Finite Group Databasebeta

← #25019140

Subgroups — #25019140

Order 11008.

2230 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D172C211yesmaximal, characteristic
2C2×#14582761C211yesmaximal, characteristic, complemented
3C2×#14582746C211yesmaximal, characteristic, complemented
4#19132843C212yesmaximal, complemented
5#19132835C212yesmaximal
6#19132831C212yesmaximal, complemented
7#19132829C212yesmaximal, complemented
8#19132822C211yesmaximal, characteristic, complemented
9(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
10(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
11C43×#1434C211yesmaximal, characteristic, complemented
12C23×D172C2211yescharacteristic
13C23×C4×D43C2211yescharacteristic
14C23×C4×D43C2211yescharacteristic
15C2×C4×D172—24no—
16C2×C4×D172—24no—
17C2×C4×D172C418yescomplemented
18C22×C4⋊Dic43C2211yescharacteristic
19C22×(C2×D43)⋊C4C2212yes—
20C22×(C2×D43)⋊C4C2212yes—
21C22×(C2×D43)⋊C4C2212yes—
22C22×(C2×D43)⋊C4C2211yescharacteristic
23C22×(C2×D43)⋊C4C2211yescharacteristic
24C22×(C2×D43)⋊C4C2212yes—
25C22×C4×Dic43C2212yes—
26#14582761—24no—
27#14582746—24no—
28C2×C43⋊#95C2211yescharacteristic
29C2×C43⋊#95C2211yescharacteristic
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2212yes—
35C22×C42×C43C2211yescharacteristic
36C2×#95×C43C2211yescharacteristic
37C2×#95×C43C2211yescharacteristic
38C2×#95×C43C2212yes—
39C2×#95×C43C2212yes—
40C24×D43C2311yescharacteristic
41C24×D43C2311yescharacteristic
42C22×D172—22no—
43C22×D172—22no—
44C22×D172—22no—
45C22×D172—22no—
46C22×D172—22no—
47C22×D172—22no—
48C22×D172C2×C414yes—
49C23×Dic43C2312yes—
50C23×Dic43C2311yescharacteristic
51C23×Dic43C2312yes—
52C23×Dic43C2311yescharacteristic
53C22×C4×D43—22no—
54C22×C4×D43—22no—
55C22×C4×D43—42no—
56C22×C4×D43—42no—
57C22×C4×D43—42no—
58C22×C4×D43—42no—
59C22×C4×D43C2×C414yes—
60C22×C4×D43C2×C414yes—
61C22×C4×D43D414yes—
62C22×C4×D43D414yes—
63C4×D172—232no—
64C2×C4⋊Dic43—22no—
65C2×C4⋊Dic43—22no—
66C2×C4⋊Dic43C2×C414yes—
67C2×(C2×D43)⋊C4—22no—
68C2×(C2×D43)⋊C4—22no—
69C2×(C2×D43)⋊C4—24no—
70C2×(C2×D43)⋊C4—24no—
71C2×(C2×D43)⋊C4—22no—
72C2×(C2×D43)⋊C4—22no—
73C2×(C2×D43)⋊C4—24no—
74C2×(C2×D43)⋊C4—24no—
75C2×(C2×D43)⋊C4—24no—
76C2×(C2×D43)⋊C4—24no—
77C2×(C2×D43)⋊C4—24no—
78C2×(C2×D43)⋊C4—24no—
79C2×(C2×D43)⋊C4—42no—
80C2×(C2×D43)⋊C4—42no—
81C2×(C2×D43)⋊C4—42no—
82C2×(C2×D43)⋊C4—42no—
83C2×(C2×D43)⋊C4C2×C414yes—
84C2×(C2×D43)⋊C4C2×C414yes—
85C2×C4×Dic43—24no—
86C2×C4×Dic43—42no—
87C2×C4×Dic43—42no—
88C43⋊#95—22no—
89C43⋊#95—22no—
90C43⋊#95—24no—
91C43⋊#95—24no—
92C43⋊#95—24no—
93C43⋊#95—42no—
94C43⋊#95—42no—
95C23×C4×C43C2312yes—
96C23×C4×C43C2311yescharacteristic
97C23×C4×C43C2312yes—
98C23×C4×C43C2311yescharacteristic
99C23×C4×C43C2311yescharacteristic
100C2×C42×C43—22no—
101C2×C42×C43—22no—
102C2×C42×C43C2×C414yes—
103#95×C43—22no—
104#95×C43—22no—
105#95×C43—24no—
106#95×C43—24no—
107C24×C43C2411yescharacteristic
108C23×D43—21no—
109C23×D43—21no—
110C23×D43—22no—
111C23×D43—22no—
112C23×D43—22no—
113C23×D43—22no—
114C23×D43—21no—
115C23×D43—21no—
