Finite Group Databasebeta

← #25140046

Subgroups — #25140046

Order 11008.

1004 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583223C211yesmaximal, characteristic, complemented
2C2×#14582893C211yesmaximal, characteristic, complemented
3#19137940C211yesmaximal, characteristic
4#19136134C211yesmaximal, characteristic, complemented
5#19135999C211yesmaximal, characteristic, complemented
6#19135798C211yesmaximal, characteristic, complemented
7#19135777C211yesmaximal, characteristic, complemented
8#19135229C211yesmaximal, characteristic, complemented
9#19135215C211yesmaximal, characteristic, complemented
10#19134907C211yesmaximal, characteristic, complemented
11#19134888C211yesmaximal, characteristic, complemented
12#19134794C211yesmaximal, characteristic, complemented
13#19134622C211yesmaximal, characteristic, complemented
14#19134533C211yesmaximal, characteristic, complemented
15C43×#2354C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C23×C43⋊C8C2211yescharacteristic
18C2×#13063304C2211yescharacteristic
19C2×#13063299C2211yescharacteristic
20#14583223—24no—
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25#14582893—24no—
26C2×#13063248C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×C22⋊(C43⋊C8)C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36C2×C22⋊(C43⋊C8)C2211yescharacteristic
37#14582814—21no—
38#14582807—21no—
39#14582805C2211yescharacteristic
40#14582801C2211yescharacteristic
41#14582775—21no—
42#14582770—21no—
43#14582759C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50C2×C4×D4×C43C2211yescharacteristic
51C2×#117×C43C2211yescharacteristic
52C2×#117×C43C2211yescharacteristic
53C43×#390—21no—
54C43×#388—21no—
55C43×#388—21no—
56C43×#384C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#380C2211yescharacteristic
59C4×C4⋊C4×C43—21no—
60C4×C4⋊C4×C43C2211yescharacteristic
61C2×#10621898—22no—
62C2×#10621898—22no—
63C2×#10621898—22no—
64C2×#10621898—22no—
65C2×#10621898—41no—
66C2×#10621898—41no—
67C22×Dic86C2311yescharacteristic
68C22×D172C2311yescharacteristic
69C22×C22⋊D43—21no—
70C22×C22⋊D43—21no—
71C22×C4×D43—21no—
72C22×C43⋊C8—22no—
73C22×C43⋊C8—22no—
74C22×C43⋊C8—41no—
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79#13063304—22no—
80#13063304—41no—
81#13063299—22no—
82#13063299—41no—
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×Dic43⋊C4—21no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91#13063258—22no—
92#13063258—41no—
93#13063258—41no—
94#13063256—22no—
95#13063248—22no—
96#13063248—22no—
97#13063248—22no—
98#13063248—41no—
99#13063245—22no—
100#13063245—22no—
101#13063245—41no—
102#13063245D414yescomplemented
103C22⋊(C43⋊C8)—22no—
104C22⋊(C43⋊C8)—22no—
105C22⋊(C43⋊C8)—41no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C22×D4×C43D411yescharacteristic
110C23×C4×C43C2311yescharacteristic
111C23×C4×C43C2311yescharacteristic
112C4×D4×C43—22no—
113C4×D4×C43—22no—
114#117×C43—22no—
115#117×C43—22no—
116#117×C43—41no—
117#117×C43—41no—
118C2×C4⋊C4×C43—21no—
119C2×C4⋊C4×C43—21no—
120C2×C4⋊C4×C43D411yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43D411yescharacteristic
130C2×C22⋊C4×C43D411yescharacteristic
131C2×C42×C43—21no—
132C2×C42×C43—21no—
133C2×C42×C43—21no—
134C2×C42×C43C2311yescharacteristic
135#95×C43—21no—
136#95×C43—21no—
137#95×C43—21no—
138C24×C43C2×D411yescharacteristic
139C24×C43C2×D411yescharacteristic
140C23×D43—21no—
141C2×D4×C43—22no—
142C2×D4×C43—22no—
143C2×D4×C43—41no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
