Finite Group Databasebeta

← #25101949

Subgroups — #25101949

Order 11008.

1318 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583484C211yesmaximal, characteristic
2#19137191C211yesmaximal, characteristic, complemented
3#19136948C211yesmaximal, characteristic, complemented
4#19135578C212yesmaximal, complemented
5#19135429C212yesmaximal, complemented
6#19135049C211yesmaximal, characteristic, complemented
7#19135048C211yesmaximal, characteristic, complemented
8#19135046C211yesmaximal, characteristic, complemented
9#99×Dic43C212yesmaximal, complemented
10#19134382C212yesmaximal, complemented
11C43×#1898C211yesmaximal, characteristic, complemented
12#14583484—22no—
13#14583484—22no—
14#14583484—22no—
15#14583484—22no—
16C2×#13063318C411yescharacteristic, complemented
17C2×#13063318C411yescharacteristic, complemented
18C2×#13063312C411yescharacteristic, complemented
19C2×#13063311C411yescharacteristic, complemented
20C2×#13063307C411yescharacteristic, complemented
21C2×#13063306C411yescharacteristic, complemented
22C2×#13063302C2211yescharacteristic
23C2×#13063297C411yescharacteristic, complemented
24C2×#13063297C2211yescharacteristic
25C2×#13063296C411yescharacteristic, complemented
26C2×#13063294C2211yescharacteristic
27C2×D4×Dic43C2211yescharacteristic
28C2×(C22⋊D43)⋊C4C2211yescharacteristic
29C22×C22⋊Dic43C2211yescharacteristic
30C22×C22⋊Dic43C2211yescharacteristic
31C2×#13063240C2212yes—
32C2×#13063239C2212yes—
33C2×#13063239C2212yes—
34#14582793—22no—
35#14582787—22no—
36#14582757C2212yes—
37#14582755C2211yescharacteristic
38C22⋊C4×Dic43—22no—
39C22⋊C4×Dic43C2212yes—
40C22⋊C4×Dic43C2212yes—
41C22⋊C4×Dic43C2212yes—
42C4×C22⋊Dic43—22no—
43#14582666C2212yes—
44#14582665C2212yes—
45#14582665C2212yes—
46C2×#120×C43C2211yescharacteristic
47C22×C22⋊C4×C43C2211yescharacteristic
48C2×#99×C43C2212yes—
49C43×#379C2211yescharacteristic
50C43×#342C2212yes—
51C22×Dic86C2×C411yescharacteristic, complemented
52C22×C22⋊D43C2×C411yescharacteristic
53C22×C22⋊D43C2×C411yescharacteristic
54C22×C22⋊D43C2×C411yescharacteristic, complemented
55C22×C22⋊D43C2311yescharacteristic
56C23×Dic43—21no—
57C23×Dic43C2×C411yescharacteristic, complemented
58C23×Dic43C2311yescharacteristic
59C23×Dic43C2311yescharacteristic
60C22×C4×D43C2×C411yescharacteristic, complemented
61#13063318—22no—
62#13063318—22no—
63#13063318—22no—
64#13063318—22no—
65#13063312—22no—
66#13063312—22no—
67#13063311—22no—
68#13063311—22no—
69#13063307—22no—
70#13063307—22no—
71#13063306—22no—
72#13063306—22no—
73#13063302—22no—
74#13063302—22no—
75#13063297—22no—
76#13063297—22no—
77#13063297—22no—
78#13063297—22no—
79#13063296—22no—
80#13063296—22no—
81#13063294—21no—
