Finite Group Databasebeta

← #25111932

Subgroups — #25111932

Order 11008.

1668 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583543C211yesmaximal, characteristic
2C2×#14582871C211yesmaximal, characteristic, complemented
3C22×#13063240C211yesmaximal, characteristic, complemented
4#19137446C212yesmaximal, complemented
5#19135429C212yesmaximal, complemented
6#19135050C212yesmaximal, complemented
7#19135046C212yesmaximal, complemented
8#19134581C211yesmaximal, characteristic, complemented
9#19134511C211yesmaximal, characteristic, complemented
10#99×Dic43C211yesmaximal, characteristic, complemented
11C43×#1781C211yesmaximal, characteristic, complemented
12C22×#10621900C2211yescharacteristic
13#14583543—22no—
14#14583543—22no—
15#14583543—22no—
16#14583543—22no—
17C2×#13063312C411yescharacteristic, complemented
18C2×#13063306C411yescharacteristic, complemented
19C2×#13063306C2211yescharacteristic
20C2×#13063304C411yescharacteristic, complemented
21C2×#13063297C411yescharacteristic, complemented
22C2×#13063297C2211yescharacteristic
23C2×#13063296C411yescharacteristic, complemented
24C2×#13063294C411yescharacteristic, complemented
25C2×#13063294C2211yescharacteristic
26C2×D4×Dic43C2211yescharacteristic
27C2×C4×C22⋊D43C411yescharacteristic, complemented
28C2×#13063281C2212yescomplemented
29C22×C22⋊Dic43C411yescharacteristic, complemented
30C22×C22⋊Dic43C2212yes—
31C22×C22⋊Dic43C2211yescharacteristic
32#14582871—24no—
33C2×#13063240—24no—
34C2×#13063240C2211yescharacteristic
35C2×#13063240C2212yes—
36C2×#13063240C2211yescharacteristic
37C2×#13063239C2212yescomplemented
38C2×#13063239C2212yescomplemented
39#14582793—22no—
40#14582787—22no—
41#14582771—22no—
42#14582760C2212yescomplemented
43#14582757C2212yescomplemented
44C22⋊C4×Dic43—22no—
45C22⋊C4×Dic43C2212yescomplemented
46#14582665C2212yescomplemented
47#14582665C2212yescomplemented
48C23×D4×C43C2211yescharacteristic
49C2×#99×C43C2211yescharacteristic
50C2×#99×C43C2211yescharacteristic
51C2×#99×C43C2212yes—
52C43×#379C2212yes—
53C2×#10621900—22no—
54C2×#10621900—22no—
55C2×#10621900—22no—
56C2×#10621900—22no—
57C2×#10621900—42no—
58C22×Dic86C2×C411yescharacteristic, complemented
59C22×C22⋊D43C2×C411yescharacteristic
60C22×C22⋊D43C2×C411yescharacteristic
61C22×C22⋊D43C2×C411yescharacteristic, complemented
62C22×C22⋊D43C2×C411yescharacteristic, complemented
63C22×C22⋊D43C2311yescharacteristic
64C23×Dic43—22no—
65C23×Dic43C2×C411yescharacteristic, complemented
66C23×Dic43C2×C411yescharacteristic, complemented
67C23×Dic43C2311yescharacteristic
68C23×Dic43C2311yescharacteristic
69C22×C4×D43C2×C411yescharacteristic, complemented
70#13063312—22no—
71#13063312—22no—
72#13063306—22no—
73#13063306—22no—
74#13063306—22no—
75#13063306—22no—
