Finite Group Databasebeta

← #25129803

Subgroups — #25129803

Order 11008.

1284 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic86C211yesmaximal, characteristic
2C2×#14583241C211yesmaximal, characteristic, complemented
3C2×#14582909C211yesmaximal, characteristic, complemented
4#19138892C211yesmaximal, characteristic
5#19135842C211yesmaximal, characteristic, complemented
6#19135842C211yesmaximal, characteristic, complemented
7#19135799C211yesmaximal, characteristic, complemented
8#19135792C211yesmaximal, characteristic, complemented
9#19135028C211yesmaximal, characteristic, complemented
10#19134866C211yesmaximal, characteristic, complemented
11#19134852C211yesmaximal, characteristic, complemented
12#19134531C211yesmaximal, characteristic, complemented
13#19134531C211yesmaximal, characteristic, complemented
14#19134531C211yesmaximal, characteristic, complemented
15C43×#1870C211yesmaximal, characteristic
16C23×Dic86C2211yescharacteristic
17C23×Dic86C2211yescharacteristic
18D4×Dic86—24no—
19D4×Dic86—24no—
20C2×#13063325C2211yescharacteristic
21C2×#13063324—21no—
22C2×#13063304C2211yescharacteristic
23C2×#13063304C2211yescharacteristic
24C2×#13063302—21no—
25C2×#13063302—21no—
26C2×C4×Dic86C2211yescharacteristic
27C2×D4×Dic43—21no—
28C2×#13063284C2211yescharacteristic
29#14583241—24no—
30C2×#13063259C2211yescharacteristic
31C2×#13063257C2211yescharacteristic
32#14582909—24no—
33C2×#13063250C2211yescharacteristic
34C2×#13063250C2211yescharacteristic
35C2×#13063250C2211yescharacteristic
36C2×#13063250C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063250C2211yescharacteristic
39C2×#13063250C2211yescharacteristic
40C2×#13063250C2211yescharacteristic
41C2×#13063250C2211yescharacteristic
42C2×#13063250C2211yescharacteristic
43C2×#13063250C2211yescharacteristic
44C2×#13063250C2211yescharacteristic
45#14582827—21no—
46#14582813—21no—
47#14582797C2211yescharacteristic
48#14582797C2211yescharacteristic
49#14582787—21no—
50#14582780—21no—
51#14582759C2211yescharacteristic
52#14582759C2211yescharacteristic
53#14582759C2211yescharacteristic
54#14582662C2211yescharacteristic
55#14582662C2211yescharacteristic
56C22×M16×C43C2211yescharacteristic
57C2×C4×D4×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×Dic86—22no—
64C22×Dic86—22no—
65C22×Dic86—22no—
66C22×Dic86—21no—
67C22×Dic86—21no—
68C22×Dic86—22no—
69C22×Dic86—22no—
70C22×Dic86—22no—
71C22×Dic86—22no—
72C22×Dic86—41no—
73C22×Dic86—41no—
74C22×Dic86—41no—
75C22×Dic86—41no—
76C22×Dic86D414yes—
77C22×Dic86C2311yescharacteristic
78C22×Dic86C2311yescharacteristic
79C22×Dic86C2311yescharacteristic
80C23×Dic43—21no—
81C23×Dic43—21no—
82#13063325—22no—
83#13063325—22no—
84#13063324—28no—
85#13063304—22no—
86#13063304—22no—
87#13063304—22no—
88#13063304D414yes—
89#13063302—28no—
90#13063302—28no—
91C4×Dic86—22no—
92C4×Dic86—22no—
93D4×Dic43—28no—
94#13063284—22no—
95#13063284—22no—
96C2×C4⋊Dic43—21no—
97C2×C4⋊Dic43—21no—
98C2×C4⋊Dic43C2311yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×C4⋊Dic43C2311yescharacteristic
101C2×C4⋊Dic43C2311yescharacteristic
102C2×C4⋊Dic43C2311yescharacteristic
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4—21no—
106C2×Dic43⋊C4—21no—
107C2×Dic43⋊C4—21no—
