Finite Group Databasebeta

← #25018643

Subgroups — #25018643

Order 11008.

2330 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D43C211yesmaximal, characteristic
2C2×#14582788C212yesmaximal, complemented
3C2×#14582761C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Dic43C211yesmaximal, characteristic, complemented
5#19132838C212yesmaximal, complemented
6#19132834C212yesmaximal
7#19132830C212yesmaximal, complemented
8Dic43⋊#95C211yesmaximal, characteristic, complemented
9#19132820C211yesmaximal, characteristic, complemented
10(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
11C43×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C22⋊D43C2211yescharacteristic
13C23×C4×D43C2211yescharacteristic
14C2×C4×C22⋊D43—28no—
15C2×C4×C22⋊D43C418yescomplemented
16C22×Dic43⋊C4C2212yes—
17C22×Dic43⋊C4C2211yescharacteristic
18C22×C22⋊Dic43C2212yes—
19C22×C22⋊Dic43C2211yescharacteristic
20C22×(C2×D43)⋊C4C2212yes—
21C22×(C2×D43)⋊C4C2212yes—
22C22×(C2×D43)⋊C4C2211yescharacteristic
23C22×C4×Dic43C2212yes—
24C22×C4×Dic43C2211yescharacteristic
25#14582788—28no—
26#14582761—24no—
27C4×C22⋊Dic43—24no—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2211yescharacteristic
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2211yescharacteristic
35C24×C4×C43C2211yescharacteristic
36C22×C22⋊C4×C43C2212yes—
37C2×#95×C43C2212yes—
38C2×#95×C43C2211yescharacteristic
39C2×#95×C43C2211yescharacteristic
40C24×D43C2311yescharacteristic
41C22×C22⋊D43—24no—
42C22×C22⋊D43—24no—
43C22×C22⋊D43—22no—
44C22×C22⋊D43—22no—
45C22×C22⋊D43C2×C414yes—
46C23×Dic43C2311yescharacteristic
47C23×Dic43C2312yes—
48C23×Dic43C2312yes—
49C23×Dic43C2311yescharacteristic
50C23×Dic43C2311yescharacteristic
51C22×C4×D43—24no—
52C22×C4×D43—22no—
53C22×C4×D43—22no—
54C22×C4×D43—42no—
55C22×C4×D43C2×C414yes—
56C4×C22⋊D43—232no—
57C2×Dic43⋊C4—24no—
58C2×Dic43⋊C4—24no—
59C2×Dic43⋊C4—24no—
60C2×Dic43⋊C4—42no—
61C2×Dic43⋊C4C2×C414yes—
62C2×C22⋊Dic43—24no—
63C2×C22⋊Dic43—24no—
64C2×C22⋊Dic43—24no—
65C2×C22⋊Dic43—24no—
66C2×C22⋊Dic43C2×C414yes—
67C2×(C2×D43)⋊C4—24no—
68C2×(C2×D43)⋊C4—24no—
69C2×(C2×D43)⋊C4—24no—
70C2×(C2×D43)⋊C4—24no—
71C2×(C2×D43)⋊C4—42no—
72C2×(C2×D43)⋊C4—42no—
73C2×(C2×D43)⋊C4C2×C414yes—
74C2×(C2×D43)⋊C4D418yes—
75C2×C4×Dic43—24no—
76C2×C4×Dic43—24no—
77C2×C4×Dic43—24no—
78C2×C4×Dic43—42no—
79C2×C4×Dic43C2×C414yes—
80C43⋊#95—22no—
81C43⋊#95—24no—
82C43⋊#95—24no—
83C43⋊#95—24no—
84C43⋊#95—24no—
85C43⋊#95—42no—
86C43⋊#95D414yescomplemented
87C25×C43C2311yescharacteristic
88C23×C4×C43—24no—
89C23×C4×C43—22no—
90C23×C4×C43—22no—
91C23×C4×C43—42no—
92C23×C4×C43C2×C414yes—
93C23×C4×C43C2312yes—
94C23×C4×C43C2312yes—
