Finite Group Databasebeta

← C2×#19147660 #25977602

Subgroups — C2×#19147660 #25977602

Order 11008.

2002 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583631C211yesmaximal, characteristic, complemented
2C2×#14583623C211yesmaximal, characteristic, complemented
3#19147660C2116yesmaximal, direct product factor
4C2×#14583285C211yesmaximal, characteristic
5C2×#14583284C211yesmaximal, characteristic, complemented
6C2×#14583123C211yesmaximal, characteristic, complemented
7C2×#14583123C211yesmaximal, characteristic, complemented
8C2×#14583097C211yesmaximal, characteristic, complemented
9C2×#14583116C211yesmaximal, characteristic, complemented
10C2×#14583111C211yesmaximal, characteristic, complemented
11C2×#14583101C211yesmaximal, characteristic, complemented
12C2×#14583027C211yesmaximal, characteristic, complemented
13C2×#14583012C211yesmaximal, characteristic, complemented
14C2×#14583006C211yesmaximal, characteristic, complemented
15C2×SD16×Dic43C211yesmaximal, characteristic, complemented
16C2×C43×#497C211yesmaximal, characteristic, complemented
17C22×#10621884C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19C22×#10621884C2211yescharacteristic
20C22×D344C2211yescharacteristic
21C22×#10621882C2211yescharacteristic
22#14583631—24no—
23#14583631C2218yescomplemented
24#14583623—24no—
25#14583623C2218yescomplemented
26C2×#13063321C2211yescharacteristic
27C2×#13063320—21no—
28C2×#13063320—21no—
29C2×#13063314C2211yescharacteristic
30C2×#13063314C2211yescharacteristic
31C2×#13063314C2211yescharacteristic
32C2×#13063311—21no—
33C2×#13063309—21no—
34C2×#13063307—21no—
35C2×#13063305—21no—
36C2×Q8×Dic43C2211yescharacteristic
37C2×Q8×Dic43C2211yescharacteristic
38C2×Q8×Dic43C2211yescharacteristic
39C2×C4×Dic86C2211yescharacteristic
40C2×C4×D172C2211yescharacteristic
41C2×C4×D172C2211yescharacteristic
42C2×D4×Dic43C2211yescharacteristic
43C2×(C22⋊D43)⋊C4—21no—
44C2×#13063283—21no—
45#14583285C2218yes—
46#14583284C2218yescomplemented
47#14583123C2218yescomplemented
48#14583123C2218yescomplemented
49#14583116C2218yescomplemented
50#14583111C2218yescomplemented
51#14583101C2218yescomplemented
52#14583097C2218yescomplemented
53#14583027C2218yescomplemented
54#14583012C2218yescomplemented
55#14583006C2218yescomplemented
56SD16×Dic43C2218yescomplemented
57C2×#13063257C2211yescharacteristic
58C2×C4⋊(C43⋊C8)C2211yescharacteristic
59C2×Dic43⋊C8C2211yescharacteristic
60C2×Dic43⋊C8C2211yescharacteristic
61C2×#13063249C2211yescharacteristic
62C2×#13063249C2211yescharacteristic
63C2×#13063249C2211yescharacteristic
64C2×#13063247C2211yescharacteristic
65C2×#13063247C2211yescharacteristic
66C2×#13063246C2211yescharacteristic
67C2×#13063235C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C22×Q16×C43C2211yescharacteristic
70C22×Q16×C43C2211yescharacteristic
71C22×SD16×C43C2211yescharacteristic
72C22×SD16×C43C2211yescharacteristic
73C2×C4⋊Q8×C43C2211yescharacteristic
74C2×#124×C43C2211yescharacteristic