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43—21no—
110C2×C22⋊Dic43—21no—
111C2×C22⋊Dic43—21no—
112C2×C22⋊Dic43—21no—
113C2×C22⋊Dic43—21no—
114C2×C4×Dic43—21no—
115C2×C4×Dic43—21no—
116#13063259—22no—
117#13063257—22no—
118#13063250—22no—
119#13063250—22no—
120#13063250—22no—
121#13063250—22no—
122#13063250—22no—
123#13063250—22no—
124#13063250—22no—
125#13063250—22no—
126#13063250—41no—
127#13063250—41no—
128#13063250—41no—
129#13063250—41no—
130C43⋊#95—21no—
131C43⋊#95—21no—
132C43⋊#95—21no—
133C43⋊#95—21no—
134C43⋊#95—21no—
135C22×D4×C43D411yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C2×M16×C43—22no—
139C2×M16×C43—41no—
140C2×M16×C43—41no—
141C22×C8×C43C2311yescharacteristic
142C22×C8×C43C2311yescharacteristic
143C22×C8×C43C2311yescharacteristic
144C22×C8×C43C2311yescharacteristic
145C4×D4×C43—22no—
146C4×D4×C43—22no—
147C2×C4⋊C4×C43D411yescharacteristic
148C2×C22⋊C4×C43D411yescharacteristic
149C2×C22⋊C4×C43D411yescharacteristic
150C2×C42×C43C2311yescharacteristic
151C22⋊C8×C43—22no—
152C22⋊C8×C43—41no—
153C22⋊C8×C43—41no—
154C24×C43C2×D411yescharacteristic
155C24×C43C2×D411yescharacteristic
156C2×D4×C43—22no—
157C2×D4×C43—22no—
158C2×D4×C43—22no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43C2×D412yes—
170C22×C4×C43C2×D412yes—
171C22×C4×C43C2×D411yescharacteristic
172C22×C4×C43C2×D411yescharacteristic
173C22×C4×C43C2×D411yescharacteristic
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43C2411yescharacteristic
176C22×Dic43—24no—
177C22×Dic43—24no—
178C22×Dic43—21no—
179C22×Dic43—21no—
180C22×Dic43—21no—
181C22×Dic43—21no—
182C22×Dic43—21no—
183C22×Dic43—21no—
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43—42no—
187C22×Dic43—42no—
188C22×Dic43—42no—
189C22×Dic43—42no—
190C2×Dic86—21no—
191C2×Dic86—21no—
192C2×Dic86—21no—
193C2×Dic86—21no—
194C2×Dic86—21no—
195C2×Dic86—21no—
196C2×Dic86—21no—
197C2×Dic86—21no—
198C2×Dic86—21no—
199C2×Dic86—21no—
200C2×Dic86—21no—
201C2×Dic86—28no—
202C2×Dic86—24no—
203C2×Dic86—24no—
204C2×Dic86—21no—
205C2×Dic86—21no—
206C2×Dic86—44no—
207C2×Dic86—44no—
208C2×Dic86—44no—
209C2×Dic86—44no—
210C2×Dic86—44no—
211C2×Dic86—44no—
212C2×Dic86—42no—
213C2×Dic86—42no—
214C2×Dic86—42no—
215C2×Dic86—42no—
216C2×Dic86—44no—
217C2×Dic86C2×D412yes—
218C2×Dic86C2×D412yes—
219C2×Dic86C2×D412yes—
220C2×Dic86#4112yes—
221C2×Dic86#4112yes—
222M16×C43—44no—
223C2×C8×C43—21no—
224C2×C8×C43—21no—
225C2×C8×C43—21no—
226C2×C8×C43—21no—
227C2×C8×C43—21no—
228C2×C8×C43—21no—
229C2×C8×C43—21no—
230C2×C8×C43—21no—
231C2×C8×C43—21no—
232C2×C8×C43—21no—
233C2×C8×C43—21no—
234C2×C8×C43—21no—
235C4⋊C4×C43—22no—
236C22⋊C4×C43—22no—
237C22⋊C4×C43—22no—
238C42×C43—21no—
239C42×C43—21no—
240C22⋊Dic43—24no—
241C22⋊Dic43—24no—
242C22⋊Dic43—42no—
243C22⋊Dic43—42no—
244C22⋊Dic43—81no—
245C22⋊Dic43—81no—
246C4⋊Dic43—24no—
247C4⋊Dic43—24no—
248C4⋊Dic43—21no—
249C4⋊Dic43—21no—
250C4⋊Dic43—21no—
251C4⋊Dic43—21no—
252C4⋊Dic43—21no—
253C4⋊Dic43—21no—
254C4⋊Dic43—21no—
255C4⋊Dic43—21no—
256C4⋊Dic43—21no—
257C4⋊Dic43C2×D412yes—
258Dic43⋊C4—24no—
259Dic43⋊C4—24no—
260Dic43⋊C4—24no—
261Dic43⋊C4—42no—
262Dic43⋊C4—81no—
263C4×Dic43—24no—
264C4×Dic43—42no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—21no—
269C23×C43—21no—
