Finite Group Databasebeta

← C2×#19145285 #25966488

Subgroups — C2×#19145285 #25966488

Order 11008.

2034 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583523C211yesmaximal, characteristic, complemented
2C2×#14583503C211yesmaximal, characteristic, complemented
3#19145285C2116yesmaximal, direct product factor
4C2×#14583305C211yesmaximal, characteristic, complemented
5C2×#14583286C211yesmaximal, characteristic, complemented
6C2×#14583254C211yesmaximal, characteristic, complemented
7C2×#14583151C211yesmaximal, characteristic, complemented
8C2×#14583144C211yesmaximal, characteristic, complemented
9C2×#14583134C211yesmaximal, characteristic, complemented
10C2×#14583127C211yesmaximal, characteristic, complemented
11C2×#14583008C211yesmaximal, characteristic, complemented
12C2×#14582996C211yesmaximal, characteristic, complemented
13C2×#14582990C211yesmaximal, characteristic, complemented
14C2×#14582979C211yesmaximal, characteristic, complemented
15C2×#14582853C211yesmaximal, characteristic, complemented
16C2×C43×#486C211yesmaximal, characteristic, complemented
17C22×#10621883C2211yescharacteristic
18C22×#10621883C2211yescharacteristic
19C22×#10621882C2211yescharacteristic
20C22×#10621882C2211yescharacteristic
21C22×#10621872C2211yescharacteristic
22C22×C8×D43C2211yescharacteristic
23#14583523—24no—
24#14583523C2218yescomplemented
25#14583503—24no—
26#14583503C2218yescomplemented
27C2×#13063320—21no—
28C2×#13063317C2211yescharacteristic
29C2×#13063314—21no—
30C2×#13063313C2211yescharacteristic
31C2×#13063310—21no—
32C2×#13063306—21no—
33C2×#13063306—21no—
34C2×#13063305C2211yescharacteristic
35C2×#13063301—21no—
36C2×#13063300C2211yescharacteristic
37C2×#13063297—21no—
38C2×#13063297—21no—
39C2×#13063296C2211yescharacteristic
40C2×#13063296C2211yescharacteristic
41C2×#13063290C2211yescharacteristic
42C2×D4×Dic43C2211yescharacteristic
43C2×D4×Dic43C2211yescharacteristic
44C2×#13063287C2211yescharacteristic
45C2×#13063282C2211yescharacteristic
46#14583305C2218yescomplemented
47#14583286C2218yescomplemented
48#14583254C2218yescomplemented
49#14583151C2218yescomplemented
50#14583144C2218yescomplemented
51#14583134C2218yescomplemented
52#14583127C2218yescomplemented
53#14583008C2218yescomplemented
54#14582996C2218yescomplemented
55#14582990C2218yescomplemented
56#14582979C2218yescomplemented
57C2×#13063258C2211yescharacteristic
58C2×#13063258C2211yescharacteristic
59C2×#13063256C2211yescharacteristic
60C2×#13063256C2211yescharacteristic
61C2×#13063250C2211yescharacteristic
62C2×#13063250C2211yescharacteristic
63C2×#13063247C2211yescharacteristic
64C2×#13063247C2211yescharacteristic
65#14582853C2218yescomplemented
66C2×#13063236C2211yescharacteristic
67C2×#13063235C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C2×C4⋊Q8×C43C2211yescharacteristic
70C2×#127×C43C2211yescharacteristic
71C43×#486C2218yescomplemented
72C2×#102×C43C2211yescharacteristic
73C2×#102×C43C2211yescharacteristic