82#13063294—21no—
83#13063294—21no—
84#13063294—21no—
85D4×Dic43—22no—
86D4×Dic43—22no—
87(C22⋊D43)⋊C4—22no—
88(C22⋊D43)⋊C4—22no—
89C2×C4⋊Dic43C2×C411yescharacteristic, complemented
90C2×C4⋊Dic43C2×C411yescharacteristic, complemented
91C2×Dic43⋊C4—22no—
92C2×Dic43⋊C4C2×C411yescharacteristic, complemented
93C2×Dic43⋊C4C2×C411yescharacteristic, complemented
94C2×Dic43⋊C4C2×C411yescharacteristic, complemented
95C2×Dic43⋊C4C2×C411yescharacteristic, complemented
96C2×C22⋊Dic43—21no—
97C2×C22⋊Dic43—24no—
98C2×C22⋊Dic43—21no—
99C2×C22⋊Dic43—21no—
100C2×C22⋊Dic43C2×C411yescharacteristic
101C2×C22⋊Dic43C2×C411yescharacteristic
102C2×C22⋊Dic43C2×C411yescharacteristic
103C2×C22⋊Dic43C2×C411yescharacteristic
104C2×C22⋊Dic43C2×C411yescharacteristic
105C2×C22⋊Dic43C2×C411yescharacteristic
106C2×C22⋊Dic43C2×C411yescharacteristic, complemented
107C2×C22⋊Dic43C2×C411yescharacteristic, complemented
108C2×C22⋊Dic43D412yes—
109C2×C22⋊Dic43D412yes—
110C2×C22⋊Dic43D412yes—
111C2×C22⋊Dic43D412yes—
112C2×C22⋊Dic43C2312yes—
113C2×C22⋊Dic43C2311yescharacteristic
114C2×C22⋊Dic43C2312yes—
115C2×(C2×D43)⋊C4C2×C411yescharacteristic, complemented
116C2×(C2×D43)⋊C4C2×C411yescharacteristic, complemented
117C2×C4×Dic43—22no—
118C2×C4×Dic43—22no—
119C2×C4×Dic43—22no—
120C2×C4×Dic43C2×C411yescharacteristic, complemented
121C2×C4×Dic43C2×C411yescharacteristic, complemented
122#13063240—24no—
123#13063239—24no—
124#13063239—24no—
125C43⋊#95—22no—
126C43⋊#95—22no—
127C43⋊#95—22no—
128C43⋊#95—22no—
129C25×C43C2311yescharacteristic
130C22×D4×C43C2×C411yescharacteristic
131C22×D4×C43C2×C411yescharacteristic
132C22×D4×C43C2311yescharacteristic
133C23×C4×C43—21no—
134#120×C43—21no—
135#120×C43—21no—
136#120×C43—21no—
137#120×C43—21no—
138C2×C22⋊C4×C43—21no—
139C2×C22⋊C4×C43—24no—
140C2×C22⋊C4×C43—21no—
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43C2×C411yescharacteristic
143C2×C22⋊C4×C43C2×C411yescharacteristic
144C2×C22⋊C4×C43C2312yes—
145C2×C22⋊C4×C43C2311yescharacteristic
146C2×C22⋊C4×C43C2312yes—
147#99×C43—24no—
148C24×C43—22no—
149C24×C43—22no—
150C24×C43—81no—
151C24×C43—81no—
152C24×C43C22×C411yescharacteristic
153C24×C43C22×C411yescharacteristic
154C24×C43C22×C411yescharacteristic
155C24×C43C2×D411yescharacteristic
156C24×C43C2×D411yescharacteristic
157C24×C43C2×D411yescharacteristic
158C24×C43C2×D411yescharacteristic
159C24×C43C2411yescharacteristic
160C23×D43C22×C411yescharacteristic
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—22no—
168C2×D4×C43—22no—
169C2×D4×C43—81no—
170C2×D4×C43—81no—
171C22×C4×C43—24no—
172C22×C4×C43—22no—
173C22×C4×C43—22no—
174C22×C4×C43—81no—
175C22×C4×C43—81no—
176C22×C4×C43C22×C411yescharacteristic
