Finite Group Databasebeta

← C2×#19144796 #25964846

Subgroups — C2×#19144796 #25964846

Order 11008.

2198 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583504C211yesmaximal, characteristic, complemented
2C2×#14583379C211yesmaximal, characteristic, complemented
3#19144796C2116yesmaximal, direct product factor
4C2×#14583218C211yesmaximal, characteristic, complemented
5C2×#14583213C211yesmaximal, characteristic, complemented
6C2×#14583207C211yesmaximal, characteristic, complemented
7C2×#14583200C211yesmaximal, characteristic, complemented
8C2×#14583100C211yesmaximal, characteristic, complemented
9C2×#14583095C211yesmaximal, characteristic, complemented
10C2×#14583046C211yesmaximal, characteristic, complemented
11C2×#14583046C211yesmaximal, characteristic, complemented
12C2×#14583012C211yesmaximal, characteristic, complemented
13C2×#14583001C211yesmaximal, characteristic, complemented
14C2×C4×#10621873C211yesmaximal, characteristic, complemented
15C2×C4×D344C211yesmaximal, characteristic, complemented
16C2×C43×#433C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C22×#10621873C2211yescharacteristic
19C22×#10621873C2211yescharacteristic
20C22×D344C2211yescharacteristic
21C22×D344C2211yescharacteristic
22#14583504—24no—
23#14583504C2218yescomplemented
24C2×#13063322C2211yescharacteristic
25C2×#13063317C2211yescharacteristic
26C2×#13063310—21no—
27C2×#13063310—21no—
28C2×#13063299C2211yescharacteristic
29C2×#13063299C2211yescharacteristic
30C2×#13063298—21no—
31C2×#13063298—21no—
32#14583379—24no—
33#14583379C2218yescomplemented
34C2×C4×Dic86C2211yescharacteristic
35C2×C4×Dic86C2211yescharacteristic
36C2×C4×D172C2211yescharacteristic
37C2×C4×D172C2211yescharacteristic
38C2×C4×D172C2211yescharacteristic
39C2×C4×D172C2211yescharacteristic
40C2×(C22⋊D43)⋊C4—21no—
41C2×(C22⋊D43)⋊C4—21no—
42C2×#13063283—21no—
43C22×C4⋊Dic43C2211yescharacteristic
44C2×C4⋊C4×D43—21no—
45#14583218C2218yescomplemented
46#14583213C2218yescomplemented
47#14583207C2218yescomplemented
48#14583200C2218yescomplemented
49#14583100C2218yescomplemented
50#14583095C2218yescomplemented
51#14583046C2218yescomplemented
52#14583046C2218yescomplemented
53#14583012C2218yescomplemented
54#14583001C2218yescomplemented
55C4×#10621873C2218yescomplemented
56C4×D344C2218yescomplemented
57C2×#13063259C2211yescharacteristic
58C2×#13063259C2211yescharacteristic
59C2×#13063257C2211yescharacteristic
60C2×#13063257C2211yescharacteristic
61C2×#13063250C2211yescharacteristic
62C2×#13063250C2211yescharacteristic
63C2×#13063247C2211yescharacteristic
64C2×#13063247C2211yescharacteristic
65C2×#13063247C2211yescharacteristic
66C2×#13063247C2211yescharacteristic
67C2×#13063247C2211yescharacteristic
68C2×#13063247C2211yescharacteristic
69C2×#117×C43C2211yescharacteristic
70C43×#433C2218yescomplemented
71C2×C4⋊C8×C43C2211yescharacteristic
72C2×C4⋊C8×C43C2211yescharacteristic
73C2×C22⋊C8×C43C2211yescharacteristic
74C2×C22⋊C8×C43C2211yescharacteristic
75C2×#97×C43C2211yescharacteristic
