Finite Group Databasebeta

← #25140288

Subgroups — #25140288

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×#14583220C211yesmaximal, characteristic, complemented
2C2×#14582904C211yesmaximal, characteristic, complemented
3#19137544C211yesmaximal, characteristic, complemented
4#19136123C211yesmaximal, characteristic, complemented
5#19135998C211yesmaximal, characteristic, complemented
6#19135781C211yesmaximal, characteristic, complemented
7#19135774C211yesmaximal, characteristic, complemented
8#19135219C211yesmaximal, characteristic, complemented
9#19135219C211yesmaximal, characteristic, complemented
10#19134918C211yesmaximal, characteristic, complemented
11#19134893C211yesmaximal, characteristic, complemented
12#19134792C211yesmaximal, characteristic, complemented
13#19134626C211yesmaximal, characteristic, complemented
14#19134526C211yesmaximal, characteristic, complemented
15C43×#2408C211yesmaximal, characteristic
16C22×#10621877C2211yescharacteristic
17C2×#13063284C2211yescharacteristic
18C2×#13063284C2211yescharacteristic, complemented
19#14583220—24no—
20C2×#13063258C2211yescharacteristic, complemented
21C2×#13063258C2211yescharacteristic, complemented
22C2×#13063256C2211yescharacteristic, complemented
23C2×#13063256C2211yescharacteristic, complemented
24#14582904—24no—
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×C22⋊(C43⋊C8)C2211yescharacteristic
34C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
35C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
36#14582802—21no—
37#14582792—21no—
38#14582792—21no—
39#14582769C2211yescharacteristic, complemented
40#14582759C2211yescharacteristic
41#14582759C2211yescharacteristic, complemented
42C4⋊C4×Dic43—21no—
43C4×C4⋊Dic43C2211yescharacteristic, complemented
44#14582661C2211yescharacteristic, complemented
45#14582661C2211yescharacteristic, complemented
46#14582661C2211yescharacteristic, complemented
47#14582661C2211yescharacteristic, complemented
48#14582654C2211yescharacteristic, complemented
49#14582654C2211yescharacteristic, complemented
50C23×D4×C43C2211yescharacteristic
51C2×#121×C43C2211yescharacteristic
52C2×#121×C43C2211yescharacteristic
53C2×#120×C43—21no—
54C2×C4×D4×C43C2211yescharacteristic
55C43×#394—21no—
56C43×#392—21no—
57C43×#390C2211yescharacteristic
58C43×#390C2211yescharacteristic
59C43×#380C2211yescharacteristic
60C43×#379—21no—
61C2×#10621877—22no—
62C2×#10621877—22no—
63C2×#10621877—41no—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68#13063284—22no—
69#13063284—22no—
70#13063284—41no—
71#13063284—41no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85#13063258—22no—
86#13063258—41no—
87#13063256—22no—
88#13063256—41no—
89#13063246—22no—
90#13063246—22no—
91#13063246—22no—
92#13063246—22no—
93#13063246—22no—
94#13063246—41no—
95#13063246—41no—
96#13063246D414yescomplemented
97C22⋊(C43⋊C8)—22no—
98C22⋊(C43⋊C8)—22no—
99C22⋊(C43⋊C8)—41no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C25×C43—21no—
104C22×D4×C43—22no—
105C22×D4×C43—22no—
106C22×D4×C43—21no—
107C22×D4×C43—21no—
108C22×D4×C43—21no—
109C22×D4×C43—22no—
110C22×D4×C43—22no—
111C22×D4×C43—41no—
112C22×D4×C43—41no—
113C22×D4×C43D411yescharacteristic
114C22×D4×C43C2311yescharacteristic
115C22×D4×C43C2311yescharacteristic
116C23×C4×C43C2311yescharacteristic
117C23×C4×C43C2311yescharacteristic
118#121×C43—22no—
119#121×C43—22no—
120#121×C43—41no—
121#121×C43—41no—
122#120×C43—44no—
123C4×D4×C43—22no—
124C4×D4×C43—22no—
125C2×C4⋊C4×C43D411yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43—21no—
133C2×C22⋊C4×C43—21no—
134C2×C22⋊C4×C43—21no—
135C2×C22⋊C4×C43D411yescharacteristic
136C2×C22⋊C4×C43D411yescharacteristic
137C2×C42×C43C2311yescharacteristic
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
149C24×C43C2×D411yescharacteristic
150C2×D4×C43—22no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—22no—
154C2×D4×C43—28no—
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—41no—
164C2×D4×C43—42no—
165C2×D4×C43—42no—
166C2×D4×C43—42no—
167C2×D4×C43—42no—
168C2×D4×C43—42no—
169C2×D4×C43—42no—
170C2×D4×C43—44no—
171C2×D4×C43—44no—
172C2×D4×C43—44no—
173C2×D4×C43—42no—
174C2×D4×C43—81no—
175C2×D4×C43—81no—
176C2×D4×C43C2×D412yes—
177C2×D4×C43#4112yes—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43#4112yes—
195C22×C4×C43#4112yes—
196C22×C4×C43C2411yescharacteristic
