Finite Group Databasebeta

← C2×#19144784 #25964833

Subgroups — C2×#19144784 #25964833

Order 11008.

2274 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583523C211yesmaximal, characteristic, complemented
2C2×#14583371C211yesmaximal, characteristic, complemented
3#19144784C2116yesmaximal, direct product factor
4C2×#14583243C211yesmaximal, characteristic, complemented
5C2×#14583225C211yesmaximal, characteristic, complemented
6C2×#14583176C211yesmaximal, characteristic, complemented
7C2×#14583115C211yesmaximal, characteristic, complemented
8C2×#14583114C211yesmaximal, characteristic, complemented
9C2×#14583051C211yesmaximal, characteristic, complemented
10C2×#14583034C211yesmaximal, characteristic
11C2×#14583010C211yesmaximal, characteristic, complemented
12C2×#14582996C211yesmaximal, characteristic, complemented
13C2×#14582986C211yesmaximal, characteristic, complemented
14C2×#14582979C211yesmaximal, characteristic, complemented
15C2×#14582959C211yesmaximal, characteristic, complemented
16C2×C43×#476C211yesmaximal, characteristic, complemented
17C22×D4×D43C2211yescharacteristic
18C22×#10621873C2211yescharacteristic
19C22×#10621883C2211yescharacteristic
20C22×D344C2211yescharacteristic
21C22×#10621882C2211yescharacteristic
22#14583523—24no—
23#14583523C2218yescomplemented
24C2×#13063320—21no—
25C2×#13063314—21no—
26C2×#13063313C2211yescharacteristic, complemented
27C2×#13063310—21no—
28C2×#13063305C2211yescharacteristic
29C2×#13063301—21no—
30C2×#13063300C2211yescharacteristic
31#14583371—24no—
32#14583371C2218yescomplemented
33C2×#13063290C2211yescharacteristic, complemented
34C2×C4×D172C2211yescharacteristic
35C2×D4×Dic43C2211yescharacteristic
36C2×#13063287C2211yescharacteristic
37C2×#13063287C2211yescharacteristic, complemented
38C2×C4×C22⋊D43—21no—
39C2×(C22⋊D43)⋊C4—21no—
40C2×#13063283C2211yescharacteristic
41C2×#13063282C2211yescharacteristic
42C22×(C2×D43)⋊C4—21no—
43C2×C22⋊C4×D43—21no—
44#14583243C2218yescomplemented
45#14583225C2218yescomplemented
46#14583176C2218yescomplemented
47#14583115C2218yescomplemented
48#14583114C2218yescomplemented
49#14583051C2218yescomplemented
50#14583034C2218yes—
51#14583010C2218yescomplemented
52#14582996C2218yescomplemented
53#14582986C2218yescomplemented
54#14582979C2218yescomplemented
55#14582959C2218yescomplemented
56C2×#13063258C2211yescharacteristic, complemented
57C2×#13063258C2211yescharacteristic, complemented
58C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
59C2×#13063250C2211yescharacteristic, complemented
60C2×#13063248C2211yescharacteristic, complemented
61C2×#13063247C2211yescharacteristic, complemented
62C2×#13063245C2211yescharacteristic
63C2×#13063245C2211yescharacteristic
64C2×#13063245C2211yescharacteristic, complemented
65C2×(C2×D43)⋊C8C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×#13063235C2211yescharacteristic, complemented