74C2×#102×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×C4×C8×C43C2211yescharacteristic
77C22×Dic86C2311yescharacteristic
78C22×D172—21no—
79C22×D172C2311yescharacteristic
80C22×C22⋊D43—21no—
81C22×C22⋊D43—21no—
82C23×Dic43—21no—
83C23×Dic43—21no—
84C22×C4×D43—21no—
85C22×C4×D43C2311yescharacteristic
86C2×#10621883—24no—
87C2×#10621883—24no—
88C2×#10621883C2314yes—
89C2×#10621883C2314yes—
90C2×#10621882—24no—
91C2×#10621882—24no—
92C2×#10621882C2314yes—
93C2×#10621882C2314yes—
94C2×#10621872—24no—
95C2×#10621872C2314yes—
96C22×C43⋊C8C2311yescharacteristic
97C22×C43⋊C8C2311yescharacteristic
98C2×C8×D43—24no—
99C2×C8×D43C2314yes—
100#13063320—28no—
101#13063317—22no—
102#13063317C2314yes—
103#13063314—28no—
104#13063313—22no—
105#13063313C2314yes—
106#13063310—28no—
107#13063306—28no—
108#13063306—28no—
109#13063305—22no—
110#13063305C2314yes—
111#13063301—28no—
112#13063300—22no—
113#13063300C2314yes—
114#13063297—28no—
115#13063297—28no—
116#13063296—22no—
117#13063296—22no—
118#13063296C2314yes—
119#13063296C2314yes—
120#13063290—22no—
121#13063290C2314yes—
122D4×Dic43—22no—
123D4×Dic43—22no—
124D4×Dic43C2314yes—
125D4×Dic43C2314yes—
126#13063287—22no—
127#13063287C2314yes—
128#13063282D414yes—
129#13063282C2314yes—
130C2×C4⋊Dic43—21no—
131C2×C4⋊Dic43C2311yescharacteristic
132C2×C4⋊Dic43C2311yescharacteristic
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4D411yescharacteristic
137C2×Dic43⋊C4D411yescharacteristic
138C2×C22⋊Dic43—21no—
139C2×C22⋊Dic43—21no—
140C2×C22⋊Dic43—21no—
141C2×C22⋊Dic43—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4D411yescharacteristic
148C2×(C2×D43)⋊C4D411yescharacteristic
149C2×C4×Dic43—21no—
150C2×C4×Dic43C2311yescharacteristic
151#13063258C2314yes—
152#13063258C2314yes—
153#13063256C2314yes—
154#13063256C2314yes—
155#13063250C2314yes—
156#13063250C2314yes—
157#13063247C2314yes—
158#13063247C2314yes—
159#13063236C2314yes—
160#13063235C2314yes—
161C8×Dic43C2314yes—
162C22×Q8×C43—21no—
163C22×D4×C43—21no—
164C22×D4×C43—21no—
165C22×D4×C43C2311yescharacteristic
166C22×D4×C43C2311yescharacteristic
167C22×C8×C43C2311yescharacteristic
168C22×C8×C43C2311yescharacteristic
169C4⋊Q8×C43—22no—
170C4⋊Q8×C43C2314yes—
171#127×C43—22no—
172#127×C43C2314yes—
173C2×C4⋊C4×C43—21no—
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C4⋊C4×C43C2311yescharacteristic
176C2×C42×C43C2311yescharacteristic
177#102×C43C2314yes—
178#102×C43C2314yes—
179#102×C43C2314yes—
180#102×C43C2314yes—
181C4×C8×C43C2314yes—
182C24×C43—21no—
183C24×C43—21no—
184C23×D43—21no—
185C23×D43C2×D411yescharacteristic
186C2×Q8×C43—24no—
187C2×Q8×C43—82no—
188C2×D4×C43—21no—
189C2×D4×C43—21no—
190C2×D4×C43—24no—
191C2×D4×C43—24no—
192C2×D4×C43—22no—
193C2×D4×C43—22no—
194C2×D4×C43—22no—
195C2×D4×C43—22no—
196C2×D4×C43—82no—
197C2×D4×C43—82no—
198C2×D4×C43C2412yes—
199C2×D4×C43C2412yes—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43C2×D411yescharacteristic
