Finite Group Databasebeta

← C2×#19140169 #25267346

Subgroups — C2×#19140169 #25267346

Order 11008.

2766 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic86C211yesmaximal, characteristic, complemented
2C22×#13063281C211yesmaximal, characteristic
3#19140169C2116yesmaximal, direct product factor
4C2×#14582833C211yesmaximal, characteristic, complemented
5C2×#14582827C211yesmaximal, characteristic
6C2×#14582819C211yesmaximal, characteristic, complemented
7C2×#14582811C211yesmaximal, characteristic
8C2×#14582787C211yesmaximal, characteristic
9C2×#14582785C211yesmaximal, characteristic, complemented
10C2×#14582784C211yesmaximal, characteristic, complemented
11C2×#14582783C211yesmaximal, characteristic, complemented
12C2×#14582781C211yesmaximal, characteristic, complemented
13C2×#14582774C211yesmaximal, characteristic
14C2×#14582771C211yesmaximal, characteristic
15C2×#14582766C211yesmaximal, characteristic, complemented
16C2×C43×#388C211yesmaximal, characteristic
17C23×Dic86C2211yescharacteristic
18C24×Dic43C2211yescharacteristic
19C2×C4×Dic86—28no—
20C2×C4×Dic86C2218yescomplemented
21C2×#13063281—28no—
22C2×#13063281C2218yes—
23C22×C4⋊Dic43C2211yescharacteristic
24C22×C4⋊Dic43C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×Dic43⋊C4C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
28C22×Dic43⋊C4C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30C22×Dic43⋊C4C2211yescharacteristic
31C22×C22⋊Dic43C2211yescharacteristic
32C22×C22⋊Dic43C2211yescharacteristic
33C22×C22⋊Dic43C2211yescharacteristic
34C22×C4×Dic43C2211yescharacteristic
35C22×C4×Dic43C2211yescharacteristic
36C22×C4×Dic43C2211yescharacteristic
37#14582833C2218yescomplemented
38#14582827C2218yes—
39#14582819C2218yescomplemented
40#14582811C2218yes—
41#14582787C2218yes—
42#14582785C2218yescomplemented
43#14582784C2218yescomplemented
44#14582783C2218yescomplemented
45#14582781C2218yescomplemented
46#14582774C2218yes—
47#14582771C2218yes—
48#14582766C2218yescomplemented
49C2×C43⋊#95C2211yescharacteristic
50C2×C43⋊#95C2211yescharacteristic
51C2×C43⋊#95C2211yescharacteristic
52C2×C43⋊#95C2211yescharacteristic
53C2×C43⋊#95C2211yescharacteristic
54C2×C43⋊#95C2211yescharacteristic
55C2×C43⋊#95C2211yescharacteristic
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C2×C43⋊#95C2211yescharacteristic
60C2×C43⋊#95C2211yescharacteristic
61C22×C4⋊C4×C43C2211yescharacteristic
62C22×C22⋊C4×C43C2211yescharacteristic
63C22×C22⋊C4×C43C2211yescharacteristic
64C22×C22⋊C4×C43C2211yescharacteristic
65C22×C42×C43C2211yescharacteristic
66C43×#388C2218yes—
67C2×#95×C43C2211yescharacteristic
68C2×#95×C43C2211yescharacteristic
69C22×Dic86—24no—
