Finite Group Databasebeta

← #25130750

Subgroups — #25130750

Order 11008.

1154 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583203C211yesmaximal, characteristic, complemented
2C2×#14582999C211yesmaximal, characteristic, complemented
3#19139517C211yesmaximal, characteristic, complemented
4#19135781C211yesmaximal, characteristic, complemented
5#19135774C211yesmaximal, characteristic, complemented
6#19135598C211yesmaximal, characteristic, complemented
7#19135598C211yesmaximal, characteristic, complemented
8#19135565C211yesmaximal, characteristic, complemented
9#19135394C211yesmaximal, characteristic, complemented
10#19134907C211yesmaximal, characteristic, complemented
11#19134902C211yesmaximal, characteristic, complemented
12#19134794C211yesmaximal, characteristic, complemented
13#19134783C211yesmaximal, characteristic, complemented
14#19134595C211yesmaximal, characteristic, complemented
15C2×C43×#553C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C2×#13063304C2211yescharacteristic
18C2×#13063304C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20#14583203—24no—
21#14582999—24no—
22C2×#13063258C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×C22⋊(C43⋊C8)C2211yescharacteristic
33C2×C22⋊(C43⋊C8)C2211yescharacteristic
34C2×C22⋊(C43⋊C8)C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36C2×#13063236C2211yescharacteristic
37#14582822—21no—
38#14582822—21no—
39#14582802—21no—
40#14582795—21no—
41#14582769C2211yescharacteristic
42#14582759C2211yescharacteristic
43#14582759C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50C43×#553—24no—
51C43×#553—24no—
52C2×#126×C43—21no—
53C2×#125×C43C2211yescharacteristic
54C2×#123×C43—21no—
55C2×#121×C43—21no—
56C2×#121×C43C2211yescharacteristic
57C2×#121×C43C2211yescharacteristic
58C2×C4×D4×C43—21no—
59C2×C4×D4×C43C2211yescharacteristic
60C2×C4×D4×C43C2211yescharacteristic
61C2×#117×C43C2211yescharacteristic
62C22×C4⋊C4×C43C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C2×#10621883—22no—
65C2×#10621883—22no—
66C2×#10621883—22no—
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71#13063304—22no—
72#13063304—22no—
73#13063304—41no—
74#13063304—41no—
75C4×Dic86—22no—
76C4×Dic86—22no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×C4×Dic43—21no—
90#13063258—22no—
91#13063258—22no—
92#13063256—22no—
93C4⋊(C43⋊C8)—22no—
94#13063248—22no—
95#13063248—22no—
96#13063248—22no—
97#13063246—22no—
98#13063246—41no—
99#13063246—41no—
100C22⋊(C43⋊C8)—22no—
101C22⋊(C43⋊C8)—22no—
102C22⋊(C43⋊C8)—41no—
103C22⋊(C43⋊C8)—41no—
104#13063236—22no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C22×D4×C43—21no—
108C22×D4×C43—21no—
109C22×D4×C43D411yescharacteristic
110C22×D4×C43C2311yescharacteristic
111C23×C4×C43—21no—
112C23×C4×C43—21no—
113C23×C4×C43C2311yescharacteristic
114C23×C4×C43C2311yescharacteristic
115#126×C43—28no—
116#125×C43—22no—
117#125×C43D414yes—
118#123×C43—28no—
119#121×C43—28no—
120#121×C43—22no—
121#121×C43—22no—
122#121×C43—22no—
123#121×C43—22no—
124C4×D4×C43—28no—
125C4×D4×C43—22no—
126C4×D4×C43—22no—
127C4×D4×C43—22no—
128C4×D4×C43D414yes—
129#117×C43—22no—
130#117×C43—22no—
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43—22no—
135C2×C4⋊C4×C43—22no—
136C2×C4⋊C4×C43D411yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C22⋊C4×C43—21no—
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43—21no—
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43D411yescharacteristic
145C2×C22⋊C4×C43D411yescharacteristic
146C2×C42×C43—21no—
