Finite Group Databasebeta

← C2×#19144559 #25964431

Subgroups — C2×#19144559 #25964431

Order 11008.

2170 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583472C211yesmaximal, characteristic
2C2×#14583379C211yesmaximal, characteristic
3#19144559C2116yesmaximal, direct product factor
4C2×#14583235C211yesmaximal, characteristic, complemented
5C2×#14583233C211yesmaximal, characteristic, complemented
6C2×#14583242C211yesmaximal, characteristic, complemented
7C2×#14583240C211yesmaximal, characteristic, complemented
8C2×#14583239C211yesmaximal, characteristic, complemented
9C2×#14583231C211yesmaximal, characteristic, complemented
10C2×#14583227C211yesmaximal, characteristic, complemented
11C2×#14582938C211yesmaximal, characteristic, complemented
12C2×#14582936C211yesmaximal, characteristic, complemented
13C2×#14582906C211yesmaximal, characteristic, complemented
14C2×#103×D43C211yesmaximal, characteristic, complemented
15C2×#14582864C211yesmaximal, characteristic
16C2×C43×#485C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C22×Q8×D43C2211yescharacteristic
19C22×#10621872C2211yescharacteristic
20C22×C8×D43C2211yescharacteristic
21#14583472—24no—
22#14583472C2218yes—
23C2×#13063324—21no—
24C2×#13063311—21no—
25C2×#13063310—21no—
26C2×#13063307—21no—
27C2×#13063305C2211yescharacteristic
28C2×#13063304C2211yescharacteristic
29C2×#13063301C2211yescharacteristic
30#14583379—24no—
31#14583379C2218yes—
32C2×C4×Dic86—21no—
33C2×C4×D172—21no—
34C2×(C22⋊D43)⋊C4—21no—
35C2×(C22⋊D43)⋊C4—21no—
36C2×#13063283C2211yescharacteristic
37C2×#13063283C2211yescharacteristic
38C2×#13063283C2211yescharacteristic
39C22×C4⋊Dic43C2211yescharacteristic
40C2×C4⋊C4×D43C2211yescharacteristic
41C2×C4⋊C4×D43C2211yescharacteristic
42#14583242C2218yescomplemented
43#14583240C2218yescomplemented
44#14583239C2218yescomplemented
45#14583235C2218yescomplemented
46#14583233C2218yescomplemented
47#14583231C2218yescomplemented
48#14583227C2218yescomplemented
49#14582938C2218yescomplemented
50#14582936C2218yescomplemented
51C2×#13063259C2211yescharacteristic
52C2×#13063259C2211yescharacteristic
53C2×#13063258C2211yescharacteristic
54C2×#13063256C2211yescharacteristic
55C2×#13063256C2211yescharacteristic
56C2×#13063256C2211yescharacteristic
57#14582906C2218yescomplemented
58C2×#13063250C2211yescharacteristic
59C2×#13063250C2211yescharacteristic
60C2×#13063249C2211yescharacteristic
61C2×#13063249C2211yescharacteristic
62C2×#13063248C2211yescharacteristic
63C2×#13063248C2211yescharacteristic
64#103×D43C2218yescomplemented
65#14582864C2218yes—
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×(C2×D43)⋊C8C2211yescharacteristic
69C2×C22⋊Q8×C43C2211yescharacteristic
70C2×#117×C43C2211yescharacteristic
71C43×#485C2218yescomplemented
72C2×#107×C43C2211yescharacteristic
73C2×#106×C43C2211yescharacteristic
74C2×#103×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×C22⋊C8×C43C2211yescharacteristic
