Finite Group Databasebeta

← #25098226

Subgroups — #25098226

Order 11008.

2126 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×#14583458C211yesmaximal, characteristic
2C2×#14583372C211yesmaximal, characteristic, complemented
3C22×#13063239C211yesmaximal, characteristic, complemented
4#19137173C211yesmaximal, characteristic, complemented
5#19135005C214yesmaximal, complemented
6#19135000C214yesmaximal, complemented
7C2×#14582666C211yesmaximal, characteristic, complemented
8C2×#14582665C211yesmaximal, characteristic, complemented
9C43×#2308C211yesmaximal, characteristic, complemented
10C23×C22⋊D43C2211yescharacteristic
11#14583458—24no—
12#14583458C418yescomplemented
13C2×#13063308C2212yes—
14C2×#13063306—21no—
15C2×#13063297—22no—
16C2×#13063294C2212yes—
17C2×#13063293—21no—
18#14583372—22no—
19#14583372—22no—
20#14583372—22no—
21#14583372C2214yes—
22C2×C4×C22⋊D43—22no—
23C2×(C22⋊D43)⋊C4—22no—
24C2×#13063281—21no—
25C22×C22⋊Dic43C2211yescharacteristic
26C22×C22⋊Dic43C2211yescharacteristic
27C22×C22⋊Dic43C2211yescharacteristic
28C2×C22⋊C4×D43—21no—
29C2×#13063239—24no—
30C2×#13063239C2214yes—
31#14582779—22no—
32#14582779—22no—
33#14582762C2212yescomplemented
34#14582755C2212yescomplemented
35#14582666C2214yescomplemented
36#14582665C2214yescomplemented
37C23×D4×C43C2211yescharacteristic
38C22×C22⋊C4×C43C2211yescharacteristic
39C22×C22⋊C4×C43C2211yescharacteristic
40C43×#386—22no—
41C43×#386—22no—
42C43×#381C2212yescomplemented
43C43×#379C2212yescomplemented
44C24×D43D411yescharacteristic
45C22×C22⋊D43—21no—
46C22×C22⋊D43—21no—
47C22×C22⋊D43—21no—
48C22×C22⋊D43—21no—
49C22×C22⋊D43—22no—
50C22×C22⋊D43—22no—
51C22×C22⋊D43—22no—
52C22×C22⋊D43C2×C414yes—
53C22×C22⋊D43D414yes—
54C22×C22⋊D43D412yes—
55C22×C22⋊D43C2312yes—
56C23×Dic43—21no—
57C23×Dic43—21no—
58C23×Dic43D411yescharacteristic
59C23×Dic43D412yescomplemented
60C22×C4×D43—22no—
61#13063308—24no—
62#13063308C2×C418yescomplemented
63#13063306—28no—
64#13063297—216no—
65#13063294—24no—
66#13063294C2×C418yescomplemented
67#13063293—28no—
68C4×C22⋊D43—28no—
69C4×C22⋊D43—28no—
70(C22⋊D43)⋊C4—28no—
71(C22⋊D43)⋊C4—28no—
72#13063281—24no—
73#13063281—24no—
74C2×Dic43⋊C4—22no—
75C2×Dic43⋊C4—22no—
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—22no—
82C2×C22⋊Dic43—22no—
83C2×C22⋊Dic43—22no—
84C2×C22⋊Dic43—22no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—24no—
87C2×C22⋊Dic43C2×C414yescomplemented
88C2×C22⋊Dic43D412yescomplemented
89C2×C22⋊Dic43C2312yes—
90C2×C22⋊Dic43C2312yes—
91C2×C22⋊Dic43C2312yes—
92C2×(C2×D43)⋊C4—22no—
93C2×(C2×D43)⋊C4—22no—
94C22⋊C4×D43—24no—
95C22⋊C4×D43—24no—
96C2×C4×Dic43—22no—
97#13063239—28no—
98C43⋊#95—24no—
99C25×C43C2311yescharacteristic
100C25×C43C2311yescharacteristic
101C22×D4×C43—21no—
102C22×D4×C43—21no—
103C22×D4×C43—21no—
104C22×D4×C43—21no—
105C22×D4×C43—22no—
106C22×D4×C43—21no—
107C22×D4×C43—21no—
108C22×D4×C43—22no—
