Finite Group Databasebeta

← #25019138

Subgroups — #25019138

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×C22⋊D43C211yesmaximal, characteristic
2C2×#14582761C211yesmaximal, characteristic, complemented
3C2×#14582746C211yesmaximal, characteristic, complemented
4#19132843C212yesmaximal, complemented
5#19132834C212yesmaximal
6#19132832C212yesmaximal, complemented
7#19132826C212yesmaximal, complemented
8#19132819C211yesmaximal, characteristic, complemented
9#19132819C211yesmaximal, characteristic, complemented
10#19132818C211yesmaximal, characteristic, complemented
11C43×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C22⋊D43C2211yescharacteristic
13C23×C4×D43C2211yescharacteristic
14C2×C4×C22⋊D43—24no—
15C2×C4×C22⋊D43—24no—
16C2×C4×C22⋊D43C418yescomplemented
17C22×Dic43⋊C4C2211yescharacteristic
18C22×C22⋊Dic43C2212yes—
19C22×C22⋊Dic43C2211yescharacteristic
20C22×(C2×D43)⋊C4C2212yes—
21C22×(C2×D43)⋊C4C2211yescharacteristic
22C22×(C2×D43)⋊C4C2212yes—
23C22×C4×Dic43C2211yescharacteristic
24C22×C4×Dic43C2212yes—
25#14582761—24no—
26#14582746—24no—
27C2×C43⋊#95C2211yescharacteristic
28C2×C43⋊#95C2211yescharacteristic
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2212yes—
35C24×C4×C43C2211yescharacteristic
36C22×C22⋊C4×C43C2212yes—
37C2×#95×C43C2211yescharacteristic
38C2×#95×C43C2211yescharacteristic
39C2×#95×C43C2212yes—
40C24×D43C2311yescharacteristic
41C22×C22⋊D43—22no—
42C22×C22⋊D43—22no—
43C22×C22⋊D43—22no—
44C22×C22⋊D43—22no—
45C22×C22⋊D43—22no—
46C22×C22⋊D43—22no—
47C22×C22⋊D43C2×C414yes—
48C23×Dic43C2312yes—
49C23×Dic43C2311yescharacteristic
50C23×Dic43C2312yes—
51C23×Dic43C2311yescharacteristic
52C23×Dic43C2311yescharacteristic
53C22×C4×D43—42no—
54C22×C4×D43—42no—
55C22×C4×D43C2×C414yes—
56C22×C4×D43D414yes—
57C22×C4×D43D414yes—
58C4×C22⋊D43—232no—
59C2×Dic43⋊C4—22no—
60C2×Dic43⋊C4—22no—
61C2×Dic43⋊C4C2×C414yes—
62C2×C22⋊Dic43—22no—
63C2×C22⋊Dic43—22no—
64C2×C22⋊Dic43—24no—
65C2×C22⋊Dic43—24no—
66C2×C22⋊Dic43—42no—
67C2×C22⋊Dic43C2×C414yes—
68C2×(C2×D43)⋊C4—22no—
69C2×(C2×D43)⋊C4—22no—
70C2×(C2×D43)⋊C4—24no—
71C2×(C2×D43)⋊C4—24no—
72C2×(C2×D43)⋊C4—24no—
73C2×(C2×D43)⋊C4—24no—
74C2×(C2×D43)⋊C4—42no—
75C2×(C2×D43)⋊C4—42no—
76C2×(C2×D43)⋊C4C2×C414yes—
77C2×C4×Dic43—22no—
78C2×C4×Dic43—22no—
79C2×C4×Dic43—24no—
80C2×C4×Dic43—42no—
81C2×C4×Dic43—42no—
82C2×C4×Dic43C2×C414yes—
83C43⋊#95—22no—
84C43⋊#95—22no—
85C43⋊#95—24no—
86C43⋊#95—24no—
87C43⋊#95—24no—
88C43⋊#95—24no—
89C43⋊#95—24no—
90C43⋊#95—42no—
91C25×C43C2311yescharacteristic
92C23×C4×C43—22no—
93C23×C4×C43—22no—
94C23×C4×C43—42no—
95C23×C4×C43—42no—
96C23×C4×C43C2×C414yes—
97C23×C4×C43C2312yes—
98C23×C4×C43C2311yescharacteristic
99C23×C4×C43C2312yes—
100C23×C4×C43C2311yescharacteristic
101C2×C22⋊C4×C43—24no—
102C2×C22⋊C4×C43—24no—
103C2×C22⋊C4×C43—42no—
104#95×C43—22no—
105#95×C43—22no—
106#95×C43—42no—
107C24×C43—21no—
108C24×C43—21no—
109C24×C43—22no—
110C24×C43—22no—
111C24×C43—21no—
112C24×C43—21no—
