Finite Group Databasebeta

← #25019722

Subgroups — #25019722

Order 11008.

2474 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582779C211yesmaximal, characteristic
2C2×#14582779C211yesmaximal, characteristic
3C2×#14582774C211yesmaximal, characteristic, complemented
4C2×#14582762C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×Dic43C211yesmaximal, characteristic, complemented
6C22×C43⋊#95C211yesmaximal, characteristic, complemented
7#19132863C212yesmaximal, complemented
8#19132840C212yesmaximal, complemented
9#19132832C212yesmaximal, complemented
10#19132824C212yesmaximal, complemented
11C22×#123×C43C211yesmaximal, characteristic
12C24×Dic43C2211yescharacteristic
13C24×Dic43C2211yescharacteristic
14C22×C4⋊Dic43C2212yes—
15C22×C22⋊Dic43C2211yescharacteristic
16C22×C22⋊Dic43C2211yescharacteristic
17C22×C22⋊Dic43C2212yes—
18C22×C22⋊Dic43C2211yescharacteristic
19C22×C22⋊Dic43C2211yescharacteristic
20C22×C4×Dic43C2212yes—
21#14582779—24no—
22#14582779—24no—
23#14582774—24no—
24#14582762—24no—
25C22⋊C4×Dic43—24no—
26C2×C43⋊#95—24no—
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2211yescharacteristic
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2212yes—
35C2×C43⋊#95C2211yescharacteristic
36C23×D4×C43C2211yescharacteristic
37C24×C4×C43C2211yescharacteristic
38C2×#123×C43—24no—
39C2×#123×C43—24no—
40C2×#123×C43C418yescomplemented
41C22×C4⋊C4×C43C2212yes—
42C22×C22⋊C4×C43C2212yes—
43C22×C22⋊C4×C43C2211yescharacteristic
44C23×Dic43—22no—
45C23×Dic43—22no—
46C23×Dic43—22no—
47C23×Dic43—24no—
48C23×Dic43—24no—
49C23×Dic43—22no—
50C23×Dic43—22no—
51C23×Dic43—42no—
52C23×Dic43—42no—
53C23×Dic43D414yes—
54C23×Dic43C2311yescharacteristic
55C23×Dic43C2311yescharacteristic
56C23×Dic43C2312yes—
57C23×Dic43C2311yescharacteristic
58C23×Dic43C2312yes—
59C23×Dic43C2311yescharacteristic
60C2×C4⋊Dic43—24no—
61C2×C4⋊Dic43—24no—
62C2×C4⋊Dic43—42no—
63C2×C22⋊Dic43—22no—
64C2×C22⋊Dic43—22no—
65C2×C22⋊Dic43—22no—
66C2×C22⋊Dic43—22no—
67C2×C22⋊Dic43—22no—
68C2×C22⋊Dic43—24no—
69C2×C22⋊Dic43—22no—
70C2×C22⋊Dic43—22no—
71C2×C22⋊Dic43—24no—
72C2×C22⋊Dic43—24no—
73C2×C22⋊Dic43—42no—
74C2×C22⋊Dic43—42no—
75C2×C22⋊Dic43D414yes—
76C2×C4×Dic43—24no—
77C2×C4×Dic43—24no—
78C2×C4×Dic43—42no—
79C43⋊#95—24no—
80C43⋊#95—24no—
81C43⋊#95—24no—
82C43⋊#95—24no—
83C43⋊#95—24no—
84C43⋊#95—24no—
85C43⋊#95—24no—
86C43⋊#95—22no—
87C43⋊#95—22no—
88C25×C43C2311yescharacteristic
89C25×C43C2311yescharacteristic
90C22×D4×C43—22no—
91C22×D4×C43—22no—
92C22×D4×C43—22no—
93C22×D4×C43—22no—
94C22×D4×C43—22no—
95C22×D4×C43—22no—
96C22×D4×C43C2×C414yes—
97C23×C4×C43—22no—
98C23×C4×C43—22no—
99C23×C4×C43—22no—
100C23×C4×C43—22no—
101C23×C4×C43—22no—
102C23×C4×C43—22no—
103C23×C4×C43C2×C414yes—
104C23×C4×C43C2312yes—
105C23×C4×C43C2311yescharacteristic
106C23×C4×C43C2312yes—
107#123×C43—232no—
108C2×C4⋊C4×C43—24no—
109C2×C4⋊C4×C43—24no—