109C22×D4×C43—22no—
110C22×D4×C43C2×C414yescomplemented
111C23×C4×C43—21no—
112C23×C4×C43D412yescomplemented
113C23×C4×C43C2311yescharacteristic
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43—21no—
118C2×C22⋊C4×C43—22no—
119C2×C22⋊C4×C43—22no—
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—24no—
122C2×C22⋊C4×C43D412yescomplemented
123C2×C22⋊C4×C43C2312yes—
124C2×C22⋊C4×C43C2312yes—
125#95×C43—24no—
126C24×C43—21no—
127C24×C43—21no—
128C24×C43—21no—
129C24×C43—21no—
130C24×C43—21no—
131C24×C43—21no—
132C24×C43—82no—
133C24×C43—82no—
134C24×C43C22×C412yes—
135C24×C43C22×C412yescomplemented
136C24×C43C2×D411yescharacteristic
137C24×C43C2×D411yescharacteristic
138C24×C43C2×D411yescharacteristic
139C24×C43C2×D411yescharacteristic
140C24×C43C2×D411yescharacteristic
141C24×C43C2×D411yescharacteristic
142C24×C43C2×D412yes—
143C24×C43#4112yes—
144C24×C43#4112yes—
145C24×C43C2411yescharacteristic
146C23×D43—21no—
147C23×D43—21no—
148C23×D43—22no—
149C23×D43—82no—
150C23×D43C22⋊C414yescomplemented
151C23×D43C2×D412yes—
152C2×D4×C43—24no—
153C2×D4×C43—24no—
154C2×D4×C43—24no—
155C2×D4×C43—24no—
156C2×D4×C43—24no—
157C2×D4×C43—24no—
158C2×D4×C43—41no—
159C2×D4×C43—41no—
160C2×D4×C43—41no—
161C2×D4×C43—41no—
162C2×D4×C43—42no—
163C2×D4×C43—42no—
164C2×D4×C43—42no—
165C2×D4×C43—42no—
166C2×D4×C43—42no—
167C2×D4×C43—42no—
168C22×C4×C43—22no—
169C22×C4×C43—22no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—22no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—42no—
178C22×C4×C43—82no—
179C22×C4×C43—82no—
180C22×C4×C43C22×C412yescomplemented
181C22×C4×C43C2×D414yes—
182C2×C22⋊D43—24no—
183C2×C22⋊D43—24no—
184C2×C22⋊D43—24no—
185C2×C22⋊D43—24no—
186C2×C22⋊D43—22no—
187C2×C22⋊D43—22no—
188C2×C22⋊D43—24no—
189C2×C22⋊D43—24no—
190C2×C22⋊D43—24no—
191C2×C22⋊D43—24no—
192C2×C22⋊D43—24no—
193C2×C22⋊D43—22no—
194C2×C22⋊D43—22no—
195C2×C22⋊D43—22no—
196C2×C22⋊D43—22no—
197C2×C22⋊D43—28no—
198C2×C22⋊D43—84no—
199C2×C22⋊D43C22⋊C418yescomplemented
200C2×C22⋊D43C22×C414yes—
201C2×C22⋊D43C2×D414yes—
202C22×Dic43—24no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205C22×Dic43—22no—
206C22×Dic43—22no—
207C22×Dic43—22no—
208C22×Dic43—22no—
209C22×Dic43—22no—
210C22×Dic43—42no—
211C22×Dic43—82no—
212C22×Dic43—82no—
213C22×Dic43—82no—
214C22×Dic43C22⋊C414yescomplemented
215C22×Dic43C2×D412yes—
216C22×Dic43C2×D414yes—
217C2×C4×D43—28no—
218C2×C4×D43—84no—
219C22⋊C4×C43—22no—
220C22⋊C4×C43—22no—
221C22⋊C4×C43—22no—
222C22⋊C4×C43—22no—
223C22⋊C4×C43—22no—
224C22⋊C4×C43—22no—
225C22⋊C4×C43—42no—
226C22⋊C4×C43—84no—
227C22⋊Dic43—28no—
228C22⋊Dic43—24no—
229C22⋊Dic43—22no—
230C22⋊Dic43—22no—
231C22⋊Dic43—22no—
232C22⋊Dic43—22no—
233C22⋊Dic43—22no—
234C22⋊Dic43—22no—
235C22⋊Dic43—22no—
236C22⋊Dic43—42no—
237C22⋊Dic43—84no—
238C22⋊Dic43C22×C414yescomplemented
239(C2×D43)⋊C4—28no—
240(C2×D43)⋊C4—28no—
241Dic43⋊C4—28no—
