Finite Group Databasebeta

← C2×#19146008 #25969509

Subgroups — C2×#19146008 #25969509

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×#14583520C211yesmaximal, characteristic, complemented
2C2×#14583504C211yesmaximal, characteristic, complemented
3#19146008C2116yesmaximal, direct product factor
4C2×#14583207C211yesmaximal, characteristic, complemented
5C2×#14583200C211yesmaximal, characteristic, complemented
6C2×#14583190C211yesmaximal, characteristic, complemented
7C2×#14583180C211yesmaximal, characteristic, complemented
8C2×#14583152C211yesmaximal, characteristic, complemented
9C2×#14583145C211yesmaximal, characteristic, complemented
10C2×#14583135C211yesmaximal, characteristic, complemented
11C2×#14583128C211yesmaximal, characteristic, complemented
12C2×#14583100C211yesmaximal, characteristic, complemented
13C2×#14583115C211yesmaximal, characteristic, complemented
14C2×#14583115C211yesmaximal, characteristic, complemented
15C2×#14583095C211yesmaximal, characteristic, complemented
16C2×C43×#424C211yesmaximal, characteristic, complemented
17C22×#10621873C2211yescharacteristic
18C22×#10621873C2211yescharacteristic
19C22×D344C2211yescharacteristic
20C22×D344C2211yescharacteristic
21#14583520—24no—
22#14583520C2218yescomplemented
23#14583504—24no—
24#14583504C2218yescomplemented
25C2×#13063325C2211yescharacteristic
26C2×#13063322C2211yescharacteristic
27C2×#13063320—21no—
28C2×#13063317C2211yescharacteristic
29C2×#13063313C2211yescharacteristic
30C2×#13063311—21no—
31C2×#13063310—21no—
32C2×#13063310—21no—
33C2×#13063307—21no—
34C2×#13063304C2211yescharacteristic
35C2×#13063303—21no—
36C2×#13063299C2211yescharacteristic
37C2×#13063299C2211yescharacteristic
38C2×#13063299C2211yescharacteristic
39C2×#13063298—21no—
40C2×#13063298—21no—
41C2×C4×Dic86C2211yescharacteristic
42C2×C4×D172C2211yescharacteristic
43C2×C4×D172C2211yescharacteristic
44C2×C4×D172C2211yescharacteristic
45#14583207C2218yescomplemented
46#14583200C2218yescomplemented
47#14583190C2218yescomplemented
48#14583180C2218yescomplemented
49#14583152C2218yescomplemented
50#14583145C2218yescomplemented
51#14583135C2218yescomplemented
52#14583128C2218yescomplemented
53#14583115C2218yescomplemented
54#14583115C2218yescomplemented
55#14583100C2218yescomplemented
56#14583095C2218yescomplemented
57C2×#13063259C2211yescharacteristic
58C2×#13063259C2211yescharacteristic
59C2×#13063257C2211yescharacteristic
60C2×#13063257C2211yescharacteristic
61C2×#13063250C2211yescharacteristic
62C2×#13063250C2211yescharacteristic
63C2×#13063247C2211yescharacteristic
64C2×#13063247C2211yescharacteristic
65C2×#13063247C2211yescharacteristic
66C2×#13063247C2211yescharacteristic
67C2×#13063247C2211yescharacteristic
68C2×#13063247C2211yescharacteristic
69C22×M16×C43C2211yescharacteristic
70C23×C8×C43C2211yescharacteristic
71C2×#117×C43C2211yescharacteristic
72C43×#424C2218yescomplemented
73C2×C4⋊C8×C43C2211yescharacteristic
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×C4⋊C8×C43C2211yescharacteristic
76C2×C4⋊C8×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×Dic86C2311yescharacteristic
79C22×D172—21no—
80C22×D172—21no—
81C22×D172C2311yescharacteristic
82C22×D172C2311yescharacteristic
