Finite Group Databasebeta

← #25022979

Subgroups — #25022979

Order 11008.

2098 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582778C211yesmaximal, characteristic
2C2×#14582778C211yesmaximal, characteristic
3C2×#14582778C211yesmaximal, characteristic
4C2×#14582772C211yesmaximal, characteristic, complemented
5#19132855C212yesmaximal, complemented
6#19132850C212yesmaximal, complemented
7#19132843C212yesmaximal, complemented
8#19132839C212yesmaximal, complemented
9#19132818C211yesmaximal, characteristic, complemented
10#19132818C211yesmaximal, characteristic, complemented
11C22×#95×C43C211yesmaximal, characteristic, complemented
12C23×C22⋊D43C2211yescharacteristic
13C22×Dic43⋊C4C2212yes—
14C22×C22⋊Dic43C2211yescharacteristic
15C22×C22⋊Dic43C2211yescharacteristic
16C22×C22⋊Dic43C2211yescharacteristic
17C22×(C2×D43)⋊C4C2211yescharacteristic
18C22×(C2×D43)⋊C4C2212yes—
19C22×(C2×D43)⋊C4C2211yescharacteristic
20C22×(C2×D43)⋊C4C2212yes—
21#14582778—24no—
22#14582778—24no—
23#14582778C418yescomplemented
24#14582772—24no—
25C2×C43⋊#95C2212yes—
26C2×C43⋊#95C2211yescharacteristic
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2211yescharacteristic
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2212yes—
34C24×C4×C43C2211yescharacteristic
35C24×C4×C43C2211yescharacteristic
36C24×C4×C43C2211yescharacteristic
37C2×#95×C43—24no—
38C2×#95×C43C2212yes—
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×Dic43C2311yescharacteristic
49C23×Dic43C2311yescharacteristic
50C23×Dic43C2312yes—
51C23×Dic43C2312yes—
52C23×Dic43C2311yescharacteristic
53C2×Dic43⋊C4—24no—
54C2×Dic43⋊C4—42no—
55C2×Dic43⋊C4—42no—
56C2×C22⋊Dic43—22no—
57C2×C22⋊Dic43—22no—
58C2×C22⋊Dic43—22no—
59C2×C22⋊Dic43—22no—
60C2×C22⋊Dic43—22no—
61C2×C22⋊Dic43—22no—
62C2×C22⋊Dic43—22no—
63C2×C22⋊Dic43—22no—
64C2×C22⋊Dic43C2×C414yes—
65C2×(C2×D43)⋊C4—24no—
66C2×(C2×D43)⋊C4—22no—
67C2×(C2×D43)⋊C4—22no—
68C2×(C2×D43)⋊C4—42no—
69C2×(C2×D43)⋊C4—42no—
70C2×(C2×D43)⋊C4—42no—
71C2×(C2×D43)⋊C4—42no—
72C2×(C2×D43)⋊C4—42no—
73C2×(C2×D43)⋊C4—42no—
74C2×(C2×D43)⋊C4C2×C418yescomplemented
75C43⋊#95—24no—
76C43⋊#95—24no—
77C43⋊#95—22no—
78C43⋊#95—22no—
79C43⋊#95—42no—
80C43⋊#95—42no—
81C43⋊#95—42no—
82C43⋊#95—42no—
83C43⋊#95C2×C418yescomplemented
84C25×C43C2311yescharacteristic
85C23×C4×C43—22no—
86C23×C4×C43—22no—
87C23×C4×C43—22no—
88C23×C4×C43—22no—
89C23×C4×C43—22no—
90C23×C4×C43—22no—
91C23×C4×C43—42no—
92C23×C4×C43—42no—
93C23×C4×C43—42no—
94C23×C4×C43—42no—
95C23×C4×C43—42no—
96C23×C4×C43—42no—
97C23×C4×C43C2×C414yes—
98C23×C4×C43D414yes—
99C23×C4×C43D414yes—
100C23×C4×C43C2312yes—
101C23×C4×C43C2312yes—
102C23×C4×C43C2311yescharacteristic
103C23×C4×C43C2311yescharacteristic
104#95×C43—24no—
105#95×C43—24no—
106C24×C43—22no—
107C24×C43—22no—
108C24×C43—22no—
109C24×C43—22no—
110C24×C43C22×C412yes—
111C24×C43C2×D412yes—
112C24×C43C2×D412yes—
113C24×C43#4112yes—
114C24×C43#4112yes—
115C24×C43#4112yes—
116C24×C43#4112yes—
117C24×C43C2411yescharacteristic
118C23×D43—21no—
119C23×D43—21no—
120C23×D43—21no—
121C23×D43—21no—
122C23×D43—21no—
123C23×D43—21no—
124C23×D43—22no—
125C23×D43—22no—
126C23×D43—22no—
127C23×D43—22no—
128C23×D43C22×C412yes—
