Finite Group Databasebeta

← #25102307

Subgroups — #25102307

Order 11008.

1468 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#10621902C211yesmaximal, characteristic
2C2×#14583064C211yesmaximal, characteristic
3C2×#14583004C211yesmaximal, characteristic, complemented
4C2×#14583001C211yesmaximal, characteristic, complemented
5C4×#13063305C211yesmaximal, characteristic, complemented
6#19134934C211yesmaximal, characteristic, complemented
7#19134930C211yesmaximal, characteristic, complemented
8#19134906C211yesmaximal, characteristic, complemented
9#19134857C211yesmaximal, characteristic, complemented
10#19134851C211yesmaximal, characteristic, complemented
11#19134797C211yesmaximal, characteristic, complemented
12#19134534C211yesmaximal, characteristic
13#19134423C211yesmaximal, characteristic, complemented
14#19134358C211yesmaximal, characteristic, complemented
15C43×#1763C211yesmaximal, characteristic, complemented
16C22×#10621902C2211yescharacteristic
17C22×#10621885C2211yescharacteristic
18C22×#10621873C2211yescharacteristic
19C2×#13063305C2211yescharacteristic
20C4×#10621902—24no—
21C4×#10621902—24no—
22C2×Q8×Dic43C2211yescharacteristic
23C2×C4×Dic86C2211yescharacteristic
24C2×C4×D172—21no—
25C2×C4×D172C2211yescharacteristic
26C2×#13063287—21no—
27C2×#13063287C2211yescharacteristic
28C2×#13063283—21no—
29C2×#13063283C2211yescharacteristic
30C2×C42×D43—21no—
31C2×C42×D43C2211yescharacteristic
32#14583064C418yescomplemented
33#14583004—24no—
34#14583001—24no—
35C2×#13063259C2211yescharacteristic
36C2×#13063256C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063249C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×#13063247C2211yescharacteristic
41C2×#13063245C2211yescharacteristic
42C2×#13063245C2211yescharacteristic
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic
45C2×#13063236C2211yescharacteristic
46#14582804C2211yescharacteristic
47#14582798C2211yescharacteristic
48#14582784—21no—
49#14582773—21no—
50#14582756C2211yescharacteristic
51C4×C4⋊Dic43—21no—
52C4×(C2×D43)⋊C4—21no—
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582653C2211yescharacteristic
56#14582653C2211yescharacteristic
57C2×C4×Q8×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#97×C43C2211yescharacteristic
61C4×C4⋊C4×C43C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C43×#340C2211yescharacteristic
64C2×#10621902—22no—
65C2×#10621902—22no—
66C2×#10621902—22no—
67C2×#10621902—22no—
68C2×#10621902—22no—
69C2×#10621902C2×C414yes—
70C22×Dic86C2311yescharacteristic
71C22×D172—21no—
72C22×D172C2311yescharacteristic
73C22×C4×D43—21no—
74C22×C4×D43—21no—
75C22×C4×D43—21no—
76C22×C4×D43D411yescharacteristic
77C22×C4×D43D411yescharacteristic
78C22×C4×D43C2311yescharacteristic
79C2×#10621885—22no—
80C2×#10621885—22no—
