Finite Group Databasebeta

← C2×#19144782 #25964831

Subgroups — C2×#19144782 #25964831

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×#14583522C211yesmaximal, characteristic, complemented
2C2×#14583373C211yesmaximal, characteristic, complemented
3#19144782C2116yesmaximal, direct product factor
4C2×#14583223C211yesmaximal, characteristic, complemented
5C2×#14583188C211yesmaximal, characteristic, complemented
6C2×#14583178C211yesmaximal, characteristic, complemented
7C2×#14583117C211yesmaximal, characteristic, complemented
8C2×#14583117C211yesmaximal, characteristic, complemented
9C2×#14583049C211yesmaximal, characteristic, complemented
10C2×#14583035C211yesmaximal, characteristic
11C2×#14583010C211yesmaximal, characteristic, complemented
12C2×#14583002C211yesmaximal, characteristic, complemented
13C2×#14582984C211yesmaximal, characteristic, complemented
14C2×#14582981C211yesmaximal, characteristic, complemented
15C2×#14582957C211yesmaximal, characteristic, complemented
16C2×C43×#485C211yesmaximal, characteristic, complemented
17C23×D172C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19C22×#10621884C2211yescharacteristic
20C22×D344C2211yescharacteristic
21C22×D344C2211yescharacteristic
22#14583522—24no—
23#14583522C2218yescomplemented
24C2×#13063324C2211yescharacteristic, complemented
25C2×#13063320—21no—
26C2×#13063314C2211yescharacteristic, complemented
27C2×#13063311—21no—
28C2×#13063307—21no—
29C2×#13063305—21no—
30C2×#13063299C2211yescharacteristic
31#14583373—24no—
32#14583373C2218yescomplemented
33C2×Q8×Dic43C2211yescharacteristic, complemented
34C2×C4×D172—21no—
35C2×C4×D172—21no—
36C2×#13063287C2211yescharacteristic
37C2×#13063287C2211yescharacteristic
38C2×#13063287C2211yescharacteristic
39C2×#13063287C2211yescharacteristic
40C2×#13063287C2211yescharacteristic, complemented
41C2×#13063284C2211yescharacteristic
42C2×C22⋊C4×D43—21no—
43C2×C22⋊C4×D43—21no—
44#14583223C2218yescomplemented
45#14583188C2218yescomplemented
46#14583178C2218yescomplemented
47#14583117C2218yescomplemented
48#14583117C2218yescomplemented
49#14583049C2218yescomplemented
50#14583035C2218yes—
51#14583010C2218yescomplemented
52#14583002C2218yescomplemented
53#14582984C2218yescomplemented
54#14582981C2218yescomplemented
55#14582957C2218yescomplemented
56C2×#13063258C2211yescharacteristic, complemented
57C2×#13063256C2211yescharacteristic, complemented
58C2×Dic43⋊C8C2211yescharacteristic, complemented
59C2×Dic43⋊C8C2211yescharacteristic, complemented
60C2×#13063247C2211yescharacteristic
61C2×#13063247C2211yescharacteristic
62C2×#13063245C2211yescharacteristic
63C2×#13063245C2211yescharacteristic
64C2×#13063245C2211yescharacteristic, complemented
65C2×#13063245C2211yescharacteristic, complemented
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×#13063235C2211yescharacteristic, complemented
