Finite Group Databasebeta

← #25116960

Subgroups — #25116960

Order 11008.

1090 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583059C211yesmaximal, characteristic
2C2×#14583004C211yesmaximal, characteristic, complemented
3C2×#14582893C211yesmaximal, characteristic
4#19137435C211yesmaximal, characteristic
5#19135479C211yesmaximal, characteristic, complemented
6#19135291C211yesmaximal, characteristic, complemented
7#19135222C211yesmaximal, characteristic, complemented
8#19135019C211yesmaximal, characteristic, complemented
9#19134950C211yesmaximal, characteristic, complemented
10#19134939C211yesmaximal, characteristic, complemented
11#19134848C211yesmaximal, characteristic, complemented
12#19134794C211yesmaximal, characteristic, complemented
13#19134428C211yesmaximal, characteristic, complemented
14#19134373C211yesmaximal, characteristic, complemented
15C43×#2362C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621885C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21C2×C4×Dic86C2211yescharacteristic
22#14583059C418yescomplemented
23#14583004—24no—
24C2×#13063258C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26#14582893—24no—
27C2×#13063249C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36C2×#13063236C2211yescharacteristic
37C2×#13063236C2211yescharacteristic
38#14582801C2211yescharacteristic
39#14582801C2211yescharacteristic
40#14582799—21no—
41#14582799—21no—
42#14582759C2211yescharacteristic
43#14582758—21no—
44#14582746—21no—
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582654C2211yescharacteristic
51C2×C22⋊Q8×C43C2211yescharacteristic
52C2×C4×Q8×C43C2211yescharacteristic
53C2×#117×C43C2211yescharacteristic
54C43×#391C2211yescharacteristic
55C43×#389C2211yescharacteristic
56C43×#388—21no—
57C43×#388—21no—
58C43×#387—21no—
59C4×C4⋊C4×C43—21no—
60C4×C4⋊C4×C43C2211yescharacteristic
61C4×C22⋊C4×C43C2211yescharacteristic
62C2×#10621898—22no—
63C2×#10621898—22no—
64C2×#10621898—22no—
65C2×#10621898—41no—
66C2×#10621898—41no—
67C2×#10621898C2×C414yes—
68C22×Dic86C2311yescharacteristic
69C22×D172C2311yescharacteristic
70C22×C22⋊D43—21no—
71C22×C4×D43—21no—
72C2×#10621885—22no—
73C2×#10621885—22no—
74C2×#10621885C2×C414yes—
75C2×#10621884—41no—
76C2×#10621884—41no—
77C2×#10621884C2×C414yes—
78C22×C43⋊C8—22no—
79C22×C43⋊C8—22no—
80C22×C43⋊C8—41no—
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85C4×Dic86—22no—
86C4×Dic86—22no—
87C4×Dic86—41no—
88C4×Dic86—41no—
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×C22⋊Dic43—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×C4×Dic43—21no—
99C2×C4×Dic43—21no—
100#13063258—41no—
101#13063256—22no—
102#13063249—22no—
103#13063249—41no—
104#13063248—22no—
105#13063248C2×C414yes—
106#13063248D414yes—
107#13063245—22no—
108#13063245—22no—
109#13063245C2×C414yes—
110C22⋊(C43⋊C8)C2×C414yes—
111#13063236—22no—
112#13063236—41no—
113C43⋊#95—21no—
114C22×Q8×C43C2311yescharacteristic
115C23×C4×C43C2311yescharacteristic
116C22⋊Q8×C43—22no—
117C22⋊Q8×C43C2×C414yes—
118C4×Q8×C43—22no—
119C4×Q8×C43—41no—
120#117×C43—22no—
121#117×C43—41no—
122C2×C4⋊C4×C43—21no—
123C2×C4⋊C4×C43—21no—
124C2×C4⋊C4×C43—21no—
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43D411yescharacteristic
131C2×C22⋊C4×C43D411yescharacteristic
132C2×C42×C43—21no—
133C2×C42×C43—21no—
134C2×C42×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C2×C42×C43C2311yescharacteristic
137#95×C43—21no—
138#95×C43—21no—
139#95×C43—21no—
140#95×C43—21no—
141#95×C43D411yescharacteristic
142#95×C43D411yescharacteristic
143C24×C43C2×D411yescharacteristic