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2411yescharacteristic
205C2×C22⋊D43—24no—
206C2×C22⋊D43—24no—
207C2×C22⋊D43—82no—
208C2×C22⋊D43—82no—
209C22×Dic43—24no—
210C22×Dic43—24no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—82no—
215C22×Dic43—82no—
216C22×Dic43C2×D411yescharacteristic
217C22×Dic43C2×D411yescharacteristic
218C22×Dic43C2×D411yescharacteristic
219C2×D172—21no—
220C2×D172—24no—
221C2×D172—22no—
222C2×D172—22no—
223C2×D172—82no—
224C2×D172C2412yes—
225C2×C4×D43—22no—
226C2×C4×D43—22no—
227C2×C4×D43—24no—
228C2×C4×D43—82no—
229C2×C4×D43C2×D412yes—
230C2×C4×D43C2412yes—
231C2×Dic86—22no—
232C2×Dic86—22no—
233C2×Dic86—21no—
234C2×Dic86C2412yes—
235C2×C8×C43—22no—
236C2×C8×C43—22no—
237C2×C8×C43C2412yes—
238C2×C8×C43C2412yes—
239C4⋊C4×C43—24no—
240C4⋊C4×C43—21no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43C2412yes—
243C4⋊C4×C43C2412yes—
244C42×C43C2×D412yes—
245C42×C43C2412yes—
246C22⋊Dic43—24no—
247C22⋊Dic43—24no—
248C22⋊Dic43—24no—
249C22⋊Dic43—24no—
250#10621883—28no—
251#10621883—28no—
252#10621882—28no—
253#10621882—28no—
254(C2×D43)⋊C4—24no—
255(C2×D43)⋊C4—24no—
256(C2×D43)⋊C4—24no—
257(C2×D43)⋊C4—24no—
258(C2×D43)⋊C4—24no—
259(C2×D43)⋊C4C2×D414yes—
260(C2×D43)⋊C4C2×D414yes—
261C4⋊Dic43—21no—
262C4⋊Dic43—21no—
263C4⋊Dic43—24no—
264C4⋊Dic43C2412yes—
265C4⋊Dic43C2412yes—
266Dic43⋊C4—24no—
267Dic43⋊C4—24no—
268Dic43⋊C4—24no—
269Dic43⋊C4C2×D414yes—
270Dic43⋊C4C2×D414yes—
271C4×Dic43—24no—
272C4×Dic43C2×D412yes—
273C4×Dic43C2412yes—
274C2×C43⋊C8#4114yes—
275C2×C43⋊C8#4114yes—
276C2×C43⋊C8C2412yes—
277C2×C43⋊C8C2412yes—
278#10621872—28no—
279C8×D43—28no—
280C23×C43—22no—
281C23×C43—22no—
282C23×C43—42no—
283C23×C43—42no—
284C23×C43—42no—
285C23×C43—42no—
286C23×C43—42no—
287C23×C43—42no—
288C23×C43C22×D411yescharacteristic
289C22×D43—22no—
290C22×D43—22no—
291C22×D43—22no—
292C22×D43—22no—
293C22×D43—42no—
294C22×D43—42no—
295C22×D43—42no—
296C22×D43C22×D412yes—
297Q8×C43—84no—
298D4×C43—22no—
299D4×C43—22no—
300D4×C43—22no—
301D4×C43—22no—
302D4×C43—42no—
303D4×C43—42no—
304D4×C43—84no—
305D4×C43—84no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—42no—
311C2×C4×C43—42no—
312C2×C4×C43C22×D412yes—
313C2×C4×C43C22×D412yes—
314C2×C4×C43C22×D411yescharacteristic
315C2×C4×C43C2×#4112yes—
316C2×C4×C43C2×#4112yes—
317C2×C4×C43C2511yescharacteristic
318C22⋊D43—84no—
319C22⋊D43—84no—
320C2×Dic43—22no—
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—84no—
330C2×Dic43—84no—
331C2×Dic43C22×D412yes—
332C2×Dic43C22×D412yes—
333C2×Dic43C22×D412yes—
334D172—22no—
335D172—22no—
336D172—42no—
337D172—84no—
338C4×D43—24no—
339C4×D43—22no—
340C4×D43—22no—
341C4×D43—84no—
342Dic86—22no—
343Dic86—22no—
344Dic86—42no—
345C8×C43—22no—
346C8×C43—22no—
347C43⋊C8C2×#4114yes—
348C43⋊C8C2×#4114yes—
349C2×#3179—431nomaximal, Sylow
350C22×C43—42no—
351C22×C43—42no—
352C22×C43—42no—
353C22×C43—42no—
354C22×C43—42no—
355C22×C43—42no—
356C22×C43—84no—
357C22×C43—84no—
358C22×C43#53212yes—
359C22×C43#57612yes—
