Finite Group Databasebeta

← #25130606

Subgroups — #25130606

Order 11008.

1152 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583595C211yesmaximal, characteristic
2C2×#14583207C211yesmaximal, characteristic, complemented
3C2×C4×#10621873C211yesmaximal, characteristic, complemented
4#19139504C211yesmaximal, characteristic, complemented
5#19135785C211yesmaximal, characteristic, complemented
6#19135778C211yesmaximal, characteristic, complemented
7#19135600C211yesmaximal, characteristic, complemented
8#19135600C211yesmaximal, characteristic, complemented
9#19135560C211yesmaximal, characteristic, complemented
10#19134905C211yesmaximal, characteristic, complemented
11#19134900C211yesmaximal, characteristic, complemented
12#19134796C211yesmaximal, characteristic, complemented
13#19134790C211yesmaximal, characteristic, complemented
14#19134606C211yesmaximal, characteristic, complemented
15C43×#1954C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17#14583595—24no—
18#14583595—24no—
19C2×#13063320—21no—
20C2×#13063317C2211yescharacteristic
21C2×#13063307—21no—
22C2×#13063304C2211yescharacteristic
23C2×#13063304C2211yescharacteristic
24C2×#13063299C2211yescharacteristic
25C2×#13063299C2211yescharacteristic
26C2×#13063297—21no—
27C2×C4×Dic86C2211yescharacteristic
28C2×C4×D172C2211yescharacteristic
29C2×(C22⋊D43)⋊C4—21no—
30C2×#13063284C2211yescharacteristic
31C22×C4⋊Dic43C2211yescharacteristic
32#14583207—24no—
33C4×#10621873—24no—
34C2×#13063259C2211yescharacteristic
35C2×#13063257C2211yescharacteristic
36C2×#13063257C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063250C2211yescharacteristic
39C2×#13063250C2211yescharacteristic
40C2×#13063247C2211yescharacteristic
41C2×#13063247C2211yescharacteristic
42C2×#13063247C2211yescharacteristic
43#14582830—21no—
44#14582813—21no—
45#14582787—21no—
46#14582787—21no—
47#14582765C2211yescharacteristic
48#14582759C2211yescharacteristic
49#14582759C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54#14582662C2211yescharacteristic
55#14582662C2211yescharacteristic
56C2×C4×D4×C43C2211yescharacteristic
57C2×C4⋊C8×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic
62C2×C4×C8×C43C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×D172C2311yescharacteristic
65C22×C22⋊D43—21no—
66C22×C22⋊D43—21no—
67C23×Dic43—21no—
68C22×C4×D43—21no—
69C2×#10621873—22no—
70C2×#10621873—22no—
71C2×#10621873—22no—
72#13063320—28no—
73#13063317—22no—
74#13063317D414yes—
75#13063307—28no—
76#13063304—22no—
77#13063304—22no—
78#13063304—41no—
79#13063304—41no—
80#13063299—22no—
81#13063299—22no—
82#13063299—22no—
83#13063299—22no—
84#13063297—28no—
85C4×Dic86—22no—
86C4×Dic86—22no—
87C4×D172—22no—
88C4×D172D414yes—
89(C22⋊D43)⋊C4—28no—
90#13063284—22no—
91#13063284—22no—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43—22no—
94C2×C4⋊Dic43—22no—
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×C4⋊Dic43C2311yescharacteristic
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4—21no—
106C2×C22⋊Dic43—21no—
107C2×C22⋊Dic43—21no—
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43—21no—