270C23×C43—21no—
271C23×C43—21no—
272C23×C43—21no—
273C23×C43—21no—
274C23×C43—21no—
275C23×C43—21no—
276C23×C43—21no—
277C23×C43#12012yes—
278C23×C43#13712yes—
279C23×C43C22×D411yescharacteristic
280D4×C43—28no—
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—22no—
288C2×C4×C43—22no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43#12012yes—
300C2×C4×C43#13712yes—
301C2×C4×C43C22×D411yescharacteristic
302C2×C4×C43C22×D411yescharacteristic
303C2×C4×C43C2×#4111yescharacteristic
304C2×C4×C43C2×#4111yescharacteristic
305C2×C4×C43H(5,𝔽2)11yescharacteristic
306C2×C4×C43H(5,𝔽2)11yescharacteristic
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—22no—
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—48no—
314C2×Dic43—48no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43—41no—
332C2×Dic43—41no—
333Dic86—22no—
334Dic86—22no—
335Dic86—22no—
336Dic86—22no—
337Dic86—22no—
338Dic86—22no—
339Dic86—22no—
340Dic86—48no—
341Dic86—48no—
342Dic86—41no—
343Dic86—41no—
344Dic86—41no—
345Dic86—41no—
346Dic86#12314yes—
347C8×C43—41no—
348C8×C43—41no—
349C8×C43—41no—
350C8×C43—41no—
351#24053—431nomaximal, Sylow
352C22×C43—22no—
353C22×C43—22no—
354C22×C43—22no—
355C22×C43—22no—
356C22×C43—22no—
357C22×C43—22no—
358C22×C43—41no—
359C22×C43—41no—
360C22×C43—41no—
361C22×C43—41no—
362C22×C43—41no—
363C22×C43—41no—
364C22×C43—41no—
365C22×C43—41no—
366C22×C43C2×#12011yescharacteristic
367C22×C43#54611yescharacteristic
368C22×C43#54611yescharacteristic
369C22×C43C2×#13711yescharacteristic
370C22×C43C2×#13711yescharacteristic
371C22×C43#57711yescharacteristic
372C22×C43#57811yescharacteristic
373C4×C43—22no—
374C4×C43—22no—
375C4×C43—41no—
376C4×C43—41no—
377C4×C43C2×#12311yescharacteristic
378C4×C43#53411yescharacteristic
379C4×C43#54611yescharacteristic
380C4×C43#54611yescharacteristic
381Dic43—24no—
382Dic43—42no—
383Dic43—42no—
384Dic43—42no—
385Dic43—81no—
386Dic43—81no—
387Dic43—81no—
388Dic43—81no—
389C2×D4×Q8—431no—
390C2×#485—431no—
391C2×#419—431no—
392#2485—431no—
393#2043—431no—
394#2043—431no—
395#2036—431no—
396#2035—431no—
397#1894—431no—
398#1870D4311yescharacteristic
399#1865—431no—
400#1863—431no—
401#1787—431no—
402#1787—431no—
403#1787—431no—
404C2×C43—42no—
405C2×C43—42no—
406C2×C43#240511yescharacteristic
407C2×C43#300411yescharacteristic
408C2×C43#301311yescharacteristic
409C2×C43#331211yescharacteristic
410C2×C43#332011yescharacteristic
411C2×C43#332811yescharacteristic
412C2×C43#332911yescharacteristic
413C23×Q8—431no—
414C23×Q8—431no—
415C22×M16C2×D4311yescharacteristic
416D4×Q8—864no—
417D4×Q8—864no—
418C2×C4⋊Q8—431no—
419C2×C4⋊Q8—861no—
420C2×C22⋊Q8—431no—
421C2×C22⋊Q8—431no—
422C2×C22⋊Q8—861no—
423C2×C22⋊Q8—861no—
424C2×C4×Q8—431no—
425C2×C4×D4—861no—
426C2×C4×D4C2×D4311yescharacteristic
427C2×#117—431no—
428#485—864no—
429C2×#107—431no—
430C2×#106—431no—
431#419—864no—
432C2×#103—431no—
433C2×#103—431no—
434C2×#103—431no—
435C2×#103—431no—
436C2×#103—431no—
437C2×#103—431no—
438C2×#103—431no—
439C2×#103—431no—
440C2×#103—431no—
441C2×#103—431no—
442C2×#103—431no—
443C2×#103—431no—
444C2×C22⋊C8C2×D4311yescharacteristic
445C2×C22⋊C8C2×D4311yescharacteristic
446C2×C22⋊C8C2×D4311yescharacteristic
447#397—861no—
448#394—861no—
449#389—431no—