110C2×C4⋊C4×C43C2×C418yescomplemented
111C2×C22⋊C4×C43—24no—
112C2×C22⋊C4×C43—24no—
113C2×C22⋊C4×C43C2×C414yes—
114C2×C22⋊C4×C43C2×C418yescomplemented
115C2×C22⋊C4×C43D414yes—
116C2×C22⋊C4×C43D414yes—
117C24×C43—22no—
118C24×C43—22no—
119C24×C43—22no—
120C24×C43—22no—
121C24×C43—21no—
122C24×C43—21no—
123C24×C43—21no—
124C24×C43—21no—
125C24×C43—21no—
126C24×C43—21no—
127C24×C43—22no—
128C24×C43—22no—
129C24×C43—22no—
130C24×C43—22no—
131C24×C43C22×C412yes—
132C24×C43C22×C412yes—
133C24×C43C2×D412yes—
134C24×C43C2×D412yes—
135C24×C43C2×D412yes—
136C24×C43C2×D412yes—
137C24×C43#4112yes—
138C24×C43#4112yes—
139C24×C43C2411yescharacteristic
140C2×D4×C43—28no—
141C2×D4×C43—28no—
142C2×D4×C43—28no—
143C2×D4×C43—44no—
144C2×D4×C43—44no—
145C2×D4×C43—44no—
146C2×D4×C43—44no—
147C22×C4×C43—28no—
148C22×C4×C43—28no—
149C22×C4×C43—28no—
150C22×C4×C43—22no—
151C22×C4×C43—22no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—22no—
155C22×C4×C43—22no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—22no—
159C22×C4×C43—22no—
160C22×C4×C43—22no—
161C22×C4×C43—22no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—22no—
165C22×C4×C43—22no—
166C22×C4×C43—44no—
167C22×C4×C43—44no—
168C22×C4×C43—44no—
169C22×C4×C43—44no—
170C22×C4×C43C22×C414yes—
171C22×C4×C43C22×C412yes—
172C22×C4×C43C22×C414yes—
173C22×C4×C43C2×D414yes—
174C22×C4×C43C2×D414yes—
175C22×Dic43—28no—
176C22×Dic43—28no—
177C22×Dic43—28no—
178C22×Dic43—21no—
179C22×Dic43—22no—
180C22×Dic43—21no—
181C22×Dic43—22no—
182C22×Dic43—22no—
183C22×Dic43—22no—
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43—21no—
187C22×Dic43—21no—
188C22×Dic43—21no—
189C22×Dic43—21no—
190C22×Dic43—21no—
191C22×Dic43—22no—
192C22×Dic43—22no—
193C22×Dic43—22no—
194C22×Dic43—22no—
195C22×Dic43—22no—
196C22×Dic43—21no—
197C22×Dic43—22no—
198C22×Dic43—22no—
199C22×Dic43—22no—
200C22×Dic43—22no—
201C22×Dic43—22no—
202C22×Dic43—22no—
203C22×Dic43—22no—
204C22×Dic43—22no—
205C22×Dic43—22no—
206C22×Dic43—22no—
207C22×Dic43—44no—
208C22×Dic43—48no—
209C22×Dic43—48no—
210C22×Dic43—48no—
211C22×Dic43—48no—
212C22×Dic43—44no—
213C22×Dic43—44no—
214C22×Dic43C2×D414yes—
215C22×Dic43C2×D412yes—
216C22×Dic43C2×D412yes—
217C22×Dic43#4114yes—
218C22×Dic43#4114yes—
219C4⋊C4×C43—216no—
220C22⋊C4×C43—216no—
221C22⋊C4×C43C22⋊C4116yescomplemented
222C22⋊Dic43—28no—
223C22⋊Dic43—48no—
224C22⋊Dic43—44no—
225C22⋊Dic43—44no—
226C22⋊Dic43—44no—
227C4⋊Dic43—48no—
228C4×Dic43—48no—
229C23×C43—24no—
230C23×C43—24no—
231C23×C43—22no—
232C23×C43—22no—
233C23×C43—24no—
234C23×C43—22no—
235C23×C43—22no—
236C23×C43—24no—
237C23×C43—24no—
238C23×C43—24no—
239C23×C43—24no—
240C23×C43—24no—
241C23×C43—24no—
242C23×C43—24no—
243C23×C43—24no—
244C23×C43—24no—
245C23×C43—22no—
246C23×C43—22no—
247C23×C43—22no—
248C23×C43—24no—