144C23×D43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43C22×C412yes—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43C22×C412yes—
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43#4112yes—
166C22×C4×C43C2411yescharacteristic
167C2×C22⋊D43—24no—
168C2×C22⋊D43—42no—
169C2×C22⋊D43—42no—
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43—21no—
173#10621898—28no—
174#10621898—44no—
175#10621898—44no—
176#10621898—44no—
177C2×D172—21no—
178C2×D172—21no—
179C2×D172—21no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172C22×C412yes—
183C2×C4×D43—24no—
184C2×C4×D43—42no—
185C2×C4×D43—42no—
186C2×Dic86—21no—
187C2×Dic86—21no—
188C2×Dic86—21no—
189C2×Dic86C22×C412yes—
190C2×Dic86C2×D412yes—
191C2×Dic86#4112yes—
192C4⋊C4×C43—24no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—42no—
198C4⋊C4×C43—42no—
199C4⋊C4×C43C22×C412yes—
200C4⋊C4×C43C2×D412yes—
201C22⋊C4×C43—24no—
202C22⋊C4×C43—41no—
203C22⋊C4×C43—41no—
204C22⋊C4×C43—42no—
205C42×C43—21no—
206C42×C43—21no—
207C42×C43—21no—
208C42×C43—21no—
209C42×C43—42no—
210C42×C43—42no—
211C42×C43—42no—
212C22⋊Dic43—81no—
213#10621885—28no—
214#10621884—44no—
215(C2×D43)⋊C4—42no—
216(C2×D43)⋊C4—42no—
217(C2×D43)⋊C4—81no—
218(C2×D43)⋊C4—81no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223Dic43⋊C4—42no—
224Dic43⋊C4—42no—
225C4×Dic43—42no—
226C4×Dic43—42no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—44no—
237C2×C43⋊C8C22×C412yes—
238C2×C43⋊C8C22×C412yes—
239C2×C43⋊C8C2×D412yes—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43C4×D412yes—
247C23×C43C22×D411yescharacteristic
248C22×D43—22no—
249C22×D43—41no—
250C22×D43—41no—
251C22×D43—41no—
252C22×D43—41no—
253C22×D43—41no—
254C22×D43—41no—
255Q8×C43—22no—
256Q8×C43—22no—
257Q8×C43—41no—
258Q8×C43—41no—
259C2×C4×C43—21no—
260C2×C4×C43—21no—
261C2×C4×C43—22no—
262C2×C4×C43—22no—
263C2×C4×C43—22no—
264C2×C4×C43—22no—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—22no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43C4×D412yes—
290C2×C4×C43C23×C411yescharacteristic
291C2×C4×C43C22×D411yescharacteristic
292C2×C4×C43C2×#4111yescharacteristic
293C2×C4×C43C2×#4111yescharacteristic
294C2×C4×C43H(5,𝔽2)11yescharacteristic
295C2×C4×C43H(5,𝔽2)11yescharacteristic
296C22⋊D43—48no—
297C2×Dic43—22no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306D172—22no—
307D172—22no—
308D172—41no—
309D172—41no—
310C4×D43—48no—
311Dic86—22no—
312Dic86—22no—
313Dic86—22no—
314Dic86C4×D414yes—
315C43⋊C8—22no—
316C43⋊C8—22no—
317C43⋊C8—22no—
318C43⋊C8—41no—
319#22861—431nomaximal, Sylow
320C22×C43—22no—
321C22×C43—22no—
322C22×C43—22no—
323C22×C43—41no—
324C22×C43—41no—
325C22×C43—41no—
326C22×C43—41no—
327C22×C43C2×C4×D411yescharacteristic
328C22×C43D4211yescharacteristic
329C22×C43#54611yescharacteristic
330C22×C43#57511yescharacteristic
331C22×C43#57511yescharacteristic
332C22×C43#57711yescharacteristic
333C22×C43#57811yescharacteristic
334C2×D43—42no—
335C2×D43—42no—
336C2×D43—42no—
337C2×D43—81no—
338C2×D43—81no—
339C2×D43—81no—
340C2×D43—81no—
341C4×C43—22no—
342C4×C43—42no—
343C4×C43—42no—
344C4×C43—41no—
345C4×C43—42no—
346C4×C43—41no—
347C4×C43—41no—
348C4×C43—41no—
349C4×C43—81no—
350C4×C43C2×C4×D411yescharacteristic
351C4×C43#51811yescharacteristic
352C4×C43#54611yescharacteristic
353C4×C43#55111yescharacteristic
354Dic43—24no—
355Dic43—81no—
356Dic43—81no—
357C2×#452—431no—
358C2×#441—431no—
359C2×#416—431no—
360#2362D4311yescharacteristic, complemented
361#2341—431no—
362#1973—431no—
363#1936—431no—
364#1926—431no—
365#1892—431no—
366#1880—431no—
367#1878—431no—
368#1863—431no—
369#1854—431no—
370#1763—431no—
371#1752—431no—