360C22×C43#57712yes—
361C22×C43C23×D411yescharacteristic
362C2×D43—22no—
363C2×D43—22no—
364C2×D43—22no—
365C2×D43—44no—
366C2×D43—42no—
367C2×D43—42no—
368C2×D43—42no—
369C2×D43—84no—
370C4×C43—22no—
371C4×C43—22no—
372C4×C43—42no—
373C4×C43—42no—
374C4×C43#53212yes—
375C4×C43C22×#4111yescharacteristic
376C4×C43C22×#4111yescharacteristic
377Dic43—22no—
378Dic43—22no—
379Dic43—22no—
380Dic43—42no—
381Dic43—42no—
382Dic43—42no—
383C2×#542—431no—
384C2×#540—431no—
385#3179—4316no—
386C2×#501—431no—
387C2×#496—431no—
388C2×#488—431no—
389C2×#486D4311yescharacteristic, complemented
390C2×#469—431no—
391C2×#468—431no—
392C2×#466—431no—
393C2×#465—431no—
394C2×#442—431no—
395C2×#440—431no—
396C2×C4×SD16—431no—
397C2×C4×D8—431no—
398C2×#405—431no—
399C2×C43—82no—
400C2×C43—82no—
401C2×C43#317914yescomplemented
402C2×C43C2×#53211yescharacteristic
403C2×C43C2×#57611yescharacteristic
404C2×C43C2×#57711yescharacteristic
405D43—42no—
406D43—82no—
407C22×SD16—431no—
408C22×SD16—431no—
409C22×D8—431no—
410C22×D8—431no—
411C22×M16—431no—
412C23×C8—431no—
413#542—438no—
414#542—864no—
415#540—438no—
416#540—864no—
417C2×C4⋊Q8C2×D4311yescharacteristic
418C2×#127C2×D4311yescharacteristic
419C2×#126—861no—
420C2×#125—431no—
421C2×#124—431no—
422C2×#124—861no—
423C2×#123—861no—
424C2×#123—861no—
425C2×#123—861no—
426C2×C22⋊Q8—431no—
427C2×C22⋊Q8—861no—
428C2×#121—431no—
429C2×#121—431no—
430C2×#121—431no—
431C2×#121—861no—
432C2×#121—861no—
433C2×C4×Q8—431no—
434C2×C4×D4—431no—
435C2×C4×D4—431no—
436C2×C4×D4—431no—
437C2×#117—431no—
438#501—438no—
439#496—438no—
440#488—438no—
441#486C2×D4318yescomplemented
442#469—438no—
443#468—438no—
444#466—438no—
445#465—438no—
446#442—438no—
447#440—438no—
448C4×SD16—438no—
449C4×D8—438no—
450C2×#107—431no—
451C2×#107—431no—
452C2×#106—431no—
453C2×#106—431no—
454C2×#103—431no—
455C2×#103—431no—
456C2×#102—431no—
457C2×#102—431no—
458C2×#102C2×D4311yescharacteristic
459C2×#102C2×D4311yescharacteristic
460C2×#102C2×D4311yescharacteristic
461C2×#102C2×D4311yescharacteristic
462#405—438no—
463C2×#97—431no—
464C2×#97—431no—
465C2×C4×C8—431no—
466C2×C4×C8C2×D4311yescharacteristic
467C43C2×#317911yescharacteristic, complemented, Sylow
468C22×Q8—21no—
469C22×Q8—431no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—431no—
473C22×D4—861no—
474C22×D4—861no—
475C22×D4—861no—
476C22×D4C22×D4311yescharacteristic
477C22×D4C22×D4311yescharacteristic
478C23×C4—431no—
479C23×C4—861no—
480C23×C4—861no—
481C23×C4—861no—
482C2×SD16—434no—
483C2×SD16—434no—
484C2×SD16—864no—
485C2×SD16—864no—
486C2×D8—434no—
487C2×D8—434no—
488C2×D8—864no—
489C2×D8—864no—
490C2×M16—434no—
491C2×M16—864no—
492C22×C8—431no—
493C22×C8—431no—
494C22×C8—434no—
495C22×C8—864no—
496C22×C8C22×D4311yescharacteristic
497C22×C8C22×D4311yescharacteristic
498C4⋊Q8—22no—
499C4⋊Q8C22×D4314yes—
500#127—22no—
501#127C22×D4314yes—
502#126—868no—
503#125—434no—
504#125—862no—
505#124—434no—
506#124—868no—
507#124—862no—