249C23×C43—24no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—42no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—42no—
260C23×C43—42no—
261C23×C43—42no—
262C23×C43—42no—
263C23×C43—42no—
264C23×C43—42no—
265C23×C43—42no—
266C23×C43—42no—
267C23×C43—42no—
268C23×C43C2×C22⋊C414yes—
269C23×C43C4×D414yes—
270C23×C43C4×D414yes—
271C23×C43#12114yes—
272C23×C43#12114yes—
273C23×C43#12414yes—
274C23×C43#12714yes—
275C23×C43C23×C411yescharacteristic
276C23×C43C22×D411yescharacteristic
277C23×C43C22×D411yescharacteristic
278C23×C43C22×D411yescharacteristic
279C23×C43C22×D411yescharacteristic
280C23×C43C2×#4112yes—
281C23×C43C2×#4112yes—
282C23×C43C2×#4111yescharacteristic
283C23×C43C2×#4111yescharacteristic
284C23×C43H(5,𝔽2)12yes—
285C23×C432−1+412yes—
286D4×C43—416no—
287C2×C4×C43—24no—
288C2×C4×C43—24no—
289C2×C4×C43—24no—
290C2×C4×C43—24no—
291C2×C4×C43—24no—
292C2×C4×C43—24no—
293C2×C4×C43—24no—
294C2×C4×C43—22no—
295C2×C4×C43—24no—
296C2×C4×C43—24no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—42no—
300C2×C4×C43—42no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—42no—
304C2×C4×C43—41no—
305C2×C4×C43—42no—
306C2×C4×C43—41no—
307C2×C4×C43—416no—
308C2×C4×C43C2×C22⋊C418yes—
309C2×Dic43—22no—
310C2×Dic43—22no—
311C2×Dic43—24no—
312C2×Dic43—24no—
313C2×Dic43—24no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—24no—
317C2×Dic43—22no—
318C2×Dic43—24no—
319C2×Dic43—24no—
320C2×Dic43—24no—
321C2×Dic43—24no—
322C2×Dic43—416no—
323C2×Dic43—416no—
324C2×Dic43—42no—
325C2×Dic43—42no—
326C2×Dic43—42no—
327C2×Dic43—42no—
328C2×Dic43—42no—
329C2×Dic43—42no—
330C2×Dic43—42no—
331C2×Dic43—42no—
332C2×Dic43—42no—
333C2×Dic43—42no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43—41no—
338C2×Dic43—41no—
339C2×Dic43—41no—
340C2×Dic43—42no—
341C2×Dic43—42no—
342C2×Dic43—42no—
343C2×Dic43—42no—
344C2×Dic43#12314yescomplemented
345#13996—431nomaximal, Sylow
346C22×C43—24no—
347C22×C43—28no—
348C22×C43—28no—
349C22×C43—24no—
350C22×C43—24no—
351C22×C43—28no—
352C22×C43—28no—
353C22×C43—24no—
354C22×C43—24no—
355C22×C43—24no—
356C22×C43—42no—
357C22×C43—44no—
358C22×C43—44no—
359C22×C43—42no—
360C22×C43—42no—
361C22×C43—81no—
362C22×C43—81no—
363C22×C43—82no—
364C22×C43—82no—
365C22×C43—81no—
366C22×C43—81no—
367C22×C43#39018yes—
368C22×C43C22×C22⋊C411yescharacteristic
369C22×C43C2×C4×D411yescharacteristic
370C22×C43C2×C4×D411yescharacteristic
371C22×C43C4×#4112yes—
372C22×C43#52012yes—
373C22×C43C2×#12111yescharacteristic
374C22×C43C2×#12111yescharacteristic
375C22×C43C2×#12311yescharacteristic
376C22×C43#52511yescharacteristic
377C22×C43C2×#12411yescharacteristic
378C22×C43#52912yes—
379C22×C43C2×#12711yescharacteristic
380C22×C43#53411yescharacteristic
381C22×C43#53611yescharacteristic
382C22×C43#53912yes—
383C22×C43#54612yes—
384C22×C43#54612yes—
385C22×C43#54612yes—
386C22×C43#54712yes—
387C22×C43#54712yes—
388C22×C43#54712yes—