177C22×C4×C43C22×C411yescharacteristic
178C22×C4×C43C22×C411yescharacteristic
179C2×C22⋊D43—22no—
180C2×C22⋊D43—21no—
181C2×C22⋊D43—21no—
182C2×C22⋊D43—21no—
183C2×C22⋊D43—21no—
184C2×C22⋊D43—21no—
185C2×C22⋊D43—21no—
186C2×C22⋊D43—22no—
187C2×C22⋊D43—22no—
188C2×C22⋊D43—81no—
189C2×C22⋊D43—81no—
190C2×C22⋊D43—81no—
191C22×Dic43—24no—
192C22×Dic43—22no—
193C22×Dic43—22no—
194C22×Dic43—22no—
195C22×Dic43—81no—
196C22×Dic43—81no—
197C22×Dic43—81no—
198C22×Dic43—81no—
199C22×Dic43—81no—
200C22×Dic43C22×C411yescharacteristic
201C22×Dic43C22×C411yescharacteristic
202C22×Dic43C22×C411yescharacteristic
203C22×Dic43C22×C411yescharacteristic
204C22×Dic43C22×C411yescharacteristic
205C22×Dic43C22×C411yescharacteristic
206C22×Dic43C22×C411yescharacteristic
207C22×Dic43C2×D412yes—
208C22×Dic43C2×D412yes—
209C22×Dic43C2×D412yes—
210C22×Dic43C2×D412yes—
211C2×C4×D43—22no—
212C2×C4×D43—81no—
213C2×Dic86—22no—
214C2×Dic86—81no—
215C22⋊C4×C43—24no—
216C22⋊C4×C43—21no—
217C22⋊C4×C43—21no—
218C22⋊C4×C43—21no—
219C22⋊C4×C43—21no—
220C22⋊C4×C43—21no—
221C22⋊C4×C43—21no—
222C22⋊C4×C43—22no—
223C22⋊C4×C43—22no—
224C22⋊C4×C43—22no—
225C22⋊C4×C43—81no—
226C22⋊C4×C43—81no—
227C22⋊C4×C43#4114yes—
228C22⋊Dic43—24no—
229C22⋊Dic43—22no—
230C22⋊Dic43—22no—
231C22⋊Dic43—21no—
232C22⋊Dic43—21no—
233C22⋊Dic43—21no—
234C22⋊Dic43—21no—
235C22⋊Dic43—21no—
236C22⋊Dic43—21no—
237C22⋊Dic43—22no—
238C22⋊Dic43—22no—
239C22⋊Dic43—22no—
240C22⋊Dic43—81no—
241C22⋊Dic43—81no—
242C22⋊Dic43C22⋊C412yes—
243C22⋊Dic43C22⋊C412yes—
244C22⋊Dic43C22⋊C412yes—
245C22⋊Dic43C22⋊C412yes—
246C22⋊Dic43C22⋊C412yes—
247C22⋊Dic43C22⋊C412yes—
248C22⋊Dic43C22⋊C412yes—
249C22⋊Dic43C22⋊C412yes—
250C22⋊Dic43#4114yes—
251(C2×D43)⋊C4—22no—
252(C2×D43)⋊C4—22no—
253C4⋊Dic43—22no—
254C4⋊Dic43—22no—
255Dic43⋊C4—22no—
256Dic43⋊C4—22no—
257Dic43⋊C4—22no—
258Dic43⋊C4—22no—
259Dic43⋊C4—82no—
260C4×Dic43—22no—
261C4×Dic43—22no—
262C4×Dic43—82no—
263C4×Dic43—82no—
264C4×Dic43—82no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—21no—
269C23×C43—22no—
270C23×C43—22no—
271C23×C43—22no—
272C23×C43—22no—
273C23×C43—21no—
274C23×C43—22no—
275C23×C43—41no—
276C23×C43—41no—
277C23×C43—41no—
278C23×C43—41no—
279C23×C43—41no—
280C23×C43—41no—
281C23×C43—41no—
282C23×C43—41no—
283C23×C43—41no—
284C23×C43—41no—
285C23×C43—41no—
286C23×C43—41no—
287C23×C43—41no—
288C23×C43—41no—
289C23×C43—41no—
290C23×C43—41no—
291C23×C43—84no—
292C23×C43—84no—
293C23×C43C2×C22⋊C411yescharacteristic
294C23×C43C2×C22⋊C411yescharacteristic
295C23×C43C2×C22⋊C411yescharacteristic
296C23×C43C2×C22⋊C411yescharacteristic
297C23×C43C23×C411yescharacteristic
298C23×C43C22×D411yescharacteristic
299C23×C43C22×D411yescharacteristic
300C23×C43C2×#4112yes—