242Dic43⋊C4—28no—
243C4×Dic43—28no—
244C23×C43—22no—
245C23×C43—22no—
246C23×C43—22no—
247C23×C43—42no—
248C23×C43—42no—
249C23×C43—42no—
250C23×C43—42no—
251C23×C43—42no—
252C23×C43—42no—
253C23×C43—42no—
254C23×C43—44no—
255C23×C43—44no—
256C23×C43—44no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—82no—
262C23×C43—82no—
263C23×C43—82no—
264C23×C43—82no—
265C23×C43—82no—
266C23×C43—82no—
267C23×C43—82no—
268C23×C43—82no—
269C23×C43C2×C22⋊C412yes—
270C23×C43C2×C22⋊C412yes—
271C23×C43C4×D412yes—
272C23×C43C4×D412yes—
273C23×C43C4×D412yes—
274C23×C43C4×D412yes—
275C23×C43#12011yescharacteristic
276C23×C43#12011yescharacteristic
277C23×C43#12011yescharacteristic
278C23×C43#12011yescharacteristic
279C23×C43#12112yes—
280C23×C43#12112yes—
281C23×C43#12112yes—
282C23×C43#12112yes—
283C23×C43#12312yes—
284C23×C43#12312yes—
285C23×C43C23×C411yescharacteristic
286C23×C43C22×D411yescharacteristic
287C23×C43C22×D411yescharacteristic
288C23×C43C22×D411yescharacteristic
289C23×C43C22×D411yescharacteristic
290C23×C43C2×#4111yescharacteristic
291C23×C43C2×#4111yescharacteristic
292C22×D43—22no—
293C22×D43—24no—
294C22×D43—22no—
295C22×D43—24no—
296C22×D43—44no—
297C22×D43—44no—
298C22×D43—84no—
299C22×D43—82no—
300C22×D43—84no—
301C22×D43C2×C22⋊C414yes—
302D4×C43—44no—
303D4×C43—44no—
304D4×C43—44no—
305D4×C43—44no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—24no—
310C2×C4×C43—44no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—44no—
316C2×C4×C43—44no—
317C2×C4×C43—42no—
318C2×C4×C43—82no—
319C2×C4×C43—84no—
320C22⋊D43—24no—
321C22⋊D43—24no—
322C22⋊D43—24no—
323C22⋊D43—24no—
324C22⋊D43—28no—
325C22⋊D43—28no—
326C22⋊D43—88no—
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—24no—
330C2×Dic43—24no—
331C2×Dic43—24no—
332C2×Dic43—24no—
333C2×Dic43—44no—
334C2×Dic43—44no—
335C2×Dic43—44no—
336C2×Dic43—44no—
337C2×Dic43—42no—
338C2×Dic43—82no—
339C2×Dic43—84no—
340C2×Dic43—84no—
341C2×Dic43C2×C22⋊C414yes—
342C4×D43—88no—
343#20960—431nomaximal, Sylow
344C22×C43—22no—
345C22×C43—22no—
346C22×C43—22no—
347C22×C43—22no—
348C22×C43—22no—
349C22×C43—22no—
350C22×C43—22no—
351C22×C43—42no—
352C22×C43—42no—
353C22×C43—41no—
354C22×C43—41no—
355C22×C43—41no—
356C22×C43—41no—
357C22×C43—42no—
358C22×C43—42no—
359C22×C43—42no—
360C22×C43—42no—
361C22×C43—42no—
362C22×C43—42no—
363C22×C43—42no—
364C22×C43—42no—
365C22×C43—42no—
366C22×C43—42no—
367C22×C43—44no—
368C22×C43—44no—
369C22×C43—44no—
370C22×C43—42no—
371C22×C43—82no—
372C22×C43—82no—
373C22×C43—82no—
374C22×C43—82no—
375C22×C43#38612yes—
376C22×C43#38612yes—
377C22×C43#38612yes—
378C22×C43#38612yes—
379C22×C43C22×C22⋊C411yescharacteristic
380C22×C43C2×C4×D411yescharacteristic
381C22×C43C2×C4×D411yescharacteristic
382C22×C43C2×#12011yescharacteristic
383C22×C43C2×#12111yescharacteristic
384C22×C43C2×#12111yescharacteristic
385C22×C43C2×#12311yescharacteristic
