Finite Group Databasebeta

← #25033277

Subgroups — #25033277

Order 11008.

1762 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582828C212yesmaximal, complemented
2C2×#14582801C211yesmaximal, characteristic
3C2×#14582800C211yesmaximal, characteristic
4C2×#14582800C211yesmaximal, characteristic
5C2×#14582795C211yesmaximal, characteristic, complemented
6#19132843C212yesmaximal, complemented
7#19132843C212yesmaximal, complemented
8#19132839C212yesmaximal, complemented
9#19132824C211yesmaximal, characteristic, complemented
10C4×C43⋊#95C211yesmaximal, characteristic, complemented
11C43×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×D172C2211yescharacteristic
13C22×C4⋊Dic43C2211yescharacteristic
14C22×Dic43⋊C4C2212yes—
15C22×(C2×D43)⋊C4C2212yes—
16C22×(C2×D43)⋊C4C2212yes—
17C22×(C2×D43)⋊C4C2212yes—
18C22×(C2×D43)⋊C4C2212yes—
19C22×(C2×D43)⋊C4C2212yes—
20C22×(C2×D43)⋊C4C2212yes—
21C22×C4×Dic43C2211yescharacteristic
22C22×C4×Dic43C2211yescharacteristic
23#14582828—28no—
24#14582801—24no—
25#14582800—24no—
26#14582800—24no—
27#14582795—24no—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2211yescharacteristic
31C2×C43⋊#95C2211yescharacteristic
32C2×C43⋊#95C2211yescharacteristic
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2211yescharacteristic
35C22×C4⋊C4×C43C2211yescharacteristic
36C22×C4⋊C4×C43C2211yescharacteristic
37C22×C42×C43C2211yescharacteristic
38C2×#95×C43C2212yes—
39C2×#95×C43C2212yes—
40C24×D43C2312yes—
41C22×D172—22no—
42C22×D172—22no—
43C22×D172—22no—
44C22×D172—22no—
45C22×D172—22no—
46C22×D172—22no—
47C22×D172D414yes—
48C23×Dic43C2311yescharacteristic
49C23×Dic43C2311yescharacteristic
50C23×Dic43C2312yes—
51C23×Dic43C2311yescharacteristic
52C23×Dic43C2311yescharacteristic
53C2×C4⋊Dic43—22no—
54C2×C4⋊Dic43—22no—
55C2×C4⋊Dic43D414yes—
56C2×Dic43⋊C4—24no—
57C2×Dic43⋊C4—24no—
58C2×Dic43⋊C4—42no—
59C2×(C2×D43)⋊C4—24no—
60C2×(C2×D43)⋊C4—24no—
61C2×(C2×D43)⋊C4—24no—
62C2×(C2×D43)⋊C4—24no—
63C2×(C2×D43)⋊C4—24no—
64C2×(C2×D43)⋊C4—24no—
65C2×(C2×D43)⋊C4—24no—
66C2×(C2×D43)⋊C4—24no—
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)⋊C4—42no—
74C2×(C2×D43)⋊C4—42no—
75C2×(C2×D43)⋊C4—42no—
76C2×(C2×D43)⋊C4—42no—
77C2×C4×Dic43—22no—
78C2×C4×Dic43—22no—
79C2×C4×Dic43—22no—
80C2×C4×Dic43—22no—
81C2×C4×Dic43—22no—
82C2×C4×Dic43—22no—
83C43⋊#95—22no—
84C43⋊#95—24no—
85C43⋊#95—24no—
86C43⋊#95—22no—
87C43⋊#95—22no—
88C43⋊#95—42no—
89C43⋊#95D414yescomplemented
90C23×C4×C43C2312yes—
91C23×C4×C43C2312yes—
92C23×C4×C43C2311yescharacteristic
93C23×C4×C43C2311yescharacteristic
94C23×C4×C43C2311yescharacteristic
95C2×C4⋊C4×C43—22no—
96C2×C4⋊C4×C43—22no—
97C2×C4⋊C4×C43—22no—
98C2×C4⋊C4×C43—22no—
99C2×C4⋊C4×C43—22no—
100C2×C4⋊C4×C43—22no—
101C2×C42×C43—22no—
102C2×C42×C43—22no—
103C2×C42×C43—22no—
104#95×C43—24no—
105#95×C43—42no—
106C24×C43C2411yescharacteristic
107C23×D43—22no—