68C2×C8×Dic43C2211yescharacteristic, complemented
69C2×C4⋊Q8×C43C2211yescharacteristic, complemented
70C2×C4×D4×C43C2211yescharacteristic
71C43×#476C2218yescomplemented
72C2×#106×C43C2211yescharacteristic, complemented
73C2×#106×C43C2211yescharacteristic, complemented
74C2×C4⋊C8×C43C2211yescharacteristic, complemented
75C2×#102×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C24×D43—21no—
78C22×Dic86C2311yescharacteristic
79C22×D172—21no—
80C22×D172C2311yescharacteristic
81C22×D172C2311yescharacteristic
82C22×C22⋊D43—21no—
83C2×D4×D43—24no—
84C2×D4×D43—24no—
85C2×D4×D43—22no—
86C2×D4×D43C2314yes—
87C23×Dic43—21no—
88C22×C4×D43—21no—
89C22×C4×D43—21no—
90C22×C4×D43—21no—
91C22×C4×D43C2311yescharacteristic
92C2×#10621873—24no—
93C2×#10621873C2314yes—
94C2×#10621883—24no—
95C2×#10621883C2314yes—
96C2×D344—24no—
97C2×D344C2314yes—
98C2×#10621882—24no—
99C2×#10621882C2314yes—
100C22×C43⋊C8C2311yescharacteristic
101C22×C43⋊C8C2311yescharacteristic
102#13063320—28no—
103#13063314—28no—
104#13063313—22no—
105#13063313C2314yescomplemented
106#13063310—28no—
107#13063305—22no—
108#13063305C2314yes—
109#13063301—28no—
110#13063300—22no—
111#13063300C2314yes—
112#13063290—22no—
113#13063290C2314yescomplemented
114C4×D172—22no—
115C4×D172C2314yes—
116D4×Dic43—22no—
117D4×Dic43C2314yes—
118#13063287—22no—
119#13063287—22no—
120#13063287C2314yes—
121#13063287C2314yescomplemented
122C4×C22⋊D43—28no—
123(C22⋊D43)⋊C4—28no—
124#13063283—22no—
125#13063283C2314yes—
126#13063282D414yes—
127#13063282C2314yes—
128C2×C4⋊Dic43—21no—
129C2×C4⋊Dic43C2311yescharacteristic
130C2×Dic43⋊C4—21no—
131C2×Dic43⋊C4D411yescharacteristic
132C2×Dic43⋊C4D411yescharacteristic
133C2×C22⋊Dic43—21no—
134C2×(C2×D43)⋊C4—21no—
135C2×(C2×D43)⋊C4—21no—
136C2×(C2×D43)⋊C4—21no—
137C2×(C2×D43)⋊C4—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4—28no—
143C2×(C2×D43)⋊C4D411yescharacteristic
144C2×(C2×D43)⋊C4D411yescharacteristic
145C22⋊C4×D43—28no—
146C2×C4×Dic43—21no—
147C2×C4×Dic43—21no—
148C2×C4×Dic43C2311yescharacteristic
149#13063258C2314yescomplemented
150#13063258C2314yescomplemented
151C4⋊(C43⋊C8)C2314yescomplemented
152#13063250C2314yescomplemented
153#13063248C2314yescomplemented
154#13063247C2314yescomplemented
155#13063245C2314yes—
156#13063245C2314yes—
157#13063245C2314yescomplemented
158(C2×D43)⋊C8C2314yes—
159(C2×D43)⋊C8C2314yes—
160#13063235C2314yescomplemented
161C8×Dic43C2314yescomplemented
162C22×Q8×C43—21no—
163C22×D4×C43C2311yescharacteristic
164C23×C4×C43—21no—
165C22×C8×C43C2311yescharacteristic
166C22×C8×C43C2311yescharacteristic
167C4⋊Q8×C43—22no—
168C4⋊Q8×C43C2314yescomplemented
169C4×D4×C43—22no—
170C4×D4×C43C2314yes—
171C2×C4⋊C4×C43—21no—
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C22⋊C4×C43—21no—
176C2×C42×C43C2311yescharacteristic
