Finite Group Databasebeta

← C2×#19144706 #25964779

Subgroups — C2×#19144706 #25964779

Order 11008.

2182 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583433C211yesmaximal, characteristic, complemented
2C2×C4×#10621898C211yesmaximal, characteristic, complemented
3#19144706C2116yesmaximal, direct product factor
4C2×#14583241C211yesmaximal, characteristic, complemented
5C2×#14583224C211yesmaximal, characteristic, complemented
6C2×#14583207C211yesmaximal, characteristic, complemented
7C2×#14583200C211yesmaximal, characteristic, complemented
8C2×#14583122C211yesmaximal, characteristic, complemented
9C2×#14583115C211yesmaximal, characteristic, complemented
10C2×#14583063C211yesmaximal, characteristic, complemented
11C2×#14583046C211yesmaximal, characteristic
12C2×#14583012C211yesmaximal, characteristic, complemented
13C2×#14583007C211yesmaximal, characteristic, complemented
14C2×#14583001C211yesmaximal, characteristic, complemented
15C2×#14583001C211yesmaximal, characteristic, complemented
16C2×C43×#432C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C22×Dic172C2211yescharacteristic
19C22×#10621873C2211yescharacteristic
20C22×#10621873C2211yescharacteristic
21C22×D344C2211yescharacteristic
22#14583433—24no—
23#14583433C2218yescomplemented
24C2×#13063319—21no—
25C2×#13063317C2211yescharacteristic
26C2×#13063313C2211yescharacteristic
27C2×#13063308—21no—
28C2×#13063304C2211yescharacteristic
29C2×#13063299C2211yescharacteristic
30C4×#10621898—24no—
31C4×#10621898C2218yescomplemented
32C2×C4×Dic86C2211yescharacteristic
33C2×C4×Dic86C2211yescharacteristic
34C2×C4×Dic86C2211yescharacteristic
35C2×C4×D172C2211yescharacteristic
36C2×C4×D172C2211yescharacteristic
37C2×C4×D172C2211yescharacteristic
38C2×C4×C22⋊D43—21no—
39C2×C4×C22⋊D43—21no—
40C2×C4×C22⋊D43—21no—
41C2×#13063284C2211yescharacteristic
42C2×#13063282—21no—
43C2×#13063282—21no—
44C2×C42×D43—21no—
45#14583241C2218yescomplemented
46#14583224C2218yescomplemented
47#14583207C2218yescomplemented
48#14583200C2218yescomplemented
49#14583122C2218yescomplemented
50#14583115C2218yescomplemented
51#14583063C2218yescomplemented
52#14583046C2218yes—
53#14583012C2218yescomplemented
54#14583007C2218yescomplemented
55#14583001C2218yescomplemented
56#14583001C2218yescomplemented
57C2×#13063259C2211yescharacteristic
58C2×#13063259C2211yescharacteristic
59C2×#13063257C2211yescharacteristic
60C2×#13063257C2211yescharacteristic
61C2×#13063250C2211yescharacteristic
62C2×#13063250C2211yescharacteristic
63C2×#13063250C2211yescharacteristic
64C2×#13063250C2211yescharacteristic
65C2×#13063247C2211yescharacteristic
66C2×#13063247C2211yescharacteristic
67C2×#13063247C2211yescharacteristic
68C2×#13063247C2211yescharacteristic
69C22×C42×C43C2211yescharacteristic
70C43×#432C2218yescomplemented
71C2×C4⋊C8×C43C2211yescharacteristic
72C2×C4⋊C8×C43C2211yescharacteristic
73C2×C22⋊C8×C43C2211yescharacteristic