81C2×#10621885C2×C414yescomplemented
82C2×#10621873—22no—
83C2×#10621873—22no—
84C2×#10621873C2×C414yescomplemented
85C22×C43⋊C8C2311yescharacteristic
86C22×C43⋊C8C2311yescharacteristic
87#13063305—22no—
88#13063305C2×C414yescomplemented
89Q8×Dic43—22no—
90Q8×Dic43—22no—
91C4×Dic86—22no—
92C4×Dic86—22no—
93C4×D172—28no—
94C4×D172—22no—
95C4×D172D414yes—
96#13063287—28no—
97#13063287—22no—
98#13063287—22no—
99#13063283—28no—
100#13063283—22no—
101#13063283—22no—
102C2×C4⋊Dic43—21no—
103C2×C4⋊Dic43—21no—
104C2×C4⋊Dic43—21no—
105C2×C4⋊Dic43C2311yescharacteristic
106C2×C4⋊Dic43C2311yescharacteristic
107C2×Dic43⋊C4—21no—
108C2×(C2×D43)⋊C4—21no—
109C2×(C2×D43)⋊C4—21no—
110C2×(C2×D43)⋊C4—21no—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4—21no—
113C2×C4×Dic43—21no—
114C2×C4×Dic43—21no—
115C2×C4×Dic43—21no—
116C2×C4×Dic43D411yescharacteristic
117C2×C4×Dic43D411yescharacteristic
118C2×C4×Dic43C2311yescharacteristic
119C42×D43—28no—
120C42×D43—22no—
121C42×D43—22no—
122#13063259—22no—
123#13063256—22no—
124#13063250—22no—
125#13063249—22no—
126#13063248—22no—
127#13063247—22no—
128#13063245—22no—
129#13063245C2×C414yescomplemented
130(C2×D43)⋊C8—22no—
131(C2×D43)⋊C8C2×C414yescomplemented
132#13063236—22no—
133C43⋊#95—21no—
134C43⋊#95—21no—
135C43⋊#95—21no—
136C43⋊#95—21no—
137C22×Q8×C43C2311yescharacteristic
138C22×C8×C43C2311yescharacteristic
139C22×C8×C43C2311yescharacteristic
140C4×Q8×C43—22no—
141C4×Q8×C43D414yes—
142C2×C4⋊C4×C43—21no—
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C42×C43—21no—
147C2×C42×C43—21no—
148C2×C42×C43C2311yescharacteristic
149#103×C43—22no—
150#103×C43C2×C414yescomplemented
151#97×C43—22no—
152#95×C43—21no—
153C23×D43—21no—
154C23×D43C2×D411yescharacteristic
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43C22×C412yes—
159C2×Q8×C43C2×D412yes—
160C2×Q8×C43#4112yes—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2411yescharacteristic
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43C2×D411yescharacteristic
172C22×Dic43C2×D411yescharacteristic
173C22×Dic43C2×D411yescharacteristic
174#10621902—28no—
175#10621902—28no—
176#10621902—28no—
177#10621902—28no—
178C2×D172—24no—
179C2×D172—24no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172—21no—
183C2×D172—24no—
184C2×D172C22×C412yes—
185C2×D172C2×D412yes—
186C2×D172#4112yes—
187C2×C4×D43—24no—
188C2×C4×D43—24no—
189C2×C4×D43—21no—
190C2×C4×D43—21no—
191C2×C4×D43—21no—
192C2×C4×D43—21no—
193C2×C4×D43—24no—
194C2×C4×D43—24no—
195C2×C4×D43—22no—
196C2×C4×D43—22no—
197C2×C4×D43—24no—
198C2×C4×D43—22no—
199C2×C4×D43—41no—
200C2×C4×D43—41no—
201C2×C4×D43—41no—
202C2×C4×D43—42no—
203C2×C4×D43—42no—
204C2×C4×D43—42no—
205C2×C4×D43—42no—
206C2×C4×D43C22×C412yes—
207C2×C4×D43#4112yes—
208C2×Dic86—21no—
209C2×Dic86—21no—
210C2×Dic86—21no—
211C2×Dic86—21no—