77C2×#10621898—24no—
78C2×#10621898—24no—
79C2×#10621898D414yes—
80C2×#10621898C2314yes—
81C22×Dic86—21no—
82C22×Dic86D411yescharacteristic
83C22×Dic86C2311yescharacteristic
84C2×Q8×D43—22no—
85C2×Q8×D43—24no—
86C2×Q8×D43—24no—
87C2×Q8×D43C2314yes—
88C22×D172D411yescharacteristic
89C22×C22⋊D43D411yescharacteristic
90C22×C22⋊D43D411yescharacteristic
91C23×Dic43—21no—
92C22×C4×D43—21no—
93C22×C4×D43—21no—
94C22×C4×D43—21no—
95C22×C4×D43C2311yescharacteristic
96C22×C4×D43C2311yescharacteristic
97C2×#10621872—24no—
98C2×#10621872C2314yes—
99C22×C43⋊C8C2311yescharacteristic
100C22×C43⋊C8C2311yescharacteristic
101C2×C8×D43—24no—
102C2×C8×D43C2314yes—
103#13063324—28no—
104#13063311—28no—
105#13063310—28no—
106#13063307—28no—
107#13063305—22no—
108#13063305C2314yes—
109#13063304—22no—
110#13063304C2314yes—
111#13063301—22no—
112#13063301C2314yes—
113C4×Dic86—28no—
114C4×D172—28no—
115(C22⋊D43)⋊C4—28no—
116(C22⋊D43)⋊C4—28no—
117#13063283—22no—
118#13063283—22no—
119#13063283—22no—
120#13063283C2314yes—
121#13063283C2314yes—
122#13063283C2314yes—
123C2×C4⋊Dic43—21no—
124C2×C4⋊Dic43—22no—
125C2×C4⋊Dic43—21no—
126C2×C4⋊Dic43C2311yescharacteristic
127C2×C4⋊Dic43C2311yescharacteristic
128C2×C4⋊Dic43C2314yes—
129C2×C4⋊Dic43C2311yescharacteristic
130C2×Dic43⋊C4—21no—
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C4⋊C4×D43—22no—
135C4⋊C4×D43—22no—
136C4⋊C4×D43C2314yes—
137C4⋊C4×D43C2314yes—
138C2×C22⋊Dic43—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×C4×Dic43—21no—
145C2×C4×Dic43—21no—
146C2×C4×Dic43—21no—
147#13063259C2314yes—
148#13063259C2314yes—
149#13063258C2314yes—
150#13063256C2314yes—
151#13063256C2314yes—
152#13063256C2314yes—
153#13063250C2314yes—
154#13063250C2314yes—
155#13063249C2314yes—
156#13063249C2314yes—
157#13063248C2314yes—
158#13063248C2314yes—
159C22⋊(C43⋊C8)C2314yes—
160(C2×D43)⋊C8C2314yes—
161(C2×D43)⋊C8C2314yes—
162C22×Q8×C43C2311yescharacteristic
163C23×C4×C43C2311yescharacteristic
164C22×C8×C43C2311yescharacteristic
165C22×C8×C43C2311yescharacteristic
166C22⋊Q8×C43—22no—
167C22⋊Q8×C43C2314yes—
168#117×C43—22no—
169#117×C43C2314yes—
170C2×C4⋊C4×C43—21no—
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×C43C2314yes—
178#106×C43C2314yes—
179#103×C43C2314yes—
180#103×C43C2314yes—
181C22⋊C8×C43C2314yes—
182C24×C43C2×D411yescharacteristic
183C23×D43C2×D411yescharacteristic
184C23×D43C2×D411yescharacteristic
185C2×Q8×C43—21no—
186C2×Q8×C43—22no—
187C2×Q8×C43—22no—
188C2×Q8×C43C2412yes—
189C22×C4×C43—22no—
190C22×C4×C43—22no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2×D412yes—
197C22×C4×C43C2412yes—
198C22×C4×C43C2411yescharacteristic
199C2×C22⋊D43—24no—
200C2×C22⋊D43—24no—
201C2×C22⋊D43C2×D414yes—
202C2×C22⋊D43C2×D414yes—
203C22×Dic43—21no—
204C22×Dic43—21no—
205C22×Dic43—21no—
206C22×Dic43—21no—
207C22×Dic43—24no—
208C22×Dic43—82no—
209C22×Dic43C2×D411yescharacteristic