76#13063304—22no—
77#13063304—22no—
78#13063297—22no—
79#13063297—22no—
80#13063297—22no—
81#13063297—22no—
82#13063296—22no—
83#13063296—22no—
84#13063294—22no—
85#13063294—22no—
86#13063294—22no—
87#13063294—22no—
88D4×Dic43—22no—
89D4×Dic43—22no—
90C4×C22⋊D43—21no—
91C4×C22⋊D43—21no—
92C4×C22⋊D43—21no—
93C4×C22⋊D43—21no—
94#13063281—24no—
95#13063281—42no—
96C2×C4⋊Dic43C2×C411yescharacteristic, complemented
97C2×Dic43⋊C4—22no—
98C2×Dic43⋊C4—22no—
99C2×Dic43⋊C4C2×C411yescharacteristic, complemented
100C2×Dic43⋊C4C2×C411yescharacteristic, complemented
101C2×Dic43⋊C4C2×C411yescharacteristic, complemented
102C2×C22⋊Dic43—21no—
103C2×C22⋊Dic43—21no—
104C2×C22⋊Dic43—21no—
105C2×C22⋊Dic43—21no—
106C2×C22⋊Dic43—24no—
107C2×C22⋊Dic43—22no—
108C2×C22⋊Dic43—42no—
109C2×C22⋊Dic43C2×C411yescharacteristic
110C2×C22⋊Dic43C2×C411yescharacteristic
111C2×C22⋊Dic43C2×C411yescharacteristic
112C2×C22⋊Dic43C2×C411yescharacteristic
113C2×C22⋊Dic43C2×C411yescharacteristic
114C2×C22⋊Dic43C2×C411yescharacteristic
115C2×C22⋊Dic43C2×C411yescharacteristic, complemented
116C2×C22⋊Dic43C2×C411yescharacteristic, complemented
117C2×C22⋊Dic43C2×C411yescharacteristic, complemented
118C2×C22⋊Dic43C2×C411yescharacteristic, complemented
119C2×C22⋊Dic43D412yes—
120C2×C22⋊Dic43D412yes—
121C2×C22⋊Dic43D412yes—
122C2×C22⋊Dic43D412yes—
123C2×C22⋊Dic43C2312yes—
124C2×C22⋊Dic43C2311yescharacteristic
125C2×C22⋊Dic43C2312yes—
126C2×(C2×D43)⋊C4C2×C411yescharacteristic, complemented
127C2×C4×Dic43—22no—
128C2×C4×Dic43—22no—
129C2×C4×Dic43C2×C411yescharacteristic, complemented
130#13063240—22no—
131#13063240—24no—
132#13063240D414yescomplemented
133#13063239—24no—
134#13063239—42no—
135C43⋊#95—22no—
136C43⋊#95—22no—
137C43⋊#95—22no—
138C43⋊#95—22no—
139C25×C43C2×C411yescharacteristic
140C25×C43C2311yescharacteristic
141C22×D4×C43—22no—
142C22×D4×C43—22no—
143C22×D4×C43—22no—
144C22×D4×C43—22no—
145C22×D4×C43—42no—
146C22×D4×C43C2×C411yescharacteristic
147C22×D4×C43C2×C411yescharacteristic
148C22×D4×C43C2311yescharacteristic
149C22×D4×C43C2311yescharacteristic
150C23×C4×C43C2×C411yescharacteristic
151C2×C22⋊C4×C43—22no—
152C2×C22⋊C4×C43—22no—
153C2×C22⋊C4×C43C2312yes—
154C2×C22⋊C4×C43C2312yes—
155#99×C43—22no—
156#99×C43—22no—
157#99×C43—42no—
158C24×C43—21no—
159C24×C43—21no—
160C24×C43—22no—
161C24×C43—21no—
162C24×C43—21no—
163C24×C43—22no—
164C24×C43—41no—
165C24×C43—42no—
166C24×C43—42no—
167C24×C43—81no—
168C24×C43—81no—
169C24×C43C22×C411yescharacteristic
170C24×C43C22×C411yescharacteristic
171C24×C43C22×C411yescharacteristic
172C24×C43C22×C411yescharacteristic
173C24×C43C2×D412yes—
174C24×C43C2×D412yes—
175C24×C43C2411yescharacteristic
176C23×D43C22×C411yescharacteristic
177C2×D4×C43—22no—
178C2×D4×C43—22no—
179C2×D4×C43—22no—
180C2×D4×C43—22no—
