Finite Group Databasebeta

← #25116885

Subgroups — #25116885

Order 11008.

1118 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583059C211yesmaximal, characteristic
2C2×#14582997C211yesmaximal, characteristic, complemented
3C2×#14582893C211yesmaximal, characteristic
4#19137426C211yesmaximal, characteristic
5#19135465C211yesmaximal, characteristic, complemented
6#19135284C211yesmaximal, characteristic, complemented
7#19135236C211yesmaximal, characteristic, complemented
8#19135019C211yesmaximal, characteristic, complemented
9#19134936C211yesmaximal, characteristic, complemented
10#19134932C211yesmaximal, characteristic, complemented
11#19134855C211yesmaximal, characteristic, complemented
12#19134794C211yesmaximal, characteristic, complemented
13#19134423C211yesmaximal, characteristic, complemented
14#19134373C211yesmaximal, characteristic, complemented
15C43×#2362C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621885C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×C4×D172C2211yescharacteristic
22#14583059C418yescomplemented
23#14582997—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#14582805C2211yescharacteristic
39#14582805C2211yescharacteristic
40#14582775—21no—
41#14582775—21no—
42#14582761—21no—
43#14582759C2211yescharacteristic
44#95×D43—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—
72C22×C4×D43—21no—
73C22×C4×D43—21no—
74C2×#10621885—41no—
75C2×#10621885—41no—
76C2×#10621885C2×C414yescomplemented
77C2×#10621884—22no—
78C2×#10621884—22no—
79C2×#10621884C2×C414yes—
80C22×C43⋊C8—22no—
81C22×C43⋊C8—22no—
82C22×C43⋊C8—41no—
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85C22×C43⋊C8C2311yescharacteristic
86C22×C43⋊C8C2311yescharacteristic
87C4×D172—22no—
88C4×D172—22no—
89C4×D172—41no—
90C4×D172—41no—
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C22⋊Dic43—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96#13063258—22no—
97#13063256—41no—
98#13063249—22no—
99#13063249—41no—
100#13063248—22no—
101#13063248—22no—
102#13063248C2×C414yescomplemented
103#13063245—22no—
104#13063245C2×C414yes—
105#13063245D414yes—
106C22⋊(C43⋊C8)C2×C414yescomplemented
107#13063236—22no—
108#13063236—41no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C22×Q8×C43C2311yescharacteristic
115C23×C4×C43C2311yescharacteristic
116C22⋊Q8×C43—22no—
117C22⋊Q8×C43C2×C414yescomplemented
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×D172C22×C412yes—
181C2×D172C2×D412yes—
182C2×D172#4112yes—
183C2×C4×D43—24no—
184C2×C4×D43—42no—
185C2×C4×D43—42no—
186C2×C4×D43—42no—
187C2×C4×D43—42no—
188C2×C4×D43—42no—
189C2×C4×D43—42no—
190C2×C4×D43—81no—
191C2×C4×D43—81no—
192C2×Dic86—21no—
193C2×Dic86—21no—
194C2×Dic86—21no—
195C2×Dic86—21no—
196C2×Dic86—21no—
197C2×Dic86C22×C412yes—
198C4⋊C4×C43—24no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—42no—
204C4⋊C4×C43—42no—
205C4⋊C4×C43C22×C412yes—
206C4⋊C4×C43C2×D412yes—
207C22⋊C4×C43—24no—
208C22⋊C4×C43—41no—
209C22⋊C4×C43—41no—
210C22⋊C4×C43—42no—