74C2×C22⋊C8×C43C2211yescharacteristic
75C2×#97×C43C2211yescharacteristic
76C2×#97×C43C2211yescharacteristic
77C2×#10621898—22no—
78C2×#10621898—24no—
79C2×#10621898—24no—
80C2×#10621898C2314yes—
81C22×Dic86C2311yescharacteristic
82C22×Dic86C2311yescharacteristic
83C22×D172C2311yescharacteristic
84C22×D172C2311yescharacteristic
85C22×C22⋊D43—21no—
86C22×C22⋊D43—21no—
87C22×C4×D43—21no—
88C22×C4×D43—21no—
89C22×C4×D43—21no—
90C22×C4×D43—21no—
91C2×Dic172—24no—
92C2×Dic172C2314yes—
93C2×#10621873—24no—
94C2×#10621873—24no—
95C2×#10621873C2314yes—
96C2×#10621873C2314yes—
97C2×D344—24no—
98C2×D344C2314yes—
99#13063319—28no—
100#13063317—22no—
101#13063317C2314yes—
102#13063313—22no—
103#13063313C2314yes—
104#13063308—28no—
105#13063304—22no—
106#13063304C2314yes—
107#13063299—22no—
108#13063299C2314yes—
109C4×Dic86—22no—
110C4×Dic86—22no—
111C4×Dic86—22no—
112C4×Dic86C2314yes—
113C4×Dic86C2314yes—
114C4×Dic86C2314yes—
115C4×D172—22no—
116C4×D172—22no—
117C4×D172—22no—
118C4×D172C2314yes—
119C4×D172C2314yes—
120C4×D172C2314yes—
121C4×C22⋊D43—28no—
122C4×C22⋊D43—28no—
123C4×C22⋊D43—28no—
124#13063284—22no—
125#13063284C2314yes—
126#13063282—28no—
127#13063282—28no—
128C2×C4⋊Dic43C2311yescharacteristic
129C2×C4⋊Dic43C2311yescharacteristic
130C2×C4⋊Dic43C2311yescharacteristic
131C2×C4⋊Dic43C2311yescharacteristic
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4—21no—
138C2×C22⋊Dic43—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×C4×Dic43—21no—
147C2×C4×Dic43—21no—
148C2×C4×Dic43—21no—
149C2×C4×Dic43—21no—
150C42×D43—28no—
151#13063259C2314yes—
152#13063259C2314yes—
153#13063257C2314yes—
154#13063257C2314yes—
155#13063250C2314yes—
156#13063250C2314yes—
157#13063250C2314yes—
158#13063250C2314yes—
159#13063247C2314yes—
160#13063247C2314yes—
161#13063247C2314yes—
162#13063247C2314yes—
163C23×C4×C43D411yescharacteristic
164C23×C4×C43D411yescharacteristic
165C23×C4×C43C2311yescharacteristic
166C22×C8×C43C2311yescharacteristic
167C22×C8×C43C2311yescharacteristic
168C22×C8×C43C2311yescharacteristic
169C22×C8×C43C2311yescharacteristic
170C2×C42×C43D411yescharacteristic
171C2×C42×C43D411yescharacteristic
172C2×C42×C43D414yes—
173C2×C42×C43C2311yescharacteristic
174C2×C42×C43C2311yescharacteristic
175C2×C42×C43C2314yes—
176C4⋊C8×C43C2314yes—
177C4⋊C8×C43C2314yes—
178C22⋊C8×C43C2314yes—
179C22⋊C8×C43C2314yes—
180#97×C43C2314yes—
181#97×C43C2314yes—
182C24×C43C2×D411yescharacteristic
183C23×D43—21no—
184C23×D43—21no—
185C22×C4×C43—22no—
186C22×C4×C43—22no—
187C22×C4×C43—42no—
188C22×C4×C43—42no—
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D412yes—
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D414yes—
196C22×C4×C43C2×D414yes—
197C22×C4×C43C2412yes—
198C22×C4×C43C2411yescharacteristic
199C2×C22⋊D43—28no—
200C2×C22⋊D43—24no—
201C2×C22⋊D43—24no—
202C2×C22⋊D43—44no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205C22×Dic43—21no—