76C2×C4×C8×C43C2211yescharacteristic
77C2×#10621898—22no—
78C2×#10621898—24no—
79C2×#10621898—24no—
80C2×#10621898C2314yes—
81C22×Dic86C2311yescharacteristic
82C22×D172—21no—
83C22×D172—21no—
84C22×D172C2311yescharacteristic
85C22×D172C2311yescharacteristic
86C22×D172C2311yescharacteristic
87C22×C22⋊D43—21no—
88C22×C22⋊D43—21no—
89C22×C22⋊D43—21no—
90C23×Dic43—21no—
91C22×C4×D43—21no—
92C22×C4×D43—21no—
93C22×C4×D43—21no—
94C22×C4×D43—21no—
95C22×C4×D43—21no—
96C2×#10621873—24no—
97C2×#10621873—24no—
98C2×#10621873C2314yes—
99C2×#10621873C2314yes—
100C2×D344—24no—
101C2×D344—24no—
102C2×D344C2314yes—
103C2×D344C2314yes—
104#13063322—22no—
105#13063322C2314yes—
106#13063317—22no—
107#13063317C2314yes—
108#13063310—28no—
109#13063310—28no—
110#13063299—22no—
111#13063299—22no—
112#13063299C2314yes—
113#13063299C2314yes—
114#13063298—28no—
115#13063298—28no—
116C4×Dic86—22no—
117C4×Dic86—22no—
118C4×Dic86C2314yes—
119C4×Dic86C2314yes—
120C4×D172—22no—
121C4×D172—22no—
122C4×D172—22no—
123C4×D172—22no—
124C4×D172C2314yes—
125C4×D172C2314yes—
126C4×D172C2314yes—
127C4×D172C2314yes—
128(C22⋊D43)⋊C4—28no—
129(C22⋊D43)⋊C4—28no—
130#13063283—28no—
131C2×C4⋊Dic43—21no—
132C2×C4⋊Dic43—22no—
133C2×C4⋊Dic43C2311yescharacteristic
134C2×C4⋊Dic43C2311yescharacteristic
135C2×C4⋊Dic43C2314yes—
136C2×C4⋊Dic43C2311yescharacteristic
137C2×C4⋊Dic43C2311yescharacteristic
138C2×Dic43⋊C4—21no—
139C2×Dic43⋊C4—21no—
140C2×Dic43⋊C4—21no—
141C2×Dic43⋊C4—21no—
142C4⋊C4×D43—28no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4—21no—
149C2×C4×Dic43—21no—
150C2×C4×Dic43—21no—
151#13063259C2314yes—
152#13063259C2314yes—
153#13063257C2314yes—
154#13063257C2314yes—
155#13063250C2314yes—
156#13063250C2314yes—
157#13063247C2314yes—
158#13063247C2314yes—
159#13063247C2314yes—
160#13063247C2314yes—
161#13063247C2314yes—
162#13063247C2314yes—
163C23×C4×C43C2311yescharacteristic
164C22×C8×C43C2311yescharacteristic
165C22×C8×C43C2311yescharacteristic
166C22×C8×C43C2311yescharacteristic
167C22×C8×C43C2311yescharacteristic
168#117×C43D414yes—
169#117×C43C2314yes—
170C2×C4⋊C4×C43D411yescharacteristic
171C2×C4⋊C4×C43D411yescharacteristic
172C2×C22⋊C4×C43D411yescharacteristic
173C2×C22⋊C4×C43D411yescharacteristic
174C2×C42×C43C2311yescharacteristic
175C2×C42×C43C2311yescharacteristic
176C4⋊C8×C43C2314yes—
177C4⋊C8×C43C2314yes—
178C22⋊C8×C43C2314yes—
179C22⋊C8×C43C2314yes—
180#97×C43C2314yes—
181C4×C8×C43C2314yes—
182C24×C43C2×D411yescharacteristic
183C23×D43—21no—
184C23×D43—21no—
185C23×D43—21no—
186C22×C4×C43—22no—
187C22×C4×C43—22no—
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D412yes—
194C22×C4×C43C2412yes—
195C22×C4×C43C2411yescharacteristic
196C2×C22⋊D43—28no—
197C2×C22⋊D43—24no—
198C2×C22⋊D43—24no—
199C2×C22⋊D43—24no—
200C2×C22⋊D43—82no—
201C2×C22⋊D43—82no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205C22×Dic43—21no—
206C22×Dic43—21no—
207C22×Dic43—24no—
208C22×Dic43—82no—
209#10621898—216no—
210#10621898—28no—