177#106×C43C2314yescomplemented
178#106×C43C2314yescomplemented
179C4⋊C8×C43C2314yescomplemented
180#102×C43C2314yes—
181#102×C43C2314yes—
182C24×C43—21no—
183C23×D43—21no—
184C23×D43—28no—
185C23×D43—24no—
186C23×D43—21no—
187C23×D43—82no—
188C23×D43—82no—
189C23×D43C2×D411yescharacteristic
190C2×Q8×C43—24no—
191C2×Q8×C43—82no—
192C2×D4×C43—21no—
193C2×D4×C43—22no—
194C2×D4×C43#4114yes—
195C2×D4×C43C2412yes—
196C22×C4×C43—24no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—82no—
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2×D411yescharacteristic
203C22×C4×C43C2411yescharacteristic
204C2×C22⋊D43—28no—
205C2×C22⋊D43—24no—
206C22×Dic43—24no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—82no—
210C22×Dic43C2×D411yescharacteristic
211C22×Dic43C2×D411yescharacteristic
212C22×Dic43C2×D411yescharacteristic
213D4×D43—216no—
214D4×D43—28no—
215D4×D43—28no—
216C2×D172—21no—
217C2×D172—22no—
218C2×D172—21no—
219C2×D172—24no—
220C2×D172—22no—
221C2×D172—22no—
222C2×D172—82no—
223C2×D172#4114yes—
224C2×D172C2412yes—
225C2×D172C2412yes—
226C2×C4×D43—22no—
227C2×C4×D43—22no—
228C2×C4×D43—24no—
229C2×C4×D43—24no—
230C2×C4×D43—24no—
231C2×C4×D43—82no—
232C2×C4×D43—82no—
233C2×C4×D43—82no—
234C2×C4×D43C2×D412yes—
235C2×C4×D43C2412yes—
236C2×Dic86—22no—
237C2×Dic86—22no—
238C2×Dic86—21no—
239C2×Dic86C2412yes—
240C2×C8×C43—22no—
241C2×C8×C43—22no—
242C2×C8×C43C2412yes—
243C2×C8×C43C2412yes—
244C4⋊C4×C43—24no—
245C4⋊C4×C43—21no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—21no—
248C4⋊C4×C43C2412yes—
249C4⋊C4×C43C2412yes—
250C4⋊C4×C43C2412yes—
251C22⋊C4×C43—24no—
252C42×C43C2×D412yes—
253C42×C43C2412yes—
254C22⋊Dic43—24no—
255#10621883—28no—
256#10621882—28no—
257(C2×D43)⋊C4—24no—
258(C2×D43)⋊C4—24no—
259(C2×D43)⋊C4—24no—
260(C2×D43)⋊C4—24no—
261(C2×D43)⋊C4—24no—
262(C2×D43)⋊C4—24no—
263(C2×D43)⋊C4—24no—
264(C2×D43)⋊C4—24no—
265(C2×D43)⋊C4C2×D414yes—
266(C2×D43)⋊C4C2×D414yes—
267C4⋊Dic43—21no—
268C4⋊Dic43—24no—
269C4⋊Dic43C2412yes—
270Dic43⋊C4—24no—
271Dic43⋊C4C2×D414yes—
272Dic43⋊C4C2×D414yes—
273C4×Dic43—24no—
274C4×Dic43—24no—
275C4×Dic43C2×D412yes—
276C4×Dic43C2412yes—
277C2×C43⋊C8—22no—
278C2×C43⋊C8—22no—
279C2×C43⋊C8C2412yes—
280C2×C43⋊C8C2412yes—
281D344—28no—
282#10621873—28no—
283C23×C43—24no—
284C23×C43—22no—
285C23×C43—42no—
286C23×C43—42no—
287C23×C43C22×D411yescharacteristic
288C22×D43—22no—
289C22×D43—24no—
290C22×D43—22no—
291C22×D43—22no—
292C22×D43—22no—
293C22×D43—216no—
294C22×D43—22no—
295C22×D43—42no—
296C22×D43—42no—
297C22×D43—42no—
298C22×D43—42no—
299C22×D43—42no—
300C22×D43—84no—
301C22×D43—84no—
302C22×D43—816no—
303C22×D43C22×D412yes—
304Q8×C43—84no—
305D4×C43—24no—
306D4×C43—22no—
307D4×C43C2×#4114yes—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—42no—
314C2×C4×C43—42no—
315C2×C4×C43—42no—
316C2×C4×C43—84no—