113C24×C43—22no—
114C24×C43—22no—
115C24×C43C22×C412yes—
116C24×C43#4112yes—
117C24×C43#4112yes—
118C24×C43C2411yescharacteristic
119C23×D43—22no—
120C23×D43—22no—
121C23×D43—21no—
122C23×D43—21no—
123C23×D43—21no—
124C23×D43—21no—
125C23×D43—22no—
126C23×D43—22no—
127C23×D43C22×C412yes—
128C23×D43C2×D412yes—
129C23×D43C2×D412yes—
130C22×C4×C43—28no—
131C22×C4×C43—22no—
132C22×C4×C43—21no—
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—22no—
148C22×C4×C43—22no—
149C22×C4×C43—22no—
150C22×C4×C43—44no—
151C22×C4×C43—44no—
152C22×C4×C43—48no—
153C22×C4×C43—48no—
154C22×C4×C43C22×C412yes—
155C22×C4×C43C22×C412yes—
156C22×C4×C43C2×D412yes—
157C22×C4×C43C2×D412yes—
158C22×C4×C43#4114yes—
159C2×C22⋊D43—28no—
160C2×C22⋊D43—28no—
161C2×C22⋊D43—28no—
162C2×C22⋊D43—28no—
163C2×C22⋊D43—28no—
164C2×C22⋊D43—28no—
165C2×C22⋊D43—28no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—22no—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43—22no—
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43—22no—
175C22×Dic43—22no—
176C22×Dic43—22no—
177C22×Dic43—22no—
178C22×Dic43—22no—
179C22×Dic43—22no—
180C22×Dic43—22no—
181C22×Dic43—22no—
182C22×Dic43—22no—
183C22×Dic43—22no—
184C22×Dic43—22no—
185C22×Dic43—22no—
186C22×Dic43—22no—
187C22×Dic43—22no—
188C22×Dic43—22no—
189C22×Dic43C22×C412yes—
190C22×Dic43C22×C412yes—
191C22×Dic43C22×C412yes—
192C22×Dic43C2×D412yes—
193C22×Dic43C2×D412yes—
194C22×Dic43#4114yes—
195C22×Dic43#4112yes—
196C22×Dic43#4112yes—
197C2×C4×D43—44no—
198C2×C4×D43—44no—
199C2×C4×D43—48no—
200C2×C4×D43—48no—
201C2×C4×D43C22⋊C4116yescomplemented
202C22⋊C4×C43—48no—
203C22⋊Dic43—28no—
204C22⋊Dic43—48no—
205(C2×D43)⋊C4—216no—
206(C2×D43)⋊C4—28no—
207(C2×D43)⋊C4—48no—
208Dic43⋊C4—28no—
209C4×Dic43—28no—
210C4×Dic43—48no—
211C23×C43—22no—
212C23×C43—22no—
213C23×C43—22no—
214C23×C43—22no—
215C23×C43—22no—
216C23×C43—22no—
217C23×C43—22no—
218C23×C43—22no—
219C23×C43—22no—
220C23×C43—22no—
221C23×C43—24no—
222C23×C43—24no—
223C23×C43—24no—
224C23×C43—24no—
225C23×C43—42no—
226C23×C43—42no—
227C23×C43—42no—
228C23×C43—42no—
229C23×C43—42no—
230C23×C43—42no—
231C23×C43—42no—
232C23×C43—42no—
233C23×C43#11714yes—
234C23×C43C23×C411yescharacteristic
235C23×C43C22×D411yescharacteristic
236C23×C43C22×D411yescharacteristic
237C23×C43C2×#4111yescharacteristic
238C23×C43C2×#4111yescharacteristic
239C23×C43C2×#4112yes—
240C23×C43C2×#4111yescharacteristic
241C23×C43C2×#4112yes—
242C23×C43C2×#4111yescharacteristic
243C23×C43H(5,𝔽2)12yes—
244C23×C43H(5,𝔽2)12yes—
245C22×D43—22no—
246C22×D43—22no—
247C22×D43—22no—
248C22×D43—22no—
249C22×D43—22no—
250C22×D43—22no—
251C22×D43—24no—
252C22×D43—22no—
253C22×D43—22no—
254C22×D43—22no—
255C22×D43—22no—
256C22×D43—24no—
257C22×D43—24no—
258C22×D43—24no—
259C22×D43—42no—
260C22×D43—42no—
261C22×D43—42no—
262C22×D43—42no—
263C22×D43—42no—
264C22×D43—42no—
265C22×D43—42no—
266C22×D43—42no—
267C22×D43C2×C22⋊C414yes—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—24no—