108C23×D43—22no—
109C23×D43—22no—
110C23×D43—22no—
111C23×D43—22no—
112C23×D43—22no—
113C23×D43—22no—
114C23×D43—22no—
115C23×D43—22no—
116C23×D43—22no—
117C23×D43—22no—
118C23×D43—22no—
119C23×D43—22no—
120C23×D43—22no—
121C23×D43C2×D414yes—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—22no—
128C22×C4×C43—22no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—22no—
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—22no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—22no—
144C22×C4×C43—22no—
145C22×C4×C43—22no—
146C22×C4×C43—22no—
147C22×C4×C43—21no—
148C22×C4×C43C2×D412yes—
149C22×C4×C43C2×D412yes—
150C22×C4×C43C2×D412yes—
151C22×C4×C43#4112yes—
152C22×C4×C43#4112yes—
153C22×C4×C43#4112yes—
154C22×C4×C43#4112yes—
155C22×C4×C43#4112yes—
156C22×C4×C43#4112yes—
157C22×Dic43—21no—
158C22×Dic43—22no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43—22no—
175C22×Dic43—22no—
176C22×Dic43—22no—
177C22×Dic43—21no—
178C22×Dic43—22no—
179C22×Dic43—21no—
180C22×Dic43—21no—
181C22×Dic43—21no—
182C22×Dic43—21no—
183C22×Dic43—22no—
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43—21no—
187C22×Dic43C2×D412yes—
188C22×Dic43C2×D414yes—
189C22×Dic43C2×D412yes—
190C22×Dic43#4112yes—
191C22×Dic43#4112yes—
192C2×D172—28no—
193C2×D172—28no—
194C2×D172—28no—
195C2×D172—44no—
196C2×D172—44no—
197C2×D172—44no—
198C2×D172—44no—
199C4⋊C4×C43—44no—
200C4⋊C4×C43—44no—
201C42×C43—44no—
202(C2×D43)⋊C4—48no—
203(C2×D43)⋊C4—48no—
204(C2×D43)⋊C4—48no—
205(C2×D43)⋊C4—48no—
206(C2×D43)⋊C4—48no—
207(C2×D43)⋊C4—48no—
208C4⋊Dic43—28no—
209Dic43⋊C4—48no—
210C4×Dic43—44no—
211C4×Dic43—44no—
212C23×C43C22×D411yescharacteristic
213C23×C43C22×D411yescharacteristic
214C23×C43C22×D411yescharacteristic
215C23×C43C2×#4111yescharacteristic
216C23×C43C2×#4111yescharacteristic
217C23×C43C2×#4111yescharacteristic
218C23×C43C2×#4111yescharacteristic
219C23×C43C2×#4111yescharacteristic
220C23×C43C2×#4111yescharacteristic
221C23×C43C2×#4111yescharacteristic
222C23×C43C2×#4111yescharacteristic
223C23×C43H(5,𝔽2)11yescharacteristic
224C23×C43H(5,𝔽2)11yescharacteristic
225C23×C43H(5,𝔽2)11yescharacteristic
226C23×C432−1+411yescharacteristic
227C22×D43—24no—
228C22×D43—24no—
229C22×D43—24no—
230C22×D43—24no—
231C22×D43—24no—
232C22×D43—24no—
233C22×D43—24no—
234C22×D43—42no—
235C22×D43—42no—
236C22×D43—42no—
237C22×D43—42no—
238C22×D43—42no—
239C22×D43—42no—
240C22×D43—42no—
241C22×D43—42no—
242C22×D43—42no—
243C22×D43—42no—
244C22×D43—42no—
245C22×D43—42no—
246C22×D43—42no—
247C22×D43—42no—
248C22×D43—42no—
249C22×D43—42no—
250C22×D43—42no—
251C22×D43—42no—
252C22×D43—42no—
253C22×D43—42no—
254C22×D43—42no—
255C22×D43—42no—
256C22×D43—42no—
257C22×D43—42no—
258C22×D43—42no—
259C22×D43—42no—
260C22×D43—42no—
261C22×D43—42no—
262C2×C4×C43—22no—
263C2×C4×C43—22no—