210C22×Dic43C2×D411yescharacteristic
211Q8×D43—28no—
212Q8×D43—28no—
213Q8×D43—48no—
214#10621898—216no—
215#10621898—28no—
216#10621898—28no—
217C2×D172—24no—
218C2×D172C2×D414yes—
219C2×C4×D43—22no—
220C2×C4×D43—22no—
221C2×C4×D43—24no—
222C2×C4×D43—24no—
223C2×C4×D43—24no—
224C2×C4×D43—44no—
225C2×C4×D43—82no—
226C2×C4×D43—82no—
227C2×C4×D43C2×D412yes—
228C2×C4×D43C2×D412yes—
229C2×C4×D43#4114yes—
230C2×C4×D43#4114yes—
231C2×C4×D43C2412yes—
232C2×C4×D43C2412yes—
233C2×Dic86—24no—
234C2×Dic86—22no—
235C2×Dic86—22no—
236C2×Dic86—21no—
237C2×Dic86—24no—
238C2×Dic86—44no—
239C2×Dic86C2×D414yes—
240C2×Dic86C2412yes—
241C2×C8×C43—22no—
242C2×C8×C43—22no—
243C2×C8×C43C2412yes—
244C2×C8×C43C2412yes—
245C4⋊C4×C43—24no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43C2412yes—
250C4⋊C4×C43C2412yes—
251C4⋊C4×C43C2412yes—
252C22⋊C4×C43—24no—
253C22⋊C4×C43—24no—
254C42×C43—24no—
255C22⋊Dic43—24no—
256(C2×D43)⋊C4—24no—
257(C2×D43)⋊C4—24no—
258(C2×D43)⋊C4—24no—
259(C2×D43)⋊C4—24no—
260(C2×D43)⋊C4—24no—
261C4⋊Dic43—21no—
262C4⋊Dic43—21no—
263C4⋊Dic43—24no—
264C4⋊Dic43—21no—
265C4⋊Dic43—24no—
266C4⋊Dic43C2412yes—
267C4⋊Dic43C2412yes—
268C4⋊Dic43C2412yes—
269Dic43⋊C4—24no—
270Dic43⋊C4—24no—
271Dic43⋊C4—24no—
272Dic43⋊C4—24no—
273C4×Dic43—24no—
274C4×Dic43—24no—
275C4×Dic43—24no—
276C2×C43⋊C8—22no—
277C2×C43⋊C8—22no—
278C2×C43⋊C8C2412yes—
279C2×C43⋊C8C2412yes—
280#10621872—28no—
281C8×D43—28no—
282C23×C43—22no—
283C23×C43—22no—
284C23×C43—22no—
285C23×C43C22×D412yes—
286C23×C43C22×D411yescharacteristic
287C22×D43—22no—
288C22×D43—22no—
289C22×D43—22no—
290C22×D43—22no—
291C22×D43—22no—
292C22×D43#12314yes—
293C22×D43C22×D412yes—
294C22×D43C22×D412yes—
295Q8×C43—22no—
296Q8×C43—22no—
297Q8×C43—42no—
298C2×C4×C43—22no—
299C2×C4×C43—24no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—42no—
307C2×C4×C43—42no—
308C2×C4×C43—42no—
309C2×C4×C43—42no—
310C2×C4×C43C22×D412yes—
311C2×C4×C43C22×D411yescharacteristic
312C2×C4×C43C2×#4112yes—
313C2×C4×C43C2×#4112yes—
314C2×C4×C43C2511yescharacteristic
315C22⋊D43—28no—
316C22⋊D43—28no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—22no—
322C2×Dic43—42no—
323C2×Dic43—42no—
324C2×Dic43—42no—
325C2×Dic43—42no—
326C2×Dic43—84no—
327C2×Dic43#12314yes—
328C2×Dic43C22×D412yes—
329C2×Dic43C22×D412yes—
330D172—28no—
331C4×D43—24no—
332C4×D43—22no—
333C4×D43—22no—
334C4×D43—48no—
335C4×D43—84no—
336C4×D43—84no—
337C4×D43#12318yes—
338C4×D43C2×#4114yes—
339C4×D43C2×#4114yes—
340Dic86—28no—
341Dic86—22no—
342Dic86—22no—
343Dic86—42no—
344Dic86—48no—
345C8×C43—22no—
346C8×C43—22no—
347C43⋊C8—22no—
348C43⋊C8—22no—
349C2×#3097—431nomaximal, Sylow
350C22×C43—22no—
351C22×C43—22no—
352C22×C43—22no—
353C22×C43—44no—
354C22×C43C2×#12312yes—
355C22×C43#57712yes—
356C22×C43#57812yes—
357C22×C43C23×D411yescharacteristic
358C2×D43—28no—
359C2×D43—22no—
360C2×D43—22no—
361C2×D43—22no—
362C2×D43—22no—
363C2×D43—22no—