129C22×C4×C43—28no—
130C22×C4×C43—28no—
131C22×C4×C43—28no—
132C22×C4×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43—22no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
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—48no—
153C22×C4×C43—44no—
154C22×C4×C43—44no—
155C22×C4×C43—48no—
156C22×C4×C43—44no—
157C22×C4×C43—44no—
158C22×C4×C43—44no—
159C22×C4×C43—44no—
160C22×C4×C43—48no—
161C22×C4×C43—48no—
162C22×C4×C43—48no—
163C22×C4×C43—48no—
164C22×C4×C43C22×C414yes—
165C22×C4×C43C2×D414yes—
166C22×C4×C43C2×D412yes—
167C22×C4×C43C2×D412yes—
168C2×C22⋊D43—28no—
169C2×C22⋊D43—28no—
170C2×C22⋊D43—28no—
171C2×C22⋊D43—44no—
172C2×C22⋊D43—44no—
173C2×C22⋊D43—44no—
174C2×C22⋊D43—44no—
175C22×Dic43—21no—
176C22×Dic43—21no—
177C22×Dic43—22no—
178C22×Dic43—21no—
179C22×Dic43—21no—
180C22×Dic43—21no—
181C22×Dic43—22no—
182C22×Dic43—21no—
183C22×Dic43—22no—
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43—21no—
187C22×Dic43—21no—
188C22×Dic43—21no—
189C22×Dic43—21no—
190C22×Dic43—22no—
191C22×Dic43—22no—
192C22×Dic43—22no—
193C22×Dic43—22no—
194C22×Dic43—22no—
195C22×Dic43—22no—
196C22×Dic43—22no—
197C22×Dic43—22no—
198C22×Dic43—22no—
199C22×Dic43—22no—
200C22×Dic43—22no—
201C22×Dic43—22no—
202C22×Dic43—22no—
203C22×Dic43—22no—
204C22×Dic43C22×C412yes—
205C22×Dic43C22×C414yes—
206C22⋊Dic43—28no—
207C22⋊Dic43—44no—
208C22⋊Dic43—44no—
209(C2×D43)⋊C4—48no—
210(C2×D43)⋊C4—44no—
211(C2×D43)⋊C4—44no—
212(C2×D43)⋊C4—48no—
213Dic43⋊C4—48no—
214C23×C43—24no—
215C23×C43—24no—
216C23×C43—22no—
217C23×C43—22no—
218C23×C43—24no—
219C23×C43—22no—
220C23×C43—22no—
221C23×C43—24no—
222C23×C43—24no—
223C23×C43—24no—
224C23×C43—24no—
225C23×C43—24no—
226C23×C43—24no—
227C23×C43—24no—
228C23×C43—24no—
229C23×C43—24no—
230C23×C43#11714yes—
231C23×C43C4×D414yes—
232C23×C43C4×D414yes—
233C23×C43#12114yes—
234C23×C43#12314yes—
235C23×C43#12414yes—
236C23×C43#12614yes—
237C23×C43C23×C411yescharacteristic
238C23×C43C22×D411yescharacteristic
239C23×C43C22×D411yescharacteristic
240C23×C43C2×#4111yescharacteristic
241C23×C43C2×#4111yescharacteristic
242C23×C43C2×#4111yescharacteristic
243C23×C43C2×#4111yescharacteristic
244C23×C43H(5,𝔽2)12yes—
245C23×C43H(5,𝔽2)12yes—
246C23×C43H(5,𝔽2)12yes—
247C23×C432−1+412yes—
248C22×D43—22no—
249C22×D43—22no—
250C22×D43—22no—
251C22×D43—24no—
252C22×D43—24no—
253C22×D43—41no—
254C22×D43—41no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43—41no—
259C22×D43—42no—
260C22×D43—41no—
261C22×D43—41no—
262C22×D43—42no—
263C22×D43—42no—
264C22×D43—42no—
265C22×D43—42no—
266C22×D43—42no—
267C22×D43—42no—
268C22×D43—42no—
269C22×D43—42no—
270C22×D43—42no—
271C2×C4×C43—24no—
272C2×C4×C43—24no—
273C2×C4×C43—24no—
274C2×C4×C43—24no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—24no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—24no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—416no—
284C2×C4×C43—416no—
285C2×C4×C43—416no—
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×C43—42no—
298C22⋊D43—416no—
299C2×Dic43—22no—
300C2×Dic43—24no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—24no—
304C2×Dic43—24no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—42no—