181C2×D4×C43—22no—
182C2×D4×C43—21no—
183C2×D4×C43—22no—
184C2×D4×C43—21no—
185C2×D4×C43—22no—
186C2×D4×C43—22no—
187C2×D4×C43—41no—
188C2×D4×C43—41no—
189C2×D4×C43—44no—
190C2×D4×C43—44no—
191C2×D4×C43—44no—
192C2×D4×C43—44no—
193C2×D4×C43C2×D412yes—
194C2×D4×C43#4112yes—
195C22×C4×C43—22no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—22no—
199C22×C4×C43—22no—
200C22×C4×C43—41no—
201C22×C4×C43C22×C411yescharacteristic
202C22×C4×C43C22×C411yescharacteristic
203C2×C22⋊D43—22no—
204C2×C22⋊D43—22no—
205C2×C22⋊D43—21no—
206C2×C22⋊D43—21no—
207C2×C22⋊D43—22no—
208C2×C22⋊D43—22no—
209C2×C22⋊D43—21no—
210C2×C22⋊D43—22no—
211C2×C22⋊D43—21no—
212C2×C22⋊D43—22no—
213C2×C22⋊D43—41no—
214C2×C22⋊D43—42no—
215C2×C22⋊D43—81no—
216C2×C22⋊D43—81no—
217C22×Dic43—21no—
218C22×Dic43—21no—
219C22×Dic43—21no—
220C22×Dic43—21no—
221C22×Dic43—22no—
222C22×Dic43—21no—
223C22×Dic43—22no—
224C22×Dic43—22no—
225C22×Dic43—21no—
226C22×Dic43—22no—
227C22×Dic43—41no—
228C22×Dic43—44no—
229C22×Dic43—44no—
230C22×Dic43—81no—
231C22×Dic43—81no—
232C22×Dic43—82no—
233C22×Dic43C22×C411yescharacteristic
234C22×Dic43C22×C411yescharacteristic
235C22×Dic43C22×C411yescharacteristic
236C22×Dic43C22×C411yescharacteristic
237C22×Dic43C22×C411yescharacteristic
238C22×Dic43C22×C411yescharacteristic
239C22×Dic43C22×C411yescharacteristic
240C22×Dic43C2×D412yes—
241C22×Dic43C2×D412yes—
242C22×Dic43C2×D412yes—
243C22×Dic43C2×D412yes—
244#10621900—44no—
245#10621900—44no—
246#10621900—44no—
247#10621900—44no—
248C2×C4×D43—22no—
249C2×C4×D43—21no—
250C2×C4×D43—21no—
251C2×C4×D43—41no—
252C2×Dic86—22no—
253C2×Dic86—22no—
254C2×Dic86—41no—
255C22⋊C4×C43—22no—
256C22⋊C4×C43—22no—
257C22⋊C4×C43—22no—
258C22⋊C4×C43—22no—
259C22⋊C4×C43—44no—
260C22⋊C4×C43—82no—
261C22⋊Dic43—21no—
262C22⋊Dic43—21no—
263C22⋊Dic43—21no—
264C22⋊Dic43—21no—
265C22⋊Dic43—22no—
266C22⋊Dic43—22no—
267C22⋊Dic43—21no—
268C22⋊Dic43—21no—
269C22⋊Dic43—22no—
270C22⋊Dic43—22no—
271C22⋊Dic43—22no—
272C22⋊Dic43—22no—
273C22⋊Dic43—22no—
274C22⋊Dic43—44no—
275C22⋊Dic43C22⋊C411yescharacteristic
276C22⋊Dic43C22⋊C411yescharacteristic
277C22⋊Dic43C22⋊C411yescharacteristic
278C22⋊Dic43C22⋊C411yescharacteristic
279C22⋊Dic43C22⋊C412yes—
280C22⋊Dic43C22⋊C412yes—
281C22⋊Dic43C22⋊C412yes—
282C22⋊Dic43C22⋊C412yes—
283C22⋊Dic43C22⋊C412yes—
284C22⋊Dic43C22⋊C412yes—
285C22⋊Dic43C2×D414yes—
286(C2×D43)⋊C4—21no—
287(C2×D43)⋊C4—21no—
288C4⋊Dic43—22no—
289Dic43⋊C4—21no—
290Dic43⋊C4—21no—
291Dic43⋊C4—22no—
292Dic43⋊C4—22no—
293Dic43⋊C4—44no—
294Dic43⋊C4—82no—
295C4×Dic43—21no—
296C4×Dic43—21no—
297C4×Dic43—44no—
298C4×Dic43—82no—
299C23×C43—21no—
300C23×C43—21no—
301C23×C43—21no—
302C23×C43—21no—
303C23×C43—22no—
304C23×C43—22no—
305C23×C43—24no—
306C23×C43—22no—
307C23×C43—21no—