95C23×C4×C43C2311yescharacteristic
96C23×C4×C43C2311yescharacteristic
97C2×C22⋊C4×C43—24no—
98C2×C22⋊C4×C43—42no—
99C2×C22⋊C4×C43—42no—
100#95×C43—24no—
101#95×C43—22no—
102#95×C43—22no—
103C24×C43—21no—
104C24×C43—22no—
105C24×C43—21no—
106C24×C43—22no—
107C24×C43—21no—
108C24×C43—21no—
109C24×C43—21no—
110C24×C43—22no—
111C24×C43—21no—
112C24×C43C22×C412yes—
113C24×C43#4114yes—
114C24×C43C2411yescharacteristic
115C23×D43—21no—
116C23×D43—22no—
117C23×D43—21no—
118C23×D43—22no—
119C23×D43—21no—
120C23×D43—21no—
121C23×D43—21no—
122C23×D43—22no—
123C23×D43—21no—
124C23×D43C22×C412yes—
125C23×D43C2×D414yes—
126C22×C4×C43—28no—
127C22×C4×C43—28no—
128C22×C4×C43—21no—
129C22×C4×C43—22no—
130C22×C4×C43—22no—
131C22×C4×C43—22no—
132C22×C4×C43—22no—
133C22×C4×C43—21no—
134C22×C4×C43—22no—
135C22×C4×C43—22no—
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—22no—
140C22×C4×C43—22no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—22no—
144C22×C4×C43—22no—
145C22×C4×C43—22no—
146C22×C4×C43—22no—
147C22×C4×C43—44no—
148C22×C4×C43—48no—
149C22×C4×C43—48no—
150C22×C4×C43C22×C412yes—
151C22×C4×C43C22×C412yes—
152C22×C4×C43C2×D414yes—
153C22×C4×C43C2×D412yes—
154C22×C4×C43#4112yes—
155C2×C22⋊D43—216no—
156C2×C22⋊D43—216no—
157C2×C22⋊D43—28no—
158C2×C22⋊D43—28no—
159C2×C22⋊D43—28no—
160C22×Dic43—22no—
161C22×Dic43—21no—
162C22×Dic43—22no—
163C22×Dic43—22no—
164C22×Dic43—22no—
165C22×Dic43—22no—
166C22×Dic43—22no—
167C22×Dic43—22no—
168C22×Dic43—22no—
169C22×Dic43—22no—
170C22×Dic43—22no—
171C22×Dic43—22no—
172C22×Dic43—22no—
173C22×Dic43—21no—
174C22×Dic43—21no—
175C22×Dic43—22no—
176C22×Dic43—22no—
177C22×Dic43—22no—
178C22×Dic43—22no—
179C22×Dic43—21no—
180C22×Dic43—22no—
181C22×Dic43C22×C412yes—
182C22×Dic43C22×C412yes—
183C22×Dic43C22×C412yes—
184C22×Dic43C2×D414yes—
185C22×Dic43C2×D414yes—
186C22×Dic43#4114yes—
187C22×Dic43#4112yes—
188C22×Dic43#4112yes—
189C2×C4×D43—28no—
190C2×C4×D43—28no—
191C2×C4×D43—44no—
192C2×C4×D43—48no—
193C2×C4×D43—48no—
194C22⋊C4×C43—48no—
195C22⋊Dic43—216no—
196C22⋊Dic43—28no—
197(C2×D43)⋊C4—48no—
198(C2×D43)⋊C4—48no—
199(C2×D43)⋊C4C22⋊C4116yescomplemented
200Dic43⋊C4—28no—
201Dic43⋊C4—48no—
202C4×Dic43—28no—
203C4×Dic43—48no—
204C23×C43—22no—
205C23×C43—22no—
206C23×C43—22no—
207C23×C43—22no—
208C23×C43—22no—
209C23×C43—22no—
210C23×C43—24no—
211C23×C43—24no—
212C23×C43—24no—
213C23×C43—24no—
214C23×C43—24no—
215C23×C43—24no—
216C23×C43—42no—
217C23×C43—42no—
218C23×C43—42no—
219C23×C43—42no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43—42no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—42no—
226C23×C43#11714yes—
227C23×C43C23×C411yescharacteristic