271C2×C4×C43—24no—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—24no—
276C2×C4×C43—24no—
277C2×C4×C43—24no—
278C2×C4×C43—416no—
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—42no—
291C2×C4×C43—42no—
292C2×C4×C43C2×C22⋊C414yes—
293C22⋊D43—232no—
294C2×Dic43—22no—
295C2×Dic43—22no—
296C2×Dic43—22no—
297C2×Dic43—22no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—24no—
303C2×Dic43—24no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—24no—
308C2×Dic43—24no—
309C2×Dic43—24no—
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×Dic43—42no—
323C2×Dic43C2×C22⋊C414yes—
324C2×Dic43#11714yes—
325C4×D43—416no—
326#13940—431nomaximal, Sylow
327C22×C43—24no—
328C22×C43—24no—
329C22×C43—24no—
330C22×C43—42no—
331C22×C43—44no—
332C22×C43—44no—
333C22×C43—44no—
334C22×C43—44no—
335C22×C43—42no—
336C22×C43—42no—
337C22×C43—42no—
338C22×C43C22×C22⋊C411yescharacteristic
339C22×C43C2×#11711yescharacteristic
340C22×C43C2×#11711yescharacteristic
341C22×C43C4×#4111yescharacteristic
342C22×C43C4×#4111yescharacteristic
343C22×C43#51811yescharacteristic
344C22×C43#51811yescharacteristic
345C22×C43#52512yes—
346C22×C43#52511yescharacteristic
347C22×C43#52511yescharacteristic
348C22×C43#52511yescharacteristic
349C22×C43#52511yescharacteristic
350C22×C43#53212yes—
351C22×C43#53412yes—
352C22×C43#53412yes—
353C22×C43#55112yes—
354C22×C43#55112yes—
355C22×C43#55312yes—
356C22×C43#55312yes—
357C22×C43#55312yes—
358C22×C43#55312yes—
359C22×C43#55912yes—
360C22×C43#55912yes—
361C2×D43—24no—
362C2×D43—24no—
363C2×D43—24no—
364C2×D43—44no—
365C2×D43—44no—
366C2×D43—44no—
367C2×D43—44no—
368C2×D43—42no—
369C2×D43—42no—
370C2×D43—42no—
371C2×D43—42no—
372C4×C43—24no—
373C4×C43—42no—
374C4×C43—44no—
375C4×C43—82no—
376Dic43—24no—
377Dic43—24no—
378Dic43—44no—
379Dic43—42no—
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#1434—431no—
390C22⋊#95—431no—
391C22⋊#95D4311yescharacteristic, complemented
392C2×C43—44no—
393C2×C43#228011yescharacteristic
394C2×C43#229711yescharacteristic
395C2×C43#230811yescharacteristic
396C2×C43#235311yescharacteristic
397C2×C43#235311yescharacteristic
398C2×C43#235711yescharacteristic
399C2×C43#235711yescharacteristic
400C2×C43#260012yes—
401C2×C43#260012yes—
402C2×C43#260212yes—
403C2×C43#260212yes—
404D43—44no—
405C23×D4—431no—
406C24×C4—431no—
407C24×C4C2×D4311yescharacteristic
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⋊C4C2×D4312yes—
418C22×C42—431no—
419C22×C42—432no—
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×#95—432no—
430C2×#95C2×D4311yescharacteristic
431C2×#95C2×D4311yescharacteristic
432C2×#95C2×D4312yes—
433C43#1394011yescharacteristic, complemented, Sylow
434C25—431no—
435C25C22×D4311yescharacteristic
436C22×D4—434no—
437C22×D4—862no—
438C22×D4—862no—
439C22×D4—862no—
440C22×D4—862no—
441C22×D4—862no—
442C22×D4—862no—
443C23×C4—22no—
444C23×C4—22no—
445C23×C4—42no—
446C23×C4—42no—
