Finite Group Databasebeta

← #25140296

Subgroups — #25140296

Order 11008.

1154 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583222C211yesmaximal, characteristic, complemented
2C2×#14582904C211yesmaximal, characteristic, complemented
3#19137945C211yesmaximal, characteristic
4#19137539C211yesmaximal, characteristic, complemented
5#19136121C211yesmaximal, characteristic, complemented
6#19136001C211yesmaximal, characteristic, complemented
7#19135782C211yesmaximal, characteristic, complemented
8#19135776C211yesmaximal, characteristic, complemented
9#19135225C211yesmaximal, characteristic, complemented
10#19135224C211yesmaximal, characteristic, complemented
11#19134914C211yesmaximal, characteristic, complemented
12#19134890C211yesmaximal, characteristic, complemented
13#19134796C211yesmaximal, characteristic, complemented
14#19134626C211yesmaximal, characteristic, complemented
15C43×#1786C211yesmaximal, characteristic, complemented
16C22×#10621877C2211yescharacteristic
17C2×#13063296C2211yescharacteristic
18C2×#13063296C2211yescharacteristic
19C2×#13063294—21no—
20C2×C4×C22⋊D43C2211yescharacteristic
21C2×#13063284C2211yescharacteristic
22C2×#13063283C2211yescharacteristic, complemented
23#14583222—24no—
24C2×#13063259C2211yescharacteristic, complemented
25C2×#13063258C2211yescharacteristic, complemented
26C2×#13063257C2211yescharacteristic, complemented
27C2×#13063256C2211yescharacteristic, complemented
28#14582904—24no—
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
34C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
35#14582813—21no—
36#14582807—21no—
37#14582802C2211yescharacteristic
38#14582802C2211yescharacteristic
39#14582799—21no—
40#14582793—21no—
41#14582788—21no—
42#14582768C2211yescharacteristic, complemented
43#14582759C2211yescharacteristic
44#14582756C2211yescharacteristic, complemented
45#14582755—21no—
46C4⋊C4×Dic43C2211yescharacteristic, complemented
47#14582750—21no—
48#14582662C2211yescharacteristic, complemented
49#14582662C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582661C2211yescharacteristic, complemented
52#14582653C2211yescharacteristic, complemented
53#14582653C2211yescharacteristic, complemented
54C23×D4×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C43×#380C2211yescharacteristic
61C22×C22⋊D43—21no—
62C22×C22⋊D43—21no—
63C22×C22⋊D43D411yescharacteristic
64C22×C4×D43C2311yescharacteristic
65C2×#10621877—22no—
66C2×#10621877—22no—
67C2×#10621877—41no—
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063296—22no—
71#13063296—22no—
72#13063296—41no—
73#13063296—41no—
74#13063294—44no—
75C4×C22⋊D43—22no—
76C4×C22⋊D43—22no—
77#13063284—22no—
78#13063284—41no—
79#13063283—22no—
80#13063283—41no—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4D411yescharacteristic
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×C22⋊Dic43—21no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—21no—
96C2×C22⋊Dic43D411yescharacteristic
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4D411yescharacteristic
100C2×C4×Dic43—21no—
101C2×C4×Dic43—21no—
102C2×C4×Dic43—21no—
103C2×C4×Dic43C2311yescharacteristic
104#13063259—41no—
105#13063258—22no—
106#13063257—22no—
107#13063256—41no—
108#13063246—22no—
109#13063246—22no—
110#13063246—22no—
111#13063246D414yescomplemented
112(C2×D43)⋊C8—22no—
113(C2×D43)⋊C8—41no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C25×C43—21no—
118C22×D4×C43—22no—
119C22×D4×C43—22no—
120C22×D4×C43—21no—
121C22×D4×C43—22no—
122C22×D4×C43—22no—
123C22×D4×C43—41no—
124C22×D4×C43—41no—
125C22×D4×C43C2311yescharacteristic
126C22×D4×C43C2311yescharacteristic
127C23×C4×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129C22×C8×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C22⋊C4×C43—21no—
