Finite Group Databasebeta

← C2×#19146006 #25969507

Subgroups — C2×#19146006 #25969507

Order 11008.

1946 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×#14583504C211yesmaximal, characteristic, complemented
2#19146006C2116yesmaximal, direct product factor
3C2×#14583206C211yesmaximal, characteristic, complemented
4C2×#14583199C211yesmaximal, characteristic, complemented
5C2×#14583186C211yesmaximal, characteristic, complemented
6C2×#14583176C211yesmaximal, characteristic, complemented
7C2×#14583150C211yesmaximal, characteristic, complemented
8C2×#14583147C211yesmaximal, characteristic, complemented
9C2×#14583133C211yesmaximal, characteristic, complemented
10C2×#14583130C211yesmaximal, characteristic, complemented
11C2×#14583099C211yesmaximal, characteristic, complemented
12C2×#14583111C211yesmaximal, characteristic, complemented
13C2×#14583111C211yesmaximal, characteristic, complemented
14C2×#14583094C211yesmaximal, characteristic, complemented
15C2×#14582926C211yesmaximal, characteristic, complemented
16C2×C43×#542C211yesmaximal, characteristic, complemented
17C22×#10621884C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19C22×#10621882C2211yescharacteristic
20C22×#10621882C2211yescharacteristic
21C22×#10621877C2211yescharacteristic
22C23×C43⋊C8C2211yescharacteristic
23#14583504—24no—
24#14583504C2218yescomplemented
25C2×#13063322C2211yescharacteristic
26C2×#13063317C2211yescharacteristic
27C2×#13063310—21no—
28C2×#13063310—21no—
29C2×#13063299C2211yescharacteristic
30C2×#13063299C2211yescharacteristic
31C2×#13063298—21no—
32C2×#13063298—21no—
33C2×C4×D172C2211yescharacteristic
34C2×C4×D172C2211yescharacteristic
35#14583206C2218yescomplemented
36#14583199C2218yescomplemented
37#14583186C2218yescomplemented
38#14583176C2218yescomplemented
39#14583150C2218yescomplemented
40#14583147C2218yescomplemented
41#14583133C2218yescomplemented
42#14583130C2218yescomplemented
43#14583111C2218yescomplemented
44#14583111C2218yescomplemented
45#14583099C2218yescomplemented
46#14583094C2218yescomplemented
47C2×#13063258C2211yescharacteristic
48C2×#13063258C2211yescharacteristic
49C2×#13063256C2211yescharacteristic
50C2×#13063256C2211yescharacteristic
51#14582926C2218yescomplemented
52C2×C4⋊(C43⋊C8)C2211yescharacteristic
53C2×C4⋊(C43⋊C8)C2211yescharacteristic
54C2×C4⋊(C43⋊C8)C2211yescharacteristic
55C2×C4⋊(C43⋊C8)C2211yescharacteristic
56C2×#13063249C2211yescharacteristic
57C2×#13063249C2211yescharacteristic
58C2×#13063246C2211yescharacteristic
59C2×#13063246C2211yescharacteristic
60C2×#13063245C2211yescharacteristic
61C2×#13063245C2211yescharacteristic
62C2×#13063245C2211yescharacteristic
63C2×#13063245C2211yescharacteristic
64C43×#542—24no—
65C43×#542C2218yescomplemented
66C2×C4⋊Q8×C43C2211yescharacteristic
67C2×#126×C43—21no—
68C2×#124×C43—21no—
69C2×#124×C43C2211yescharacteristic
70C2×#123×C43—21no—
71C2×C22⋊Q8×C43—21no—
72C2×C22⋊Q8×C43C2211yescharacteristic
73C2×#121×C43C2211yescharacteristic
74C2×C4×Q8×C43C2211yescharacteristic