70C22×Dic86—24no—
71C22×Dic86—24no—
72C22×Dic86C2314yes—
73C23×Dic43—24no—
74C23×Dic43—24no—
75C23×Dic43—24no—
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C23×Dic43C2314yes—
81C23×Dic43C2311yescharacteristic
82C23×Dic43C2311yescharacteristic
83C23×Dic43C2311yescharacteristic
84C23×Dic43C2311yescharacteristic
85C4×Dic86—232no—
86#13063281—232no—
87C2×C4⋊Dic43—24no—
88C2×C4⋊Dic43—24no—
89C2×C4⋊Dic43C2314yes—
90C2×C4⋊Dic43C2314yes—
91C2×Dic43⋊C4—24no—
92C2×Dic43⋊C4—24no—
93C2×Dic43⋊C4—24no—
94C2×Dic43⋊C4—24no—
95C2×Dic43⋊C4—24no—
96C2×Dic43⋊C4—24no—
97C2×Dic43⋊C4C2314yes—
98C2×Dic43⋊C4C2314yes—
99C2×Dic43⋊C4C2314yes—
100C2×Dic43⋊C4C2314yes—
101C2×Dic43⋊C4C2314yes—
102C2×Dic43⋊C4C2314yes—
103C2×C22⋊Dic43—24no—
104C2×C22⋊Dic43—24no—
105C2×C22⋊Dic43—24no—
106C2×C22⋊Dic43C2314yes—
107C2×C22⋊Dic43C2314yes—
108C2×C22⋊Dic43C2314yes—
109C2×C4×Dic43—24no—
110C2×C4×Dic43—24no—
111C2×C4×Dic43D418yes—
112C2×C4×Dic43C2314yes—
113C2×C4×Dic43C2314yes—
114C2×C4×Dic43C2314yes—
115C43⋊#95C2314yes—
116C43⋊#95C2314yes—
117C43⋊#95C2314yes—
118C43⋊#95C2314yes—
119C43⋊#95C2314yes—
120C43⋊#95C2314yes—
121C43⋊#95C2314yes—
122C43⋊#95C2314yes—
123C43⋊#95C2314yes—
124C43⋊#95C2314yes—
125C43⋊#95C2314yes—
126C43⋊#95C2314yes—
127C25×C43C2311yescharacteristic
128C23×C4×C43C2311yescharacteristic
129C23×C4×C43C2311yescharacteristic
130C23×C4×C43C2311yescharacteristic
131C23×C4×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43—24no—
135C2×C4⋊C4×C43C2314yes—
136C2×C22⋊C4×C43—24no—
137C2×C22⋊C4×C43—24no—
138C2×C22⋊C4×C43—24no—
139C2×C22⋊C4×C43C2314yes—
140C2×C22⋊C4×C43C2314yes—
141C2×C22⋊C4×C43C2314yes—
142C2×C42×C43—24no—
143C2×C42×C43C2314yes—
144#95×C43C2314yes—
145#95×C43C2314yes—
146C24×C43—22no—
147C24×C43—22no—
148C24×C43—22no—
149C24×C43—22no—
150C24×C43—22no—
151C24×C43—22no—
152C24×C43#4114yes—
153C24×C43C2412yes—
154C24×C43C2411yescharacteristic
155C22×C4×C43—22no—
156C22×C4×C43—22no—
157C22×C4×C43—22no—
158C22×C4×C43—22no—
159C22×C4×C43—22no—
160C22×C4×C43—22no—
161C22×C4×C43—22no—
162C22×C4×C43—22no—
163C22×C4×C43—22no—
164C22×C4×C43—22no—
165C22×C4×C43—22no—
166C22×C4×C43—22no—
167C22×C4×C43—22no—
168C22×C4×C43—22no—
169C22×C4×C43—22no—
170C22×C4×C43—22no—
171C22×C4×C43C2×D414yes—
172C22×C4×C43#4114yes—
173C22×C4×C43C2412yes—
174C22×C4×C43C2412yes—
175C22×C4×C43C2412yes—
176C22×C4×C43C2412yes—
177C22×C4×C43C2412yes—
178C22×C4×C43C2412yes—
179C22×Dic43—232no—
180C22×Dic43—28no—
181C22×Dic43—28no—
182C22×Dic43—22no—
183C22×Dic43—22no—
184C22×Dic43—22no—
185C22×Dic43—22no—
186C22×Dic43—22no—
187C22×Dic43—28no—
188C22×Dic43—22no—
189C22×Dic43—22no—
190C22×Dic43—22no—
191C22×Dic43—22no—
192C22×Dic43—22no—
193C22×Dic43—22no—