110C2×C22⋊Dic43—21no—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×C4×Dic43—21no—
115C2×C4×Dic43—21no—
116#13063259—22no—
117#13063257—22no—
118#13063257—22no—
119#13063250—22no—
120#13063250—22no—
121#13063250—22no—
122#13063247—22no—
123#13063247—41no—
124#13063247—41no—
125C43⋊#95—21no—
126C43⋊#95—21no—
127C43⋊#95—21no—
128C43⋊#95—21no—
129C22×D4×C43D411yescharacteristic
130C23×C4×C43C2311yescharacteristic
131C23×C4×C43C2311yescharacteristic
132C22×C8×C43C2311yescharacteristic
133C22×C8×C43C2311yescharacteristic
134C22×C8×C43C2311yescharacteristic
135C22×C8×C43C2311yescharacteristic
136C4×D4×C43—22no—
137C4×D4×C43—22no—
138C2×C4⋊C4×C43D411yescharacteristic
139C2×C22⋊C4×C43D411yescharacteristic
140C2×C22⋊C4×C43D411yescharacteristic
141C2×C42×C43C2311yescharacteristic
142C4⋊C8×C43—22no—
143C22⋊C8×C43—22no—
144C22⋊C8×C43—22no—
145C22⋊C8×C43—41no—
146C22⋊C8×C43—41no—
147C4×C8×C43—22no—
148C24×C43C2×D411yescharacteristic
149C24×C43C2×D411yescharacteristic
150C23×D43—21no—
151C2×D4×C43—22no—
152C2×D4×C43—22no—
153C2×D4×C43—41no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
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×C43C2×D411yescharacteristic
167C22×C4×C43C2×D411yescharacteristic
168C22×C4×C43C2×D411yescharacteristic
169C22×C4×C43C2×D411yescharacteristic
170C22×C4×C43C2411yescharacteristic
171C2×C22⋊D43—24no—
172C2×C22⋊D43—24no—
173C2×C22⋊D43—42no—
174C2×C22⋊D43—42no—
175C2×C22⋊D43—81no—
176C2×C22⋊D43—81no—
177C22×Dic43—24no—
178C22×Dic43—21no—
179C22×Dic43—21no—
180C22×Dic43—21no—
181C22×Dic43—21no—
182C22×Dic43—21no—
183C22×Dic43—21no—
184C22×Dic43—21no—
185C22×Dic43—81no—
186C22×Dic43—81no—
187C2×D172—21no—
188C2×D172—21no—
189C2×D172—21no—
190C2×D172—21no—
191C2×D172—21no—
192C2×D172C2×D412yes—
193C2×C4×D43—24no—
194C2×C4×D43—81no—
195C2×C4×D43—81no—
196C2×Dic86—21no—
197C2×Dic86—21no—
198C2×Dic86—21no—
199C2×Dic86—21no—
200C2×Dic86—21no—
201C2×Dic86#4112yes—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43—21no—
213C2×C8×C43#4112yes—
214C4⋊C4×C43—22no—
215C22⋊C4×C43—22no—
216C22⋊C4×C43—22no—
217C42×C43C2×D412yes—
218C42×C43C2×D412yes—
219C22⋊Dic43—24no—
220C22⋊Dic43—42no—
221C22⋊Dic43—42no—
222C22⋊Dic43—42no—
223C22⋊Dic43—42no—
224(C2×D43)⋊C4—24no—
225(C2×D43)⋊C4—24no—
226(C2×D43)⋊C4—24no—
227C4⋊Dic43—24no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C4⋊Dic43—21no—
236C4⋊Dic43—21no—
237C4⋊Dic43C2×D412yes—
238C4⋊Dic43C2×D412yes—
239C4⋊Dic43C2×D412yes—
240Dic43⋊C4—24no—
241Dic43⋊C4—24no—
242Dic43⋊C4—42no—
243Dic43⋊C4—42no—
244Dic43⋊C4—42no—
245C4×Dic43—24no—
246C4×Dic43—42no—
247#10621873—28no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43#13512yes—
262C23×C43C22×D411yescharacteristic
263C22×D43—22no—
264C22×D43—41no—
265C22×D43—41no—
266C22×D43—41no—
267C22×D43—41no—
268C22×D43—41no—
269C22×D43—41no—
270D4×C43—44no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
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—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#12012yes—
290C2×C4×C43#12012yes—
291C2×C4×C43C22×D411yescharacteristic