75C2×C4×D4×C43C2211yescharacteristic
76C2×#117×C43C2211yescharacteristic
77C22×D172—21no—
78C22×D172—21no—
79C22×D172C2311yescharacteristic
80C22×D172C2311yescharacteristic
81C22×C22⋊D43—21no—
82C22×C22⋊D43—21no—
83C22×C4×D43—21no—
84C22×C4×D43—21no—
85C2×#10621884—42no—
86C2×#10621884—42no—
87C2×#10621884C2314yes—
88C2×#10621884C2314yes—
89C2×#10621882—42no—
90C2×#10621882—42no—
91C2×#10621882C2314yes—
92C2×#10621882C2314yes—
93C2×#10621877—42no—
94C2×#10621877C2314yes—
95C22×C43⋊C8—42no—
96C22×C43⋊C8C2311yescharacteristic
97C22×C43⋊C8C2311yescharacteristic
98C22×C43⋊C8C2311yescharacteristic
99C22×C43⋊C8C2311yescharacteristic
100C22×C43⋊C8C2314yes—
101#13063322—22no—
102#13063322C2314yes—
103#13063317—22no—
104#13063317C2314yes—
105#13063310—28no—
106#13063310—28no—
107#13063299—22no—
108#13063299—22no—
109#13063299C2314yes—
110#13063299C2314yes—
111#13063298—28no—
112#13063298—28no—
113C4×D172—22no—
114C4×D172—22no—
115C4×D172C2314yes—
116C4×D172C2314yes—
117C2×C4⋊Dic43C2311yescharacteristic
118C2×C4⋊Dic43C2311yescharacteristic
119C2×Dic43⋊C4—21no—
120C2×Dic43⋊C4—21no—
121C2×(C2×D43)⋊C4—21no—
122C2×(C2×D43)⋊C4—21no—
123C2×(C2×D43)⋊C4—21no—
124C2×(C2×D43)⋊C4—21no—
125#13063258C2314yes—
126#13063258C2314yes—
127#13063256C2314yes—
128#13063256C2314yes—
129C4⋊(C43⋊C8)C2314yes—
130C4⋊(C43⋊C8)C2314yes—
131C4⋊(C43⋊C8)C2314yes—
132C4⋊(C43⋊C8)C2314yes—
133#13063249C2314yes—
134#13063249C2314yes—
135#13063246C2314yes—
136#13063246C2314yes—
137#13063245C2314yes—
138#13063245C2314yes—
139#13063245C2314yes—
140#13063245C2314yes—
141C22×Q8×C43—21no—
142C22×Q8×C43C2311yescharacteristic
143C22×D4×C43—21no—
144C22×D4×C43C2311yescharacteristic
145C23×C4×C43—21no—
146C23×C4×C43C2311yescharacteristic
147C4⋊Q8×C43—22no—
148C4⋊Q8×C43C2314yes—
149#126×C43—28no—
150#124×C43—28no—
151#124×C43—22no—
152#124×C43C2314yes—
153#123×C43—28no—
154C22⋊Q8×C43—22no—
155C22⋊Q8×C43—28no—
156C22⋊Q8×C43C2314yes—
157#121×C43—22no—
158#121×C43C2314yes—
159C4×Q8×C43—22no—
160C4×Q8×C43C2314yes—
161C4×D4×C43—22no—
162C4×D4×C43C2314yes—
163#117×C43D414yes—
164#117×C43C2314yes—
165C2×C4⋊C4×C43—21no—
166C2×C4⋊C4×C43—21no—
167C2×C4⋊C4×C43—21no—
168C2×C4⋊C4×C43D411yescharacteristic
169C2×C4⋊C4×C43D411yescharacteristic
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C4⋊C4×C43C2311yescharacteristic
172C2×C22⋊C4×C43—21no—
173C2×C22⋊C4×C43—21no—
174C2×C22⋊C4×C43—21no—
175C2×C22⋊C4×C43—21no—
176C2×C22⋊C4×C43—21no—
177C2×C22⋊C4×C43D411yescharacteristic
178C2×C22⋊C4×C43D411yescharacteristic
179C2×C42×C43—21no—
180C2×C42×C43C2311yescharacteristic
181C2×C42×C43C2311yescharacteristic
182C24×C43—21no—
183C24×C43C2×D411yescharacteristic
184C23×D43—21no—
185C23×D43—21no—
186C2×Q8×C43—21no—
187C2×Q8×C43—24no—
188C2×Q8×C43—22no—
189C2×Q8×C43—22no—
190C2×Q8×C43—82no—
191C2×Q8×C43C2412yes—
192C2×D4×C43—21no—
193C2×D4×C43—24no—
194C2×D4×C43—22no—
195C2×D4×C43—22no—
196C2×D4×C43—82no—
197C2×D4×C43C2412yes—
198C22×C4×C43—22no—
199C22×C4×C43—22no—
200C22×C4×C43—24no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—82no—