68C2×C8×Dic43C2211yescharacteristic, complemented
69C2×C22⋊Q8×C43C2211yescharacteristic
70C2×#117×C43C2211yescharacteristic
71C43×#485C2218yescomplemented
72C2×#107×C43C2211yescharacteristic, complemented
73C2×#106×C43C2211yescharacteristic, complemented
74C2×#103×C43C2211yescharacteristic, complemented
75C2×#103×C43C2211yescharacteristic, complemented
76C2×C22⋊C8×C43C2211yescharacteristic
77C24×D43—21no—
78C22×Dic86—21no—
79C22×D172—21no—
80C22×D172—22no—
81C22×D172—24no—
82C22×D172—24no—
83C22×D172C2314yes—
84C22×D172C2311yescharacteristic
85C22×D172C2311yescharacteristic
86C22×D172C2311yescharacteristic
87C22×C22⋊D43—21no—
88C22×C4×D43—21no—
89C22×C4×D43—21no—
90C22×C4×D43—21no—
91C22×C4×D43—21no—
92C22×C4×D43—21no—
93C2×#10621884—24no—
94C2×#10621884—24no—
95C2×#10621884C2314yes—
96C2×#10621884C2314yes—
97C2×D344—24no—
98C2×D344—24no—
99C2×D344C2314yes—
100C2×D344C2314yes—
101C22×C43⋊C8C2311yescharacteristic
102C22×C43⋊C8C2311yescharacteristic
103#13063324—22no—
104#13063324C2314yescomplemented
105#13063320—28no—
106#13063314—22no—
107#13063314C2314yescomplemented
108#13063311—28no—
109#13063307—28no—
110#13063305—28no—
111#13063299—22no—
112#13063299C2314yes—
113Q8×Dic43—22no—
114Q8×Dic43C2314yescomplemented
115C4×D172—28no—
116C4×D172—28no—
117#13063287—22no—
118#13063287—22no—
119#13063287—22no—
120#13063287—22no—
121#13063287—22no—
122#13063287C2314yes—
123#13063287C2314yes—
124#13063287C2314yes—
125#13063287C2314yes—
126#13063287C2314yescomplemented
127#13063284D414yes—
128#13063284C2314yes—
129C2×C4⋊Dic43—21no—
130C2×C4⋊Dic43D411yescharacteristic
131C2×C4⋊Dic43D411yescharacteristic
132C2×C4⋊Dic43C2311yescharacteristic
133C2×Dic43⋊C4—21no—
134C2×C22⋊Dic43D411yescharacteristic
135C2×C22⋊Dic43D411yescharacteristic
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—21no—
143C2×(C2×D43)⋊C4—21no—
144C22⋊C4×D43—28no—
145C22⋊C4×D43—28no—
146C2×C4×Dic43—21no—
147C2×C4×Dic43C2311yescharacteristic
148C2×C4×Dic43C2311yescharacteristic
149#13063258C2314yescomplemented
150#13063256C2314yescomplemented
151Dic43⋊C8C2314yescomplemented
152Dic43⋊C8C2314yescomplemented
153#13063247C2314yes—
154#13063247C2314yes—
155#13063245C2314yes—
156#13063245C2314yes—
157#13063245C2314yescomplemented
158#13063245C2314yescomplemented
159C22⋊(C43⋊C8)C2314yes—
160#13063235C2314yescomplemented
161C8×Dic43C2314yescomplemented
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×C43C2314yescomplemented
178#106×C43C2314yescomplemented
179#103×C43C2314yescomplemented
180#103×C43C2314yescomplemented
181C22⋊C8×C43C2314yes—
182C24×C43C2×D411yescharacteristic
183C23×D43—21no—
184C23×D43—21no—
185C23×D43—28no—
186C23×D43—24no—
187C23×D43—21no—
188C23×D43—82no—
189C23×D43—82no—
190C2×Q8×C43—21no—
191C2×Q8×C43—22no—
192C2×Q8×C43—22no—
193C2×Q8×C43C2412yes—
194C22×C4×C43—22no—
195C22×C4×C43—22no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2×D412yes—