317C2×C4×C43C22×D412yes—
318C2×C4×C43C22×D412yes—
319C2×C4×C43C22×D411yescharacteristic
320C2×C4×C43C2×#4112yes—
321C2×C4×C43C2×#4112yes—
322C2×C4×C43C2511yescharacteristic
323C22⋊D43—216no—
324C2×Dic43—22no—
325C2×Dic43—22no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—42no—
330C2×Dic43—42no—
331C2×Dic43—84no—
332C2×Dic43C22×D412yes—
333C2×Dic43C22×D412yes—
334C2×Dic43C22×D412yes—
335D172—24no—
336D172—22no—
337D172—22no—
338D172—22no—
339D172—42no—
340D172—84no—
341D172C2×#4114yes—
342C4×D43—24no—
343C4×D43—22no—
344C4×D43—22no—
345C4×D43—84no—
346C4×D43—84no—
347C4×D43—84no—
348Dic86—22no—
349Dic86—22no—
350Dic86—42no—
351C8×C43—22no—
352C8×C43—22no—
353C43⋊C8—22no—
354C43⋊C8—22no—
355C2×#3118—431nomaximal, Sylow
356C22×C43—24no—
357C22×C43—48no—
358C22×C43—42no—
359C22×C43—42no—
360C22×C43#52512yes—
361C22×C43#57612yes—
362C22×C43#57712yes—
363C22×C43C23×D411yescharacteristic
364C2×D43—22no—
365C2×D43—24no—
366C2×D43—22no—
367C2×D43—22no—
368C2×D43—44no—
369C2×D43—48no—
370C2×D43—42no—
371C2×D43—42no—
372C2×D43—42no—
373C2×D43—42no—
374C2×D43—42no—
375C2×D43—816no—
376C2×D43—84no—
377C4×C43—22no—
378C4×C43—22no—
379C4×C43—42no—
380C4×C43—42no—
381C4×C43—42no—
382C4×C43#52512yes—
383C4×C43C22×#4111yescharacteristic
384C4×C43C22×#4111yescharacteristic
385Dic43—22no—
386Dic43—22no—
387Dic43—22no—
388Dic43—42no—
389Dic43—42no—
390C2×#542—431no—
391C2×#518—431no—
392#3118—4316no—
393C2×#485—431no—
394C2×#482—431no—
395C2×#476D4311yescharacteristic, complemented
396C2×#474—431no—
397C2×#463—431no—
398C2×#463—431no—
399C2×#450—431no—
400C2×#447—431no—
401C2×#442—431no—
402C2×#440—431no—
403C2×C4×SD16—431no—
404C2×C4×D8—431no—
405C2×#433—431no—
406C2×C43—44no—
407C2×C43#311814yescomplemented
408C2×C43C2×#52511yescharacteristic
409C2×C43C2×#57611yescharacteristic
410C2×C43C2×#57711yescharacteristic
411D43—42no—
412D43—44no—
413D43—82no—
414C23×D4—431no—
415C22×SD16—431no—
416C22×SD16—431no—
417C22×D8—431no—
418C22×D8—431no—
419#542—438no—
420#542—864no—
421C2×C4⋊Q8C2×D4311yescharacteristic, complemented
422C2×#126—861no—
423C2×#124—431no—
424C2×#124—861no—
425C2×#123—861no—
426C2×C22⋊Q8—431no—
427C2×C22⋊Q8—861no—
428C2×#121—431no—
429#518—438no—
430#518—864no—
431C2×C4×Q8—431no—
432C2×C4×D4—431no—
433C2×C4×D4—431no—
434C2×C4×D4—431no—
435C2×C4×D4—431no—
436C2×C4×D4—861no—
437C2×C4×D4—861no—
438C2×C4×D4C2×D4311yescharacteristic
439C2×#117—431no—
440C2×#117—431no—
441C22×C22⋊C4—861no—
442C22×C22⋊C4—861no—
443#485—438no—
444#482—438no—
445#476C2×D4318yescomplemented
446#474—438no—
447#463—438no—
448#463—438no—
449#450—438no—
450#447—438no—
451#442—438no—
452#440—438no—
453C4×SD16—438no—
454C4×D8—438no—
455#433—438no—
456C2×#107—431no—
457C2×#107—431no—
458C2×#106C2×D4311yescharacteristic, complemented
459C2×#106C2×D4311yescharacteristic, complemented