194C22×Dic43—22no—
195C22×Dic43—22no—
196C22×Dic43—22no—
197C22×Dic43—22no—
198C22×Dic43—22no—
199C22×Dic43—22no—
200C22×Dic43—22no—
201C22×Dic43—22no—
202C22×Dic43—22no—
203C22×Dic43C2×D414yes—
204C22×Dic43C2×D414yes—
205C22×Dic43#4114yes—
206C22×Dic43#4114yes—
207C22×Dic43C2412yes—
208C22×Dic43C2412yes—
209C22×Dic43C2412yes—
210C22×Dic43C2412yes—
211C22×Dic43C2412yes—
212C22×Dic43C2412yes—
213C22×Dic43C2412yes—
214C22×Dic43C2412yes—
215C2×Dic86—232no—
216C2×Dic86—28no—
217C2×Dic86—28no—
218C2×Dic86—28no—
219C4⋊C4×C43—28no—
220C22⋊C4×C43—28no—
221C22⋊C4×C43—28no—
222C22⋊C4×C43—28no—
223C42×C43—28no—
224C22⋊Dic43—28no—
225C22⋊Dic43—28no—
226C22⋊Dic43—28no—
227C4⋊Dic43—28no—
228C4⋊Dic43—28no—
229Dic43⋊C4—28no—
230Dic43⋊C4—28no—
231Dic43⋊C4—28no—
232Dic43⋊C4—28no—
233Dic43⋊C4—28no—
234Dic43⋊C4—28no—
235C4×Dic43—28no—
236C4×Dic43—28no—
237C4×Dic43C2×D4116yes—
238C23×C43—28no—
239C23×C43—28no—
240C23×C43—28no—
241C23×C43—22no—
242C23×C43—22no—
243C23×C43—22no—
244C23×C43—22no—
245C23×C43—22no—
246C23×C43—22no—
247C23×C43—44no—
248C23×C43—44no—
249C23×C43—44no—
250C23×C43—44no—
251C23×C43C22×D412yes—
252C23×C43C2×#4112yes—
253C23×C43C2×#4112yes—
254C23×C43C2×#4112yes—
255C23×C43C2×#4114yes—
256C23×C43C2×#4112yes—
257C23×C432−1+412yes—
258C23×C432−1+412yes—
259C23×C43C2511yescharacteristic
260C2×C4×C43—28no—
261C2×C4×C43—28no—
262C2×C4×C43—22no—
263C2×C4×C43—22no—
264C2×C4×C43—22no—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43—22no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—44no—
279C2×C4×C43—44no—
280C2×C4×C43—44no—
281C2×C4×C43—44no—
282C2×C4×C43C22×D414yes—
283C2×C4×C43C2×#4114yes—
284C2×Dic43—232no—
285C2×Dic43—28no—
286C2×Dic43—28no—
287C2×Dic43—28no—
288C2×Dic43—28no—
289C2×Dic43—22no—
290C2×Dic43—22no—
291C2×Dic43—22no—
292C2×Dic43—22no—
293C2×Dic43—22no—
294C2×Dic43—22no—
295C2×Dic43—22no—
296C2×Dic43—22no—
297C2×Dic43—22no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—44no—
310C2×Dic43—44no—
311C2×Dic43—44no—
312C2×Dic43—44no—
313C2×Dic43C22×D414yes—
314C2×Dic43C22×D414yes—
315C2×Dic43C2×#4114yes—
316C2×Dic43C2×#4114yes—
317Dic86—232no—
318C2×#2599—431nomaximal, Sylow
319C22×C43—24no—
320C22×C43—24no—
321C22×C43—24no—
322C22×C43—416no—
323C22×C43—42no—
324C22×C43—42no—
325C22×C43—42no—
326C22×C43—42no—
327C22×C43#52514yes—
328C22×C43#52514yes—
329C22×C43#53614yes—
330C22×C43#55214yes—
331C22×C43#55214yes—
332C22×C43#55614yes—
333C22×C43#55614yes—
334C22×C43C23×D411yescharacteristic
335C22×C43C22×#4111yescharacteristic
336C22×C43C22×#4111yescharacteristic
337C22×C43C22×#4111yescharacteristic
338C22×C43C22×#4111yescharacteristic
339C22×C43C2×2−1+411yescharacteristic
