Finite Group Databasebeta

← #25130619

Subgroups — #25130619

Order 11008.

1088 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×#14583589C211yesmaximal, characteristic
2C2×#14583206C211yesmaximal, characteristic, complemented
3C2×C4×#10621885C211yesmaximal, characteristic, complemented
4#19135798C211yesmaximal, characteristic, complemented
5#19135791C211yesmaximal, characteristic, complemented
6#19135603C211yesmaximal, characteristic, complemented
7#19135603C211yesmaximal, characteristic, complemented
8#19135559C211yesmaximal, characteristic, complemented
9#19135390C211yesmaximal, characteristic
10#19134908C211yesmaximal, characteristic, complemented
11#19134903C211yesmaximal, characteristic, complemented
12#19134792C211yesmaximal, characteristic, complemented
13#19134782C211yesmaximal, characteristic, complemented
14#19134607C211yesmaximal, characteristic, complemented
15C43×#2536C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic
17#14583589—24no—
18#14583589—24no—
19C2×#13063318—21no—
20C2×#13063317C2211yescharacteristic
21C2×#13063315—21no—
22C2×#13063306—21no—
23C2×#13063304C2211yescharacteristic
24C2×#13063304C2211yescharacteristic
25C2×C4×Dic86C2211yescharacteristic
26C2×#13063284C2211yescharacteristic
27C2×#13063281—21no—
28C22×C4⋊Dic43C2211yescharacteristic
29#14583206—24no—
30C4×#10621885—24no—
31C2×#13063258C2211yescharacteristic
32C2×#13063258C2211yescharacteristic
33C2×#13063256C2211yescharacteristic
34C2×C4⋊(C43⋊C8)C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063249C2211yescharacteristic
37C2×#13063249C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×#13063248C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×C22⋊(C43⋊C8)C2211yescharacteristic
44C2×C22⋊(C43⋊C8)C2211yescharacteristic
45C2×C4×C43⋊C8C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52C2×C22⋊Q8×C43C2211yescharacteristic
53C2×C22⋊Q8×C43C2211yescharacteristic
54C2×C4×Q8×C43C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C43×#398—21no—
57C43×#394—21no—
58C43×#388—21no—
59C43×#388—21no—
60C43×#382C2211yescharacteristic
61C43×#380C2211yescharacteristic
62C43×#380C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C23×Dic43—21no—
65C2×#10621885—22no—
66C2×#10621885—22no—
67C2×#10621885—22no—
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72#13063318—28no—
73#13063317—22no—
74#13063317D414yes—
75#13063315—28no—
76#13063306—28no—
77#13063304—22no—
78#13063304—22no—
79#13063304—22no—
80#13063304—22no—
81C4×Dic86—22no—
82C4×Dic86D414yes—
83#13063284—22no—
84#13063284—22no—
85#13063281—28no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43—22no—
88C2×C4⋊Dic43—22no—
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×C22⋊Dic43—21no—
98C2×C22⋊Dic43—21no—
99C2×C22⋊Dic43—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43—21no—
102#13063258—22no—
103#13063258—22no—
104#13063256—22no—
105C4⋊(C43⋊C8)—22no—
106#13063249—22no—
107#13063249—22no—
108#13063249—22no—
109#13063248—22no—
110#13063248—41no—
111#13063248—41no—
112C22⋊(C43⋊C8)—22no—
113C22⋊(C43⋊C8)—22no—
114C22⋊(C43⋊C8)—41no—
115C22⋊(C43⋊C8)—41no—
116C4×C43⋊C8—22no—
117C22×Q8×C43C2311yescharacteristic
118C22×D4×C43D411yescharacteristic
119C23×C4×C43C2311yescharacteristic
120C23×C4×C43C2311yescharacteristic
121C22⋊Q8×C43—22no—
122C22⋊Q8×C43—22no—
123C22⋊Q8×C43—41no—
124C22⋊Q8×C43—41no—
125C4×Q8×C43—22no—
126C4×Q8×C43—22no—
127C4×D4×C43—22no—
128C4×D4×C43—22no—
129C2×C4⋊C4×C43—21no—
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43D411yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C22⋊C4×C43—21no—
