Finite Group Databasebeta

← C2×#19147067 #25975162

Subgroups — C2×#19147067 #25975162

Order 11008.

2158 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583595C211yesmaximal, characteristic, complemented
2C2×#14583553C211yesmaximal, characteristic, complemented
3#19147067C2116yesmaximal, direct product factor
4C2×#14583308C211yesmaximal, characteristic, complemented
5C2×#14583218C211yesmaximal, characteristic, complemented
6C2×#14583218C211yesmaximal, characteristic, complemented
7C2×#14583224C211yesmaximal, characteristic, complemented
8C2×#14583213C211yesmaximal, characteristic, complemented
9C2×#14583200C211yesmaximal, characteristic, complemented
10C2×#14583190C211yesmaximal, characteristic, complemented
11C2×#14583152C211yesmaximal, characteristic, complemented
12C2×#14583135C211yesmaximal, characteristic, complemented
13C2×#14583012C211yesmaximal, characteristic, complemented
14C2×#14582941C211yesmaximal, characteristic, complemented
15C22×#13063257C211yesmaximal, characteristic, complemented
16C2×C43×#435C211yesmaximal, characteristic, complemented
17C22×#10621900—21no—
18C22×D344C2211yescharacteristic
19#14583595—24no—
20#14583595C2218yescomplemented
21#14583553—24no—
22#14583553C2218yescomplemented
23C2×#13063325C2211yescharacteristic
24C2×#13063320—21no—
25C2×#13063317C2211yescharacteristic
26C2×#13063309—21no—
27C2×#13063309—21no—
28C2×#13063307—21no—
29C2×#13063305—21no—
30C2×#13063299C2211yescharacteristic
31C2×#13063299C2211yescharacteristic
32C2×#13063299C2211yescharacteristic
33C2×#13063299C2211yescharacteristic
34C2×#13063297—21no—
35C2×C4×D172C2211yescharacteristic
36C2×C4×D172C2211yescharacteristic
37C2×(C22⋊D43)⋊C4—21no—
38C2×#13063284C2211yescharacteristic
39C22×C4⋊Dic43C2211yescharacteristic
40C22×C4⋊Dic43C2211yescharacteristic
41C22×C4⋊Dic43C2211yescharacteristic
42#14583308C2218yescomplemented
43#14583224C2218yescomplemented
44#14583218C2218yescomplemented
45#14583218C2218yescomplemented
46#14583213C2218yescomplemented
47#14583200C2218yescomplemented
48#14583190C2218yescomplemented
49#14583152C2218yescomplemented
50#14583135C2218yescomplemented
51#14583012C2218yescomplemented
52#14582941C2218yescomplemented
53C2×#13063259C2211yescharacteristic
54C2×#13063259C2211yescharacteristic
55C2×#13063259C2211yescharacteristic
56C2×#13063257C2211yescharacteristic
57C2×#13063257C2211yescharacteristic
58C2×#13063257C2211yescharacteristic
59C2×#13063257C2211yescharacteristic
60C2×#13063257C2211yescharacteristic
61C2×#13063257C2211yescharacteristic
62C2×#13063257C2218yescomplemented
63C2×#13063247C2211yescharacteristic
64C2×#13063247C2211yescharacteristic
65C2×#13063247C2211yescharacteristic
66C2×#13063247C2211yescharacteristic
67C2×#13063247C2211yescharacteristic
68C2×#13063247C2211yescharacteristic
69C22×M16×C43C2211yescharacteristic
70C23×C8×C43C2211yescharacteristic
71C2×C4×D4×C43C2211yescharacteristic
72C43×#435C2218yescomplemented
73C2×C4⋊C8×C43C2211yescharacteristic
74C2×C22⋊C8×C43C2211yescharacteristic