389C22×C43#55112yes—
390C22×C43#55212yes—
391C4×C43—28no—
392C4×C43—44no—
393C4×C43—42no—
394Dic43—24no—
395Dic43—42no—
396Dic43—44no—
397Dic43—44no—
398Dic43—81no—
399Dic43—81no—
400C22×#123D4311yescharacteristic
401C2×#386—431no—
402C2×#386—431no—
403C2×#385—431no—
404C2×#381—431no—
405C2×C4×C22⋊C4—431no—
406C22×#95—431no—
407#1445—432no—
408#1439—432no—
409#1437—432no—
410C4⋊#95—432no—
411C2×C43—28no—
412C2×C43—82no—
413C2×C43C2×#39011yescharacteristic
414C2×C43C4×#12311yescharacteristic
415C2×C43#232211yescharacteristic
416C2×C43#233912yes—
417C2×C43#235912yes—
418C2×C43#241211yescharacteristic
419C2×C43#241311yescharacteristic
420C2×C43#242512yes—
421C2×C43#248812yes—
422C2×C43#250111yescharacteristic
423C2×C43#253911yescharacteristic
424C23×D4C2×D4311yescharacteristic
425C24×C4—431no—
426C24×C4—431no—
427C24×C4C2×D4311yescharacteristic
428C2×#123—24no—
429C2×#123—24no—
430C2×#123Dic4318yescomplemented
431C22×C4⋊C4—432no—
432C22×C4⋊C4C2×D4312yes—
433C22×C22⋊C4—431no—
434C22×C22⋊C4—431no—
435C22×C22⋊C4—431no—
436C22×C22⋊C4—432no—
437C22×C22⋊C4—431no—
438C22×C22⋊C4C2×D4312yes—
439C22×C22⋊C4C2×D4311yescharacteristic
440C22×C42—432no—
441#386—864no—
442#386—864no—
443#385—864no—
444#381—864no—
445C4×C22⋊C4—864no—
446C2×#95—431no—
447C2×#95—432no—
448C2×#95—432no—
449C2×#95—432no—
450C2×#95—432no—
451C2×#95—432no—
452C2×#95—432no—
453C2×#95—432no—
454C2×#95—431no—
455C2×#95—864no—
456C43#1399611yescharacteristic, complemented, Sylow
457C25C22×D4311yescharacteristic
458C25C22×D4311yescharacteristic
459C22×D4—22no—
460C22×D4—22no—
461C22×D4—22no—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—22no—
465C22×D4C2×Dic4314yes—
466C23×C4—22no—
467C23×C4—22no—
468C23×C4—22no—
469C23×C4—22no—
470C23×C4—22no—
471C23×C4—22no—
472C23×C4—431no—
473C23×C4—432no—
474C23×C4—432no—
475C23×C4—431no—
476C23×C4—434no—
477C23×C4—431no—
478C23×C4—431no—
479C23×C4—864no—
480C23×C4—864no—
481C23×C4—862no—
482C23×C4—862no—
483C23×C4—862no—
484C23×C4—862no—
485C23×C4—862no—
486C23×C4—1722no—
487C23×C4—1722no—
488C23×C4C2×Dic4314yes—
489C23×C4C22×D4312yes—
490C23×C4C22×D4311yescharacteristic
491C23×C4C22×D4312yes—
492#123—232no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4—24no—
495C2×C4⋊C4—864no—
496C2×C4⋊C4—864no—
497C2×C4⋊C4—1722no—
498C2×C4⋊C4C2×Dic4318yescomplemented
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—434no—
502C2×C22⋊C4—862no—
503C2×C22⋊C4—862no—
504C2×C22⋊C4—864no—
505C2×C22⋊C4—864no—
506C2×C22⋊C4—862no—
507C2×C22⋊C4—864no—
508C2×C22⋊C4—862no—
509C2×C22⋊C4—862no—
510C2×C22⋊C4—862no—
511C2×C22⋊C4—862no—
512C2×C22⋊C4—1722no—
513C2×C22⋊C4—1722no—
514C2×C22⋊C4C2×Dic4314yes—
515C2×C22⋊C4C2×Dic4318yescomplemented
516C2×C22⋊C4C22⋊D4314yes—
517C2×C22⋊C4C22⋊D4314yes—
518C2×C42—864no—
519C2×C42—864no—
520C2×C42—1722no—
521#95—864no—
522#95—864no—
523#95—864no—
524#95—864no—
525#95—862no—