83C22×D172C2311yescharacteristic
84C22×C22⋊D43—21no—
85C22×C22⋊D43—21no—
86C22×C22⋊D43—21no—
87C22×C4×D43—21no—
88C22×C4×D43—21no—
89C22×C4×D43—21no—
90C2×#10621873—42no—
91C2×#10621873—42no—
92C2×#10621873C2314yes—
93C2×#10621873C2314yes—
94C2×D344—42no—
95C2×D344—42no—
96C2×D344C2314yes—
97C2×D344C2314yes—
98#13063325—22no—
99#13063325C2314yes—
100#13063322—22no—
101#13063322C2314yes—
102#13063320—28no—
103#13063317—22no—
104#13063317C2314yes—
105#13063313—22no—
106#13063313C2314yes—
107#13063311—28no—
108#13063310—28no—
109#13063310—28no—
110#13063307—28no—
111#13063304—22no—
112#13063304C2314yes—
113#13063303—28no—
114#13063299—22no—
115#13063299—22no—
116#13063299—22no—
117#13063299C2314yes—
118#13063299C2314yes—
119#13063299C2314yes—
120#13063298—28no—
121#13063298—28no—
122C4×Dic86—22no—
123C4×Dic86C2314yes—
124C4×D172—22no—
125C4×D172—22no—
126C4×D172—22no—
127C4×D172C2314yes—
128C4×D172C2314yes—
129C4×D172C2314yes—
130C2×C4⋊Dic43—21no—
131C2×C4⋊Dic43C2311yescharacteristic
132C2×C4⋊Dic43C2311yescharacteristic
133C2×C4⋊Dic43C2311yescharacteristic
134C2×C4⋊Dic43C2311yescharacteristic
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4—21no—
138C2×Dic43⋊C4—21no—
139C2×C22⋊Dic43—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4—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)⋊C4—21no—
148C2×C4×Dic43—21no—
149#13063259C2314yes—
150#13063259C2314yes—
151#13063257C2314yes—
152#13063257C2314yes—
153#13063250C2314yes—
154#13063250C2314yes—
155#13063247C2314yes—
156#13063247C2314yes—
157#13063247C2314yes—
158#13063247C2314yes—
159#13063247C2314yes—
160#13063247C2314yes—
161C23×C4×C43C2311yescharacteristic
162C2×M16×C43—42no—
163C2×M16×C43C2314yes—
164C22×C8×C43—42no—
165C22×C8×C43C2311yescharacteristic
166C22×C8×C43C2311yescharacteristic
167C22×C8×C43C2311yescharacteristic
168C22×C8×C43C2311yescharacteristic
169C22×C8×C43C2314yes—
170#117×C43D414yes—
171#117×C43C2314yes—
172C2×C4⋊C4×C43D411yescharacteristic
173C2×C4⋊C4×C43D411yescharacteristic
174C2×C22⋊C4×C43D411yescharacteristic
175C2×C22⋊C4×C43D411yescharacteristic
176C2×C42×C43C2311yescharacteristic
177C2×C42×C43C2311yescharacteristic
178C4⋊C8×C43C2314yes—
179C4⋊C8×C43C2314yes—
180C4⋊C8×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—24no—
197C2×C22⋊D43—24no—
198C2×C22⋊D43—24no—
199C2×C22⋊D43—82no—
200C2×C22⋊D43—82no—
201C2×C22⋊D43—82no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205C22×Dic43—21no—
206C22×Dic43—21no—
207C2×D172—21no—
208C2×D172—21no—
209C2×D172—21no—
210C2×D172—24no—
211C2×D172—24no—
212C2×D172—22no—
213C2×D172—22no—
214C2×D172—22no—
215C2×D172—22no—
216C2×D172—22no—
217C2×D172—22no—
218C2×D172—82no—
219C2×D172—82no—
220C2×D172C2412yes—
221C2×D172C2412yes—
222C2×D172C2412yes—
223C2×C4×D43—24no—
224C2×C4×D43—24no—
225C2×C4×D43—24no—
226C2×C4×D43—82no—
227C2×C4×D43—82no—
228C2×C4×D43—82no—
229C2×Dic86—22no—
230C2×Dic86—22no—
231C2×Dic86—21no—
232C2×Dic86—24no—
233C2×Dic86—82no—
234C2×Dic86C2412yes—
235M16×C43—44no—
236C2×C8×C43—22no—
237C2×C8×C43—22no—
238C2×C8×C43—22no—
239C2×C8×C43—22no—
240C2×C8×C43—44no—
241C2×C8×C43C2412yes—
242C2×C8×C43C2412yes—
243C2×C8×C43C2412yes—
244C2×C8×C43C2412yes—
245C4⋊C4×C43C2×D414yes—
246C4⋊C4×C43C2×D414yes—
