2−1+411yescharacteristic
295C2×D43—24no—
296C2×D43—24no—
297C2×D43—24no—
298C2×D43—24no—
299C2×D43—24no—
300C2×D43—24no—
301C2×D43—232no—
302C2×D43C2×#12118yes—
303C4×C43—44no—
304C4×C43—42no—
305C4×C43—44no—
306C4×C43C2×#12318yescomplemented
307Dic43—24no—
308Dic43—24no—
309Dic43—44no—
310Dic43—42no—
311Dic43—44no—
312C22×#123—432no—
313C22×C4×D4—431no—
314C23×C4⋊C4—431no—
315#2486—4316no—
316C2×#398—432no—
317C2×#397—432no—
318C2×#389—431no—
319C2×#389—431no—
320C2×#381—432no—
321C2×#380—431no—
322C2×#380—431no—
323C2×#380D4311yescharacteristic, complemented
324C2×C43—44no—
325C2×C43#248618yescomplemented
326C2×C43C22×#12111yescharacteristic
327C2×C43C22×#12311yescharacteristic
328C2×C43C2×#53611yescharacteristic
329C2×C43C2×#54711yescharacteristic
330C2×C43C2×#54711yescharacteristic
331C2×C43C2×#55211yescharacteristic
332C2×C43C2×#55211yescharacteristic
333D43—28no—
334C23×D4—431no—
335C24×C4—431no—
336C24×C4—432no—
337C24×C4C2×D4311yescharacteristic
338C2×#123—4316no—
339C2×#123—8616no—
340C2×C4×D4—438no—
341C2×C4×D4—868no—
342C22×C4⋊C4—432no—
343C22×C4⋊C4—431no—
344C22×C4⋊C4—432no—
345C22×C4⋊C4—432no—
346C22×C4⋊C4—431no—
347C22×C4⋊C4—431no—
348C22×C4⋊C4—438no—
349C22×C4⋊C4—868no—
350C22×C4⋊C4C2×D4311yescharacteristic
351C22×C4⋊C4C2×D4311yescharacteristic
352C22×C22⋊C4—431no—
353C22×C22⋊C4—432no—
354C22×C22⋊C4—431no—
355C22×C22⋊C4—432no—
356C22×C22⋊C4C2×D4312yes—
357C22×C42—431no—
358#398—4316no—
359#397—4316no—
360#389—438no—
361#389—438no—
362#381—4316no—
363#380—438no—
364#380—438no—
365#380C2×D4318yescomplemented
366C2×#95—432no—
367C2×#95—432no—
368C2×#95—432no—
369C2×#95—432no—
370C2×#95C2×D4312yes—
371C43C2×#248611yescharacteristic, complemented, Sylow
372C25—431no—
373C25C22×D4311yescharacteristic
374C22×D4—438no—
375C22×D4—434no—
376C22×D4—864no—
377C22×D4—864no—
378C23×C4—24no—
379C23×C4—24no—
380C23×C4—24no—
381C23×C4—431no—
382C23×C4—431no—
383C23×C4—438no—
384C23×C4—434no—
385C23×C4—432no—
386C23×C4—431no—
387C23×C4—432no—
388C23×C4—438no—
389C23×C4—868no—
390C23×C4—868no—
391C23×C4—868no—
392C23×C4—864no—
393C23×C4—864no—
394C23×C4C22×D4314yes—
395C23×C4C22×D4312yes—
396C23×C4C22×D4311yescharacteristic
397C23×C4C22×D4312yes—
398C23×C4C22×D4311yescharacteristic
399#123—8664no—
400C4×D4—8632no—
401C2×C4⋊C4—24no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—438no—
404C2×C4⋊C4—434no—
405C2×C4⋊C4—434no—
406C2×C4⋊C4—438no—
407C2×C4⋊C4—438no—
408C2×C4⋊C4—434no—
409C2×C4⋊C4—8632no—
410C2×C4⋊C4—868no—
411C2×C4⋊C4—864no—
412C2×C4⋊C4—868no—
413C2×C4⋊C4—868no—
414C2×C4⋊C4—864no—
415C2×C4⋊C4—864no—