264C2×C4×C43—22no—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43—22no—
268C2×C4×C43—41no—
269C2×C4×C43—41no—
270C2×C4×C43—41no—
271C2×C4×C43—41no—
272C2×C4×C43—41no—
273C2×C4×C43—41no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
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×C43—42no—
285C2×C4×C43—42no—
286C2×C4×C43—42no—
287C2×C4×C43—42no—
288C2×C4×C43—42no—
289C2×C4×C43—42no—
290C2×C4×C43#12114yes—
291C2×C4×C43#12314yes—
292C2×C4×C43#12314yes—
293C2×C4×C43#12314yes—
294C2×C4×C43#12414yes—
295C2×C4×C43#12614yes—
296C2×C4×C43#12614yes—
297C2×Dic43—24no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—24no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—24no—
309C2×Dic43—22no—
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—42no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—42no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—42no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43—42no—
332D172—416no—
333#15138—431nomaximal, Sylow
334C22×C43C2×#12111yescharacteristic
335C22×C43C2×#12311yescharacteristic
336C22×C43C2×#12311yescharacteristic
337C22×C43C2×#12311yescharacteristic
338C22×C43C2×#12411yescharacteristic
339C22×C43C2×#12611yescharacteristic
340C22×C43C2×#12611yescharacteristic
341C22×C43#52911yescharacteristic
342C22×C43#52911yescharacteristic
343C22×C43#52911yescharacteristic
344C22×C43#53211yescharacteristic
345C22×C43#53211yescharacteristic
346C22×C43#53211yescharacteristic
347C22×C43#54011yescharacteristic
348C22×C43#54011yescharacteristic
349C22×C43#54011yescharacteristic
350C22×C43#54211yescharacteristic
351C22×C43#54211yescharacteristic
352C22×C43#54211yescharacteristic
353C22×C43D4211yescharacteristic
354C22×C43D4211yescharacteristic
355C22×C43#54611yescharacteristic
356C22×C43#54611yescharacteristic
357C22×C43#54611yescharacteristic
358C22×C43#54711yescharacteristic
359C22×C43#54711yescharacteristic
360C22×C43#54811yescharacteristic
361C22×C43#55011yescharacteristic
362C22×C43#55011yescharacteristic
363C22×C43#55311yescharacteristic
364C22×C43#55311yescharacteristic
365C22×C43#55511yescharacteristic
366C22×C43#55611yescharacteristic
367C22×C43#55911yescharacteristic
368C22×C43#55911yescharacteristic
369C2×D43—44no—
370C2×D43—44no—
371C2×D43—44no—
372C2×D43—44no—
373C2×D43—44no—
374C2×D43—44no—
375C2×D43—44no—
376C2×D43—82no—
377C2×D43—82no—
378C2×D43—82no—
379C2×D43—82no—
380C2×D43—82no—
381C2×D43—82no—
382C2×D43—82no—
383C2×D43—82no—
384C4×C43—42no—
385C4×C43—42no—
386C4×C43—82no—
387C4×C43—82no—
388C4×C43#39718yescomplemented
389Dic43—42no—
390Dic43—42no—
391Dic43—42no—
392Dic43—42no—
393Dic43—44no—
394C2×#397—432no—
395C2×#390—431no—
396C2×#390—431no—
397C2×#390—431no—
398C2×#389—431no—
399#1440—432no—
400#1440—432no—
401#1439—432no—
402C4⋊#95—431no—
403C4⋊#95D4311yescharacteristic, complemented
404C4×#95—431no—
405C2×C43C2×#39711yescharacteristic