228C23×C43C22×D412yes—
229C23×C43C22×D411yescharacteristic
230C23×C43C2×#4111yescharacteristic
231C23×C43C2×#4111yescharacteristic
232C23×C43C2×#4112yes—
233C23×C43C2×#4111yescharacteristic
234C23×C43C2×#4112yes—
235C23×C43H(5,𝔽2)12yes—
236C23×C43H(5,𝔽2)11yescharacteristic
237C23×C432−1+411yescharacteristic
238C22×D43—22no—
239C22×D43—22no—
240C22×D43—22no—
241C22×D43—22no—
242C22×D43—22no—
243C22×D43—22no—
244C22×D43—24no—
245C22×D43—24no—
246C22×D43—24no—
247C22×D43—24no—
248C22×D43—24no—
249C22×D43—24no—
250C22×D43—42no—
251C22×D43—42no—
252C22×D43—42no—
253C22×D43—42no—
254C22×D43—41no—
255C22×D43—41no—
256C22×D43—42no—
257C22×D43—41no—
258C22×D43—41no—
259C22×D43—42no—
260C22×D43C2×C22⋊C414yes—
261C2×C4×C43—22no—
262C2×C4×C43—22no—
263C2×C4×C43—22no—
264C2×C4×C43—22no—
265C2×C4×C43—24no—
266C2×C4×C43—24no—
267C2×C4×C43—24no—
268C2×C4×C43—24no—
269C2×C4×C43—416no—
270C2×C4×C43—42no—
271C2×C4×C43—42no—
272C2×C4×C43—42no—
273C2×C4×C43—42no—
274C2×C4×C43—42no—
275C2×C4×C43—42no—
276C2×C4×C43—42no—
277C2×C4×C43—42no—
278C2×C4×C43—42no—
279C2×C4×C43—42no—
280C2×C4×C43—42no—
281C2×C4×C43—42no—
282C2×C4×C43—42no—
283C2×C4×C43—42no—
284C2×C4×C43C2×C22⋊C414yes—
285C2×C4×C43C4×D414yes—
286C22⋊D43—232no—
287C2×Dic43—22no—
288C2×Dic43—22no—
289C2×Dic43—22no—
290C2×Dic43—22no—
291C2×Dic43—24no—
292C2×Dic43—24no—
293C2×Dic43—24no—
294C2×Dic43—24no—
295C2×Dic43—22no—
296C2×Dic43—22no—
297C2×Dic43—22no—
298C2×Dic43—24no—
299C2×Dic43—24no—
300C2×Dic43—24no—
301C2×Dic43—24no—
302C2×Dic43—24no—
303C2×Dic43—24no—
304C2×Dic43—42no—
305C2×Dic43—42no—
306C2×Dic43—42no—
307C2×Dic43—42no—
308C2×Dic43—42no—
309C2×Dic43—42no—
310C2×Dic43—42no—
311C2×Dic43—42no—
312C2×Dic43—42no—
313C2×Dic43—42no—
314C2×Dic43C2×C22⋊C414yes—
315C2×Dic43#11714yes—
316C4×D43—416no—
317#13886—431nomaximal, Sylow
318C22×C43—24no—
319C22×C43—24no—
320C22×C43—24no—
321C22×C43—42no—
322C22×C43—42no—
323C22×C43—42no—
324C22×C43—42no—
325C22×C43—44no—
326C22×C43—44no—
327C22×C43—44no—
328C22×C43—44no—
329C22×C43C22×C22⋊C411yescharacteristic
330C22×C43C2×#11711yescharacteristic
331C22×C43C2×#11711yescharacteristic
332C22×C43C2×C4×D411yescharacteristic
333C22×C43C4×#4111yescharacteristic
334C22×C43#51811yescharacteristic
335C22×C43#52011yescharacteristic
336C22×C43#52512yes—
337C22×C43#52512yes—
338C22×C43#52512yes—
339C22×C43#52912yes—
340C22×C43#53812yes—
341C22×C43#53912yes—
342C22×C43D4212yes—
343C22×C43#54612yes—
344C22×C43#54612yes—
345C22×C43#54712yes—
346C22×C43#54711yescharacteristic
347C22×C43#55011yescharacteristic
348C22×C43#55312yes—
349C22×C43#55511yescharacteristic
350C22×C43#55611yescharacteristic