211C42×C43—21no—
212C42×C43—21no—
213C42×C43—21no—
214C42×C43—21no—
215C42×C43—42no—
216C42×C43—42no—
217C42×C43—42no—
218C22⋊Dic43—81no—
219#10621885—44no—
220#10621884—28no—
221(C2×D43)⋊C4—42no—
222(C2×D43)⋊C4—42no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
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—22no—
250C22×D43—22no—
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—41no—
299C2×Dic43—41no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306D172—22no—
307D172—22no—
308D172—22no—
309D172C4×D414yes—
310C4×D43—48no—
311C4×D43—84no—
312C4×D43—84no—
313Dic86—22no—
314Dic86—22no—
315Dic86—41no—
316Dic86—41no—
317C43⋊C8—22no—
318C43⋊C8—22no—
319C43⋊C8—22no—
320C43⋊C8—41no—
321#22856—431nomaximal, Sylow
322C22×C43—22no—
323C22×C43—22no—
324C22×C43—22no—
325C22×C43—41no—
326C22×C43—41no—
327C22×C43—41no—
328C22×C43—41no—
329C22×C43C2×C4×D411yescharacteristic
330C22×C43D4211yescharacteristic
331C22×C43#54611yescharacteristic
332C22×C43#57511yescharacteristic
333C22×C43#57511yescharacteristic
334C22×C43#57711yescharacteristic
335C22×C43#57811yescharacteristic
336C2×D43—24no—
337C2×D43—42no—
338C2×D43—42no—
339C2×D43—42no—
340C2×D43—42no—
341C2×D43—42no—
342C2×D43—42no—
343C4×C43—22no—
344C4×C43—42no—
345C4×C43—42no—
346C4×C43—41no—
347C4×C43—42no—
348C4×C43—41no—
349C4×C43—41no—
350C4×C43—41no—
351C4×C43—81no—
352C4×C43C2×C4×D411yescharacteristic
353C4×C43#51811yescharacteristic
354C4×C43#54611yescharacteristic
355C4×C43#55111yescharacteristic
356Dic43—42no—
357Dic43—81no—
358Dic43—81no—
359C2×#452—431no—
360C2×#440—431no—
361C2×#416—431no—
362#2362D4311yescharacteristic, complemented
363#2339—431no—
364#1971—431no—
365#1935—431no—
366#1928—431no—
367#1892—431no—
368#1878—431no—
369#1877—431no—
370#1864—431no—
371#1854—431no—
372#1762—431no—
373#1752—431no—
374C2×C43—42no—
375C2×C43#235811yescharacteristic
376C2×C43#294311yescharacteristic
377C2×C43#294711yescharacteristic
378C2×C43#326711yescharacteristic
379C2×C43#326911yescharacteristic
380C2×C43#331111yescharacteristic
381C2×C43#331511yescharacteristic
382D43—44no—
383C22×#41—431no—
384C22×Q16—431no—
385C22×SD16—431no—
386C23×C8—431no—
387C2×C22⋊Q8C2×D4311yescharacteristic
388C2×C4×Q8C2×D4311yescharacteristic
389C2×C4×D4—431no—
390C2×C4×D4—431no—
391C2×#117C2×D4311yescharacteristic
392#452—438no—
393#440—864no—
394C2×#107—431no—
395C2×#106—431no—
396#416—864no—
397C2×#103—431no—
398C2×#103—431no—
399C2×#103—431no—
400C2×#103—431no—
401C2×#103—431no—
402C2×#102—431no—
403C2×#102—431no—
404C2×#102—431no—
405C2×C22⋊C8—431no—
406C2×#97—431no—
407C2×#97—431no—
408#391—431no—
409#391—431no—
410#391C2×D4311yescharacteristic
411#389C2×D4311yescharacteristic
412#388—21no—
413#388—21no—
414#387—21no—
415#386—861no—
416#386—861no—
417#381—861no—
418#380—431no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4C2×D4311yescharacteristic
421C4×C22⋊C4C2×D4311yescharacteristic
422C2×#95—861no—
423#340—431no—
424#340—431no—
425#340—431no—