205C22×C4×C43C2×D411yescharacteristic
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2×D411yescharacteristic
209C22×C4×C43C2×D411yescharacteristic
210C22×C4×C43C2×D412yes—
211C22×C4×C43C2412yes—
212C22×C4×C43C2411yescharacteristic
213C2×C22⋊D43—24no—
214C2×C22⋊D43—24no—
215C2×C22⋊D43—82no—
216C2×C22⋊D43—82no—
217C22×Dic43—21no—
218C22×Dic43—21no—
219C2×D172—21no—
220C2×D172—21no—
221C2×D172—24no—
222C2×D172—24no—
223C2×D172—22no—
224C2×D172—22no—
225C2×D172—22no—
226C2×D172—22no—
227C2×D172—82no—
228C2×D172—82no—
229C2×D172C2412yes—
230C2×D172C2412yes—
231C2×C4×D43—24no—
232C2×C4×D43—24no—
233C2×C4×D43—82no—
234C2×C4×D43—82no—
235C4⋊C4×C43—24no—
236C4⋊C4×C43—24no—
237C4⋊C4×C43—24no—
238C4⋊C4×C43—21no—
239C4⋊C4×C43—21no—
240C4⋊C4×C43C2×D414yes—
241C4⋊C4×C43C2×D414yes—
242C4⋊C4×C43C2412yes—
243C4⋊C4×C43C2412yes—
244C22⋊C4×C43—24no—
245C22⋊C4×C43—24no—
246C22⋊C4×C43—24no—
247C22⋊C4×C43—24no—
248C22⋊C4×C43—24no—
249C22⋊C4×C43C2×D414yes—
250C22⋊C4×C43C2×D414yes—
251C42×C43—24no—
252C42×C43C2×D412yes—
253C42×C43C2×D412yes—
254C42×C43C2412yes—
255C42×C43C2412yes—
256#10621884—44no—
257#10621884—44no—
258#10621882—44no—
259#10621882—44no—
260(C2×D43)⋊C4—24no—
261(C2×D43)⋊C4—24no—
262(C2×D43)⋊C4—24no—
263(C2×D43)⋊C4—24no—
264C4⋊Dic43—21no—
265C4⋊Dic43—21no—
266C4⋊Dic43C2412yes—
267C4⋊Dic43C2412yes—
268Dic43⋊C4—24no—
269Dic43⋊C4—24no—
270#10621877—44no—
271C2×C43⋊C8—22no—
272C2×C43⋊C8—22no—
273C2×C43⋊C8—22no—
274C2×C43⋊C8—22no—
275C2×C43⋊C8—44no—
276C2×C43⋊C8C2412yes—
277C2×C43⋊C8C2412yes—
278C2×C43⋊C8C2412yes—
279C2×C43⋊C8C2412yes—
280C23×C43—22no—
281C23×C43—22no—
282C23×C43—22no—
283C23×C43—22no—
284C23×C43—42no—
285C23×C43—42no—
286C23×C43—42no—
287C23×C43C22×D412yes—
288C23×C43C22×D411yescharacteristic
289C22×D43—22no—
290C22×D43—22no—
291C22×D43—42no—
292C22×D43—42no—
293C22×D43—42no—
294C22×D43—42no—
295C22×D43—42no—
296C22×D43—42no—
297Q8×C43—22no—
298Q8×C43—22no—
299Q8×C43—42no—
300Q8×C43—84no—
301D4×C43—22no—
302D4×C43—22no—
303D4×C43—42no—
304D4×C43—84no—
305C2×C4×C43—22no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—24no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—42no—
317C2×C4×C43—42no—
318C2×C4×C43—42no—
319C2×C4×C43—84no—
320C2×C4×C43C22×D412yes—
321C2×C4×C43C22×D412yes—
322C2×C4×C43C22×D412yes—
323C2×C4×C43C22×D412yes—
324C2×C4×C43C22×D412yes—
325C2×C4×C43C22×D411yescharacteristic
326C2×C4×C43H(5,𝔽2)12yes—
327C2×C4×C432−1+412yes—
328C2×C4×C43C2511yescharacteristic
329C22⋊D43—84no—
330C22⋊D43—84no—
331C2×Dic43—22no—
332C2×Dic43—22no—
333C2×Dic43—42no—
334C2×Dic43—42no—
335D172—22no—
336D172—22no—
337D172—22no—
338D172—22no—
339D172—42no—
340D172—42no—
341D172—84no—
342D172—84no—
343C4×D43—84no—
344C4×D43—84no—
345C43⋊C8—22no—
346C43⋊C8—22no—
347C43⋊C8—22no—
348C43⋊C8—22no—
349C2×#3257—431nomaximal, Sylow
350C22×C43—22no—
351C22×C43—22no—
352C22×C43—22no—
353C22×C43—44no—
354C22×C43—42no—
355C22×C43—42no—
356C22×C43—42no—
357C22×C43—84no—
358C22×C43#53712yes—