247C22⋊C4×C43C2×D414yes—
248C22⋊C4×C43C2×D414yes—
249C42×C43C2×D412yes—
250C42×C43C2×D412yes—
251C42×C43C2412yes—
252C42×C43C2412yes—
253C22⋊Dic43—24no—
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)⋊C4—24no—
260(C2×D43)⋊C4—24no—
261(C2×D43)⋊C4—24no—
262C4⋊Dic43—24no—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43C2412yes—
268C4⋊Dic43C2412yes—
269C4⋊Dic43C2412yes—
270C4⋊Dic43C2412yes—
271Dic43⋊C4—24no—
272Dic43⋊C4—24no—
273Dic43⋊C4—24no—
274Dic43⋊C4—24no—
275C4×Dic43—24no—
276D344—44no—
277D344—44no—
278#10621873—44no—
279#10621873—44no—
280C23×C43—22no—
281C23×C43—22no—
282C23×C43—22no—
283C23×C43C22×D412yes—
284C23×C43C22×D411yescharacteristic
285C22×D43—22no—
286C22×D43—22no—
287C22×D43—22no—
288C22×D43—42no—
289C22×D43—42no—
290C22×D43—42no—
291C22×D43—42no—
292C22×D43—42no—
293C22×D43—42no—
294C22×D43—42no—
295C22×D43—42no—
296C22×D43—42no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—24no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43C22×D412yes—
306C2×C4×C43C22×D412yes—
307C2×C4×C43C22×D412yes—
308C2×C4×C43C22×D412yes—
309C2×C4×C43C22×D412yes—
310C2×C4×C43C22×D411yescharacteristic
311C2×C4×C43H(5,𝔽2)12yes—
312C2×C4×C432−1+412yes—
313C2×C4×C43C2511yescharacteristic
314C22⋊D43—84no—
315C22⋊D43—84no—
316C22⋊D43—84no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—22no—
322C2×Dic43—42no—
323C2×Dic43—42no—
324C2×Dic43—42no—
325C2×Dic43—42no—
326C2×Dic43—42no—
327D172—22no—
328D172—22no—
329D172—22no—
330D172—22no—
331D172—22no—
332D172—22no—
333D172—42no—
334D172—42no—
335D172—42no—
336D172—84no—
337D172—84no—
338C4×D43—84no—
339C4×D43—84no—
340C4×D43—84no—
341Dic86—22no—
342Dic86—22no—
343Dic86—42no—
344Dic86—84no—
345C8×C43—22no—
346C8×C43—22no—
347C8×C43—22no—
348C8×C43—22no—
349C2×#3257—431nomaximal, Sylow
350C22×C43—22no—
351C22×C43—22no—
352C22×C43—22no—
353C22×C43—44no—
354C22×C43#53712yes—
355C22×C43#57612yes—
356C22×C43#57712yes—
357C22×C43C23×D411yescharacteristic
358C2×D43—42no—
359C2×D43—42no—
360C2×D43—42no—
361C2×D43—42no—
362C2×D43—42no—
363C2×D43—42no—
364C2×D43—42no—
365C2×D43—42no—
366C2×D43—42no—
367C2×D43—84no—
368C2×D43—84no—
369C2×D43—84no—
370C4×C43—22no—
371C4×C43—22no—
372C4×C43—22no—
373C4×C43—22no—
374C4×C43—22no—
375C4×C43#53712yes—
376C4×C43C2×H(5,𝔽2)11yescharacteristic
377C4×C43C2×2−1+411yescharacteristic
378Dic43—42no—
379Dic43—42no—
380Dic43—42no—
381Dic43—42no—
382Dic43—42no—
383C2×#542—431no—
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×#424D4311yescharacteristic, complemented
399C2×C43—42no—
400C2×C43#325714yescomplemented
401C2×C43C2×#53711yescharacteristic
402C2×C43C2×#57611yescharacteristic
403C2×C43C2×#57711yescharacteristic
404D43—82no—
405D43—82no—
406D43—82no—
407C22×SD16—431no—
408C22×SD16—431no—
409C22×D8—431no—
410C22×D8—431no—
411C22×M16C2×D4311yescharacteristic
412C23×C8C2×D4311yescharacteristic
413#542—438no—
414#542—864no—
415#540—438no—
416#540—864no—
417C2×C4⋊Q8—431no—
418C2×#127—431no—
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×#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#424C2×D4318yescomplemented
455C2×C4⋊C8C2×D4311yescharacteristic
456C2×C4⋊C8C2×D4311yescharacteristic
457C2×C4⋊C8C2×D4311yescharacteristic