460C2×C4⋊C8—431no—
461C2×C4⋊C8C2×D4311yescharacteristic, complemented
462C2×#103—431no—
463C2×#103—431no—
464C2×#102—431no—
465C2×#102—431no—
466C2×#102—431no—
467C2×#102—431no—
468C2×#102C2×D4311yescharacteristic
469C2×#102C2×D4311yescharacteristic
470C2×C22⋊C8—431no—
471C2×C22⋊C8—431no—
472C2×#97—431no—
473C2×C4×C8—431no—
474C43C2×#311811yescharacteristic, complemented, Sylow
475C25—861no—
476C22×Q8—21no—
477C22×Q8—431no—
478C22×D4—434no—
479C22×D4—431no—
480C22×D4—431no—
481C22×D4—861no—
482C22×D4—862no—
483C22×D4—861no—
484C22×D4—864no—
485C22×D4—864no—
486C22×D4C22×D4311yescharacteristic
487C23×C4—21no—
488C23×C4—431no—
489C23×C4—861no—
490C23×C4—861no—
491C23×C4—861no—
492C23×C4—861no—
493C2×SD16—434no—
494C2×SD16—434no—
495C2×SD16—864no—
496C2×SD16—864no—
497C2×D8—434no—
498C2×D8—434no—
499C2×D8—864no—
500C2×D8—864no—
501C22×C8—431no—
502C22×C8—431no—
503C22×C8C22×D4311yescharacteristic
504C22×C8C22×D4311yescharacteristic
505C4⋊Q8—22no—
506C4⋊Q8C22×D4314yescomplemented
507#126—868no—
508#124—434no—
509#124—868no—
510#124—862no—
511#123—868no—
512C22⋊Q8—434no—
513C22⋊Q8—862no—
514C22⋊Q8—868no—
515#121—434no—
516#121—862no—
517C4×Q8—434no—
518C4×Q8—862no—
519C4×D4—22no—
520C4×D4—434no—
521C4×D4—434no—
522C4×D4—434no—
523C4×D4—434no—
524C4×D4—862no—
525C4×D4—862no—
526C4×D4—862no—
527C4×D4—868no—
528C4×D4—868no—
529C4×D4—862no—
530C4×D4C22×D4314yes—
531#117—434no—
532#117—434no—
533#117—434no—
534#117—862no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—431no—
537C2×C4⋊C4—431no—
538C2×C4⋊C4—431no—
539C2×C4⋊C4—861no—
540C2×C4⋊C4—861no—
541C2×C4⋊C4C22×D4311yescharacteristic
542C2×C4⋊C4C22×D4311yescharacteristic
543C2×C4⋊C4C22×D4311yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—431no—
546C2×C22⋊C4—431no—
547C2×C22⋊C4—868no—
548C2×C22⋊C4—868no—
549C2×C22⋊C4—861no—
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×C22⋊C4—861no—
558C2×C42—431no—
559C2×C42—861no—
560C2×C42—861no—
561C2×C42C22×D4311yescharacteristic
562#107—434no—
563#107—434no—
564#106C22×D4314yescomplemented
565#106C22×D4314yescomplemented
566C4⋊C8—434no—
567C4⋊C8C22×D4314yescomplemented
568#103—434no—
569#103—434no—
570#102—434no—
571#102—434no—
572#102—434no—
573#102—434no—
574#102C22×D4314yes—
575#102C22×D4314yes—
576C22⋊C8—434no—
577C22⋊C8—434no—
578#97—434no—
579C4×C8—434no—
580C24—21no—
581C24—431no—
582C24—864no—
583C24—868no—
584C24—861no—
585C24—861no—
586C24—3442no—
587C24—3442no—
588C2×Q8—24no—
589C2×Q8—82no—
590C2×Q8—432no—
591C2×Q8—861no—
592C2×Q8—862no—
593C2×Q8—862no—
594C2×D4—21no—
595C2×D4—22no—
596C2×D4—434no—
597C2×D4—432no—
598C2×D4—432no—
599C2×D4—864no—
600C2×D4—864no—
601C2×D4—868no—
602C2×D4—8616no—
603C2×D4—868no—
604C2×D4—868no—
605C2×D4—861no—
606C2×D4—861no—
607C2×D4—862no—
608C2×D4—862no—
609C2×D4—862no—
610C2×D4—3442no—
611C2×D4#1062190214yes—