364C2×D43—44no—
365C2×D43C2×#12314yes—
366C4×C43—22no—
367C4×C43—42no—
368C4×C43—42no—
369C4×C43—42no—
370C4×C43—42no—
371C4×C43C2×#12312yes—
372C4×C43C22×#4111yescharacteristic
373C4×C43C22×#4111yescharacteristic
374Dic43—22no—
375Dic43—42no—
376Dic43—42no—
377Dic43—42no—
378Dic43—42no—
379Dic43C2×#12314yes—
380C2×#536—431no—
381C2×#520—431no—
382#3097—4316no—
383C2×#484—431no—
384C2×#484—431no—
385C2×#485—431no—
386C2×#485—431no—
387C2×#485—431no—
388C2×#485D4311yescharacteristic, complemented
389C2×#483—431no—
390C2×#483—431no—
391C2×#428—431no—
392C2×#427—431no—
393C2×#419—431no—
394C22×#103—431no—
395C2×#408—431no—
396C2×C43—42no—
397C2×C43#309714yescomplemented
398C2×C43C22×#12311yescharacteristic
399C2×C43C2×#57711yescharacteristic
400C2×C43C2×#57811yescharacteristic
401D43—24no—
402D43—42no—
403C22×#41—431no—
404C23×Q8—431no—
405C22×M16—431no—
406C23×C8—431no—
407#536—438no—
408#536—864no—
409C2×C4⋊Q8—861no—
410C2×#124—861no—
411C2×#123—861no—
412C2×#123—861no—
413C2×C22⋊Q8—431no—
414C2×C22⋊Q8—431no—
415C2×C22⋊Q8—431no—
416C2×C22⋊Q8C2×D4311yescharacteristic
417#520—438no—
418#520—864no—
419C2×C4×Q8—861no—
420C2×C4×D4—861no—
421C2×C4×D4—861no—
422C2×C4×D4—861no—
423C2×#117—431no—
424C2×#117—431no—
425C2×#117—431no—
426C2×#117C2×D4311yescharacteristic
427C22×C4⋊C4—431no—
428C22×C4⋊C4—431no—
429C22×C4⋊C4—431no—
430#485—438no—
431#485—438no—
432#485—438no—
433#485C2×D4318yescomplemented
434#484—438no—
435#484—438no—
436#483—438no—
437#483—438no—
438#428—438no—
439#427—438no—
440C2×#107—431no—
441C2×#107—431no—
442C2×#107—431no—
443C2×#107C2×D4311yescharacteristic
444C2×#106—431no—
445C2×#106—431no—
446C2×#106—431no—
447C2×#106C2×D4311yescharacteristic
448#419—438no—
449C2×#103—431no—
450C2×#103—431no—
451C2×#103—431no—
452C2×#103—431no—
453C2×#103—431no—
454C2×#103—431no—
455C2×#103—438no—
456C2×#103C2×D4311yescharacteristic
457C2×#103C2×D4311yescharacteristic
458#408—438no—
459C2×C22⋊C8—431no—
460C2×C22⋊C8—431no—
461C2×C22⋊C8—431no—
462C2×C22⋊C8C2×D4311yescharacteristic
463C43C2×#309711yescharacteristic, complemented, Sylow
464C2×#41—434no—
465C2×#41—434no—
466C2×#41—864no—
467C2×#41—864no—
468C22×Q8—431no—
469C22×Q8—434no—
470C22×Q8—431no—
471C22×Q8—861no—
472C22×Q8—862no—
473C22×Q8—864no—
474C22×Q8—864no—
475C22×Q8C22×D4311yescharacteristic
476C22×D4—431no—
477C22×D4—431no—
478C22×D4—431no—
479C23×C4—431no—
480C23×C4—431no—
481C23×C4—861no—
482C23×C4—861no—
483C23×C4—861no—
484C23×C4—861no—
485C23×C4C22×D4311yescharacteristic
486C2×M16—434no—
487C2×M16—864no—
488C22×C8—431no—
489C22×C8—431no—
490C22×C8—434no—
491C22×C8—864no—
492C22×C8C22×D4311yescharacteristic
493C22×C8C22×D4311yescharacteristic
494C4⋊Q8—868no—
495#124—868no—
496#123—868no—
497#123—868no—
498C22⋊Q8—22no—
499C22⋊Q8—434no—
500C22⋊Q8—434no—
501C22⋊Q8—434no—
502C22⋊Q8—862no—
503C22⋊Q8—862no—
504C22⋊Q8—862no—
505C22⋊Q8C22×D4314yes—
506C4×Q8—868no—
507C4×D4—868no—
508C4×D4—868no—