133#102×C43—22no—
134#102×C43—22no—
135#102×C43—41no—
136#102×C43—41no—
137C22⋊C8×C43—22no—
138#95×C43—21no—
139C24×C43—21no—
140C24×C43—21no—
141C24×C43—42no—
142C24×C43—42no—
143C24×C43—42no—
144C24×C43—42no—
145C24×C43—42no—
146C24×C43—81no—
147C24×C43—81no—
148C24×C43C2×D411yescharacteristic
149C23×D43C2×D411yescharacteristic
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—28no—
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—42no—
162C2×D4×C43—42no—
163C2×D4×C43—44no—
164C2×D4×C43—44no—
165C2×D4×C43—44no—
166C2×D4×C43—42no—
167C2×D4×C43C2×D412yes—
168C2×D4×C43#4112yes—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43#4112yes—
177C22×C4×C43#4112yes—
178C22×C4×C43C2411yescharacteristic
179C2×C22⋊D43—22no—
180C2×C22⋊D43—22no—
181C2×C22⋊D43—41no—
182C2×C22⋊D43—42no—
183C2×C22⋊D43—42no—
184C2×C22⋊D43—42no—
185C2×C22⋊D43—42no—
186C2×C22⋊D43—81no—
187C2×C22⋊D43—81no—
188C22×Dic43—21no—
189C22×Dic43—21no—
190C22×Dic43—21no—
191C22×Dic43—21no—
192C22×Dic43C2×D411yescharacteristic
193C22×Dic43C2×D411yescharacteristic
194C22×Dic43C2×D411yescharacteristic
195C2×C4×D43—21no—
196C2×C4×D43—21no—
197C2×C4×D43—21no—
198C2×C4×D43—21no—
199C2×C4×D43—21no—
200C2×C4×D43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C22⋊C4×C43—81no—
212C22⋊Dic43—22no—
213C22⋊Dic43—42no—
214C22⋊Dic43—42no—
215C22⋊Dic43—42no—
216C22⋊Dic43—42no—
217C22⋊Dic43—42no—
218C22⋊Dic43—42no—
219C22⋊Dic43—81no—
220C22⋊Dic43—81no—
221(C2×D43)⋊C4—22no—
222(C2×D43)⋊C4—42no—
223(C2×D43)⋊C4—81no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43C2×D412yes—
232Dic43⋊C4—22no—
233Dic43⋊C4—42no—
234Dic43⋊C4—81no—
235C4×Dic43—21no—
236C4×Dic43—21no—
237C4×Dic43—42no—
238C4×Dic43—42no—
239C4×Dic43—42no—
240#10621877—44no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8C2×D412yes—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—22no—
254C23×C43—22no—
255C23×C43—48no—
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—84no—
269C23×C43—84no—
270C23×C43—84no—
271C23×C43—84no—
272C23×C43—84no—
273C23×C43—84no—
274C23×C43#12312yes—
275C23×C43C22×D411yescharacteristic
276C22×D43—21no—
277C22×D43—21no—
278C22×D43—21no—
279C22×D43—21no—
280C22×D43—21no—
281C22×D43—21no—
282C22×D43—21no—
283D4×C43—22no—
284D4×C43—22no—
285D4×C43—22no—
286D4×C43—22no—
287D4×C43—48no—
288D4×C43—41no—
289D4×C43—41no—
290D4×C43—41no—
291D4×C43—41no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43#12312yes—
305C2×C4×C43C22×D411yescharacteristic
306C2×C4×C43C2×#4111yescharacteristic
307C2×C4×C43C2×#4111yescharacteristic
308C2×C4×C43C2×#4111yescharacteristic
309C2×C4×C43H(5,𝔽2)11yescharacteristic
310C2×C4×C43H(5,𝔽2)11yescharacteristic
311C22⋊D43—44no—
312C22⋊D43—84no—
313C22⋊D43—84no—
314C2×Dic43—21no—
315C2×Dic43—21no—
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43—22no—
319C2×Dic43—21no—
320C2×Dic43—21no—
321C2×Dic43—21no—
322C2×Dic43—21no—
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—
334C2×Dic43AGL(1,ℤ/8)12yes—
335C4×D43—41no—
336C4×D43—41no—
337C4×D43—41no—
338C4×D43—41no—
339C8×C43—41no—
340C8×C43—41no—
341C43⋊C8—22no—
342C43⋊C8—41no—
343#24890—431nomaximal, Sylow
344C22×C43—22no—
345C22×C43—22no—
346C22×C43—22no—
347C22×C43—41no—
348C22×C43—41no—
349C22×C43—41no—
350C22×C43—41no—
351C22×C43—42no—
352C22×C43—42no—
353C22×C43—42no—
354C22×C43—42no—
355C22×C43—42no—
356C22×C43—42no—
357C22×C43—816no—
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×C43C2×#12311yescharacteristic
367C22×C43D4211yescharacteristic
368C22×C43#54611yescharacteristic
369C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
370C22×C43#57511yescharacteristic
371C22×C43#57611yescharacteristic
372C22×C43#57711yescharacteristic