301C23×C43C2×#4112yes—
302C22×D43—21no—
303C22×D43—22no—
304C22×D43—41no—
305C22×D43—41no—
306D4×C43—41no—
307D4×C43—41no—
308D4×C43—42no—
309D4×C43—81no—
310D4×C43—81no—
311D4×C43—81no—
312D4×C43—81no—
313C2×C4×C43—21no—
314C2×C4×C43—21no—
315C2×C4×C43—21no—
316C2×C4×C43—22no—
317C2×C4×C43—24no—
318C2×C4×C43—42no—
319C2×C4×C43—42no—
320C2×C4×C43—41no—
321C2×C4×C43—41no—
322C2×C4×C43—42no—
323C2×C4×C43—42no—
324C2×C4×C43—42no—
325C2×C4×C43—84no—
326C22⋊D43—41no—
327C22⋊D43—41no—
328C22⋊D43—42no—
329C22⋊D43—82no—
330C22⋊D43—81no—
331C22⋊D43—81no—
332C22⋊D43—81no—
333C22⋊D43—81no—
334C2×Dic43—21no—
335C2×Dic43—21no—
336C2×Dic43—21no—
337C2×Dic43—22no—
338C2×Dic43—24no—
339C2×Dic43—42no—
340C2×Dic43—42no—
341C2×Dic43—42no—
342C2×Dic43—42no—
343C2×Dic43—41no—
344C2×Dic43—41no—
345C2×Dic43—41no—
346C2×Dic43—41no—
347C2×Dic43—42no—
348C2×Dic43—42no—
349C2×Dic43—41no—
350C2×Dic43—41no—
351C2×Dic43—42no—
352C2×Dic43—42no—
353C2×Dic43—42no—
354C2×Dic43—82no—
355C2×Dic43—84no—
356C2×Dic43C2×C22⋊C412yes—
357C2×Dic43C2×C22⋊C412yes—
358C2×Dic43C2×C22⋊C412yes—
359C2×Dic43C2×C22⋊C412yes—
360C4×D43—82no—
361Dic86—82no—
362#21422—431nomaximal, Sylow
363C22×C43—21no—
364C22×C43—21no—
365C22×C43—21no—
366C22×C43—21no—
367C22×C43—21no—
368C22×C43—21no—
369C22×C43—21no—
370C22×C43—21no—
371C22×C43—21no—
372C22×C43—21no—
373C22×C43—21no—
374C22×C43—21no—
375C22×C43—21no—
376C22×C43—21no—
377C22×C43—21no—
378C22×C43—21no—
379C22×C43—21no—
380C22×C43—21no—
381C22×C43—42no—
382C22×C43—42no—
383C22×C43—42no—
384C22×C43—42no—
385C22×C43—42no—
386C22×C43—42no—
387C22×C43—41no—
388C22×C43—41no—
389C22×C43—41no—
390C22×C43—82no—
391C22×C43—82no—
392C22×C43—82no—
393C22×C43—82no—
394C22×C43—82no—
395C22×C43C22×C22⋊C411yescharacteristic
396C22×C43C4×#4112yes—
397C22×C43#52511yescharacteristic
398C22×C43#52511yescharacteristic
399C22×C43#53212yes—
400C2×D43—41no—
401C2×D43—41no—
402C2×D43—41no—
403C2×D43—82no—
404C4×C43—44no—
405C4×C43—41no—
406C4×C43—41no—
407C4×C43—41no—
408C4×C43—82no—
409Dic43—22no—
410Dic43—22no—
411Dic43—22no—
412Dic43—22no—
413Dic43—44no—
414Dic43—41no—
415Dic43—41no—
416Dic43—41no—
417Dic43—82no—
418C2×#538—431no—
419#2312—431no—
420#2273—431no—
421#1996—432no—
422#1964—432no—
423#1898—431no—
424#1898—431no—
425#1898—431no—
426#1898D4311yescharacteristic, complemented
427C4×#99—432no—
428C4×#99—432no—
429C2×C43—21no—
430C2×C43—22no—
431C2×C43—21no—
432C2×C43—22no—
433C2×C43—41no—
434C2×C43—41no—
435C2×C43—41no—
436C2×C43—41no—
437C2×C43—81no—
438C2×C43#229711yescharacteristic
439C2×C43#288311yescharacteristic
440C2×C43#288311yescharacteristic
441D43—81no—
442#538—862no—
443#538—862no—
444#538—862no—
445#538—862no—
446C2×#126—431no—