340C22×C43C2×2−1+411yescharacteristic
341C4×C43—24no—
342C4×C43—24no—
343C4×C43—42no—
344C4×C43—42no—
345C4×C43—42no—
346C4×C43—42no—
347Dic43—24no—
348Dic43—24no—
349Dic43—24no—
350Dic43—24no—
351Dic43—42no—
352Dic43—42no—
353Dic43—42no—
354Dic43—42no—
355C22×C4×Q8—431no—
356C22×#117—431no—
357#2599—4316no—
358C2×#398—431no—
359C2×#397—431no—
360C2×#395—431no—
361C2×#393—431no—
362C2×#388—431no—
363C2×#388D4311yescharacteristic
364C2×#387—431no—
365C2×#387—431no—
366C2×#387—431no—
367C2×#387—431no—
368C2×#385—431no—
369C2×#385—431no—
370C2×#383—431no—
371C2×C43—44no—
372C2×C43#259918yescomplemented
373C2×C43C2×#52511yescharacteristic
374C2×C43C2×#52511yescharacteristic
375C2×C43C2×#53611yescharacteristic
376C2×C43C2×#55211yescharacteristic
377C2×C43C2×#55211yescharacteristic
378C2×C43C2×#55611yescharacteristic
379C2×C43C2×#55611yescharacteristic
380C23×Q8—431no—
381C24×C4—431no—
382C2×C4×Q8—438no—
383C2×C4×Q8—868no—
384C2×#117—438no—
385C2×#117—868no—
386C22×C4⋊C4—431no—
387C22×C4⋊C4—431no—
388C22×C4⋊C4—431no—
389C22×C4⋊C4—431no—
390C22×C4⋊C4—431no—
391C22×C4⋊C4—431no—
392C22×C4⋊C4—431no—
393C22×C4⋊C4—431no—
394C22×C4⋊C4C2×D4311yescharacteristic
395C22×C22⋊C4—431no—
396C22×C22⋊C4—431no—
397C22×C22⋊C4—431no—
398C22×C22⋊C4C2×D4311yescharacteristic
399C22×C22⋊C4C2×D4311yescharacteristic
400C22×C22⋊C4C2×D4311yescharacteristic
401C22×C42—431no—
402C22×C42—431no—
403C22×C42—431no—
404C22×C42C2×D4311yescharacteristic
405#398—438no—
406#397—438no—
407#395—438no—
408#393—438no—
409#388—438no—
410#388C2×D4318yes—
411#387—438no—
412#387—438no—
413#387—438no—
414#387—438no—
415#385—438no—
416#385—438no—
417#383—438no—
418C2×#95—431no—
419C2×#95—431no—
420C2×#95—431no—
421C2×#95—431no—
422C2×#95—431no—
423C2×#95—431no—
424C2×#95—431no—
425C2×#95—431no—
426C2×#95—431no—
427C2×#95—431no—
428C2×#95—431no—
429C2×#95—431no—
430C2×#95C2×D4311yescharacteristic
431C2×#95C2×D4311yescharacteristic
432C43C2×#259911yescharacteristic, complemented, Sylow
433C25C22×D4311yescharacteristic
434C22×Q8—434no—
435C22×Q8—864no—
436C22×Q8—864no—
437C22×Q8—864no—
438C23×C4—431no—
439C23×C4—431no—
440C23×C4—431no—
441C23×C4—431no—
442C23×C4—434no—
443C23×C4—431no—
444C23×C4—431no—
445C23×C4—431no—
446C23×C4—431no—
447C23×C4—864no—
448C23×C4—864no—
449C23×C4—864no—
450C23×C4C22×D4311yescharacteristic
451C23×C4C22×D4311yescharacteristic
452C23×C4C22×D4311yescharacteristic
453C23×C4C22×D4311yescharacteristic
454C23×C4C22×D4311yescharacteristic
455C23×C4C22×D4311yescharacteristic
456C4×Q8—8632no—
457#117—8632no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—434no—
460C2×C4⋊C4—434no—
461C2×C4⋊C4—434no—
462C2×C4⋊C4—434no—
