Finite Group Databasebeta

← #25131151

Subgroups — #25131151

Order 11008.

1086 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583181C211yesmaximal, characteristic, complemented
2C2×#14583118C211yesmaximal, characteristic, complemented
3#19137277C211yesmaximal, characteristic, complemented
4#19135788C211yesmaximal, characteristic, complemented
5#19135781C211yesmaximal, characteristic
6#19135603C211yesmaximal, characteristic, complemented
7#19135598C211yesmaximal, characteristic
8#19135544C211yesmaximal, characteristic, complemented
9#19135528C211yesmaximal, characteristic, complemented
10#19134936C211yesmaximal, characteristic, complemented
11#19134929C211yesmaximal, characteristic, complemented
12#19134863C211yesmaximal, characteristic, complemented
13#19134856C211yesmaximal, characteristic, complemented
14#19134579C211yesmaximal, characteristic, complemented
15C2×C43×#542C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C2×#13063304C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20#14583181—24no—
21#14583118—24no—
22C2×#13063256C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×C4⋊(C43⋊C8)C2211yescharacteristic
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×C22⋊(C43⋊C8)C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36#14582805C2211yescharacteristic
37#14582797C2211yescharacteristic
38#14582794—21no—
39#14582793—21no—
40#14582787—21no—
41#14582780—21no—
42#14582759C2211yescharacteristic
43C4×C4⋊Dic43C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50C43×#542—24no—
51C43×#542—24no—
52C2×C4⋊Q8×C43C2211yescharacteristic
53C2×#126×C43—21no—
54C2×#124×C43—21no—
55C2×#124×C43C2211yescharacteristic
56C2×#123×C43—21no—
57C2×C22⋊Q8×C43—21no—
58C2×C22⋊Q8×C43C2211yescharacteristic
59C2×#121×C43C2211yescharacteristic
60C2×C4×Q8×C43C2211yescharacteristic
61C2×C4×D4×C43C2211yescharacteristic
62C2×#117×C43C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C2×#10621885—22no—
65C2×#10621885—22no—
66C2×#10621885—41no—
67C2×#10621883—22no—
68C2×#10621883—22no—
69C2×#10621883—41no—
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74#13063304—22no—
75#13063304—22no—
76C4×Dic86—22no—
77C4×Dic86—22no—
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88#13063256—22no—
89#13063256—22no—
90C4⋊(C43⋊C8)—22no—
91C4⋊(C43⋊C8)—22no—
92#13063249—22no—
93#13063249—22no—
94#13063249—41no—
95#13063248—22no—
96#13063248—22no—
97#13063246—22no—
98#13063246—22no—
99#13063246—41no—
100C22⋊(C43⋊C8)—41no—
101C22⋊(C43⋊C8)—41no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C22×Q8×C43—21no—
108C22×Q8×C43C2311yescharacteristic
109C22×D4×C43—21no—
110C22×D4×C43C2311yescharacteristic
111C23×C4×C43—21no—
112C23×C4×C43C2311yescharacteristic
113C4⋊Q8×C43—22no—
114C4⋊Q8×C43D414yes—
115#126×C43—28no—
116#124×C43—28no—
117#124×C43—22no—
118#124×C43D414yes—
119#123×C43—28no—
120C22⋊Q8×C43—28no—
121C22⋊Q8×C43—22no—
122C22⋊Q8×C43—22no—
123#121×C43—22no—
124#121×C43—22no—
125C4×Q8×C43—22no—
126C4×Q8×C43—22no—
127C4×D4×C43—22no—
128C4×D4×C43—22no—
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×C43D411yescharacteristic
135C2×C4⋊C4×C43D411yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C22⋊C4×C43—21no—
139C2×C22⋊C4×C43—21no—
140C2×C22⋊C4×C43—21no—
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43—21no—
143C2×C22⋊C4×C43D411yescharacteristic
144C2×C22⋊C4×C43D411yescharacteristic
145C2×C42×C43—21no—
146C2×C42×C43C2311yescharacteristic
147C2×C42×C43C2311yescharacteristic
148C24×C43—21no—
