Finite Group Databasebeta

← #25003104

Subgroups — #25003104

Order 11008.

1922 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063300C211yesmaximal, characteristic
2C22×#13063247C211yesmaximal, characteristic, complemented
3C22×#13063245C211yesmaximal, characteristic, complemented
4C22×(C2×D43)⋊C8C211yesmaximal, characteristic, complemented
5C2×#14582756C211yesmaximal, characteristic, complemented
6C2×#14582661C211yesmaximal, characteristic, complemented
7C2×C43×#340C211yesmaximal, characteristic, complemented
8C23×D172—21no—
9C23×D172C2211yescharacteristic
10C23×C4×D43C2211yescharacteristic
11C23×C43⋊C8C2211yescharacteristic
12C2×#13063300—22no—
13C2×#13063300—22no—
14C2×#13063300—22no—
15C2×#13063300—22no—
16C2×#13063300—22no—
17C2×#13063300C414yescomplemented
18C22×C4⋊Dic43C2211yescharacteristic
19C22×(C2×D43)⋊C4—21no—
20C22×(C2×D43)⋊C4—21no—
21C2×#13063247—22no—
22C2×#13063247—22no—
23C2×#13063247—22no—
24C2×#13063245—22no—
25C2×#13063245—22no—
26C2×#13063245—22no—
27C2×(C2×D43)⋊C8—22no—
28C2×(C2×D43)⋊C8—22no—
29C2×(C2×D43)⋊C8—22no—
30#14582756—22no—
31#14582756—22no—
32C2×C43⋊#95—21no—
33#14582661—22no—
34C23×C8×C43C2211yescharacteristic
35C22×C4⋊C4×C43C2211yescharacteristic
36C22×C4⋊C4×C43C2211yescharacteristic
37C43×#340—22no—
38C24×D43—21no—
39C24×D43D411yescharacteristic
40C22×D172—21no—
41C22×D172—21no—
42C22×D172—21no—
43C22×D172—21no—
44C22×D172—21no—
45C22×D172—21no—
46C22×D172—21no—
47C22×D172—21no—
48C22×D172—24no—
49C22×D172—24no—
50C22×D172—24no—
51C22×D172—21no—
52C22×D172—21no—
53C22×D172—21no—
54C22×D172—42no—
55C22×D172—42no—
56C22×D172—42no—
57C22×D172—42no—
58C22×D172C2×C412yes—
59C22×D172D412yes—
60C22×D172D412yes—
61C23×Dic43—21no—
62C23×Dic43D411yescharacteristic
63C22×C4×D43—21no—
64C22×C4×D43—21no—
65C22×C4×D43—21no—
66C22×C4×D43—21no—
67C22×C4×D43—21no—
68C22×C4×D43—21no—
69C22×C4×D43—21no—
70C22×C4×D43—21no—
71C22×C4×D43—21no—
72C22×C4×D43—21no—
73C22×C4×D43—21no—
74C22×C4×D43—21no—
75C22×C4×D43C2×C412yes—
76C22×C4×D43D412yes—
77C22×C43⋊C8—21no—
78C22×C43⋊C8—21no—
79C22×C43⋊C8—21no—
80C22×C43⋊C8—21no—
81C22×C43⋊C8—21no—
82C22×C43⋊C8—21no—
83C22×C43⋊C8D412yescomplemented
84#13063300—28no—
85#13063300—28no—
86#13063300—28no—
87#13063300—28no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43D412yescomplemented
94C2×(C2×D43)⋊C4—24no—
95C2×(C2×D43)⋊C4—24no—
96C2×(C2×D43)⋊C4—24no—
97C2×(C2×D43)⋊C4—24no—
98C2×(C2×D43)⋊C4—42no—