211#10621898—28no—
212C2×D172—21no—
213C2×D172—22no—
214C2×D172—21no—
215C2×D172—21no—
216C2×D172—24no—
217C2×D172—24no—
218C2×D172—22no—
219C2×D172—22no—
220C2×D172—22no—
221C2×D172—22no—
222C2×D172—82no—
223C2×D172—82no—
224C2×D172#4114yes—
225C2×D172C2412yes—
226C2×D172C2412yes—
227C2×D172C2412yes—
228C2×C4×D43—28no—
229C2×C4×D43—24no—
230C2×C4×D43—24no—
231C2×C4×D43—24no—
232C2×C4×D43—24no—
233C2×C4×D43—24no—
234C2×C4×D43—82no—
235C2×C4×D43—82no—
236C2×C4×D43—82no—
237C2×C4×D43—82no—
238C2×Dic86—21no—
239C2×Dic86—22no—
240C2×Dic86#4114yes—
241C2×Dic86C2412yes—
242C2×C8×C43—22no—
243C2×C8×C43—22no—
244C2×C8×C43—22no—
245C2×C8×C43—22no—
246C2×C8×C43C2412yes—
247C2×C8×C43C2412yes—
248C2×C8×C43C2412yes—
249C2×C8×C43C2412yes—
250C4⋊C4×C43C2×D414yes—
251C4⋊C4×C43C2×D414yes—
252C22⋊C4×C43C2×D414yes—
253C22⋊C4×C43C2×D414yes—
254C42×C43C2×D412yes—
255C42×C43C2×D412yes—
256C42×C43C2412yes—
257C42×C43C2412yes—
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—
264C4⋊Dic43—24no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43—21no—
268C4⋊Dic43—21no—
269C4⋊Dic43C2412yes—
270C4⋊Dic43C2412yes—
271C4⋊Dic43C2412yes—
272C4⋊Dic43C2412yes—
273Dic43⋊C4—24no—
274Dic43⋊C4—24no—
275Dic43⋊C4—24no—
276Dic43⋊C4—24no—
277C4×Dic43—24no—
278C4×Dic43—24no—
279D344—28no—
280D344—28no—
281#10621873—28no—
282#10621873—28no—
283C23×C43—22no—
284C23×C43—22no—
285C23×C43—22no—
286C23×C43C22×D412yes—
287C23×C43C22×D411yescharacteristic
288C22×D43—24no—
289C22×D43—22no—
290C22×D43—22no—
291C22×D43—22no—
292C22×D43—42no—
293C22×D43—42no—
294C22×D43—42no—
295C22×D43—42no—
296C22×D43—42no—
297C22×D43—42no—
298C22×D43—42no—
299C22×D43—42no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—24no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43C22×D412yes—
309C2×C4×C43C22×D412yes—
310C2×C4×C43C22×D412yes—
311C2×C4×C43C22×D412yes—
312C2×C4×C43C22×D412yes—
313C2×C4×C43C22×D411yescharacteristic
314C2×C4×C43C2×#4112yes—
315C2×C4×C43C2×#4112yes—
316C2×C4×C43C2511yescharacteristic
317C22⋊D43—216no—
318C22⋊D43—84no—
319C22⋊D43—84no—
320C2×Dic43—24no—
321C2×Dic43—22no—
322C2×Dic43—22no—
323C2×Dic43—22no—
324C2×Dic43—22no—
325C2×Dic43—22no—
326C2×Dic43—42no—
327C2×Dic43—42no—
328C2×Dic43—42no—
329C2×Dic43—42no—
330C2×Dic43—84no—
331D172—24no—
332D172—22no—
333D172—22no—
334D172—22no—
335D172—22no—
336D172—22no—
337D172—42no—
338D172—42no—
339D172—84no—
340D172—84no—
341D172C2×#4114yes—
342C4×D43—216no—
343C4×D43—84no—
344C4×D43—84no—
345C4×D43—84no—
346C4×D43—84no—
347Dic86—24no—
348Dic86—22no—
349Dic86C2×#4114yes—
350C8×C43—22no—
351C8×C43—22no—
352C8×C43—22no—
353C8×C43—22no—
354C2×#3119—431nomaximal, Sylow
355C22×C43—22no—
356C22×C43—22no—
357C22×C43—22no—
358C22×C43—44no—
359C22×C43#52512yes—
360C22×C43#57612yes—
361C22×C43#57712yes—
362C22×C43C23×D411yescharacteristic
363C2×D43—24no—
364C2×D43—48no—
365C2×D43—42no—
366C2×D43—42no—
367C2×D43—42no—
368C2×D43—42no—
369C2×D43—42no—
370C2×D43—42no—
371C2×D43—42no—
372C2×D43—42no—
373C2×D43—84no—