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×C43C2×D411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43#4112yes—
163C22×C4×C43#4112yes—
164C22×C4×C43C2411yescharacteristic
165C2×C22⋊D43—42no—
166C2×C22⋊D43—42no—
167C2×C22⋊D43—42no—
168C2×C22⋊D43—42no—
169C2×C22⋊D43—42no—
170C2×C22⋊D43—81no—
171C22×Dic43—21no—
172C22×Dic43—21no—
173C22×Dic43—21no—
174#10621898—28no—
175#10621898—44no—
176#10621898—44no—
177#10621898—44no—
178C2×D172—21no—
179C2×D172—21no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172—21no—
183C2×D172C2×D412yes—
184C2×C4×D43—42no—
185C2×C4×D43—42no—
186C2×C4×D43—42no—
187C2×Dic86—21no—
188C2×Dic86—21no—
189C2×Dic86—21no—
190C2×Dic86—21no—
191C2×Dic86—21no—
192C2×Dic86#4112yes—
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—21no—
201C4⋊C4×C43—42no—
202C4⋊C4×C43—81no—
203C4⋊C4×C43C2×D412yes—
204C22⋊C4×C43—22no—
205C22⋊C4×C43—22no—
206C22⋊C4×C43—42no—
207C22⋊C4×C43—42no—
208C22⋊C4×C43—81no—
209C22⋊C4×C43—81no—
210C42×C43—21no—
211C42×C43—21no—
212C42×C43—42no—
213C42×C43—42no—
214C42×C43—42no—
215C22⋊Dic43—42no—
216C22⋊Dic43—81no—
217(C2×D43)⋊C4—42no—
218(C2×D43)⋊C4—42no—
219(C2×D43)⋊C4—81no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224Dic43⋊C4—42no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—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⋊C8C2×D412yes—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—21no—
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#12312yes—
252C23×C43C22×D411yescharacteristic
253C22×D43—22no—
254C22×D43—41no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43—41no—
259C22×D43—41no—
260D4×C43—44no—
261C2×C4×C43—21no—
262C2×C4×C43—21no—
263C2×C4×C43—21no—
264C2×C4×C43—21no—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43—22no—
268C2×C4×C43—22no—
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—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#12312yes—
292C2×C4×C43#13512yes—
293C2×C4×C43C22×D411yescharacteristic
294C2×C4×C43C2×#4111yescharacteristic
295C2×C4×C43C2×#4111yescharacteristic
296C2×C4×C43C2×#4111yescharacteristic
297C2×C4×C43H(5,𝔽2)11yescharacteristic
298C2×C4×C43H(5,𝔽2)11yescharacteristic
299C22⋊D43—48no—
300C22⋊D43—84no—
301C2×Dic43—22no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310D172—22no—
311D172—22no—
312D172—41no—
313D172—41no—
314C4×D43—48no—
315Dic86—22no—
316Dic86—22no—
317Dic86—41no—
318Dic86—41no—
319C43⋊C8—22no—
320C43⋊C8—41no—
321C43⋊C8—41no—
322C43⋊C8—41no—
323#24874—431nomaximal, Sylow
324C22×C43—22no—
325C22×C43—22no—
326C22×C43—22no—
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×C43—41no—
337C22×C43—41no—
338C22×C43C2×#12311yescharacteristic
339C22×C43D4211yescharacteristic
340C22×C43#54611yescharacteristic
341C22×C43C2×#13511yescharacteristic
342C22×C43#57511yescharacteristic
343C22×C43#57611yescharacteristic
344C22×C43#57811yescharacteristic
345C2×D43—42no—
346C2×D43—42no—
347C2×D43—42no—
348C2×D43—81no—
349C2×D43—81no—
350C2×D43—81no—
351C2×D43—81no—
352C4×C43—22no—
353C4×C43—22no—
354C4×C43—41no—
355C4×C43—41no—
356C4×C43—42no—
357C4×C43—81no—
358C4×C43—81no—
359C4×C43—81no—
360C4×C43#52511yescharacteristic
361C4×C43#53811yescharacteristic
362C4×C43#54611yescharacteristic
363C4×C43#55111yescharacteristic
364Dic43—42no—
365Dic43—81no—
366Dic43—81no—
367C2×#482—431no—
368C2×#416—431no—
369#2407—431no—
370#2354D4311yescharacteristic, complemented
371#2095—431no—
372#2071—431no—
373#2036—431no—
374#2033—431no—
375#1927—431no—
376#1925—431no—
377#1873—431no—
