Finite Group Databasebeta

← #25124971

Subgroups — #25124971

Order 11008.

1114 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583511C211yesmaximal, characteristic, complemented
2C2×#14582999C211yesmaximal, characteristic, complemented
3C2×C4×#10621883C211yesmaximal, characteristic, complemented
4#19135933C211yesmaximal, characteristic, complemented
5#19135841C211yesmaximal, characteristic, complemented
6#19135798C211yesmaximal, characteristic, complemented
7#19135791C211yesmaximal, characteristic, complemented
8#19135741C211yesmaximal, characteristic, complemented
9#19135677C211yesmaximal, characteristic, complemented
10#19135598C211yesmaximal, characteristic
11#19135598C211yesmaximal, characteristic
12#19134428C211yesmaximal, characteristic, complemented
13C4×#13063248C211yesmaximal, characteristic, complemented
14#19134361C211yesmaximal, characteristic, complemented
15C43×#2324C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18#14583511—24no—
19#14583511—24no—
20C2×#13063325C2211yescharacteristic
21C2×#13063318—21no—
22C2×#13063318—21no—
23C2×#13063317C2211yescharacteristic
24C2×#13063315—21no—
25C2×#13063315—21no—
26C2×#13063304C2211yescharacteristic
27C2×#13063304C2211yescharacteristic
28C2×C4×Dic86C2211yescharacteristic
29C2×C4×Dic86C2211yescharacteristic
30#14582999—24no—
31C4×#10621883—24no—
32C2×#13063258C2211yescharacteristic
33C2×#13063256C2211yescharacteristic
34C2×#13063248C2211yescharacteristic
35C2×#13063248C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×#13063246C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×C22⋊(C43⋊C8)C2211yescharacteristic
44C2×#13063236C2211yescharacteristic
45C2×C4×C43⋊C8C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582654C2211yescharacteristic
52C2×#121×C43C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C2×#117×C43C2211yescharacteristic
55C43×#390—21no—
56C43×#390C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#388—21no—
59C43×#386—21no—
60C43×#385—21no—
61C43×#380C2211yescharacteristic
62C4×C4⋊C4×C43C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×Dic86C2311yescharacteristic
65C2×#10621883—22no—
66C2×#10621883—22no—
67C2×#10621883—22no—
68C2×#10621883—22no—
69C2×#10621883—22no—
70C2×#10621883—22no—
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75#13063325—22no—
76#13063325—22no—
77#13063318—28no—
78#13063318—28no—
79#13063317—22no—
80#13063317—22no—
81#13063315—28no—
82#13063315—28no—
83#13063304—22no—
84#13063304—22no—
85#13063304—22no—
86#13063304—22no—
87C4×Dic86—22no—
88C4×Dic86—22no—
89C4×Dic86D414yescomplemented
90C4×Dic86D414yescomplemented
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×C22⋊Dic43—21no—
102C2×C22⋊Dic43—21no—
103C2×C4×Dic43—21no—
104C2×C4×Dic43—21no—
105#13063258—22no—
106#13063256—22no—
107#13063248—22no—
108#13063248—22no—
109#13063248—22no—
110#13063248—22no—
111#13063248—22no—
112#13063248—22no—
113#13063246—22no—
114#13063246—22no—
115C22⋊(C43⋊C8)—22no—
116C22⋊(C43⋊C8)—22no—
117#13063236—22no—
118C4×C43⋊C8—22no—
119C22×D4×C43—21no—
120C22×D4×C43C2311yescharacteristic
121C23×C4×C43—21no—
122C23×C4×C43C2311yescharacteristic
123#121×C43—22no—
124#121×C43—22no—
125C4×D4×C43—22no—
126C4×D4×C43—22no—
127#117×C43—22no—
128#117×C43—22no—
129C2×C4⋊C4×C43—21no—
130C2×C4⋊C4×C43D411yescharacteristic
131C2×C4⋊C4×C43D411yescharacteristic
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C22⋊C4×C43—21no—
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
144C2×C42×C43C2311yescharacteristic
145#95×C43—21no—
146#95×C43—21no—