351C22×C43#55912yes—
352C2×D43—24no—
353C2×D43—24no—
354C2×D43—24no—
355C2×D43—42no—
356C2×D43—42no—
357C2×D43—42no—
358C2×D43—44no—
359C2×D43—44no—
360C2×D43—44no—
361C2×D43—44no—
362C2×D43—42no—
363C4×C43—24no—
364C4×C43—24no—
365C4×C43—82no—
366C4×C43—82no—
367Dic43—24no—
368Dic43—24no—
369Dic43—42no—
370Dic43—44no—
371Dic43—44no—
372C22×C4×D4—431no—
373C2×#388—432no—
374C2×#381—431no—
375C2×C4×C22⋊C4—431no—
376#1439—432no—
377#1438—432no—
378#1436—432no—
379C4⋊#95—431no—
380#1434—431no—
381C22⋊#95—431no—
382C22⋊#95D4311yescharacteristic, complemented
383C2×C43—44no—
384C2×C43#228011yescharacteristic
385C2×C43#229011yescharacteristic
386C2×C43#231811yescharacteristic
387C2×C43D4×C22⋊C411yescharacteristic
388C2×C43#233911yescharacteristic
389C2×C43#235411yescharacteristic
390C2×C43#235711yescharacteristic
391C2×C43#245512yes—
392C2×C43#245612yes—
393C2×C43#245912yes—
394C2×C43#246612yes—
395D43—44no—
396C23×D4—431no—
397C24×C4—431no—
398C24×C4C2×D4311yescharacteristic
399C2×C4×D4—438no—
400C2×C4×D4—868no—
401C22×C4⋊C4—431no—
402C22×C4⋊C4—432no—
403C22×C22⋊C4—431no—
404C22×C22⋊C4—431no—
405C22×C22⋊C4—432no—
406C22×C22⋊C4—432no—
407C22×C22⋊C4—432no—
408C22×C22⋊C4C2×D4312yes—
409C22×C42—431no—
410C22×C42—432no—
411#388—868no—
412#381—864no—
413C4×C22⋊C4—864no—
414C2×#95—431no—
415C2×#95—431no—
416C2×#95—432no—
417C2×#95—432no—
418C2×#95—432no—
419C2×#95—432no—
420C2×#95—432no—
421C2×#95C2×D4311yescharacteristic
422C2×#95C2×D4311yescharacteristic
423C2×#95C2×D4312yes—
424C43#1388611yescharacteristic, complemented, Sylow
425C25—431no—
426C25C22×D4311yescharacteristic
427C22×D4—434no—
428C22×D4—862no—
429C22×D4—862no—
430C22×D4—864no—
431C22×D4—864no—
432C23×C4—24no—
433C23×C4—22no—
434C23×C4—22no—
435C23×C4—42no—
436C23×C4—431no—
437C23×C4—431no—
438C23×C4—432no—
439C23×C4—432no—
440C23×C4—431no—
441C23×C4—434no—
442C23×C4—864no—
443C23×C4—862no—
444C23×C4—862no—
445C23×C4—1722no—
446C23×C4C4×D4314yes—
447C23×C4C22×D4312yes—
448C23×C4C22×D4312yes—
449C23×C4C22×D4311yescharacteristic
450C23×C4C22×D4311yescharacteristic
451C4×D4—8632no—
452C2×C4⋊C4—434no—
453C2×C4⋊C4—864no—
454C2×C4⋊C4—864no—
455C2×C4⋊C4—864no—
456C2×C4⋊C4—1722no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—42no—
459C2×C22⋊C4—42no—
460C2×C22⋊C4—434no—
461C2×C22⋊C4—438no—
462C2×C22⋊C4—434no—
463C2×C22⋊C4—864no—
464C2×C22⋊C4—864no—
465C2×C22⋊C4—864no—
466C2×C22⋊C4—864no—
467C2×C22⋊C4—864no—
468C2×C22⋊C4—864no—
469C2×C22⋊C4—864no—
470C2×C22⋊C4—864no—
471C2×C22⋊C4—1722no—
472C2×C22⋊C4—1722no—
473C2×C42—434no—
474C2×C42—864no—
475C2×C42—864no—
476C2×C42—864no—
477C2×C42—1722no—
478#95—22no—
479#95—24no—
480#95—22no—
481#95—434no—