378#1869—431no—
379#1854—431no—
380#1808—431no—
381#1788—431no—
382C2×C43—42no—
383C2×C43—81no—
384C2×C43#241811yescharacteristic
385C2×C43#309111yescharacteristic
386C2×C43#309811yescharacteristic
387C2×C43#326811yescharacteristic
388C2×C43#328311yescharacteristic
389C2×C43#330511yescharacteristic
390C2×C43#331311yescharacteristic
391D43—82no—
392C22×#41—431no—
393C23×C8—431no—
394C2×C22⋊Q8—431no—
395C2×#121—431no—
396C2×C4×D4C2×D4311yescharacteristic
397C2×#117C2×D4311yescharacteristic
398C2×#117C2×D4311yescharacteristic
399#482—864no—
400C2×#107—431no—
401C2×#107—431no—
402C2×#107—431no—
403C2×#106—431no—
404#416—864no—
405C2×#103—431no—
406C2×#103—431no—
407C2×#103—431no—
408C2×#103—431no—
409C2×#102—431no—
410C2×#102—431no—
411C2×#102—431no—
412C2×#102—431no—
413C2×C22⋊C8—431no—
414C2×C22⋊C8—431no—
415C2×C22⋊C8—431no—
416#394—861no—
417#392—861no—
418#391—431no—
419#390—21no—
420#390—431no—
421#388—21no—
422#388—21no—
423#386—861no—
424#385—861no—
425#384C2×D4311yescharacteristic
426#380—431no—
427#380C2×D4311yescharacteristic
428#380C2×D4311yescharacteristic
429C4×C4⋊C4—21no—
430C4×C4⋊C4C2×D4311yescharacteristic
431#340—431no—
432#340—431no—
433#340—431no—
434#340—431no—
435#336—431no—
436#336—431no—
437C43#2487411yescharacteristic, complemented, Sylow
438C2×#41—862no—
439C2×#41—862no—
440C2×#41—862no—
441C2×#41—862no—
442C2×#41—1721no—
443C2×#41—1721no—
444C22×Q8—431no—
445C22×D4—431no—
446C22×D4—861no—
447C22×D4—861no—
448C22×D4C22⋊D4311yescharacteristic
449C23×C4—861no—
450C23×C4C22×D4311yescharacteristic
451C23×C4C22×D4311yescharacteristic
452C22×C8—431no—
453C22×C8—431no—
454C22×C8—431no—
455C22×C8—431no—
456C22×C8—862no—
457C22×C8—862no—
458C22×C8—1721no—
459C22⋊Q8—862no—
460C22⋊Q8—1721no—
461#121—862no—
462#121—1721no—
463C4×D4—22no—
464C4×D4—22no—
465#117—22no—
466#117—22no—
467#117—41no—
468#117—41no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—431no—
472C2×C4⋊C4—431no—
473C2×C4⋊C4—861no—
474C2×C4⋊C4C22⋊D4311yescharacteristic
475C2×C4⋊C4C22×D4311yescharacteristic
476C2×C4⋊C4C22×D4311yescharacteristic
477C2×C4⋊C4C22×D4311yescharacteristic
478C2×C4⋊C4C22×D4311yescharacteristic
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—861no—
484C2×C22⋊C4—861no—
485C2×C22⋊C4—861no—
486C2×C22⋊C4—861no—
487C2×C22⋊C4—861no—
488C2×C22⋊C4C22⋊D4311yescharacteristic
489C2×C22⋊C4C22⋊D4311yescharacteristic
490C2×C42—21no—
491C2×C42—21no—
492C2×C42—21no—
493C2×C42C22×D4311yescharacteristic
494#107—862no—
495#107—1721no—
496#107—1721no—
497#106—862no—
498#103—862no—
499#103—862no—
500#103—862no—
501#103—1721no—
502#102—434no—
503#102—862no—
504#102—862no—
505#102—1721no—
506C22⋊C8—862no—
507C22⋊C8—862no—
508C22⋊C8—1721no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—861no—
513#95—861no—
514#95—861no—
515C24—861no—
516C24C2×C22⋊D4311yescharacteristic
517C24C2×C22⋊D4311yescharacteristic
518#41—868no—
519#41—1724no—
520#41—1724no—
521#41—1724no—
522C2×Q8—432no—
523C2×Q8—861no—
524C2×Q8—861no—
525C2×Q8—861no—
526C2×Q8—861no—
527C2×Q8—861no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—41no—
531C2×D4—432no—
532C2×D4—861no—
533C2×D4—861no—
534C2×D4—861no—
535C2×D4—861no—
536C2×D4—861no—
537C2×D4—3441no—
538C2×D4—1722no—
539C2×D4—1722no—
540C2×D4—1722no—
541C2×D4—1722no—
542C2×D4—1722no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—861no—
558C22×C4—861no—
559C22×C4—861no—
560C22×C4—1722no—
561C22×C4—1722no—
562C22×C4—1722no—
563C22×C4#1062189812yes—
564C22×C4#1062189812yes—
565C22×C4C2×C22⋊D4311yescharacteristic