426#340—431no—
427#336—431no—
428#336—431no—
429C43#2285611yescharacteristic, complemented, Sylow
430C2×#41—434no—
431C2×#41—862no—
432C2×#41—862no—
433C2×#41—862no—
434C2×#41—1721no—
435C2×#41—1721no—
436C22×Q8—431no—
437C22×Q8C22×D4311yescharacteristic
438C22×D4—431no—
439C22×D4—861no—
440C23×C4—861no—
441C23×C4—861no—
442C23×C4—861no—
443C23×C4C22×D4311yescharacteristic
444C2×Q16—434no—
445C2×Q16—1721no—
446C2×Q16—1721no—
447C2×SD16—434no—
448C2×SD16—862no—
449C2×SD16—862no—
450C22×C8—431no—
451C22×C8—431no—
452C22×C8—431no—
453C22×C8—431no—
454C22×C8—862no—
455C22×C8—862no—
456C22×C8—1721no—
457C22⋊Q8—22no—
458C22⋊Q8C4×D4314yescomplemented
459C4×Q8—22no—
460C4×Q8—41no—
461C4×D4—862no—
462C4×D4—862no—
463C4×D4—1721no—
464C4×D4—1721no—
465#117—22no—
466#117—41no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—431no—
471C2×C4⋊C4—431no—
472C2×C4⋊C4C22×D4311yescharacteristic
473C2×C4⋊C4C22×D4311yescharacteristic
474C2×C4⋊C4C22×D4311yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
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×C42C22×D4311yescharacteristic
486C2×C42C22×D4311yescharacteristic
487#107—862no—
488#106—1721no—
489#103—434no—
490#103—862no—
491#103—862no—
492#103—862no—
493#103—1721no—
494#102—434no—
495#102—434no—
496#102—862no—
497C22⋊C8—434no—
498#97—862no—
499#97—1721no—
500#95—21no—
501#95—21no—
502#95—21no—
503#95—21no—
504#95—861no—
505#95—861no—
506#95—861no—
507#95—861no—
508#95—861no—
509#95C22⋊D4311yescharacteristic
510#95C22⋊D4311yescharacteristic
511C24—861no—
512C24C2×C22⋊D4311yescharacteristic
513#41—868no—
514#41—1724no—
515#41—1724no—
516#41—1724no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—432no—
523C2×Q8—861no—
524C2×Q8—861no—
525C2×Q8—861no—
526C2×Q8—861no—
527C2×Q8—861no—
528C2×Q8C2×C4×D4312yes—
529C2×D4—432no—
530C2×D4—432no—
531C2×D4—432no—
532C2×D4—864no—
533C2×D4—861no—
534C2×D4—861no—
535C2×D4—861no—
536C2×D4—1722no—
537C2×D4—1722no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—861no—
547C22×C4—864no—
548C22×C4—861no—
549C22×C4—861no—
550C22×C4—3441no—
551C22×C4—3441no—
552C22×C4—1722no—
553C22×C4—1722no—
554C22×C4—1722no—
555C22×C4—1722no—
556C22×C4—1722no—
557C22×C4—1722no—
558C22×C4C2×C4×D4312yes—
559C22×C4#1062189812yes—
560C22×C4C2×C22⋊D4311yescharacteristic
561C22×C4C2×C22⋊D4311yescharacteristic
562C22×C4C2×C22⋊D4311yescharacteristic
563C22×C4C2×C22⋊D4311yescharacteristic
564C22×C4C2×C22⋊D4311yescharacteristic
565C22×C4C23×D4311yescharacteristic
566Q16—1724no—
567SD16—868no—
568C2×C8—432no—
569C2×C8—432no—
570C2×C8—432no—
571C2×C8—861no—
572C2×C8—861no—
573C2×C8—861no—
574C2×C8—861no—
575C2×C8—861no—
576C2×C8—861no—
577C2×C8—861no—
578C2×C8—861no—
579C2×C8—861no—
580C2×C8—1724no—
581C4⋊C4—24no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—861no—
589C4⋊C4—861no—
590C4⋊C4—861no—
591C4⋊C4—861no—
592C4⋊C4C2×C4×D4312yes—
593C4⋊C4D4×D4312yes—
594C22⋊C4—24no—
595C22⋊C4—41no—
596C22⋊C4—41no—
597C22⋊C4—42no—
598C22⋊C4—3441no—