308C23×C43—21no—
309C23×C43—22no—
310C23×C43—22no—
311C23×C43—21no—
312C23×C43—21no—
313C23×C43—21no—
314C23×C43—42no—
315C23×C43—41no—
316C23×C43—41no—
317C23×C43—41no—
318C23×C43—42no—
319C23×C43—41no—
320C23×C43—41no—
321C23×C43—42no—
322C23×C43—42no—
323C23×C43—42no—
324C23×C43—41no—
325C23×C43—41no—
326C23×C43—42no—
327C23×C43—41no—
328C23×C43—41no—
329C23×C43—42no—
330C23×C43—81no—
331C23×C43—81no—
332C23×C43—82no—
333C23×C43—82no—
334C23×C43—84no—
335C23×C43—84no—
336C23×C43—84no—
337C23×C43C2×C22⋊C411yescharacteristic
338C23×C43C2×C22⋊C412yes—
339C23×C43C2×C22⋊C411yescharacteristic
340C23×C43C4×D412yes—
341C23×C43C23×C411yescharacteristic
342C23×C43C22×D412yes—
343C23×C43C22×D411yescharacteristic
344C23×C43C2×#4111yescharacteristic
345C23×C43H(5,𝔽2)12yes—
346C22×D43—21no—
347C22×D43—21no—
348C22×D43—21no—
349C22×D43—41no—
350C22×D43—41no—
351D4×C43—24no—
352D4×C43—24no—
353D4×C43—44no—
354D4×C43—44no—
355D4×C43—42no—
356D4×C43—42no—
357C2×C4×C43—21no—
358C2×C4×C43—21no—
359C2×C4×C43—21no—
360C2×C4×C43—21no—
361C2×C4×C43—21no—
362C2×C4×C43—42no—
363C2×C4×C43—42no—
364C2×C4×C43—42no—
365C2×C4×C43—42no—
366C2×C4×C43—42no—
367C2×C4×C43—42no—
368C2×C4×C43—42no—
369C2×C4×C43—42no—
370C2×C4×C43C4×D412yes—
371C22⋊D43—44no—
372C22⋊D43—42no—
373C22⋊D43—42no—
374C22⋊D43—42no—
375C22⋊D43—42no—
376C22⋊D43—82no—
377C22⋊D43—82no—
378C2×Dic43—21no—
379C2×Dic43—21no—
380C2×Dic43—21no—
381C2×Dic43—21no—
382C2×Dic43—22no—
383C2×Dic43—22no—
384C2×Dic43—22no—
385C2×Dic43—22no—
386C2×Dic43—21no—
387C2×Dic43—21no—
388C2×Dic43—21no—
389C2×Dic43—21no—
390C2×Dic43—21no—
391C2×Dic43—24no—
392C2×Dic43—42no—
393C2×Dic43—42no—
394C2×Dic43—41no—
395C2×Dic43—41no—
396C2×Dic43—42no—
397C2×Dic43—42no—
398C2×Dic43—42no—
399C2×Dic43—42no—
400C2×Dic43—41no—
401C2×Dic43—41no—
402C2×Dic43—42no—
403C2×Dic43—42no—
404C2×Dic43—42no—
405C2×Dic43—81no—
406C2×Dic43—81no—
407C2×Dic43—88no—
408C2×Dic43C2×C22⋊C411yescharacteristic
409C2×Dic43C2×C22⋊C411yescharacteristic
410C2×Dic43C2×C22⋊C412yes—
411C2×Dic43C2×C22⋊C412yes—
412C2×Dic43C2×C22⋊C411yescharacteristic
413C2×Dic43C2×C22⋊C411yescharacteristic
414C4×D43—42no—
415C4×D43—42no—
416Dic86—44no—
417#22405—431nomaximal, Sylow
418C22×C43—21no—
419C22×C43—21no—
420C22×C43—22no—
421C22×C43—21no—
422C22×C43—21no—
423C22×C43—22no—
424C22×C43—21no—
425C22×C43—22no—
426C22×C43—22no—
427C22×C43—21no—
428C22×C43—22no—
429C22×C43—21no—
430C22×C43—22no—
431C22×C43—41no—
432C22×C43—41no—
433C22×C43—42no—
434C22×C43—44no—
435C22×C43—42no—
436C22×C43—42no—
437C22×C43—44no—
438C22×C43—42no—
439C22×C43—42no—
440C22×C43—41no—
441C22×C43—41no—
442C22×C43—41no—
443C22×C43—41no—
444C22×C43—41no—
445C22×C43—82no—
446C22×C43—82no—
447C22×C43—81no—
448C22×C43—81no—
449C22×C43—84no—
450C22×C43—81no—