75C43×#497C2218yescomplemented
76C2×#97×C43C2211yescharacteristic
77C22×Dic86D411yescharacteristic
78C22×D172C2311yescharacteristic
79C22×D172C2311yescharacteristic
80C22×C22⋊D43—21no—
81C22×C22⋊D43—21no—
82C23×Dic43—21no—
83C22×C4×D43—21no—
84C22×C4×D43—21no—
85C2×#10621884—42no—
86C2×#10621884—42no—
87C2×#10621884—42no—
88C2×#10621884C2314yes—
89C2×#10621884C2314yes—
90C2×#10621884C2314yes—
91C2×D344—24no—
92C2×D344C2314yes—
93C2×#10621882—42no—
94C2×#10621882C2314yes—
95C22×C43⋊C8C2311yescharacteristic
96C22×C43⋊C8C2311yescharacteristic
97#13063321—22no—
98#13063321C2314yes—
99#13063320—28no—
100#13063320—28no—
101#13063314—22no—
102#13063314—22no—
103#13063314—22no—
104#13063314C2314yes—
105#13063314C2314yes—
106#13063314C2314yes—
107#13063311—28no—
108#13063309—28no—
109#13063307—28no—
110#13063305—28no—
111Q8×Dic43—22no—
112Q8×Dic43—22no—
113Q8×Dic43—22no—
114Q8×Dic43C2314yes—
115Q8×Dic43C2314yes—
116Q8×Dic43C2314yes—
117C4×Dic86D414yes—
118C4×Dic86C2314yes—
119C4×D172—22no—
120C4×D172—22no—
121C4×D172C2314yes—
122C4×D172C2314yes—
123D4×Dic43—22no—
124D4×Dic43C2314yes—
125(C22⋊D43)⋊C4—28no—
126#13063283—28no—
127C2×C4⋊Dic43—21no—
128C2×C4⋊Dic43—21no—
129C2×C4⋊Dic43—21no—
130C2×C4⋊Dic43D411yescharacteristic
131C2×C4⋊Dic43C2311yescharacteristic
132C2×C4⋊Dic43C2311yescharacteristic
133C2×Dic43⋊C4D411yescharacteristic
134C2×Dic43⋊C4D411yescharacteristic
135C2×C22⋊Dic43—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—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×C4×Dic43—21no—
145C2×C4×Dic43—21no—
146C2×C4×Dic43—21no—
147C2×C4×Dic43C2311yescharacteristic
148C2×C4×Dic43C2311yescharacteristic
149#13063257C2314yes—
150C4⋊(C43⋊C8)C2314yes—
151Dic43⋊C8C2314yes—
152Dic43⋊C8C2314yes—
153#13063249C2314yes—
154#13063249C2314yes—
155#13063249C2314yes—
156#13063247C2314yes—
157#13063247C2314yes—
158#13063246C2314yes—
159#13063235C2314yes—
160C8×Dic43C2314yes—
161C22×Q8×C43C2311yescharacteristic
162C22×Q8×C43C2311yescharacteristic
163C22×Q8×C43C2311yescharacteristic
164C22×D4×C43C2311yescharacteristic
165C2×Q16×C43—24no—
166C2×Q16×C43—42no—
167C2×Q16×C43C2314yes—
168C2×Q16×C43C2314yes—
169C2×SD16×C43—24no—
170C2×SD16×C43—42no—
171C2×SD16×C43C2314yes—
172C2×SD16×C43C2314yes—
173C22×C8×C43C2311yescharacteristic
174C22×C8×C43C2311yescharacteristic
175C4⋊Q8×C43—22no—
176C4⋊Q8×C43C2314yes—
177#124×C43—22no—
178#124×C43C2314yes—
179C2×C4⋊C4×C43—21no—
180C2×C4⋊C4×C43—21no—
181C2×C22⋊C4×C43—21no—
182C2×C22⋊C4×C43—21no—
183C2×C42×C43C2311yescharacteristic
184#97×C43C2314yes—
185C24×C43—21no—
186C23×D43—21no—
187C23×D43—21no—
188C2×Q8×C43—21no—
189C2×Q8×C43—21no—
190C2×Q8×C43—21no—
191C2×Q8×C43—22no—
192C2×Q8×C43—22no—
193C2×Q8×C43—22no—
194C2×Q8×C43—22no—
195C2×Q8×C43—22no—
196C2×Q8×C43—22no—
197C2×Q8×C43C2412yes—
198C2×Q8×C43C2412yes—
199C2×Q8×C43C2412yes—
200C2×D4×C43—21no—
201C2×D4×C43—22no—
202C2×D4×C43—22no—
203C2×D4×C43C2412yes—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2×D411yescharacteristic