508#123—868no—
509#123—868no—
510#123—868no—
511C22⋊Q8—434no—
512C22⋊Q8—862no—
513C22⋊Q8—868no—
514#121—434no—
515#121—434no—
516#121—434no—
517#121—868no—
518#121—868no—
519#121—862no—
520#121—862no—
521#121—862no—
522C4×Q8—434no—
523C4×Q8—862no—
524C4×D4—434no—
525C4×D4—434no—
526C4×D4—434no—
527C4×D4—862no—
528C4×D4—862no—
529C4×D4—862no—
530#117—434no—
531#117—434no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—431no—
534C2×C4⋊C4—431no—
535C2×C4⋊C4—431no—
536C2×C4⋊C4—431no—
537C2×C4⋊C4—861no—
538C2×C4⋊C4—861no—
539C2×C4⋊C4—861no—
540C2×C4⋊C4—861no—
541C2×C4⋊C4C22×D4311yescharacteristic
542C2×C4⋊C4C22×D4311yescharacteristic
543C2×C22⋊C4—431no—
544C2×C22⋊C4—431no—
545C2×C22⋊C4—861no—
546C2×C22⋊C4—861no—
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×C42—431no—
555C2×C42—861no—
556C2×C42C22×D4311yescharacteristic
557#107—434no—
558#107—434no—
559#106—434no—
560#106—434no—
561#103—434no—
562#103—434no—
563#102—434no—
564#102—434no—
565#102C22×D4314yes—
566#102C22×D4314yes—
567#102C22×D4314yes—
568#102C22×D4314yes—
569#97—434no—
570#97—434no—
571C4×C8—434no—
572C4×C8C22×D4314yes—
573C24—21no—
574C24—21no—
575C24—431no—
576C24—861no—
577C2×Q8—24no—
578C2×Q8—82no—
579C2×Q8—432no—
580C2×Q8—861no—
581C2×Q8—862no—
582C2×Q8—862no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—24no—
586C2×D4—24no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—82no—
592C2×D4—82no—
593C2×D4—432no—
594C2×D4—864no—
595C2×D4—864no—
596C2×D4—864no—
597C2×D4—861no—
598C2×D4—862no—
599C2×D4—862no—
600C2×D4—3442no—
601C2×D4—3442no—
602C2×D4—3442no—
603C2×D4C23×D4312yes—
604C2×D4C23×D4312yes—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—431no—
608C22×C4—431no—
609C22×C4—431no—
610C22×C4—432no—
611C22×C4—432no—
612C22×C4—864no—
613C22×C4—864no—
614C22×C4—864no—
615C22×C4—862no—
616C22×C4—862no—
617C22×C4—861no—
618C22×C4—861no—
619C22×C4—861no—
620C22×C4—3442no—
621C22×C4—3442no—
622C22×C4—3442no—
623C22×C4D4×D4311yescharacteristic
624C22×C4D4×D4311yescharacteristic
625C22×C4C23×D4311yescharacteristic
626SD16—868no—
627SD16—868no—
628D8—868no—
629D8—868no—
630M16—868no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—434no—
634C2×C8—434no—
635C2×C8—432no—
636C2×C8—432no—
637C2×C8—868no—
638C2×C8C23×D4312yes—
639C2×C8C23×D4312yes—
640C4⋊C4—24no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—434no—
644C4⋊C4—434no—
645C4⋊C4—432no—
646C4⋊C4—432no—
647C4⋊C4—864no—
648C4⋊C4—864no—
649C4⋊C4—861no—
650C4⋊C4—861no—
651C4⋊C4—864no—
652C4⋊C4—864no—
653C4⋊C4C23×D4312yes—
654C4⋊C4C23×D4312yes—
655C22⋊C4—434no—
656C22⋊C4—434no—
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—864no—
669C42D4×D4312yes—
670C42C23×D4312yes—
671C23—22no—
672C23—22no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—432no—
680C23—862no—
681C23—862no—
682C23—862no—
683C23—862no—
684C23—1722no—
685C23—1722no—
686C23—1722no—
687C23C2×D4×D4311yescharacteristic
688Q8—84no—
689Q8—862no—
690Q8—862no—