447C23×C4—431no—
448C23×C4—431no—
449C23×C4—434no—
450C23×C4—434no—
451C23×C4—434no—
452C23×C4—431no—
453C23×C4—432no—
454C23×C4—432no—
455C23×C4—1722no—
456C23×C4—1722no—
457C23×C4C4×D4314yes—
458C23×C4C22×D4312yes—
459C23×C4C22×D4311yescharacteristic
460C23×C4C22×D4312yes—
461C23×C4C22×D4311yescharacteristic
462C4×D4—8632no—
463C2×C4⋊C4—434no—
464C2×C4⋊C4—862no—
465C2×C4⋊C4—862no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—42no—
469C2×C22⋊C4—434no—
470C2×C22⋊C4—434no—
471C2×C22⋊C4—864no—
472C2×C22⋊C4—862no—
473C2×C22⋊C4—862no—
474C2×C22⋊C4—864no—
475C2×C22⋊C4—862no—
476C2×C22⋊C4—862no—
477C2×C22⋊C4—864no—
478C2×C22⋊C4—864no—
479C2×C22⋊C4—864no—
480C2×C22⋊C4—864no—
481C2×C22⋊C4—1722no—
482C2×C22⋊C4—1722no—
483C2×C22⋊C4—1722no—
484C2×C42—434no—
485C2×C42—862no—
486C2×C42—862no—
487C2×C42—864no—
488C2×C42—1722no—
489C2×C42—1722no—
490#95—22no—
491#95—22no—
492#95—42no—
493#95—864no—
494#95—864no—
495#95—864no—
496#95—864no—
497#95—864no—
498#95—862no—
499#95—862no—
500#95—1722no—
501C24—21no—
502C24—21no—
503C24—22no—
504C24—21no—
505C24—21no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—432no—
510C24—432no—
511C24—432no—
512C24—862no—
513C24—861no—
514C24—861no—
515C24—861no—
516C24—862no—
517C24—861no—
518C24—862no—
519C24—862no—
520C24C2×C4×D4312yes—
521C24#1062190012yes—
522C24#1062190212yes—
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—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—28no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—48no—
554C22×C4—48no—
555C22×C4—432no—
556C22×C4—432no—
557C22×C4—432no—
558C22×C4—432no—
559C22×C4—432no—
560C22×C4—432no—
561C22×C4—4316no—
562C22×C4—432no—
563C22×C4—434no—
564C22×C4—861no—
565C22×C4—861no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—862no—
569C22×C4—862no—
570C22×C4—862no—
571C22×C4—861no—
572C22×C4—861no—
573C22×C4—862no—
574C22×C4—862no—
575C22×C4—862no—
576C22×C4—862no—
577C22×C4—862no—
578C22×C4—862no—
579C22×C4—862no—
580C22×C4—862no—
581C22×C4—862no—
582C22×C4—862no—
583C22×C4—862no—
584C22×C4—862no—
585C22×C4—862no—
586C22×C4—862no—
587C22×C4—1724no—
588C22×C4—1724no—
589C22×C4—1728no—
590C22×C4—1728no—
591C22×C4C2×C4×D4312yes—
592C22×C4C2×C4×D4312yes—
593C22×C4#1062189814yes—
594C22×C4D4×D4312yes—
595C22×C4D4×D4312yes—
596C4⋊C4—868no—
597C22⋊C4—48no—
598C22⋊C4—868no—
599C22⋊C4—8616no—
600C22⋊C4—868no—
601C22⋊C4—1728no—
602C22⋊C4—1728no—
603C42—868no—
604C42—1728no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—434no—
628C23—862no—
629C23—862no—
630C23—862no—
631C23—862no—
632C23—862no—
633C23—862no—
634C23—864no—
635C23—862no—
636C23—862no—
637C23—862no—
638C23—862no—
639C23—864no—
640C23—864no—
641C23—864no—
642C23—1722no—
643C23—1722no—
644C23—1722no—
645C23—1722no—
646C23—1722no—
647C23—1722no—
648C23—1722no—
649C23—1722no—
650C23#1306328314yes—
651C23C22×C4×D4311yescharacteristic
652C23C2×D4×D4311yescharacteristic
653C23C2×D4×D4311yescharacteristic