116C23×D43—21no—
117C23×D43—21no—
118C23×D43—21no—
119C23×D43—21no—
120C23×D43—22no—
121C23×D43—22no—
122C23×D43—22no—
123C23×D43—22no—
124C23×D43C22×C412yes—
125C23×D43C22×C412yes—
126C23×D43C2×D412yes—
127C23×D43C2×D412yes—
128C23×D43#4112yes—
129C23×D43#4112yes—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—22no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—22no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
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—22no—
148C22×C4×C43—22no—
149C22×C4×C43—22no—
150C22×C4×C43—22no—
151C22×C4×C43—22no—
152C22×C4×C43—22no—
153C22×C4×C43C22×C412yes—
154C22×C4×C43C22×C412yes—
155C22×C4×C43C22×C412yes—
156C22×C4×C43C2×D412yes—
157C22×C4×C43C2×D412yes—
158C22×C4×C43#4114yes—
159C22×C4×C43#4112yes—
160C22×C4×C43#4112yes—
161C22×Dic43—22no—
162C22×Dic43—21no—
163C22×Dic43—21no—
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—22no—
174C22×Dic43—22no—
175C22×Dic43—22no—
176C22×Dic43—22no—
177C22×Dic43—22no—
178C22×Dic43—22no—
179C22×Dic43—22no—
180C22×Dic43C22×C412yes—
181C22×Dic43C22×C412yes—
182C22×Dic43C2×D412yes—
183C22×Dic43C2×D412yes—
184C22×Dic43#4114yes—
185C2×D172—28no—
186C2×D172—28no—
187C2×D172—28no—
188C2×D172—28no—
189C2×D172—28no—
190C2×D172—28no—
191C2×D172—28no—
192C2×C4×D43—28no—
193C2×C4×D43—44no—
194C2×C4×D43—44no—
195C2×C4×D43—44no—
196C2×C4×D43—44no—
197C2×C4×D43—48no—
198C2×C4×D43—48no—
199C2×C4×D43—48no—
200C2×C4×D43—48no—
201C2×C4×D43C22⋊C4116yescomplemented
202C42×C43—28no—
203(C2×D43)⋊C4—216no—
204(C2×D43)⋊C4—28no—
205(C2×D43)⋊C4—28no—
206(C2×D43)⋊C4—48no—
207(C2×D43)⋊C4—48no—
208(C2×D43)⋊C4—48no—
209C4⋊Dic43—28no—
210C4×Dic43—48no—
211C23×C43C23×C411yescharacteristic
212C23×C43C22×D411yescharacteristic
213C23×C43C22×D411yescharacteristic
214C23×C43C2×#4111yescharacteristic
215C23×C43C2×#4111yescharacteristic
216C23×C43C2×#4112yes—
217C23×C43C2×#4111yescharacteristic
218C23×C43C2×#4112yes—
219C23×C43C2×#4111yescharacteristic
220C23×C43H(5,𝔽2)12yes—
221C23×C43H(5,𝔽2)12yes—
222C22×D43—22no—
223C22×D43—22no—
224C22×D43—22no—
225C22×D43—22no—
226C22×D43—22no—
227C22×D43—22no—
228C22×D43—22no—
229C22×D43—22no—
230C22×D43—22no—
231C22×D43—22no—
232C22×D43—22no—
233C22×D43—22no—
234C22×D43—24no—
235C22×D43—22no—
236C22×D43—22no—
237C22×D43—22no—
238C22×D43—22no—
239C22×D43—22no—
240C22×D43—22no—
241C22×D43—22no—
242C22×D43—22no—
243C22×D43—24no—
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—42no—
255C22×D43—42no—
256C22×D43—42no—
257C22×D43—42no—
258C22×D43—42no—
259C22×D43—42no—
260C22×D43—42no—
261C22×D43—42no—
262C22×D43—42no—
263C22×D43—42no—
264C22×D43—42no—
265C22×D43—42no—
266C22×D43C2×C22⋊C414yes—
267C22×D43#11714yes—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—24no—
277C2×C4×C43—24no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—24no—
282C2×C4×C43—24no—
283C2×C4×C43—24no—
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—42no—
291C2×C4×C43—42no—
292C2×C4×C43—42no—
293C2×C4×C43—42no—
294C2×C4×C43—42no—
295C2×C4×C43—42no—
296C2×C4×C43—42no—