212C2×Dic86—21no—
213C2×Dic86C22×C412yes—
214C2×C8×C43—21no—
215C2×C8×C43—21no—
216C2×C8×C43—21no—
217C2×C8×C43—21no—
218C2×C8×C43—21no—
219C2×C8×C43C22×C412yes—
220C4⋊C4×C43—24no—
221C4⋊C4×C43—21no—
222C4⋊C4×C43—21no—
223C4⋊C4×C43—21no—
224C4⋊C4×C43—21no—
225C4⋊C4×C43C22×C412yes—
226C4⋊C4×C43C2×D412yes—
227C42×C43—24no—
228C42×C43—42no—
229C42×C43C2×D412yes—
230C42×C43C2×D412yes—
231#10621885—28no—
232(C2×D43)⋊C4—24no—
233(C2×D43)⋊C4—24no—
234(C2×D43)⋊C4—24no—
235(C2×D43)⋊C4—24no—
236(C2×D43)⋊C4—42no—
237C4⋊Dic43—24no—
238C4⋊Dic43—21no—
239C4⋊Dic43—24no—
240C4⋊Dic43—21no—
241C4⋊Dic43—21no—
242C4⋊Dic43—42no—
243C4⋊Dic43C2×D412yes—
244Dic43⋊C4—42no—
245C4×Dic43—24no—
246C4×Dic43—24no—
247C4×Dic43—22no—
248C4×Dic43—22no—
249C4×Dic43—21no—
250C4×Dic43—21no—
251C4×Dic43—42no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8—21no—
257C2×C43⋊C8C22×C412yes—
258#10621873—28no—
259C23×C43C22×D411yescharacteristic
260C22×D43—22no—
261C22×D43—21no—
262C22×D43—22no—
263C22×D43—21no—
264C22×D43—22no—
265C22×D43—21no—
266C22×D43—21no—
267C22×D43—21no—
268C22×D43—21no—
269C22×D43—41no—
270C22×D43—41no—
271C22×D43—41no—
272C22×D43—41no—
273C22×D43C4×D412yes—
274Q8×C43—22no—
275Q8×C43—22no—
276Q8×C43—22no—
277Q8×C43C4×D414yes—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43#12012yes—
295C2×C4×C43#12012yes—
296C2×C4×C43C23×C411yescharacteristic
297C2×C4×C43C22×D411yescharacteristic
298C2×C4×C43C22×D411yescharacteristic
299C2×C4×C43C2×#4111yescharacteristic
300C2×C4×C43C2×#4111yescharacteristic
301C2×C4×C43C2×#4111yescharacteristic
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—21no—
305C2×Dic43—21no—
306C2×Dic43—22no—
307C2×Dic43—21no—
308C2×Dic43—22no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43C4×D412yes—
319C2×Dic43#13712yes—
320D172—216no—
321D172—22no—
322D172—22no—
323D172—22no—
324D172C4×D414yes—
325C4×D43—216no—
326C4×D43—22no—
327C4×D43—22no—
328C4×D43—22no—
329C4×D43—22no—
330C4×D43—44no—
331C4×D43—48no—
332C4×D43—44no—
333C4×D43—48no—
334Dic86—22no—
335Dic86—22no—
336Dic86—41no—
337Dic86—41no—
338C8×C43—22no—
339C8×C43—41no—
340C43⋊C8—22no—
341C43⋊C8—41no—
342#21457—431nomaximal, Sylow
343C22×C43C2×C4×D411yescharacteristic
344C22×C43C2×#12011yescharacteristic
345C22×C43#52511yescharacteristic
346C22×C43C2×#13711yescharacteristic
347C22×C43#57511yescharacteristic
348C22×C43#57511yescharacteristic
349C22×C43#57511yescharacteristic
350C2×D43—22no—
351C2×D43—22no—
352C2×D43—24no—
353C2×D43—22no—
354C2×D43—41no—
355C2×D43—42no—
356C2×D43—41no—
357C2×D43—42no—
358C2×D43—42no—
359C2×D43—42no—
360C2×D43—41no—
361C2×D43—42no—
362C2×D43—41no—
363C2×D43—42no—
364C4×C43—22no—
365C4×C43—22no—
366C4×C43—24no—
367C4×C43—42no—
368C4×C43—42no—
369C4×C43—81no—
370C4×C43C2×C4×D411yescharacteristic
371C4×C43C2×C4×D411yescharacteristic