451C22×C43—81no—
452C22×C43—84no—
453C22×C43#41012yescomplemented
454C22×C43C22×C22⋊C411yescharacteristic
455C22×C43C2×C4×D411yescharacteristic
456C22×C43#51811yescharacteristic
457C22×C43D4212yes—
458C22×C43#54612yes—
459C2×D43—41no—
460C2×D43—41no—
461C2×D43—41no—
462C2×D43—81no—
463C2×D43—81no—
464C4×C43—22no—
465C4×C43—41no—
466C4×C43—82no—
467C4×C43—82no—
468Dic43—22no—
469Dic43—21no—
470Dic43—21no—
471Dic43—21no—
472Dic43—21no—
473Dic43—22no—
474Dic43—44no—
475Dic43—41no—
476Dic43—41no—
477Dic43—41no—
478Dic43—82no—
479C2×#546—431no—
480C2×#410—431no—
481C22×#99—431no—
482#2342—432no—
483#1964—432no—
484#1899—432no—
485#1898—432no—
486#1799—431no—
487#1782—431no—
488#1781D4311yescharacteristic, complemented
489C4×#99—431no—
490C2×C43—22no—
491C2×C43—22no—
492C2×C43—21no—
493C2×C43—21no—
494C2×C43—22no—
495C2×C43—42no—
496C2×C43—41no—
497C2×C43—42no—
498C2×C43—81no—
499C2×C43D4×C22⋊C411yescharacteristic
500C2×C43C2×#41011yescharacteristic
501C2×C43#288311yescharacteristic
502D43—81no—
503C22×#41—431no—
504C23×D4C2×D4311yescharacteristic
505#546—862no—
506#546—862no—
507#546—862no—
508#546—862no—
509C2×#124—431no—
510C2×#123—431no—
511C2×#123—431no—
512C2×C22⋊Q8—431no—
513C2×#121—431no—
514C2×#121—431no—
515C2×#121—431no—
516C2×#120—431no—
517C2×#120—431no—
518C2×C4×D4—431no—
519C2×C4×D4—431no—
520C2×#117—432no—
521C22×C22⋊C4—431no—
522C22×C22⋊C4—431no—
523C22×C22⋊C4—432no—
524#410—864no—
525C2×#99—431no—
526C2×#99—431no—
527C2×#99—432no—
528C2×#99—432no—
529C2×#99—432no—
530C2×#99—864no—
531C2×#99C2×D4311yescharacteristic
532C2×#99C2×D4311yescharacteristic
533C2×#99C2×D4312yes—
534#388—862no—
535#388—862no—
536#385—862no—
537#381—432no—
538#380—432no—
539#379C2×D4312yes—
540C4×C22⋊C4—432no—
541C4×C22⋊C4—862no—
542#342—432no—
543#342—432no—
544C43#2240511yescharacteristic, complemented, Sylow
545C25C4×D4311yescharacteristic
546C25C22×D4311yescharacteristic
547C2×#41—862no—
548C2×#41—862no—
549C2×#41—862no—
550C2×#41—862no—
551C2×#41—1722no—
552C22×Q8—431no—
553C22×D4—22no—
554C22×D4—22no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—42no—
558C22×D4—431no—
559C22×D4—431no—
560C22×D4—431no—
561C22×D4—431no—
562C22×D4—431no—
563C22×D4C4×D4311yescharacteristic
564C22×D4C4×D4311yescharacteristic
565C22×D4C22×D4311yescharacteristic
566C22×D4C22×D4311yescharacteristic
567C23×C4—431no—
568C23×C4—431no—
569C23×C4—431no—
570C23×C4—431no—
571C23×C4—431no—
572C23×C4—862no—
573C23×C4C4×D4311yescharacteristic
574#124—862no—
575#124—862no—
576#123—862no—
577#123—862no—
578#123—862no—
579#123—862no—
580C22⋊Q8—862no—
581C22⋊Q8—862no—
582#121—862no—
583#121—862no—
584#121—862no—
585#121—862no—
586#121—862no—
587#121—862no—
588#120—862no—
589#120—862no—
590#120—862no—
591#120—862no—
592C4×D4—861no—
593C4×D4—861no—