458C2×C4⋊C8C2×D4311yescharacteristic
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—431no—
469C22×Q8—861no—
470C22×D4—431no—
471C22×D4—431no—
472C22×D4—431no—
473C22×D4—861no—
474C22×D4—861no—
475C22×D4—861no—
476C22×D4—861no—
477C22×D4—861no—
478C23×C4—861no—
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—42no—
491C2×M16C22×D4314yes—
492C22×C8—42no—
493C22×C8C22×D4311yescharacteristic
494C22×C8C22×D4311yescharacteristic
495C22×C8C22×D4311yescharacteristic
496C22×C8C22×D4311yescharacteristic
497C22×C8C22×D4314yes—
498C4⋊Q8—434no—
499C4⋊Q8—862no—
500#127—434no—
501#127—862no—
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—862no—
518#121—862no—
519#121—862no—
520#121—868no—
521#121—868no—
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#117D17214yes—
531#117C22×D4314yes—
532C2×C4⋊C4—431no—
533C2×C4⋊C4—431no—
534C2×C4⋊C4—431no—
535C2×C4⋊C4—431no—
536C2×C4⋊C4—861no—
537C2×C4⋊C4—861no—
538C2×C4⋊C4—861no—
539C2×C4⋊C4—861no—
540C2×C4⋊C4—861no—
541C2×C4⋊C4D17211yescharacteristic
542C2×C4⋊C4D17211yescharacteristic
543C2×C22⋊C4—861no—
544C2×C22⋊C4—861no—
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⋊C4D17211yescharacteristic
553C2×C22⋊C4D17211yescharacteristic
554C2×C42—861no—
555C2×C42C22×D4311yescharacteristic
556C2×C42C22×D4311yescharacteristic
557#107—434no—
558#107—434no—
559#106—434no—
560#106—434no—
561C4⋊C8C22×D4314yes—
562C4⋊C8C22×D4314yes—
563C4⋊C8C22×D4314yes—
564C4⋊C8C22×D4314yes—
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—861no—
574C24—861no—
575C24—861no—
576C24C2×D17211yescharacteristic
577C2×Q8—432no—
578C2×Q8—864no—
579C2×Q8—861no—
580C2×Q8—862no—
581C2×Q8—862no—
582C2×Q8—3442no—
583C2×D4—432no—
584C2×D4—432no—
585C2×D4—432no—
586C2×D4—864no—
587C2×D4—864no—
588C2×D4—864no—
589C2×D4—864no—
590C2×D4—864no—
591C2×D4—861no—
592C2×D4—861no—
593C2×D4—861no—
594C2×D4—862no—
595C2×D4—862no—
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×D4—3442no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—861no—
608C22×C4—861no—
609C22×C4—861no—
610C22×C4—861no—
611C22×C4—861no—
612C22×C4—864no—
613C22×C4—864no—
614C22×C4—864no—
615C22×C4—3442no—
616C22×C4—3442no—
617C22×C4—3442no—
618C22×C4C2×D17212yes—
619C22×C4C2×D17211yescharacteristic
620C22×C4C2×D17211yescharacteristic
621C22×C4C2×D17211yescharacteristic
622C22×C4C2×D17211yescharacteristic
623C22×C4C2×D17211yescharacteristic
624C22×C4C23×D4312yes—
625C22×C4C23×D4311yescharacteristic
626SD16—1724no—
627SD16—1724no—
628D8—1724no—
629D8—1724no—
630M16—44no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—44no—
636C2×C8C23×D4312yes—
637C2×C8C23×D4312yes—
638C2×C8C23×D4312yes—
639C2×C8C23×D4312yes—
640C4⋊C4—432no—
641C4⋊C4—432no—
642C4⋊C4—432no—
643C4⋊C4—432no—
644C4⋊C4—861no—
645C4⋊C4—861no—
646C4⋊C4—861no—
647C4⋊C4—861no—
648C4⋊C4—864no—
649C4⋊C4—864no—
650C4⋊C4—864no—
651C4⋊C4—864no—
652C4⋊C4—864no—
653C4⋊C4C2×D17214yes—
654C4⋊C4C2×D17214yes—
655C22⋊C4—864no—
656C22⋊C4—864no—
657C22⋊C4—864no—
658C22⋊C4—864no—
659C22⋊C4—864no—
660C22⋊C4—864no—
661C22⋊C4—864no—
662C22⋊C4—864no—
663C22⋊C4—864no—
664C22⋊C4C2×D17214yes—
665C22⋊C4C2×D17214yes—
666C42—864no—
667C42C2×D17212yes—
668C42C2×D17212yes—
669C42C23×D4312yes—