374C2×D43—84no—
375C4×C43—22no—
376C4×C43—22no—
377C4×C43—22no—
378C4×C43—22no—
379C4×C43—22no—
380C4×C43#52512yes—
381C4×C43C22×#4111yescharacteristic
382C4×C43C22×#4111yescharacteristic
383Dic43—24no—
384Dic43—42no—
385Dic43—42no—
386Dic43—42no—
387Dic43—42no—
388C2×#540—431no—
389C2×#520—431no—
390#3119—4316no—
391C2×#481—431no—
392C2×#480—431no—
393C2×#479—431no—
394C2×#478—431no—
395C2×#460—431no—
396C2×#459—431no—
397C2×#449—431no—
398C2×#449—431no—
399C2×#442—431no—
400C2×#440—431no—
401C2×C4×SD16—431no—
402C2×C4×D8—431no—
403C2×#433D4311yescharacteristic, complemented
404C2×C43—42no—
405C2×C43#311914yescomplemented
406C2×C43C2×#52511yescharacteristic
407C2×C43C2×#57611yescharacteristic
408C2×C43C2×#57711yescharacteristic
409D43—44no—
410D43—82no—
411D43—82no—
412C22×#41—431no—
413C22×SD16—431no—
414C22×SD16—431no—
415C22×D8—431no—
416C22×D8—431no—
417#540—438no—
418#540—864no—
419C2×#127—431no—
420C2×#125—431no—
421C2×#123—861no—
422C2×#123—861no—
423C2×#121—431no—
424C2×#121—431no—
425C2×#121—861no—
426C2×#121—861no—
427#520—438no—
428#520—864no—
429C2×C4×Q8—431no—
430C2×C4×Q8—431no—
431C2×C4×D4—431no—
432C2×C4×D4—431no—
433C2×C4×D4—431no—
434C2×C4×D4—431no—
435C2×C4×D4—861no—
436C2×C4×D4—861no—
437C2×#117—861no—
438C2×#117C2×D4311yescharacteristic
439C22×C4⋊C4—431no—
440C22×C4⋊C4—861no—
441#481—438no—
442#480—438no—
443#479—438no—
444#478—438no—
445#460—438no—
446#459—438no—
447#449—438no—
448#449—438no—
449#442—438no—
450#440—438no—
451C4×SD16—438no—
452C4×D8—438no—
453#433C2×D4318yescomplemented
454C2×#107—431no—
455C2×#107—431no—
456C2×#106—431no—
457C2×#106—431no—
458C2×C4⋊C8C2×D4311yescharacteristic
459C2×C4⋊C8C2×D4311yescharacteristic
460C2×#103—431no—
461C2×#103—431no—
462C2×#102—431no—
463C2×#102—431no—
464C2×#102—431no—
465C2×#102—431no—
466C2×#102—431no—
467C2×#102—431no—
468C2×C22⋊C8C2×D4311yescharacteristic
469C2×C22⋊C8C2×D4311yescharacteristic
470C2×#97C2×D4311yescharacteristic
471C2×C4×C8C2×D4311yescharacteristic
472C43C2×#311911yescharacteristic, complemented, Sylow
473C2×#41—434no—
474C2×#41—864no—
475C2×#41—864no—
476C2×#41—862no—
477C22×Q8—431no—
478C22×D4—431no—
479C22×D4—431no—
480C22×D4—431no—
481C22×D4—861no—
482C22×D4—861no—
483C22×D4—861no—
484C22×D4—861no—
485C22×D4—861no—
486C23×C4—861no—
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×C8C22×D4311yescharacteristic
502C22×C8C22×D4311yescharacteristic
503C22×C8C22×D4311yescharacteristic
504C22×C8C22×D4311yescharacteristic
505#127—434no—
506#127—862no—
507#125—434no—
508#125—862no—
509#123—868no—
510#123—868no—
511#121—434no—
512#121—434no—
513#121—862no—
514#121—862no—
515#121—868no—
516#121—868no—
517C4×Q8—434no—
518C4×Q8—434no—
519C4×Q8—862no—
520C4×Q8—862no—
521C4×D4—434no—
522C4×D4—434no—
523C4×D4—434no—
524C4×D4—434no—
525C4×D4—868no—
526C4×D4—868no—
527C4×D4—862no—
528C4×D4—862no—
529C4×D4—862no—
530C4×D4—862no—
531#117—868no—
532#117D17214yes—
533#117C22×D4314yes—
534C2×C4⋊C4—431no—
535C2×C4⋊C4—431no—
536C2×C4⋊C4—434no—