206C22×Dic43—21no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209#10621898—216no—
210#10621898—28no—
211#10621898—28no—
212C2×D172—21no—
213C2×D172—22no—
214C2×D172—21no—
215C2×D172—22no—
216C2×D172—22no—
217C2×D172#4114yes—
218C2×D172C2412yes—
219C2×D172C2412yes—
220C2×C4×D43—28no—
221C2×C4×D43—24no—
222C2×C4×D43—24no—
223C2×C4×D43—24no—
224C2×C4×D43—24no—
225C2×C4×D43—44no—
226C2×C4×D43—44no—
227C2×C4×D43—44no—
228C2×Dic86—21no—
229C2×Dic86—22no—
230C2×Dic86—22no—
231C2×Dic86—22no—
232C2×Dic86—21no—
233C2×Dic86#4114yes—
234C2×Dic86C2412yes—
235C2×Dic86C2412yes—
236C2×C8×C43—22no—
237C2×C8×C43—22no—
238C2×C8×C43—22no—
239C2×C8×C43—22no—
240C2×C8×C43C2412yes—
241C2×C8×C43C2412yes—
242C2×C8×C43C2412yes—
243C2×C8×C43C2412yes—
244C42×C43C2×D414yes—
245C42×C43C2×D414yes—
246C42×C43C2×D412yes—
247C42×C43C2×D412yes—
248C42×C43C2412yes—
249C42×C43C2412yes—
250C22⋊Dic43—24no—
251C22⋊Dic43—24no—
252(C2×D43)⋊C4—24no—
253(C2×D43)⋊C4—24no—
254(C2×D43)⋊C4—24no—
255(C2×D43)⋊C4—24no—
256(C2×D43)⋊C4—24no—
257(C2×D43)⋊C4—24no—
258C4⋊Dic43—21no—
259C4⋊Dic43—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43C2412yes—
263C4⋊Dic43C2412yes—
264C4⋊Dic43C2412yes—
265C4⋊Dic43C2412yes—
266Dic43⋊C4—24no—
267Dic43⋊C4—24no—
268Dic43⋊C4—24no—
269Dic43⋊C4—24no—
270Dic43⋊C4—24no—
271Dic43⋊C4—24no—
272C4×Dic43—24no—
273C4×Dic43—24no—
274C4×Dic43—24no—
275C4×Dic43—24no—
276Dic172—28no—
277D344—28no—
278#10621873—28no—
279#10621873—28no—
280C23×C43—22no—
281C23×C43—22no—
282C23×C43—22no—
283C23×C43C22×D412yes—
284C23×C43C22×D411yescharacteristic
285C22×D43—24no—
286C22×D43—22no—
287C22×D43—22no—
288C22×D43—42no—
289C22×D43—42no—
290C22×D43—42no—
291C22×D43—42no—
292C22×D43—42no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—24no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—44no—
302C2×C4×C43—44no—
303C2×C4×C43C22×D412yes—
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×C43C2×#4112yes—
311C2×C4×C43C2511yescharacteristic
312C22⋊D43—216no—
313C22⋊D43—48no—
314C2×Dic43—24no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—42no—
322C2×Dic43—42no—
323C2×Dic43—42no—
324C2×Dic43—42no—
325C2×Dic43—42no—
326D172—24no—
327D172—22no—
328D172—22no—
329D172—22no—
330D172—42no—
331D172C2×#4114yes—
332C4×D43—216no—
333C4×D43—48no—
334C4×D43—48no—
335C4×D43—48no—
336Dic86—24no—
337Dic86—22no—
338Dic86—22no—
339Dic86—22no—
340Dic86—42no—
341Dic86C2×#4114yes—
342C8×C43—22no—
343C8×C43—22no—
344C8×C43—22no—
345C8×C43—22no—
346C2×#3111—431nomaximal, Sylow
347C22×C43—22no—
348C22×C43—22no—
349C22×C43—22no—
350C22×C43—44no—
351C22×C43#52512yes—
352C22×C43#57512yes—
353C22×C43#57512yes—
354C22×C43C23×D411yescharacteristic
355C2×D43—24no—
356C2×D43—48no—
357C2×D43—42no—
358C2×D43—42no—
359C2×D43—42no—
360C2×D43—42no—
361C2×D43—42no—
362C2×D43—84no—
363C4×C43—22no—
364C4×C43—22no—
365C4×C43—22no—
366C4×C43—22no—
367C4×C43—22no—
368C4×C43#52512yes—
369C4×C43C22×#4111yescharacteristic
370C4×C43C22×#4111yescharacteristic