373C2×D43—41no—
374C2×D43—41no—
375C2×D43—41no—
376C2×D43—41no—
377C2×D43—41no—
378C2×D43—41no—
379C2×D43—41no—
380C4×C43—22no—
381C4×C43—81no—
382C4×C43—81no—
383C4×C43#52511yescharacteristic
384C4×C43#53811yescharacteristic
385C4×C43#54611yescharacteristic
386C4×C43#55111yescharacteristic
387Dic43—22no—
388Dic43—41no—
389Dic43—41no—
390Dic43—42no—
391Dic43—81no—
392Dic43—81no—
393Dic43—81no—
394C2×#482—431no—
395C2×#418—431no—
396#2408—431no—
397#2354—431no—
398#2093—431no—
399#2071—431no—
400#2034—431no—
401#2033—431no—
402#1926—431no—
403#1926—431no—
404#1875—431no—
405#1870—431no—
406#1854—431no—
407#1809—431no—
408#1786D4311yescharacteristic, complemented
409C2×C43—42no—
410C2×C43—82no—
411C2×C43—82no—
412C2×C43#241811yescharacteristic
413C2×C43#309411yescharacteristic
414C2×C43#309611yescharacteristic
415C2×C43#326711yescharacteristic
416C2×C43#327411yescharacteristic
417C2×C43#331911yescharacteristic
418C2×C43#332411yescharacteristic
419D43—81no—
420C23×D4C2×D4311yescharacteristic
421C22×M16—431no—
422C2×#121—431no—
423C2×#121—431no—
424C2×#120—861no—
425C2×C4×D4—431no—
426C2×#117—431no—
427C2×#117—431no—
428#482—864no—
429C2×#107—431no—
430C2×#107—431no—
431C2×#106—431no—
432C2×#106—431no—
433#418—864no—
434C2×#102—431no—
435C2×#102—431no—
436C2×#102—431no—
437C2×#102—431no—
438C2×#102C2×D4311yescharacteristic
439C2×#102C2×D4311yescharacteristic
440C2×#102C2×D4311yescharacteristic
441C2×#102C2×D4311yescharacteristic
442C2×C22⋊C8—431no—
443C2×C22⋊C8—431no—
444C2×C22⋊C8C2×D4311yescharacteristic
445#394—861no—
446#392—861no—
447#390—431no—
448#390—431no—
449#390—861no—
450#388—861no—
451#388—861no—
452#384—431no—
453#380—431no—
454#380—431no—
455#380C2×D4311yescharacteristic
456#379—861no—
457C4×C4⋊C4—431no—
458C4×C4⋊C4—861no—
459#340—431no—
460#340—431no—
461#340—431no—
462#340—431no—
463#336—431no—
464#336—431no—
465C43#2489011yescharacteristic, complemented, Sylow
466C25—21no—
467C22×D4—22no—
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—21no—
471C22×D4—22no—
472C22×D4—41no—
473C22×D4—41no—
474C22×D4—431no—
475C22×D4—861no—
476C22×D4—861no—
477C22×D4C22×D4311yescharacteristic
478C22×D4C22×D4311yescharacteristic
479C23×C4—431no—
480C23×C4C22×D4311yescharacteristic
481C2×M16—862no—
482C2×M16—862no—
483C2×M16—1721no—
484C22×C8—431no—
485C22×C8—431no—
486C22×C8C22×D4311yescharacteristic
487C22×C8C22×D4311yescharacteristic
488#121—862no—
489#121—862no—
490#121—1721no—
491#121—1721no—
492#120—1724no—
493C4×D4—862no—
494C4×D4—862no—
495#117—862no—
496#117—862no—
497#117—1721no—
498#117—1721no—
499C2×C4⋊C4—431no—
500C2×C4⋊C4—431no—
501C2×C4⋊C4—431no—
502C2×C4⋊C4—431no—
503C2×C4⋊C4—431no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4—861no—
506C2×C4⋊C4C22×D4311yescharacteristic
507C2×C4⋊C4C22×D4311yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—431no—
510C2×C22⋊C4—431no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4—861no—
515C2×C22⋊C4—861no—
516C2×C22⋊C4—861no—
517C2×C22⋊C4—861no—
518C2×C22⋊C4—861no—
519C2×C22⋊C4—861no—
520C2×C22⋊C4—861no—
521C2×C42—431no—
522C2×C42—861no—
523C2×C42—861no—
524C2×C42—861no—
525#107—862no—
526#107—1721no—
527#106—862no—
528#106—1721no—
529#102—22no—
530#102—22no—
531#102—41no—
532#102—41no—
533#102—434no—
534#102—862no—
535#102—862no—
536#102—862no—
537C22⋊C8—22no—
538C22⋊C8—862no—
539C22⋊C8—1721no—
540#95—21no—
541#95—861no—
542#95—861no—
543#95—861no—
544C24—21no—
545C24—21no—
546C24—42no—
547C24—42no—
548C24—42no—
549C24—42no—
550C24—42no—
551C24—81no—
552C24—81no—
553C24—431no—
554C24D4×D4311yescharacteristic
555C2×D4—28no—
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—42no—
569C2×D4—42no—
570C2×D4—44no—
571C2×D4—42no—
572C2×D4—862no—
573C2×D4—862no—