99C2×(C2×D43)⋊C4—42no—
100#13063247—28no—
101#13063245—28no—
102(C2×D43)⋊C8—28no—
103C43⋊#95—24no—
104C23×C4×C43—21no—
105C23×C4×C43—21no—
106C23×C4×C43C2311yescharacteristic
107C22×C8×C43—21no—
108C22×C8×C43—21no—
109C22×C8×C43—21no—
110C22×C8×C43—21no—
111C22×C8×C43—21no—
112C22×C8×C43—21no—
113C22×C8×C43D412yescomplemented
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43—21no—
119C2×C4⋊C4×C43—21no—
120C2×C4⋊C4×C43—21no—
121C2×C4⋊C4×C43—21no—
122C2×C4⋊C4×C43C2×C412yes—
123C2×C4⋊C4×C43D412yes—
124C2×C4⋊C4×C43D412yes—
125C2×C4⋊C4×C43D412yescomplemented
126C24×C43C2×D411yescharacteristic
127C23×D43—21no—
128C23×D43—21no—
129C23×D43—21no—
130C23×D43—21no—
131C23×D43—21no—
132C23×D43—21no—
133C23×D43—21no—
134C23×D43—21no—
135C23×D43—21no—
136C23×D43—21no—
137C23×D43—21no—
138C23×D43—21no—
139C23×D43—22no—
140C23×D43—22no—
141C23×D43—22no—
142C23×D43—41no—
143C23×D43—41no—
144C23×D43—41no—
145C23×D43—41no—
146C23×D43—41no—
147C23×D43—41no—
148C23×D43—41no—
149C23×D43—41no—
150C23×D43—41no—
151C23×D43—41no—
152C23×D43—41no—
153C23×D43—41no—
154C23×D43C22⋊C412yes—
155C23×D43D812yes—
156C23×D43SD1612yes—
157C22×C4×C43—22no—
158C22×C4×C43—22no—
159C22×C4×C43—22no—
160C22×C4×C43—22no—
161C22×C4×C43—41no—
162C22×C4×C43—41no—
163C22×C4×C43—41no—
164C22×C4×C43—41no—
165C22×C4×C43—41no—
166C22×C4×C43—41no—
167C22×C4×C43—41no—
168C22×C4×C43—41no—
169C22×C4×C43—41no—
170C22×C4×C43—41no—
171C22×C4×C43C22×C411yescharacteristic
172C22×C4×C43C2×D411yescharacteristic
173C22×C4×C43C2×D411yescharacteristic
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43#4111yescharacteristic
182C22×C4×C43#4111yescharacteristic
183C22×C4×C43#4111yescharacteristic
184C22×C4×C43#4111yescharacteristic
185C22×Dic43—21no—
186C22×Dic43—21no—
187C22×Dic43—21no—
188C22×Dic43—22no—
189C22×Dic43—21no—
190C22×Dic43—21no—
191C22×Dic43—21no—
192C22×Dic43—41no—
193C22×Dic43—41no—
194C22×Dic43—41no—
195C22×Dic43—41no—
196C22×Dic43—41no—
197C22×Dic43—41no—
198C22×Dic43C22⋊C412yes—
199C2×D172—216no—
200C2×D172—22no—
201C2×D172—22no—
202C2×D172—22no—
203C2×D172—22no—
204C2×D172—22no—
205C2×D172—22no—
206C2×D172—22no—
207C2×D172—22no—
208C2×D172—22no—
209C2×D172—22no—
210C2×D172—22no—
211C2×D172—22no—
212C2×D172—22no—
213C2×D172—22no—
214C2×D172—22no—
215C2×D172—48no—
216C2×D172—48no—
217C2×D172—48no—
218C2×D172—48no—
219C2×D172—48no—
220C2×D172—41no—
221C2×D172—41no—
222C2×D172—41no—
223C2×D172—41no—
224C2×D172—41no—