526#95—864no—
527#95—862no—
528#95—864no—
529#95—864no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—21no—
535C24—21no—
536C24—21no—
537C24—21no—
538C24—22no—
539C24—22no—
540C24—21no—
541C24—21no—
542C24—22no—
543C24—22no—
544C24D4×D4312yes—
545C24D4×D4312yes—
546C24#1062190012yes—
547C24#1062190012yes—
548C24C22×Dic4312yes—
549C24C22×Dic4312yes—
550C24C2×C22⋊D4312yes—
551C24C2×C22⋊D4312yes—
552C24C23×D4311yescharacteristic
553C2×D4—28no—
554C2×D4—28no—
555C2×D4—28no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—44no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—28no—
565C22×C4—28no—
566C22×C4—28no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—432no—
584C22×C4—434no—
585C22×C4—434no—
586C22×C4—432no—
587C22×C4—434no—
588C22×C4—868no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—862no—
592C22×C4—868no—
593C22×C4—868no—
594C22×C4—862no—
595C22×C4—862no—
596C22×C4—861no—
597C22×C4—862no—
598C22×C4—862no—
599C22×C4—862no—
600C22×C4—862no—
601C22×C4—862no—
602C22×C4—862no—
603C22×C4—862no—
604C22×C4—861no—
605C22×C4—862no—
606C22×C4—862no—
607C22×C4—862no—
608C22×C4—862no—
609C22×C4—862no—
610C22×C4—861no—
611C22×C4—861no—
612C22×C4—861no—
613C22×C4—861no—
614C22×C4—861no—
615C22×C4—861no—
616C22×C4—862no—
617C22×C4—862no—
618C22×C4—862no—
619C22×C4—862no—
620C22×C4—1724no—
621C22×C4—1728no—
622C22×C4—1728no—
623C22×C4—1728no—
624C22×C4—1728no—
625C22×C4—1724no—
626C22×C4—1724no—
627C22×C4C22×Dic4314yes—
628C22×C4C22×Dic4312yes—
629C22×C4C22×Dic4314yes—
630C22×C4C2×C22⋊D4314yes—
631C22×C4C2×C22⋊D4314yes—
632C4⋊C4—216no—
633C4⋊C4—1728no—
634C22⋊C4—216no—
635C22⋊C4—868no—
636C22⋊C4—1724no—
637C22⋊C4—1728no—
638C22⋊C4—1724no—
639C22⋊C4—1724no—
640C22⋊C4C22⋊Dic43116yescomplemented
641C42—1728no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—22no—
647C23—22no—
648C23—24no—
649C23—22no—
650C23—22no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—24no—
662C23—24no—
663C23—42no—
664C23—42no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—42no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23C2×C22⋊Dic4314yes—
682C23D4×Dic4314yes—
683C23D4×Dic4314yes—
684C23#1306329614yes—
685C23#1306329614yes—
686C23#1306331214yes—
687C23#1306332114yes—
688C23C23×Dic4311yescharacteristic
689C23C2×D4×D4311yescharacteristic
690C23C2×D4×D4311yescharacteristic
691C23C22×C22⋊D4311yescharacteristic
692C23C22×C22⋊D4311yescharacteristic
693C23#41×D4312yes—
694C23#41×D4312yes—
695C23C2×#1062190011yescharacteristic
696C23C2×#1062190011yescharacteristic
697C23#1306337112yes—
698C23#1306337212yes—
699D4—416no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—416no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—434no—
722C2×C4—864no—
723C2×C4—862no—
724C2×C4—862no—
725C2×C4—864no—
726C2×C4—864no—
727C2×C4—862no—
728C2×C4—862no—
729C2×C4—864no—
730C2×C4—862no—