574C2×D4—3441no—
575C2×D4—3441no—
576C2×D4—1721no—
577C2×D4—1722no—
578C2×D4—1722no—
579C2×D4—1722no—
580C2×D4—1722no—
581C2×D4D4×D4312yes—
582C2×D4#1062190012yes—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—431no—
590C22×C4—431no—
591C22×C4—431no—
592C22×C4—861no—
593C22×C4—861no—
594C22×C4—861no—
595C22×C4—861no—
596C22×C4—861no—
597C22×C4—861no—
598C22×C4—861no—
599C22×C4—861no—
600C22×C4—861no—
601C22×C4—861no—
602C22×C4#1062189812yes—
603C22×C4D4×D4311yescharacteristic
604C22×C4#1062190012yes—
605C22×C4C23×D4311yescharacteristic
606M16—1724no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—432no—
614C2×C8—861no—
615C2×C8—861no—
616C2×C8—861no—
617C2×C8—861no—
618C2×C8—861no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—432no—
624C4⋊C4—862no—
625C4⋊C4—861no—
626C4⋊C4—861no—
627C4⋊C4—861no—
628C4⋊C4—861no—
629C4⋊C4—861no—
630C4⋊C4—861no—
631C4⋊C4—861no—
632C4⋊C4—3441no—
633C4⋊C4—1722no—
634C22⋊C4—81no—
635C22⋊C4—862no—
636C22⋊C4—862no—
637C22⋊C4—3441no—
638C22⋊C4—3441no—
639C22⋊C4—3441no—
640C22⋊C4—1722no—
641C22⋊C4—1722no—
642C22⋊C4—1722no—
643C22⋊C4—1722no—
644C22⋊C4—1722no—
645C22⋊C4—1722no—
646C22⋊C4—1722no—
647C42—861no—
648C42—861no—
649C42—1722no—
650C42—1722no—
651C42—1722no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—22no—
659C23—22no—
660C23—48no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—84no—
674C23—84no—
675C23—84no—
676C23—84no—
677C23—84no—
678C23—84no—
679C23—861no—
680C23—861no—
681C23—861no—
682C23—861no—
683C23—861no—
684C23—861no—
685C23—861no—
686C23#1306330712yes—
687C23C2×D4×D4311yescharacteristic
688D4—22no—
689D4—22no—
690D4—22no—
691D4—22no—
692D4—48no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—3444no—
698D4—3444no—
699D4—1724no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—432no—
713C2×C4—861no—
714C2×C4—861no—
715C2×C4—861no—
716C2×C4—861no—
717C2×C4—861no—
718C2×C4—861no—
719C2×C4—862no—
720C2×C4—861no—
721C2×C4—861no—
722C2×C4—1721no—
723C2×C4—1721no—
724C2×C4—1721no—
725C2×C4—1721no—
726C2×C4—1721no—
727C2×C4—1721no—
728C2×C4—1721no—
729C2×C4—1721no—
730C2×C4—1721no—
731C2×C4—1721no—
732C2×C4—1721no—
733C2×C4—1721no—
734C2×C4—1721no—
735C2×C4—1721no—
736C2×C4—1721no—
737C2×C4#1306330712yes—
738C2×C4C2×D4×D4311yescharacteristic
739C2×C4C2×#1062190011yescharacteristic
740C2×C4C2×#1062190011yescharacteristic
741C2×C4C2×#1062189811yescharacteristic
742C2×C4#1306337011yescharacteristic
743C2×C4#1306337011yescharacteristic
744C8—41no—
745C8—41no—
746C8—862no—
747C8—1721no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—816no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—1721no—
771C22—1721no—
772C22—1721no—
773C22—1721no—
774C22—1721no—
775C22—1721no—
776C22—1721no—
777C22C2×#1306330711yescharacteristic
778C22#1458353111yescharacteristic
779C22#1458353611yescharacteristic
780C22AGL(1,ℤ/8)×D4311yescharacteristic
781C22#1458369511yescharacteristic
782C22#1458370011yescharacteristic
783C22#1458370511yescharacteristic
784C4—22no—
785C4—81no—
786C4—81no—
787C4—862no—
788C4—3441no—
789C4—3441no—
790C4—3441no—
791C4—1721no—
792C4—1721no—
793C4—1722no—
794C4#1458340511yescharacteristic
795C4#1458348411yescharacteristic
796C4#1458353911yescharacteristic
797C4#1458357511yescharacteristic
798C2—42no—
799C2—82no—
800C2—82no—
801C2—3441no—
802C2#1913806111yescharacteristic
803C2#1914453311yescharacteristic
804C2#1914454911yescharacteristic
805C2#1914611811yescharacteristic
806C2#1914621311yescharacteristic
807C2#1914674411yescharacteristic
808C2#1914681911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1786C2
socleC23×C43C22×D4
prime radical#19137945C2
hypercenter#1786D43
hypocenterC43#24890
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