75C2×C22⋊C8×C43C2211yescharacteristic
76C2×#97×C43C2211yescharacteristic
77C2×#10621900—28no—
78C2×#10621900—48no—
79C22×Dic86—21no—
80C22×D172C2311yescharacteristic
81C22×D172C2311yescharacteristic
82C22×C22⋊D43—21no—
83C22×C22⋊D43—21no—
84C22×C22⋊D43—21no—
85C22×C22⋊D43—21no—
86C23×Dic43—21no—
87C23×Dic43—21no—
88C23×Dic43—21no—
89C22×C4×D43—21no—
90C22×C4×D43—21no—
91C2×D344—24no—
92C2×D344C2314yes—
93#13063325—22no—
94#13063325C2314yes—
95#13063320—28no—
96#13063317—22no—
97#13063317C2314yes—
98#13063309—28no—
99#13063309—28no—
100#13063307—28no—
101#13063305—28no—
102#13063299—22no—
103#13063299—22no—
104#13063299—22no—
105#13063299—22no—
106#13063299C2314yes—
107#13063299C2314yes—
108#13063299C2314yes—
109#13063299C2314yes—
110#13063297—28no—
111C4×D172—22no—
112C4×D172—22no—
113C4×D172C2314yes—
114C4×D172C2314yes—
115(C22⋊D43)⋊C4—28no—
116#13063284—22no—
117#13063284C2314yes—
118C2×C4⋊Dic43—22no—
119C2×C4⋊Dic43—22no—
120C2×C4⋊Dic43—22no—
121C2×C4⋊Dic43—21no—
122C2×C4⋊Dic43—21no—
123C2×C4⋊Dic43—21no—
124C2×C4⋊Dic43—21no—
125C2×C4⋊Dic43C2314yes—
126C2×C4⋊Dic43C2314yes—
127C2×C4⋊Dic43C2314yes—
128C2×C4⋊Dic43C2311yescharacteristic
129C2×C4⋊Dic43C2311yescharacteristic
130C2×C4⋊Dic43C2311yescharacteristic
131C2×C4⋊Dic43C2311yescharacteristic
132C2×C4⋊Dic43C2311yescharacteristic
133C2×C4⋊Dic43C2311yescharacteristic
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×C22⋊Dic43—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×C4×Dic43—21no—
144#13063259C2314yes—
145#13063259C2314yes—
146#13063259C2314yes—
147#13063257C2314yes—
148#13063257C2314yes—
149#13063257C2314yes—
150#13063257C2314yes—
151#13063257C2314yes—
152#13063257C2314yes—
153#13063247C2314yes—
154#13063247C2314yes—
155#13063247C2314yes—
156#13063247C2314yes—
157#13063247C2314yes—
158#13063247C2314yes—
159C22×D4×C43D411yescharacteristic
160C23×C4×C43C2311yescharacteristic
161C23×C4×C43C2311yescharacteristic
162C2×M16×C43—24no—
163C2×M16×C43C2314yes—
164C22×C8×C43—24no—
165C22×C8×C43C2314yes—
166C22×C8×C43C2311yescharacteristic
167C22×C8×C43C2311yescharacteristic
168C22×C8×C43C2311yescharacteristic
169C22×C8×C43C2311yescharacteristic
170C4×D4×C43D414yes—
171C4×D4×C43C2314yes—
172C2×C4⋊C4×C43D411yescharacteristic
173C2×C22⋊C4×C43D411yescharacteristic
174C2×C22⋊C4×C43D411yescharacteristic
175C2×C42×C43C2311yescharacteristic
176C4⋊C8×C43C2314yes—
177C22⋊C8×C43C2314yes—
178C22⋊C8×C43C2314yes—
179#97×C43C2314yes—
180C24×C43C2×D411yescharacteristic
181C24×C43C2×D411yescharacteristic
182C23×D43—21no—
183C23×D43—21no—
184C2×D4×C43—24no—
185C2×D4×C43C2×D414yes—
186C22×C4×C43—22no—
187C22×C4×C43—22no—
188C22×C4×C43—22no—
189C22×C4×C43—22no—
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2×D412yes—
195C22×C4×C43C2×D412yes—
196C22×C4×C43C2412yes—
197C22×C4×C43C2412yes—
198C22×C4×C43C2411yescharacteristic
199C2×C22⋊D43—24no—
200C2×C22⋊D43—24no—
201C2×C22⋊D43—24no—
202C2×C22⋊D43—24no—
203C2×C22⋊D43—44no—
204C2×C22⋊D43—44no—
205C2×C22⋊D43—44no—