612C2×D4C23×D4312yes—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—24no—
617C22×C4—82no—
618C22×C4—431no—
619C22×C4—431no—
620C22×C4—431no—
621C22×C4—432no—
622C22×C4—432no—
623C22×C4—864no—
624C22×C4—864no—
625C22×C4—864no—
626C22×C4—862no—
627C22×C4—862no—
628C22×C4—861no—
629C22×C4—861no—
630C22×C4—864no—
631C22×C4—3442no—
632C22×C4—3442no—
633C22×C4—3442no—
634C22×C4—3442no—
635C22×C4D4×D4311yescharacteristic
636C22×C4D4×D4311yescharacteristic
637C22×C4C23×D4311yescharacteristic
638SD16—868no—
639SD16—868no—
640D8—868no—
641D8—868no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—432no—
645C2×C8—432no—
646C2×C8—862no—
647C2×C8—862no—
648C2×C8C23×D4312yes—
649C2×C8C23×D4312yes—
650C4⋊C4—24no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—434no—
655C4⋊C4—434no—
656C4⋊C4—432no—
657C4⋊C4—864no—
658C4⋊C4—864no—
659C4⋊C4—861no—
660C4⋊C4C23×D4312yes—
661C4⋊C4C23×D4312yes—
662C4⋊C4C23×D4312yes—
663C22⋊C4—24no—
664C22⋊C4—434no—
665C22⋊C4—434no—
666C22⋊C4—864no—
667C22⋊C4—864no—
668C22⋊C4—864no—
669C22⋊C4—864no—
670C22⋊C4—864no—
671C22⋊C4—864no—
672C22⋊C4—864no—
673C22⋊C4—864no—
674C22⋊C4—864no—
675C42—432no—
676C42—432no—
677C42—864no—
678C42—864no—
679C42D4×D4312yes—
680C42C23×D4312yes—
681C23—24no—
682C23—22no—
683C23—42no—
684C23—42no—
685C23—432no—
686C23—8616no—
687C23—862no—
688C23—864no—
689C23—862no—
690C23—862no—
691C23—862no—
692C23—862no—
693C23—3444no—
694C23—3444no—
695C23—34416no—
696C23—1722no—
697C23—1722no—
698C23—1722no—
699C23—1722no—
700C23—1722no—
701C23C2×D4×D4311yescharacteristic
702Q8—84no—
703Q8—862no—
704Q8—862no—
705Q8—1722no—
706D4—24no—
707D4—22no—
708D4—434no—
709D4—8616no—
710D4—864no—
711D4—862no—
712D4—862no—
713D4—862no—
714D4—3444no—
715D4—1722no—
716D4C2×#1062190214yes—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—84no—
726C2×C4—432no—
727C2×C4—432no—
728C2×C4—432no—
729C2×C4—862no—
730C2×C4—862no—
731C2×C4—862no—
732C2×C4—864no—
733C2×C4—862no—
734C2×C4—862no—
735C2×C4—862no—
736C2×C4—862no—
737C2×C4—3444no—
738C2×C4—3444no—
739C2×C4—3444no—
740C2×C4—3444no—
741C2×C4—1722no—
742C2×C4—1722no—
743C2×C4C2×D4×D4312yes—
744C2×C4C2×D4×D4312yes—
745C2×C4C2×D4×D4311yescharacteristic
746C2×C4#41×D4312yes—
747C2×C4C2×#1062190212yes—
748C2×C4C24×D4311yescharacteristic
749C8—22no—
750C8—22no—
751C8—862no—
752C8—862no—
753C22—24no—
754C22—42no—
755C22—42no—
756C22—48no—
757C22—862no—
758C22—862no—
759C22—862no—
760C22—864no—
761C22—34416no—
762C22—3444no—
763C22—1722no—
764C22—1722no—
765C22—1722no—
766C22—1722no—
767C22—1722no—
768C22—1724no—
769C22—1728no—
770C22#1458341212yes—
771C22#1458370312yes—
772C22#1458370512yes—
773C22C22×D4×D4311yescharacteristic
774C4—22no—
775C4—22no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—862no—
780C4—862no—
781C4—862no—
782C4—1722no—
783C4—1722no—
784C4#1458341212yes—