147C2×C42×C43C2311yescharacteristic
148C24×C43—21no—
149C24×C43C2×D411yescharacteristic
150C24×C43C2×D411yescharacteristic
151C2×D4×C43—24no—
152C2×D4×C43—24no—
153C2×D4×C43—22no—
154C2×D4×C43—21no—
155C2×D4×C43—22no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—41no—
161C2×D4×C43—42no—
162C2×D4×C43—42no—
163C2×D4×C43—81no—
164C2×D4×C43—81no—
165C2×D4×C43C2×D412yes—
166C22×C4×C43—24no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—24no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—81no—
184C22×C4×C43—81no—
185C22×C4×C43—81no—
186C22×C4×C43—81no—
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2411yescharacteristic
192C22×Dic43—21no—
193C22×Dic43—21no—
194C22×Dic43—21no—
195C22×Dic43—21no—
196C2×Dic86—21no—
197C2×Dic86—21no—
198C2×Dic86—21no—
199C2×Dic86—21no—
200C2×Dic86—21no—
201C2×Dic86#4112yes—
202C4⋊C4×C43—24no—
203C4⋊C4×C43—24no—
204C4⋊C4×C43—24no—
205C4⋊C4×C43—22no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C4⋊C4×C43C2×D412yes—
210C4⋊C4×C43C2×D412yes—
211C4⋊C4×C43C2×D412yes—
212C22⋊C4×C43—24no—
213C22⋊C4×C43—24no—
214C22⋊C4×C43—24no—
215C22⋊C4×C43—24no—
216C22⋊C4×C43—22no—
217C22⋊C4×C43—22no—
218C42×C43—24no—
219C42×C43C2×D412yes—
220C42×C43C2×D412yes—
221C22⋊Dic43—42no—
222C22⋊Dic43—42no—
223C22⋊Dic43—81no—
224C22⋊Dic43—81no—
225#10621883—28no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—42no—
233C4⋊Dic43—81no—
234Dic43⋊C4—42no—
235Dic43⋊C4—42no—
236Dic43⋊C4—42no—
237C4×Dic43—42no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8#4112yes—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—22no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43#13712yes—
271C23×C43C22×D411yescharacteristic
272D4×C43—22no—
273D4×C43—22no—
274D4×C43—44no—
275D4×C43—48no—
276D4×C43—41no—
277D4×C43—41no—
278D4×C43—84no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—21no—
287C2×C4×C43—22no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—84no—
307C2×C4×C43—84no—
308C2×C4×C43#12012yes—
309C2×C4×C43#12012yes—
310C2×C4×C43C22×D411yescharacteristic
311C2×C4×C43C22×D411yescharacteristic
312C2×C4×C43C2×#4111yescharacteristic
313C2×C4×C43C2×#4111yescharacteristic
314C2×C4×C43H(5,𝔽2)11yescharacteristic
315C2×C4×C432−1+411yescharacteristic
316C2×Dic43—22no—
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—
328Dic86—22no—
329Dic86—22no—
330Dic86—41no—
331Dic86—41no—
332C43⋊C8—22no—
333C43⋊C8—41no—
334C43⋊C8—41no—
335C43⋊C8—41no—
336#24138—431nomaximal, Sylow
337C22×C43—22no—
338C22×C43—22no—
339C22×C43—22no—
340C22×C43—41no—
341C22×C43—41no—
342C22×C43—41no—
343C22×C43—41no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—41no—
347C22×C43—42no—
348C22×C43—41no—
349C22×C43—42no—
350C22×C43—41no—
351C22×C43—42no—
352C22×C43—41no—
353C22×C43—41no—
354C22×C43—81no—
355C22×C43—81no—
356C22×C43—81no—
357C22×C43—81no—
358C22×C43C2×#12011yescharacteristic
359C22×C43#54611yescharacteristic
360C22×C43#54711yescharacteristic
361C22×C43C2×#13711yescharacteristic
362C22×C43#57511yescharacteristic
363C22×C43#57611yescharacteristic
364C22×C43#57711yescharacteristic
365C4×C43—22no—
366C4×C43—22no—
367C4×C43—41no—
368C4×C43—41no—
369C4×C43—42no—
370C4×C43—42no—
371C4×C43—42no—
372C4×C43#52511yescharacteristic
373C4×C43#53711yescharacteristic
374C4×C43#54811yescharacteristic
375C4×C43#55011yescharacteristic
376Dic43—42no—
377Dic43—81no—
378Dic43—81no—
379Dic43—81no—
380C2×#553D4311yescharacteristic
381C2×#479—431no—
382C2×#440—431no—
383#2538—431no—
384#2034—431no—
385#2033—431no—
386#2000—431no—
387#2000—431no—
388#1992—431no—