386C2×D43—24no—
387C2×D43—48no—
388C2×D43—44no—
389C2×D43—44no—
390C2×D43—82no—
391C2×D43—84no—
392C4×C43—44no—
393C4×C43—42no—
394C4×C43—82no—
395Dic43—24no—
396Dic43—44no—
397Dic43—44no—
398Dic43—82no—
399C2×#534—431no—
400C2×#518—431no—
401C22×#99—431no—
402#2308—431no—
403#2308D4311yescharacteristic, complemented
404#1890—434no—
405#1889—434no—
406C2×#342—431no—
407C2×#342—431no—
408C2×C43—21no—
409C2×C43—21no—
410C2×C43—21no—
411C2×C43—22no—
412C2×C43—21no—
413C2×C43—22no—
414C2×C43—21no—
415C2×C43—21no—
416C2×C43—22no—
417C2×C43—22no—
418C2×C43—82no—
419C2×C43C2×#38611yescharacteristic
420C2×C43#302612yes—
421D43—44no—
422C23×D4—431no—
423C23×D4C2×D4311yescharacteristic
424#534—438no—
425#534—864no—
426C2×#123—432no—
427C2×#123—861no—
428C2×#121—862no—
429C2×#120—432no—
430C2×#120—861no—
431#518—434no—
432#518—862no—
433#518—862no—
434#518—862no—
435C2×C4×D4—862no—
436C2×C4×D4—862no—
437C2×#117—861no—
438C22×C22⋊C4—431no—
439C22×C22⋊C4—431no—
440C22×C22⋊C4—431no—
441C22×C22⋊C4—861no—
442C22×C22⋊C4C2×D4311yescharacteristic
443C22×C22⋊C4C2×D4311yescharacteristic
444C2×#99—434no—
445C2×#99—864no—
446#386—22no—
447#386—22no—
448#386—862no—
449#386—862no—
450#381—432no—
451#381C2×D4312yescomplemented
452#379—432no—
453#379C2×D4312yescomplemented
454#342—434no—
455#342—434no—
456C43#2096011yescharacteristic, complemented, Sylow
457C25—431no—
458C25C22×D4311yescharacteristic
459C25C22×D4311yescharacteristic
460C22×D4—22no—
461C22×D4—21no—
462C22×D4—21no—
463C22×D4—22no—
464C22×D4—21no—
465C22×D4—21no—
466C22×D4—22no—
467C22×D4—21no—
468C22×D4—21no—
469C22×D4—434no—
470C22×D4—432no—
471C22×D4—434no—
472C22×D4—432no—
473C22×D4—862no—
474C22×D4—861no—
475C22×D4—861no—
476C22×D4—862no—
477C22×D4—861no—
478C22×D4—861no—
479C22×D4—862no—
480C22×D4C4×D4314yescomplemented
481C23×C4—21no—
482C23×C4—431no—
483C23×C4—432no—
484C23×C4—862no—
485C23×C4—861no—
486C23×C4—861no—
487C23×C4C22⋊D4312yescomplemented
488C23×C4C22×D4311yescharacteristic
489#123—438no—
490#123—864no—
491#123—868no—
492#121—8616no—
493#120—438no—
494#120—868no—
495#120—864no—
496C4×D4—868no—
497C4×D4—868no—
498C4×D4—868no—
499C4×D4—868no—
500#117—864no—
501#117—864no—
502C2×C4⋊C4—862no—
503C2×C4⋊C4—862no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—434no—
513C2×C22⋊C4—432no—
514C2×C22⋊C4—432no—
515C2×C22⋊C4—432no—
516C2×C22⋊C4—432no—
517C2×C22⋊C4—864no—
518C2×C22⋊C4—864no—
519C2×C22⋊C4—862no—
520C2×C22⋊C4—862no—
521C2×C22⋊C4—862no—
522C2×C22⋊C4—861no—
523C2×C22⋊C4—861no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4—862no—
526C2×C22⋊C4—861no—
527C2×C22⋊C4—861no—
528C2×C22⋊C4—862no—
529C2×C22⋊C4—862no—
530C2×C22⋊C4—864no—
531C2×C22⋊C4—861no—
532C2×C22⋊C4C22⋊D4312yescomplemented
533C2×C22⋊C4C22×D4312yes—
534C2×C22⋊C4C22×D4312yes—
535C2×C42—862no—
536#99—868no—
537#95—24no—
538#95—864no—
539C24—21no—
540C24—21no—
541C24—21no—
542C24—21no—
