Finite Group Databasebeta

← C2×#19144523 #25964381

Subgroups — C2×#19144523 #25964381

Order 11008.

2346 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583409C211yesmaximal, characteristic
2C2×#117×D43C211yesmaximal, characteristic, complemented
3#19144523C2116yesmaximal, direct product factor
4C2×#14583243C211yesmaximal, characteristic, complemented
5C2×#14583242C211yesmaximal, characteristic, complemented
6C2×#14583241C211yesmaximal, characteristic, complemented
7C2×#14583240C211yesmaximal, characteristic, complemented
8C2×#14583222C211yesmaximal, characteristic, complemented
9C2×#14583221C211yesmaximal, characteristic, complemented
10C2×#14583220C211yesmaximal, characteristic, complemented
11C2×#14582940C211yesmaximal, characteristic, complemented
12C2×#14582938C211yesmaximal, characteristic, complemented
13C2×#14582897C211yesmaximal, characteristic, complemented
14C2×#14582897C211yesmaximal, characteristic, complemented
15C2×#14582861C211yesmaximal, characteristic, complemented
16C2×C43×#482C211yesmaximal, characteristic, complemented
17C22×#10621900C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C22×#10621872C2211yescharacteristic
20C22×#10621872C2211yescharacteristic
21#14583409—24no—
22#14583409C2218yes—
23C2×#13063307—21no—
24C2×#13063305C2211yescharacteristic
25C2×#13063304C2211yescharacteristic
26C2×#13063296C2211yescharacteristic
27C2×#13063293—21no—
28C2×D4×Dic43—21no—
29C2×(C22⋊D43)⋊C4—21no—
30C2×#13063284C2211yescharacteristic
31C2×#13063283C2211yescharacteristic
32C2×#13063283C2211yescharacteristic
33C2×#13063283C2211yescharacteristic
34C2×#13063282—21no—
35C2×#13063281—21no—
36#117×D43—24no—
37#117×D43C2218yescomplemented
38C2×C4⋊C4×D43C2211yescharacteristic
39C2×C4⋊C4×D43C2211yescharacteristic
40C2×C22⋊C4×D43—21no—
41C2×C42×D43—21no—
42#14583243C2218yescomplemented
43#14583242C2218yescomplemented
44#14583241C2218yescomplemented
45#14583240C2218yescomplemented
46#14583222C2218yescomplemented
47#14583221C2218yescomplemented
48#14583220C2218yescomplemented
49#14582940C2218yescomplemented
50#14582938C2218yescomplemented
51C2×#13063259C2211yescharacteristic, complemented
52C2×#13063258C2211yescharacteristic, complemented
53C2×#13063258C2211yescharacteristic, complemented
54C2×#13063257C2211yescharacteristic, complemented
55C2×#13063256C2211yescharacteristic, complemented
56C2×#13063256C2211yescharacteristic, complemented
57#14582897C2218yescomplemented
58#14582897C2218yescomplemented
59C2×#13063250C2211yescharacteristic, complemented
60C2×#13063250C2211yescharacteristic, complemented
61C2×#13063248C2211yescharacteristic, complemented
62C2×#13063248C2211yescharacteristic, complemented
63C2×#13063246C2211yescharacteristic, complemented
64C2×#13063246C2211yescharacteristic, complemented
65#14582861C2218yescomplemented