537C2×C4⋊C4—431no—
538C2×C4⋊C4—431no—
539C2×C4⋊C4—861no—
540C2×C4⋊C4—862no—
541C2×C4⋊C4—861no—
542C2×C4⋊C4—861no—
543C2×C4⋊C4—861no—
544C2×C4⋊C4—861no—
545C2×C4⋊C4—868no—
546C2×C4⋊C4D17211yescharacteristic
547C2×C4⋊C4D17211yescharacteristic
548C2×C22⋊C4—861no—
549C2×C22⋊C4—861no—
550C2×C22⋊C4—861no—
551C2×C22⋊C4—861no—
552C2×C22⋊C4—861no—
553C2×C22⋊C4—861no—
554C2×C22⋊C4D17211yescharacteristic
555C2×C22⋊C4D17211yescharacteristic
556C2×C42—861no—
557C2×C42—861no—
558C2×C42C22×D4311yescharacteristic
559C2×C42C22×D4311yescharacteristic
560#107—434no—
561#107—434no—
562#106—434no—
563#106—434no—
564C4⋊C8C22×D4314yes—
565C4⋊C8C22×D4314yes—
566#103—434no—
567#103—434no—
568#102—434no—
569#102—434no—
570#102—434no—
571#102—434no—
572#102—434no—
573#102—434no—
574C22⋊C8C22×D4314yes—
575C22⋊C8C22×D4314yes—
576#97C22×D4314yes—
577C4×C8C22×D4314yes—
578C24—861no—
579C24—861no—
580C24—861no—
581C24C2×D17211yescharacteristic
582#41—868no—
583#41—868no—
584#41—8616no—
585C2×Q8—434no—
586C2×Q8—432no—
587C2×Q8—861no—
588C2×Q8—862no—
589C2×D4—434no—
590C2×D4—432no—
591C2×D4—432no—
592C2×D4—432no—
593C2×D4—868no—
594C2×D4—864no—
595C2×D4—864no—
596C2×D4—864no—
597C2×D4—861no—
598C2×D4—864no—
599C2×D4—864no—
600C2×D4—861no—
601C2×D4—861no—
602C2×D4—862no—
603C2×D4—862no—
604C2×D4—862no—
605C2×D4—862no—
606C2×D4—862no—
607C2×D4—3442no—
608C2×D4—3442no—
609C2×D4—3442no—
610C2×D4—3442no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—868no—
614C22×C4—861no—
615C22×C4—864no—
616C22×C4—864no—
617C22×C4—861no—
618C22×C4—861no—
619C22×C4—861no—
620C22×C4—861no—
621C22×C4—864no—
622C22×C4—864no—
623C22×C4—864no—
624C22×C4—864no—
625C22×C4—3442no—
626C22×C4—3442no—
627C22×C4—3442no—
628C22×C4—3442no—
629C22×C4—3442no—
630C22×C4C2×D17212yes—
631C22×C4C2×D17211yescharacteristic
632C22×C4C2×D17211yescharacteristic
633C22×C4C2×D17211yescharacteristic
634C22×C4C2×D17211yescharacteristic
635C22×C4C2×D17211yescharacteristic
636C22×C4C23×D4312yes—
637C22×C4C23×D4311yescharacteristic
638SD16—868no—
639SD16—868no—
640D8—868no—
641D8—868no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8C23×D4312yes—
647C2×C8C23×D4312yes—
648C2×C8C23×D4312yes—
649C2×C8C23×D4312yes—
650C4⋊C4—432no—
651C4⋊C4—432no—
652C4⋊C4—432no—
653C4⋊C4—432no—
654C4⋊C4—864no—
655C4⋊C4—861no—
656C4⋊C4—861no—
657C4⋊C4—861no—
658C4⋊C4—861no—
659C4⋊C4—864no—
660C4⋊C4—864no—
661C4⋊C4—864no—
662C4⋊C4—864no—
663C4⋊C4C2×D17214yes—
664C4⋊C4C2×D17214yes—
665C22⋊C4—864no—
666C22⋊C4—864no—
667C22⋊C4—864no—
668C22⋊C4—864no—
669C22⋊C4—864no—
670C22⋊C4—864no—
671C22⋊C4C2×D17214yes—
672C22⋊C4C2×D17214yes—
673C42—864no—
674C42—864no—
675C42C2×D17212yes—
676C42C2×D17212yes—
677C42C23×D4312yes—
678C42C23×D4312yes—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—864no—
683C23—862no—
684C23—862no—
685C23—862no—
686C23—1722no—
687C23—1722no—
688C23—1722no—
689C23—1722no—
690C23—1722no—
691C23—1722no—
692C23—1722no—
693C23—1722no—
694C23C22×D17212yes—
695C23C22×D17211yescharacteristic
696Q8—434no—