297C2×C4×C43C2×C22⋊C414yes—
298C2×C4×C43#11714yes—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—24no—
302C2×Dic43—24no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—24no—
307C2×Dic43—24no—
308C2×Dic43—24no—
309C2×Dic43—42no—
310C2×Dic43—42no—
311C2×Dic43—42no—
312C2×Dic43—42no—
313C2×Dic43—42no—
314C2×Dic43—42no—
315C2×Dic43—42no—
316C2×Dic43—42no—
317C2×Dic43—42no—
318C2×Dic43—42no—
319C2×Dic43—42no—
320C2×Dic43—42no—
321C2×Dic43—42no—
322C2×Dic43C2×C22⋊C414yes—
323D172—232no—
324C4×D43—416no—
325C4×D43—416no—
326#13940—431nomaximal, Sylow
327C22×C43C22×C22⋊C411yescharacteristic
328C22×C43C2×#11711yescharacteristic
329C22×C43C2×#11711yescharacteristic
330C22×C43C4×#4111yescharacteristic
331C22×C43C4×#4111yescharacteristic
332C22×C43#51811yescharacteristic
333C22×C43#51811yescharacteristic
334C22×C43#52512yes—
335C22×C43#52511yescharacteristic
336C22×C43#52511yescharacteristic
337C22×C43#52511yescharacteristic
338C22×C43#52511yescharacteristic
339C22×C43#53212yes—
340C22×C43#53412yes—
341C22×C43#53412yes—
342C22×C43#55112yes—
343C22×C43#55112yes—
344C22×C43#55312yes—
345C22×C43#55312yes—
346C22×C43#55312yes—
347C22×C43#55312yes—
348C22×C43#55912yes—
349C22×C43#55912yes—
350C2×D43—24no—
351C2×D43—24no—
352C2×D43—24no—
353C2×D43—24no—
354C2×D43—24no—
355C2×D43—24no—
356C2×D43—42no—
357C2×D43—44no—
358C2×D43—44no—
359C2×D43—44no—
360C2×D43—44no—
361C2×D43—44no—
362C2×D43—44no—
363C2×D43—44no—
364C2×D43—44no—
365C2×D43—42no—
366C2×D43—42no—
367C2×D43—42no—
368C2×D43—42no—
369C2×D43—42no—
370C2×D43—42no—
371C2×D43—42no—
372C4×C43—24no—
373C4×C43—24no—
374C4×C43—44no—
375C4×C43—42no—
376C4×C43—82no—
377Dic43—24no—
378Dic43—42no—
379Dic43—44no—
380Dic43—82no—
381C22×C4×D4—431no—
382C2×#381—431no—
383C2×C4×C22⋊C4—431no—
384#1440—432no—
385#1438—432no—
386#1437—432no—
387#1436—432no—
388#1434—431no—
389#1434D4311yescharacteristic, complemented
390C22⋊#95—431no—
391C22⋊#95—431no—
392C2×C43#228011yescharacteristic
393C2×C43#229711yescharacteristic
394C2×C43#230811yescharacteristic
395C2×C43#235311yescharacteristic
396C2×C43#235311yescharacteristic
397C2×C43#235711yescharacteristic
398C2×C43#235711yescharacteristic
399C2×C43#260012yes—
400C2×C43#260012yes—
401C2×C43#260212yes—
402C2×C43#260212yes—
403D43—44no—
404D43—44no—
405C23×D4—431no—
406C24×C4—431no—
407C24×C4—431no—
408C2×C4×D4—438no—
409C2×C4×D4—864no—
410C2×C4×D4—864no—
411C22×C4⋊C4—431no—
412C22×C22⋊C4—431no—
413C22×C22⋊C4—431no—
414C22×C22⋊C4—432no—
415C22×C22⋊C4—432no—
416C22×C22⋊C4—432no—
417C22×C22⋊C4—432no—
418C22×C42—432no—
419C22×C42C2×D4311yescharacteristic
420#381—864no—
421C4×C22⋊C4—864no—
422C2×#95—431no—
423C2×#95—431no—
424C2×#95—432no—
425C2×#95—432no—
426C2×#95—432no—
427C2×#95—432no—
428C2×#95—432no—
429C2×#95C2×D4311yescharacteristic
430C2×#95C2×D4311yescharacteristic
431C2×#95C2×D4312yes—
432C2×#95C2×D4312yes—
433C43#1394011yescharacteristic, complemented, Sylow
434C25—431no—
435C25—431no—
436C22×D4—434no—
437C22×D4—862no—
438C22×D4—862no—
439C22×D4—862no—
440C22×D4—862no—
441C22×D4—862no—