310C2×Dic43—42no—
311C2×Dic43—42no—
312C2×Dic43—42no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—42no—
316C2×Dic43—42no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—42no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—42no—
323C2×Dic43—42no—
324C2×Dic43—42no—
325C2×Dic43—42no—
326C2×Dic43—42no—
327C2×Dic43—42no—
328C2×Dic43—42no—
329C2×Dic43—42no—
330#14259—431nomaximal, Sylow
331C22×C43—28no—
332C22×C43—24no—
333C22×C43—24no—
334C22×C43—28no—
335C22×C43—24no—
336C22×C43—24no—
337C22×C43—24no—
338C22×C43—24no—
339C22×C43—28no—
340C22×C43—28no—
341C22×C43#38818yes—
342C22×C43C2×#11711yescharacteristic
343C22×C43C2×C4×D411yescharacteristic
344C22×C43C2×C4×D411yescharacteristic
345C22×C43#51812yes—
346C22×C43#52012yes—
347C22×C43C2×#12111yescharacteristic
348C22×C43C2×#12311yescharacteristic
349C22×C43C2×#12411yescharacteristic
350C22×C43C2×#12611yescharacteristic
351C22×C43#53411yescharacteristic
352C22×C43#53411yescharacteristic
353C22×C43#53412yes—
354C22×C43#53511yescharacteristic
355C22×C43#53611yescharacteristic
356C22×C43#53712yes—
357C22×C43#53812yes—
358C22×C43#53812yes—
359C22×C43#53812yes—
360C22×C43#53812yes—
361C22×C43#53912yes—
362C22×C43#53912yes—
363C22×C43#53912yes—
364C22×C43#53912yes—
365C2×D43—44no—
366C2×D43—42no—
367C2×D43—42no—
368C2×D43—44no—
369C2×D43—42no—
370C2×D43—81no—
371C2×D43—81no—
372C2×D43—81no—
373C2×D43—81no—
374C2×D43—82no—
375C2×D43—82no—
376C4×C43—44no—
377C4×C43—44no—
378C4×C43—42no—
379C4×C43—42no—
380Dic43—44no—
381Dic43—42no—
382Dic43—81no—
383Dic43—81no—
384Dic43—82no—
385C2×#386—431no—
386C2×#386—431no—
387C2×#386—431no—
388C2×#385—431no—
389C22×#95D4311yescharacteristic, complemented
390#1443—432no—
391#1442—432no—
392#1440—432no—
393#1439—432no—
394C22⋊#95—431no—
395C22⋊#95—431no—
396C2×C43—28no—
397C2×C43C2×#38811yescharacteristic
398C2×C43#231812yes—
399C2×C43#232111yescharacteristic
400C2×C43#232211yescharacteristic
401C2×C43#232512yes—
402C2×C43#261711yescharacteristic
403C2×C43#261811yescharacteristic
404C2×C43#262211yescharacteristic
405C2×C43#262311yescharacteristic
406C2×C43#263912yes—
407C2×C43#264312yes—
408D43—82no—
409C23×D4—431no—
410C24×C4C2×D4311yescharacteristic
411C24×C4C2×D4311yescharacteristic
412C24×C4C2×D4311yescharacteristic
413C22×C4⋊C4—432no—
414C22×C22⋊C4—431no—
415C22×C22⋊C4—432no—
416C22×C22⋊C4—431no—
417C22×C22⋊C4—431no—
418C22×C22⋊C4—431no—
419C22×C22⋊C4—432no—
420C22×C22⋊C4—431no—
421#386—438no—
422#386—864no—
423#386—864no—
424#385—864no—
425C2×#95—24no—
426C2×#95—432no—
427C2×#95—432no—
428C2×#95—431no—
429C2×#95—432no—
430C2×#95—431no—
431C2×#95—432no—
432C2×#95—432no—
433C2×#95—432no—
434C2×#95—432no—
435C2×#95C2×D4312yes—
436C2×#95C2×D4312yes—
437C43#1425911yescharacteristic, complemented, Sylow
438C25—431no—
439C25C22×D4311yescharacteristic
440C22×D4—434no—
441C22×D4—862no—
442C22×D4—862no—
443C22×D4—862no—
444C22×D4—862no—
445C22×D4—862no—
446C22×D4—862no—
447C23×C4—22no—
448C23×C4—22no—
449C23×C4—22no—
450C23×C4—22no—
451C23×C4—22no—
452C23×C4—22no—
453C23×C4—42no—
454C23×C4—42no—
455C23×C4—42no—
456C23×C4—42no—
457C23×C4—42no—
458C23×C4—42no—