137C2×C22⋊C4×C43—21no—
138C2×C22⋊C4×C43—21no—
139C2×C22⋊C4×C43—21no—
140C2×C22⋊C4×C43D411yescharacteristic
141C2×C22⋊C4×C43D411yescharacteristic
142C2×C42×C43—21no—
143C2×C42×C43C2311yescharacteristic
144#95×C43—21no—
145#95×C43—21no—
146#95×C43—21no—
147#95×C43—21no—
148C24×C43C2×D411yescharacteristic
149C24×C43C2×D411yescharacteristic
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43#4112yes—
156C2×D4×C43—22no—
157C2×D4×C43—22no—
158C2×D4×C43—41no—
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×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2411yescharacteristic
180C22×Dic43—24no—
181C22×Dic43—21no—
182C22×Dic43—21no—
183C22×Dic43—21no—
184C22×Dic43—21no—
185C22×Dic43—42no—
186C22×Dic43—42no—
187C2×Dic86—21no—
188C2×Dic86—21no—
189C2×Dic86—21no—
190C2×Dic86—21no—
191C2×Dic86—21no—
192C2×Dic86C2×D412yes—
193C4⋊C4×C43—22no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—42no—
201C4⋊C4×C43—42no—
202C4⋊C4×C43—42no—
203C22⋊C4×C43—22no—
204C22⋊C4×C43—22no—
205C22⋊C4×C43—42no—
206C22⋊C4×C43—42no—
207C22⋊C4×C43—42no—
208C22⋊C4×C43—42no—
209C42×C43—42no—
210C42×C43C2×D412yes—
211C42×C43C2×D412yes—
212C22⋊Dic43—24no—
213C22⋊Dic43—24no—
214C22⋊Dic43—24no—
215#10621885—28no—
216C4⋊Dic43—24no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43C2×D412yes—
221C4⋊Dic43C2×D412yes—
222C4⋊Dic43C2×D412yes—
223Dic43⋊C4—24no—
224Dic43⋊C4—24no—
225Dic43⋊C4—24no—
226Dic43⋊C4—24no—
227Dic43⋊C4—24no—
228C4×Dic43—24no—
229C4×Dic43—24no—
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—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8#4112yes—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43#13512yes—
256C23×C43C22×D411yescharacteristic
257Q8×C43—22no—
258Q8×C43—22no—
259Q8×C43—41no—
260Q8×C43—41no—
261D4×C43—44no—
262C2×C4×C43—21no—
263C2×C4×C43—21no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—22no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—41no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
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×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43#12012yes—
293C2×C4×C43#12012yes—
294C2×C4×C43C22×D411yescharacteristic
295C2×C4×C43C22×D411yescharacteristic
296C2×C4×C43C2×#4111yescharacteristic
297C2×C4×C43C2×#4111yescharacteristic
298C2×C4×C43H(5,𝔽2)11yescharacteristic
299C2×C4×C432−1+411yescharacteristic
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—48no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313Dic86—22no—
314Dic86—22no—
315Dic86—41no—
316Dic86—41no—
317C43⋊C8—22no—
318C43⋊C8—41no—
319C43⋊C8—41no—
320C43⋊C8—41no—
321#24127—431nomaximal, Sylow
322C22×C43—22no—
323C22×C43—22no—
324C22×C43—22no—
325C22×C43—41no—
326C22×C43—41no—
327C22×C43—41no—
328C22×C43—41no—
329C22×C43—41no—
330C22×C43—41no—
331C22×C43—41no—
332C22×C43—41no—
333C22×C43—41no—
334C22×C43—41no—
335C22×C43—41no—
336C22×C43C2×#12011yescharacteristic
337C22×C43#54611yescharacteristic
338C22×C43#54711yescharacteristic
339C22×C43C2×#13511yescharacteristic
340C22×C43#57511yescharacteristic
341C22×C43#57811yescharacteristic
342C22×C43#57811yescharacteristic
343C4×C43—22no—
344C4×C43—22no—
345C4×C43—41no—
346C4×C43—41no—
347C4×C43—42no—
348C4×C43—81no—
349C4×C43—81no—
350C4×C43—81no—
351C4×C43#52511yescharacteristic
352C4×C43#53711yescharacteristic
353C4×C43#54811yescharacteristic
354C4×C43#55011yescharacteristic
355Dic43—42no—
356Dic43—42no—
357Dic43—42no—
358Dic43—42no—
359C2×#552—431no—
360C2×#479—431no—
