Finite Group Databasebeta

← #25116970

Subgroups — #25116970

Order 11008.

1134 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×#14583061C211yesmaximal, characteristic
2C2×#14582999C211yesmaximal, characteristic, complemented
3C2×#14582900C211yesmaximal, characteristic
4#19137598C211yesmaximal, characteristic, complemented
5#19135455C211yesmaximal, characteristic, complemented
6#19135288C211yesmaximal, characteristic, complemented
7#19135233C211yesmaximal, characteristic, complemented
8#19135026C211yesmaximal, characteristic, complemented
9#19134939C211yesmaximal, characteristic, complemented
10#19134929C211yesmaximal, characteristic, complemented
11#19134842C211yesmaximal, characteristic, complemented
12#19134782C211yesmaximal, characteristic, complemented
13C4×#13063246C211yesmaximal, characteristic, complemented
14#19134379C211yesmaximal, characteristic, complemented
15C43×#2339C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C2×#13063304C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21C22×C4⋊Dic43C2211yescharacteristic
22#14583061C418yescomplemented
23#14582999—24no—
24C2×#13063258C2211yescharacteristic
25C2×#13063258C2211yescharacteristic
26#14582900—24no—
27C2×#13063249C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36C2×#13063236C2211yescharacteristic
37C2×C4×C43⋊C8C2211yescharacteristic
38#14582805C2211yescharacteristic
39#14582797C2211yescharacteristic
40#14582796—21no—
41#14582786—21no—
42#14582771—21no—
43C4×C4⋊Dic43C2211yescharacteristic
44C22⋊C4×Dic43—21no—
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582654C2211yescharacteristic
51C22×#41×C43C2211yescharacteristic
52C2×C4×D4×C43C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C43×#391C2211yescharacteristic
55C43×#391C2211yescharacteristic
56C43×#386—21no—
57C43×#386—21no—
58C43×#381—21no—
59C43×#380C2211yescharacteristic
60C4×C22⋊C4×C43C2211yescharacteristic
61C2×#95×C43—21no—
62C22×Dic86C2311yescharacteristic
63C23×Dic43—21no—
64C2×#10621885—41no—
65C2×#10621885—41no—
66C2×#10621885C2×C414yescomplemented
67C2×#10621883—22no—
68C2×#10621883—22no—
69C2×#10621883C2×C414yescomplemented
70C2×#10621877—22no—
71C2×#10621877—22no—
72C2×#10621877—41no—
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77#13063304—22no—
78#13063304C2×C414yescomplemented
79C4×Dic86—22no—
80C4×Dic86—41no—
81C2×C4⋊Dic43—22no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43—41no—
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×C22⋊Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93#13063258—22no—
94#13063258—41no—
95#13063249—22no—
96#13063249—22no—
97#13063249C2×C414yescomplemented
98#13063248—22no—
99#13063248—41no—
100#13063246—22no—
101#13063246C2×C414yescomplemented
102#13063246D414yes—
103C22⋊(C43⋊C8)C2×C414yescomplemented
104#13063236—22no—
105C4×C43⋊C8—41no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C2×#41×C43—22no—
111C2×#41×C43—22no—
112C2×#41×C43—22no—
