Finite Group Databasebeta

← #25135378

Subgroups — #25135378

Order 11008.

1098 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582957C211yesmaximal, characteristic, complemented
2#19140385C211yesmaximal, characteristic, complemented
3#19137177C211yesmaximal, characteristic, complemented
4#19135981C211yesmaximal, characteristic, complemented
5#19135967C211yesmaximal, characteristic, complemented
6#19135903C211yesmaximal, characteristic, complemented
7#19135903C211yesmaximal, characteristic, complemented
8#19135472C211yesmaximal, characteristic, complemented
9#19135462C211yesmaximal, characteristic, complemented
10#19135289C211yesmaximal, characteristic, complemented
11#19135275C211yesmaximal, characteristic, complemented
12#19134918C211yesmaximal, characteristic, complemented
13#19134796C211yesmaximal, characteristic, complemented
14#19134526C211yesmaximal, characteristic, complemented
15C2×C43×#447C211yesmaximal, characteristic
16C2×#13063284C2211yescharacteristic
17C2×#13063284C2211yescharacteristic
18#14582957—24no—
19C2×#13063259C2211yescharacteristic, complemented
20C2×#13063257C2211yescharacteristic, complemented
21C2×Dic43⋊C8C2211yescharacteristic, complemented
22C2×Dic43⋊C8C2211yescharacteristic, complemented
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic, complemented
28C2×#13063246C2211yescharacteristic, complemented
29C2×C22⋊(C43⋊C8)C2211yescharacteristic
30C2×#13063235C2211yescharacteristic, complemented
31C2×C8×Dic43C2211yescharacteristic, complemented
32#14582835—21no—
33#14582824—21no—
34#14582813—21no—
35#14582813—21no—
36#14582802—21no—
37#14582802—21no—
38#14582802C2211yescharacteristic
39#14582802C2211yescharacteristic
40#14582802C2211yescharacteristic
41#14582802C2211yescharacteristic
42#14582802C2211yescharacteristic, complemented
43#14582802C2211yescharacteristic, complemented
44#14582795C2211yescharacteristic, complemented
45#14582795C2211yescharacteristic, complemented
46#14582759C2211yescharacteristic
47#14582755—21no—
48#14582755—21no—
49#14582662C2211yescharacteristic, complemented
50#14582662C2211yescharacteristic, complemented
51#14582661C2211yescharacteristic, complemented
52#14582661C2211yescharacteristic, complemented
53C23×D4×C43C2211yescharacteristic
54C22×D8×C43C2211yescharacteristic
55C22×D8×C43C2211yescharacteristic
56C2×#121×C43C2211yescharacteristic
57C43×#447—24no—
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63#13063284—22no—
64#13063284—22no—
65#13063284—41no—
66#13063284—41no—
67C2×C4⋊Dic43D411yescharacteristic
68C2×C4⋊Dic43D411yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×C22⋊Dic43—21no—
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43D411yescharacteristic
90C2×C22⋊Dic43D411yescharacteristic
91C2×C4×Dic43—21no—
92C2×C4×Dic43C2311yescharacteristic
93C2×C4×Dic43C2311yescharacteristic
94#13063259—41no—
95#13063257—41no—
96Dic43⋊C8—22no—
97Dic43⋊C8—22no—
98#13063246—22no—
99#13063246—22no—
100#13063246—41no—
101#13063246—41no—
102#13063246—41no—
103#13063246—41no—
104C22⋊(C43⋊C8)—22no—