594C4×D4—861no—
595C4×D4—861no—
596C4×D4—862no—
597C4×D4—862no—
598#117—864no—
599#117—1722no—
600C2×C4⋊C4—431no—
601C2×C4⋊C4—431no—
602C2×C4⋊C4—431no—
603C2×C4⋊C4—431no—
604C2×C4⋊C4—862no—
605C2×C4⋊C4—862no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—22no—
608C2×C22⋊C4—431no—
609C2×C22⋊C4—431no—
610C2×C22⋊C4—431no—
611C2×C22⋊C4—431no—
612C2×C22⋊C4—432no—
613C2×C22⋊C4—432no—
614C2×C22⋊C4—432no—
615C2×C22⋊C4—432no—
616C2×C22⋊C4—432no—
617C2×C22⋊C4—431no—
618C2×C22⋊C4—431no—
619C2×C22⋊C4—431no—
620C2×C22⋊C4—431no—
621C2×C22⋊C4—431no—
622C2×C22⋊C4—431no—
623C2×C22⋊C4—431no—
624C2×C22⋊C4—431no—
625C2×C22⋊C4—432no—
626C2×C22⋊C4—861no—
627C2×C22⋊C4—861no—
628C2×C22⋊C4—861no—
629C2×C22⋊C4—861no—
630C2×C22⋊C4—864no—
631C2×C22⋊C4—862no—
632C2×C22⋊C4—1722no—
633C2×C22⋊C4C22×D4312yes—
634C2×C22⋊C4C22×D4312yes—
635C2×C42—431no—
636C2×C42—862no—
637C2×C42—862no—
638#99—22no—
639#99—22no—
640#99—42no—
641#99—434no—
642#99—864no—
643#99—864no—
644#99—862no—
645#99—1722no—
646#95—862no—
647#95—862no—
648#95—862no—
649#95—862no—
650C24—21no—
651C24—21no—
652C24—22no—
653C24—21no—
654C24—21no—
655C24—22no—
656C24—41no—
657C24—42no—
658C24—42no—
659C24—81no—
660C24—81no—
661C24—431no—
662C24C2×C4×D4311yescharacteristic
663C24C2×C4×D4311yescharacteristic
664C24C2×C4×D4311yescharacteristic
665C24C2×C4×D4311yescharacteristic
666C24D4×D4312yes—
667C24D4×D4312yes—
668C24C23×D4311yescharacteristic
669#41—1724no—
670#41—1724no—
671#41—1724no—
672#41—1724no—
673C2×Q8—862no—
674C2×Q8—862no—
675C2×Q8—1721no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—22no—
679C2×D4—22no—
680C2×D4—22no—
681C2×D4—21no—
682C2×D4—22no—
683C2×D4—21no—
684C2×D4—22no—
685C2×D4—22no—
686C2×D4—41no—
687C2×D4—41no—
688C2×D4—44no—
689C2×D4—44no—
690C2×D4—44no—
691C2×D4—44no—
692C2×D4—862no—
693C2×D4—862no—
694C2×D4—862no—
695C2×D4—861no—
696C2×D4—861no—
697C2×D4—862no—
698C2×D4—861no—
699C2×D4—862no—
700C2×D4—861no—
701C2×D4—862no—
702C2×D4—3441no—
703C2×D4—3441no—
704C2×D4—1721no—
705C2×D4—1722no—
706C2×D4D4×D4312yes—
707C2×D4#1062190012yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—41no—
714C22×C4—431no—
715C22×C4—431no—
716C22×C4—432no—
717C22×C4—432no—
718C22×C4—431no—
719C22×C4—431no—
720C22×C4—432no—
721C22×C4—432no—
722C22×C4—431no—
723C22×C4—431no—
724C22×C4—431no—
725C22×C4—861no—
726C22×C4—861no—
727C22×C4—861no—
728C22×C4—861no—
729C22×C4—861no—
730C22×C4—861no—
731C22×C4—861no—
732C22×C4—861no—
733C22×C4—862no—
734C22×C4—862no—
735C22×C4—862no—
736C22×C4—862no—
737C22×C4—862no—
738C22×C4—3442no—
739C22×C4—3441no—
740C22×C4—3441no—
741C22×C4—1721no—
742C22×C4—1721no—
743C22×C4—1724no—
744C22×C4—1724no—
745C22×C4C2×C4×D4311yescharacteristic
746C22×C4C2×C4×D4311yescharacteristic
747C4⋊C4—862no—
748C4⋊C4—861no—