113C2×#41×C43—41no—
114C2×#41×C43—41no—
115C2×#41×C43C2×C414yes—
116C22×Q8×C43C2311yescharacteristic
117C22×D4×C43—21no—
118C22×D4×C43C2311yescharacteristic
119C23×C4×C43—21no—
120C23×C4×C43—21no—
121C23×C4×C43—21no—
122C23×C4×C43C2311yescharacteristic
123C4×D4×C43—22no—
124C4×D4×C43—22no—
125C4×D4×C43—41no—
126C4×D4×C43—41no—
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43D411yescharacteristic
133C2×C22⋊C4×C43D411yescharacteristic
134C2×C42×C43C2311yescharacteristic
135C2×C42×C43C2311yescharacteristic
136#95×C43—21no—
137#95×C43—21no—
138#95×C43—21no—
139#95×C43—21no—
140#95×C43—21no—
141#95×C43D411yescharacteristic
142#95×C43D411yescharacteristic
143C24×C43—21no—
144C24×C43C2×D411yescharacteristic
145#41×C43—28no—
146#41×C43—44no—
147#41×C43—44no—
148#41×C43—44no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43C22×C412yes—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—24no—
159C2×D4×C43—42no—
160C2×D4×C43—42no—
161C2×D4×C43C22×C412yes—
162C2×D4×C43C2×D412yes—
163C2×D4×C43#4112yes—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—24no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—42no—
173C22×C4×C43—42no—
174C22×C4×C43—42no—
175C22×C4×C43—42no—
176C22×C4×C43—42no—
177C22×C4×C43—42no—
178C22×C4×C43—81no—
179C22×C4×C43—81no—
180C22×C4×C43C22×C412yes—
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43#4112yes—
187C22×C4×C43C2411yescharacteristic
188C22×Dic43—21no—
189C22×Dic43—21no—
190C22×Dic43—21no—
191C22×Dic43—21no—
192C22×Dic43—42no—
193C22×Dic43—42no—
194C22×Dic43—81no—
195C2×Dic86—21no—
196C2×Dic86—21no—
197C2×Dic86—21no—
198C2×Dic86—21no—
199C2×Dic86—21no—
200C2×Dic86C22×C412yes—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C22⋊C4×C43—22no—
206C22⋊C4×C43—41no—
207C22⋊C4×C43—42no—
208C22⋊C4×C43—42no—
209C22⋊C4×C43—81no—
210C42×C43—21no—
211C42×C43—21no—
212C42×C43—21no—
213C42×C43—21no—
214C22⋊Dic43—24no—
215#10621885—44no—
216#10621883—28no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—42no—
222C4⋊Dic43C22×C412yes—
223C4⋊Dic43C2×D412yes—
224Dic43⋊C4—24no—
225Dic43⋊C4—42no—
226Dic43⋊C4—81no—
227C4×Dic43—42no—
228C4×Dic43—81no—
229#10621877—44no—
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⋊C8C22×C412yes—
240C2×C43⋊C8C22×C412yes—
241C2×C43⋊C8C2×D412yes—
242C23×C43—22no—
243C23×C43—22no—
244C23×C43—21no—
245C23×C43—22no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43C4×D412yes—
256C23×C43C22×D411yescharacteristic
257Q8×C43—22no—
258Q8×C43—22no—
259Q8×C43—41no—
260Q8×C43—41no—
261D4×C43—22no—
262D4×C43—22no—
263D4×C43—22no—
264D4×C43—48no—
265D4×C43C4×D414yes—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—48no—
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—84no—
294C2×C4×C43—84no—
295C2×C4×C43C4×D412yes—
296C2×C4×C43#13712yes—
297C2×C4×C43C23×C411yescharacteristic
298C2×C4×C43C22×D411yescharacteristic
299C2×C4×C43C2×#4111yescharacteristic
300C2×C4×C43C2×#4111yescharacteristic