442C22×D4—862no—
443C23×C4—431no—
444C23×C4—434no—
445C23×C4—434no—
446C23×C4—434no—
447C23×C4—432no—
448C23×C4—431no—
449C23×C4—434no—
450C23×C4—432no—
451C23×C4—862no—
452C23×C4—862no—
453C23×C4—1722no—
454C23×C4—1722no—
455C23×C4—1722no—
456C23×C4—1722no—
457C23×C4C22×D4312yes—
458C23×C4C22×D4311yescharacteristic
459C23×C4C22×D4312yes—
460C23×C4C22×D4311yescharacteristic
461C23×C4C22×D4311yescharacteristic
462C4×D4—8632no—
463C2×C4⋊C4—434no—
464C2×C4⋊C4—862no—
465C2×C4⋊C4—862no—
466C2×C22⋊C4—434no—
467C2×C22⋊C4—434no—
468C2×C22⋊C4—862no—
469C2×C22⋊C4—862no—
470C2×C22⋊C4—864no—
471C2×C22⋊C4—862no—
472C2×C22⋊C4—862no—
473C2×C22⋊C4—864no—
474C2×C22⋊C4—864no—
475C2×C22⋊C4—864no—
476C2×C22⋊C4—864no—
477C2×C22⋊C4—864no—
478C2×C22⋊C4—864no—
479C2×C22⋊C4—864no—
480C2×C22⋊C4—1722no—
481C2×C22⋊C4—1722no—
482C2×C22⋊C4—1722no—
483C2×C22⋊C4—1722no—
484C2×C42—22no—
485C2×C42—22no—
486C2×C42—864no—
487C2×C42—1722no—
488C2×C42—1722no—
489C2×C42C4×D4314yes—
490#95—24no—
491#95—22no—
492#95—22no—
493#95—24no—
494#95—864no—
495#95—864no—
496#95—862no—
497#95—862no—
498#95—864no—
499#95—1722no—
500#95—1722no—
501C24—432no—
502C24—432no—
503C24—432no—
504C24—432no—
505C24—432no—
506C24—432no—
507C24—861no—
508C24—861no—
509C24—862no—
510C24—862no—
511C24—861no—
512C24—861no—
513C24—861no—
514C24—861no—
515C24—862no—
516C24—862no—
517C24—861no—
518C24—861no—
519C24—862no—
520C24—862no—
521C24—862no—
522C24—862no—
523C24C23×D4311yescharacteristic
524C2×D4—868no—
525C2×D4—868no—
526C2×D4—868no—
527C2×D4—868no—
528C2×D4—868no—
529C2×D4—868no—
530C2×D4—868no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—432no—
555C22×C4—432no—
556C22×C4—432no—
557C22×C4—4316no—
558C22×C4—432no—
559C22×C4—434no—
560C22×C4—862no—
561C22×C4—862no—
562C22×C4—862no—
563C22×C4—861no—
564C22×C4—861no—
565C22×C4—862no—
566C22×C4—862no—
567C22×C4—862no—
568C22×C4—862no—
569C22×C4—862no—
570C22×C4—862no—
571C22×C4—862no—
572C22×C4—868no—
573C22×C4—862no—
574C22×C4—862no—
575C22×C4—862no—
576C22×C4—862no—
577C22×C4—862no—
578C22×C4—862no—
579C22×C4—862no—
580C22×C4—1724no—
581C22×C4—1724no—
582C22×C4—1724no—
583C22×C4—1724no—
584C22×C4—1728no—
585C22×C4—1728no—
586C22×C4—1728no—
587C22×C4—1728no—
588C22×C4C2×C4×D4312yes—
589C22×C4C2×C4×D4312yes—
590C22×C4C2×C4×D4312yes—
591C22×C4#1062189814yes—
592C22×C4D4×D4312yes—
593C22×C4D4×D4312yes—
594C22×C4#1062190012yes—
595C22×C4#1062190212yes—
596C4⋊C4—868no—
597C22⋊C4—868no—
598C22⋊C4—868no—
599C22⋊C4—8616no—
600C22⋊C4—1728no—
601C22⋊C4—1728no—
602C22⋊C4—1728no—
603C42—28no—
604C42—1728no—
605C23—434no—
606C23—434no—
607C23—864no—
608C23—864no—
609C23—864no—
610C23—864no—
611C23—862no—
612C23—862no—
613C23—862no—
614C23—862no—
615C23—862no—
616C23—862no—
617C23—862no—
618C23—862no—
619C23—862no—
620C23—862no—
621C23—862no—
622C23—862no—
623C23—864no—
624C23—862no—
625C23—862no—
626C23—862no—
627C23—862no—
628C23—862no—
629C23—862no—
630C23—862no—
631C23—862no—
632C23—864no—
633C23—864no—
634C23—864no—
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—