206C2×C22⋊D43—82no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43—24no—
214C22×Dic43—24no—
215C22×Dic43—24no—
216C22×Dic43—44no—
217C22×Dic43—44no—
218C22×Dic43—82no—
219#10621900—432no—
220C2×D172—21no—
221C2×D172—21no—
222C2×D172—22no—
223C2×D172—22no—
224C2×D172—22no—
225C2×D172—22no—
226C2×D172C2412yes—
227C2×D172C2412yes—
228C2×C4×D43—24no—
229C2×C4×D43—24no—
230C2×C4×D43—44no—
231C2×C4×D43—82no—
232C2×Dic86—24no—
233C2×Dic86—44no—
234M16×C43—28no—
235C2×C8×C43—22no—
236C2×C8×C43—22no—
237C2×C8×C43—22no—
238C2×C8×C43—28no—
239C2×C8×C43#4114yescomplemented
240C2×C8×C43C2412yes—
241C2×C8×C43C2412yes—
242C2×C8×C43C2412yes—
243C2×C8×C43C2412yes—
244C4⋊C4×C43C2×D414yes—
245C22⋊C4×C43C2×D414yes—
246C22⋊C4×C43C2×D414yes—
247C42×C43C2×D412yes—
248C42×C43C2412yes—
249C22⋊Dic43—24no—
250(C2×D43)⋊C4—24no—
251(C2×D43)⋊C4—24no—
252(C2×D43)⋊C4—24no—
253(C2×D43)⋊C4—24no—
254(C2×D43)⋊C4—24no—
255(C2×D43)⋊C4—24no—
256C4⋊Dic43—21no—
257C4⋊Dic43—21no—
258C4⋊Dic43—21no—
259C4⋊Dic43—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43—24no—
262C4⋊Dic43—24no—
263C4⋊Dic43—24no—
264C4⋊Dic43—24no—
265C4⋊Dic43—21no—
266C4⋊Dic43C2412yes—
267C4⋊Dic43C2412yes—
268C4⋊Dic43C2412yes—
269C4⋊Dic43C2412yes—
270C4⋊Dic43C2412yes—
271C4⋊Dic43C2412yes—
272Dic43⋊C4—24no—
273Dic43⋊C4—24no—
274C4×Dic43—24no—
275D344—28no—
276C23×C43—22no—
277C23×C43—22no—
278C23×C43—22no—
279C23×C43—22no—
280C23×C43—22no—
281C23×C43AGL(1,ℤ/8)14yes—
282C23×C43C22×D412yes—
283C23×C43C22×D412yes—
284C23×C43C22×D411yescharacteristic
285C22×D43—22no—
286C22×D43—22no—
287C22×D43—42no—
288C22×D43—42no—
289C22×D43—42no—
290C22×D43—42no—
291C22×D43—42no—
292C22×D43—42no—
293D4×C43—28no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—24no—
299C2×C4×C43—24no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43C22×D412yes—
305C2×C4×C43C22×D412yes—
306C2×C4×C43C22×D412yes—
307C2×C4×C43C22×D412yes—
308C2×C4×C43C22×D411yescharacteristic
309C2×C4×C43C2×#4112yes—
310C2×C4×C432−1+412yes—
311C2×C4×C43C2511yescharacteristic
312C22⋊D43—48no—
313C22⋊D43—48no—
314C22⋊D43—48no—
315C22⋊D43—84no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—22no—
322C2×Dic43—48no—
323C2×Dic43—42no—
324C2×Dic43—42no—
325C2×Dic43—42no—
326C2×Dic43—48no—
327C2×Dic43—42no—
328C2×Dic43—42no—
329C2×Dic43—42no—
330C2×Dic43—84no—
331D172—22no—
332D172—22no—
333D172—22no—
334D172—22no—
335D172—42no—
336D172—42no—
337C4×D43—48no—
338C4×D43—84no—
339Dic86—48no—
340C8×C43—22no—
341C8×C43—22no—
342C8×C43—22no—
343C8×C43C2×#4114yescomplemented
344C2×#3345—431nomaximal, Sylow
345C22×C43—28no—
346C22×C43—22no—
347C22×C43—22no—
348C22×C43—22no—
349C22×C43—22no—
350C22×C43—22no—
351C22×C43—44no—
352C22×C43#54712yes—
353C22×C43C2×AGL(1,ℤ/8)14yes—
354C22×C43C2×AGL(1,ℤ/8)12yes—
355C22×C43#57712yes—
356C22×C43C23×D411yescharacteristic
357C2×D43—42no—
358C2×D43—42no—
359C2×D43—42no—
360C2×D43—42no—
361C2×D43—42no—
362C2×D43—42no—
363C2×D43—84no—
364C2×D43—84no—
365C4×C43—22no—
366C4×C43—22no—
367C4×C43—22no—
368C4×C43—22no—
369C4×C43#54712yes—