147#95×C43—21no—
148C24×C43—21no—
149C24×C43C2×D411yescharacteristic
150C2×D4×C43—24no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—81no—
157C2×D4×C43—81no—
158C2×D4×C43#4112yes—
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—42no—
169C22×C4×C43—81no—
170C22×C4×C43—81no—
171C22×C4×C43C2×D411yescharacteristic
172C22×C4×C43C2×D411yescharacteristic
173C22×C4×C43C2×D411yescharacteristic
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2411yescharacteristic
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43—21no—
180C22×Dic43—21no—
181C2×Dic86—21no—
182C2×Dic86—21no—
183C2×Dic86—21no—
184C2×Dic86—21no—
185C2×Dic86—21no—
186C2×Dic86—21no—
187C2×Dic86—21no—
188C2×Dic86—21no—
189C2×Dic86—21no—
190C2×Dic86—21no—
191C2×Dic86C2×D412yes—
192C2×Dic86C2×D412yes—
193C4⋊C4×C43—22no—
194C4⋊C4×C43—22no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—81no—
201C4⋊C4×C43#4112yes—
202C22⋊C4×C43—24no—
203C22⋊C4×C43—22no—
204C22⋊C4×C43—22no—
205C22⋊C4×C43—42no—
206C22⋊C4×C43—81no—
207C22⋊C4×C43—81no—
208C22⋊C4×C43—81no—
209C42×C43—21no—
210C42×C43—21no—
211C42×C43—81no—
212C42×C43C2×D412yes—
213C42×C43C2×D412yes—
214C22⋊Dic43—24no—
215C22⋊Dic43—24no—
216#10621883—28no—
217#10621883—28no—
218C4⋊Dic43—24no—
219C4⋊Dic43—24no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43C2×D412yes—
223C4⋊Dic43C2×D412yes—
224Dic43⋊C4—24no—
225Dic43⋊C4—24no—
226Dic43⋊C4—24no—
227Dic43⋊C4—24no—
228Dic43⋊C4—24no—
229Dic43⋊C4—24no—
230C4×Dic43—24no—
231C4×Dic43—24no—
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#4112yes—
243C2×C43⋊C8#4112yes—
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
259D4×C43—22no—
260D4×C43—22no—
261D4×C43—41no—
262D4×C43—41no—
263D4×C43—84no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—22no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
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—84no—
291C2×C4×C43#12012yes—
292C2×C4×C43#12012yes—
293C2×C4×C43C22×D411yescharacteristic
294C2×C4×C43C22×D411yescharacteristic
295C2×C4×C43C2×#4111yescharacteristic
296C2×C4×C43C2×#4111yescharacteristic
297C2×C4×C43C2×#4111yescharacteristic
298C2×C4×C43C2×#4111yescharacteristic
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311Dic86—22no—
312Dic86—22no—
313Dic86—22no—
314Dic86—22no—
315Dic86—41no—
316Dic86—41no—
317Dic86—41no—
318Dic86—41no—
319C43⋊C8—22no—
320C43⋊C8—22no—
321C43⋊C8—41no—
322C43⋊C8—41no—
323#23584—431nomaximal, Sylow
324C22×C43—41no—
325C22×C43—42no—
326C22×C43—41no—
327C22×C43—42no—
328C22×C43—41no—
329C22×C43—42no—
330C22×C43—41no—
331C22×C43—41no—
332C22×C43—41no—
333C22×C43—41no—
334C22×C43—81no—
335C22×C43—81no—
336C22×C43—81no—
337C22×C43—81no—
338C22×C43C2×#12011yescharacteristic
339C22×C43#52511yescharacteristic
340C22×C43#53211yescharacteristic
341C22×C43#57711yescharacteristic
342C22×C43#57711yescharacteristic
343C22×C43#57711yescharacteristic
344C22×C43#57811yescharacteristic
345C4×C43—22no—
346C4×C43—22no—
347C4×C43—42no—
348C4×C43—41no—
349C4×C43—41no—
350C4×C43—41no—
351C4×C43—81no—
352C4×C43—81no—
353C4×C43#52511yescharacteristic
354C4×C43#52511yescharacteristic
355C4×C43#53211yescharacteristic
356C4×C43#53211yescharacteristic
357Dic43—42no—
358Dic43—42no—
359Dic43—42no—
360Dic43—42no—
361C2×#541—431no—
362C2×#440—431no—
363C2×C4×SD16—431no—
364#2324D4311yescharacteristic
365#2059—431no—
366#2043—431no—
367#2036—431no—
368#2035—431no—
369#2025—431no—
370#2013—431no—
371#2000—431no—
372#2000—431no—
373#1763—431no—
374C4×#103—431no—
375#1750—431no—
376C2×C43—81no—
377C2×C43—82no—