292C2×C4×C43C22×D411yescharacteristic
293C2×C4×C43C2×#4111yescharacteristic
294C2×C4×C43C2×#4111yescharacteristic
295C2×C4×C43H(5,𝔽2)11yescharacteristic
296C2×C4×C432−1+411yescharacteristic
297C22⋊D43—48no—
298C22⋊D43—84no—
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—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—84no—
321D172—22no—
322D172—22no—
323D172—41no—
324D172—41no—
325C4×D43—84no—
326Dic86—22no—
327Dic86—22no—
328Dic86—41no—
329Dic86—41no—
330C8×C43—22no—
331C8×C43—41no—
332C8×C43—41no—
333C8×C43—41no—
334#24126—431nomaximal, Sylow
335C22×C43—22no—
336C22×C43—22no—
337C22×C43—22no—
338C22×C43—41no—
339C22×C43—41no—
340C22×C43—41no—
341C22×C43—41no—
342C22×C43—41no—
343C22×C43—41no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—41no—
347C22×C43—41no—
348C22×C43—41no—
349C22×C43C2×#12011yescharacteristic
350C22×C43#54611yescharacteristic
351C22×C43#54711yescharacteristic
352C22×C43C2×#13511yescharacteristic
353C22×C43#57511yescharacteristic
354C22×C43#57711yescharacteristic
355C22×C43#57711yescharacteristic
356C2×D43—42no—
357C2×D43—42no—
358C2×D43—42no—
359C2×D43—81no—
360C2×D43—81no—
361C2×D43—81no—
362C2×D43—81no—
363C4×C43—22no—
364C4×C43—22no—
365C4×C43—41no—
366C4×C43—41no—
367C4×C43#52511yescharacteristic
368C4×C43#53711yescharacteristic
369C4×C43#54811yescharacteristic
370C4×C43#55011yescharacteristic
371Dic43—42no—
372Dic43—42no—
373Dic43—42no—
374Dic43—42no—
375Dic43—81no—
376Dic43—81no—
377Dic43—81no—
378C2×#553—431no—
379C2×#479—431no—
380C2×C4×SD16—431no—
381#2536—431no—
382#2034—431no—
383#2033—431no—
384#2000—431no—
385#2000—431no—
386#1991—431no—
387#1954D4311yescharacteristic, complemented
388#1873—431no—
389#1872—431no—
390#1854—431no—
391#1853—431no—
392#1804—431no—
393C2×C43—42no—
394C2×C43—81no—
395C2×C43#240711yescharacteristic
396C2×C43#300211yescharacteristic
397C2×C43#300911yescharacteristic
398C2×C43#330111yescharacteristic
399C2×C43#332611yescharacteristic
400C2×C43#333711yescharacteristic
401C2×C43#335111yescharacteristic
402D43—82no—
403C22×SD16—431no—
404#553—864no—
405#553—864no—
406C2×#126—861no—
407C2×#125—431no—
408C2×#123—861no—
409C2×C22⋊Q8—431no—
410C2×C22⋊Q8—431no—
411C2×#121—431no—
412C2×#121—431no—
413C2×#121—861no—
414C2×C4×Q8—431no—
415C2×C4×D4—431no—
416C2×C4×D4—861no—
417C2×C4×D4C2×D4311yescharacteristic
418C2×#117—431no—
419C22×C4⋊C4—431no—
420#479—864no—
421C4×SD16—864no—
422C2×#107—431no—
423C2×#106—431no—
424C2×#106—431no—
425C2×C4⋊C8C2×D4311yescharacteristic
426C2×#103—431no—
427C2×#103—431no—
428C2×#103—431no—
429C2×#102—431no—
430C2×#102—431no—
431C2×#102—431no—
432C2×C22⋊C8C2×D4311yescharacteristic
433C2×C22⋊C8C2×D4311yescharacteristic
434C2×C22⋊C8C2×D4311yescharacteristic
435C2×C22⋊C8C2×D4311yescharacteristic
436C2×C4×C8C2×D4311yescharacteristic
437#398—861no—
438#394—861no—
439#388—861no—
440#388—861no—
441#382—431no—
442#380—431no—
443#380—431no—
444#340—431no—
445#340—431no—
446#340—431no—
447#340—431no—
448#340—431no—
449#340—431no—
450C43#2412611yescharacteristic, complemented, Sylow
451C22×Q8—431no—
452C22×D4—431no—
453C22×D4—861no—