450#389—431no—
451#388—861no—
452#387—861no—
453#380—431no—
454#380—431no—
455#380—431no—
456#340—431no—
457#340—431no—
458#336C2×D4311yescharacteristic
459#336C2×D4311yescharacteristic
460C43#2405311yescharacteristic, complemented, Sylow
461C22×Q8—434no—
462C22×Q8—431no—
463C22×Q8—431no—
464C22×Q8—431no—
465C22×Q8—862no—
466C22×Q8—862no—
467C22×Q8—862no—
468C22×Q8—862no—
469C22×Q8—862no—
470C22×Q8—862no—
471C22×Q8—861no—
472C22×Q8—861no—
473C22×Q8—862no—
474C22×Q8—1721no—
475C22×Q8—1721no—
476C22×Q8—1721no—
477C22×Q8—1721no—
478C22×D4D17211yescharacteristic
479C23×C4—861no—
480C23×C4—861no—
481C23×C4C22×D4311yescharacteristic
482C23×C4C22×D4311yescharacteristic
483C2×M16—22no—
484C2×M16—41no—
485C2×M16—41no—
486C22×C8C22×D4311yescharacteristic
487C22×C8C22×D4311yescharacteristic
488C22×C8C22×D4311yescharacteristic
489C22×C8C22×D4311yescharacteristic
490C4⋊Q8—862no—
491C4⋊Q8—862no—
492C4⋊Q8—868no—
493C22⋊Q8—434no—
494C22⋊Q8—868no—
495C22⋊Q8—868no—
496C22⋊Q8—862no—
497C22⋊Q8—862no—
498C22⋊Q8—862no—
499C4×Q8—862no—
500C4×Q8—862no—
501C4×D4—22no—
502C4×D4—22no—
503C4×D4—868no—
504#117—862no—
505#117—862no—
506C2×C4⋊C4—431no—
507C2×C4⋊C4—431no—
508C2×C4⋊C4—431no—
509C2×C4⋊C4—431no—
510C2×C4⋊C4—431no—
511C2×C4⋊C4—861no—
512C2×C4⋊C4—861no—
513C2×C4⋊C4—861no—
514C2×C4⋊C4—861no—
515C2×C4⋊C4—861no—
516C2×C4⋊C4—861no—
517C2×C4⋊C4—861no—
518C2×C4⋊C4D17211yescharacteristic
519C2×C22⋊C4—861no—
520C2×C22⋊C4—861no—
521C2×C22⋊C4—861no—
522C2×C22⋊C4—861no—
523C2×C22⋊C4—861no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4D17211yescharacteristic
526C2×C22⋊C4D17211yescharacteristic
527C2×C42—861no—
528C2×C42—861no—
529C2×C42C22×D4311yescharacteristic
530#107—862no—
531#106—862no—
532#103—862no—
533#103—862no—
534#103—862no—
535#103—862no—
536#103—862no—
537#103—862no—
538#103—862no—
539#103—862no—
540#103—1721no—
541#103—1721no—
542#103—1721no—
543#103—1721no—
544C22⋊C8—22no—
545C22⋊C8—41no—
546C22⋊C8—41no—
547#95—861no—
548#95—861no—
549#95—861no—
550#95—861no—
551#95—861no—
552C24C2×D17211yescharacteristic
553C24C2×D17211yescharacteristic
554C2×Q8—432no—
555C2×Q8—432no—
556C2×Q8—432no—
557C2×Q8—432no—
558C2×Q8—432no—
559C2×Q8—864no—
560C2×Q8—868no—
561C2×Q8—864no—
562C2×Q8—861no—
563C2×Q8—861no—
564C2×Q8—861no—
565C2×Q8—861no—
566C2×Q8—861no—
567C2×Q8—861no—
568C2×Q8—861no—
569C2×Q8—861no—
570C2×Q8—861no—
571C2×Q8—861no—
572C2×Q8—861no—
573C2×Q8—861no—
574C2×Q8—861no—
575C2×Q8—1722no—
576C2×Q8—1722no—
577C2×Q8—1722no—
578C2×Q8—1722no—
579C2×Q8—1724no—
580C2×Q8—1724no—
581C2×Q8—1724no—
582C2×Q8—1724no—
583C2×Q8—1724no—
584C2×Q8—1724no—
585C2×Q8—1724no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—861no—
600C22×C4—864no—
601C22×C4—864no—
602C22×C4—861no—
603C22×C4—861no—
604C22×C4—861no—
605C22×C4—861no—
606C22×C4—861no—
607C22×C4—861no—
608C22×C4—861no—
609C22×C4—1722no—
610C22×C4—1722no—
611C22×C4—1722no—
612C22×C4—1722no—
613C22×C4C2×D17211yescharacteristic
614C22×C4C2×D17211yescharacteristic
615C22×C4C2×D17211yescharacteristic
616C22×C4C2×D17211yescharacteristic
617C22×C4D4×D4312yes—
618C22×C4D4×D4312yes—
619C22×C4C23×D4311yescharacteristic
620M16—44no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C4⋊C4—22no—
634C4⋊C4—432no—
635C4⋊C4—864no—