509C4×D4—868no—
510#117—22no—
511#117—434no—
512#117—434no—
513#117—434no—
514#117—862no—
515#117—862no—
516#117—862no—
517#117C22×D4314yes—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—431no—
520C2×C4⋊C4—431no—
521C2×C4⋊C4—434no—
522C2×C4⋊C4—431no—
523C2×C4⋊C4—434no—
524C2×C4⋊C4—434no—
525C2×C4⋊C4—862no—
526C2×C4⋊C4—862no—
527C2×C4⋊C4—861no—
528C2×C4⋊C4—861no—
529C2×C4⋊C4—861no—
530C2×C4⋊C4—861no—
531C2×C4⋊C4—861no—
532C2×C4⋊C4—862no—
533C2×C4⋊C4—861no—
534C2×C4⋊C4C22×D4311yescharacteristic
535C2×C4⋊C4C22×D4311yescharacteristic
536C2×C4⋊C4C22×D4311yescharacteristic
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—861no—
540C2×C22⋊C4—861no—
541C2×C22⋊C4—861no—
542C2×C22⋊C4—861no—
543C2×C22⋊C4—861no—
544C2×C22⋊C4—861no—
545C2×C42—21no—
546C2×C42—861no—
547C2×C42—861no—
548C2×C42—861no—
549#107—434no—
550#107—434no—
551#107—434no—
552#107C22×D4314yes—
553#106—434no—
554#106—434no—
555#106—434no—
556#106C22×D4314yes—
557#103—434no—
558#103—434no—
559#103—434no—
560#103—434no—
561#103—434no—
562#103—434no—
563#103C22×D4314yes—
564#103C22×D4314yes—
565C22⋊C8—434no—
566C22⋊C8—434no—
567C22⋊C8—434no—
568C22⋊C8C22×D4314yes—
569C24—431no—
570C24—431no—
571C24D4×D4311yescharacteristic
572#41—8616no—
573#41—868no—
574#41—868no—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—22no—
578C2×Q8—434no—
579C2×Q8—432no—
580C2×Q8—864no—
581C2×Q8—864no—
582C2×Q8—868no—
583C2×Q8—868no—
584C2×Q8—861no—
585C2×Q8—862no—
586C2×Q8—862no—
587C2×Q8—1724no—
588C2×Q8—1728no—
589C2×Q8C23×D4312yes—
590C2×D4—434no—
591C2×D4—434no—
592C2×D4—434no—
593C2×D4—864no—
594C2×D4—864no—
595C2×D4—864no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—431no—
603C22×C4—432no—
604C22×C4—434no—
605C22×C4—434no—
606C22×C4—432no—
607C22×C4—431no—
608C22×C4—432no—
609C22×C4—432no—
610C22×C4—864no—
611C22×C4—864no—
612C22×C4—864no—
613C22×C4—862no—
614C22×C4—862no—
615C22×C4—864no—
616C22×C4—861no—
617C22×C4—861no—
618C22×C4—861no—
619C22×C4—861no—
620C22×C4—3442no—
621C22×C4—3442no—
622C22×C4—3442no—
623C22×C4—1724no—
624C22×C4D4×D4312yes—
625C22×C4D4×D4311yescharacteristic
626C22×C4C23×D4312yes—
627C22×C4C23×D4311yescharacteristic
628M16—868no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—432no—
632C2×C8—432no—
633C2×C8—868no—
634C2×C8—862no—
635C2×C8—862no—
636C2×C8C23×D4312yes—
637C2×C8C23×D4312yes—
638C4⋊C4—24no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—432no—
643C4⋊C4—432no—
644C4⋊C4—432no—
645C4⋊C4—864no—
646C4⋊C4—864no—
647C4⋊C4—864no—
648C4⋊C4—864no—
649C4⋊C4—861no—
650C4⋊C4—861no—
651C4⋊C4—864no—
652C4⋊C4—861no—
653C4⋊C4—864no—
654C4⋊C4C23×D4312yes—
655C4⋊C4C23×D4312yes—
656C4⋊C4C23×D4312yes—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—864no—
660C22⋊C4—864no—
661C22⋊C4—864no—
662C22⋊C4—864no—
663C22⋊C4—864no—
664C22⋊C4—864no—
665C42—24no—
666C42—864no—
667C42—864no—
668C42—864no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—434no—