749C4⋊C4—861no—
750C4⋊C4—862no—
751C4⋊C4—862no—
752C4⋊C4—3442no—
753C4⋊C4—1724no—
754C22⋊C4—22no—
755C22⋊C4—22no—
756C22⋊C4—22no—
757C22⋊C4—22no—
758C22⋊C4—44no—
759C22⋊C4—82no—
760C22⋊C4—431no—
761C22⋊C4—431no—
762C22⋊C4—431no—
763C22⋊C4—431no—
764C22⋊C4—432no—
765C22⋊C4—432no—
766C22⋊C4—432no—
767C22⋊C4—432no—
768C22⋊C4—432no—
769C22⋊C4—432no—
770C22⋊C4—434no—
771C22⋊C4—861no—
772C22⋊C4—861no—
773C22⋊C4—861no—
774C22⋊C4—861no—
775C22⋊C4—861no—
776C22⋊C4—861no—
777C22⋊C4—862no—
778C22⋊C4—862no—
779C22⋊C4—861no—
780C22⋊C4—861no—
781C22⋊C4—862no—
782C22⋊C4—862no—
783C22⋊C4—862no—
784C22⋊C4—862no—
785C22⋊C4—862no—
786C22⋊C4—1724no—
787C42—861no—
788C42—861no—
789C42—3442no—
790C42—1724no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—24no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—21no—
800C23—21no—
801C23—22no—
802C23—22no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—42no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—42no—
811C23—41no—
812C23—41no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—41no—
817C23—41no—
818C23—42no—
819C23—41no—
820C23—41no—
821C23—42no—
822C23—81no—
823C23—81no—
824C23—82no—
825C23—82no—
826C23—84no—
827C23—84no—
828C23—84no—
829C23—861no—
830C23—861no—
831C23—861no—
832C23—1721no—
833C23—1721no—
834C23C22⋊C4×D4311yescharacteristic
835C23C22⋊C4×D4312yes—
836C23C22⋊C4×D4311yescharacteristic
837C23(C22⋊D43)⋊C412yes—
838C23C22×C4×D4311yescharacteristic
839C23C2×D4×D4312yes—
840C23C2×D4×D4311yescharacteristic
841C23C2×#1062190011yescharacteristic
842C23#1306337012yes—
843Q8—1724no—
844D4—24no—
845D4—24no—
846D4—44no—
847D4—44no—
848D4—42no—
849D4—42no—
850D4—3442no—
851D4—3442no—
852D4—1724no—
853D4—1722no—
854D4—1722no—
855D4—1722no—
856D4—1722no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—431no—
871C2×C4—431no—
872C2×C4—432no—
873C2×C4—431no—
874C2×C4—431no—
875C2×C4—432no—
876C2×C4—861no—
877C2×C4—861no—
878C2×C4—861no—
879C2×C4—861no—
880C2×C4—862no—
881C2×C4—862no—
882C2×C4—862no—
883C2×C4—862no—
884C2×C4—861no—
885C2×C4—861no—
886C2×C4—861no—
887C2×C4—861no—
888C2×C4—861no—
889C2×C4—864no—
890C2×C4—3441no—
891C2×C4—3441no—
892C2×C4—3448no—
893C2×C4—1722no—
894C2×C4—1722no—
895C2×C4—1722no—
896C2×C4—1722no—
897C2×C4—1721no—
898C2×C4—1721no—
899C2×C4—1722no—
900C2×C4—1722no—
901C2×C4—1722no—
902C2×C4—1722no—
903C2×C4—1722no—
904C2×C4—1722no—
905C2×C4—1722no—
906C2×C4—1721no—
907C2×C4—1721no—
908C2×C4(C22⋊D43)⋊C412yes—
909C22—21no—
910C22—22no—
911C22—21no—
912C22—22no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—22no—
917C22—22no—
918C22—21no—
919C22—22no—
920C22—22no—
921C22—21no—
922C22—41no—
923C22—41no—
924C22—42no—
925C22—44no—
926C22—42no—
927C22—42no—
928C22—44no—
929C22—42no—
930C22—42no—
931C22—41no—