416C2×C4⋊C4C22×D4314yes—
417C2×C4⋊C4C22×D4314yes—
418C2×C22⋊C4—28no—
419C2×C22⋊C4—434no—
420C2×C22⋊C4—438no—
421C2×C22⋊C4—434no—
422C2×C22⋊C4—438no—
423C2×C22⋊C4—864no—
424C2×C22⋊C4—868no—
425C2×C22⋊C4—864no—
426C2×C22⋊C4—868no—
427C2×C22⋊C4C22×D4318yes—
428C2×C42—434no—
429C2×C42—864no—
430#95—438no—
431#95—438no—
432#95—438no—
433#95—438no—
434#95C22×D4318yes—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—434no—
442C24—434no—
443C24—434no—
444C24—432no—
445C24—862no—
446C24—862no—
447C24—862no—
448C24—862no—
449C24D4×D4314yes—
450C24C23×D4312yes—
451C24C23×D4311yescharacteristic
452C2×D4—4316no—
453C2×D4—868no—
454C2×D4—8632no—
455C2×D4—868no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—28no—
466C22×C4—28no—
467C22×C4—28no—
468C22×C4—416no—
469C22×C4—434no—
470C22×C4—434no—
471C22×C4—432no—
472C22×C4—432no—
473C22×C4—4316no—
474C22×C4—432no—
475C22×C4—434no—
476C22×C4—434no—
477C22×C4—8616no—
478C22×C4—8616no—
479C22×C4—8616no—
480C22×C4—862no—
481C22×C4—862no—
482C22×C4—862no—
483C22×C4—862no—
484C22×C4—8632no—
485C22×C4—868no—
486C22×C4—868no—
487C22×C4—862no—
488C22×C4—864no—
489C22×C4—864no—
490C22×C4—864no—
491C22×C4—864no—
492C22×C4—864no—
493C22×C4—862no—
494C22×C4—862no—
495C22×C4—864no—
496C22×C4—17232no—
497C22×C4#1062189814yes—
498C22×C4D4×D4314yes—
499C22×C4#1062190014yes—
500C22×C4C23×D4312yes—
501C22×C4C23×D4314yes—
502C22×C4C23×D4314yes—
503C22×C4C23×D4312yes—
504C4⋊C4—28no—
505C4⋊C4—28no—
506C4⋊C4—8616no—
507C4⋊C4—868no—
508C4⋊C4—8616no—
509C4⋊C4—8616no—
510C4⋊C4—868no—
511C4⋊C4—868no—
512C22⋊C4—216no—
513C22⋊C4—868no—
514C22⋊C4—8616no—
515C22⋊C4—868no—
516C22⋊C4—8616no—
517C42—868no—
518C23—28no—
519C23—22no—
520C23—22no—
521C23—22no—
522C23—22no—
523C23—22no—
524C23—22no—
525C23—28no—
526C23—28no—
527C23—44no—
528C23—44no—
529C23—44no—
530C23—44no—
531C23—4316no—
532C23—434no—
533C23—434no—
534C23—434no—
535C23—868no—
536C23—868no—
537C23—868no—
538C23—862no—
539C23—862no—
540C23—868no—
541C23—862no—
542C23—862no—
543C23—868no—
544C23—868no—
545C23C2×D4×D4314yes—
546C23C2×D4×D4312yes—
547C23C2×D4×D4312yes—
548C23#41×D4312yes—
549C23C2×#1062190012yes—
550C23C2×#1062189812yes—
551C23#1306337212yes—
552C23#1306337312yes—
553C23C24×D4311yescharacteristic
554D4—8632no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—24no—
564C2×C4—48no—
565C2×C4—44no—
566C2×C4—48no—
567C2×C4—416no—
568C2×C4—434no—
569C2×C4—434no—
570C2×C4—868no—
571C2×C4—868no—
572C2×C4—862no—
573C2×C4—862no—
574C2×C4—862no—
575C2×C4—862no—
576C2×C4—8632no—
577C2×C4—862no—
578C2×C4—864no—
579C2×C4—864no—
580C2×C4—864no—