209C22×C4×C43C2411yescharacteristic
210C2×C22⋊D43—24no—
211C2×C22⋊D43—24no—
212C2×C22⋊D43—44no—
213C2×C22⋊D43—82no—
214C22×Dic43—24no—
215C22×Dic43—21no—
216C22×Dic43—21no—
217C22×Dic43—82no—
218C22×Dic43C2×D411yescharacteristic
219C22×Dic43C2×D411yescharacteristic
220C22×Dic43C2×D411yescharacteristic
221C22×Dic43C2×D411yescharacteristic
222C2×D172—21no—
223C2×D172—21no—
224C2×D172—22no—
225C2×D172—22no—
226C2×D172—22no—
227C2×D172—22no—
228C2×D172C2412yes—
229C2×D172C2412yes—
230C2×C4×D43—24no—
231C2×C4×D43—24no—
232C2×C4×D43—44no—
233C2×C4×D43—82no—
234C2×Dic86—42no—
235C2×Dic86C2×D414yes—
236Q16×C43—28no—
237Q16×C43—44no—
238SD16×C43—28no—
239SD16×C43—44no—
240C2×C8×C43—22no—
241C2×C8×C43#4114yes—
242C2×C8×C43C2412yes—
243C2×C8×C43C2412yes—
244C4⋊C4×C43—24no—
245C4⋊C4×C43—24no—
246C22⋊C4×C43—24no—
247C22⋊C4×C43—24no—
248C42×C43C2×D412yes—
249C42×C43C2412yes—
250C22⋊Dic43—24no—
251#10621884—44no—
252#10621884—44no—
253#10621884—44no—
254#10621882—44no—
255(C2×D43)⋊C4—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—
261(C2×D43)⋊C4—24no—
262(C2×D43)⋊C4—24no—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43—24no—
266C4⋊Dic43—24no—
267C4⋊Dic43—24no—
268C4⋊Dic43C2×D414yes—
269C4⋊Dic43C2412yes—
270C4⋊Dic43C2412yes—
271Dic43⋊C4C2×D414yes—
272Dic43⋊C4C2×D414yes—
273C4×Dic43—24no—
274C4×Dic43—24no—
275C4×Dic43—24no—
276C4×Dic43C2×D412yes—
277C4×Dic43C2×D412yes—
278C4×Dic43C2412yes—
279C4×Dic43C2412yes—
280C2×C43⋊C8—22no—
281C2×C43⋊C8—22no—
282C2×C43⋊C8C2412yes—
283C2×C43⋊C8C2412yes—
284D344—28no—
285C23×C43—22no—
286C23×C43—42no—
287C23×C43—42no—
288C23×C43—42no—
289C23×C43C22×D411yescharacteristic
290C22×D43—22no—
291C22×D43—22no—
292C22×D43—42no—
293C22×D43—42no—
294C22×D43—42no—
295C22×D43—42no—
296C22×D43—42no—
297C22×D43—42no—
298Q8×C43—22no—
299Q8×C43—22no—
300Q8×C43—22no—
301Q8×C43—22no—
302Q8×C43—22no—
303Q8×C43—22no—
304Q8×C43—42no—
305Q8×C43—42no—
306Q8×C43—42no—
307D4×C43—22no—
308D4×C43—22no—
309D4×C43—42no—
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×C43C22×D412yes—
319C2×C4×C43C22×D412yes—
320C2×C4×C43C22×D411yescharacteristic
321C2×C4×C43C2×#4112yes—
322C2×C4×C43H(5,𝔽2)12yes—
323C2×C4×C43C2511yescharacteristic
324C22⋊D43—48no—
325C22⋊D43—84no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—42no—
333C2×Dic43—42no—
334C2×Dic43—84no—
335C2×Dic43C22×D412yes—
336C2×Dic43C22×D412yes—
337C2×Dic43C22×D412yes—
338C2×Dic43C22×D412yes—
339D172—22no—
340D172—22no—
341D172—22no—
342D172—22no—
343D172—42no—
344D172—42no—
345C4×D43—48no—
346C4×D43—84no—
347Dic86—44no—
348C8×C43—22no—
349C8×C43C2×#4114yes—
350C43⋊C8—22no—
351C43⋊C8—22no—
352C2×#3401—431nomaximal, Sylow
353C22×C43—42no—
354C22×C43—42no—
355C22×C43—42no—
356C22×C43—84no—
357C22×C43#55012yes—
358C22×C43#57512yes—
359C22×C43#57712yes—
360C22×C43C23×D411yescharacteristic
361C2×D43—42no—
362C2×D43—42no—
363C2×D43—42no—
364C2×D43—42no—
365C2×D43—42no—
366C2×D43—42no—
367C2×D43—84no—
368C2×D43—84no—