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×(C2×D43)⋊C8C2211yescharacteristic
69C2×#121×C43C2211yescharacteristic
70C2×#117×C43C2211yescharacteristic
71C43×#482C2218yescomplemented
72C2×#107×C43C2211yescharacteristic, complemented
73C2×#106×C43C2211yescharacteristic, complemented
74C2×#102×C43C2211yescharacteristic, complemented
75C2×#102×C43C2211yescharacteristic, complemented
76C2×C22⋊C8×C43C2211yescharacteristic
77C24×D43D411yescharacteristic
78C2×#10621900—22no—
79C2×#10621900—24no—
80C2×#10621900—24no—
81C2×#10621900C2314yes—
82C22×Dic86C2311yescharacteristic
83C22×C22⋊D43—21no—
84C22×C22⋊D43—21no—
85C23×Dic43—21no—
86C23×Dic43D411yescharacteristic
87C22×C4×D43—24no—
88C22×C4×D43—24no—
89C22×C4×D43—21no—
90C22×C4×D43—21no—
91C22×C4×D43D411yescharacteristic
92C22×C4×D43D414yes—
93C22×C4×D43D411yescharacteristic
94C22×C4×D43C2314yes—
95C22×C4×D43C2311yescharacteristic
96C22×C4×D43C2311yescharacteristic
97C2×#10621872—24no—
98C2×#10621872—24no—
99C2×#10621872C2314yes—
100C2×#10621872C2314yes—
101C22×C43⋊C8C2311yescharacteristic
102C22×C43⋊C8C2311yescharacteristic
103#13063307—28no—
104#13063305—22no—
105#13063305C2314yes—
106#13063304—22no—
107#13063304C2314yes—
108#13063296—22no—
109#13063296C2314yes—
110#13063293—28no—
111D4×Dic43—28no—
112(C22⋊D43)⋊C4—28no—
113#13063284—22no—
114#13063284C2314yes—
115#13063283—22no—
116#13063283—22no—
117#13063283—22no—
118#13063283C2314yes—
119#13063283C2314yes—
120#13063283C2314yes—
121#13063282—28no—
122#13063281—28no—
123C2×C4⋊Dic43—21no—
124C2×C4⋊Dic43C2311yescharacteristic
125C2×C4⋊Dic43C2311yescharacteristic
126C2×C4⋊Dic43C2311yescharacteristic
127C2×Dic43⋊C4—21no—
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4—21no—
130C4⋊C4×D43—22no—
131C4⋊C4×D43—22no—
132C4⋊C4×D43C2314yes—
133C4⋊C4×D43C2314yes—
134C2×C22⋊Dic43—21no—
135C2×C22⋊Dic43—21no—
136C2×C22⋊Dic43—21no—
137C2×(C2×D43)⋊C4—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4—21no—
141C22⋊C4×D43—28no—
142C2×C4×Dic43—21no—
143C2×C4×Dic43—21no—
144C2×C4×Dic43—21no—
145C2×C4×Dic43—21no—
146C42×D43—28no—
147#13063259C2314yescomplemented
148#13063258C2314yescomplemented
149#13063258C2314yescomplemented
150#13063257C2314yescomplemented
151#13063256C2314yescomplemented
152#13063256C2314yescomplemented
153#13063250C2314yescomplemented
154#13063250C2314yescomplemented
155#13063248C2314yescomplemented
156#13063248C2314yescomplemented
157#13063246C2314yescomplemented
158#13063246C2314yescomplemented
159C22⋊(C43⋊C8)C2314yes—
160(C2×D43)⋊C8C2314yes—
161(C2×D43)⋊C8C2314yes—
162C22×D4×C43—21no—
163C22×D4×C43C2311yescharacteristic
164C23×C4×C43C2311yescharacteristic
165C22×C8×C43C2311yescharacteristic
166C22×C8×C43C2311yescharacteristic
167#121×C43—22no—
168#121×C43C2314yes—
169#117×C43—22no—
170#117×C43C2314yes—
171C2×C4⋊C4×C43C2311yescharacteristic
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C22⋊C4×C43—21no—