370C4×C43C22×#4111yescharacteristic
371C4×C43C2×2−1+411yescharacteristic
372Dic43—42no—
373Dic43—42no—
374Dic43—42no—
375Dic43—42no—
376Dic43—42no—
377Dic43—42no—
378C2×#553—431no—
379C2×#547—431no—
380#3345—4316no—
381C2×#501—431no—
382C2×#481—431no—
383C2×#481—431no—
384C2×#482—431no—
385C2×#480—431no—
386C2×#478—431no—
387C2×#476—431no—
388C2×#469—431no—
389C2×#466—431no—
390C2×#442—431no—
391C2×#435D4311yescharacteristic, complemented
392C2×#428—431no—
393C22×#106—431no—
394C2×C43—24no—
395C2×C43—42no—
396C2×C43#334514yescomplemented
397C2×C43C2×#54711yescharacteristic
398C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
399C2×C43C2×#57711yescharacteristic
400D43—82no—
401D43—82no—
402C22×#41—861no—
403C22×D8—431no—
404C22×M16C2×D4311yescharacteristic
405C23×C8C2×D4311yescharacteristic
406#553—438no—
407#553—864no—
408#547—438no—
409#547—864no—
410C2×C4⋊Q8—431no—
411C2×#126—861no—
412C2×#125—431no—
413C2×#123—861no—
414C2×#123—861no—
415C2×#123—861no—
416C2×C22⋊Q8—861no—
417C2×#121—431no—
418C2×#121—431no—
419C2×#121—431no—
420C2×#121—431no—
421C2×#121—861no—
422C2×C4×D4—431no—
423C2×C4×D4—431no—
424C2×C4×D4—861no—
425C2×C4×D4C2×D4311yescharacteristic
426C2×#117—431no—
427C22×C4⋊C4—431no—
428C22×C4⋊C4—431no—
429C22×C4⋊C4—431no—
430#501—438no—
431#482—438no—
432#481—438no—
433#481—438no—
434#480—438no—
435#478—438no—
436#476—438no—
437#469—438no—
438#466—438no—
439#442—438no—
440#435C2×D4318yescomplemented
441#428—438no—
442C2×#107—431no—
443C2×#107—431no—
444C2×#107—431no—
445C2×#106—431no—
446C2×#106—431no—
447C2×#106—431no—
448C2×#106—431no—
449C2×#106—438no—
450C2×#106—431no—
451C2×#106—431no—
452C2×C4⋊C8C2×D4311yescharacteristic
453C2×#102—431no—
454C2×#102—431no—
455C2×#102—431no—
456C2×#102—431no—
457C2×#102—431no—
458C2×#102—431no—
459C2×C22⋊C8C2×D4311yescharacteristic
460C2×C22⋊C8C2×D4311yescharacteristic
461C2×#97C2×D4311yescharacteristic
462C43C2×#334511yescharacteristic, complemented, Sylow
463C2×#41—868no—
464C2×#41—1728no—
465C22×Q8—861no—
466C22×D4—431no—
467C22×D4—431no—
468C22×D4—861no—
469C22×D4—861no—
470C22×D4—861no—
471C22×D4—861no—
472C22×D4D17211yescharacteristic
473C23×C4—861no—
474C23×C4—861no—
475C23×C4—861no—
476C23×C4—861no—
477C23×C4—861no—
478C23×C4C22×D4311yescharacteristic
479C23×C4C22×D4311yescharacteristic
480C2×D8—434no—
481C2×D8—864no—
482C2×M16—24no—
483C2×M16C22×D4314yes—
484C22×C8—24no—
485C22×C8C22×D4311yescharacteristic
486C22×C8C22×D4314yes—
487C22×C8C22×D4311yescharacteristic
488C22×C8C22×D4311yescharacteristic
489C22×C8C22×D4311yescharacteristic
490C4⋊Q8—434no—
491C4⋊Q8—862no—
492#126—868no—
493#125—434no—
494#125—862no—
495#123—868no—
496#123—868no—
497#123—868no—
498C22⋊Q8—868no—
499#121—434no—
500#121—434no—
501#121—434no—
502#121—434no—
503#121—868no—
504#121—862no—
505#121—862no—
506#121—862no—
507#121—862no—
508C4×D4—434no—
509C4×D4—434no—
510C4×D4—868no—
511C4×D4—862no—
512C4×D4—862no—
513C4×D4D17214yes—
514C4×D4C22×D4314yes—
515#117—434no—
516#117—862no—
517C2×C4⋊C4—431no—
518C2×C4⋊C4—431no—