301C2×C4×C43H(5,𝔽2)11yescharacteristic
302C2×C4×C43H(5,𝔽2)11yescharacteristic
303C2×Dic43—22no—
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—84no—
316Dic86—22no—
317Dic86—22no—
318Dic86—41no—
319Dic86—41no—
320C43⋊C8—22no—
321C43⋊C8—22no—
322C43⋊C8—22no—
323C43⋊C8—41no—
324#22862—431nomaximal, Sylow
325C22×C43—24no—
326C22×C43—22no—
327C22×C43—22no—
328C22×C43—22no—
329C22×C43—42no—
330C22×C43—42no—
331C22×C43—41no—
332C22×C43—42no—
333C22×C43—41no—
334C22×C43—42no—
335C22×C43—41no—
336C22×C43—42no—
337C22×C43—41no—
338C22×C43—42no—
339C22×C43C2×C4×D411yescharacteristic
340C22×C43D4211yescharacteristic
341C22×C43#54611yescharacteristic
342C22×C43C2×#13711yescharacteristic
343C22×C43#57511yescharacteristic
344C22×C43#57611yescharacteristic
345C22×C43#57811yescharacteristic
346C4×C43—22no—
347C4×C43—22no—
348C4×C43—42no—
349C4×C43—41no—
350C4×C43—41no—
351C4×C43—41no—
352C4×C43—81no—
353C4×C43—81no—
354C4×C43C2×C4×D411yescharacteristic
355C4×C43#51811yescharacteristic
356C4×C43#54611yescharacteristic
357C4×C43#55111yescharacteristic
358Dic43—42no—
359Dic43—42no—
360Dic43—42no—
361Dic43—81no—
362C2×#452—431no—
363C2×#440—431no—
364C2×#417—431no—
365#2360—431no—
366#2339D4311yescharacteristic
367#1969—431no—
368#1935—431no—
369#1928—431no—
370#1894—431no—
371#1878—431no—
372#1877—431no—
373#1862—431no—
374#1852—431no—
375C4×#102—431no—
376#1753—431no—
377C2×C43—42no—
378C2×C43—44no—
379C2×C43#235811yescharacteristic
380C2×C43C4×#13711yescharacteristic
381C2×C43#295111yescharacteristic
382C2×C43#327311yescharacteristic
383C2×C43#327611yescharacteristic
384C2×C43#331411yescharacteristic
385C2×C43#331511yescharacteristic
386C22×#41C2×D4311yescharacteristic
387C22×Q16—431no—
388C22×SD16—431no—
389C22×M16—431no—
390C2×C22⋊Q8—431no—
391C2×C4×Q8—431no—
392C2×C4×D4C2×D4311yescharacteristic
393C2×C4×D4C2×D4311yescharacteristic
394C22×C4⋊C4—431no—
395#452—438no—
396#440—864no—
397C2×#107—431no—
398C2×#107—431no—
399#417—864no—
400C2×#103—431no—
401C2×#103—431no—
402C2×#103—431no—
403C2×#103—431no—
404C2×#103—431no—
405C2×#102—431no—
406C2×#102—431no—
407C2×#102—431no—
408C2×C22⋊C8—431no—
409C2×#97—431no—
410C2×C4×C8—431no—
411#391—431no—
412#391C2×D4311yescharacteristic
413#391C2×D4311yescharacteristic
414#389—431no—
415#389—861no—
416#387—861no—
417#386—21no—
418#386—21no—
419#385—861no—
420#381—21no—
421#380C2×D4311yescharacteristic
422C4×C4⋊C4—431no—
423C4×C22⋊C4—861no—
424C4×C22⋊C4C2×D4311yescharacteristic
425C2×#95—21no—
426#340—431no—
427#340—431no—
428#340—431no—
429#340—431no—
430#336—431no—
431#336—431no—
432C43#2286211yescharacteristic, complemented, Sylow
433C2×#41—22no—
434C2×#41—22no—
435C2×#41—22no—
436C2×#41—41no—
437C2×#41—41no—
438C2×#41C4×D4314yes—
439C22×Q8—431no—
440C22×Q8C22×D4311yescharacteristic
441C22×D4—21no—
442C22×D4C22×D4311yescharacteristic
443C23×C4—21no—
444C23×C4—21no—
445C23×C4—21no—
446C23×C4—861no—
447C23×C4C22×D4311yescharacteristic