447C2×#126—431no—
448C2×#124—431no—
449C2×#124—431no—
450C2×#123—431no—
451C2×#123—431no—
452C2×C22⋊Q8—431no—
453C2×#121—431no—
454C2×#121—431no—
455C2×#121—431no—
456C2×#120—431no—
457C2×#120C2×D4311yescharacteristic
458C2×C4×D4—431no—
459C2×C4×D4—431no—
460C22×C22⋊C4—431no—
461C22×C22⋊C4—431no—
462C22×C22⋊C4C2×D4311yescharacteristic
463C2×#99—432no—
464C2×#99—432no—
465C2×#99—432no—
466C2×#99C2×D4312yes—
467#388—862no—
468#388—862no—
469#380—432no—
470#379—431no—
471#379C2×D4311yescharacteristic
472C4×C22⋊C4—432no—
473C4×C22⋊C4—432no—
474C4×C22⋊C4—432no—
475C4×C22⋊C4—862no—
476C4×C22⋊C4—862no—
477#342—432no—
478#342—432no—
479#342—432no—
480#342C2×D4312yes—
481C43#2142211yescharacteristic, complemented, Sylow
482C25C22×D4311yescharacteristic
483C22×Q8—431no—
484C22×D4—431no—
485C22×D4—431no—
486C22×D4—431no—
487C22×D4—431no—
488C22×D4C4×D4311yescharacteristic
489C22×D4C4×D4311yescharacteristic
490C22×D4C22×D4311yescharacteristic
491C23×C4—21no—
492C23×C4—431no—
493C23×C4—431no—
494C23×C4—431no—
495C23×C4—431no—
496C23×C4—861no—
497#126—862no—
498#126—862no—
499#126—862no—
500#126—862no—
501#124—862no—
502#124—862no—
503#124—862no—
504#124—862no—
505#123—862no—
506#123—862no—
507#123—862no—
508#123—862no—
509C22⋊Q8—862no—
510C22⋊Q8—862no—
511#121—862no—
512#121—862no—
513#121—862no—
514#121—862no—
515#121—862no—
516#121—862no—
517#120—21no—
518#120—21no—
519#120—21no—
520#120—21no—
521#120—861no—
522#120—861no—
523#120—861no—
524#120—861no—
525C4×D4—862no—
526C4×D4—862no—
527C4×D4—862no—
528C4×D4—862no—
529C2×C4⋊C4—431no—
530C2×C4⋊C4—431no—
531C2×C4⋊C4—431no—
532C2×C4⋊C4—431no—
533C2×C4⋊C4—431no—
534C2×C4⋊C4—431no—
535C2×C4⋊C4—862no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—431no—
541C2×C22⋊C4—431no—
542C2×C22⋊C4—431no—
543C2×C22⋊C4—431no—
544C2×C22⋊C4—432no—
545C2×C22⋊C4—432no—
546C2×C22⋊C4—432no—
547C2×C22⋊C4—432no—
548C2×C22⋊C4—432no—
549C2×C22⋊C4—431no—
550C2×C22⋊C4—431no—
551C2×C22⋊C4—431no—
552C2×C22⋊C4—431no—
553C2×C22⋊C4—431no—
554C2×C22⋊C4—431no—
555C2×C22⋊C4—431no—
556C2×C22⋊C4—432no—
557C2×C22⋊C4—864no—
558C2×C22⋊C4—861no—
559C2×C22⋊C4—861no—
560C2×C22⋊C4—861no—
561C2×C22⋊C4C4×D4311yescharacteristic
562C2×C22⋊C4C4×D4311yescharacteristic
563C2×C22⋊C4C22×D4312yes—
564C2×C22⋊C4C22×D4311yescharacteristic
565C2×C22⋊C4C22×D4312yes—
566C2×C42—431no—
567C2×C42—431no—
568C2×C42—862no—
569C2×C42—862no—
570C2×C42—862no—
571#99—24no—
572#99—864no—
573#99—864no—
574#99—864no—
575#95—862no—
576#95—862no—
577#95—862no—
578#95—862no—
579C24—22no—
580C24—22no—
581C24—81no—
582C24—81no—
583C24—431no—
584C24C2×C4×D4311yescharacteristic
585C24C2×C4×D4311yescharacteristic
586C24C2×C4×D4311yescharacteristic