105#13063235—22no—
106C8×Dic43—22no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C25×C43—21no—
111C22×D4×C43—22no—
112C22×D4×C43—22no—
113C22×D4×C43—21no—
114C22×D4×C43—21no—
115C22×D4×C43—22no—
116C22×D4×C43—22no—
117C22×D4×C43—41no—
118C22×D4×C43—41no—
119C22×D4×C43C2311yescharacteristic
120C22×D4×C43C2311yescharacteristic
121C22×D4×C43C2311yescharacteristic
122C23×C4×C43C2311yescharacteristic
123C2×D8×C43—22no—
124C2×D8×C43—22no—
125C2×D8×C43—22no—
126C2×D8×C43—22no—
127C2×D8×C43—41no—
128C2×D8×C43—41no—
129C22×C8×C43C2311yescharacteristic
130C22×C8×C43C2311yescharacteristic
131#121×C43—22no—
132#121×C43—22no—
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C22⋊C4×C43—21no—
135#102×C43—22no—
136#102×C43—22no—
137C22⋊C8×C43D414yes—
138C24×C43—24no—
139C24×C43—21no—
140C24×C43—21no—
141C24×C43—21no—
142C24×C43—42no—
143C24×C43—42no—
144C24×C43—81no—
145C24×C43—81no—
146C24×C43—81no—
147C24×C43—81no—
148C24×C43C2×D411yescharacteristic
149C2×D4×C43—24no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—44no—
167C2×D4×C43—44no—
168C2×D4×C43—44no—
169C2×D4×C43—44no—
170C2×D4×C43—42no—
171C2×D4×C43—42no—
172C2×D4×C43—42no—
173C2×D4×C43—81no—
174C2×D4×C43—81no—
175C2×D4×C43#4112yes—
176C2×D4×C43#4112yes—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43C2×D412yes—
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43#4112yes—
185C22×C4×C43C2411yescharacteristic
186C22×Dic43—21no—
187C22×Dic43—21no—
188C22×Dic43—21no—
189C22×Dic43—21no—
190C22×Dic43C2×D411yescharacteristic
191C22×Dic43C2×D411yescharacteristic
192C22×Dic43C2×D411yescharacteristic
193C22×Dic43C2×D411yescharacteristic
194D8×C43—44no—
195D8×C43—44no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43C2×D412yes—
201C2×C8×C43C2×D412yes—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C22⋊C4×C43—42no—
205C22⋊Dic43—22no—
206C22⋊Dic43—22no—
207C22⋊Dic43—42no—
208C22⋊Dic43—81no—
209C22⋊Dic43—81no—
210C22⋊Dic43—81no—
211C22⋊Dic43—81no—
212C22⋊Dic43—81no—
213C22⋊Dic43—81no—
214C22⋊Dic43—81no—
215C22⋊Dic43—81no—
216C22⋊Dic43—81no—
217C22⋊Dic43—81no—
218C22⋊Dic43—81no—
219C22⋊Dic43—81no—
220C22⋊Dic43—81no—
221C4⋊Dic43—22no—
222C4⋊Dic43—22no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231Dic43⋊C4—81no—
232Dic43⋊C4—81no—
233C4×Dic43—21no—
234C4×Dic43—21no—
235C4×Dic43—21no—
236C4×Dic43—21no—
237C4×Dic43—42no—
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—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—22no—
251C23×C43—22no—
252C23×C43—48no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—84no—
273C23×C43—84no—
274C23×C43—84no—
275C23×C43—84no—
276C23×C43—84no—
277C23×C43—84no—
278C23×C43#12112yes—
279C23×C43C22×D411yescharacteristic
280D4×C43—22no—
281D4×C43—22no—
282D4×C43—22no—
283D4×C43—22no—
284D4×C43—48no—
285D4×C43—41no—
286D4×C43—41no—
287D4×C43—41no—
288D4×C43—41no—
289D4×C43—41no—
290D4×C43—41no—
291D4×C43—41no—
292D4×C43—41no—
293D4×C43—84no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43#12112yes—
304C2×C4×C43C22×D411yescharacteristic
305C2×C4×C43C2×#4111yescharacteristic