149C24×C43C2×D411yescharacteristic
150C2×Q8×C43—24no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—81no—
157C2×Q8×C43—81no—
158C2×Q8×C43C2×D412yes—
159C2×D4×C43—24no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—81no—
166C2×D4×C43—81no—
167C2×D4×C43C2×D412yes—
168C22×C4×C43—24no—
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—81no—
179C22×C4×C43—81no—
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2411yescharacteristic
186C22×Dic43—21no—
187C22×Dic43—21no—
188C22×Dic43—21no—
189C22×Dic43—21no—
190C2×Dic86—21no—
191C2×Dic86—21no—
192C2×Dic86—21no—
193C2×Dic86—21no—
194C2×Dic86—21no—
195C2×Dic86#4112yes—
196C4⋊C4×C43—24no—
197C4⋊C4×C43—24no—
198C4⋊C4×C43—24no—
199C4⋊C4×C43—22no—
200C4⋊C4×C43—22no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43C2×D412yes—
204C4⋊C4×C43C2×D412yes—
205C22⋊C4×C43—24no—
206C22⋊C4×C43—24no—
207C22⋊C4×C43—24no—
208C22⋊C4×C43—24no—
209C22⋊C4×C43—24no—
210C22⋊C4×C43—22no—
211C22⋊C4×C43—22no—
212C42×C43—24no—
213C42×C43—21no—
214C42×C43—21no—
215C42×C43C2×D412yes—
216C42×C43C2×D412yes—
217C22⋊Dic43—24no—
218C22⋊Dic43—81no—
219#10621885—44no—
220#10621883—44no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43#4112yes—
227Dic43⋊C4—24no—
228Dic43⋊C4—42no—
229Dic43⋊C4—81no—
230C4×Dic43—42no—
231C4×Dic43—81no—
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—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C23×C43—21no—
245C23×C43—22no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43C22×D411yescharacteristic
259Q8×C43—22no—
260Q8×C43—22no—
261Q8×C43—41no—
262Q8×C43—41no—
263Q8×C43—84no—
264D4×C43—22no—
265D4×C43—22no—
266D4×C43—41no—
267D4×C43—41no—
268D4×C43—84no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—22no—
275C2×C4×C43—21no—
276C2×C4×C43—22no—
277C2×C4×C43—21no—
278C2×C4×C43—22no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
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—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—84no—
296C2×C4×C43#12012yes—
297C2×C4×C43#12012yes—
298C2×C4×C43C22×D411yescharacteristic
299C2×C4×C43C22×D411yescharacteristic
300C2×C4×C43C2×#4111yescharacteristic
301C2×C4×C43C2×#4111yescharacteristic
302C2×C4×C43H(5,𝔽2)11yescharacteristic
303C2×C4×C432−1+411yescharacteristic
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316Dic86—22no—
317Dic86—22no—
318Dic86—41no—
319Dic86—41no—
320C43⋊C8—41no—
321C43⋊C8—41no—
322C43⋊C8—41no—
323C43⋊C8—41no—
324#24169—431nomaximal, Sylow
325C22×C43—41no—
326C22×C43—41no—
327C22×C43—41no—
328C22×C43—42no—
329C22×C43—41no—
330C22×C43—41no—
331C22×C43—41no—
332C22×C43—42no—
333C22×C43—41no—
334C22×C43—42no—
335C22×C43—81no—
336C22×C43—81no—
337C22×C43—81no—
338C22×C43—81no—
339C22×C43C2×#12011yescharacteristic
340C22×C43#52511yescharacteristic
341C22×C43#53711yescharacteristic
342C22×C43#57711yescharacteristic
343C22×C43#57711yescharacteristic
344C22×C43#57711yescharacteristic
345C22×C43#57811yescharacteristic
346C4×C43—22no—
347C4×C43—22no—
348C4×C43—41no—
349C4×C43—42no—
350C4×C43—41no—
351C4×C43—42no—
352C4×C43—42no—
353C4×C43—41no—
354C4×C43#54611yescharacteristic
355C4×C43#54711yescharacteristic
356C4×C43#54811yescharacteristic
357C4×C43#55011yescharacteristic
358Dic43—42no—
359Dic43—42no—
360Dic43—81no—
361Dic43—81no—
362C2×#542D4311yescharacteristic
363C2×#475—431no—
364C2×#464—431no—
365#2323—431no—
366#2035—431no—
367#2034—431no—
368#2001—431no—
369#2000—431no—
370#1987—431no—
371#1983—431no—
372#1878—431no—
373#1877—431no—