670C42C23×D4312yes—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—862no—
675C23—862no—
676C23—862no—
677C23—1722no—
678C23—1722no—
679C23—1722no—
680C23—1722no—
681C23—1722no—
682C23—1722no—
683C23—1722no—
684C23—1722no—
685C23—1722no—
686C23C22×D17212yes—
687C23C22×D17211yescharacteristic
688Q8—862no—
689Q8—862no—
690Q8—3444no—
691Q8—1722no—
692D4—862no—
693D4—862no—
694D4—862no—
695D4—862no—
696D4—862no—
697D4—862no—
698D4—3444no—
699D4—3444no—
700D4—3444no—
701D4—3444no—
702D4—3444no—
703D4—1722no—
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—862no—
715C2×C4—862no—
716C2×C4—862no—
717C2×C4—862no—
718C2×C4—862no—
719C2×C4—3444no—
720C2×C4—3444no—
721C2×C4—3444no—
722C2×C4—1722no—
723C2×C4—1722no—
724C2×C4—1722no—
725C2×C4—1722no—
726C2×C4—1722no—
727C2×C4C22×D17212yes—
728C2×C4C22×D17212yes—
729C2×C4C22×D17212yes—
730C2×C4C22×D17212yes—
731C2×C4C22×D17212yes—
732C2×C4C22×D17211yescharacteristic
733C2×C4#1306337012yes—
734C2×C4#1306337312yes—
735C2×C4C24×D4311yescharacteristic
736C8—22no—
737C8—22no—
738C8—22no—
739C8—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—44no—
744C22—3444no—
745C22—3444no—
746C22—3444no—
747C22—1722no—
748C22—1722no—
749C22—1722no—
750C22—1722no—
751C22—1722no—
752C22—1722no—
753C22—1722no—
754C22—1722no—
755C22—1722no—
756C22#1458348012yes—
757C22#1458370412yes—
758C22#1458371112yes—
759C22C23×D17211yescharacteristic
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—22no—
765C4—1722no—
766C4—1722no—
767C4—1722no—
768C4—1722no—
769C4—1722no—
770C4#1458348012yes—
771C4C2×#1306337011yescharacteristic
772C4C2×#1306337311yescharacteristic
773C2—42no—
774C2—3442no—
775C2—3442no—
776C2—3442no—
777C2#1914600814yesdirect product factor
778C2C2×#1458348011yescharacteristic
779C2C2×#1458370411yescharacteristic
780C2C2×#1458371111yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#424C2
socleC23×C43C22×D4
hypercenterC2×#424D43
hypocenterC43C2×#3257
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
1. C2×#14583520C2semidirect
2. C2×#14583504C2semidirect
3. #19146008C2direct (N × H)
4. C2×#14583207C2semidirect
5. C2×#14583200C2semidirect
6. C2×#14583190C2semidirect
7. C2×#14583180C2semidirect
8. C2×#14583152C2semidirect
9. C2×#14583145C2semidirect
10. C2×#14583135C2semidirect
11. C2×#14583128C2semidirect
12. C2×#14583100C2semidirect
13. C2×#14583115C2semidirect
14. C2×#14583115C2semidirect
15. C2×#14583095C2semidirect
16. C2×C43×#424C2semidirect
22. #14583520C22semidirect
24. #14583504C22semidirect
45. #14583207C22semidirect
46. #14583200C22semidirect
47. #14583190C22semidirect
48. #14583180C22semidirect
49. #14583152C22semidirect
50. #14583145C22semidirect
51. #14583135C22semidirect
52. #14583128C22semidirect
53. #14583115C22semidirect
54. #14583115C22semidirect
55. #14583100C22semidirect
56. #14583095C22semidirect
72. C43×#424C22semidirect
398. C2×#424D43semidirect
400. C2×C43#3257semidirect
454. #424C2×D43semidirect
467. C43C2×#3257semidirect
777. C2#19146008direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835202
C2×#145835042
#191460082
C2×#145832072
C2×#145832002
C2×#145831902
C2×#145831802
C2×#145831522
C2×#145831452
C2×#145831352
C2×#145831282
C2×#145831002
C2×#145831152
C2×#145830952
C2×C43×#4242
C2×#325743