361C2×C4×Q16—431no—
362#2536D4311yescharacteristic
363#2036—431no—
364#2035—431no—
365#2001—431no—
366#2001—431no—
367#1991—431no—
368#1954—431no—
369#1873—431no—
370#1872—431no—
371#1854—431no—
372#1852—431no—
373#1805—431no—
374C2×C43—42no—
375C2×C43—81no—
376C2×C43#240711yescharacteristic
377C2×C43#300211yescharacteristic
378C2×C43#301111yescharacteristic
379C2×C43#330011yescharacteristic
380C2×C43#332711yescharacteristic
381C2×C43#333611yescharacteristic
382C2×C43#335211yescharacteristic
383C22×Q16—431no—
384#552—864no—
385#552—864no—
386C2×#126—861no—
387C2×#125—431no—
388C2×#125—861no—
389C2×#123—861no—
390C2×C22⋊Q8—431no—
391C2×C22⋊Q8—431no—
392C2×C22⋊Q8C2×D4311yescharacteristic
393C2×C22⋊Q8C2×D4311yescharacteristic
394C2×C4×Q8—431no—
395C2×C4×Q8C2×D4311yescharacteristic
396C2×C4×D4C2×D4311yescharacteristic
397C2×#117—431no—
398C2×#117—861no—
399C22×C4⋊C4—431no—
400#479—864no—
401C4×Q16—864no—
402C2×#107—431no—
403C2×#107—431no—
404C2×#106—431no—
405C2×C4⋊C8—431no—
406C2×#103—431no—
407C2×#103—431no—
408C2×#103—431no—
409C2×#103—431no—
410C2×#103—431no—
411C2×#103—431no—
412C2×C22⋊C8—431no—
413C2×C22⋊C8—431no—
414C2×C22⋊C8—431no—
415C2×C22⋊C8—431no—
416C2×C4×C8—431no—
417#398—21no—
418#394—21no—
419#388—21no—
420#388—21no—
421#382C2×D4311yescharacteristic
422#380C2×D4311yescharacteristic
423#380C2×D4311yescharacteristic
424#340—431no—
425#340—431no—
426#340—431no—
427#340—431no—
428#340—431no—
429#340—431no—
430C43#2412711yescharacteristic, complemented, Sylow
431C22×Q8—431no—
432C22×Q8C22×D4311yescharacteristic
433C22×D4C22⋊D4311yescharacteristic
434C23×C4—861no—
435C23×C4C22×D4311yescharacteristic
436C23×C4C22×D4311yescharacteristic
437C2×Q16—862no—
438C2×Q16—862no—
439C2×Q16—862no—
440C22×C8—431no—
441C22×C8—431no—
442C22×C8—431no—
443C22×C8—431no—
444#126—868no—
445#125—434no—
446#125—868no—
447#125—862no—
448#123—868no—
449C22⋊Q8—22no—
450C22⋊Q8—22no—
451C22⋊Q8—41no—
452C22⋊Q8—41no—
453C22⋊Q8—862no—
454C22⋊Q8—862no—
455C22⋊Q8—862no—
456C22⋊Q8—862no—
457C4×Q8—22no—
458C4×Q8—22no—
459C4×Q8—434no—
460C4×Q8—862no—
461C4×D4—22no—
462C4×D4—22no—
463#117—868no—
464#117—862no—
465#117—862no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—431no—
470C2×C4⋊C4—431no—
471C2×C4⋊C4—431no—
472C2×C4⋊C4—862no—
473C2×C4⋊C4—862no—
474C2×C4⋊C4—861no—
475C2×C4⋊C4—861no—
476C2×C4⋊C4—861no—
477C2×C4⋊C4—861no—
478C2×C4⋊C4—861no—
479C2×C4⋊C4—861no—
480C2×C4⋊C4C22⋊D4311yescharacteristic
481C2×C4⋊C4C22×D4311yescharacteristic
482C2×C4⋊C4C22×D4311yescharacteristic
483C2×C4⋊C4C22×D4311yescharacteristic
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—861no—
489C2×C22⋊C4—861no—
490C2×C22⋊C4—861no—
491C2×C22⋊C4C22⋊D4311yescharacteristic
492C2×C22⋊C4C22⋊D4311yescharacteristic
493C2×C42—21no—
494C2×C42—861no—
495C2×C42—861no—
496C2×C42C22×D4311yescharacteristic
497#107—862no—
498#107—862no—
499#106—862no—
500C4⋊C8—862no—
501#103—862no—
502#103—862no—
503#103—862no—
504#103—862no—
505#103—1721no—
506#103—1721no—
507C22⋊C8—862no—
508C22⋊C8—862no—
509C22⋊C8—1721no—
510C22⋊C8—1721no—
511C4×C8—862no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516C24C2×C22⋊D4311yescharacteristic
517C24C2×C22⋊D4311yescharacteristic
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—432no—
524C2×Q8—861no—
525C2×Q8—861no—
526C2×Q8—861no—
527C2×Q8—861no—
528C2×Q8—861no—
529C2×Q8#1062190012yes—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—41no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
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—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—864no—