785C4C2×#41×D4311yescharacteristic
786C4C22×#1062190211yescharacteristic
787C2—44no—
788C2—3442no—
789C2—1722no—
790C2—1724no—
791C2#1914478414yesdirect product factor
792C2C2×#1458341211yescharacteristic
793C2C2×#1458370311yescharacteristic
794C2C2×#1458370511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#476C2
socleC23×C43C22×D4
prime radicalC2×#14583034C2
hypercenterC2×#476D43
hypocenterC43C2×#3118
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#14583523C2semidirect
2. C2×#14583371C2semidirect
3. #19144784C2direct (N × H)
4. C2×#14583243C2semidirect
5. C2×#14583225C2semidirect
6. C2×#14583176C2semidirect
7. C2×#14583115C2semidirect
8. C2×#14583114C2semidirect
9. C2×#14583051C2semidirect
11. C2×#14583010C2semidirect
12. C2×#14582996C2semidirect
13. C2×#14582986C2semidirect
14. C2×#14582979C2semidirect
15. C2×#14582959C2semidirect
16. C2×C43×#476C2semidirect
23. #14583523C22semidirect
26. C2×#13063313C22semidirect
32. #14583371C22semidirect
33. C2×#13063290C22semidirect
37. C2×#13063287C22semidirect
44. #14583243C22semidirect
45. #14583225C22semidirect
46. #14583176C22semidirect
47. #14583115C22semidirect
48. #14583114C22semidirect
49. #14583051C22semidirect
51. #14583010C22semidirect
52. #14582996C22semidirect
53. #14582986C22semidirect
54. #14582979C22semidirect
55. #14582959C22semidirect
56. C2×#13063258C22semidirect
57. C2×#13063258C22semidirect
58. C2×C4⋊(C43⋊C8)C22semidirect
59. C2×#13063250C22semidirect
60. C2×#13063248C22semidirect
61. C2×#13063247C22semidirect
64. C2×#13063245C22semidirect
67. C2×#13063235C22semidirect
68. C2×C8×Dic43C22semidirect
69. C2×C4⋊Q8×C43C22semidirect
71. C43×#476C22semidirect
72. C2×#106×C43C22semidirect
73. C2×#106×C43C22semidirect
74. C2×C4⋊C8×C43C22semidirect
105. #13063313C23semidirect
113. #13063290C23semidirect
121. #13063287C23semidirect
149. #13063258C23semidirect
150. #13063258C23semidirect
151. C4⋊(C43⋊C8)C23semidirect
152. #13063250C23semidirect
153. #13063248C23semidirect
154. #13063247C23semidirect
157. #13063245C23semidirect
160. #13063235C23semidirect
161. C8×Dic43C23semidirect
168. C4⋊Q8×C43C23semidirect
177. #106×C43C23semidirect
178. #106×C43C23semidirect
179. C4⋊C8×C43C23semidirect
395. C2×#476D43semidirect
407. C2×C43#3118semidirect
421. C2×C4⋊Q8C2×D43semidirect
445. #476C2×D43semidirect
458. C2×#106C2×D43semidirect
459. C2×#106C2×D43semidirect
461. C2×C4⋊C8C2×D43semidirect
474. C43C2×#3118semidirect
506. C4⋊Q8C22×D43semidirect
564. #106C22×D43semidirect
565. #106C22×D43semidirect
567. C4⋊C8C22×D43semidirect
791. C2#19144784direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835232
C2×#145833712
#191447842
C2×#145832432
C2×#145832252
C2×#145831762
C2×#145831152
C2×#145831142
C2×#145830512
C2×#145830342
C2×#145830102
C2×#145829962
C2×#145829862
C2×#145829792
C2×#145829592
C2×C43×#4762
C2×#311843