406C2×C43#242011yescharacteristic
407C2×C43#242211yescharacteristic
408C2×C43#242711yescharacteristic
409C2×C43#242811yescharacteristic
410C2×C43#244511yescharacteristic
411C2×C43#244511yescharacteristic
412C2×C43#244711yescharacteristic
413C2×C43#244811yescharacteristic
414C2×C43#249011yescharacteristic
415C2×C43#249111yescharacteristic
416C2×C43#251211yescharacteristic
417C2×C43#251311yescharacteristic
418C2×C43#264411yescharacteristic
419C2×C43#286011yescharacteristic
420D43—84no—
421C23×D4—431no—
422C22×C4⋊C4—431no—
423C22×C4⋊C4—432no—
424C22×C4⋊C4C2×D4311yescharacteristic
425C22×C4⋊C4C2×D4311yescharacteristic
426C22×C22⋊C4—432no—
427C22×C22⋊C4—432no—
428C22×C22⋊C4—432no—
429C22×C22⋊C4—432no—
430C22×C22⋊C4—432no—
431C22×C22⋊C4—432no—
432C22×C42—431no—
433C22×C42—431no—
434C22×C42C2×D4311yescharacteristic
435#397—868no—
436#390—864no—
437#390—864no—
438#390—864no—
439#389—864no—
440C2×#95—431no—
441C2×#95—432no—
442C2×#95—431no—
443C2×#95—431no—
444C2×#95—431no—
445C2×#95—432no—
446C2×#95—432no—
447C2×#95C2×D4312yes—
448C2×#95C2×D4312yes—
449C43#1513811yescharacteristic, complemented, Sylow
450C25—432no—
451C22×D4—434no—
452C22×D4—862no—
453C22×D4—862no—
454C22×D4—862no—
455C22×D4—862no—
456C22×D4—862no—
457C22×D4—862no—
458C23×C4—432no—
459C23×C4—431no—
460C23×C4—431no—
461C23×C4—431no—
462C23×C4—431no—
463C23×C4C22×D4312yes—
464C23×C4C22×D4312yes—
465C23×C4C22×D4311yescharacteristic
466C23×C4C22×D4311yescharacteristic
467C23×C4C22×D4311yescharacteristic
468C2×C4⋊C4—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—434no—
475C2×C4⋊C4—862no—
476C2×C4⋊C4—862no—
477C2×C4⋊C4—864no—
478C2×C4⋊C4—864no—
479C2×C4⋊C4—1722no—
480C2×C22⋊C4—864no—
481C2×C22⋊C4—864no—
482C2×C22⋊C4—864no—
483C2×C22⋊C4—864no—
484C2×C22⋊C4—864no—
485C2×C22⋊C4—864no—
486C2×C22⋊C4—864no—
487C2×C22⋊C4—864no—
488C2×C22⋊C4—864no—
489C2×C22⋊C4—864no—
490C2×C22⋊C4—864no—
491C2×C22⋊C4—864no—
492C2×C22⋊C4—1722no—
493C2×C22⋊C4—1722no—
494C2×C22⋊C4—1722no—
495C2×C22⋊C4—1722no—
496C2×C22⋊C4—1722no—
497C2×C22⋊C4—1722no—
498C2×C42—22no—
499C2×C42—22no—
500C2×C42—22no—
501C2×C42—862no—
502C2×C42—862no—
503C2×C42—862no—
504C2×C42—862no—
505C2×C42—862no—
506C2×C42—862no—
507#95—24no—
508#95—42no—
509#95—434no—
510#95—862no—
511#95—862no—
512#95—864no—
513#95—864no—
514#95—862no—
515#95—1722no—
516C24—434no—
517C24—862no—
518C24—862no—
519C24—862no—
520C24—862no—
521C24—862no—
522C24—862no—
523C24—862no—
524C24—862no—
525C24—862no—
526C24—862no—
527C24—862no—
528C24—862no—
529C24—862no—
530C24—862no—
531C24C23×D4311yescharacteristic
532C2×D4—868no—
533C2×D4—868no—
534C2×D4—868no—
535C2×D4—1724no—
536C2×D4—1724no—
537C2×D4—1724no—
538C2×D4—1724no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—432no—
566C22×C4—432no—
567C22×C4—434no—
568C22×C4—432no—
569C22×C4—432no—
570C22×C4—861no—
571C22×C4—862no—
572C22×C4—861no—