197C22×Dic43—21no—
198C22×Dic43—21no—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C4⋊C4×C43—22no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C22⋊C4×C43—22no—
207C22⋊C4×C43—22no—
208C22⋊C4×C43—42no—
209C22⋊C4×C43—42no—
210C22⋊C4×C43—42no—
211C22⋊C4×C43—42no—
212C22⋊C4×C43—42no—
213C22⋊C4×C43—81no—
214C22⋊C4×C43—81no—
215C42×C43—21no—
216C42×C43—21no—
217C22⋊Dic43—42no—
218C22⋊Dic43—42no—
219C22⋊Dic43—81no—
220C22⋊Dic43—81no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—42no—
229C4⋊Dic43—81no—
230C4⋊Dic43C2×D412yes—
231C4×Dic43—42no—
232C4×Dic43—42no—
233C4×Dic43—42no—
234#10621877—44no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
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—21no—
254C23×C43—21no—
255C23×C43—22no—
256C23×C43—22no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—48no—
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—41no—
273C23×C43—41no—
274C23×C43—41no—
275C23×C43—84no—
276C23×C43—84no—
277C23×C43—84no—
278C23×C43—84no—
279C23×C43—84no—
280C23×C43—84no—
281C23×C43#12312yes—
282C23×C43C22×D411yescharacteristic
283D4×C43—22no—
284D4×C43—22no—
285D4×C43—22no—
286D4×C43—22no—
287D4×C43—44no—
288D4×C43—48no—
289D4×C43—41no—
290D4×C43—41no—
291D4×C43—41no—
292D4×C43—41no—
293D4×C43—84no—
294D4×C43—84no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—21no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43#12312yes—
320C2×C4×C43AGL(1,ℤ/8)12yes—
321C2×C4×C43C22×D411yescharacteristic
322C2×C4×C43C2×#4111yescharacteristic
323C2×C4×C43C2×#4111yescharacteristic
324C2×C4×C43C2×#4111yescharacteristic
325C2×C4×C43H(5,𝔽2)11yescharacteristic
326C2×C4×C43H(5,𝔽2)11yescharacteristic
327C2×Dic43—22no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43—41no—
332C2×Dic43—41no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43—41no—
338C2×Dic43—41no—
339C43⋊C8—22no—
340C43⋊C8—41no—
341C43⋊C8—41no—
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—41no—
352C22×C43—41no—
353C22×C43—41no—
354C22×C43—42no—
355C22×C43—42no—
356C22×C43—41no—
357C22×C43—42no—
358C22×C43—41no—
359C22×C43—42no—
360C22×C43—41no—
361C22×C43—42no—
362C22×C43—41no—
363C22×C43—42no—
364C22×C43—816no—
365C22×C43—81no—
366C22×C43—81no—
367C22×C43—81no—
368C22×C43—81no—
369C22×C43—81no—
370C22×C43—81no—
371C22×C43—81no—
372C22×C43—81no—
373C22×C43C2×#12311yescharacteristic
374C22×C43D4211yescharacteristic
375C22×C43#54611yescharacteristic
376C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
377C22×C43#57511yescharacteristic
378C22×C43#57611yescharacteristic
379C22×C43#57711yescharacteristic
380C4×C43—22no—
381C4×C43—22no—
382C4×C43—41no—
383C4×C43—41no—
384C4×C43—81no—
385C4×C43—81no—
386C4×C43#52511yescharacteristic
387C4×C43#53811yescharacteristic
388C4×C43#54611yescharacteristic
389C4×C43#55111yescharacteristic
390Dic43—42no—
391Dic43—81no—
392Dic43—81no—
393Dic43—81no—
394C2×#482—431no—
395C2×#418—431no—
396#2408D4311yescharacteristic
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#1786—431no—
409C2×C43—42no—
410C2×C43—81no—
411C2×C43—82no—
412C2×C43—82no—
413C2×C43#241811yescharacteristic
414C2×C43#309411yescharacteristic
415C2×C43#309611yescharacteristic
416C2×C43#326711yescharacteristic
417C2×C43#327411yescharacteristic
418C2×C43#331911yescharacteristic
419C2×C43#332411yescharacteristic
420C23×D4C2×D4311yescharacteristic
421C22×M16—431no—
422C2×#121C2×D4311yescharacteristic
423C2×#121C2×D4311yescharacteristic
424C2×#120—21no—
425C2×C4×D4C2×D4311yescharacteristic
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×#102—431no—
439C2×#102—431no—
440C2×#102—431no—
441C2×#102—431no—
442C2×C22⋊C8—431no—
443C2×C22⋊C8—431no—
444C2×C22⋊C8—431no—
445#394—21no—
446#392—21no—
447#390—861no—
448#390C2×D4311yescharacteristic
449#390C2×D4311yescharacteristic
450#388—861no—
451#388—861no—
452#384—431no—
453#380—431no—
454#380—431no—
455#380C2×D4311yescharacteristic
456#379—21no—
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—21no—
470C22×D4—21no—
471C22×D4—22no—
472C22×D4—22no—
473C22×D4—21no—
474C22×D4—41no—
475C22×D4—41no—
476C22×D4C22⋊D4311yescharacteristic
477C22×D4C22×D4311yescharacteristic
478C22×D4C22×D4311yescharacteristic
479C23×C4C22×D4311yescharacteristic
480C23×C4C22×D4311yescharacteristic
481C2×M16—862no—
482C2×M16—862no—
483C2×M16—1721no—
484C22×C8—431no—
485C22×C8—431no—
486C22×C8—431no—