202C22×C4×C43C2412yes—
203C22×C4×C43C2411yescharacteristic
204C2×C22⋊D43—24no—
205C2×C22⋊D43—82no—
206C22×Dic43—21no—
207C22×Dic43C2×D411yescharacteristic
208C22×Dic43C2×D411yescharacteristic
209C22×Dic43C2×D411yescharacteristic
210C22×Dic43C2×D411yescharacteristic
211C2×D172—28no—
212C2×D172—216no—
213C2×D172—21no—
214C2×D172—21no—
215C2×D172—24no—
216C2×D172—22no—
217C2×D172—22no—
218C2×D172—28no—
219C2×D172—28no—
220C2×D172—21no—
221C2×D172—22no—
222C2×D172—22no—
223C2×D172#4114yes—
224C2×D172#4114yes—
225C2×D172C2412yes—
226C2×D172C2412yes—
227C2×D172C2412yes—
228C2×C4×D43—24no—
229C2×C4×D43—24no—
230C2×C4×D43—24no—
231C2×C4×D43—24no—
232C2×C4×D43—24no—
233C2×C4×D43—82no—
234C2×C4×D43—82no—
235C2×C4×D43—82no—
236C2×C4×D43—82no—
237C2×C4×D43—82no—
238C2×Dic86—24no—
239C2×Dic86—82no—
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—
252C22⋊C4×C43—24no—
253C42×C43—24no—
254C22⋊Dic43C2×D414yes—
255C22⋊Dic43C2×D414yes—
256#10621884—28no—
257#10621884—28no—
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)⋊C4—24no—
266C4⋊Dic43—21no—
267C4⋊Dic43—24no—
268C4⋊Dic43C2×D414yes—
269C4⋊Dic43C2×D414yes—
270C4⋊Dic43C2412yes—
271Dic43⋊C4—24no—
272C4×Dic43—24no—
273C4×Dic43C2×D412yes—
274C4×Dic43C2×D412yes—
275C4×Dic43C2412yes—
276C4×Dic43C2412yes—
277C2×C43⋊C8—22no—
278C2×C43⋊C8—22no—
279C2×C43⋊C8C2412yes—
280C2×C43⋊C8C2412yes—
281D344—28no—
282D344—28no—
283C23×C43—22no—
284C23×C43—22no—
285C23×C43—22no—
286C23×C43C22×D412yes—
287C23×C43C22×D411yescharacteristic
288C22×D43—24no—
289C22×D43—24no—
290C22×D43—22no—
291C22×D43—22no—
292C22×D43—216no—
293C22×D43—22no—
294C22×D43—42no—
295C22×D43—42no—
296C22×D43—42no—
297C22×D43—42no—
298C22×D43—42no—
299C22×D43—42no—
300C22×D43—42no—
301C22×D43—84no—
302C22×D43—84no—
303C22×D43—816no—
304Q8×C43—22no—
305Q8×C43—22no—
306Q8×C43—42no—
307C2×C4×C43—22no—
308C2×C4×C43—24no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—42no—
316C2×C4×C43—42no—
317C2×C4×C43—42no—
318C2×C4×C43—42no—
319C2×C4×C43C22×D412yes—
320C2×C4×C43C22×D411yescharacteristic
321C2×C4×C43C2×#4112yes—
322C2×C4×C43C2×#4112yes—
323C2×C4×C43C2511yescharacteristic
324C22⋊D43—84no—
325C2×Dic43—22no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—42no—
331C2×Dic43C22×D412yes—
332C2×Dic43C22×D412yes—
333C2×Dic43C22×D412yes—
334C2×Dic43C22×D412yes—
335D172—216no—
336D172—24no—
337D172—24no—
338D172—22no—
339D172—22no—
340D172—22no—
341D172—22no—
342D172—42no—
343D172C2×#4114yes—
344D172C2×#4114yes—
345C4×D43—84no—
346C4×D43—84no—
347C4×D43—84no—
348C4×D43—84no—
349C4×D43—84no—
350Dic86—84no—
351C8×C43—22no—
352C8×C43—22no—
353C43⋊C8—22no—
354C43⋊C8—22no—
355C2×#3118—431nomaximal, Sylow
356C22×C43—22no—
357C22×C43—22no—
358C22×C43—22no—
359C22×C43—44no—
360C22×C43#52512yes—
361C22×C43#57612yes—
362C22×C43#57712yes—
363C22×C43C23×D411yescharacteristic