482#95—864no—
483#95—864no—
484#95—864no—
485#95—864no—
486#95—862no—
487#95—1722no—
488C24—21no—
489C24—22no—
490C24—22no—
491C24—21no—
492C24—21no—
493C24—21no—
494C24—21no—
495C24—22no—
496C24—21no—
497C24—432no—
498C24—434no—
499C24—861no—
500C24—862no—
501C24—861no—
502C24—861no—
503C24—861no—
504C24—862no—
505C24—861no—
506C24—862no—
507C24—861no—
508C24C2×C4×D4312yes—
509C24#1062189814yes—
510C24C23×D4311yescharacteristic
511C2×D4—868no—
512C2×D4—868no—
513C2×D4—8616no—
514C2×D4—8616no—
515C2×D4—868no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—28no—
522C22×C4—28no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—44no—
538C22×C4—48no—
539C22×C4—48no—
540C22×C4—432no—
541C22×C4—432no—
542C22×C4—434no—
543C22×C4—432no—
544C22×C4—432no—
545C22×C4—432no—
546C22×C4—434no—
547C22×C4—434no—
548C22×C4—868no—
549C22×C4—862no—
550C22×C4—862no—
551C22×C4—862no—
552C22×C4—861no—
553C22×C4—861no—
554C22×C4—861no—
555C22×C4—862no—
556C22×C4—862no—
557C22×C4—862no—
558C22×C4—862no—
559C22×C4—862no—
560C22×C4—862no—
561C22×C4—862no—
562C22×C4—861no—
563C22×C4—862no—
564C22×C4—862no—
565C22×C4—862no—
566C22×C4—862no—
567C22×C4—862no—
568C22×C4—862no—
569C22×C4—862no—
570C22×C4—868no—
571C22×C4—1724no—
572C22×C4—1728no—
573C22×C4—1728no—
574C22×C4C2×C4×D4312yes—
575C22×C4C2×C4×D4312yes—
576C22×C4D4×D4314yes—
577C22×C4D4×D4312yes—
578C22×C4#1062190012yes—
579C4⋊C4—868no—
580C4⋊C4—1728no—
581C22⋊C4—48no—
582C22⋊C4—4316no—
583C22⋊C4—868no—
584C22⋊C4—8616no—
585C22⋊C4—1728no—
586C22⋊C4—1728no—
587C42—868no—
588C42—1728no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—41no—
602C23—42no—
603C23—41no—
604C23—41no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—41no—
610C23—42no—
611C23—434no—
612C23—862no—
613C23—862no—
614C23—862no—
615C23—862no—
616C23—862no—
617C23—862no—
618C23—864no—
619C23—864no—
620C23—864no—
621C23—864no—
622C23—864no—
623C23—864no—
624C23—1721no—
625C23—1722no—
626C23—1721no—
627C23—1721no—
628C23—1722no—
629C23—1722no—
630C23—1722no—
631C23—1722no—
632C23—1722no—
633C23—1721no—
634C23#1306328214yes—
635C23C22×C4×D4311yescharacteristic
636C23C2×D4×D4311yescharacteristic
637C23C2×D4×D4312yes—
638C23#41×D4311yescharacteristic
639C23#41×D4312yes—
640C23#41×D4311yescharacteristic
641C23C2×#1062190011yescharacteristic
642C23C2×#1062189812yes—
643C23#1306337011yescharacteristic
644C23#1306337012yes—
645C23#1306337311yescharacteristic
646D4—8632no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—416no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—434no—
671C2×C4—434no—
672C2×C4—862no—
673C2×C4—862no—
674C2×C4—862no—
675C2×C4—862no—
676C2×C4—864no—