654C23#41×D4312yes—
655C23#41×D4311yescharacteristic
656C23#41×D4311yescharacteristic
657C23C2×#1062190011yescharacteristic
658C23C2×#1062189812yes—
659C23C2×#1062190211yescharacteristic
660C23#1306337012yes—
661C23#1306337012yes—
662D4—8632no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—416no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
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—434no—
688C2×C4—434no—
689C2×C4—862no—
690C2×C4—862no—
691C2×C4—862no—
692C2×C4—862no—
693C2×C4—862no—
694C2×C4—862no—
695C2×C4—862no—
696C2×C4—862no—
697C2×C4—864no—
698C2×C4—864no—
699C2×C4—864no—
700C2×C4—864no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—862no—
704C2×C4—864no—
705C2×C4—17216no—
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×C4—1722no—
719C2×C4C22⋊C4×D4314yes—
720C22—24no—
721C22—24no—
722C22—24no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—44no—
727C22—44no—
728C22—44no—
729C22—44no—
730C22—42no—
731C22—864no—
732C22—864no—
733C22—864no—
734C22—1722no—
735C22—1722no—
736C22—1722no—
737C22—1724no—
738C22—1724no—
739C22—1724no—
740C22—1724no—
741C22—1722no—
742C22C2×C22⋊C4×D4311yescharacteristic
743C22#117×D4311yescharacteristic
744C22C2×#1306328311yescharacteristic
745C22#1458336711yescharacteristic
746C22C4×#1062189811yescharacteristic
747C22#1458337211yescharacteristic
748C22#1458337211yescharacteristic
749C22#1458340812yes—
750C22#1458340911yescharacteristic
751C22#1458340911yescharacteristic
752C22#1458341211yescharacteristic
753C22#1458341211yescharacteristic
754C22#1458344612yes—
755C22#1458345912yes—
756C22#1458345912yes—
757C22#1458357512yes—
758C22#1458357612yes—
759C22#1458359212yes—
760C22#1458359412yes—
761C22#1458359712yes—
762C22#1458359812yes—
763C22#1458363212yes—
764C22#1458363312yes—
765C4—24no—
766C4—44no—
767C4—42no—
768C4—82no—
769C4—864no—
770C4—864no—
771C4—3442no—
772C4—1722no—
773C4—1724no—
774C2—44no—
775C2—1724no—
776C2#1913697711yescharacteristic
777C2#1913708111yescharacteristic
778C2#1913717111yescharacteristic
779C2#1913753111yescharacteristic
780C2#1913753711yescharacteristic
781C2#1913756311yescharacteristic
782C2#1913756911yescharacteristic
783C2#1914017912yes—
784C2#1914018112yes—
785C2#1914020312yes—
786C2#1914021112yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×C22⋊#95C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenterC22⋊#95D43
hypocenterC43#13940
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#14582761C2semidirect
3. C2×#14582746C2semidirect
4. #19132843C2semidirect
6. #19132832C2semidirect
7. #19132826C2semidirect
8. #19132819C2semidirect
9. #19132819C2semidirect
10. #19132818C2semidirect
11. C43×C22⋊#95C2semidirect
16. C2×C4×C22⋊D43C4semidirect
201. C2×C4×D43C22⋊C4semidirect
391. C22⋊#95D43semidirect
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×C22⋊D432
C2×#145827612
C2×#145827462
#191328432
#191328342
#191328322
#191328262
#191328192
#191328182
C43×C22⋊#952
#1394043