487C22×C8—431no—
488#121—22no—
489#121—22no—
490#121—41no—
491#121—41no—
492#120—44no—
493C4×D4—22no—
494C4×D4—22no—
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—861no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4C22⋊D4311yescharacteristic
506C2×C4⋊C4C22×D4311yescharacteristic
507C2×C4⋊C4C22×D4311yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—861no—
516C2×C22⋊C4—861no—
517C2×C22⋊C4—861no—
518C2×C22⋊C4—861no—
519C2×C22⋊C4C22⋊D4311yescharacteristic
520C2×C22⋊C4C22⋊D4311yescharacteristic
521C2×C42—861no—
522C2×C42—861no—
523C2×C42—861no—
524C2×C42C22×D4311yescharacteristic
525#107—862no—
526#107—1721no—
527#106—862no—
528#106—1721no—
529#102—434no—
530#102—862no—
531#102—862no—
532#102—862no—
533#102—862no—
534#102—862no—
535#102—1721no—
536#102—1721no—
537C22⋊C8—862no—
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—
553C24C2×C22⋊D4311yescharacteristic
554C24C2×C22⋊D4311yescharacteristic
555C2×D4—28no—
556C2×D4—22no—
557C2×D4—22no—
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—21no—
567C2×D4—21no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—41no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—44no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—81no—
580C2×D4—81no—
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—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—861no—
596C22×C4—861no—
597C22×C4—861no—
598C22×C4—861no—
599C22×C4#1062190012yes—
600C22×C4#1062190012yes—
601C22×C4C2×C22⋊D4311yescharacteristic
602C22×C4C2×C22⋊D4311yescharacteristic
603C22×C4C2×C22⋊D4311yescharacteristic
604C22×C4C2×C22⋊D4311yescharacteristic
605C22×C4C23×D4311yescharacteristic
606M16—1724no—
607C2×C8—432no—
608C2×C8—861no—
609C2×C8—861no—
610C2×C8—861no—
611C2×C8—861no—
612C2×C8—861no—
613C2×C8—861no—
614C2×C8—861no—
615C2×C8—861no—
616C2×C8—861no—
617C2×C8—861no—
618C2×C8—861no—
619C4⋊C4—22no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—432no—
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—22no—
635C22⋊C4—22no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—81no—
642C22⋊C4—81no—
643C22⋊C4—3441no—
644C22⋊C4—3441no—
645C22⋊C4—1722no—
646C22⋊C4—1722no—
647C42—21no—
648C42—21no—
649C42—1722no—
650C42—1722no—
651C42—1722no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—22no—
664C23—21no—
665C23—22no—
666C23—21no—
667C23—48no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—84no—
681C23—84no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23#1306330612yes—
687C23C22×C22⋊D4311yescharacteristic
688D4—22no—
689D4—22no—
690D4—22no—
691D4—22no—
692D4—44no—
693D4—48no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—84no—
699D4—84no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—862no—
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#1306330612yes—
737C2×C4#1306335112yes—
738C2×C4C2×D4×D4311yescharacteristic
739C2×C4C2×#1062190011yescharacteristic
740C2×C4C2×#1062190011yescharacteristic
741C2×C4C2×#1062190011yescharacteristic
742C2×C4#1306337011yescharacteristic
743C2×C4#1306337011yescharacteristic
744C8—862no—
745C8—1721no—
746C8—1721no—
747C8—1721no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—42no—
757C22—42no—
758C22—41no—
759C22—42no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—42no—
764C22—41no—
765C22—42no—
766C22—41no—
767C22—42no—
768C22—816no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22C2×#1306330611yescharacteristic
778C22D4×C22⋊D4311yescharacteristic
779C22#1458354311yescharacteristic
780C22C2×#1306335111yescharacteristic
781C22#1458369711yescharacteristic
782C22#1458370211yescharacteristic
783C22#1458371011yescharacteristic
784C4—22no—
785C4—22no—
786C4—41no—
787C4—41no—
788C4—81no—
789C4—81no—
790C4—3441no—
791C4—3441no—
792C4—3441no—
793C4—1722no—
794C4#1458340511yescharacteristic
795C4#1458348411yescharacteristic
796C4#1458353611yescharacteristic
797C4#1458358011yescharacteristic
798C2—42no—
799C2—81no—
800C2—82no—
801C2—82no—
802C2#1913805311yescharacteristic
803C2#1914453111yescharacteristic
804C2#1914454711yescharacteristic
805C2#1914611611yescharacteristic
806C2#1914621111yescharacteristic
807C2#1914675111yescharacteristic
808C2#1914682611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC43×#2408C2
socleC23×C43C22×D4
hypercenter#2408D43
hypocenterC43#24890
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2408