519C2×C4⋊C4—431no—
520C2×C4⋊C4—431no—
521C2×C4⋊C4—431no—
522C2×C4⋊C4—434no—
523C2×C4⋊C4—434no—
524C2×C4⋊C4—434no—
525C2×C4⋊C4—431no—
526C2×C4⋊C4—861no—
527C2×C4⋊C4—861no—
528C2×C4⋊C4—861no—
529C2×C4⋊C4—862no—
530C2×C4⋊C4—862no—
531C2×C4⋊C4—862no—
532C2×C4⋊C4—861no—
533C2×C4⋊C4—861no—
534C2×C4⋊C4—861no—
535C2×C4⋊C4D17211yescharacteristic
536C2×C22⋊C4—861no—
537C2×C22⋊C4—861no—
538C2×C22⋊C4—861no—
539C2×C22⋊C4—861no—
540C2×C22⋊C4—861no—
541C2×C22⋊C4—861no—
542C2×C22⋊C4—861no—
543C2×C22⋊C4D17211yescharacteristic
544C2×C22⋊C4D17211yescharacteristic
545C2×C42—861no—
546C2×C42C22×D4311yescharacteristic
547#107—434no—
548#107—434no—
549#107—434no—
550#106—434no—
551#106—434no—
552#106—434no—
553#106—434no—
554#106—434no—
555#106—434no—
556C4⋊C8C22×D4314yes—
557#102—434no—
558#102—434no—
559#102—434no—
560#102—434no—
561#102—434no—
562#102—434no—
563C22⋊C8C22×D4314yes—
564C22⋊C8C22×D4314yes—
565#97C22×D4314yes—
566C24—861no—
567C24—861no—
568C24C2×D17211yescharacteristic
569C24C2×D17211yescharacteristic
570#41—17232no—
571C2×Q8—864no—
572C2×Q8—1724no—
573C2×D4—24no—
574C2×D4—432no—
575C2×D4—432no—
576C2×D4—864no—
577C2×D4—864no—
578C2×D4—864no—
579C2×D4—864no—
580C2×D4—861no—
581C2×D4—861no—
582C2×D4—862no—
583C2×D4—862no—
584C2×D4—862no—
585C2×D4—862no—
586C2×D4—3442no—
587C2×D4—1724no—
588C2×D4—1724no—
589C2×D4—1724no—
590C2×D4C2×D17214yes—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—864no—
596C22×C4—864no—
597C22×C4—864no—
598C22×C4—861no—
599C22×C4—861no—
600C22×C4—861no—
601C22×C4—861no—
602C22×C4—861no—
603C22×C4—861no—
604C22×C4—864no—
605C22×C4—864no—
606C22×C4—3442no—
607C22×C4—3442no—
608C22×C4—1724no—
609C22×C4—1724no—
610C22×C4—1724no—
611C22×C4C2×D17212yes—
612C22×C4C2×D17212yes—
613C22×C4C2×D17211yescharacteristic
614C22×C4C2×D17211yescharacteristic
615C22×C4C2×D17211yescharacteristic
616C22×C4C2×D17211yescharacteristic
617C22×C4C23×D4312yes—
618C22×C4C23×D4312yes—
619C22×C4C23×D4311yescharacteristic
620D8—868no—
621M16—28no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—28no—
626C2×C8#1062190014yescomplemented
627C2×C8C23×D4312yes—
628C2×C8C23×D4312yes—
629C2×C8C23×D4312yes—
630C2×C8C23×D4312yes—
631C4⋊C4—432no—
632C4⋊C4—432no—
633C4⋊C4—432no—
634C4⋊C4—432no—
635C4⋊C4—432no—
636C4⋊C4—432no—
637C4⋊C4—861no—
638C4⋊C4—861no—
639C4⋊C4—861no—
640C4⋊C4—861no—
641C4⋊C4—861no—
642C4⋊C4—864no—
643C4⋊C4—864no—
644C4⋊C4—864no—
645C4⋊C4—861no—
646C4⋊C4—864no—
647C4⋊C4—864no—
648C4⋊C4—864no—
649C4⋊C4C2×D17214yes—
650C22⋊C4—864no—
651C22⋊C4—864no—
652C22⋊C4—864no—
653C22⋊C4—864no—
654C22⋊C4—864no—
655C22⋊C4—864no—
656C22⋊C4—864no—
657C22⋊C4C2×D17214yes—
658C22⋊C4C2×D17214yes—
659C42—864no—
660C42C2×D17212yes—
661C42C23×D4312yes—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—862no—
668C23—862no—
669C23—1722no—
670C23—1722no—
671C23—1722no—
672C23—1722no—
673C23—1722no—
674C23—1722no—
675C23#1306335314yes—
676C23C22×D17212yes—
677C23C22×D17212yes—
678C23C22×D17211yescharacteristic
679Q8—1728no—
680D4—28no—
681D4—862no—