459C23×C4—432no—
460C23×C4—431no—
461C23×C4—431no—
462C23×C4—431no—
463C23×C4—432no—
464C23×C4C4×D4314yes—
465C23×C4D17214yes—
466C23×C4C22⋊D4314yes—
467C23×C4C22×D4312yes—
468C23×C4C22×D4312yes—
469C23×C4C22×D4311yescharacteristic
470C23×C4C22×D4311yescharacteristic
471C2×C4⋊C4—864no—
472C2×C4⋊C4—1722no—
473C2×C4⋊C4—1722no—
474C2×C22⋊C4—434no—
475C2×C22⋊C4—438no—
476C2×C22⋊C4—862no—
477C2×C22⋊C4—862no—
478C2×C22⋊C4—862no—
479C2×C22⋊C4—862no—
480C2×C22⋊C4—862no—
481C2×C22⋊C4—862no—
482C2×C22⋊C4—862no—
483C2×C22⋊C4—862no—
484C2×C22⋊C4—864no—
485C2×C22⋊C4—862no—
486C2×C22⋊C4—862no—
487C2×C22⋊C4—1722no—
488C2×C22⋊C4—1722no—
489C2×C22⋊C4—1722no—
490C2×C22⋊C4—1722no—
491C2×C22⋊C4—1722no—
492C2×C22⋊C4—1722no—
493#95—24no—
494#95—24no—
495#95—438no—
496#95—864no—
497#95—864no—
498#95—862no—
499#95—862no—
500#95—1722no—
501#95—1722no—
502#95—1722no—
503#95—1722no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—432no—
509C24—861no—
510C24—861no—
511C24—861no—
512C24—861no—
513C24—861no—
514C24—861no—
515C24—862no—
516C24—862no—
517C24—862no—
518C24—862no—
519C24C2×C4×D4312yes—
520C24C2×D17212yes—
521C24#1062189812yes—
522C24#1062189812yes—
523C24#1062189812yes—
524C24#1062189812yes—
525C24C2×C22⋊D4312yes—
526C24C23×D4311yescharacteristic
527C2×D4—868no—
528C2×D4—868no—
529C2×D4—868no—
530C2×D4—1724no—
531C2×D4—1724no—
532C2×D4—1724no—
533C2×D4—1724no—
534C22×C4—28no—
535C22×C4—28no—
536C22×C4—28no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
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—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—48no—
558C22×C4—48no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—432no—
570C22×C4—434no—
571C22×C4—861no—
572C22×C4—861no—
573C22×C4—862no—
574C22×C4—862no—
575C22×C4—861no—
576C22×C4—861no—
577C22×C4—861no—
578C22×C4—861no—
579C22×C4—862no—
580C22×C4—862no—
581C22×C4—862no—
582C22×C4—862no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—862no—
587C22×C4—861no—
588C22×C4—861no—
589C22×C4—861no—
590C22×C4—862no—
591C22×C4—862no—
592C22×C4—862no—
593C22×C4—862no—
594C22×C4—862no—
595C22×C4—862no—
596C22×C4—862no—
597C22×C4—862no—
598C22×C4—862no—
599C22×C4—862no—
600C22×C4C2×C4×D4314yes—
601C22×C4C2×D17214yes—
602C22×C4C2×C22⋊D4312yes—
603C22×C4C2×C22⋊D4312yes—
604C4⋊C4—1728no—
605C22⋊C4—868no—
606C22⋊C4—1728no—
607C22⋊C4—1724no—
608C22⋊C4—1724no—
609C22⋊C4—1728no—
610C22⋊C4—1724no—
611C22⋊C4—1724no—
612C23—24no—
613C23—24no—
614C23—22no—
615C23—22no—
616C23—24no—
617C23—22no—
618C23—22no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—862no—
629C23—862no—
630C23—862no—
631C23—864no—
632C23—864no—
633C23—1721no—
634C23—1721no—
635C23—1721no—
636C23—1721no—
637C23—1721no—
638C23—1721no—
639C23—1722no—
640C23—1721no—
641C23—1721no—
642C23—1722no—
643C23—1722no—
644C23—1722no—
645C23—1722no—
646C23—1722no—
647C23—1722no—
648C23—1722no—
649C23—1722no—
650C23—1722no—
651C23#1306328214yes—
652C23C4×C22⋊D4314yes—
653C23C4×D17214yes—
654C23#1306329914yes—
655C23#1306330814yes—
656C23#1306331314yes—
657C23#1306331914yes—
658C23C22×C4×D4311yescharacteristic
659C23C22×C22⋊D4311yescharacteristic
660C23C22×D17211yescharacteristic