306C2×C4×C43C2×#4111yescharacteristic
307C2×C4×C43C2×#4111yescharacteristic
308C2×C4×C43H(5,𝔽2)11yescharacteristic
309C2×C4×C43H(5,𝔽2)11yescharacteristic
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—21no—
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43—21no—
319C2×Dic43—21no—
320C2×Dic43—21no—
321C2×Dic43—21no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43—41no—
332C2×Dic43—41no—
333C2×Dic43—41no—
334C8×C43—22no—
335C8×C43—22no—
336C43⋊C8—41no—
337C43⋊C8—41no—
338#24512—431nomaximal, Sylow
339C22×C43—22no—
340C22×C43—22no—
341C22×C43—22no—
342C22×C43—41no—
343C22×C43—41no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—42no—
347C22×C43—42no—
348C22×C43—42no—
349C22×C43—42no—
350C22×C43—42no—
351C22×C43—42no—
352C22×C43—816no—
353C22×C43—81no—
354C22×C43—81no—
355C22×C43—81no—
356C22×C43—81no—
357C22×C43—81no—
358C22×C43—81no—
359C22×C43—81no—
360C22×C43—81no—
361C22×C43—81no—
362C22×C43—81no—
363C22×C43—81no—
364C22×C43—81no—
365C22×C43—81no—
366C22×C43—81no—
367C22×C43—81no—
368C22×C43C2×#12111yescharacteristic
369C22×C43#52511yescharacteristic
370C22×C43#53511yescharacteristic
371C22×C43#57611yescharacteristic
372C22×C43#57611yescharacteristic
373C22×C43#57611yescharacteristic
374C22×C43#57711yescharacteristic
375C4×C43—22no—
376C4×C43—81no—
377C4×C43#54611yescharacteristic
378C4×C43#54611yescharacteristic
379C4×C43#55111yescharacteristic
380C4×C43#55111yescharacteristic
381Dic43—41no—
382Dic43—41no—
383Dic43—41no—
384Dic43—41no—
385Dic43—81no—
386Dic43—81no—
387Dic43—81no—
388Dic43—81no—
389C2×#447D4311yescharacteristic
390C2×#433—431no—
391#2624—431no—
392#2309—431no—
393#2067—431no—
394#2065—431no—
395#2054—431no—
396#2054—431no—
397#1972—431no—
398#1970—431no—
399#1936—431no—
400#1934—431no—
401#1875—431no—
402#1854—431no—
403#1786—431no—
404C2×C43—42no—
405C2×C43—82no—
406C2×C43—82no—
407C2×C43—161no—
408C2×C43#241111yescharacteristic
409C2×C43#305811yescharacteristic
410C2×C43#306211yescharacteristic
411C2×C43#311811yescharacteristic
412C2×C43#312211yescharacteristic
413C2×C43#322011yescharacteristic
414C2×C43#322411yescharacteristic
415C23×D4C2×D4311yescharacteristic
416C22×D8C2×D4311yescharacteristic
417C22×D8C2×D4311yescharacteristic
418C2×#121C2×D4311yescharacteristic
419C2×#117—431no—
420C2×#117—431no—
421#447—24no—
422#433—864no—
423C2×#107—431no—
424C2×#106—431no—
425C2×C4⋊C8—431no—
426C2×C4⋊C8—431no—
427C2×#102—431no—
428C2×#102—431no—
429C2×#102—431no—
430C2×#102—431no—
431C2×#102—431no—
432C2×#102—431no—
433C2×#102C2×D4311yescharacteristic
434C2×#102C2×D4311yescharacteristic
435C2×C22⋊C8—431no—
436C2×C22⋊C8C2×D4311yescharacteristic
437C2×#97—431no—
438C2×C4×C8—431no—
439#399—861no—
440#397—861no—
441#394—861no—
442#394—861no—
443#390—431no—
444#390—431no—
445#390—431no—
446#390—431no—
447#390—431no—
448#390—431no—
449#390—861no—
450#390—861no—
451#389—431no—
452#389—431no—
453#380—431no—
454#379—861no—
455#379—861no—
456#340—431no—
457#340—431no—
458#340—431no—
459#340—431no—
460C43#2451211yescharacteristic, complemented, Sylow