454C22×D4—861no—
455C22×D4D17211yescharacteristic
456C23×C4—861no—
457C23×C4—861no—
458C23×C4C22×D4311yescharacteristic
459C23×C4C22×D4311yescharacteristic
460C2×SD16—862no—
461C2×SD16—862no—
462C2×SD16—862no—
463C22×C8C22×D4311yescharacteristic
464C22×C8C22×D4311yescharacteristic
465C22×C8C22×D4311yescharacteristic
466C22×C8C22×D4311yescharacteristic
467#126—868no—
468#125—434no—
469#125—862no—
470#123—868no—
471C22⋊Q8—862no—
472C22⋊Q8—862no—
473C22⋊Q8—1721no—
474C22⋊Q8—1721no—
475#121—862no—
476#121—862no—
477#121—862no—
478#121—862no—
479#121—868no—
480C4×Q8—862no—
481C4×Q8—862no—
482C4×D4—22no—
483C4×D4—22no—
484C4×D4—434no—
485C4×D4—868no—
486C4×D4—862no—
487#117—862no—
488#117—862no—
489C2×C4⋊C4—431no—
490C2×C4⋊C4—431no—
491C2×C4⋊C4—431no—
492C2×C4⋊C4—431no—
493C2×C4⋊C4—431no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—862no—
496C2×C4⋊C4—862no—
497C2×C4⋊C4—861no—
498C2×C4⋊C4—861no—
499C2×C4⋊C4—861no—
500C2×C4⋊C4—861no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4D17211yescharacteristic
504C2×C22⋊C4—861no—
505C2×C22⋊C4—861no—
506C2×C22⋊C4—861no—
507C2×C22⋊C4—861no—
508C2×C22⋊C4—861no—
509C2×C22⋊C4—861no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4D17211yescharacteristic
513C2×C22⋊C4D17211yescharacteristic
514C2×C42—861no—
515C2×C42—861no—
516C2×C42C22×D4311yescharacteristic
517#107—862no—
518#106—862no—
519#106—862no—
520C4⋊C8—22no—
521#103—862no—
522#103—862no—
523#103—862no—
524#102—862no—
525#102—1721no—
526#102—1721no—
527C22⋊C8—22no—
528C22⋊C8—22no—
529C22⋊C8—41no—
530C22⋊C8—41no—
531C4×C8—22no—
532#95—861no—
533#95—861no—
534#95—861no—
535#95—861no—
536C24—861no—
537C24C2×D17211yescharacteristic
538C24C2×D17211yescharacteristic
539C2×Q8—432no—
540C2×Q8—861no—
541C2×Q8—861no—
542C2×Q8—861no—
543C2×Q8—861no—
544C2×Q8—861no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—41no—
548C2×D4—432no—
549C2×D4—864no—
550C2×D4—864no—
551C2×D4—861no—
552C2×D4—861no—
553C2×D4—861no—
554C2×D4—861no—
555C2×D4—861no—
556C2×D4—3441no—
557C2×D4—3441no—
558C2×D4—1722no—
559C2×D4—1722no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—864no—
573C22×C4—861no—
574C22×C4—861no—
575C22×C4—861no—
576C22×C4—861no—
577C22×C4—864no—
578C22×C4—861no—
579C22×C4—861no—
580C22×C4—861no—
581C22×C4—3441no—
582C22×C4—3441no—
583C22×C4—3441no—
584C22×C4—3441no—
585C22×C4C2×D17211yescharacteristic
586C22×C4C2×D17211yescharacteristic
587C22×C4C2×D17211yescharacteristic
588C22×C4C2×D17211yescharacteristic
589C22×C4C23×D4311yescharacteristic
590SD16—868no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8#1062190012yes—
603C4⋊C4—22no—
604C4⋊C4—432no—
605C4⋊C4—432no—
606C4⋊C4—432no—
607C4⋊C4—864no—
608C4⋊C4—864no—
609C4⋊C4—864no—
610C4⋊C4—861no—
611C4⋊C4—861no—
612C4⋊C4—861no—
613C4⋊C4—861no—
614C4⋊C4—861no—
615C4⋊C4—861no—
616C4⋊C4—861no—
617C4⋊C4—861no—
618C4⋊C4—861no—
619C4⋊C4—1722no—
620C4⋊C4—1722no—
621C4⋊C4—1722no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—864no—
625C22⋊C4—864no—
626C22⋊C4—864no—
627C22⋊C4—864no—
628C22⋊C4—1722no—
629C22⋊C4—1722no—
630C22⋊C4—1722no—
631C22⋊C4—1722no—
632C42—864no—