371Dic43—24no—
372Dic43—42no—
373Dic43—42no—
374Dic43—42no—
375Dic43—42no—
376Dic43—42no—
377C2×#529—431no—
378C2×C4×#41—431no—
379#3111—4316no—
380C2×#485—431no—
381C2×#482—431no—
382C2×#479—431no—
383C2×#478—431no—
384C2×#464—431no—
385C2×#463—431no—
386C2×#452—431no—
387C2×#449—431no—
388C2×#442—431no—
389C2×#441—431no—
390C2×#440—431no—
391C2×#440—431no—
392C2×#432D4311yescharacteristic, complemented
393C2×C43—42no—
394C2×C43#311114yescomplemented
395C2×C43C2×#52511yescharacteristic
396C2×C43C2×#57511yescharacteristic
397C2×C43C2×#57511yescharacteristic
398D43—44no—
399D43—82no—
400C22×#41—431no—
401C22×Q16—431no—
402C22×SD16—431no—
403C22×SD16—431no—
404C22×D8—431no—
405#529—438no—
406#529—864no—
407C2×#126—861no—
408C2×#125—431no—
409C2×#124—431no—
410C2×#123—861no—
411C2×C22⋊Q8—431no—
412C2×#121—431no—
413C4×#41—438no—
414C4×#41—864no—
415C2×C4×Q8—431no—
416C2×C4×Q8—431no—
417C2×C4×Q8—431no—
418C2×C4×D4—431no—
419C2×C4×D4—431no—
420C2×C4×D4—431no—
421C2×C4×D4—861no—
422C2×C4×D4—861no—
423C2×C4×D4—861no—
424C2×#117—431no—
425C2×#117—861no—
426C2×#117—861no—
427C22×C42—861no—
428C22×C42C2×D4311yescharacteristic
429#485—438no—
430#482—438no—
431#479—438no—
432#478—438no—
433#464—438no—
434#463—438no—
435#452—438no—
436#449—438no—
437#442—438no—
438#441—438no—
439#440—438no—
440#440—438no—
441#432C2×D4318yescomplemented
442C2×#107—431no—
443C2×#107—431no—
444C2×#106—431no—
445C2×#106—431no—
446C2×C4⋊C8C2×D4311yescharacteristic
447C2×C4⋊C8C2×D4311yescharacteristic
448C2×#103—431no—
449C2×#103—431no—
450C2×#103—431no—
451C2×#103—431no—
452C2×#102—431no—
453C2×#102—431no—
454C2×#102—431no—
455C2×#102—431no—
456C2×C22⋊C8C2×D4311yescharacteristic
457C2×C22⋊C8C2×D4311yescharacteristic
458C2×#97C2×D4311yescharacteristic
459C2×#97C2×D4311yescharacteristic
460C43C2×#311111yescharacteristic, complemented, Sylow
461C2×#41—434no—
462C2×#41—864no—
463C2×#41—864no—
464C2×#41—862no—
465C22×Q8—431no—
466C22×Q8—431no—
467C22×D4—431no—
468C22×D4—431no—
469C22×D4—861no—
470C22×D4—861no—
471C23×C4—861no—
472C23×C4—861no—
473C23×C4—861no—
474C23×C4—861no—
475C23×C4D17211yescharacteristic
476C23×C4D17211yescharacteristic
477C23×C4C22×D4311yescharacteristic
478C2×Q16—434no—
479C2×Q16—864no—
480C2×SD16—434no—
481C2×SD16—434no—
482C2×SD16—864no—
483C2×SD16—864no—
484C2×D8—434no—
485C2×D8—864no—
486C22×C8C22×D4311yescharacteristic
487C22×C8C22×D4311yescharacteristic
488C22×C8C22×D4311yescharacteristic
489C22×C8C22×D4311yescharacteristic
490#126—868no—
491#125—434no—
492#125—862no—
493#124—434no—
494#124—862no—
495#123—868no—
496C22⋊Q8—434no—
497C22⋊Q8—862no—
498#121—434no—
499#121—862no—
500C4×Q8—434no—
501C4×Q8—434no—
502C4×Q8—434no—
503C4×Q8—862no—
504C4×Q8—862no—
505C4×Q8—862no—
506C4×D4—434no—
507C4×D4—434no—
508C4×D4—434no—
509C4×D4—868no—
510C4×D4—868no—
511C4×D4—868no—
512C4×D4—862no—
513C4×D4—862no—
514C4×D4—862no—
515#117—434no—
516#117—862no—
517#117—868no—