661C23C2×#1062189811yescharacteristic
662C23C2×#1062189811yescharacteristic
663C23C2×#1062189811yescharacteristic
664C23C2×#1062189811yescharacteristic
665C23#1306337012yes—
666C23#1306337012yes—
667C23#1306337012yes—
668C23#1306337312yes—
669D4—17216no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—416no—
683C2×C4—416no—
684C2×C4—416no—
685C2×C4—42no—
686C2×C4—42no—
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—862no—
698C2×C4—862no—
699C2×C4—864no—
700C2×C4—862no—
701C2×C4—864no—
702C2×C4—864no—
703C2×C4—1721no—
704C2×C4—1721no—
705C2×C4—1722no—
706C2×C4—1721no—
707C2×C4—1721no—
708C2×C4—1722no—
709C2×C4—1722no—
710C2×C4—1721no—
711C2×C4—1721no—
712C2×C4—1722no—
713C2×C4—1722no—
714C2×C4—1722no—
715C2×C4—1722no—
716C2×C4—1722no—
717C2×C4—1722no—
718C2×C4—1722no—
719C2×C4—1722no—
720C2×C4—1721no—
721C2×C4—1721no—
722C2×C4—1721no—
723C2×C4—1721no—
724C2×C4—1722no—
725C2×C4—1722no—
726C2×C4—1722no—
727C2×C4—1722no—
728C22—24no—
729C22—28no—
730C22—24no—
731C22—28no—
732C22—28no—
733C22—28no—
734C22—24no—
735C22—24no—
736C22—24no—
737C22—24no—
738C22—3441no—
739C22—3441no—
740C22—3442no—
741C22—3442no—
742C22—3441no—
743C22—3441no—
744C22—1722no—
745C22—1724no—
746C22—1724no—
747C22—1722no—
748C22—1722no—
749C22#1458279018yes—
750C22C2×#1306328211yescharacteristic
751C22C2×C4×C22⋊D4311yescharacteristic
752C22C2×C4×D17211yescharacteristic
753C22#1458337212yes—
754C22#1458338012yes—
755C22C2×#1306329911yescharacteristic
756C22C2×#1306330811yescharacteristic
757C22C2×#1306331311yescharacteristic
758C22C2×#1306331911yescharacteristic
759C22#1458345811yescharacteristic
760C22#1458345811yescharacteristic
761C22#1458346112yes—
762C22#1458346611yescharacteristic
763C22#1458347311yescharacteristic
764C22#1458348012yes—
765C22#1458348712yes—
766C22#1458348712yes—
767C22#1458348712yes—
768C22#1458348712yes—
769C22#1458349612yes—
770C22#1458349612yes—
771C22#1458349612yes—
772C22#1458349612yes—
773C4—42no—
774C4—42no—
775C4—44no—
776C4—44no—
777C4—3442no—
778C4—3441no—
779C4—3441no—
780C4—1722no—
781C4—1724no—
782C2—28no—
783C2—3442no—
784C2C2×#1458279011yescharacteristic
785C2#1913722912yes—
786C2#1913725311yescharacteristic
787C2#1913726411yescharacteristic
788C2#1913729812yes—
789C2#1914032911yescharacteristic
790C2#1914033711yescharacteristic
791C2#1914036811yescharacteristic
792C2#1914037511yescharacteristic
793C2#1914052312yes—
794C2#1914054812yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC22×#95×C43C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenterC22×#95D43
hypocenterC43#14259
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
4. C2×#14582772C2semidirect
5. #19132855C2semidirect
6. #19132850C2semidirect
7. #19132843C2semidirect
8. #19132839C2semidirect
9. #19132818C2semidirect
10. #19132818C2semidirect
11. C22×#95×C43C2semidirect
23. #14582778C4semidirect
74. C2×(C2×D43)⋊C4C2×C4semidirect
83. C43⋊#95C2×C4semidirect
389. C22×#95D43semidirect
437. C43#14259semidirect

Maximal subgroups

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

subgroupindex
C2×#145827782
C2×#145827722
#191328552
#191328502
#191328432
#191328392
#191328182
C22×#95×C432
#1425943