587C24D4×D4311yescharacteristic
588C24D4×D4311yescharacteristic
589C24D4×D4311yescharacteristic
590C24D4×D4311yescharacteristic
591C24C23×D4311yescharacteristic
592C2×Q8—862no—
593C2×Q8—3441no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—81no—
603C2×D4—81no—
604C2×D4—862no—
605C2×D4—861no—
606C2×D4—861no—
607C2×D4—861no—
608C2×D4—861no—
609C2×D4—861no—
610C2×D4—861no—
611C2×D4—862no—
612C2×D4—862no—
613C2×D4—3441no—
614C2×D4—3441no—
615C2×D4—3441no—
616C22×C4—22no—
617C22×C4—24no—
618C22×C4—22no—
619C22×C4—81no—
620C22×C4—81no—
621C22×C4—431no—
622C22×C4—431no—
623C22×C4—431no—
624C22×C4—431no—
625C22×C4—432no—
626C22×C4—432no—
627C22×C4—432no—
628C22×C4—432no—
629C22×C4—431no—
630C22×C4—431no—
631C22×C4—431no—
632C22×C4—862no—
633C22×C4—862no—
634C22×C4—864no—
635C22×C4—862no—
636C22×C4—862no—
637C22×C4—3441no—
638C22×C4—3441no—
639C22×C4—3441no—
640C22×C4—3441no—
641C22×C4—3441no—
642C22×C4—3441no—
643C22×C4C2×C4×D4311yescharacteristic
644C22×C4C2×C4×D4311yescharacteristic
645C22×C4C2×C4×D4311yescharacteristic
646C4⋊C4—862no—
647C4⋊C4—862no—
648C4⋊C4—862no—
649C4⋊C4—862no—
650C4⋊C4—862no—
651C4⋊C4—862no—
652C4⋊C4—3442no—
653C22⋊C4—24no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—81no—
664C22⋊C4—81no—
665C22⋊C4—432no—
666C22⋊C4—432no—
667C22⋊C4—432no—
668C22⋊C4—432no—
669C22⋊C4—432no—
670C22⋊C4—432no—
671C22⋊C4—432no—
672C22⋊C4—432no—
673C22⋊C4—434no—
674C22⋊C4—862no—
675C22⋊C4—862no—
676C22⋊C4—862no—
677C22⋊C4—862no—
678C22⋊C4—864no—
679C22⋊C4—861no—
680C22⋊C4—861no—
681C22⋊C4—861no—
682C22⋊C4—861no—
683C22⋊C4—861no—
684C22⋊C4—861no—
685C22⋊C4—862no—
686C22⋊C4—862no—
687C22⋊C4—862no—
688C22⋊C4—3441no—
689C22⋊C4—3441no—
690C22⋊C4#1062190014yes—
691C42—862no—
692C42—862no—
693C42—3442no—
694C42—3442no—
695C42—3442no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—21no—
705C23—22no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—84no—
723C23—84no—
724C23—862no—
725C23—861no—
726C23—1721no—
727C23—1721no—
728C23C22⋊C4×D4311yescharacteristic
729C23C22⋊C4×D4311yescharacteristic
730C23C22⋊C4×D4311yescharacteristic
731C23C22⋊C4×D4311yescharacteristic
732C23C22×C4×D4311yescharacteristic
733C23C2×D4×D4311yescharacteristic
734C23C2×D4×D4311yescharacteristic
735C23#41×D4312yes—
736C23C2×#1062190012yes—
737Q8—3442no—
738D4—41no—
739D4—41no—
740D4—42no—
741D4—81no—
742D4—81no—
743D4—81no—
744D4—81no—
745D4—3442no—
746D4—3441no—
747D4—3441no—
748D4—3441no—
749D4—3441no—
750D4—1721no—
751D4—1721no—
752D4—1722no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—24no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—84no—
766C2×C4—432no—
767C2×C4—432no—
768C2×C4—432no—
769C2×C4—432no—
770C2×C4—861no—
771C2×C4—861no—