359C22×C43#57612yes—
360C22×C43#57712yes—
361C22×C43C23×D411yescharacteristic
362C2×D43—42no—
363C2×D43—42no—
364C2×D43—42no—
365C2×D43—42no—
366C2×D43—42no—
367C2×D43—42no—
368C2×D43—84no—
369C2×D43—84no—
370C4×C43—22no—
371C4×C43—22no—
372C4×C43—22no—
373C4×C43—22no—
374C4×C43—22no—
375C4×C43—42no—
376C4×C43—42no—
377C4×C43—42no—
378C4×C43#53712yes—
379C4×C43C2×H(5,𝔽2)11yescharacteristic
380C4×C43C2×2−1+411yescharacteristic
381Dic43—42no—
382Dic43—42no—
383C2×#542D4311yescharacteristic, complemented
384C2×#540—431no—
385#3257—4316no—
386C2×#479—431no—
387C2×#478—431no—
388C2×#476—431no—
389C2×#474—431no—
390C2×#469—431no—
391C2×#468—431no—
392C2×#466—431no—
393C2×#465—431no—
394C2×#460—431no—
395C2×#463—431no—
396C2×#463—431no—
397C2×#459—431no—
398C2×#424—431no—
399C2×C43—42no—
400C2×C43—82no—
401C2×C43#325714yescomplemented
402C2×C43C2×#53711yescharacteristic
403C2×C43C2×#57611yescharacteristic
404C2×C43C2×#57711yescharacteristic
405D43—82no—
406D43—82no—
407C22×SD16—431no—
408C22×SD16—431no—
409C22×D8—431no—
410C22×D8—431no—
411C22×M16—431no—
412C23×C8—431no—
413#542—24no—
414#542C2×D4318yescomplemented
415#540—438no—
416#540—864no—
417C2×C4⋊Q8C2×D4311yescharacteristic
418C2×#127—431no—
419C2×#126—21no—
420C2×#125—431no—
421C2×#124—21no—
422C2×#124C2×D4311yescharacteristic
423C2×#123—21no—
424C2×#123—861no—
425C2×#123—861no—
426C2×C22⋊Q8—21no—
427C2×C22⋊Q8C2×D4311yescharacteristic
428C2×#121—431no—
429C2×#121—431no—
430C2×#121—861no—
431C2×#121—861no—
432C2×#121C2×D4311yescharacteristic
433C2×C4×Q8C2×D4311yescharacteristic
434C2×C4×D4—431no—
435C2×C4×D4—431no—
436C2×C4×D4C2×D4311yescharacteristic
437C2×#117C2×D4311yescharacteristic
438#479—438no—
439#478—438no—
440#476—438no—
441#474—438no—
442#469—438no—
443#468—438no—
444#466—438no—
445#465—438no—
446#463—438no—
447#463—438no—
448#460—438no—
449#459—438no—
450C2×#107—431no—
451C2×#107—431no—
452C2×#106—431no—
453C2×#106—431no—
454#424—438no—
455C2×C4⋊C8—431no—
456C2×C4⋊C8—431no—
457C2×C4⋊C8—431no—
458C2×C4⋊C8—431no—
459C2×#103—431no—
460C2×#103—431no—
461C2×#102—431no—
462C2×#102—431no—
463C2×#102—431no—
464C2×#102—431no—
465C2×#102—431no—
466C2×#102—431no—
467C43C2×#325711yescharacteristic, complemented, Sylow
468C22×Q8—21no—
469C22×Q8C22×D4311yescharacteristic
470C22×D4—21no—
471C22×D4—431no—
472C22×D4—431no—
473C22×D4—861no—
474C22×D4—861no—
475C22×D4—861no—
476C22×D4—861no—
477C22×D4C22×D4311yescharacteristic
478C23×C4—21no—
479C23×C4—861no—
480C23×C4—861no—
481C23×C4C22×D4311yescharacteristic
482C2×SD16—434no—
483C2×SD16—434no—
484C2×SD16—1722no—
485C2×SD16—1722no—
486C2×D8—434no—
487C2×D8—434no—
488C2×D8—1722no—
489C2×D8—1722no—
490C2×M16—434no—
491C2×M16—1722no—
492C22×C8—431no—
493C22×C8—431no—
494C22×C8—431no—
495C22×C8—431no—
496C22×C8—434no—
497C22×C8—1722no—
498C4⋊Q8—22no—
499C4⋊Q8C22×D4314yes—
500#127—434no—
501#127—862no—
502#126—28no—
503#125—434no—
504#125—862no—
505#124—28no—
506#124—22no—
507#124C22×D4314yes—
508#123—28no—
509#123—868no—
510#123—868no—