461C25—21no—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—21no—
465C22×D4—21no—
466C22×D4—22no—
467C22×D4—22no—
468C22×D4—41no—
469C22×D4—41no—
470C22×D4C22×D4311yescharacteristic
471C22×D4C22×D4311yescharacteristic
472C22×D4C22×D4311yescharacteristic
473C23×C4C22×D4311yescharacteristic
474C2×D8—22no—
475C2×D8—22no—
476C2×D8—22no—
477C2×D8—22no—
478C2×D8—41no—
479C2×D8—41no—
480C22×C8—431no—
481C22×C8—431no—
482C22×C8C22×D4311yescharacteristic
483C22×C8C22×D4311yescharacteristic
484#121—22no—
485#121—22no—
486#117—862no—
487#117—862no—
488#117—1721no—
489#117—1721no—
490C2×C4⋊C4—431no—
491C2×C4⋊C4—431no—
492C2×C4⋊C4—431no—
493C2×C4⋊C4—431no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—861no—
497C2×C4⋊C4—861no—
498C2×C4⋊C4C22×D4311yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—431no—
501C2×C22⋊C4—431no—
502C2×C22⋊C4—861no—
503C2×C22⋊C4—861no—
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⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4—861no—
515C2×C22⋊C4—861no—
516C2×C42—431no—
517C2×C42—431no—
518C2×C42—861no—
519#107—1721no—
520#106—1721no—
521C4⋊C8—862no—
522C4⋊C8—862no—
523#102—22no—
524#102—22no—
525#102—862no—
526#102—862no—
527#102—1721no—
528#102—1721no—
529#102—1721no—
530#102—1721no—
531C22⋊C8—862no—
532C22⋊C8C22⋊D4314yes—
533#97—862no—
534C4×C8—862no—
535#95—861no—
536#95—861no—
537#95—861no—
538C24—24no—
539C24—21no—
540C24—21no—
541C24—21no—
542C24—42no—
543C24—42no—
544C24—81no—
545C24—81no—
546C24—81no—
547C24—81no—
548C24D4×D4311yescharacteristic
549C2×D4—24no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4#1062190012yes—
576C2×D4#1062190012yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—431no—
583C22×C4—431no—
584C22×C4—431no—
585C22×C4—431no—
586C22×C4—861no—
587C22×C4—861no—
588C22×C4—861no—
589C22×C4—861no—
590C22×C4D4×D4311yescharacteristic
591C22×C4#1062190012yes—
592C22×C4C2×C22⋊D4312yes—
593C22×C4C23×D4311yescharacteristic
594D8—44no—
595D8—44no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—861no—
601C2×C8—861no—
602C2×C8—861no—
603C2×C8—861no—
604C2×C8—861no—
605C2×C8—861no—
606C2×C8C2×C22⋊D4312yes—
607C2×C8C2×C22⋊D4312yes—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—862no—
611C4⋊C4—862no—
612C4⋊C4—861no—
613C4⋊C4—861no—
614C4⋊C4—861no—
615C4⋊C4—861no—
616C4⋊C4—861no—
617C4⋊C4—861no—
618C4⋊C4—861no—
619C4⋊C4—861no—
620C4⋊C4—3441no—
621C4⋊C4—3441no—
622C22⋊C4—42no—
623C22⋊C4—862no—
624C22⋊C4—862no—
625C22⋊C4—3441no—
626C22⋊C4—3441no—
627C22⋊C4—3441no—
628C22⋊C4—3441no—
629C22⋊C4—3441no—
630C22⋊C4—3441no—
631C22⋊C4—3441no—
632C22⋊C4—3441no—
633C22⋊C4—3441no—
634C22⋊C4—3441no—
635C22⋊C4—3441no—
636C22⋊C4—3441no—
637C22⋊C4—3441no—
638C22⋊C4—1722no—
639C42—861no—
640C42—861no—
641C42—861no—
642C42—861no—
643C42—1722no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—22no—
651C23—22no—
652C23—48no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—84no—
673C23—84no—
674C23—84no—
675C23—84no—
676C23—84no—
677C23—84no—
678C23#1306329612yes—
679C23C2×D4×D4311yescharacteristic