673C23—432no—
674C23—432no—
675C23—862no—
676C23—862no—
677C23—862no—
678C23—862no—
679C23—862no—
680C23C2×D4×D4312yes—
681C23C2×D4×D4311yescharacteristic
682Q8—22no—
683Q8—22no—
684Q8—42no—
685Q8—868no—
686Q8—862no—
687Q8—862no—
688Q8—1728no—
689Q8—1722no—
690D4—868no—
691D4—868no—
692D4—868no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—434no—
706C2×C4—432no—
707C2×C4—438no—
708C2×C4—434no—
709C2×C4—434no—
710C2×C4—432no—
711C2×C4—862no—
712C2×C4—864no—
713C2×C4—862no—
714C2×C4—862no—
715C2×C4—862no—
716C2×C4—862no—
717C2×C4—862no—
718C2×C4—862no—
719C2×C4—3444no—
720C2×C4—3444no—
721C2×C4—3444no—
722C2×C4—1728no—
723C2×C4—1722no—
724C2×C4—1722no—
725C2×C4—1722no—
726C2×C4—1722no—
727C2×C4C2×D4×D4312yes—
728C2×C4C2×D4×D4311yescharacteristic
729C2×C4#41×D4312yes—
730C2×C4#41×D4312yes—
731C2×C4C24×D4311yescharacteristic
732C8—22no—
733C8—22no—
734C8—862no—
735C8—862no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—44no—
740C22—434no—
741C22—862no—
742C22—862no—
743C22—868no—
744C22—862no—
745C22—862no—
746C22—862no—
747C22—1724no—
748C22#123×D4312yes—
749C22#1458370812yes—
750C22#1458371312yes—
751C22C22×D4×D4311yescharacteristic
752C4—22no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—434no—
758C4—862no—
759C4—1722no—
760C4—1722no—
761C4—1722no—
762C4—1722no—
763C4#123×D4312yes—
764C4C2×#41×D4311yescharacteristic
765C4C2×#41×D4311yescharacteristic
766C2—42no—
767C2—864no—
768C2—1722no—
769C2#1914455914yesdirect product factor
770C2C2×#123×D4311yescharacteristic
771C2C2×#1458370811yescharacteristic
772C2C2×#1458371311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#485C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
hypercenterC2×#485D43
hypocenterC43C2×#3097
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
3. #19144559C2direct (N × H)
4. C2×#14583235C2semidirect
5. C2×#14583233C2semidirect
6. C2×#14583242C2semidirect
7. C2×#14583240C2semidirect
8. C2×#14583239C2semidirect
9. C2×#14583231C2semidirect
10. C2×#14583227C2semidirect
11. C2×#14582938C2semidirect
12. C2×#14582936C2semidirect
13. C2×#14582906C2semidirect
14. C2×#103×D43C2semidirect
16. C2×C43×#485C2semidirect
42. #14583242C22semidirect
43. #14583240C22semidirect
44. #14583239C22semidirect
45. #14583235C22semidirect
46. #14583233C22semidirect
47. #14583231C22semidirect
48. #14583227C22semidirect
49. #14582938C22semidirect
50. #14582936C22semidirect
57. #14582906C22semidirect
64. #103×D43C22semidirect
71. C43×#485C22semidirect
388. C2×#485D43semidirect
397. C2×C43#3097semidirect
433. #485C2×D43semidirect
463. C43C2×#3097semidirect
769. C2#19144559direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834722
C2×#145833792
#191445592
C2×#145832352
C2×#145832332
C2×#145832422
C2×#145832402
C2×#145832392
C2×#145832312
C2×#145832272
C2×#145829382
C2×#145829362
C2×#145829062
C2×#103×D432
C2×#145828642
C2×C43×#4852
C2×#309743