677C2×C4—864no—
678C2×C4—864no—
679C2×C4—864no—
680C2×C4—864no—
681C2×C4—862no—
682C2×C4—862no—
683C2×C4—862no—
684C2×C4—864no—
685C2×C4—864no—
686C2×C4—864no—
687C2×C4—864no—
688C2×C4—864no—
689C2×C4—17216no—
690C2×C4—1722no—
691C2×C4—1722no—
692C2×C4—1722no—
693C2×C4—1722no—
694C2×C4—1722no—
695C2×C4—1722no—
696C2×C4—1722no—
697C2×C4—1722no—
698C2×C4—1722no—
699C2×C4—1722no—
700C2×C4C22⋊C4×D4314yes—
701C2×C4(C22⋊D43)⋊C414yes—
702C22—24no—
703C22—24no—
704C22—24no—
705C22—42no—
706C22—42no—
707C22—44no—
708C22—42no—
709C22—42no—
710C22—44no—
711C22—44no—
712C22—44no—
713C22—864no—
714C22—864no—
715C22—864no—
716C22—1722no—
717C22—1722no—
718C22—1722no—
719C22—1724no—
720C22—1724no—
721C22—1724no—
722C22—1722no—
723C22—1724no—
724C22C2×C22⋊C4×D4311yescharacteristic
725C22#117×D4311yescharacteristic
726C22C2×#1306328211yescharacteristic
727C22C2×(C22⋊D43)⋊C411yescharacteristic
728C22#1458336711yescharacteristic
729C22#1458337211yescharacteristic
730C22#1458338011yescharacteristic
731C22#1458340812yes—
732C22#1458340812yes—
733C22#1458340812yes—
734C22#1458342912yes—
735C22#1458348712yes—
736C22#1458349612yes—
737C22#1458353112yes—
738C22#1458353612yes—
739C22#1458354612yes—
740C22#1458355111yescharacteristic
741C22#1458355112yes—
742C22#1458356711yescharacteristic
743C22#1458359412yes—
744C22#1458361311yescharacteristic
745C22#1458362011yescharacteristic
746C22#1458363312yes—
747C4—24no—
748C4—24no—
749C4—82no—
750C4—82no—
751C4—864no—
752C4—864no—
753C4—1722no—
754C4—1724no—
755C4—1724no—
756C2—44no—
757C2—1724no—
758C2#1913697611yescharacteristic
759C2#1913703411yescharacteristic
760C2#1913722911yescharacteristic
761C2#1913741111yescharacteristic
762C2#1913742311yescharacteristic
763C2#1913753911yescharacteristic
764C2#1913756311yescharacteristic
765C2#1913847712yes—
766C2#1913848912yes—
767C2#1913853412yes—
768C2#1913863312yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×C22⋊#95C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenterC22⋊#95D43
hypocenterC43#13886
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#14582788C2semidirect
3. C2×#14582761C2semidirect
4. C2×C4×C22⋊Dic43C2semidirect
5. #19132838C2semidirect
7. #19132830C2semidirect
8. Dic43⋊#95C2semidirect
9. #19132820C2semidirect
10. (C2×D43)⋊#95C2semidirect
11. C43×C22⋊#95C2semidirect
15. C2×C4×C22⋊D43C4semidirect
86. C43⋊#95D4semidirect
199. (C2×D43)⋊C4C22⋊C4semidirect
382. C22⋊#95D43semidirect
424. C43#13886semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D432
C2×#145827882
C2×#145827612
C2×C4×C22⋊Dic432
#191328382
#191328342
#191328302
Dic43⋊#952
#191328202
(C2×D43)⋊#952
C43×C22⋊#952
#1388643