175C2×C22⋊C4×C43—21no—
176C2×C42×C43—21no—
177#107×C43C2314yescomplemented
178#106×C43C2314yescomplemented
179#102×C43C2314yescomplemented
180#102×C43C2314yescomplemented
181C22⋊C8×C43C2314yes—
182C24×C43—21no—
183C24×C43C2×D411yescharacteristic
184C23×D43—24no—
185C23×D43—42no—
186C23×D43—42no—
187C23×D43C2×D411yescharacteristic
188C23×D43C2×D411yescharacteristic
189C23×D43C2×D414yes—
190C2×D4×C43—21no—
191C2×D4×C43—24no—
192C2×D4×C43—22no—
193C2×D4×C43—22no—
194C2×D4×C43—44no—
195C2×D4×C43C2412yes—
196C22×C4×C43—22no—
197C22×C4×C43—22no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2×D412yes—
203C22×C4×C43C2412yes—
204C22×C4×C43C2411yescharacteristic
205C2×C22⋊D43—24no—
206C2×C22⋊D43—24no—
207C2×C22⋊D43—44no—
208C2×C22⋊D43—44no—
209C22×Dic43—24no—
210C22×Dic43—24no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—44no—
216C22×Dic43C2×D411yescharacteristic
217C22×Dic43C2×D414yes—
218C22×Dic43C2×D411yescharacteristic
219#10621900—28no—
220#10621900—28no—
221#10621900—48no—
222C2×C4×D43—22no—
223C2×C4×D43—22no—
224C2×C4×D43—24no—
225C2×C4×D43—216no—
226C2×C4×D43—28no—
227C2×C4×D43—28no—
228C2×C4×D43—24no—
229C2×C4×D43—24no—
230C2×C4×D43—24no—
231C2×C4×D43—44no—
232C2×C4×D43—44no—
233C2×C4×D43C2×D414yes—
234C2×C4×D43C2×D414yes—
235C2×C4×D43C2×D412yes—
236C2×C4×D43C2×D412yes—
237C2×C4×D43#4114yes—
238C2×C4×D43#4114yes—
239C2×C4×D43C2412yes—
240C2×C4×D43C2412yes—
241C2×Dic86—22no—
242C2×Dic86—22no—
243C2×Dic86—21no—
244C2×Dic86C2412yes—
245C2×C8×C43—22no—
246C2×C8×C43—22no—
247C2×C8×C43C2412yes—
248C2×C8×C43C2412yes—
249C4⋊C4×C43—21no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43—21no—
252C4⋊C4×C43C2412yes—
253C4⋊C4×C43C2412yes—
254C4⋊C4×C43C2412yes—
255C22⋊C4×C43—24no—
256C22⋊C4×C43—24no—
257C42×C43—24no—
258C22⋊Dic43—24no—
259C22⋊Dic43—24no—
260C22⋊Dic43—24no—
261(C2×D43)⋊C4—24no—
262(C2×D43)⋊C4—24no—
263(C2×D43)⋊C4—24no—
264(C2×D43)⋊C4—24no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43—21no—
268C4⋊Dic43—24no—
269C4⋊Dic43C2412yes—
270C4⋊Dic43C2412yes—
271C4⋊Dic43C2412yes—
272Dic43⋊C4—24no—
273Dic43⋊C4—24no—
274Dic43⋊C4—24no—
275C4×Dic43—24no—
276C4×Dic43—24no—
277C4×Dic43—24no—
278C4×Dic43—24no—
279C2×C43⋊C8—22no—
280C2×C43⋊C8—22no—
281C2×C43⋊C8C2412yes—
282C2×C43⋊C8C2412yes—
283#10621872—28no—
284#10621872—28no—
285C23×C43—22no—
286C23×C43—22no—
287C23×C43—22no—
288C23×C43—22no—
289C23×C43—42no—
290C23×C43—42no—
291C23×C43—42no—
292C23×C43C22×D412yes—
293C23×C43C22×D411yescharacteristic
294C22×D43—22no—
295C22×D43—22no—
296C22×D43—22no—
297C22×D43—22no—
298C22×D43—22no—
299C22×D43—28no—
300C22×D43—44no—
301C22×D43—44no—
302C22×D43—416no—
303C22×D43#12314yes—
304C22×D43C22×D412yes—
305C22×D43C22×D412yes—
306D4×C43—22no—
307D4×C43—22no—
308D4×C43—48no—
309D4×C43—42no—
310C2×C4×C43—22no—
311C2×C4×C43—24no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—42no—