550C22×C4—861no—
551C22×C4—861no—
552C22×C4—861no—
553C22×C4—861no—
554C22×C4—1722no—
555C22×C4—1722no—
556C22×C4C2×C22⋊D4311yescharacteristic
557C22×C4C2×C22⋊D4311yescharacteristic
558C22×C4C2×C22⋊D4311yescharacteristic
559C22×C4C2×C22⋊D4311yescharacteristic
560C22×C4C23×D4311yescharacteristic
561Q16—868no—
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—861no—
573C2×C8—861no—
574C4⋊C4—22no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—432no—
585C4⋊C4—432no—
586C4⋊C4—432no—
587C4⋊C4—864no—
588C4⋊C4—864no—
589C4⋊C4—864no—
590C4⋊C4—864no—
591C4⋊C4—864no—
592C4⋊C4—864no—
593C4⋊C4—861no—
594C4⋊C4—861no—
595C4⋊C4—861no—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—42no—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—864no—
603C22⋊C4—864no—
604C22⋊C4—864no—
605C42—42no—
606C42—864no—
607C42—864no—
608C42D4×D4312yes—
609C42D4×D4312yes—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23#1306334512yes—
624C23C22×C22⋊D4311yescharacteristic
625Q8—22no—
626Q8—22no—
627Q8—41no—
628Q8—41no—
629Q8—862no—
630Q8—862no—
631Q8—1721no—
632Q8—1721no—
633D4—44no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—22no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
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—862no—
668C2×C4—1728no—
669C2×C4—1721no—
670C2×C4—1721no—
671C2×C4—1721no—
672C2×C4—1721no—
673C2×C4—1721no—
674C2×C4—1721no—
675C2×C4—1721no—
676C2×C4—1721no—
677C2×C4#1306329312yes—
678C2×C4#1306329312yes—
679C2×C4C2×D4×D4311yescharacteristic
680C2×C4C2×D4×D4311yescharacteristic
681C2×C4#41×D4311yescharacteristic
682C2×C4C2×#1062190011yescharacteristic
683C2×C4#1306337011yescharacteristic
684C2×C4#1306337211yescharacteristic
685C8—862no—
686C8—1721no—
687C8—1721no—
688C8—1721no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22C2×#1306329311yescharacteristic
704C22#1458354311yescharacteristic
705C22#1458354811yescharacteristic
706C22C2×#1306334511yescharacteristic
707C22#1458369711yescharacteristic
708C22#1458371411yescharacteristic
709C22#1458371411yescharacteristic
710C4—22no—
711C4—22no—
712C4—41no—
713C4—41no—
714C4—42no—
715C4—81no—
716C4—81no—
717C4—81no—
718C4—1722no—
719C4—1722no—
720C4—1722no—
721C4—1722no—
722C4#1458340911yescharacteristic
723C4#1458347811yescharacteristic
724C4#1458355511yescharacteristic
725C4#1458356711yescharacteristic
726C2—42no—
727C2—81no—
728C2#1913793611yescharacteristic
729C2#1914381111yescharacteristic
730C2#1914388811yescharacteristic
731C2#1914648211yescharacteristic
732C2#1914686311yescharacteristic
733C2#1914695711yescharacteristic
734C2#1914716411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2536C2
socleC23×C43C22×D4
prime radicalC22×D4×C43D4
hypercenter#2536D43
hypocenterC43#24127
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2536

Complements

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

NH ≅ G/Ntype
2. C2×#14583206C2semidirect
3. C2×C4×#10621885C2semidirect
4. #19135798C2semidirect
5. #19135791C2semidirect
6. #19135603C2semidirect
7. #19135603C2semidirect
8. #19135559C2semidirect
10. #19134908C2semidirect
11. #19134903C2semidirect
12. #19134792C2semidirect
13. #19134782C2semidirect
14. #19134607C2semidirect
430. C43#24127semidirect

Maximal subgroups

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

subgroupindex
C2×#145835892
C2×#145832062
C2×C4×#106218852
#191357982
#191357912
#191356032
#191355592
#191353902
#191349082
#191349032
#191347922
#191347822
#191346072
C43×#25362
#2412743