518#117—868no—
519C2×C4⋊C4—431no—
520C2×C4⋊C4—431no—
521C2×C4⋊C4—431no—
522C2×C4⋊C4—431no—
523C2×C4⋊C4—861no—
524C2×C4⋊C4—861no—
525C2×C4⋊C4—861no—
526C2×C4⋊C4—861no—
527C2×C4⋊C4—861no—
528C2×C4⋊C4—861no—
529C2×C22⋊C4—861no—
530C2×C22⋊C4—861no—
531C2×C22⋊C4—861no—
532C2×C22⋊C4—861no—
533C2×C22⋊C4—861no—
534C2×C22⋊C4—861no—
535C2×C22⋊C4—861no—
536C2×C22⋊C4—861no—
537C2×C42—861no—
538C2×C42—861no—
539C2×C42—861no—
540C2×C42—861no—
541C2×C42—868no—
542C2×C42D17211yescharacteristic
543C2×C42D17214yes—
544C2×C42D17211yescharacteristic
545C2×C42C22×D4311yescharacteristic
546C2×C42C22×D4311yescharacteristic
547C2×C42C22×D4314yes—
548#107—434no—
549#107—434no—
550#106—434no—
551#106—434no—
552C4⋊C8C22×D4314yes—
553C4⋊C8C22×D4314yes—
554#103—434no—
555#103—434no—
556#103—434no—
557#103—434no—
558#102—434no—
559#102—434no—
560#102—434no—
561#102—434no—
562C22⋊C8C22×D4314yes—
563C22⋊C8C22×D4314yes—
564#97C22×D4314yes—
565#97C22×D4314yes—
566C24—861no—
567C24—861no—
568C24C2×D17211yescharacteristic
569#41—868no—
570#41—868no—
571#41—8616no—
572C2×Q8—434no—
573C2×Q8—432no—
574C2×Q8—432no—
575C2×Q8—861no—
576C2×Q8—861no—
577C2×Q8—862no—
578C2×Q8—862no—
579C2×Q8—862no—
580C2×D4—434no—
581C2×D4—432no—
582C2×D4—432no—
583C2×D4—868no—
584C2×D4—864no—
585C2×D4—864no—
586C2×D4—861no—
587C2×D4—861no—
588C2×D4—862no—
589C2×D4—862no—
590C2×D4—862no—
591C2×D4—1724no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—868no—
597C22×C4—861no—
598C22×C4—864no—
599C22×C4—861no—
600C22×C4—861no—
601C22×C4—861no—
602C22×C4—861no—
603C22×C4—861no—
604C22×C4—864no—
605C22×C4—864no—
606C22×C4—864no—
607C22×C4—1724no—
608C22×C4—1724no—
609C22×C4—1724no—
610C22×C4C2×D17212yes—
611C22×C4C2×D17211yescharacteristic
612C22×C4C2×D17211yescharacteristic
613C22×C4C2×D17211yescharacteristic
614C22×C4C2×D17211yescharacteristic
615C22×C4C2×D17211yescharacteristic
616C22×C4C2×D17214yes—
617C22×C4C2×D17214yes—
618C22×C4C23×D4312yes—
619C22×C4C23×D4311yescharacteristic
620Q16—868no—
621SD16—868no—
622SD16—868no—
623D8—868no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8C23×D4312yes—
629C2×C8C23×D4312yes—
630C2×C8C23×D4312yes—
631C2×C8C23×D4312yes—
632C4⋊C4—432no—
633C4⋊C4—432no—
634C4⋊C4—432no—
635C4⋊C4—432no—
636C4⋊C4—861no—
637C4⋊C4—861no—
638C4⋊C4—861no—
639C4⋊C4—861no—
640C4⋊C4—864no—
641C4⋊C4—864no—
642C4⋊C4—864no—
643C4⋊C4—864no—
644C4⋊C4—864no—
645C4⋊C4—864no—
646C22⋊C4—864no—
647C22⋊C4—864no—
648C22⋊C4—864no—
649C22⋊C4—864no—
650C22⋊C4—864no—
651C22⋊C4—864no—
652C22⋊C4—864no—
653C22⋊C4—864no—
654C42—864no—
655C42—864no—
656C42—864no—
657C42—864no—
658C42C2×D17214yes—
659C42C2×D17214yes—
660C42C2×D17212yes—
661C42C2×D17212yes—
662C42C23×D4312yes—
663C42C23×D4312yes—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—864no—
668C23—862no—
669C23—862no—
670C23—1722no—
671C23—1722no—
672C23—1722no—
673C23—1722no—
674C23—1722no—
675C23C22×D17212yes—
676C23C22×D17211yescharacteristic