581C2×C4—864no—
582C2×C4—864no—
583C2×C4—862no—
584C2×C4—864no—
585C2×C4—862no—
586C2×C4—17232no—
587C2×C4—1728no—
588C2×C4—1724no—
589C2×C4—1728no—
590C2×C4#13063307116yescomplemented
591C2×C4C2×D4×D4314yes—
592C2×C4C2×#1062190014yes—
593C2×C4C2×#1062189814yes—
594C22—24no—
595C22—24no—
596C22—24no—
597C22—42no—
598C22—42no—
599C22—42no—
600C22—416no—
601C22—42no—
602C22—438no—
603C22—864no—
604C22—864no—
605C22—864no—
606C22—864no—
607C22—864no—
608C22—8632no—
609C22—864no—
610C22#121×D4314yes—
611C22C2×#1306330714yes—
612C22#1458347214yes—
613C22#1458354914yes—
614C22#1458355014yes—
615C22#1458358314yes—
616C22#1458358814yes—
617C22C22×D4×D4311yescharacteristic
618C22C22×D4×D4311yescharacteristic
619C22C2×#41×D4311yescharacteristic
620C22C22×#1062190011yescharacteristic
621C22C22×#1062189811yescharacteristic
622C22C2×#1306337211yescharacteristic
623C22C2×#1306337311yescharacteristic
624C4—44no—
625C4—44no—
626C4—42no—
627C4—864no—
628C4—864no—
629C4—1724no—
630C4—1724no—
631C4—1722no—
632C4C2×#1306330718yescomplemented
633C2—44no—
634C2—868no—
635C2#1913889918yesdirect product factor
636C2C2×#121×D4311yescharacteristic
637C2C22×#1306330711yescharacteristic
638C2C2×#1458347211yescharacteristic
639C2C2×#1458354911yescharacteristic
640C2C2×#1458355011yescharacteristic
641C2C2×#1458358311yescharacteristic
642C2C2×#1458358811yescharacteristic
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×#380C2
socleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenterC2×#380D43
hypocenterC43C2×#2486
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
3. C22×C4⋊C4×D43C2semidirect
4. #19138899C2direct (N × H)
5. C2×#14582833C2semidirect
6. C2×#14582827C2semidirect
7. C2×#14582798C2semidirect
8. C2×#14582795C2semidirect
9. C2×#14582761C2semidirect
10. C2×#14582759C2semidirect
11. C2×#14582756C2semidirect
12. C2×C43×#380C2semidirect
27. C2×C4⋊C4×D43C22semidirect
33. #14582833C22semidirect
34. #14582827C22semidirect
35. #14582798C22semidirect
36. #14582795C22semidirect
37. #14582761C22semidirect
38. #14582759C22semidirect
39. #14582756C22semidirect
48. C43×#380C22semidirect
245. C2×C4×C43#123semidirect
306. C4×C43C2×#123semidirect
323. C2×#380D43semidirect
325. C2×C43#2486semidirect
365. #380C2×D43semidirect
371. C43C2×#2486semidirect
590. C2×C4#13063307semidirect
632. C4C2×#13063307semidirect
635. C2#19138899direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633072
C22×C4×C22⋊D432
C22×C4⋊C4×D432
#191388992
C2×#145828332
C2×#145828272
C2×#145827982
C2×#145827952
C2×#145827612
C2×#145827592
C2×#145827562
C2×C43×#3802
C2×#248643