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

NH ≅ G/Ntype
1. C2×#14583222C2semidirect
2. C2×#14582904C2semidirect
4. #19137539C2semidirect
5. #19136121C2semidirect
6. #19136001C2semidirect
7. #19135782C2semidirect
8. #19135776C2semidirect
9. #19135225C2semidirect
10. #19135224C2semidirect
11. #19134914C2semidirect
12. #19134890C2semidirect
13. #19134796C2semidirect
14. #19134626C2semidirect
15. C43×#1786C2semidirect
22. C2×#13063283C22semidirect
24. C2×#13063259C22semidirect
25. C2×#13063258C22semidirect
26. C2×#13063257C22semidirect
27. C2×#13063256C22semidirect
33. C2×(C2×D43)⋊C8C22semidirect
34. C2×(C2×D43)⋊C8C22semidirect
42. #14582768C22semidirect
44. #14582756C22semidirect
46. C4⋊C4×Dic43C22semidirect
48. #14582662C22semidirect
49. #14582662C22semidirect
50. #14582661C22semidirect
51. #14582661C22semidirect
52. #14582653C22semidirect
53. #14582653C22semidirect
111. #13063246D4semidirect
408. #1786D43semidirect
465. C43#24890semidirect

Maximal subgroups

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

subgroupindex
C2×#145832222
C2×#145829042
#191379452
#191375392
#191361212
#191360012
#191357822
#191357762
#191352252
#191352242
#191349142
#191348902
#191347962
#191346262
C43×#17862
#2489043