543C24—21no—
544C24—21no—
545C24—82no—
546C24—82no—
547C24—434no—
548C24—432no—
549C24—861no—
550C24—862no—
551C24—861no—
552C24—3442no—
553C24C2×C4×D4312yes—
554C24C2×C4×D4312yescomplemented
555C24#1062189812yes—
556C24D4×D4311yescharacteristic
557C24D4×D4311yescharacteristic
558C24D4×D4311yescharacteristic
559C24D4×D4311yescharacteristic
560C24D4×D4312yes—
561C24#1062190012yes—
562C24C2×C22⋊D4311yescharacteristic
563C24C2×C22⋊D4311yescharacteristic
564C24C23×D4311yescharacteristic
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—24no—
568C2×D4—24no—
569C2×D4—24no—
570C2×D4—24no—
571C2×D4—41no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—438no—
582C2×D4—434no—
583C2×D4—434no—
584C2×D4—864no—
585C2×D4—864no—
586C2×D4—864no—
587C2×D4—864no—
588C2×D4—862no—
589C2×D4—862no—
590C2×D4—864no—
591C2×D4—864no—
592C2×D4—864no—
593C2×D4—864no—
594C2×D4—864no—
595C2×D4—862no—
596C2×D4—862no—
597C2×D4—862no—
598C2×D4—862no—
599C2×D4—868no—
600C2×D4—3444no—
601C22×C4—22no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—42no—
611C22×C4—82no—
612C22×C4—82no—
613C22×C4—434no—
614C22×C4—432no—
615C22×C4—434no—
616C22×C4—868no—
617C22×C4—861no—
618C22×C4—861no—
619C22×C4—862no—
620C22×C4—864no—
621C22×C4—862no—
622C22×C4—862no—
623C22×C4—862no—
624C22×C4—862no—
625C22×C4—3444no—
626C22×C4—3442no—
627C22×C4—3442no—
628C22×C4—3442no—
629C22×C4—1722no—
630C22×C4C2×C4×D4312yescomplemented
631C22×C4C2×C22⋊D4314yes—
632C4⋊C4—868no—
633C4⋊C4—868no—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—42no—
641C22⋊C4—84no—
642C22⋊C4—434no—
643C22⋊C4—868no—
644C22⋊C4—868no—
645C22⋊C4—868no—
646C22⋊C4—864no—
647C22⋊C4—862no—
648C22⋊C4—862no—
649C22⋊C4—862no—
650C22⋊C4—862no—
651C22⋊C4—862no—
652C22⋊C4—862no—
653C22⋊C4—862no—
654C22⋊C4—3444no—
655C22⋊C4—1722no—
656C42—868no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—82no—
675C23—82no—
676C23—82no—
677C23—82no—
678C23—82no—
679C23—82no—
680C23—82no—
681C23—82no—
682C23—434no—
683C23—862no—
684C23—864no—
685C23—862no—
686C23—864no—
687C23—3442no—
688C23—3444no—
689C23—3444no—
690C23—1724no—
691C23—1724no—
692C23C22⋊C4×D4312yes—
693C23C22⋊C4×D4312yes—
694C23(C22⋊D43)⋊C412yes—
695C23(C22⋊D43)⋊C412yes—
696C23C4×C22⋊D4312yes—
697C23C4×C22⋊D4312yes—
698C23#1306329311yescharacteristic
699C23#1306329311yescharacteristic
700C23#1306329311yescharacteristic
701C23#1306329311yescharacteristic
702C23#1306329612yes—
703C23#1306329612yes—
704C23#1306329812yes—
705C23#1306329812yes—
706C23#1306330712yes—
707C23#1306330712yes—
708C23C22×C4×D4311yescharacteristic
709C23C2×D4×D4311yescharacteristic
710C23C2×D4×D4311yescharacteristic
711C23C2×D4×D4311yescharacteristic
712C23C22×C22⋊D4311yescharacteristic
713C23C2×#1062190011yescharacteristic
714C23C2×#1062189811yescharacteristic
715D4—44no—
716D4—44no—
717D4—44no—
718D4—44no—
719D4—864no—
720D4—864no—
721D4—864no—
722D4—864no—
723D4—868no—