374#1865—431no—
375#1864—431no—
376#1798—431no—
377C2×C43—81no—
378C2×C43—82no—
379C2×C43#240711yescharacteristic
380C2×C43#300911yescharacteristic
381C2×C43#301311yescharacteristic
382C2×C43#312111yescharacteristic
383C2×C43#312511yescharacteristic
384C2×C43#325811yescharacteristic
385C2×C43#326311yescharacteristic
386C22×Q16—431no—
387C22×SD16—431no—
388#542—24no—
389#542—24no—
390C2×C4⋊Q8C2×D4311yescharacteristic
391C2×#126—21no—
392C2×#124—21no—
393C2×#124C2×D4311yescharacteristic
394C2×#123—21no—
395C2×C22⋊Q8—21no—
396C2×C22⋊Q8—431no—
397C2×C22⋊Q8C2×D4311yescharacteristic
398C2×#121C2×D4311yescharacteristic
399C2×C4×Q8—431no—
400C2×C4×Q8C2×D4311yescharacteristic
401C2×C4×D4C2×D4311yescharacteristic
402C2×#117C2×D4311yescharacteristic
403#475—864no—
404#464—864no—
405C2×#106—431no—
406C2×#106—431no—
407C2×C4⋊C8—431no—
408C2×C4⋊C8—431no—
409C2×#103—431no—
410C2×#103—431no—
411C2×#103—431no—
412C2×#103—431no—
413C2×#103—431no—
414C2×#102—431no—
415C2×#102—431no—
416C2×#102—431no—
417C2×C22⋊C8—431no—
418C2×C22⋊C8—431no—
419#391—431no—
420#389—431no—
421#389—861no—
422#388—861no—
423#388—861no—
424#387—861no—
425#380—431no—
426C4×C4⋊C4—431no—
427#340—431no—
428#340—431no—
429#340—431no—
430#340—431no—
431#336—431no—
432#336—431no—
433C43#2416911yescharacteristic, complemented, Sylow
434C22×Q8—21no—
435C22×Q8—431no—
436C22×Q8C22×D4311yescharacteristic
437C22×D4—21no—
438C22×D4C22×D4311yescharacteristic
439C23×C4—21no—
440C23×C4C22×D4311yescharacteristic
441C2×Q16—862no—
442C2×Q16—862no—
443C2×Q16—1721no—
444C2×SD16—862no—
445C2×SD16—862no—
446C2×SD16—1721no—
447C22×C8—431no—
448C22×C8—431no—
449C22×C8—431no—
450C22×C8—431no—
451C4⋊Q8—22no—
452C4⋊Q8C22⋊D4314yes—
453#126—28no—
454#124—28no—
455#124—22no—
456#124C22⋊D4314yes—
457#123—28no—
458C22⋊Q8—28no—
459C22⋊Q8—22no—
460C22⋊Q8—22no—
461C22⋊Q8—862no—
462C22⋊Q8—862no—
463#121—22no—
464#121—22no—
465C4×Q8—22no—
466C4×Q8—22no—
467C4×Q8—862no—
468C4×Q8—862no—
469C4×D4—22no—
470C4×D4—22no—
471#117—22no—
472#117—22no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—431no—
477C2×C4⋊C4—431no—
478C2×C4⋊C4—431no—
479C2×C4⋊C4—861no—
480C2×C4⋊C4—861no—
481C2×C4⋊C4—861no—
482C2×C4⋊C4C22⋊D4311yescharacteristic
483C2×C4⋊C4C22⋊D4311yescharacteristic
484C2×C4⋊C4C22×D4311yescharacteristic
485C2×C4⋊C4C22×D4311yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—861no—
492C2×C22⋊C4—861no—
493C2×C22⋊C4C22⋊D4311yescharacteristic
494C2×C22⋊C4C22⋊D4311yescharacteristic
495C2×C42—21no—
496C2×C42—861no—
497C2×C42—861no—
498C2×C42C22×D4311yescharacteristic
499C2×C42C22×D4311yescharacteristic
500#106—862no—
501#106—862no—
502C4⋊C8—862no—
503C4⋊C8—862no—
504#103—862no—
505#103—862no—
506#103—862no—
507#103—862no—
508#103—1721no—
509#102—862no—
510#102—862no—
511#102—1721no—
512C22⋊C8—1721no—
513C22⋊C8—1721no—
514#95—861no—
515#95—861no—
516#95—861no—
517#95—861no—
518#95—861no—
519C24—21no—
520C24C2×C22⋊D4311yescharacteristic
521C2×Q8—24no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—81no—
528C2×Q8—81no—
529C2×Q8—432no—
530C2×Q8—861no—
531C2×Q8—861no—
532C2×Q8—861no—
533C2×Q8—861no—
534C2×Q8—861no—
535C2×Q8C2×C22⋊D4312yes—
536C2×D4—24no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—81no—
543C2×D4—81no—
544C2×D4C2×C22⋊D4312yes—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—24no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—81no—
556C22×C4—81no—
557C22×C4—861no—
558C22×C4—861no—
559C22×C4—861no—
560C22×C4—861no—
561C22×C4C2×C22⋊D4311yescharacteristic