573C22×C4—861no—
574C22×C4—861no—
575C22×C4—861no—
576C22×C4—861no—
577C22×C4—861no—
578C22×C4—861no—
579C22×C4—861no—
580C22×C4—861no—
581C22×C4—861no—
582C22×C4—861no—
583C22×C4—862no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—861no—
587C22×C4—861no—
588C22×C4—862no—
589C22×C4—862no—
590C22×C4—861no—
591C22×C4—861no—
592C22×C4—861no—
593C22×C4—862no—
594C22×C4—861no—
595C22×C4—861no—
596C22×C4—862no—
597C22×C4—861no—
598C22×C4—861no—
599C22×C4—861no—
600C22×C4#1062189812yes—
601C22×C4#1062189812yes—
602C22×C4#1062189812yes—
603C22×C4D4×D4312yes—
604C22×C4D4×D4312yes—
605C22×C4D4×D4312yes—
606C22×C4#1062190012yes—
607C22×C4#1062190212yes—
608C22×C4#1062190212yes—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—868no—
612C4⋊C4—1728no—
613C22⋊C4—1728no—
614C22⋊C4—1728no—
615C22⋊C4—1728no—
616C22⋊C4—1728no—
617C22⋊C4—1728no—
618C22⋊C4—1728no—
619C42—44no—
620C42—1724no—
621C42—1724no—
622C23—864no—
623C23—864no—
624C23—864no—
625C23—864no—
626C23—864no—
627C23—864no—
628C23—864no—
629C23—1722no—
630C23—1722no—
631C23—1722no—
632C23—1722no—
633C23—1722no—
634C23—1722no—
635C23—1722no—
636C23—1722no—
637C23—1722no—
638C23—1722no—
639C23—1722no—
640C23—1722no—
641C23—1722no—
642C23—1722no—
643C23—1722no—
644C23—1722no—
645C23—1722no—
646C23—1722no—
647C23—1722no—
648C23—1722no—
649C23—1722no—
650C23—1722no—
651C23—1722no—
652C23—1722no—
653C23—1722no—
654C23—1722no—
655C23—1722no—
656C23—1722no—
657C23C2×D4×D4311yescharacteristic
658C23C2×D4×D4311yescharacteristic
659C23C2×D4×D4311yescharacteristic
660C23#41×D4311yescharacteristic
661C23#41×D4311yescharacteristic
662C23C2×#1062190011yescharacteristic
663C23C2×#1062189811yescharacteristic
664C23C2×#1062189811yescharacteristic
665C23C2×#1062189811yescharacteristic
666C23C2×#1062190211yescharacteristic
667C23C2×#1062190211yescharacteristic
668C23#1306337011yescharacteristic
669C23#1306337111yescharacteristic
670C23#1306337111yescharacteristic
671C23#1306337311yescharacteristic
672D4—17216no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—864no—
704C2×C4—862no—
705C2×C4—862no—
706C2×C4—862no—
707C2×C4—862no—
708C2×C4—864no—
709C2×C4—862no—
710C2×C4—862no—
711C2×C4—862no—
712C2×C4—864no—
713C2×C4—862no—
714C2×C4—862no—
715C2×C4—862no—
716C2×C4—1721no—
717C2×C4—1721no—
718C2×C4—1721no—
719C2×C4—1722no—
720C2×C4—1721no—
721C2×C4—1721no—
722C2×C4—1722no—
723C2×C4—1721no—
724C2×C4—1721no—
725C2×C4—1721no—
726C2×C4—1721no—
727C2×C4—1722no—
728C2×C4—1721no—
729C2×C4—1721no—
730C2×C4—1722no—
731C2×C4—1721no—
732C2×C4—1721no—
733C2×C4—1721no—
734C2×C4—1721no—
735C2×C4—1721no—
736C2×C4#1306329814yes—
737C2×C4#1306330714yes—
738C2×C4#1306331014yes—
739C2×C4#1306331014yes—
740C2×C4#1306331114yes—
741C2×C4#1306331914yes—
742C2×C4#1306332014yes—
743C22—3442no—
744C22—3442no—
745C22—3442no—
746C22—3442no—
747C22—3442no—
748C22—3442no—