633C42—1722no—
634C42D4×D4312yes—
635C42D4×D4312yes—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—862no—
650C23—1721no—
651C23—1721no—
652C23—1721no—
653C23—1721no—
654C23—1721no—
655C23—1721no—
656C23#1306334712yes—
657C23C22×D17211yescharacteristic
658Q8—862no—
659Q8—862no—
660Q8—1721no—
661Q8—1721no—
662D4—44no—
663D4—862no—
664D4—862no—
665D4—3444no—
666D4—1728no—
667D4—1721no—
668D4—1721no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—862no—
688C2×C4—862no—
689C2×C4—862no—
690C2×C4—862no—
691C2×C4—3444no—
692C2×C4—3444no—
693C2×C4—1721no—
694C2×C4—1721no—
695C2×C4—1721no—
696C2×C4—1721no—
697C2×C4—1721no—
698C2×C4—1721no—
699C2×C4—1721no—
700C2×C4—1721no—
701C2×C4—1721no—
702C2×C4—1721no—
703C2×C4—1721no—
704C2×C4—1721no—
705C2×C4—1721no—
706C2×C4—1721no—
707C2×C4—1721no—
708C2×C4—1721no—
709C2×C4—1721no—
710C2×C4#1306329512yes—
711C2×C4#1306329512yes—
712C2×C4C2×D4×D4311yescharacteristic
713C2×C4C2×D4×D4311yescharacteristic
714C2×C4#41×D4311yescharacteristic
715C2×C4C2×#1062190011yescharacteristic
716C2×C4#1306337011yescharacteristic
717C2×C4#1306337211yescharacteristic
718C8—22no—
719C8—41no—
720C8—41no—
721C8—41no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—3441no—
737C22—3441no—
738C22—3441no—
739C22—3441no—
740C22—1722no—
741C22—1722no—
742C22—1722no—
743C22C2×#1306329511yescharacteristic
744C22#1458354411yescharacteristic
745C22#1458355311yescharacteristic
746C22C2×#1306334711yescharacteristic
747C22#1458369911yescharacteristic
748C22#1458371111yescharacteristic
749C22#1458371111yescharacteristic
750C4—22no—
751C4—22no—
752C4—41no—
753C4—41no—
754C4—3441no—
755C4—3441no—
756C4—3441no—
757C4—1722no—
758C4—1722no—
759C4—1722no—
760C4—1722no—
761C4#1458340911yescharacteristic
762C4#1458347811yescharacteristic
763C4#1458355711yescharacteristic
764C4#1458356911yescharacteristic
765C2—42no—
766C2—81no—
767C2—3442no—
768C2#1913793811yescharacteristic
769C2#1914381711yescharacteristic
770C2#1914387411yescharacteristic
771C2#1914649911yescharacteristic
772C2#1914685011yescharacteristic
773C2#1914697611yescharacteristic
774C2#1914715711yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1954C2
socleC23×C43C22×D4
prime radicalC2×#14583595C2
hypercenter#1954D43
hypocenterC43#24126
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #1954

Complements

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

NH ≅ G/Ntype
2. C2×#14583207C2semidirect
3. C2×C4×#10621873C2semidirect
4. #19139504C2semidirect
5. #19135785C2semidirect
6. #19135778C2semidirect
7. #19135600C2semidirect
8. #19135600C2semidirect
9. #19135560C2semidirect
10. #19134905C2semidirect
11. #19134900C2semidirect
12. #19134796C2semidirect
13. #19134790C2semidirect
14. #19134606C2semidirect
15. C43×#1954C2semidirect
387. #1954D43semidirect
450. C43#24126semidirect

Maximal subgroups

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

subgroupindex
C2×#145835952
C2×#145832072
C2×C4×#106218732
#191395042
#191357852
#191357782
#191356002
#191355602
#191349052
#191349002
#191347962
#191347902
#191346062
C43×#19542
#2412643