599C22⋊C4—1722no—
600C22⋊C4—1722no—
601C42—21no—
602C42—21no—
603C42—21no—
604C42—21no—
605C42—42no—
606C42—42no—
607C42—42no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—862no—
615C23—862no—
616C23—862no—
617C23—1721no—
618C23—1721no—
619C23—1721no—
620C23—1721no—
621C23C4×C22⋊D4312yes—
622C23C22×C22⋊D4311yescharacteristic
623Q8—22no—
624Q8—22no—
625Q8—41no—
626Q8—41no—
627Q8—862no—
628Q8—862no—
629Q8—1721no—
630Q8—1721no—
631D4—434no—
632D4—862no—
633D4—862no—
634D4—862no—
635D4—1728no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
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—21no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—862no—
667C2×C4—3444no—
668C2×C4—3444no—
669C2×C4—1728no—
670C2×C4—1721no—
671C2×C4—1721no—
672C2×C4—1721no—
673C2×C4—1721no—
674C2×C4—1721no—
675C2×C4—1721no—
676C2×C4—1721no—
677C2×C4—1721no—
678C2×C4C4×C22⋊D4312yes—
679C2×C4C22×C4×D4311yescharacteristic
680C2×C4C2×D4×D4311yescharacteristic
681C2×C4#41×D4311yescharacteristic
682C2×C4C2×#1062189811yescharacteristic
683C2×C4#1306337011yescharacteristic
684C2×C4#1306337111yescharacteristic
685C8—862no—
686C8—862no—
687C8—862no—
688C8—1721no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—864no—
697C22—1722no—
698C22—1722no—
699C22—1722no—
700C22—1722no—
701C22—1722no—
702C22—1722no—
703C22C2×C4×C22⋊D4311yescharacteristic
704C22D4×C22⋊D4311yescharacteristic
705C22#1458353711yescharacteristic
706C22#1458369711yescharacteristic
707C22#1458369711yescharacteristic
708C22#1458370711yescharacteristic
709C22#1458371411yescharacteristic
710C4—22no—
711C4—42no—
712C4—41no—
713C4—41no—
714C4—42no—
715C4—41no—
716C4—41no—
717C4—42no—
718C4—81no—
719C4—3441no—
720C4—3441no—
721C4—1722no—
722C4C4×D4×D4311yescharacteristic
723C4#1458337111yescharacteristic
724C4#1458354511yescharacteristic
725C4#1458357811yescharacteristic
726C2—42no—
727C2—1724no—
728C2#1913757211yescharacteristic
729C2#1914339311yescharacteristic
730C2#1914343811yescharacteristic
731C2#1914612111yescharacteristic
732C2#1914615111yescharacteristic
733C2#1914662511yescharacteristic
734C2#1914668511yescharacteristic
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#22856
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×#14582997C2semidirect
5. #19135465C2semidirect
6. #19135284C2semidirect
7. #19135236C2semidirect
8. #19135019C2semidirect
9. #19134936C2semidirect
10. #19134932C2semidirect
11. #19134855C2semidirect
12. #19134794C2semidirect
13. #19134423C2semidirect
14. #19134373C2semidirect
15. C43×#2362C2semidirect
22. #14583059C4semidirect
76. C2×#10621885C2×C4semidirect
102. #13063248C2×C4semidirect
106. C22⋊(C43⋊C8)C2×C4semidirect
117. C22⋊Q8×C43C2×C4semidirect
362. #2362D43semidirect
429. C43#22856semidirect
458. C22⋊Q8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830592
C2×#145829972
C2×#145828932
#191374262
#191354652
#191352842
#191352362
#191350192
#191349362
#191349322
#191348552
#191347942
#191344232
#191343732
C43×#23622
#2285643