372C2×C43—42no—
373C2×C43#235811yescharacteristic
374C2×C43#294311yescharacteristic
375C2×C43#294711yescharacteristic
376C2×C43#326911yescharacteristic
377C2×C43#327111yescharacteristic
378C2×C43#331311yescharacteristic
379C2×C43#331711yescharacteristic
380D43—82no—
381C22×#41—431no—
382C22×Q16—431no—
383C22×SD16—431no—
384C23×C8—431no—
385C2×C22⋊Q8C2×D4311yescharacteristic
386C2×C4×Q8—431no—
387C2×C4×Q8—431no—
388C2×C4×Q8C2×D4311yescharacteristic
389C2×#117C2×D4311yescharacteristic
390#452—438no—
391#441—864no—
392C2×#107—431no—
393C2×#106—431no—
394#416—864no—
395C2×#103—431no—
396C2×#103—431no—
397C2×#103—431no—
398C2×#103—431no—
399C2×#103—431no—
400C2×#102—431no—
401C2×#102—431no—
402C2×#102—431no—
403C2×C22⋊C8—431no—
404C2×#97—431no—
405C2×#97—431no—
406#391C2×D4311yescharacteristic
407#390—431no—
408#390—431no—
409#390—861no—
410#390—861no—
411#389C2×D4311yescharacteristic
412#388—21no—
413#388—21no—
414#387—21no—
415#380—431no—
416#380—861no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4C2×D4311yescharacteristic
419C4×C22⋊C4—861no—
420C4×C22⋊C4C2×D4311yescharacteristic
421#340—431no—
422#340—431no—
423#340—431no—
424#340—431no—
425#336—431no—
426#336—431no—
427C43#2286111yescharacteristic, complemented, Sylow
428C2×#41—434no—
429C2×#41—862no—
430C2×#41—862no—
431C2×#41—862no—
432C2×#41—1721no—
433C2×#41—1721no—
434C22×Q8—431no—
435C22×Q8C22×D4311yescharacteristic
436C22×D4—431no—
437C22×D4—861no—
438C23×C4—861no—
439C23×C4C22×D4311yescharacteristic
440C2×Q16—434no—
441C2×Q16—862no—
442C2×Q16—862no—
443C2×SD16—434no—
444C2×SD16—1721no—
445C2×SD16—1721no—
446C22×C8—431no—
447C22×C8—431no—
448C22×C8—431no—
449C22×C8—431no—
450C22×C8—862no—
451C22×C8—862no—
452C22×C8—1721no—
453C22⋊Q8—22no—
454C22⋊Q8C4×D4314yes—
455C4×Q8—22no—
456C4×Q8—41no—
457C4×Q8—862no—
458C4×Q8—862no—
459C4×Q8—1721no—
460C4×Q8—1721no—
461#117—22no—
462#117—41no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—431no—
467C2×C4⋊C4—431no—
468C2×C4⋊C4—861no—
469C2×C4⋊C4—861no—
470C2×C4⋊C4C22×D4311yescharacteristic
471C2×C4⋊C4C22×D4311yescharacteristic
472C2×C4⋊C4C22×D4311yescharacteristic
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—861no—
476C2×C22⋊C4—861no—
477C2×C22⋊C4—861no—
478C2×C22⋊C4—861no—
479C2×C22⋊C4—861no—
480C2×C22⋊C4C22⋊D4311yescharacteristic
481C2×C22⋊C4C22⋊D4311yescharacteristic
482C2×C42—21no—
483C2×C42—21no—
484C2×C42—21no—
485C2×C42—861no—
486C2×C42—861no—
487C2×C42C22×D4311yescharacteristic
488C2×C42C22×D4311yescharacteristic
489#107—1721no—
490#106—862no—
491#103—434no—
492#103—434no—
493#103—862no—
494#103—862no—
495#103—1721no—
496#102—434no—
497#102—862no—
498#102—862no—
499C22⋊C8—434no—
500#97—862no—
501#97—1721no—
502#95—21no—
503#95—21no—
504#95—21no—
505#95—21no—
506#95—861no—
507#95C22⋊D4311yescharacteristic
508#95C22⋊D4311yescharacteristic
509C24—861no—
510C24C2×C22⋊D4311yescharacteristic
511#41—868no—
512#41—1724no—
513#41—1724no—
514#41—1724no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—432no—
521C2×Q8—432no—
522C2×Q8—432no—
523C2×Q8—861no—
524C2×Q8—861no—
525C2×Q8—861no—
526C2×Q8C2×C4×D4312yes—
527C2×D4—432no—
528C2×D4—864no—
529C2×D4—861no—
530C2×D4—861no—
531C2×D4—861no—
532C2×D4—861no—
533C2×D4—861no—
534C2×D4—1722no—
535C2×D4—1722no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—861no—
545C22×C4—864no—
546C22×C4—861no—
547C22×C4—861no—
548C22×C4—1722no—
549C22×C4—1722no—
550C22×C4C2×C4×D4312yes—
551C22×C4#1062189812yes—
552C22×C4C2×C22⋊D4311yescharacteristic
553C22×C4C2×C22⋊D4311yescharacteristic
554C22×C4C2×C22⋊D4311yescharacteristic
555C22×C4C2×C22⋊D4311yescharacteristic