724D4—868no—
725D4—3448no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—44no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—42no—
738C2×C4—82no—
739C2×C4—84no—
740C2×C4—434no—
741C2×C4—862no—
742C2×C4—862no—
743C2×C4—864no—
744C2×C4—864no—
745C2×C4—864no—
746C2×C4—864no—
747C2×C4—3448no—
748C2×C4—3444no—
749C2×C4—3442no—
750C2×C4—3444no—
751C2×C4—1724no—
752C2×C4—1722no—
753C2×C4—1724no—
754C2×C4—1724no—
755C2×C4—1724no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—42no—
783C22—82no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—864no—
788C22—3444no—
789C22—3442no—
790C22—1724no—
791C22—1728no—
792C22—1724no—
793C22#1458277512yes—
794C22#1458277512yes—
795C22#1458277512yes—
796C22#1458277512yes—
797C22C2×C22⋊C4×D4311yescharacteristic
798C22C2×(C22⋊D43)⋊C411yescharacteristic
799C22C2×C4×C22⋊D4311yescharacteristic
800C22C2×#1306329311yescharacteristic
801C22C2×#1306329611yescharacteristic
802C22C2×#1306329811yescharacteristic
803C22C2×#1306330711yescharacteristic
804C4—44no—
805C4—42no—
806C4—82no—
807C4—864no—
808C4—3442no—
809C4—1724no—
810C4—1724no—
811C2—21no—
812C2—21no—
813C2—21no—
814C2—21no—
815C2—21no—
816C2—21no—
817C2—22no—
818C2—22no—
819C2—22no—
820C2—22no—
821C2—82no—
822C2—1724no—
823C2C2×#1458277511yescharacteristic
824C2#1914399112yes—
subgroupG/H
centerC22C2×#13063293
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#2308C2
socleC22×C43C2×#120
prime radicalC2×#14583458C2
cosocleC24×C43C24
hypercenter#2308D43
hypocenterC43#20960
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C25 ◁ #2308

Complements

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

NH ≅ G/Ntype
2. C2×#14583372C2semidirect
3. C22×#13063239C2semidirect
4. #19137173C2semidirect
5. #19135005C2semidirect
6. #19135000C2semidirect
7. C2×#14582666C2semidirect
8. C2×#14582665C2semidirect
9. C43×#2308C2semidirect
12. #14583458C4semidirect
33. #14582762C22semidirect
34. #14582755C22semidirect
35. #14582666C22semidirect
36. #14582665C22semidirect
42. C43×#381C22semidirect
43. C43×#379C22semidirect
59. C23×Dic43D4semidirect
62. #13063308C2×C4semidirect
66. #13063294C2×C4semidirect
87. C2×C22⋊Dic43C2×C4semidirect
88. C2×C22⋊Dic43D4semidirect
110. C22×D4×C43C2×C4semidirect
112. C23×C4×C43D4semidirect
122. C2×C22⋊C4×C43D4semidirect
135. C24×C43C22×C4semidirect
150. C23×D43C22⋊C4semidirect
180. C22×C4×C43C22×C4semidirect
199. C2×C22⋊D43C22⋊C4semidirect
214. C22×Dic43C22⋊C4semidirect
238. C22⋊Dic43C22×C4semidirect
403. #2308D43semidirect
451. #381C2×D43semidirect
453. #379C2×D43semidirect
456. C43#20960semidirect
480. C22×D4C4×D43semidirect
487. C23×C4C22⋊D43semidirect
532. C2×C22⋊C4C22⋊D43semidirect
554. C24C2×C4×D43semidirect
630. C22×C4C2×C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834582
C2×#145833722
C22×#130632392
#191371732
#191350052
#191350002
C2×#145826662
C2×#145826652
C43×#23082
#2096043