318C2×C4×C43—42no—
319C2×C4×C43—42no—
320C2×C4×C43C22×D412yes—
321C2×C4×C43C22×D411yescharacteristic
322C2×C4×C43C2×#4112yes—
323C2×C4×C43C2×#4112yes—
324C2×C4×C43C2511yescharacteristic
325C22⋊D43—48no—
326C22⋊D43—48no—
327C2×Dic43—22no—
328C2×Dic43—28no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—22no—
333C2×Dic43—42no—
334C2×Dic43—42no—
335C2×Dic43—42no—
336C2×Dic43—42no—
337C2×Dic43—48no—
338C2×Dic43#12314yes—
339C2×Dic43C22×D412yes—
340C2×Dic43C22×D412yes—
341C4×D43—28no—
342C4×D43—24no—
343C4×D43—22no—
344C4×D43—22no—
345C4×D43—28no—
346C4×D43—48no—
347C4×D43—48no—
348C4×D43#12318yes—
349C4×D43C2×#4114yes—
350C4×D43C2×#4114yes—
351Dic86—22no—
352Dic86—22no—
353Dic86—42no—
354C8×C43—22no—
355C8×C43—22no—
356C43⋊C8—22no—
357C43⋊C8—22no—
358C2×#3093—431nomaximal, Sylow
359C22×C43—22no—
360C22×C43—22no—
361C22×C43—22no—
362C22×C43—44no—
363C22×C43—42no—
364C22×C43—42no—
365C22×C43—42no—
366C22×C43—84no—
367C22×C43C2×#12312yes—
368C22×C43#57512yes—
369C22×C43#57512yes—
370C22×C43C23×D411yescharacteristic
371C2×D43—28no—
372C2×D43—22no—
373C2×D43—22no—
374C2×D43—22no—
375C2×D43—22no—
376C2×D43—22no—
377C2×D43—416no—
378C2×D43—44no—
379C2×D43C2×#12314yes—
380C4×C43—22no—
381C4×C43—42no—
382C4×C43—42no—
383C4×C43—42no—
384C4×C43C2×#12312yes—
385C4×C43C22×#4111yescharacteristic
386C4×C43C22×#4111yescharacteristic
387Dic43—22no—
388Dic43—42no—
389Dic43—42no—
390Dic43—42no—
391Dic43—42no—
392Dic43C2×#12314yes—
393C2×#525—431no—
394C22×#117—431no—
395#3093—4316no—
396C2×#485—431no—
397C2×#485—431no—
398C2×#485—431no—
399C2×#485—431no—
400C2×#482—431no—
401C2×#482—431no—
402C2×#482—431no—
403C2×#482D4311yescharacteristic, complemented
404C2×#428—431no—
405C2×#428—431no—
406C2×#417—431no—
407C2×#417—431no—
408C2×#407—431no—
409C2×C43—42no—
410C2×C43—82no—
411C2×C43#309314yescomplemented
412C2×C43C22×#12311yescharacteristic
413C2×C43C2×#57511yescharacteristic
414C2×C43C2×#57511yescharacteristic
415D43—24no—
416D43—42no—
417C22×#41—431no—
418C24×C4—431no—
419C22×M16—431no—
420C22×M16—431no—
421#525—438no—
422#525—864no—
423C2×#123—861no—
424C2×C22⋊Q8—431no—
425C2×C22⋊Q8—431no—
426C2×#121—431no—
427C2×#121C2×D4311yescharacteristic
428C2×#120—861no—
429C2×C4×D4—861no—
430C2×C4×D4—861no—
431C2×#117—431no—
432C2×#117—438no—
433C2×#117—431no—
434C2×#117—431no—
435C2×#117—431no—
436C2×#117—861no—
437C2×#117—861no—
438C2×#117—864no—
439C2×#117C2×D4311yescharacteristic
440C22×C4⋊C4—431no—
441C22×C4⋊C4—431no—
442C22×C22⋊C4—861no—
443C22×C42—861no—
444#485—438no—
445#485—438no—
446#485—438no—
447#485—438no—
448#482—438no—
449#482—438no—
450#482—438no—
451#482C2×D4318yescomplemented
452#428—438no—
453#428—438no—
454C2×#107—431no—
455C2×#107—431no—
456C2×#107—431no—
457C2×#107C2×D4311yescharacteristic, complemented
458C2×#106—431no—
459C2×#106—431no—