749C22—3442no—
750C22—3442no—
751C22—1724no—
752C22—1724no—
753C22—1724no—
754C22—1724no—
755C22—1724no—
756C22—1724no—
757C22—1724no—
758C22C2×#1306329811yescharacteristic
759C22C2×#1306330711yescharacteristic
760C22C2×#1306331011yescharacteristic
761C22C2×#1306331011yescharacteristic
762C22C2×#1306331111yescharacteristic
763C22C2×#1306331911yescharacteristic
764C22C2×#1306332011yescharacteristic
765C22#1458343411yescharacteristic
766C22#1458343511yescharacteristic
767C22#1458343611yescharacteristic
768C22#1458344411yescharacteristic
769C22#1458344611yescharacteristic
770C22#1458345011yescharacteristic
771C22#1458350011yescharacteristic
772C22#1458350211yescharacteristic
773C22#1458350511yescharacteristic
774C22#1458352111yescharacteristic
775C22#1458352211yescharacteristic
776C22#1458352311yescharacteristic
777C22#1458353311yescharacteristic
778C22#1458353411yescharacteristic
779C22#1458354011yescharacteristic
780C22#1458354211yescharacteristic
781C22#1458354211yescharacteristic
782C22#1458355011yescharacteristic
783C22#1458355211yescharacteristic
784C22#1458355911yescharacteristic
785C22#1458356711yescharacteristic
786C22#1458357011yescharacteristic
787C22#1458359311yescharacteristic
788C22#1458359711yescharacteristic
789C22#1458361211yescharacteristic
790C22#1458362111yescharacteristic
791C22#1458363211yescharacteristic
792C22#1458363411yescharacteristic
793C4—42no—
794C4—42no—
795C4—82no—
796C4—82no—
797C4—1722no—
798C4—1724no—
799C4—1722no—
800C4—1722no—
801C4—1722no—
802C4#1458282818yescomplemented
803C2—3444no—
804C2C2×#1458282811yescharacteristic
805C2#1913809011yescharacteristic
806C2#1913811211yescharacteristic
807C2#1913817311yescharacteristic
808C2#1913818411yescharacteristic
809C2#1913836211yescharacteristic
810C2#1913836311yescharacteristic
811C2#1913838511yescharacteristic
812C2#1913839511yescharacteristic
813C2#1913894311yescharacteristic
814C2#1913895411yescharacteristic
815C2#1913917511yescharacteristic
816C2#1913918611yescharacteristic
817C2#1914055811yescharacteristic
818C2#1914296311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutator, socle, cosocleC24×C43C24
FittingC43×C4⋊#95C2
prime radicalC23×D172C22
hypercenterC4⋊#95D43
hypocenterC43#15138
LCSG ▷ C24×C43 ▷ C43
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
1. C2×#14582828C2semidirect
5. C2×#14582795C2semidirect
6. #19132843C2semidirect
7. #19132843C2semidirect
8. #19132839C2semidirect
9. #19132824C2semidirect
10. C4×C43⋊#95C2semidirect
11. C43×C4⋊#95C2semidirect
89. C43⋊#95D4semidirect
388. C4×C43#397semidirect
403. C4⋊#95D43semidirect
449. C43#15138semidirect
802. C4#14582828semidirect

Maximal subgroups

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

subgroupindex
C2×#145828282
C2×#145828012
C2×#145828002
C2×#145827952
#191328432
#191328392
#191328242
C4×C43⋊#952
C43×C4⋊#952
#1513843