Complements

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

NH ≅ G/Ntype
1. C2×#14583220C2semidirect
2. C2×#14582904C2semidirect
3. #19137544C2semidirect
4. #19136123C2semidirect
5. #19135998C2semidirect
6. #19135781C2semidirect
7. #19135774C2semidirect
8. #19135219C2semidirect
9. #19135219C2semidirect
10. #19134918C2semidirect
11. #19134893C2semidirect
12. #19134792C2semidirect
13. #19134626C2semidirect
14. #19134526C2semidirect
18. C2×#13063284C22semidirect
20. C2×#13063258C22semidirect
21. C2×#13063258C22semidirect
22. C2×#13063256C22semidirect
23. C2×#13063256C22semidirect
34. C2×C22⋊(C43⋊C8)C22semidirect
35. C2×C22⋊(C43⋊C8)C22semidirect
39. #14582769C22semidirect
41. #14582759C22semidirect
43. C4×C4⋊Dic43C22semidirect
44. #14582661C22semidirect
45. #14582661C22semidirect
46. #14582661C22semidirect
47. #14582661C22semidirect
48. #14582654C22semidirect
49. #14582654C22semidirect
96. #13063246D4semidirect
465. C43#24890semidirect

Maximal subgroups

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

subgroupindex
C2×#145832202
C2×#145829042
#191375442
#191361232
#191359982
#191357812
#191357742
#191352192
#191349182
#191348932
#191347922
#191346262
#191345262
C43×#24082
#2489043