389#1955—431no—
390#1873—431no—
391#1872—431no—
392#1854—431no—
393#1852—431no—
394#1802—431no—
395C2×C43—42no—
396C2×C43—81no—
397C2×C43—82no—
398C2×C43#240711yescharacteristic
399C2×C43#300711yescharacteristic
400C2×C43#301211yescharacteristic
401C2×C43#330911yescharacteristic
402C2×C43#332011yescharacteristic
403C2×C43#334611yescharacteristic
404C2×C43#335011yescharacteristic
405C22×SD16—431no—
406#553—24no—
407#553—24no—
408C2×#126—21no—
409C2×#125C2×D4311yescharacteristic
410C2×#123—21no—
411C2×C22⋊Q8—431no—
412C2×C22⋊Q8—431no—
413C2×#121—21no—
414C2×#121C2×D4311yescharacteristic
415C2×#121C2×D4311yescharacteristic
416C2×C4×Q8—431no—
417C2×C4×D4—21no—
418C2×C4×D4C2×D4311yescharacteristic
419C2×C4×D4C2×D4311yescharacteristic
420C2×#117C2×D4311yescharacteristic
421C22×C4⋊C4C2×D4311yescharacteristic
422#479—864no—
423#440—864no—
424C2×#107—431no—
425C2×#107—431no—
426C2×#106—431no—
427C2×C4⋊C8—431no—
428C2×#103—431no—
429C2×#103—431no—
430C2×#103—431no—
431C2×#102—431no—
432C2×#102—431no—
433C2×#102—431no—
434C2×C22⋊C8—431no—
435C2×C22⋊C8—431no—
436C2×C22⋊C8—431no—
437C2×C22⋊C8—431no—
438C2×#97—431no—
439#396—861no—
440#396—861no—
441#390—861no—
442#389—861no—
443#384—431no—
444#380—431no—
445#380—431no—
446#340—431no—
447#340—431no—
448#340—431no—
449#340—431no—
450#340—431no—
451#340—431no—
452C43#2413811yescharacteristic, complemented, Sylow
453C22×Q8—431no—
454C22×D4—21no—
455C22×D4—21no—
456C22×D4C22⋊D4311yescharacteristic
457C22×D4C22×D4311yescharacteristic
458C23×C4—21no—
459C23×C4—21no—
460C23×C4C22×D4311yescharacteristic
461C23×C4C22×D4311yescharacteristic
462C2×SD16—862no—
463C2×SD16—862no—
464C2×SD16—862no—
465C22×C8—431no—
466C22×C8—431no—
467C22×C8—431no—
468C22×C8—431no—
469#126—28no—
470#125—22no—
471#125C22⋊D4314yes—
472#123—28no—
473C22⋊Q8—862no—
474C22⋊Q8—862no—
475C22⋊Q8—1721no—
476C22⋊Q8—1721no—
477#121—28no—
478#121—22no—
479#121—22no—
480#121—22no—
481#121—22no—
482C4×Q8—862no—
483C4×Q8—862no—
484C4×D4—28no—
485C4×D4—22no—
486C4×D4—22no—
487C4×D4—22no—
488C4×D4C22⋊D4314yes—
489#117—22no—
490#117—22no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—431no—
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⋊C4—861no—
504C2×C4⋊C4C22⋊D4311yescharacteristic
505C2×C4⋊C4C22×D4311yescharacteristic
506C2×C4⋊C4C22×D4311yescharacteristic
507C2×C4⋊C4C22×D4311yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4—861no—
515C2×C22⋊C4—861no—
516C2×C22⋊C4C22⋊D4311yescharacteristic
517C2×C22⋊C4C22⋊D4311yescharacteristic
518C2×C42—21no—
519C2×C42—861no—
520C2×C42C22×D4311yescharacteristic
521#107—862no—
522#107—862no—
523#106—862no—
524C4⋊C8—862no—
525#103—862no—
526#103—862no—
527#103—862no—
528#102—862no—
529#102—1721no—
530#102—1721no—
531C22⋊C8—862no—
532C22⋊C8—862no—
533C22⋊C8—1721no—
534C22⋊C8—1721no—
535#97—862no—
536#95—861no—
537#95—861no—
538C24—21no—
539C24C2×C22⋊D4311yescharacteristic
540C24C2×C22⋊D4311yescharacteristic
541C2×Q8—432no—
542C2×Q8—861no—
543C2×Q8—861no—
544C2×Q8—861no—
545C2×Q8—861no—
546C2×Q8—861no—
547C2×D4—24no—
548C2×D4—22no—
549C2×D4—24no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—41no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—81no—
560C2×D4—81no—
561C2×D4C2×C22⋊D4312yes—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—24no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—24no—
579C22×C4—81no—
580C22×C4—81no—
581C22×C4—81no—
582C22×C4—81no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—861no—
587C22×C4C2×C22⋊D4311yescharacteristic
588C22×C4C2×C22⋊D4311yescharacteristic