677Q8—434no—
678Q8—864no—
679Q8—862no—
680Q8—862no—
681Q8—862no—
682Q8—1722no—
683D4—434no—
684D4—8616no—
685D4—864no—
686D4—862no—
687D4—862no—
688D4—862no—
689D4—1728no—
690D4—1722no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—8616no—
702C2×C4—864no—
703C2×C4—862no—
704C2×C4—862no—
705C2×C4—862no—
706C2×C4—862no—
707C2×C4—862no—
708C2×C4—862no—
709C2×C4—1728no—
710C2×C4—1728no—
711C2×C4—1728no—
712C2×C4—1722no—
713C2×C4—1722no—
714C2×C4—1722no—
715C2×C4—1722no—
716C2×C4—1722no—
717C2×C4C22×D17212yes—
718C2×C4C22×D17212yes—
719C2×C4C22×D17212yes—
720C2×C4C22×D17212yes—
721C2×C4C22×D17212yes—
722C2×C4C22×D17211yescharacteristic
723C2×C4#41×D4312yes—
724C2×C4#41×D4312yes—
725C2×C4C24×D4311yescharacteristic
726C8—22no—
727C8—22no—
728C8—22no—
729C8—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—864no—
735C22—3444no—
736C22—1722no—
737C22—1722no—
738C22—1722no—
739C22—1728no—
740C22—1722no—
741C22—1722no—
742C22#1458341112yes—
743C22#1458369912yes—
744C22#1458369912yes—
745C22C23×D17211yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—864no—
752C4—1722no—
753C4—1722no—
754C4—1722no—
755C4—1722no—
756C4—1722no—
757C4#1458341112yes—
758C4C2×#41×D4311yescharacteristic
759C4C2×#41×D4311yescharacteristic
760C2—42no—
761C2—3442no—
762C2—1724no—
763C2#1914470614yesdirect product factor
764C2C2×#1458341111yescharacteristic
765C2C2×#1458369911yescharacteristic
766C2C2×#1458369911yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#432C2
socleC23×C43C22×D4
prime radicalC2×#14583046C2
hypercenterC2×#432D43
hypocenterC43C2×#3111
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#432

Complements

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

NH ≅ G/Ntype
1. C2×#14583433C2semidirect
2. C2×C4×#10621898C2semidirect
3. #19144706C2direct (N × H)
4. C2×#14583241C2semidirect
5. C2×#14583224C2semidirect
6. C2×#14583207C2semidirect
7. C2×#14583200C2semidirect
8. C2×#14583122C2semidirect
9. C2×#14583115C2semidirect
10. C2×#14583063C2semidirect
12. C2×#14583012C2semidirect
13. C2×#14583007C2semidirect
14. C2×#14583001C2semidirect
15. C2×#14583001C2semidirect
16. C2×C43×#432C2semidirect
23. #14583433C22semidirect
31. C4×#10621898C22semidirect
45. #14583241C22semidirect
46. #14583224C22semidirect
47. #14583207C22semidirect
48. #14583200C22semidirect
49. #14583122C22semidirect
50. #14583115C22semidirect
51. #14583063C22semidirect
53. #14583012C22semidirect
54. #14583007C22semidirect
55. #14583001C22semidirect
56. #14583001C22semidirect
70. C43×#432C22semidirect
392. C2×#432D43semidirect
394. C2×C43#3111semidirect
441. #432C2×D43semidirect
460. C43C2×#3111semidirect
763. C2#19144706direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834332
C2×C4×#106218982
#191447062
C2×#145832412
C2×#145832242
C2×#145832072
C2×#145832002
C2×#145831222
C2×#145831152
C2×#145830632
C2×#145830462
C2×#145830122
C2×#145830072
C2×#145830012
C2×C43×#4322
C2×#311143