463C2×C4⋊C4—434no—
464C2×C4⋊C4—434no—
465C2×C4⋊C4—434no—
466C2×C4⋊C4—434no—
467C2×C4⋊C4—864no—
468C2×C4⋊C4—864no—
469C2×C4⋊C4—864no—
470C2×C4⋊C4—864no—
471C2×C4⋊C4—864no—
472C2×C4⋊C4—864no—
473C2×C4⋊C4—864no—
474C2×C4⋊C4—864no—
475C2×C4⋊C4C22×D4314yes—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—434no—
480C2×C22⋊C4—434no—
481C2×C22⋊C4—434no—
482C2×C22⋊C4—864no—
483C2×C22⋊C4—864no—
484C2×C22⋊C4—864no—
485C2×C22⋊C4C22×D4314yes—
486C2×C22⋊C4C22×D4314yes—
487C2×C22⋊C4C22×D4314yes—
488C2×C42—24no—
489C2×C42—438no—
490C2×C42—434no—
491C2×C42—434no—
492C2×C42—434no—
493C2×C42—864no—
494C2×C42—864no—
495C2×C42C22×D4314yes—
496#95—434no—
497#95—434no—
498#95—434no—
499#95—434no—
500#95—434no—
501#95—434no—
502#95—434no—
503#95—434no—
504#95—434no—
505#95—434no—
506#95—434no—
507#95—434no—
508#95C22×D4314yes—
509#95C22×D4314yes—
510C24—22no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24#1062189814yes—
517C24C23×D4312yes—
518C24C23×D4311yescharacteristic
519C2×Q8—868no—
520C2×Q8—868no—
521C2×Q8—8632no—
522C2×Q8—868no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—434no—
540C22×C4—434no—
541C22×C4—434no—
542C22×C4—434no—
543C22×C4—432no—
544C22×C4—432no—
545C22×C4—432no—
546C22×C4—432no—
547C22×C4—432no—
548C22×C4—432no—
549C22×C4—432no—
550C22×C4—432no—
551C22×C4—868no—
552C22×C4—868no—
553C22×C4—8632no—
554C22×C4—862no—
555C22×C4—862no—
556C22×C4—862no—
557C22×C4—862no—
558C22×C4—862no—
559C22×C4—862no—
560C22×C4—868no—
561C22×C4—862no—
562C22×C4—862no—
563C22×C4—862no—
564C22×C4—862no—
565C22×C4—862no—
566C22×C4—862no—
567C22×C4—862no—
568C22×C4—862no—
569C22×C4—862no—
570C22×C4—862no—
571C22×C4—862no—
572C22×C4—862no—
573C22×C4—862no—
574C22×C4—862no—
575C22×C4D4×D4314yes—
576C22×C4#1062190014yes—
577C22×C4C23×D4312yes—
578C22×C4C23×D4312yes—
579C22×C4C23×D4312yes—
580C22×C4C23×D4312yes—
581C22×C4C23×D4312yes—
582C22×C4C23×D4312yes—
583C4⋊C4—28no—
584C4⋊C4—868no—
585C4⋊C4—868no—
586C4⋊C4—868no—
587C4⋊C4—868no—
588C4⋊C4—868no—
589C4⋊C4—868no—
590C4⋊C4—868no—
591C4⋊C4—868no—
592C22⋊C4—28no—
593C22⋊C4—28no—
594C22⋊C4—28no—
595C22⋊C4—868no—
596C22⋊C4—868no—
597C22⋊C4—868no—
598C42—28no—
599C42—4316no—
600C42—868no—
601C42—868no—
602C23—28no—
603C23—28no—
604C23—28no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—44no—
612C23—44no—
613C23—44no—
614C23—44no—
615C23C2×D4×D4312yes—
616C23#41×D4312yes—
617C23#41×D4312yes—
618C23C2×#1062190012yes—
619C23C2×#1062189814yes—
620C23C2×#1062189812yes—
621C23#1306337212yes—
622C23#1306337212yes—
623C23C24×D4311yescharacteristic
624Q8—8632no—
625C2×C4—28no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—28no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—44no—