460C2×#106—431no—
461C2×#106C2×D4311yescharacteristic, complemented
462#417—438no—
463#417—438no—
464C2×#103—431no—
465C2×#103—431no—
466C2×#103—431no—
467C2×#103—431no—
468C2×#102—431no—
469C2×#102—431no—
470C2×#102C2×D4311yescharacteristic, complemented
471C2×#102C2×D4311yescharacteristic, complemented
472#407—438no—
473C2×C22⋊C8—431no—
474C2×C22⋊C8—431no—
475C2×C22⋊C8—431no—
476C2×C22⋊C8C2×D4311yescharacteristic
477C43C2×#309311yescharacteristic, complemented, Sylow
478C25—431no—
479C2×#41—434no—
480C2×#41—862no—
481C2×#41—864no—
482C2×#41—864no—
483C22×Q8—431no—
484C22×D4—21no—
485C22×D4—861no—
486C22×D4—861no—
487C22×D4C22×D4311yescharacteristic
488C23×C4—431no—
489C23×C4—431no—
490C23×C4—431no—
491C23×C4—434no—
492C23×C4—431no—
493C23×C4—431no—
494C23×C4—434no—
495C23×C4—864no—
496C23×C4—864no—
497C23×C4—861no—
498C23×C4—861no—
499C23×C4—861no—
500C23×C4C22×D4311yescharacteristic
501C2×M16—434no—
502C2×M16—434no—
503C2×M16—864no—
504C2×M16—864no—
505C22×C8—431no—
506C22×C8—431no—
507C22×C8C22×D4311yescharacteristic
508C22×C8C22×D4311yescharacteristic
509#123—868no—
510C22⋊Q8—434no—
511C22⋊Q8—434no—
512C22⋊Q8—862no—
513C22⋊Q8—862no—
514#121—22no—
515#121—434no—
516#121—862no—
517#121C22×D4314yes—
518#120—868no—
519C4×D4—868no—
520C4×D4—868no—
521#117—22no—
522#117—434no—
523#117—434no—
524#117—434no—
525#117—434no—
526#117—868no—
527#117—868no—
528#117—862no—
529#117—862no—
530#117—862no—
531#117—862no—
532#117C22×D4314yes—
533C2×C4⋊C4—431no—
534C2×C4⋊C4—431no—
535C2×C4⋊C4—431no—
536C2×C4⋊C4—434no—
537C2×C4⋊C4—434no—
538C2×C4⋊C4—862no—
539C2×C4⋊C4—862no—
540C2×C4⋊C4—861no—
541C2×C4⋊C4—861no—
542C2×C4⋊C4—861no—
543C2×C4⋊C4—861no—
544C2×C4⋊C4C22×D4311yescharacteristic
545C2×C4⋊C4C22×D4311yescharacteristic
546C2×C4⋊C4C22×D4311yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—868no—
550C2×C22⋊C4—861no—
551C2×C22⋊C4—861no—
552C2×C22⋊C4—861no—
553C2×C22⋊C4—861no—
554C2×C22⋊C4—861no—
555C2×C22⋊C4—861no—
556C2×C22⋊C4—861no—
557C2×C42—21no—
558C2×C42—868no—
559C2×C42—861no—
560C2×C42—861no—
561C2×C42—861no—
562C2×C42—861no—
563#107—434no—
564#107—434no—
565#107—434no—
566#107C22×D4314yescomplemented
567#106—434no—
568#106—434no—
569#106—434no—
570#106C22×D4314yescomplemented
571#103—434no—
572#103—434no—
573#103—434no—
574#103—434no—
575#102—434no—
576#102—434no—
577#102C22×D4314yescomplemented
578#102C22×D4314yescomplemented
579C22⋊C8—434no—
580C22⋊C8—434no—
581C22⋊C8—434no—
582C22⋊C8C22×D4314yes—
583C24—21no—
584C24—431no—
585C24—431no—
586C24—434no—
587C24—864no—
588C24—1722no—
589C24—1722no—
590C24D4×D4311yescharacteristic
591#41—868no—
592#41—868no—
593#41—1728no—
594C2×Q8—432no—
595C2×Q8—861no—
596C2×Q8—862no—
597C2×Q8—862no—
598C2×D4—24no—
599C2×D4—21no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—44no—
603C2×D4—864no—
604C2×D4—864no—
605C2×D4—1724no—
606C2×D4—1724no—