511C22⋊Q8—22no—
512C22⋊Q8—28no—
513C22⋊Q8C22×D4314yes—
514#121—22no—
515#121—434no—
516#121—434no—
517#121—862no—
518#121—862no—
519#121—868no—
520#121—868no—
521#121C22×D4314yes—
522C4×Q8—22no—
523C4×Q8C22×D4314yes—
524C4×D4—22no—
525C4×D4—434no—
526C4×D4—434no—
527C4×D4—862no—
528C4×D4—862no—
529C4×D4C22×D4314yes—
530#117C22⋊D4314yes—
531#117C22×D4314yes—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—431no—
536C2×C4⋊C4—431no—
537C2×C4⋊C4—861no—
538C2×C4⋊C4—861no—
539C2×C4⋊C4C22⋊D4311yescharacteristic
540C2×C4⋊C4C22⋊D4311yescharacteristic
541C2×C4⋊C4C22×D4311yescharacteristic
542C2×C4⋊C4C22×D4311yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—861no—
549C2×C22⋊C4—861no—
550C2×C22⋊C4—861no—
551C2×C22⋊C4—861no—
552C2×C22⋊C4C22⋊D4311yescharacteristic
553C2×C22⋊C4C22⋊D4311yescharacteristic
554C2×C42—21no—
555C2×C42C22×D4311yescharacteristic
556C2×C42C22×D4311yescharacteristic
557#107—434no—
558#107—434no—
559#106—434no—
560#106—434no—
561C4⋊C8—434no—
562C4⋊C8—434no—
563C4⋊C8—434no—
564C4⋊C8—434no—
565#103—434no—
566#103—434no—
567#102—434no—
568#102—434no—
569#102—434no—
570#102—434no—
571#102—434no—
572#102—434no—
573C24—21no—
574C24—861no—
575C24—861no—
576C24C2×C22⋊D4311yescharacteristic
577C2×Q8—21no—
578C2×Q8—24no—
579C2×Q8—22no—
580C2×Q8—22no—
581C2×Q8—82no—
582C2×Q8C23×D4312yes—
583C2×D4—24no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—82no—
588C2×D4—432no—
589C2×D4—432no—
590C2×D4—864no—
591C2×D4—864no—
592C2×D4—864no—
593C2×D4—864no—
594C2×D4—861no—
595C2×D4—861no—
596C2×D4—862no—
597C2×D4—862no—
598C2×D4—862no—
599C2×D4—862no—
600C2×D4—3442no—
601C2×D4—3442no—
602C2×D4—3442no—
603C2×D4—3442no—
604C2×D4C23×D4312yes—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—24no—
611C22×C4—82no—
612C22×C4—861no—
613C22×C4—861no—
614C22×C4—864no—
615C22×C4—864no—
616C22×C4—3442no—
617C22×C4—3442no—
618C22×C4C2×C22⋊D4312yes—
619C22×C4C2×C22⋊D4311yescharacteristic
620C22×C4C2×C22⋊D4311yescharacteristic
621C22×C4C2×C22⋊D4311yescharacteristic
622C22×C4C2×C22⋊D4311yescharacteristic
623C22×C4C2×C22⋊D4311yescharacteristic
624C22×C4C23×D4312yes—
625C22×C4C23×D4311yescharacteristic
626SD16—1724no—
627SD16—1724no—
628D8—1724no—
629D8—1724no—
630M16—1724no—
631C2×C8—432no—
632C2×C8—432no—
633C2×C8—432no—
634C2×C8—432no—
635C2×C8—862no—
636C2×C8—862no—
637C2×C8—862no—
638C2×C8—862no—
639C2×C8—1724no—
640C4⋊C4—24no—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—432no—
646C4⋊C4—432no—
647C4⋊C4—861no—
648C4⋊C4—861no—
649C4⋊C4—864no—
650C4⋊C4—864no—
651C4⋊C4C2×C22⋊D4314yes—
652C4⋊C4C2×C22⋊D4314yes—
653C4⋊C4C23×D4312yes—
654C4⋊C4C23×D4312yes—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—24no—
660C22⋊C4—864no—
661C22⋊C4—864no—
662C22⋊C4—864no—
663C22⋊C4—864no—
664C22⋊C4C2×C22⋊D4314yes—
665C22⋊C4C2×C22⋊D4314yes—
666C42—24no—
667C42C2×C22⋊D4312yes—
668C42C2×C22⋊D4312yes—
669C42C23×D4312yes—
670C42C23×D4312yes—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—862no—
679C23—862no—
680C23—1722no—
681C23—1722no—