682D4—862no—
683D4—862no—
684D4—862no—
685D4—3444no—
686D4—1728no—
687D4—1728no—
688D4—1728no—
689D4—1722no—
690D4—1722no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—862no—
704C2×C4—862no—
705C2×C4—862no—
706C2×C4—862no—
707C2×C4—3444no—
708C2×C4—3444no—
709C2×C4—1728no—
710C2×C4—1728no—
711C2×C4—1722no—
712C2×C4—1722no—
713C2×C4—1722no—
714C2×C4—1728no—
715C2×C4—1722no—
716C2×C4—1722no—
717C2×C4—1722no—
718C2×C4C22×D17212yes—
719C2×C4C22×D17212yes—
720C2×C4C22×D17212yes—
721C2×C4C22×D17212yes—
722C2×C4C22×D17211yescharacteristic
723C2×C4C2×#1062190012yes—
724C2×C4#1306337212yes—
725C2×C4C24×D4311yescharacteristic
726C8—22no—
727C8—22no—
728C8—22no—
729C8C2×#1062190014yescomplemented
730C22—22no—
731C22—22no—
732C22—28no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—44no—
737C22—3444no—
738C22—3444no—
739C22—1722no—
740C22—1722no—
741C22—1722no—
742C22—1722no—
743C22—1722no—
744C22—1722no—
745C22#1458355312yes—
746C22C2×#1306335314yes—
747C22C2×#1306335312yes—
748C22#1458371112yes—
749C22C23×D17211yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—1722no—
755C4—1722no—
756C4—1722no—
757C4—1722no—
758C4—1722no—
759C4—1722no—
760C4#1458355312yes—
761C4C22×#1062190011yescharacteristic
762C4C2×#1306337211yescharacteristic
763C2—24no—
764C2—42no—
765C2—3442no—
766C2—3442no—
767C2#1914706714yesdirect product factor
768C2C2×#1458355311yescharacteristic
769C2C22×#1306335311yescharacteristic
770C2C2×#1458371111yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#435C2
socleC23×C43C22×D4
hypercenterC2×#435D43
hypocenterC43C2×#3345
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#14583595C2semidirect
2. C2×#14583553C2semidirect
3. #19147067C2direct (N × H)
4. C2×#14583308C2semidirect
5. C2×#14583218C2semidirect
6. C2×#14583218C2semidirect
7. C2×#14583224C2semidirect
8. C2×#14583213C2semidirect
9. C2×#14583200C2semidirect
10. C2×#14583190C2semidirect
11. C2×#14583152C2semidirect
12. C2×#14583135C2semidirect
13. C2×#14583012C2semidirect
14. C2×#14582941C2semidirect
15. C22×#13063257C2semidirect
16. C2×C43×#435C2semidirect
20. #14583595C22semidirect
22. #14583553C22semidirect
42. #14583308C22semidirect
43. #14583224C22semidirect
44. #14583218C22semidirect
45. #14583218C22semidirect
46. #14583213C22semidirect
47. #14583200C22semidirect
48. #14583190C22semidirect
49. #14583152C22semidirect
50. #14583135C22semidirect
51. #14583012C22semidirect
52. #14582941C22semidirect
62. C2×#13063257C22semidirect
72. C43×#435C22semidirect
239. C2×C8×C43#41semidirect
343. C8×C43C2×#41semidirect
391. C2×#435D43semidirect
396. C2×C43#3345semidirect
440. #435C2×D43semidirect
462. C43C2×#3345semidirect
626. C2×C8#10621900semidirect
729. C8C2×#10621900semidirect
767. C2#19147067direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835952
C2×#145835532
#191470672
C2×#145833082
C2×#145832182
C2×#145832242
C2×#145832132
C2×#145832002
C2×#145831902
C2×#145831522
C2×#145831352
C2×#145830122
C2×#145829412
C22×#130632572
C2×C43×#4352
C2×#334543