691Q8—1722no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—22no—
696D4—42no—
697D4—42no—
698D4—84no—
699D4—84no—
700D4—862no—
701D4—862no—
702D4—3444no—
703D4—3444no—
704D4—3444no—
705D4—1722no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—432no—
713C2×C4—432no—
714C2×C4—432no—
715C2×C4—862no—
716C2×C4—862no—
717C2×C4—862no—
718C2×C4—864no—
719C2×C4—862no—
720C2×C4—862no—
721C2×C4—862no—
722C2×C4—862no—
723C2×C4—862no—
724C2×C4—3444no—
725C2×C4—3444no—
726C2×C4—3444no—
727C2×C4—1722no—
728C2×C4—1722no—
729C2×C4—1722no—
730C2×C4C2×D4×D4312yes—
731C2×C4C2×D4×D4312yes—
732C2×C4C2×D4×D4311yescharacteristic
733C2×C4#41×D4312yes—
734C2×C4#41×D4312yes—
735C2×C4C24×D4311yescharacteristic
736C8—22no—
737C8—22no—
738C8—434no—
739C8—434no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—84no—
747C22—84no—
748C22—862no—
749C22—862no—
750C22—862no—
751C22—3444no—
752C22—1722no—
753C22—1722no—
754C22—1722no—
755C22—1724no—
756C22#1458344812yes—
757C22#1458370012yes—
758C22#1458370512yes—
759C22C22×D4×D4311yescharacteristic
760C4—22no—
761C4—22no—
762C4—42no—
763C4—42no—
764C4—862no—
765C4—862no—
766C4—862no—
767C4—1722no—
768C4—1722no—
769C4—1722no—
770C4#1458344812yes—
771C4C2×#41×D4311yescharacteristic
772C4C2×#41×D4311yescharacteristic
773C2—82no—
774C2—82no—
775C2—3442no—
776C2—1722no—
777C2#1914528514yesdirect product factor
778C2C2×#1458344811yescharacteristic
779C2C2×#1458370011yescharacteristic
780C2C2×#1458370511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#486C2
socleC23×C43C22×D4
hypercenterC2×#486D43
hypocenterC43C2×#3179
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#486

Complements

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

NH ≅ G/Ntype
1. C2×#14583523C2semidirect
2. C2×#14583503C2semidirect
3. #19145285C2direct (N × H)
4. C2×#14583305C2semidirect
5. C2×#14583286C2semidirect
6. C2×#14583254C2semidirect
7. C2×#14583151C2semidirect
8. C2×#14583144C2semidirect
9. C2×#14583134C2semidirect
10. C2×#14583127C2semidirect
11. C2×#14583008C2semidirect
12. C2×#14582996C2semidirect
13. C2×#14582990C2semidirect
14. C2×#14582979C2semidirect
15. C2×#14582853C2semidirect
16. C2×C43×#486C2semidirect
24. #14583523C22semidirect
26. #14583503C22semidirect
46. #14583305C22semidirect
47. #14583286C22semidirect
48. #14583254C22semidirect
49. #14583151C22semidirect
50. #14583144C22semidirect
51. #14583134C22semidirect
52. #14583127C22semidirect
53. #14583008C22semidirect
54. #14582996C22semidirect
55. #14582990C22semidirect
56. #14582979C22semidirect
65. #14582853C22semidirect
71. C43×#486C22semidirect
389. C2×#486D43semidirect
401. C2×C43#3179semidirect
441. #486C2×D43semidirect
467. C43C2×#3179semidirect
777. C2#19145285direct (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×#145835032
#191452852
C2×#145833052
C2×#145832862
C2×#145832542
C2×#145831512
C2×#145831442
C2×#145831342
C2×#145831272
C2×#145830082
C2×#145829962
C2×#145829902
C2×#145829792
C2×#145828532
C2×C43×#4862
C2×#317943