697Q8—864no—
698Q8—862no—
699D4—434no—
700D4—8616no—
701D4—864no—
702D4—862no—
703D4—862no—
704D4—862no—
705D4—862no—
706D4—862no—
707D4—3444no—
708D4—3444no—
709D4—3444no—
710D4—3444no—
711D4—1722no—
712D4—1722no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—8616no—
722C2×C4—864no—
723C2×C4—862no—
724C2×C4—862no—
725C2×C4—862no—
726C2×C4—862no—
727C2×C4—862no—
728C2×C4—3444no—
729C2×C4—3444no—
730C2×C4—3444no—
731C2×C4—3444no—
732C2×C4—3444no—
733C2×C4—1722no—
734C2×C4—1722no—
735C2×C4—1722no—
736C2×C4—1722no—
737C2×C4C22×D17212yes—
738C2×C4C22×D17212yes—
739C2×C4C22×D17212yes—
740C2×C4C22×D17212yes—
741C2×C4C22×D17212yes—
742C2×C4C22×D17211yescharacteristic
743C2×C4#41×D4312yes—
744C2×C4#41×D4312yes—
745C2×C4C24×D4311yescharacteristic
746C8—22no—
747C8—22no—
748C8—22no—
749C8—22no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—44no—
754C22—864no—
755C22—3444no—
756C22—3444no—
757C22—1722no—
758C22—1722no—
759C22—1722no—
760C22—1722no—
761C22—1722no—
762C22—1722no—
763C22—1722no—
764C22—1722no—
765C22—1728no—
766C22#1458341112yes—
767C22#1458370412yes—
768C22#1458371112yes—
769C22C23×D17211yescharacteristic
770C4—22no—
771C4—22no—
772C4—22no—
773C4—22no—
774C4—22no—
775C4—864no—
776C4—1722no—
777C4—1722no—
778C4—1722no—
779C4—1722no—
780C4#1458341112yes—
781C4C2×#41×D4311yescharacteristic
782C4C2×#41×D4311yescharacteristic
783C2—42no—
784C2—3442no—
785C2—3442no—
786C2—1724no—
787C2#1914479614yesdirect product factor
788C2C2×#1458341111yescharacteristic
789C2C2×#1458370411yescharacteristic
790C2C2×#1458371111yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#433C2
socleC23×C43C22×D4
hypercenterC2×#433D43
hypocenterC43C2×#3119
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#14583504C2semidirect
2. C2×#14583379C2semidirect
3. #19144796C2direct (N × H)
4. C2×#14583218C2semidirect
5. C2×#14583213C2semidirect
6. C2×#14583207C2semidirect
7. C2×#14583200C2semidirect
8. C2×#14583100C2semidirect
9. C2×#14583095C2semidirect
10. C2×#14583046C2semidirect
11. C2×#14583046C2semidirect
12. C2×#14583012C2semidirect
13. C2×#14583001C2semidirect
14. C2×C4×#10621873C2semidirect
15. C2×C4×D344C2semidirect
16. C2×C43×#433C2semidirect
23. #14583504C22semidirect
33. #14583379C22semidirect
45. #14583218C22semidirect
46. #14583213C22semidirect
47. #14583207C22semidirect
48. #14583200C22semidirect
49. #14583100C22semidirect
50. #14583095C22semidirect
51. #14583046C22semidirect
52. #14583046C22semidirect
53. #14583012C22semidirect
54. #14583001C22semidirect
55. C4×#10621873C22semidirect
56. C4×D344C22semidirect
70. C43×#433C22semidirect
403. C2×#433D43semidirect
405. C2×C43#3119semidirect
453. #433C2×D43semidirect
472. C43C2×#3119semidirect
787. C2#19144796direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835042
C2×#145833792
#191447962
C2×#145832182
C2×#145832132
C2×#145832072
C2×#145832002
C2×#145831002
C2×#145830952
C2×#145830462
C2×#145830122
C2×#145830012
C2×C4×#106218732
C2×C4×D3442
C2×C43×#4332
C2×#311943