369C4×C43—22no—
370C4×C43—22no—
371C4×C43—42no—
372C4×C43—42no—
373C4×C43—42no—
374C4×C43#55012yes—
375C4×C43C22×#4111yescharacteristic
376C4×C43C2×H(5,𝔽2)11yescharacteristic
377Dic43—22no—
378Dic43—22no—
379Dic43—22no—
380Dic43—22no—
381Dic43—42no—
382Dic43—42no—
383C2×#559—431no—
384C2×#556—431no—
385#3401—4316no—
386C2×#497D4311yescharacteristic, complemented
387C2×#496—431no—
388C2×#495—431no—
389C2×#464—431no—
390C2×#464—431no—
391C2×#460—431no—
392C2×#463—431no—
393C2×#463—431no—
394C2×#461—431no—
395C2×#446—431no—
396C2×#442—431no—
397C2×#441—431no—
398C2×C4×SD16—431no—
399C2×C43—82no—
400C2×C43#340114yescomplemented
401C2×C43C2×#55011yescharacteristic
402C2×C43C2×#57511yescharacteristic
403C2×C43C2×#57711yescharacteristic
404D43—82no—
405D43—82no—
406C22×Q16C2×D4311yescharacteristic
407C22×Q16C2×D4311yescharacteristic
408C22×SD16—431no—
409C22×SD16—431no—
410C22×SD16—431no—
411C22×SD16C2×D4311yescharacteristic
412C22×SD16C2×D4311yescharacteristic
413C22×D8—431no—
414C22×D8—431no—
415#559—438no—
416#559—864no—
417#556—438no—
418#556—864no—
419C2×C4⋊Q8C2×D4311yescharacteristic
420C2×#127—431no—
421C2×#126—861no—
422C2×#126—861no—
423C2×#124—431no—
424C2×#124—431no—
425C2×#124—431no—
426C2×#124—861no—
427C2×#124C2×D4311yescharacteristic
428C2×#123—861no—
429C2×#123—861no—
430C2×C22⋊Q8—861no—
431C2×C4×Q8—431no—
432C2×C4×Q8—431no—
433C2×C4×Q8—431no—
434C2×C4×Q8—431no—
435C2×C4×D4—431no—
436C2×C4×D4—431no—
437C2×C4×D4—431no—
438C2×C4×D4—861no—
439C2×#117—861no—
440#497C2×D4318yescomplemented
441#496—438no—
442#495—438no—
443#464—438no—
444#464—438no—
445#463—438no—
446#463—438no—
447#461—438no—
448#460—438no—
449#446—438no—
450#442—438no—
451#441—438no—
452C4×SD16—438no—
453C2×#106—431no—
454C2×C4⋊C8—431no—
455C2×C4⋊C8—431no—
456C2×C4⋊C8—431no—
457C2×#103—431no—
458C2×#103—431no—
459C2×#103—431no—
460C2×#102—431no—
461C2×#102—431no—
462C2×#102—431no—
463C2×#97—431no—
464C2×#97C2×D4311yescharacteristic
465C2×C4×C8—431no—
466C43C2×#340111yescharacteristic, complemented, Sylow
467C22×Q8—431no—
468C22×Q8C22×D4311yescharacteristic
469C22×Q8C22×D4311yescharacteristic
470C22×Q8C22×D4311yescharacteristic
471C22×D4—431no—
472C22×D4—431no—
473C22×D4—861no—
474C22×D4—861no—
475C22×D4C22×D4311yescharacteristic
476C23×C4—861no—
477C23×C4—861no—
478C23×C4—861no—
479C2×Q16—24no—
480C2×Q16—42no—
481C2×Q16C22×D4314yes—
482C2×Q16C22×D4314yes—
483C2×SD16—24no—
484C2×SD16—42no—
485C2×SD16—434no—
486C2×SD16—434no—
487C2×SD16—434no—
488C2×SD16—1722no—
489C2×SD16—1722no—
490C2×SD16—1722no—
491C2×SD16C22×D4314yes—
492C2×SD16C22×D4314yes—
493C2×D8—434no—
494C2×D8—434no—
495C2×D8—864no—
496C2×D8—1722no—
497C22×C8—431no—
498C22×C8—431no—
499C22×C8C22×D4311yescharacteristic
500C22×C8C22×D4311yescharacteristic
501C4⋊Q8—22no—
502C4⋊Q8C22×D4314yes—
503#127—434no—
504#127—862no—
505#126—868no—
506#126—868no—
507#124—22no—
508#124—434no—
509#124—434no—
510#124—434no—
511#124—862no—
512#124—862no—
513#124—862no—
514#124—868no—