372C4×C43#52511yescharacteristic
373C4×C43#52511yescharacteristic
374Dic43—22no—
375Dic43—22no—
376Dic43—41no—
377Dic43—42no—
378Dic43—42no—
379Dic43—81no—
380C2×C4×#41—431no—
381C2×#452—431no—
382C2×#441—431no—
383C2×#440—431no—
384C4×C22⋊Q8—431no—
385#1878—431no—
386#1877—431no—
387#1873—431no—
388#1864—431no—
389#1863—431no—
390#1854—431no—
391#1788—431no—
392#1763D4311yescharacteristic, complemented
393#1762—431no—
394#1749—431no—
395C2×C43C4×#12011yescharacteristic
396C2×C43#294311yescharacteristic
397C2×C43C4×#13711yescharacteristic
398C2×C43#300511yescharacteristic
399C2×C43#300711yescharacteristic
400C2×C43#311111yescharacteristic
401C2×C43#311611yescharacteristic
402D43—42no—
403D43—44no—
404C22×#41—431no—
405C22×Q16—431no—
406C22×SD16—431no—
407C2×C22⋊Q8—431no—
408C4×#41—864no—
409C4×#41—864no—
410C2×C4×Q8—431no—
411C2×C4×Q8—431no—
412C2×C4×Q8C2×D4311yescharacteristic
413C2×C4×D4—431no—
414C2×C4×D4—431no—
415C2×C4×D4—861no—
416C2×C4×D4—861no—
417C2×#117—431no—
418C2×#117—861no—
419C22×C42—431no—
420C22×C42—861no—
421#452—438no—
422#441—864no—
423#440—864no—
424C2×#107—431no—
425C2×#106—431no—
426C2×#103—431no—
427C2×#103—431no—
428C2×#103—431no—
429C2×#103C2×D4311yescharacteristic
430C2×#103C2×D4311yescharacteristic
431C2×#102—431no—
432C2×#102—431no—
433C2×#102—431no—
434C2×C22⋊C8—431no—
435C2×C22⋊C8—431no—
436C2×#97—431no—
437C2×#97C2×D4311yescharacteristic
438#391—431no—
439#389—431no—
440#387—861no—
441#385—861no—
442#380—431no—
443C4×C4⋊C4—861no—
444C4×C4⋊C4C2×D4311yescharacteristic
445C4×C22⋊C4—861no—
446#340—431no—
447#340—431no—
448#340C2×D4311yescharacteristic
449#340C2×D4311yescharacteristic
450#336—431no—
451#336—431no—
452C43#2145711yescharacteristic, complemented, Sylow
453C2×#41—434no—
454C2×#41—862no—
455C2×#41—862no—
456C2×#41—862no—
457C2×#41—862no—
458C2×#41—862no—
459C22×Q8—431no—
460C22×Q8C22×D4311yescharacteristic
461C22×D4—431no—
462C22×D4—861no—
463C23×C4—431no—
464C23×C4—431no—
465C23×C4—431no—
466C23×C4—861no—
467C23×C4—861no—
468C23×C4—861no—
469C2×Q16—434no—
470C2×Q16—862no—
471C2×Q16—862no—
472C2×SD16—434no—
473C2×SD16—862no—
474C2×SD16—862no—
475C22×C8—431no—
476C22×C8—431no—
477C22×C8C22×D4311yescharacteristic
478C22×C8C22×D4311yescharacteristic
479C22⋊Q8—434no—
480C22⋊Q8—862no—
481C4×Q8—22no—
482C4×Q8—862no—
483C4×Q8—862no—
484C4×Q8—862no—
485C4×Q8—862no—
486C4×Q8D17214yes—
487C4×D4—434no—
488C4×D4—868no—
489C4×D4—862no—
490C4×D4—868no—
491C4×D4—862no—
492C4×D4—862no—
493#117—862no—
494#117—868no—
495#117—862no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4—861no—
500C2×C4⋊C4—861no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4C22×D4311yescharacteristic
504C2×C4⋊C4C22×D4311yescharacteristic
505C2×C4⋊C4C22×D4311yescharacteristic
506C2×C22⋊C4—861no—
507C2×C22⋊C4—861no—