589C22×C4C2×C22⋊D4311yescharacteristic
590C22×C4C2×C22⋊D4311yescharacteristic
591C22×C4C23×D4311yescharacteristic
592SD16—868no—
593C2×C8—432no—
594C2×C8—861no—
595C2×C8—861no—
596C2×C8—861no—
597C2×C8—861no—
598C2×C8—861no—
599C2×C8—861no—
600C2×C8—861no—
601C2×C8—861no—
602C2×C8—861no—
603C2×C8—861no—
604C2×C8—861no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—22no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—861no—
613C4⋊C4—861no—
614C4⋊C4—861no—
615C4⋊C4—861no—
616C4⋊C4—861no—
617C4⋊C4—861no—
618C4⋊C4—3441no—
619C4⋊C4—1722no—
620C4⋊C4—1722no—
621C4⋊C4—1722no—
622C4⋊C4—1722no—
623C4⋊C4C2×C22⋊D4312yes—
624C4⋊C4C2×C22⋊D4312yes—
625C4⋊C4C2×C22⋊D4312yes—
626C22⋊C4—24no—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—3441no—
633C22⋊C4—3441no—
634C22⋊C4—1722no—
635C22⋊C4—1722no—
636C42—24no—
637C42—1722no—
638C42C2×C22⋊D4312yes—
639C42C2×C22⋊D4312yes—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23#1306335512yes—
661C23C22×C22⋊D4311yescharacteristic
662Q8—862no—
663Q8—862no—
664Q8—1721no—
665Q8—1721no—
666D4—22no—
667D4—22no—
668D4—44no—
669D4—48no—
670D4—41no—
671D4—41no—
672D4—84no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—84no—
701C2×C4—84no—
702C2×C4—862no—
703C2×C4—1721no—
704C2×C4—1721no—
705C2×C4—1721no—
706C2×C4—1721no—
707C2×C4—1721no—
708C2×C4—1721no—
709C2×C4—1721no—
710C2×C4—1721no—
711C2×C4—1721no—
712C2×C4—1721no—
713C2×C4—1721no—
714C2×C4#1306329412yes—
715C2×C4#1306329412yes—
716C2×C4C22×C22⋊D4311yescharacteristic
717C2×C4C22×C22⋊D4311yescharacteristic
718C2×C4#41×D4311yescharacteristic
719C2×C4#41×D4311yescharacteristic
720C2×C4#1306337111yescharacteristic
721C2×C4#1306337211yescharacteristic
722C8—862no—
723C8—1721no—
724C8—1721no—
725C8—1721no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—42no—
739C22—41no—
740C22—42no—
741C22—42no—
742C22—41no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22C2×#1306329411yescharacteristic
748C22#1458353711yescharacteristic
749C22#1458354811yescharacteristic
750C22C2×#1306335511yescharacteristic
751C22#1458369711yescharacteristic
752C22#1458370211yescharacteristic
753C22#1458371011yescharacteristic
754C4—22no—
755C4—22no—
756C4—41no—
757C4—41no—
758C4—42no—
759C4—42no—
760C4—42no—
761C4—3441no—
762C4—3441no—
763C4—3441no—
764C4—1722no—
765C4#1458340611yescharacteristic
766C4#1458347711yescharacteristic
767C4#1458355611yescharacteristic
768C4#1458356811yescharacteristic
769C2—42no—
770C2—81no—
771C2—82no—
772C2#1913793411yescharacteristic
773C2#1914385511yescharacteristic
774C2#1914389911yescharacteristic
775C2#1914659511yescharacteristic
776C2#1914676011yescharacteristic
777C2#1914708011yescharacteristic
778C2#1914713411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#553C2
socleC23×C43C22×D4
hypercenterC2×#553D43
hypocenterC43#24138
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#14583203C2semidirect
2. C2×#14582999C2semidirect
3. #19139517C2semidirect
4. #19135781C2semidirect
5. #19135774C2semidirect
6. #19135598C2semidirect
7. #19135598C2semidirect
8. #19135565C2semidirect
9. #19135394C2semidirect
10. #19134907C2semidirect
11. #19134902C2semidirect
12. #19134794C2semidirect
13. #19134783C2semidirect
14. #19134595C2semidirect
452. C43#24138semidirect

Maximal subgroups

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

subgroupindex
C2×#145832032
C2×#145829992
#191395172
#191357812
#191357742
#191355982
#191355652
#191353942
#191349072
#191349022
#191347942
#191347832
#191345952
C2×C43×#5532
#2413843