448C2×Q16—434no—
449C2×Q16—1721no—
450C2×Q16—1721no—
451C2×SD16—434no—
452C2×SD16—862no—
453C2×SD16—862no—
454C2×M16—862no—
455C2×M16—862no—
456C2×M16—1721no—
457C22×C8—431no—
458C22×C8—431no—
459C22×C8—431no—
460C22×C8—431no—
461C22⋊Q8—434no—
462C22⋊Q8—862no—
463C4×Q8—862no—
464C4×Q8—1721no—
465C4×D4—22no—
466C4×D4—22no—
467C4×D4—41no—
468C4×D4—41no—
469C2×C4⋊C4—431no—
470C2×C4⋊C4—431no—
471C2×C4⋊C4—431no—
472C2×C4⋊C4—862no—
473C2×C4⋊C4—861no—
474C2×C4⋊C4—861no—
475C2×C4⋊C4—861no—
476C2×C4⋊C4—861no—
477C2×C4⋊C4—1721no—
478C2×C4⋊C4C22×D4311yescharacteristic
479C2×C4⋊C4C22×D4311yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—861no—
484C2×C22⋊C4C22⋊D4311yescharacteristic
485C2×C22⋊C4C22⋊D4311yescharacteristic
486C2×C42—861no—
487C2×C42—861no—
488C2×C42C22×D4311yescharacteristic
489C2×C42C22×D4311yescharacteristic
490#107—862no—
491#107—1721no—
492#103—434no—
493#103—862no—
494#103—862no—
495#103—862no—
496#103—1721no—
497#102—434no—
498#102—434no—
499#102—862no—
500C22⋊C8—434no—
501#97—862no—
502C4×C8—1721no—
503#95—21no—
504#95—21no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95—861no—
509#95—861no—
510#95—861no—
511#95—861no—
512#95C22⋊D4311yescharacteristic
513#95C22⋊D4311yescharacteristic
514C24—21no—
515C24C2×C22⋊D4311yescharacteristic
516#41—28no—
517#41—44no—
518#41—44no—
519#41—44no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—432no—
526C2×Q8—861no—
527C2×Q8—861no—
528C2×Q8—861no—
529C2×Q8—861no—
530C2×Q8—861no—
531C2×Q8C2×C4×D4312yes—
532C2×D4—24no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4C2×C4×D4312yes—
539C2×D4D4×D4312yes—
540C2×D4#1062190012yes—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—24no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—81no—
556C22×C4—81no—
557C22×C4—861no—
558C22×C4—861no—
559C22×C4—861no—
560C22×C4—861no—
561C22×C4—3441no—
562C22×C4—1722no—
563C22×C4—1722no—
564C22×C4C2×C4×D4312yes—
565C22×C4#1062189812yes—
566C22×C4C2×C22⋊D4311yescharacteristic
567C22×C4C2×C22⋊D4311yescharacteristic
568C22×C4C2×C22⋊D4311yescharacteristic
569C22×C4C2×C22⋊D4311yescharacteristic
570C22×C4C2×C22⋊D4311yescharacteristic
571C22×C4C23×D4311yescharacteristic
572Q16—1724no—
573SD16—868no—
574M16—1724no—
575C2×C8—432no—
576C2×C8—432no—
577C2×C8—432no—
578C2×C8—861no—
579C2×C8—861no—
580C2×C8—861no—
581C2×C8—861no—
582C2×C8—861no—
583C2×C8—861no—
584C2×C8—861no—
585C2×C8—861no—
586C2×C8—861no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—432no—
592C4⋊C4—432no—
593C4⋊C4—864no—
594C4⋊C4—861no—
595C4⋊C4—861no—
596C4⋊C4—861no—
597C4⋊C4—861no—
598C4⋊C4—3441no—
599C4⋊C4—1722no—
600C4⋊C4—1722no—
601C22⋊C4—22no—
602C22⋊C4—41no—
603C22⋊C4—42no—
604C22⋊C4—42no—
605C22⋊C4—81no—
606C22⋊C4—864no—
607C42—21no—
608C42—21no—
609C42—21no—
610C42—21no—
611C42—3441no—
612C42—1722no—
613C23—22no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—22no—
619C23—21no—
620C23—22no—
621C23—21no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23C4×C22⋊D4312yes—