607C2×D4C23×D4312yes—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—431no—
614C22×C4—432no—
615C22×C4—434no—
616C22×C4—434no—
617C22×C4—432no—
618C22×C4—434no—
619C22×C4—431no—
620C22×C4—434no—
621C22×C4—434no—
622C22×C4—432no—
623C22×C4—432no—
624C22×C4—864no—
625C22×C4—8616no—
626C22×C4—868no—
627C22×C4—868no—
628C22×C4—864no—
629C22×C4—864no—
630C22×C4—864no—
631C22×C4—864no—
632C22×C4—864no—
633C22×C4—862no—
634C22×C4—862no—
635C22×C4—861no—
636C22×C4—861no—
637C22×C4—861no—
638C22×C4—861no—
639C22×C4—1724no—
640C22×C4—1724no—
641C22×C4—1724no—
642C22×C4D4×D4312yes—
643C22×C4D4×D4311yescharacteristic
644C22×C4C23×D4312yes—
645C22×C4C23×D4311yescharacteristic
646M16—868no—
647M16—868no—
648C2×C8—22no—
649C2×C8—22no—
650C2×C8—432no—
651C2×C8—432no—
652C2×C8—862no—
653C2×C8—862no—
654C2×C8C23×D4312yes—
655C2×C8C23×D4312yes—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—432no—
660C4⋊C4—432no—
661C4⋊C4—432no—
662C4⋊C4—864no—
663C4⋊C4—864no—
664C4⋊C4—864no—
665C4⋊C4—861no—
666C4⋊C4—861no—
667C4⋊C4—861no—
668C4⋊C4—864no—
669C4⋊C4C23×D4312yes—
670C4⋊C4C23×D4312yes—
671C4⋊C4C23×D4312yes—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—864no—
675C22⋊C4—864no—
676C22⋊C4—864no—
677C22⋊C4—864no—
678C22⋊C4—864no—
679C22⋊C4—864no—
680C22⋊C4—864no—
681C42—24no—
682C42—864no—
683C42—864no—
684C42—864no—
685C42—864no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—434no—
694C23—432no—
695C23—432no—
696C23—868no—
697C23—862no—
698C23—862no—
699C23—862no—
700C23—862no—
701C23—862no—
702C23—1724no—
703C23—1724no—
704C23—17216no—
705C23C2×D4×D4312yes—
706C23C2×D4×D4311yescharacteristic
707Q8—862no—
708Q8—862no—
709Q8—1722no—
710D4—22no—
711D4—22no—
712D4—48no—
713D4—42no—
714D4—1728no—
715D4—1728no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—434no—
727C2×C4—432no—
728C2×C4—438no—
729C2×C4—434no—
730C2×C4—434no—
731C2×C4—432no—
732C2×C4—868no—
733C2×C4—868no—
734C2×C4—868no—
735C2×C4—862no—
736C2×C4—864no—
737C2×C4—862no—
738C2×C4—862no—
739C2×C4—862no—
740C2×C4—862no—
741C2×C4—862no—
742C2×C4—862no—
743C2×C4—1728no—
744C2×C4—1728no—
745C2×C4—1728no—
746C2×C4—1722no—
747C2×C4—1722no—
748C2×C4—1722no—
749C2×C4—1722no—
750C2×C4C2×D4×D4312yes—
751C2×C4C2×D4×D4311yescharacteristic
752C2×C4#41×D4312yes—
753C2×C4#41×D4312yes—
754C2×C4C24×D4311yescharacteristic
755C8—22no—
756C8—22no—
757C8—862no—
758C8—862no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—44no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—84no—
767C22—434no—
768C22—862no—
769C22—862no—
770C22—868no—
771C22—862no—
772C22—862no—
773C22—862no—
774C22—17216no—
775C22—1724no—
776C22#123×D4312yes—
777C22#1458369512yes—
778C22#1458369612yes—
779C22C22×D4×D4311yescharacteristic
780C4—22no—
781C4—42no—
782C4—42no—
783C4—42no—
784C4—434no—
785C4—862no—
786C4—1722no—
787C4—1722no—
788C4—1722no—