636C4⋊C4—864no—
637C4⋊C4—864no—
638C4⋊C4—864no—
639C4⋊C4—864no—
640C4⋊C4—861no—
641C4⋊C4—861no—
642C4⋊C4—861no—
643C4⋊C4—861no—
644C4⋊C4—861no—
645C4⋊C4—861no—
646C4⋊C4—861no—
647C4⋊C4—861no—
648C4⋊C4—861no—
649C4⋊C4—3441no—
650C4⋊C4—1722no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—864no—
654C22⋊C4—864no—
655C22⋊C4—3441no—
656C22⋊C4—3441no—
657C22⋊C4—1722no—
658C22⋊C4—1722no—
659C42—21no—
660C42—21no—
661C42—864no—
662C42—1722no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23#1306329512yes—
676C23#1306335812yes—
677C23C22×D17211yescharacteristic
678Q8—434no—
679Q8—862no—
680Q8—862no—
681Q8—862no—
682Q8—862no—
683Q8—862no—
684Q8—862no—
685Q8—862no—
686Q8—1728no—
687Q8—1728no—
688Q8—1721no—
689Q8—1721no—
690Q8—1721no—
691Q8—1721no—
692D4—28no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—862no—
712C2×C4—862no—
713C2×C4—862no—
714C2×C4—862no—
715C2×C4—862no—
716C2×C4—862no—
717C2×C4—1728no—
718C2×C4—1728no—
719C2×C4—1721no—
720C2×C4—1721no—
721C2×C4—1721no—
722C2×C4—1721no—
723C2×C4—1721no—
724C2×C4—1721no—
725C2×C4—1721no—
726C2×C4—1721no—
727C2×C4—1721no—
728C2×C4—1721no—
729C2×C4—1721no—
730C2×C4—1721no—
731C2×C4—1721no—
732C2×C4—1721no—
733C2×C4—1721no—
734C2×C4—1721no—
735C2×C4—1721no—
736C2×C4—1721no—
737C2×C4#1306329512yes—
738C2×C4#1306335812yes—
739C2×C4C2×D4×D4311yescharacteristic
740C2×C4C2×D4×D4311yescharacteristic
741C2×C4#41×D4311yescharacteristic
742C2×C4#41×D4311yescharacteristic
743C2×C4#1306337011yescharacteristic
744C2×C4#1306337011yescharacteristic
745C8—41no—
746C8—41no—
747C8—41no—
748C8—41no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22C2×#1306329511yescharacteristic
764C22#1458354411yescharacteristic
765C22#1458354411yescharacteristic
766C22C2×#1306335811yescharacteristic
767C22C2×#1306335811yescharacteristic
768C22#1458371111yescharacteristic
769C22#1458371611yescharacteristic
770C4—22no—
771C4—22no—
772C4—41no—
773C4—41no—
774C4—864no—
775C4—3441no—
776C4—3441no—
777C4—3441no—
778C4—3441no—
779C4—1722no—
780C4—1722no—
781C4—1722no—
782C4#123×D4311yescharacteristic
783C4#1458345911yescharacteristic
784C4#1458353811yescharacteristic
785C4#1458353811yescharacteristic
786C2—42no—
787C2—42no—
788C2#1913792111yescharacteristic
789C2#1914383211yescharacteristic
790C2#1914391311yescharacteristic
791C2#1914664811yescharacteristic
792C2#1914676811yescharacteristic
793C2#1914687911yescharacteristic
794C2#1914689011yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1870C2
socleC23×C43C22×D4
prime radicalC22×D4×C43D4
hypercenter#1870D43
hypocenterC43#24053
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #1870

Complements

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

NH ≅ G/Ntype
2. C2×#14583241C2semidirect
3. C2×#14582909C2semidirect
5. #19135842C2semidirect
6. #19135842C2semidirect
7. #19135799C2semidirect
8. #19135792C2semidirect
9. #19135028C2semidirect
10. #19134866C2semidirect
11. #19134852C2semidirect
12. #19134531C2semidirect
13. #19134531C2semidirect
14. #19134531C2semidirect
460. C43#24053semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic862
C2×#145832412
C2×#145829092
#191388922
#191358422
#191357992
#191357922
#191350282
#191348662
#191348522
#191345312
C43×#18702
#2405343