556C22×C4C2×C22⋊D4311yescharacteristic
557C22×C4C23×D4311yescharacteristic
558Q16—868no—
559SD16—1724no—
560C2×C8—432no—
561C2×C8—432no—
562C2×C8—432no—
563C2×C8—861no—
564C2×C8—861no—
565C2×C8—861no—
566C2×C8—861no—
567C2×C8—861no—
568C2×C8—861no—
569C2×C8—861no—
570C2×C8—861no—
571C2×C8—861no—
572C2×C8—1724no—
573C4⋊C4—24no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—861no—
581C4⋊C4—861no—
582C4⋊C4—861no—
583C4⋊C4—861no—
584C4⋊C4—1722no—
585C4⋊C4—1722no—
586C4⋊C4C2×C4×D4312yes—
587C4⋊C4D4×D4312yes—
588C22⋊C4—24no—
589C22⋊C4—41no—
590C22⋊C4—41no—
591C22⋊C4—42no—
592C22⋊C4—3441no—
593C22⋊C4—3441no—
594C22⋊C4—3441no—
595C22⋊C4—1722no—
596C22⋊C4—1722no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—21no—
601C42—42no—
602C42—42no—
603C42—42no—
604C42—1722no—
605C42—1722no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—862no—
613C23—1721no—
614C23—1721no—
615C23—1721no—
616C23—1721no—
617C23—1721no—
618C23—1721no—
619C23C4×C22⋊D4312yes—
620C23C22×C22⋊D4311yescharacteristic
621Q8—22no—
622Q8—22no—
623Q8—41no—
624Q8—41no—
625Q8—434no—
626Q8—862no—
627Q8—862no—
628Q8—862no—
629D4—862no—
630D4—862no—
631D4—1728no—
632D4—1721no—
633D4—1721no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—862no—
665C2×C4—862no—
666C2×C4—862no—
667C2×C4—1728no—
668C2×C4—1721no—
669C2×C4—1721no—
670C2×C4—1721no—
671C2×C4—1721no—
672C2×C4—1721no—
673C2×C4—1721no—
674C2×C4C4×C22⋊D4312yes—
675C2×C4C22×C4×D4311yescharacteristic
676C2×C4C2×D4×D4311yescharacteristic
677C2×C4#41×D4311yescharacteristic
678C2×C4C2×#1062189811yescharacteristic
679C2×C4#1306337011yescharacteristic
680C2×C4#1306337111yescharacteristic
681C8—862no—
682C8—862no—
683C8—862no—
684C8—1721no—
685C22—22no—
686C22—22no—
687C22—22no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—3441no—
693C22—3441no—
694C22—3441no—
695C22—3441no—
696C22—1722no—
697C22—1722no—
698C22—1722no—
699C22C2×C4×C22⋊D4311yescharacteristic
700C22D4×C22⋊D4311yescharacteristic
701C22#1458353711yescharacteristic
702C22#1458369711yescharacteristic
703C22#1458369711yescharacteristic
704C22#1458370711yescharacteristic
705C22#1458371411yescharacteristic
706C4—22no—
707C4—42no—
708C4—41no—
709C4—41no—
710C4—42no—
711C4—41no—
712C4—41no—
713C4—42no—
714C4—81no—
715C4—864no—
716C4—3441no—
717C4—3441no—
718C4C4×D4×D4311yescharacteristic
719C4#1458337111yescharacteristic
720C4#1458354511yescharacteristic
721C4#1458357811yescharacteristic
722C2—42no—
723C2—3442no—
724C2#1913757211yescharacteristic
725C2#1914339311yescharacteristic
726C2#1914343811yescharacteristic
727C2#1914614611yescharacteristic
728C2#1914618111yescharacteristic
729C2#1914665511yescharacteristic
730C2#1914671511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2362C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenter#2362D43
hypocenterC43#22861
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2362

Complements

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

NH ≅ G/Ntype
2. C2×#14583004C2semidirect
5. #19135479C2semidirect
6. #19135291C2semidirect
7. #19135222C2semidirect
8. #19135019C2semidirect
9. #19134950C2semidirect
10. #19134939C2semidirect
11. #19134848C2semidirect
12. #19134794C2semidirect
13. #19134428C2semidirect
14. #19134373C2semidirect
15. C43×#2362C2semidirect
22. #14583059C4semidirect
360. #2362D43semidirect
427. C43#22861semidirect

Maximal subgroups

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

subgroupindex
C2×#145830592
C2×#145830042
C2×#145828932
#191374352
#191354792
#191352912
#191352222
#191350192
#191349502
#191349392
#191348482
#191347942
#191344282
#191343732
C43×#23622
#2286143