789C4—1722no—
790C4#123×D4312yes—
791C4C2×#41×D4311yescharacteristic
792C4C2×#41×D4311yescharacteristic
793C2—42no—
794C2—82no—
795C2—864no—
796C2—1722no—
797C2#1914452314yesdirect product factor
798C2C2×#123×D4311yescharacteristic
799C2C2×#1458369511yescharacteristic
800C2C2×#1458369611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#482C2
socleC23×C43C22×D4
prime radicalC2×#14583409C2
hypercenterC2×#482D43
hypocenterC43C2×#3093
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
2. C2×#117×D43C2semidirect
3. #19144523C2direct (N × H)
4. C2×#14583243C2semidirect
5. C2×#14583242C2semidirect
6. C2×#14583241C2semidirect
7. C2×#14583240C2semidirect
8. C2×#14583222C2semidirect
9. C2×#14583221C2semidirect
10. C2×#14583220C2semidirect
11. C2×#14582940C2semidirect
12. C2×#14582938C2semidirect
13. C2×#14582897C2semidirect
14. C2×#14582897C2semidirect
15. C2×#14582861C2semidirect
16. C2×C43×#482C2semidirect
37. #117×D43C22semidirect
42. #14583243C22semidirect
43. #14583242C22semidirect
44. #14583241C22semidirect
45. #14583240C22semidirect
46. #14583222C22semidirect
47. #14583221C22semidirect
48. #14583220C22semidirect
49. #14582940C22semidirect
50. #14582938C22semidirect
51. C2×#13063259C22semidirect
52. C2×#13063258C22semidirect
53. C2×#13063258C22semidirect
54. C2×#13063257C22semidirect
55. C2×#13063256C22semidirect
56. C2×#13063256C22semidirect
57. #14582897C22semidirect
58. #14582897C22semidirect
59. C2×#13063250C22semidirect
60. C2×#13063250C22semidirect
61. C2×#13063248C22semidirect
62. C2×#13063248C22semidirect
63. C2×#13063246C22semidirect
64. C2×#13063246C22semidirect
65. #14582861C22semidirect
71. C43×#482C22semidirect
72. C2×#107×C43C22semidirect
73. C2×#106×C43C22semidirect
74. C2×#102×C43C22semidirect
75. C2×#102×C43C22semidirect
147. #13063259C23semidirect
148. #13063258C23semidirect
149. #13063258C23semidirect
150. #13063257C23semidirect
151. #13063256C23semidirect
152. #13063256C23semidirect
153. #13063250C23semidirect
154. #13063250C23semidirect
155. #13063248C23semidirect
156. #13063248C23semidirect
157. #13063246C23semidirect
158. #13063246C23semidirect
177. #107×C43C23semidirect
178. #106×C43C23semidirect
179. #102×C43C23semidirect
180. #102×C43C23semidirect
403. C2×#482D43semidirect
411. C2×C43#3093semidirect
451. #482C2×D43semidirect
457. C2×#107C2×D43semidirect
461. C2×#106C2×D43semidirect
470. C2×#102C2×D43semidirect
471. C2×#102C2×D43semidirect
477. C43C2×#3093semidirect
566. #107C22×D43semidirect
570. #106C22×D43semidirect
577. #102C22×D43semidirect
578. #102C22×D43semidirect
797. C2#19144523direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834092
C2×#117×D432
#191445232
C2×#145832432
C2×#145832422
C2×#145832412
C2×#145832402
C2×#145832222
C2×#145832212
C2×#145832202
C2×#145829402
C2×#145829382
C2×#145828972
C2×#145828612
C2×C43×#4822
C2×#309343