508C2×C22⋊C4—861no—
509C2×C22⋊C4—861no—
510C2×C22⋊C4—861no—
511C2×C42—21no—
512C2×C42—21no—
513C2×C42—431no—
514C2×C42—431no—
515C2×C42—431no—
516C2×C42—868no—
517C2×C42—861no—
518C2×C42—861no—
519C2×C42—862no—
520C2×C42—862no—
521C2×C42—861no—
522C2×C42C22×D4311yescharacteristic
523#107—862no—
524#106—862no—
525#103—22no—
526#103—862no—
527#103—862no—
528#103—862no—
529#103C4×D4314yescomplemented
530#102—434no—
531#102—862no—
532#102—862no—
533C22⋊C8—434no—
534C22⋊C8—862no—
535#97—22no—
536#97—862no—
537#95—21no—
538#95—861no—
539#95—861no—
540#95—861no—
541#95—861no—
542C24—431no—
543C24—861no—
544#41—868no—
545#41—868no—
546#41—868no—
547#41—868no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—432no—
552C2×Q8—861no—
553C2×Q8—861no—
554C2×Q8—861no—
555C2×Q8—861no—
556C2×Q8—861no—
557C2×Q8C2×C4×D4312yes—
558C2×Q8C2×D17212yes—
559C2×Q8#1062189812yes—
560C2×D4—432no—
561C2×D4—432no—
562C2×D4—432no—
563C2×D4—864no—
564C2×D4—864no—
565C2×D4—864no—
566C2×D4—861no—
567C2×D4—861no—
568C2×D4—861no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—431no—
574C22×C4—431no—
575C22×C4—432no—
576C22×C4—432no—
577C22×C4—431no—
578C22×C4—864no—
579C22×C4—862no—
580C22×C4—864no—
581C22×C4—864no—
582C22×C4—864no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—861no—
587C22×C4—861no—
588C22×C4—861no—
589C22×C4—864no—
590C22×C4—862no—
591C22×C4—862no—
592C22×C4—861no—
593C22×C4—1721no—
594C22×C4—1721no—
595C22×C4—1721no—
596C22×C4—1722no—
597C22×C4—1722no—
598C22×C4—1722no—
599C22×C4—1722no—
600C22×C4D4×D4311yescharacteristic
601C22×C4D4×D4311yescharacteristic
602C22×C4C23×D4311yescharacteristic
603Q16—868no—
604SD16—868no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—432no—
611C2×C8—861no—
612C2×C8—861no—
613C2×C8—861no—
614C2×C8—861no—
615C2×C8—861no—
616C2×C8C2×C4×D4312yes—
617C4⋊C4—24no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—432no—
623C4⋊C4—864no—
624C4⋊C4—864no—
625C4⋊C4—861no—
626C4⋊C4—861no—
627C4⋊C4—861no—
628C4⋊C4—1722no—
629C4⋊C4—1722no—
630C4⋊C4C2×C4×D4312yes—
631C4⋊C4C2×D17212yes—
632C22⋊C4—864no—
633C22⋊C4—864no—
634C22⋊C4—864no—
635C22⋊C4—864no—
636C22⋊C4—1722no—
637C42—24no—
638C42—42no—
639C42—864no—
640C42—864no—
641C42—862no—
642C42—862no—
643C42—861no—
644C42—861no—
645C42—1722no—
646C42C2×D17212yes—
647C42D4×D4312yes—
648C23—432no—
649C23—862no—
650C23—862no—
651C23—861no—
652C23—862no—
653C23—861no—
654C23—861no—
655C23—861no—
656C23—861no—
657C23—861no—
658C23—1721no—
659C23—1721no—
660C23—1721no—
661C23—1721no—
662C23C2×D4×D4311yescharacteristic
663Q8—22no—
664Q8—22no—
665Q8—22no—
666Q8—862no—
667Q8—862no—
668Q8—1721no—
669Q8—1721no—
670Q8C4×D17214yes—
671D4—434no—
672D4—8616no—
673D4—862no—
674D4—862no—
675D4—862no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—432no—
693C2×C4—432no—