772C2×C4—861no—
773C2×C4—862no—
774C2×C4—864no—
775C2×C4—3442no—
776C2×C4—3442no—
777C2×C4—3444no—
778C2×C4—1722no—
779C2×C4—1722no—
780C2×C4—1722no—
781C2×C4—1722no—
782C2×C4—1721no—
783C2×C4—1721no—
784C2×C4—1721no—
785C2×C4—1721no—
786C2×C4—1722no—
787C2×C4—1722no—
788C2×C4—1722no—
789C2×C4—1722no—
790C2×C4—1722no—
791C2×C4—1721no—
792C2×C4—1721no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—82no—
821C22—82no—
822C22—82no—
823C22—82no—
824C22—82no—
825C22—3442no—
826C22—1721no—
827C22—1721no—
828C22—1721no—
829C22C2×C22⋊C4×D4311yescharacteristic
830C22C4×#1062190012yes—
831C22#1458340511yescharacteristic
832C22#1458340711yescharacteristic
833C22#1458344412yes—
834C4—44no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—82no—
839C4—862no—
840C4—862no—
841C4—862no—
842C4—862no—
843C4—3442no—
844C4—1724no—
845C4—1721no—
846C4—1721no—
847C4—1721no—
848C2—21no—
849C2—22no—
850C2—21no—
851C2—22no—
852C2—41no—
853C2—41no—
854C2—41no—
855C2—41no—
856C2—81no—
857C2—3441no—
858C2#1913708011yescharacteristic
859C2#1914305311yescharacteristic
860C2#1914305311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#1898C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583484C2
cosocleC24×C43C24
hypercenter#1898D43
hypocenterC43#21422
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C25 ◁ #1898

Complements

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

NH ≅ G/Ntype
2. #19137191C2semidirect
3. #19136948C2semidirect
4. #19135578C2semidirect
5. #19135429C2semidirect
6. #19135049C2semidirect
7. #19135048C2semidirect
8. #19135046C2semidirect
9. #99×Dic43C2semidirect
10. #19134382C2semidirect
11. C43×#1898C2semidirect
16. C2×#13063318C4semidirect
17. C2×#13063318C4semidirect
18. C2×#13063312C4semidirect
19. C2×#13063311C4semidirect
20. C2×#13063307C4semidirect
21. C2×#13063306C4semidirect
23. C2×#13063297C4semidirect
25. C2×#13063296C4semidirect
51. C22×Dic86C2×C4semidirect
54. C22×C22⋊D43C2×C4semidirect
57. C23×Dic43C2×C4semidirect
60. C22×C4×D43C2×C4semidirect
89. C2×C4⋊Dic43C2×C4semidirect
90. C2×C4⋊Dic43C2×C4semidirect
92. C2×Dic43⋊C4C2×C4semidirect
93. C2×Dic43⋊C4C2×C4semidirect
94. C2×Dic43⋊C4C2×C4semidirect
95. C2×Dic43⋊C4C2×C4semidirect
106. C2×C22⋊Dic43C2×C4semidirect
107. C2×C22⋊Dic43C2×C4semidirect
115. C2×(C2×D43)⋊C4C2×C4semidirect
116. C2×(C2×D43)⋊C4C2×C4semidirect
120. C2×C4×Dic43C2×C4semidirect
121. C2×C4×Dic43C2×C4semidirect
426. #1898D43semidirect
481. C43#21422semidirect

Maximal subgroups

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

subgroupindex
C2×#145834842
#191371912
#191369482
#191355782
#191354292
#191350492
#191350482
#191350462
#99×Dic432
#191343822
C43×#18982
#2142243