378C2×C43#238811yescharacteristic
379C2×C43#301011yescharacteristic
380C2×C43#301311yescharacteristic
381C2×C43#312011yescharacteristic
382C2×C43#312311yescharacteristic
383C2×C43#317411yescharacteristic
384C2×C43#317811yescharacteristic
385C22×SD16—431no—
386C22×SD16—431no—
387#541—864no—
388#541—864no—
389C2×C4⋊Q8—431no—
390C2×#126—861no—
391C2×#126—861no—
392C2×#125—431no—
393C2×#125—861no—
394C2×#125—861no—
395C2×C22⋊Q8—431no—
396C2×C22⋊Q8—431no—
397C2×#121C2×D4311yescharacteristic
398C2×C4×Q8—431no—
399C2×C4×Q8—431no—
400C2×C4×D4C2×D4311yescharacteristic
401C2×#117C2×D4311yescharacteristic
402#440—864no—
403C4×SD16—864no—
404C2×#107—431no—
405C2×#106—431no—
406C2×#103—431no—
407C2×#103—431no—
408C2×#103—431no—
409C2×#103—431no—
410C2×#103—431no—
411C2×#103—431no—
412C2×#102—431no—
413C2×#102—431no—
414C2×C22⋊C8—431no—
415C2×C22⋊C8—431no—
416C2×#97—431no—
417C2×C4×C8—431no—
418#390—21no—
419#390C2×D4311yescharacteristic
420#389C2×D4311yescharacteristic
421#388—21no—
422#386—21no—
423#385—21no—
424#380C2×D4311yescharacteristic
425C4×C4⋊C4C2×D4311yescharacteristic
426#340—431no—
427#340—431no—
428#340—431no—
429#340—431no—
430#336—431no—
431#336—431no—
432C43#2358411yescharacteristic, complemented, Sylow
433C22×Q8—431no—
434C22×Q8—431no—
435C22×D4—21no—
436C22×D4C22×D4311yescharacteristic
437C23×C4—21no—
438C23×C4C22×D4311yescharacteristic
439C2×SD16—862no—
440C2×SD16—862no—
441C2×SD16—862no—
442C2×SD16—862no—
443C2×SD16—862no—
444C2×SD16—862no—
445C22×C8—431no—
446C22×C8—431no—
447C22×C8—431no—
448C22×C8—431no—
449C4⋊Q8—862no—
450C4⋊Q8—862no—
451#126—868no—
452#126—868no—
453#125—862no—
454#125—862no—
455#125—868no—
456#125—868no—
457C22⋊Q8—862no—
458C22⋊Q8—862no—
459C22⋊Q8—862no—
460C22⋊Q8—862no—
461#121—22no—
462#121—22no—
463C4×Q8—434no—
464C4×Q8—434no—
465C4×Q8—862no—
466C4×Q8—862no—
467C4×D4—22no—
468C4×D4—22no—
469#117—22no—
470#117—22no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—431no—
473C2×C4⋊C4—431no—
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⋊C4—861no—
481C2×C4⋊C4—861no—
482C2×C4⋊C4C22⋊D4311yescharacteristic
483C2×C4⋊C4C22⋊D4311yescharacteristic
484C2×C4⋊C4C22×D4311yescharacteristic
485C2×C4⋊C4C22×D4311yescharacteristic
486C2×C4⋊C4C22×D4311yescharacteristic
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—861no—
493C2×C22⋊C4—861no—
494C2×C22⋊C4C22⋊D4311yescharacteristic
495C2×C22⋊C4C22⋊D4311yescharacteristic
496C2×C42—21no—
497C2×C42—861no—
498C2×C42—861no—
499C2×C42C22×D4311yescharacteristic
500C2×C42C22×D4311yescharacteristic
501#107—862no—
502#106—862no—
503#103—862no—
504#103—862no—
505#103—862no—
506#103—862no—
507#103—862no—
508#103—862no—
509#102—862no—
510#102—862no—
511C22⋊C8—862no—
512C22⋊C8—862no—
513#97—862no—
514C4×C8—862no—
515#95—21no—
516#95—21no—
517#95—21no—
518C24—21no—
519C24C2×C22⋊D4311yescharacteristic
520C2×Q8—432no—
521C2×Q8—432no—
522C2×Q8—861no—
523C2×Q8—861no—
524C2×Q8—861no—
525C2×Q8—861no—
526C2×Q8—861no—
527C2×Q8—861no—
528C2×Q8—861no—
529C2×Q8—861no—
530C2×Q8—861no—
531C2×Q8—861no—
532C2×D4—24no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—81no—
539C2×D4—81no—
540C2×D4#1062189812yes—
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—21no—
550C22×C4—42no—
551C22×C4—81no—
552C22×C4—81no—
553C22×C4—861no—
554C22×C4—861no—
555C22×C4—861no—
556C22×C4—861no—
557C22×C4C2×C22⋊D4311yescharacteristic
558C22×C4C2×C22⋊D4311yescharacteristic
559C22×C4C2×C22⋊D4311yescharacteristic
560C22×C4C2×C22⋊D4311yescharacteristic
561C22×C4C2×C22⋊D4311yescharacteristic