694C2×C4—8616no—
695C2×C4—861no—
696C2×C4—861no—
697C2×C4—861no—
698C2×C4—861no—
699C2×C4—862no—
700C2×C4—862no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—862no—
704C2×C4—862no—
705C2×C4—861no—
706C2×C4—861no—
707C2×C4—861no—
708C2×C4—1724no—
709C2×C4—1724no—
710C2×C4—1728no—
711C2×C4—1728no—
712C2×C4—1721no—
713C2×C4—1721no—
714C2×C4—1721no—
715C2×C4—1721no—
716C2×C4—1721no—
717C2×C4—1721no—
718C2×C4—1721no—
719C2×C4#1306329512yes—
720C2×C4#1306329512yes—
721C2×C4C22×C4×D4311yescharacteristic
722C2×C4C2×D4×D4311yescharacteristic
723C2×C4C22×D17211yescharacteristic
724C2×C4#41×D4311yescharacteristic
725C2×C4#41×D4311yescharacteristic
726C2×C4C2×#1062189811yescharacteristic
727C8—22no—
728C8—41no—
729C8—862no—
730C8—1721no—
731C22—864no—
732C22—862no—
733C22—862no—
734C22—862no—
735C22—1721no—
736C22—1722no—
737C22—1721no—
738C22—1722no—
739C22—1721no—
740C22—1722no—
741C22—1722no—
742C22—1722no—
743C22—1721no—
744C22—1722no—
745C22C4×D4×D4311yescharacteristic
746C22C2×#1306329511yescharacteristic
747C22#1458340811yescharacteristic
748C22#137×D4311yescharacteristic
749C22#1458369511yescharacteristic
750C22#1458369811yescharacteristic
751C22#1458369811yescharacteristic
752C4—24no—
753C4—22no—
754C4—22no—
755C4—42no—
756C4—42no—
757C4—81no—
758C4—862no—
759C4—862no—
760C4—3441no—
761C4—1722no—
762C4—1721no—
763C4—1722no—
764C4C4×D4×D4311yescharacteristic
765C4C2×C4×D17211yescharacteristic
766C4#1458340811yescharacteristic
767C4#1458341111yescharacteristic
768C2—1722no—
769C2—1724no—
770C2C4×#1306329511yescharacteristic
771C2#1914339011yescharacteristic
772C2#1914341111yescharacteristic
773C2#1914384111yescharacteristic
774C2#1914385611yescharacteristic
775C2#1914470211yescharacteristic
776C2#1914475511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1763C2
socleC23×C43C22×D4
prime radicalC22×#10621902C22
cosocleC22×C4×C43C24
hypercenter#1763D43
hypocenterC43#21457
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
3. C2×#14583004C2semidirect
4. C2×#14583001C2semidirect
5. C4×#13063305C2semidirect
6. #19134934C2semidirect
7. #19134930C2semidirect
8. #19134906C2semidirect
9. #19134857C2semidirect
10. #19134851C2semidirect
11. #19134797C2semidirect
13. #19134423C2semidirect
14. #19134358C2semidirect
15. C43×#1763C2semidirect
32. #14583064C4semidirect
81. C2×#10621885C2×C4semidirect
84. C2×#10621873C2×C4semidirect
88. #13063305C2×C4semidirect
129. #13063245C2×C4semidirect
131. (C2×D43)⋊C8C2×C4semidirect
150. #103×C43C2×C4semidirect
392. #1763D43semidirect
452. C43#21457semidirect
529. #103C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#106219022
C2×#145830642
C2×#145830042
C2×#145830012
C4×#130633052
#191349342
#191349302
#191349062
#191348572
#191348512
#191347972
#191345342
#191344232
#191343582
C43×#17632
#2145743