651C23C22×C4×D4311yescharacteristic
652C23C2×D4×D4311yescharacteristic
653C23C2×D4×D4311yescharacteristic
654C23#41×D4311yescharacteristic
655C23#41×D4311yescharacteristic
656C23#41×D4312yes—
657C23C2×#1062190011yescharacteristic
658C23C2×#1062189812yes—
659C23C2×#1062190211yescharacteristic
660C23#1306337112yes—
661C23#1306337112yes—
662D4—8632no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—434no—
693C2×C4—862no—
694C2×C4—862no—
695C2×C4—864no—
696C2×C4—864no—
697C2×C4—864no—
698C2×C4—862no—
699C2×C4—864no—
700C2×C4—862no—
701C2×C4—862no—
702C2×C4—864no—
703C2×C4—17216no—
704C2×C4—17216no—
705C2×C4—1722no—
706C2×C4—1722no—
707C2×C4—1722no—
708C2×C4—1722no—
709C2×C4—1722no—
710C2×C4—1722no—
711C2×C4—1722no—
712C2×C4—1722no—
713C2×C4—1722no—
714C2×C4—1722no—
715C2×C4—1722no—
716C2×C4—1722no—
717C2×C4—1722no—
718C2×C4C22⋊C4×D4314yes—
719C2×C4#1306328314yes—
720C22—864no—
721C22—864no—
722C22—864no—
723C22—864no—
724C22—864no—
725C22—864no—
726C22—1722no—
727C22—1722no—
728C22—1722no—
729C22—1722no—
730C22—1722no—
731C22—1722no—
732C22—1724no—
733C22—1724no—
734C22—1724no—
735C22—1724no—
736C22—1724no—
737C22—1724no—
738C22—1724no—
739C22—1724no—
740C22—1722no—
741C22—1722no—
742C22C2×C22⋊C4×D4311yescharacteristic
743C22#117×D4311yescharacteristic
744C22C2×#1306328311yescharacteristic
745C22#1458336711yescharacteristic
746C22C4×#1062189811yescharacteristic
747C22#1458337311yescharacteristic
748C22#1458337311yescharacteristic
749C22#1458340812yes—
750C22#1458340911yescharacteristic
751C22#1458340911yescharacteristic
752C22#1458341211yescharacteristic
753C22#1458341211yescharacteristic
754C22#1458344612yes—
755C22#1458346012yes—
756C22#1458346012yes—
757C22#1458357312yes—
758C22#1458357412yes—
759C22#1458359312yes—
760C22#1458359512yes—
761C22#1458360012yes—
762C22#1458360212yes—
763C22#1458363112yes—
764C22#1458363412yes—
765C4—24no—
766C4—24no—
767C4—42no—
768C4—44no—
769C4—82no—
770C4—864no—
771C4—3442no—
772C4—1724no—
773C4—1722no—
774C2—1724no—
775C2—1724no—
776C2#1913697711yescharacteristic
777C2#1913708111yescharacteristic
778C2#1913717211yescharacteristic
779C2#1913752811yescharacteristic
780C2#1913753611yescharacteristic
781C2#1913756611yescharacteristic
782C2#1913757011yescharacteristic
783C2#1914018012yes—
784C2#1914018412yes—
785C2#1914020512yes—
786C2#1914021312yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1434C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenter#1434D43
hypocenterC43#13940
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. C2×#14582761C2semidirect
3. C2×#14582746C2semidirect
4. #19132843C2semidirect
6. #19132831C2semidirect
7. #19132829C2semidirect
8. #19132822C2semidirect
9. (C2×D43)⋊#95C2semidirect
10. (C2×D43)⋊#95C2semidirect
11. C43×#1434C2semidirect
17. C2×C4×D172C4semidirect
201. C2×C4×D43C22⋊C4semidirect
389. #1434D43semidirect
433. C43#13940semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D1722
C2×#145827612
C2×#145827462
#191328432
#191328352
#191328312
#191328292
#191328222
(C2×D43)⋊#952
C43×#14342
#1394043