515#124C22×D4314yes—
516#123—868no—
517#123—868no—
518C22⋊Q8—868no—
519C4×Q8—434no—
520C4×Q8—434no—
521C4×Q8—434no—
522C4×Q8—434no—
523C4×Q8—434no—
524C4×Q8—862no—
525C4×Q8—862no—
526C4×Q8—862no—
527C4×D4—434no—
528C4×D4—434no—
529C4×D4—434no—
530C4×D4—862no—
531C4×D4—868no—
532C4×D4—862no—
533C4×D4—862no—
534#117—868no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—431no—
538C2×C4⋊C4—431no—
539C2×C4⋊C4—431no—
540C2×C4⋊C4—431no—
541C2×C4⋊C4—431no—
542C2×C4⋊C4—861no—
543C2×C4⋊C4—861no—
544C2×C4⋊C4—861no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—861no—
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⋊C4—861no—
555C2×C22⋊C4—861no—
556C2×C42—431no—
557C2×C42—431no—
558C2×C42—861no—
559C2×C42—861no—
560C2×C42—861no—
561C2×C42C22×D4311yescharacteristic
562#106—434no—
563C4⋊C8—434no—
564C4⋊C8—434no—
565C4⋊C8—434no—
566#103—434no—
567#103—434no—
568#103—434no—
569#102—434no—
570#102—434no—
571#102—434no—
572#97—434no—
573#97C22×D4314yes—
574C4×C8—434no—
575C24—21no—
576C24—861no—
577C24—861no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—22no—
582C2×Q8—22no—
583C2×Q8—22no—
584C2×Q8—22no—
585C2×Q8—22no—
586C2×Q8—22no—
587C2×Q8—434no—
588C2×Q8—1722no—
589C2×Q8C23×D4312yes—
590C2×Q8C23×D4312yes—
591C2×Q8C23×D4312yes—
592C2×D4—21no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—432no—
596C2×D4—432no—
597C2×D4—864no—
598C2×D4—864no—
599C2×D4—861no—
600C2×D4—861no—
601C2×D4—862no—
602C2×D4—862no—
603C2×D4—862no—
604C2×D4—862no—
605C2×D4—3442no—
606C2×D4—1724no—
607C2×D4C23×D4312yes—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—431no—
612C22×C4—431no—
613C22×C4—431no—
614C22×C4—431no—
615C22×C4—864no—
616C22×C4—861no—
617C22×C4—861no—
618C22×C4—864no—
619C22×C4—864no—
620C22×C4—3442no—
621C22×C4—3442no—
622C22×C4—1724no—
623C22×C4D4×D4311yescharacteristic
624C22×C4D4×D4311yescharacteristic
625C22×C4C23×D4311yescharacteristic
626Q16—28no—
627Q16—44no—
628SD16—28no—
629SD16—44no—
630SD16—1724no—
631SD16—1724no—
632SD16—1724no—
633D8—868no—
634D8—1724no—
635C2×C8—22no—
636C2×C8—432no—
637C2×C8—432no—
638C2×C8—862no—
639C2×C8—862no—
640C2×C8#1062190014yes—
641C2×C8C23×D4312yes—
642C2×C8C23×D4312yes—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—434no—
646C4⋊C4—434no—
647C4⋊C4—434no—
648C4⋊C4—432no—
649C4⋊C4—432no—
650C4⋊C4—864no—
651C4⋊C4—864no—
652C4⋊C4—864no—
653C4⋊C4—861no—
654C4⋊C4—861no—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—864no—
658C22⋊C4—864no—
659C22⋊C4—864no—
660C22⋊C4—864no—
661C22⋊C4—864no—
662C22⋊C4—864no—
663C22⋊C4—864no—
664C22⋊C4—864no—
665C22⋊C4—864no—
666C42—432no—
667C42—432no—
668C42—432no—
669C42—432no—
670C42—864no—
671C42—864no—
672C42—864no—
673C42D4×D4312yes—
674C42C23×D4312yes—
675C23—22no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—862no—
680C23—862no—
681C23—1722no—
682C23—1722no—
683C23—1722no—
684C23—1722no—
685C23—1722no—
686C23—1722no—
687C23C2×D4×D4311yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—22no—