932C22—41no—
933C22—41no—
934C22—41no—
935C22—41no—
936C22—82no—
937C22—82no—
938C22—81no—
939C22—81no—
940C22—84no—
941C22—81no—
942C22—81no—
943C22—84no—
944C22—3441no—
945C22—3441no—
946C22—1721no—
947C22—1721no—
948C22—1721no—
949C22#1458287112yescomplemented
950C22C2×C22⋊C4×D4311yescharacteristic
951C22C2×(C22⋊D43)⋊C411yescharacteristic
952C22#1458337211yescharacteristic
953C22#1458353112yes—
954C22#1458353612yes—
955C4—22no—
956C4—41no—
957C4—82no—
958C4—82no—
959C4—861no—
960C4—861no—
961C4—862no—
962C4—861no—
963C4—861no—
964C4—862no—
965C4—3442no—
966C4—1724no—
967C4—1721no—
968C4—1721no—
969C4—1721no—
970C2—22no—
971C2—22no—
972C2—21no—
973C2—21no—
974C2—22no—
975C2—41no—
976C2—42no—
977C2—42no—
978C2—81no—
979C2—3441no—
980C2#1913741111yescharacteristic
981C2C2×#1458287111yescharacteristic
982C2#1914305311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#1781C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583543C2
cosocleC24×C43C24
hypercenter#1781D43
hypocenterC43#22405
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C25 ◁ #1781

Complements

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

NH ≅ G/Ntype
2. C2×#14582871C2semidirect
3. C22×#13063240C2semidirect
4. #19137446C2semidirect
5. #19135429C2semidirect
6. #19135050C2semidirect
7. #19135046C2semidirect
8. #19134581C2semidirect
9. #19134511C2semidirect
10. #99×Dic43C2semidirect
11. C43×#1781C2semidirect
17. C2×#13063312C4semidirect
18. C2×#13063306C4semidirect
20. C2×#13063304C4semidirect
21. C2×#13063297C4semidirect
23. C2×#13063296C4semidirect
24. C2×#13063294C4semidirect
27. C2×C4×C22⋊D43C4semidirect
28. C2×#13063281C22semidirect
29. C22×C22⋊Dic43C4semidirect
37. C2×#13063239C22semidirect
38. C2×#13063239C22semidirect
42. #14582760C22semidirect
43. #14582757C22semidirect
45. C22⋊C4×Dic43C22semidirect
46. #14582665C22semidirect
47. #14582665C22semidirect
58. C22×Dic86C2×C4semidirect
61. C22×C22⋊D43C2×C4semidirect
62. C22×C22⋊D43C2×C4semidirect
65. C23×Dic43C2×C4semidirect
66. C23×Dic43C2×C4semidirect
69. C22×C4×D43C2×C4semidirect
96. C2×C4⋊Dic43C2×C4semidirect
99. C2×Dic43⋊C4C2×C4semidirect
100. C2×Dic43⋊C4C2×C4semidirect
101. C2×Dic43⋊C4C2×C4semidirect
115. C2×C22⋊Dic43C2×C4semidirect
116. C2×C22⋊Dic43C2×C4semidirect
117. C2×C22⋊Dic43C2×C4semidirect
118. C2×C22⋊Dic43C2×C4semidirect
126. C2×(C2×D43)⋊C4C2×C4semidirect
129. C2×C4×Dic43C2×C4semidirect
132. #13063240D4semidirect
453. C22×C43#410semidirect
488. #1781D43semidirect
544. C43#22405semidirect
949. C22#14582871semidirect

Maximal subgroups

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

subgroupindex
C2×#145835432
C2×#145828712
C22×#130632402
#191374462
#191354292
#191350502
#191350462
#191345812
#191345112
#99×Dic432
C43×#17812
#2240543