566C22×C4C2×C22⋊D4311yescharacteristic
567C22×C4C2×C22⋊D4311yescharacteristic
568C22×C4C2×C22⋊D4311yescharacteristic
569C22×C4C23×D4311yescharacteristic
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—861no—
581C2×C8—861no—
582C2×C8—1724no—
583C4⋊C4—22no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—42no—
592C4⋊C4—81no—
593C4⋊C4—861no—
594C4⋊C4—861no—
595C4⋊C4—861no—
596C4⋊C4—861no—
597C4⋊C4—1722no—
598C4⋊C4D4×D4312yes—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—81no—
604C22⋊C4—81no—
605C22⋊C4—3441no—
606C22⋊C4—3441no—
607C22⋊C4—1722no—
608C22⋊C4—1722no—
609C22⋊C4—1722no—
610C42—21no—
611C42—21no—
612C42—42no—
613C42—42no—
614C42—42no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—862no—
629C23—1721no—
630C23—1721no—
631C23—1721no—
632C23—1721no—
633C23—1721no—
634C23—1721no—
635C23#1306330812yes—
636C23C22×C22⋊D4311yescharacteristic
637Q8—862no—
638Q8—862no—
639Q8—1721no—
640Q8—1721no—
641D4—44no—
642D4—862no—
643D4—862no—
644D4—3444no—
645D4—1728no—
646D4—1721no—
647D4—1721no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—862no—
679C2×C4—1728no—
680C2×C4—1721no—
681C2×C4—1721no—
682C2×C4—1721no—
683C2×C4—1721no—
684C2×C4—1721no—
685C2×C4—1721no—
686C2×C4—1721no—
687C2×C4—1721no—
688C2×C4#1306330812yes—
689C2×C4#1306334512yes—
690C2×C4C2×D4×D4311yescharacteristic
691C2×C4#41×D4311yescharacteristic
692C2×C4C2×#1062189811yescharacteristic
693C2×C4C2×#1062189811yescharacteristic
694C2×C4#1306337011yescharacteristic
695C2×C4#1306337111yescharacteristic
696C8—862no—
697C8—1721no—
698C8—1721no—
699C8—1721no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—3441no—
715C22—3441no—
716C22—3441no—
717C22—3441no—
718C22—1722no—
719C22—1722no—
720C22—1722no—
721C22C2×#1306330811yescharacteristic
722C22D4×C22⋊D4311yescharacteristic
723C22#1458353711yescharacteristic
724C22C2×#1306334511yescharacteristic
725C22#1458369711yescharacteristic
726C22#1458370211yescharacteristic
727C22#1458371411yescharacteristic
728C4—22no—
729C4—22no—
730C4—41no—
731C4—42no—
732C4—41no—
733C4—81no—
734C4—81no—
735C4—81no—
736C4—3441no—
737C4—3441no—
738C4—1722no—
739C4#1458340811yescharacteristic
740C4#1458348211yescharacteristic
741C4#1458354511yescharacteristic
742C4#1458357811yescharacteristic
743C2—42no—
744C2—81no—
745C2—3442no—
746C2#1913805111yescharacteristic
747C2#1914450811yescharacteristic
748C2#1914457311yescharacteristic
749C2#1914613611yescharacteristic
750C2#1914631311yescharacteristic
751C2#1914653911yescharacteristic
752C2#1914665511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2354C2
socleC23×C43C22×D4
prime radical#19137940C2
hypercenter#2354D43
hypocenterC43#24874
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2354

Complements

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

NH ≅ G/Ntype
1. C2×#14583223C2semidirect
2. C2×#14582893C2semidirect
4. #19136134C2semidirect
5. #19135999C2semidirect
6. #19135798C2semidirect
7. #19135777C2semidirect
8. #19135229C2semidirect
9. #19135215C2semidirect
10. #19134907C2semidirect
11. #19134888C2semidirect
12. #19134794C2semidirect
13. #19134622C2semidirect
14. #19134533C2semidirect
15. C43×#2354C2semidirect
102. #13063245D4semidirect
370. #2354D43semidirect
437. C43#24874semidirect

Maximal subgroups

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

subgroupindex
C2×#145832232
C2×#145828932
#191379402
#191361342
#191359992
#191357982
#191357772
#191352292
#191352152
#191349072
#191348882
#191347942
#191346222
#191345332
C43×#23542
#2487443