691Q8—22no—
692Q8—22no—
693Q8—22no—
694Q8—42no—
695Q8—42no—
696Q8—42no—
697Q8—1724no—
698D4—22no—
699D4—22no—
700D4—42no—
701D4—862no—
702D4—862no—
703D4—862no—
704D4—862no—
705D4—3444no—
706D4—1728no—
707D4—1722no—
708D4—1722no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—432no—
718C2×C4—432no—
719C2×C4—432no—
720C2×C4—432no—
721C2×C4—862no—
722C2×C4—862no—
723C2×C4—862no—
724C2×C4—862no—
725C2×C4—862no—
726C2×C4—862no—
727C2×C4—3444no—
728C2×C4—3444no—
729C2×C4—1728no—
730C2×C4—1722no—
731C2×C4—1722no—
732C2×C4C2×D4×D4312yes—
733C2×C4C2×D4×D4312yes—
734C2×C4C2×D4×D4311yescharacteristic
735C2×C4C2×#1062190012yes—
736C2×C4#1306337012yes—
737C2×C4C24×D4311yescharacteristic
738C8—22no—
739C8—862no—
740C8—862no—
741C8C2×#1062190014yes—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—84no—
746C22—3444no—
747C22—3444no—
748C22—1722no—
749C22—1722no—
750C22—1722no—
751C22—1722no—
752C22—1722no—
753C22—1722no—
754C22#1458356912yes—
755C22#1458369812yes—
756C22#1458370812yes—
757C22C22×D4×D4311yescharacteristic
758C4—22no—
759C4—22no—
760C4—42no—
761C4—42no—
762C4—42no—
763C4—862no—
764C4—862no—
765C4—862no—
766C4—862no—
767C4—1722no—
768C4—1722no—
769C4#1458356912yes—
770C4C22×#1062190011yescharacteristic
771C4C2×#1306337011yescharacteristic
772C2—82no—
773C2—3442no—
774C2—3442no—
775C2#1914766014yesdirect product factor
776C2C2×#1458356911yescharacteristic
777C2C2×#1458369811yescharacteristic
778C2C2×#1458370811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#497C2
socleC23×C43C22×D4
prime radicalC2×#14583285C2
hypercenterC2×#497D43
hypocenterC43C2×#3401
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#497

Complements

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

NH ≅ G/Ntype
1. C2×#14583631C2semidirect
2. C2×#14583623C2semidirect
3. #19147660C2direct (N × H)
5. C2×#14583284C2semidirect
6. C2×#14583123C2semidirect
7. C2×#14583123C2semidirect
8. C2×#14583097C2semidirect
9. C2×#14583116C2semidirect
10. C2×#14583111C2semidirect
11. C2×#14583101C2semidirect
12. C2×#14583027C2semidirect
13. C2×#14583012C2semidirect
14. C2×#14583006C2semidirect
15. C2×SD16×Dic43C2semidirect
16. C2×C43×#497C2semidirect
23. #14583631C22semidirect
25. #14583623C22semidirect
46. #14583284C22semidirect
47. #14583123C22semidirect
48. #14583123C22semidirect
49. #14583116C22semidirect
50. #14583111C22semidirect
51. #14583101C22semidirect
52. #14583097C22semidirect
53. #14583027C22semidirect
54. #14583012C22semidirect
55. #14583006C22semidirect
56. SD16×Dic43C22semidirect
75. C43×#497C22semidirect
386. C2×#497D43semidirect
400. C2×C43#3401semidirect
440. #497C2×D43semidirect
466. C43C2×#3401semidirect
775. C2#19147660direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836312
C2×#145836232
#191476602
C2×#145832852
C2×#145832842
C2×#145831232
C2×#145830972
C2×#145831162
C2×#145831112
C2×#145831012
C2×#145830272
C2×#145830122
C2×#145830062
C2×SD16×Dic432
C2×C43×#4972
C2×#340143