562C22×C4C2×C22⋊D4311yescharacteristic
563C22×C4C2×C22⋊D4311yescharacteristic
564C22×C4C2×C22⋊D4311yescharacteristic
565C22×C4C2×C22⋊D4311yescharacteristic
566C22×C4C23×D4311yescharacteristic
567Q16—1724no—
568SD16—1724no—
569C2×C8—861no—
570C2×C8—861no—
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—861no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—432no—
589C4⋊C4—864no—
590C4⋊C4—861no—
591C4⋊C4—861no—
592C4⋊C4—861no—
593C4⋊C4—861no—
594C4⋊C4—861no—
595C4⋊C4—3441no—
596C4⋊C4—1722no—
597C4⋊C4C2×C22⋊D4312yes—
598C4⋊C4C2×C22⋊D4312yes—
599C22⋊C4—24no—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—24no—
603C22⋊C4—24no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—864no—
607C22⋊C4—3441no—
608C42—24no—
609C42—21no—
610C42—21no—
611C42—3441no—
612C42—1722no—
613C42C2×C22⋊D4312yes—
614C42C2×C22⋊D4312yes—
615C23—21no—
616C23—22no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23C22×C22⋊D4311yescharacteristic
630Q8—22no—
631Q8—22no—
632Q8—41no—
633Q8—41no—
634Q8—84no—
635Q8—862no—
636Q8—862no—
637Q8—1721no—
638Q8—1721no—
639D4—22no—
640D4—22no—
641D4—41no—
642D4—41no—
643D4—84no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—84no—
671C2×C4—862no—
672C2×C4—862no—
673C2×C4—1721no—
674C2×C4—1721no—
675C2×C4—1721no—
676C2×C4—1721no—
677C2×C4—1721no—
678C2×C4—1721no—
679C2×C4—1721no—
680C2×C4—1721no—
681C2×C4—1721no—
682C2×C4—1721no—
683C2×C4#1306329412yes—
684C2×C4#1306329412yes—
685C2×C4C22×C22⋊D4311yescharacteristic
686C2×C4C22×C22⋊D4311yescharacteristic
687C2×C4#41×D4311yescharacteristic
688C2×C4#41×D4311yescharacteristic
689C2×C4#1306337111yescharacteristic
690C2×C4#1306337211yescharacteristic
691C8—1721no—
692C8—1721no—
693C8—1721no—
694C8—1721no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—42no—
700C22—41no—
701C22—42no—
702C22—41no—
703C22—41no—
704C22—42no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22C2×#1306329411yescharacteristic
710C22#1458340611yescharacteristic
711C22#1458347711yescharacteristic
712C22#1458370711yescharacteristic
713C22#1458371011yescharacteristic
714C22#1458371011yescharacteristic
715C22#1458371411yescharacteristic
716C4—22no—
717C4—22no—
718C4—41no—
719C4—42no—
720C4—41no—
721C4—42no—
722C4—42no—
723C4—41no—
724C4—3441no—
725C4—3441no—
726C4—1722no—
727C4—1722no—
728C4#1458353711yescharacteristic
729C4#1458354811yescharacteristic
730C4#1458355611yescharacteristic
731C4#1458356811yescharacteristic
732C2—81no—
733C2—82no—
734C2#1913793411yescharacteristic
735C2#1914387211yescharacteristic
736C2#1914391011yescharacteristic
737C2#1914481811yescharacteristic
738C2#1914486611yescharacteristic
739C2#1914602111yescharacteristic
740C2#1914606011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#542C2
socleC23×C43C22×D4
prime radicalC2×#121×C43C22
hypercenterC2×#542D43
hypocenterC43#24169
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#14583181C2semidirect
2. C2×#14583118C2semidirect
3. #19137277C2semidirect
4. #19135788C2semidirect
6. #19135603C2semidirect
8. #19135544C2semidirect
9. #19135528C2semidirect
10. #19134936C2semidirect
11. #19134929C2semidirect
12. #19134863C2semidirect
13. #19134856C2semidirect
14. #19134579C2semidirect
433. C43#24169semidirect

Maximal subgroups

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

subgroupindex
C2×#145831812
C2×#145831182
#191372772
#191357882
#191357812
#191356032
#191355982
#191355442
#191355282
#191349362
#191349292
#191348632
#191348562
#191345792
C2×C43×#5422
#2416943