364C2×D43—24no—
365C2×D43—24no—
366C2×D43—48no—
367C2×D43—48no—
368C2×D43—42no—
369C2×D43—42no—
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—42no—
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—22no—
389Dic43—42no—
390C2×#542—431no—
391C2×#518—431no—
392#3118—4316no—
393C2×#485D4311yescharacteristic, complemented
394C2×#482—431no—
395C2×#476—431no—
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—42no—
407C2×C43#311814yescomplemented
408C2×C43C2×#52511yescharacteristic
409C2×C43C2×#57611yescharacteristic
410C2×C43C2×#57711yescharacteristic
411D43—44no—
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⋊Q8—431no—
422C2×#126—861no—
423C2×#124—431no—
424C2×#124—861no—
425C2×#123—861no—
426C2×C22⋊Q8—861no—
427C2×C22⋊Q8C2×D4311yescharacteristic
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—431no—
437C2×C4×D4—861no—
438C2×C4×D4—861no—
439C2×#117—431no—
440C2×#117C2×D4311yescharacteristic
441C22×C22⋊C4—861no—
442C22×C22⋊C4—861no—
443#485C2×D4318yescomplemented
444#482—438no—
445#476—438no—
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×#107C2×D4311yescharacteristic, complemented
458C2×#106—431no—
459C2×#106C2×D4311yescharacteristic, complemented
460C2×C4⋊C8—431no—
461C2×C4⋊C8—431no—
462C2×#103C2×D4311yescharacteristic, complemented
463C2×#103C2×D4311yescharacteristic, complemented
464C2×#102—431no—
465C2×#102—431no—
466C2×#102—431no—
467C2×#102—431no—
468C2×#102—431no—
469C2×#102—431no—
470C2×C22⋊C8—431no—
471C2×C22⋊C8C2×D4311yescharacteristic
472C2×#97—431no—
473C2×C4×C8—431no—
474C43C2×#311811yescharacteristic, complemented, Sylow
475C25—861no—
476C22×Q8—861no—
477C22×Q8C22×D4311yescharacteristic
478C22×D4—431no—
479C22×D4—431no—
480C22×D4—431no—
481C22×D4—434no—
482C22×D4—864no—
483C22×D4—864no—
484C22×D4—861no—
485C22×D4—861no—
486C22×D4—862no—
487C23×C4—861no—
488C23×C4—861no—
489C23×C4—861no—
490C23×C4—861no—
491C23×C4—861no—
492C23×C4C22×D4311yescharacteristic
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—434no—
506C4⋊Q8—862no—
507#126—868no—
508#124—434no—
509#124—862no—
510#124—868no—
511#123—868no—
512C22⋊Q8—22no—
513C22⋊Q8—868no—
514C22⋊Q8C22×D4314yes—
515#121—434no—
516#121—862no—
517C4×Q8—434no—
518C4×Q8—862no—
519C4×D4—434no—
520C4×D4—434no—
521C4×D4—434no—
522C4×D4—434no—
523C4×D4—434no—
524C4×D4—868no—
525C4×D4—868no—
526C4×D4—862no—
527C4×D4—862no—
528C4×D4—862no—
529C4×D4—862no—
530C4×D4—862no—
531#117—22no—
532#117—434no—
533#117—434no—
534#117C22×D4314yes—
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—21no—
546C2×C22⋊C4—431no—
547C2×C22⋊C4—431no—
548C2×C22⋊C4—868no—
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×C22⋊C4—861no—
558C2×C42—21no—
559C2×C42—431no—
560C2×C42—431no—
561C2×C42—861no—
562#107—434no—
563#107C22×D4314yescomplemented
564#106—434no—
565#106C22×D4314yescomplemented
566C4⋊C8—434no—
567C4⋊C8—434no—