627C23C22×C22⋊D4311yescharacteristic
628Q8—22no—
629Q8—22no—
630Q8—41no—
631Q8—41no—
632Q8—862no—
633Q8—862no—
634Q8—1721no—
635Q8—1721no—
636D4—22no—
637D4—22no—
638D4—22no—
639D4—48no—
640D4(C22⋊D43)⋊C414yes—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—48no—
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—84no—
670C2×C4—862no—
671C2×C4—862no—
672C2×C4—862no—
673C2×C4—3444no—
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×C4C4×C22⋊D4312yes—
684C2×C4#1306335512yes—
685C2×C4C22×C4×D4311yescharacteristic
686C2×C4C2×D4×D4311yescharacteristic
687C2×C4C2×#1062190011yescharacteristic
688C2×C4C2×#1062189811yescharacteristic
689C2×C4#1306337011yescharacteristic
690C2×C4#1306337011yescharacteristic
691C8—862no—
692C8—862no—
693C8—862no—
694C8—1721no—
695C22—22no—
696C22—24no—
697C22—22no—
698C22—22no—
699C22—42no—
700C22—42no—
701C22—41no—
702C22—41no—
703C22—42no—
704C22—42no—
705C22—41no—
706C22—42no—
707C22—41no—
708C22—42no—
709C22C2×C4×C22⋊D4311yescharacteristic
710C22D4×C22⋊D4311yescharacteristic
711C22#1458354311yescharacteristic
712C22C2×#1306335511yescharacteristic
713C22#1458369711yescharacteristic
714C22#1458370211yescharacteristic
715C22#1458371411yescharacteristic
716C4—22no—
717C4—22no—
718C4—42no—
719C4—41no—
720C4—41no—
721C4—41no—
722C4—81no—
723C4—81no—
724C4—3441no—
725C4—1722no—
726C4—1722no—
727C4—1722no—
728C4C2×(C22⋊D43)⋊C411yescharacteristic
729C4#1458337211yescharacteristic
730C4#1458353911yescharacteristic
731C4#1458357511yescharacteristic
732C2—42no—
733C2—44no—
734C2#1913757411yescharacteristic
735C2C4×#1306335511yescharacteristic
736C2#1914346811yescharacteristic
737C2#1914620211yescharacteristic
738C2#1914623711yescharacteristic
739C2#1914667611yescharacteristic
740C2#1914669111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2339C2
socleC23×C43C22×D4
prime radicalC22×#41×C43C22
cosocleC22×C4×C43C24
hypercenter#2339D43
hypocenterC43#22862
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2339

Complements

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

NH ≅ G/Ntype
2. C2×#14582999C2semidirect
4. #19137598C2semidirect
5. #19135455C2semidirect
6. #19135288C2semidirect
7. #19135233C2semidirect
8. #19135026C2semidirect
9. #19134939C2semidirect
10. #19134929C2semidirect
11. #19134842C2semidirect
12. #19134782C2semidirect
13. C4×#13063246C2semidirect
14. #19134379C2semidirect
22. #14583061C4semidirect
66. C2×#10621885C2×C4semidirect
69. C2×#10621883C2×C4semidirect
78. #13063304C2×C4semidirect
97. #13063249C2×C4semidirect
101. #13063246C2×C4semidirect
103. C22⋊(C43⋊C8)C2×C4semidirect
432. C43#22862semidirect

Maximal subgroups

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

subgroupindex
C2×#145830612
C2×#145829992
C2×#145829002
#191375982
#191354552
#191352882
#191352332
#191350262
#191349392
#191349292
#191348422
#191347822
C4×#130632462
#191343792
C43×#23392
#2286243