647C2×C4—434no—
648C2×C4—434no—
649C2×C4—434no—
650C2×C4—434no—
651C2×C4—8632no—
652C2×C4—868no—
653C2×C4—868no—
654C2×C4—868no—
655C2×C4—868no—
656C2×C4—862no—
657C2×C4—862no—
658C2×C4—862no—
659C2×C4—862no—
660C2×C4—862no—
661C2×C4—862no—
662C2×C4—862no—
663C2×C4—862no—
664C2×C4—862no—
665C2×C4—862no—
666C2×C4—862no—
667C2×C4—862no—
668C2×C4—862no—
669C2×C4—862no—
670C2×C4—862no—
671C2×C4—862no—
672C2×C4—862no—
673C2×C4—862no—
674C2×C4—862no—
675C2×C4—862no—
676C2×C4—1724no—
677C2×C4—1724no—
678C2×C4—1724no—
679C2×C4—1724no—
680C2×C4C2×D4×D4314yes—
681C2×C4C2×#1062190014yes—
682C22—24no—
683C22—24no—
684C22—24no—
685C22—42no—
686C22—416no—
687C22—42no—
688C22—42no—
689C22—42no—
690C22#1458340814yes—
691C22#1458340914yes—
692C22#1458347114yes—
693C22#1458358214yes—
694C22#1458358914yes—
695C22#1458361614yes—
696C22#1458361814yes—
697C22C22×D4×D4311yescharacteristic
698C22C2×#41×D4311yescharacteristic
699C22C2×#41×D4311yescharacteristic
700C22C22×#1062190011yescharacteristic
701C22C22×#1062189811yescharacteristic
702C22C2×#1306337211yescharacteristic
703C22C2×#1306337211yescharacteristic
704C4—24no—
705C4—24no—
706C4—42no—
707C4—42no—
708C4—42no—
709C4—42no—
710C4—864no—
711C4—864no—
712C4—864no—
713C4—864no—
714C4—1722no—
715C4—1722no—
716C4—1722no—
717C4—1722no—
718C2—44no—
719C2#1914016918yesdirect product factor
720C2C2×#1458340811yescharacteristic
721C2C2×#1458340911yescharacteristic
722C2C2×#1458347111yescharacteristic
723C2C2×#1458358211yescharacteristic
724C2C2×#1458358911yescharacteristic
725C2C2×#1458361611yescharacteristic
726C2C2×#1458361811yescharacteristic
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×#388C2
socleC24×C43C24
prime radicalC25×C43C23
hypercenterC2×#388D43
hypocenterC43C2×#2599
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×C4×Dic86C2semidirect
3. #19140169C2direct (N × H)
4. C2×#14582833C2semidirect
6. C2×#14582819C2semidirect
9. C2×#14582785C2semidirect
10. C2×#14582784C2semidirect
11. C2×#14582783C2semidirect
12. C2×#14582781C2semidirect
15. C2×#14582766C2semidirect
20. C2×C4×Dic86C22semidirect
37. #14582833C22semidirect
39. #14582819C22semidirect
42. #14582785C22semidirect
43. #14582784C22semidirect
44. #14582783C22semidirect
45. #14582781C22semidirect
48. #14582766C22semidirect
372. C2×C43#2599semidirect
432. C43C2×#2599semidirect
719. C2#19140169direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×Dic862
C22×#130632812
#191401692
C2×#145828332
C2×#145828272
C2×#145828192
C2×#145828112
C2×#145827872
C2×#145827852
C2×#145827842
C2×#145827832
C2×#145827812
C2×#145827742
C2×#145827712
C2×#145827662
C2×C43×#3882
C2×#259943