682C23—1722no—
683C23—1722no—
684C23—1722no—
685C23—1722no—
686C23C22×C22⋊D4312yes—
687C23C22×C22⋊D4311yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—42no—
691Q8—84no—
692D4—22no—
693D4—22no—
694D4—42no—
695D4—84no—
696D4—862no—
697D4—862no—
698D4—862no—
699D4—862no—
700D4—3444no—
701D4—3444no—
702D4—3444no—
703D4—3444no—
704D4—1722no—
705D4—1722no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—84no—
721C2×C4—862no—
722C2×C4—862no—
723C2×C4—3444no—
724C2×C4—3444no—
725C2×C4—1722no—
726C2×C4—1722no—
727C2×C4C22×C22⋊D4312yes—
728C2×C4C22×C22⋊D4312yes—
729C2×C4C22×C22⋊D4312yes—
730C2×C4C22×C22⋊D4312yes—
731C2×C4C22×C22⋊D4312yes—
732C2×C4C22×C22⋊D4311yescharacteristic
733C2×C4#1306337112yes—
734C2×C4#1306337212yes—
735C2×C4C24×D4311yescharacteristic
736C8—862no—
737C8—862no—
738C8—862no—
739C8—862no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—44no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—84no—
748C22—3444no—
749C22—3444no—
750C22—1722no—
751C22—1722no—
752C22—1722no—
753C22—1722no—
754C22—1722no—
755C22—1722no—
756C22#1458347712yes—
757C22#1458370212yes—
758C22#1458370712yes—
759C22C23×C22⋊D4311yescharacteristic
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—22no—
765C4—42no—
766C4—42no—
767C4—42no—
768C4—1722no—
769C4—1722no—
770C4#1458347712yes—
771C4C2×#1306337111yescharacteristic
772C4C2×#1306337211yescharacteristic
773C2—42no—
774C2—82no—
775C2—3442no—
776C2—3442no—
777C2#1914600614yesdirect product factor
778C2C2×#1458347711yescharacteristic
779C2C2×#1458370211yescharacteristic
780C2C2×#1458370711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#542C2
socleC23×C43C22×D4
hypercenterC2×#542D43
hypocenterC43C2×#3257
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#14583504C2semidirect
2. #19146006C2direct (N × H)
3. C2×#14583206C2semidirect
4. C2×#14583199C2semidirect
5. C2×#14583186C2semidirect
6. C2×#14583176C2semidirect
7. C2×#14583150C2semidirect
8. C2×#14583147C2semidirect
9. C2×#14583133C2semidirect
10. C2×#14583130C2semidirect
11. C2×#14583099C2semidirect
12. C2×#14583111C2semidirect
13. C2×#14583111C2semidirect
14. C2×#14583094C2semidirect
15. C2×#14582926C2semidirect
16. C2×C43×#542C2semidirect
24. #14583504C22semidirect
35. #14583206C22semidirect
36. #14583199C22semidirect
37. #14583186C22semidirect
38. #14583176C22semidirect
39. #14583150C22semidirect
40. #14583147C22semidirect
41. #14583133C22semidirect
42. #14583130C22semidirect
43. #14583111C22semidirect
44. #14583111C22semidirect
45. #14583099C22semidirect
46. #14583094C22semidirect
51. #14582926C22semidirect
65. C43×#542C22semidirect
383. C2×#542D43semidirect
401. C2×C43#3257semidirect
414. #542C2×D43semidirect
467. C43C2×#3257semidirect
777. C2#19146006direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835042
#191460062
C2×#145832062
C2×#145831992
C2×#145831862
C2×#145831762
C2×#145831502
C2×#145831472
C2×#145831332
C2×#145831302
C2×#145830992
C2×#145831112
C2×#145830942
C2×#145829262
C2×C43×#5422
C2×#325743