568#103C22×D4314yescomplemented
569#103C22×D4314yescomplemented
570#102—434no—
571#102—434no—
572#102—434no—
573#102—434no—
574#102—434no—
575#102—434no—
576C22⋊C8—434no—
577C22⋊C8C22×D4314yes—
578#97—434no—
579C4×C8—434no—
580C24—868no—
581C24—864no—
582C24—861no—
583C24—861no—
584C24—861no—
585C24—3442no—
586C24—3442no—
587C24D4×D4311yescharacteristic
588C2×Q8—21no—
589C2×Q8—22no—
590C2×Q8—22no—
591C2×Q8—864no—
592C2×Q8—3442no—
593C2×Q8C23×D4312yes—
594C2×D4—434no—
595C2×D4—434no—
596C2×D4—432no—
597C2×D4—432no—
598C2×D4—432no—
599C2×D4—868no—
600C2×D4—868no—
601C2×D4—868no—
602C2×D4—8616no—
603C2×D4—864no—
604C2×D4—864no—
605C2×D4—861no—
606C2×D4—861no—
607C2×D4—861no—
608C2×D4—862no—
609C2×D4—862no—
610C2×D4—862no—
611C2×D4—862no—
612C2×D4—3442no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—431no—
620C22×C4—431no—
621C22×C4—431no—
622C22×C4—431no—
623C22×C4—864no—
624C22×C4—864no—
625C22×C4—864no—
626C22×C4—864no—
627C22×C4—864no—
628C22×C4—861no—
629C22×C4—3442no—
630C22×C4—3442no—
631C22×C4—3442no—
632C22×C4—3442no—
633C22×C4—3442no—
634C22×C4D4×D4312yes—
635C22×C4D4×D4311yescharacteristic
636C22×C4C23×D4312yes—
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—24no—
665C22⋊C4—434no—
666C22⋊C4—434no—
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—24no—
676C42—432no—
677C42—432no—
678C42—432no—
679C42—432no—
680C42—864no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—8616no—
685C23—864no—
686C23—864no—
687C23—862no—
688C23—862no—
689C23—862no—
690C23—3444no—
691C23—3444no—
692C23—34416no—
693C23—1722no—
694C23—1722no—
695C23—1722no—
696C23—1722no—
697C23—1722no—
698C23—1722no—
699C23—1722no—
700C23C2×D4×D4312yes—
701C23C2×D4×D4311yescharacteristic
702Q8—22no—
703Q8—22no—
704Q8—42no—
705Q8—3444no—
706D4—434no—
707D4—434no—
708D4—8616no—
709D4—864no—
710D4—864no—
711D4—862no—
712D4—862no—
713D4—862no—
714D4—862no—
715D4—3444no—
716D4—1722no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—432no—
730C2×C4—432no—
731C2×C4—432no—
732C2×C4—432no—
733C2×C4—862no—
734C2×C4—862no—
735C2×C4—862no—
736C2×C4—862no—
737C2×C4—862no—
738C2×C4—3444no—
739C2×C4—3444no—
740C2×C4—3444no—
741C2×C4—3444no—
742C2×C4—3444no—
743C2×C4—1722no—
744C2×C4C2×D4×D4312yes—
745C2×C4C2×D4×D4311yescharacteristic
746C2×C4#41×D4312yes—
747C2×C4#41×D4312yes—
748C2×C4C24×D4311yescharacteristic
749C8—22no—
750C8—22no—
751C8—862no—
752C8—862no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—44no—
757C22—864no—
758C22—864no—
759C22—34416no—
760C22—3444no—
761C22—1722no—
762C22—1722no—
763C22—1722no—
764C22—1722no—
765C22—1722no—
766C22—1722no—
767C22—1722no—
768C22—1728no—
769C22—1728no—
770C22#1458340712yes—
771C22#1458370112yes—
772C22#1458370812yes—
773C22C22×D4×D4311yescharacteristic
774C4—22no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—862no—
780C4—862no—
781C4—862no—