680D4—22no—
681D4—22no—
682D4—22no—
683D4—22no—
684D4—48no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—84no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—861no—
704C2×C4—861no—
705C2×C4—861no—
706C2×C4—861no—
707C2×C4—861no—
708C2×C4—861no—
709C2×C4—861no—
710C2×C4—861no—
711C2×C4—861no—
712C2×C4—861no—
713C2×C4—861no—
714C2×C4—861no—
715C2×C4—1721no—
716C2×C4—1721no—
717C2×C4—1721no—
718C2×C4—1721no—
719C2×C4—1721no—
720C2×C4—1721no—
721C2×C4—1721no—
722C2×C4—1721no—
723C2×C4—1721no—
724C2×C4—1721no—
725C2×C4—1721no—
726C2×C4—1721no—
727C2×C4#1306329612yes—
728C2×C4C22×C22⋊D4311yescharacteristic
729C2×C4C2×#1062190011yescharacteristic
730C2×C4C2×#1062190011yescharacteristic
731C2×C4C2×#1062190011yescharacteristic
732C2×C4#1306337011yescharacteristic
733C2×C4#1306337011yescharacteristic
734C8—22no—
735C8—22no—
736C8—1721no—
737C8—1721no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—816no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22C2×#1306329611yescharacteristic
768C22#1458340511yescharacteristic
769C22#1458346411yescharacteristic
770C22#1458370011yescharacteristic
771C22#1458370011yescharacteristic
772C22#1458370311yescharacteristic
773C22#1458370911yescharacteristic
774C4—22no—
775C4—81no—
776C4—3441no—
777C4—3441no—
778C4—3441no—
779C4—3441no—
780C4—1721no—
781C4—1721no—
782C4—1721no—
783C4—1721no—
784C4#1458354311yescharacteristic
785C4#1458354311yescharacteristic
786C4#1458358011yescharacteristic
787C4#1458358011yescharacteristic
788C2—42no—
789C2—82no—
790C2—82no—
791C2—161no—
792C2#1913797611yescharacteristic
793C2#1914423911yescharacteristic
794C2#1914426911yescharacteristic
795C2#1914477211yescharacteristic
796C2#1914483211yescharacteristic
797C2#1914564111yescharacteristic
798C2#1914568511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#447C2
socleC23×C43C22×D4
hypercenterC2×#447D43
hypocenterC43#24512
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
1. C2×#14582957C2semidirect
2. #19140385C2semidirect
3. #19137177C2semidirect
4. #19135981C2semidirect
5. #19135967C2semidirect
6. #19135903C2semidirect
7. #19135903C2semidirect
8. #19135472C2semidirect
9. #19135462C2semidirect
10. #19135289C2semidirect
11. #19135275C2semidirect
12. #19134918C2semidirect
13. #19134796C2semidirect
14. #19134526C2semidirect
19. C2×#13063259C22semidirect
20. C2×#13063257C22semidirect
21. C2×Dic43⋊C8C22semidirect
22. C2×Dic43⋊C8C22semidirect
27. C2×#13063246C22semidirect
28. C2×#13063246C22semidirect
30. C2×#13063235C22semidirect
31. C2×C8×Dic43C22semidirect
42. #14582802C22semidirect
43. #14582802C22semidirect
44. #14582795C22semidirect
45. #14582795C22semidirect
49. #14582662C22semidirect
50. #14582662C22semidirect
51. #14582661C22semidirect
52. #14582661C22semidirect
460. C43#24512semidirect

Maximal subgroups

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

subgroupindex
C2×#145829572
#191403852
#191371772
#191359812
#191359672
#191359032
#191354722
#191354622
#191352892
#191352752
#191349182
#191347962
#191345262
C2×C43×#4472
#2451243