731C2×C4—864no—
732C2×C4—864no—
733C2×C4—864no—
734C2×C4—864no—
735C2×C4—17216no—
736C2×C4—1721no—
737C2×C4—1721no—
738C2×C4—1721no—
739C2×C4—1721no—
740C2×C4—1721no—
741C2×C4—1721no—
742C2×C4—1722no—
743C2×C4—1722no—
744C2×C4—1722no—
745C2×C4—1722no—
746C2×C4—17216no—
747C2×C4—1722no—
748C2×C4—1722no—
749C2×C4—1722no—
750C2×C4—1722no—
751C2×C4—1722no—
752C2×C4—1722no—
753C2×C4—1722no—
754C2×C4—1722no—
755C2×C4—1722no—
756C2×C4—1722no—
757C2×C4C2×C22⋊Dic4318yes—
758C22—28no—
759C22—24no—
760C22—28no—
761C22—28no—
762C22—28no—
763C22—24no—
764C22—24no—
765C22—24no—
766C22—24no—
767C22—24no—
768C22—42no—
769C22—44no—
770C22—42no—
771C22—44no—
772C22—42no—
773C22—82no—
774C22—82no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22#1458280218yes—
780C22C22×C22⋊Dic4311yescharacteristic
781C22C2×D4×Dic4311yescharacteristic
782C22C2×D4×Dic4311yescharacteristic
783C22#41×Dic4312yes—
784C22#1458338212yes—
785C22C2×#1306329611yescharacteristic
786C22C2×#1306329611yescharacteristic
787C22#123×D4311yescharacteristic
788C22#1458340711yescharacteristic
789C22C2×#1306331211yescharacteristic
790C22#1458342612yes—
791C22C2×#1306332111yescharacteristic
792C22#1458346011yescharacteristic
793C22#1458347111yescharacteristic
794C22#1458349312yes—
795C22#1458353712yes—
796C22#1458353712yes—
797C22#1458354112yes—
798C22#1458354712yes—
799C22#1458354812yes—
800C22#1458354812yes—
801C22#1458357212yes—
802C22#1458358612yes—
803C4—28no—
804C4—44no—
805C4—42no—
806C4—864no—
807C4—3441no—
808C4—3441no—
809C4—1724no—
810C4—1722no—
811C4—1724no—
812C2—28no—
813C2—82no—
814C2C2×#1458280211yescharacteristic
815C2#123×Dic4311yescharacteristic
816C2#1913726711yescharacteristic
817C2#1913742512yes—
818C2#1913759112yes—
819C2#1913798711yescharacteristic
820C2#1913799811yescharacteristic
821C2#1913814212yes—
822C2#1913892512yes—
823C2#1913906411yescharacteristic
824C2#1913952511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC22×#123×C43C2
socle, cosocleC24×C43C24
prime radicalC23×D4×C43C22
hypercenterC22×#123D43
hypocenterC43#13996
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
3. C2×#14582774C2semidirect
4. C2×#14582762C2semidirect
5. C2×C22⋊C4×Dic43C2semidirect
6. C22×C43⋊#95C2semidirect
7. #19132863C2semidirect
8. #19132840C2semidirect
9. #19132832C2semidirect
10. #19132824C2semidirect
40. C2×#123×C43C4semidirect
110. C2×C4⋊C4×C43C2×C4semidirect
114. C2×C22⋊C4×C43C2×C4semidirect
221. C22⋊C4×C43C22⋊C4semidirect
344. C2×Dic43#123semidirect
430. C2×#123Dic43semidirect
456. C43#13996semidirect
498. C2×C4⋊C4C2×Dic43semidirect
515. C2×C22⋊C4C2×Dic43semidirect
640. C22⋊C4C22⋊Dic43semidirect

Maximal subgroups

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

subgroupindex
C2×#145827792
C2×#145827742
C2×#145827622
C2×C22⋊C4×Dic432
C22×C43⋊#952
#191328632
#191328402
#191328322
#191328242
C22×#123×C432
#1399643