782C4—862no—
783C4—1722no—
784C4#1458340712yes—
785C4C2×#41×D4311yescharacteristic
786C4C2×#41×D4311yescharacteristic
787C2—42no—
788C2—3442no—
789C2—1724no—
790C2—1724no—
791C2#1914478214yesdirect product factor
792C2C2×#1458340711yescharacteristic
793C2C2×#1458370111yescharacteristic
794C2C2×#1458370811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#485C2
socleC23×C43C22×D4
prime radicalC2×#14583035C2
hypercenterC2×#485D43
hypocenterC43C2×#3118
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
1. C2×#14583522C2semidirect
2. C2×#14583373C2semidirect
3. #19144782C2direct (N × H)
4. C2×#14583223C2semidirect
5. C2×#14583188C2semidirect
6. C2×#14583178C2semidirect
7. C2×#14583117C2semidirect
8. C2×#14583117C2semidirect
9. C2×#14583049C2semidirect
11. C2×#14583010C2semidirect
12. C2×#14583002C2semidirect
13. C2×#14582984C2semidirect
14. C2×#14582981C2semidirect
15. C2×#14582957C2semidirect
16. C2×C43×#485C2semidirect
23. #14583522C22semidirect
24. C2×#13063324C22semidirect
26. C2×#13063314C22semidirect
32. #14583373C22semidirect
33. C2×Q8×Dic43C22semidirect
40. C2×#13063287C22semidirect
44. #14583223C22semidirect
45. #14583188C22semidirect
46. #14583178C22semidirect
47. #14583117C22semidirect
48. #14583117C22semidirect
49. #14583049C22semidirect
51. #14583010C22semidirect
52. #14583002C22semidirect
53. #14582984C22semidirect
54. #14582981C22semidirect
55. #14582957C22semidirect
56. C2×#13063258C22semidirect
57. C2×#13063256C22semidirect
58. C2×Dic43⋊C8C22semidirect
59. C2×Dic43⋊C8C22semidirect
64. C2×#13063245C22semidirect
65. C2×#13063245C22semidirect
67. C2×#13063235C22semidirect
68. C2×C8×Dic43C22semidirect
71. C43×#485C22semidirect
72. C2×#107×C43C22semidirect
73. C2×#106×C43C22semidirect
74. C2×#103×C43C22semidirect
75. C2×#103×C43C22semidirect
104. #13063324C23semidirect
107. #13063314C23semidirect
114. Q8×Dic43C23semidirect
126. #13063287C23semidirect
149. #13063258C23semidirect
150. #13063256C23semidirect
151. Dic43⋊C8C23semidirect
152. Dic43⋊C8C23semidirect
157. #13063245C23semidirect
158. #13063245C23semidirect
160. #13063235C23semidirect
161. C8×Dic43C23semidirect
177. #107×C43C23semidirect
178. #106×C43C23semidirect
179. #103×C43C23semidirect
180. #103×C43C23semidirect
393. C2×#485D43semidirect
407. C2×C43#3118semidirect
443. #485C2×D43semidirect
457. C2×#107C2×D43semidirect
459. C2×#106C2×D43semidirect
462. C2×#103C2×D43semidirect
463. C2×#103C2×D43semidirect
474. C43C2×#3118semidirect
563. #107C22×D43semidirect
565. #106C22×D43semidirect
568. #103C22×D43semidirect
569. #103C22×D43semidirect
791. C2#19144782direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835222
C2×#145833732
#191447822
C2×#145832232
C2×#145831882
C2×#145831782
C2×#145831172
C2×#145830492
C2×#145830352
C2×#145830102
C2×#145830022
C2×#145829842
C2×#145829812
C2×#145829572
C2×C43×#4852
C2×#311843