562C22×C4C23×D4311yescharacteristic
563SD16—868no—
564SD16—868no—
565C2×C8—432no—
566C2×C8—432no—
567C2×C8—861no—
568C2×C8—861no—
569C2×C8—861no—
570C2×C8—861no—
571C2×C8—861no—
572C2×C8—861no—
573C2×C8—861no—
574C2×C8—861no—
575C2×C8—861no—
576C2×C8—861no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—81no—
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—864no—
594C4⋊C4—864no—
595C4⋊C4—861no—
596C4⋊C4—861no—
597C4⋊C4#1062189812yes—
598C22⋊C4—24no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—42no—
602C22⋊C4—81no—
603C22⋊C4—81no—
604C22⋊C4—81no—
605C22⋊C4—864no—
606C22⋊C4—864no—
607C42—21no—
608C42—21no—
609C42—81no—
610C42—864no—
611C42—864no—
612C42D4×D4312yes—
613C42D4×D4312yes—
614C23—21no—
615C23—22no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23C22×C22⋊D4311yescharacteristic
629Q8—862no—
630Q8—862no—
631Q8—862no—
632Q8—862no—
633Q8—1721no—
634Q8—1721no—
635Q8—1721no—
636Q8—1721no—
637D4—22no—
638D4—22no—
639D4—41no—
640D4—41no—
641D4—84no—
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—22no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
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—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—84no—
669C2×C4—862no—
670C2×C4—862no—
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#1306329312yes—
682C2×C4#1306329312yes—
683C2×C4C2×D4×D4311yescharacteristic
684C2×C4C2×D4×D4311yescharacteristic
685C2×C4#41×D4311yescharacteristic
686C2×C4#41×D4311yescharacteristic
687C2×C4C2×#1062189811yescharacteristic
688C2×C4C2×#1062189811yescharacteristic
689C8—862no—
690C8—862no—
691C8—1721no—
692C8—1721no—
693C22—41no—
694C22—41no—
695C22—42no—
696C22—41no—
697C22—41no—
698C22—42no—
699C22—41no—
700C22—42no—
701C22—41no—
702C22—41no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22C2×#1306329311yescharacteristic
708C22#1458341011yescharacteristic
709C22#1458344511yescharacteristic
710C22#1458371011yescharacteristic
711C22#1458371011yescharacteristic
712C22#1458371011yescharacteristic
713C22#1458371411yescharacteristic
714C4—22no—
715C4—22no—
716C4—41no—
717C4—42no—
718C4—41no—
719C4—41no—
720C4—81no—
721C4—81no—
722C4—1722no—
723C4—1722no—
724C4—1722no—
725C4—1722no—
726C4#1458340811yescharacteristic
727C4#1458340811yescharacteristic
728C4#1458344611yescharacteristic
729C4#1458344611yescharacteristic
730C2—81no—
731C2—82no—
732C2#1913781011yescharacteristic
733C2#1914387911yescharacteristic
734C2#1914390711yescharacteristic
735C2#1914480911yescharacteristic
736C2#1914484711yescharacteristic
737C2#1914521711yescharacteristic
738C2#1914525711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2324C2
socleC23×C43C22×D4
prime radicalC2×#121×C43C22
hypercenter#2324D43
hypocenterC43#23584
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2324

Complements

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

NH ≅ G/Ntype
1. C2×#14583511C2semidirect
2. C2×#14582999C2semidirect
3. C2×C4×#10621883C2semidirect
4. #19135933C2semidirect
5. #19135841C2semidirect
6. #19135798C2semidirect
7. #19135791C2semidirect
8. #19135741C2semidirect
9. #19135677C2semidirect
12. #19134428C2semidirect
13. C4×#13063248C2semidirect
14. #19134361C2semidirect
89. C4×Dic86D4semidirect
90. C4×Dic86D4semidirect
432. C43#23584semidirect

Maximal subgroups

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

subgroupindex
C2×#145835112
C2×#145829992
C2×C4×#106218832
#191359332
#191358412
#191357982
#191357912
#191357412
#191356772
#191355982
#191344282
C4×#130632482
#191343612
C43×#23242
#2358443