225C2×D172—41no—
226C2×D172—41no—
227C2×D172—41no—
228C2×D172—41no—
229C2×D172—41no—
230C2×D172—41no—
231C2×D172—41no—
232C2×D172—48no—
233C2×D172C22⋊C414yescomplemented
234C2×C4×D43—22no—
235C2×C4×D43—22no—
236C2×C4×D43—22no—
237C2×C4×D43—22no—
238C2×C4×D43—22no—
239C2×C4×D43—22no—
240C2×C4×D43—22no—
241C2×C4×D43—22no—
242C2×C4×D43—22no—
243C2×C4×D43—22no—
244C2×C4×D43—22no—
245C2×C4×D43—22no—
246C2×C4×D43—41no—
247C2×C4×D43—41no—
248C2×C4×D43—41no—
249C2×C4×D43—41no—
250C2×C4×D43—41no—
251C2×C4×D43—41no—
252C2×C4×D43—41no—
253C2×C4×D43—41no—
254C2×C4×D43—41no—
255C2×C4×D43—41no—
256C2×C4×D43—41no—
257C2×C4×D43—41no—
258C2×C4×D43—41no—
259C2×C4×D43—41no—
260C2×C4×D43—41no—
261C2×C4×D43—41no—
262C2×C8×C43—22no—
263C2×C8×C43—22no—
264C2×C8×C43—22no—
265C2×C8×C43—41no—
266C2×C8×C43—41no—
267C2×C8×C43—41no—
268C2×C8×C43—41no—
269C4⋊C4×C43—22no—
270C4⋊C4×C43—22no—
271C4⋊C4×C43—22no—
272C4⋊C4×C43—22no—
273C4⋊C4×C43—22no—
274C4⋊C4×C43—41no—
275C4⋊C4×C43—41no—
276C4⋊C4×C43C22⋊C414yescomplemented
277(C2×D43)⋊C4—216no—
278(C2×D43)⋊C4—48no—
279C4⋊Dic43—22no—
280C4⋊Dic43—22no—
281C4⋊Dic43—41no—
282C4⋊Dic43—41no—
283C2×C43⋊C8—22no—
284C2×C43⋊C8—22no—
285C2×C43⋊C8—22no—
286C2×C43⋊C8—41no—
287C2×C43⋊C8—41no—
288C2×C43⋊C8—41no—
289C2×C43⋊C8—41no—
290C23×C43C2×C22⋊C411yescharacteristic
291C23×C43#12011yescharacteristic
292C23×C43#12011yescharacteristic
293C23×C43#12011yescharacteristic
294C23×C43#12111yescharacteristic
295C23×C43#12111yescharacteristic
296C23×C43#12311yescharacteristic
297C23×C43C2×D811yescharacteristic
298C23×C43C2×SD1611yescharacteristic
299C23×C43#13511yescharacteristic
300C23×C43#13511yescharacteristic
301C23×C43AGL(1,ℤ/8)11yescharacteristic
302C23×C43AGL(1,ℤ/8)11yescharacteristic
303C23×C43AGL(1,ℤ/8)11yescharacteristic
304C23×C43#13711yescharacteristic
305C22×D43—22no—
306C22×D43—22no—
307C22×D43—22no—
308C22×D43—22no—
309C22×D43—22no—
310C22×D43—22no—
311C22×D43—22no—
312C22×D43—22no—
313C22×D43—22no—
314C22×D43—22no—
315C22×D43—22no—
316C22×D43—22no—
317C22×D43—22no—
318C22×D43—22no—
319C22×D43—22no—
320C22×D43—22no—
321C22×D43—22no—
322C22×D43—22no—
323C22×D43—24no—
324C22×D43—41no—
325C22×D43—41no—
326C22×D43—41no—
327C22×D43—41no—
328C22×D43—41no—
329C22×D43—41no—
330C22×D43—41no—
331C22×D43—41no—
332C22×D43—41no—
333C22×D43—41no—
334C22×D43—41no—
335C22×D43—41no—
336C22×D43—41no—
337C22×D43—41no—
338C22×D43—41no—
339C22×D43—41no—
340C22×D43—42no—
341C22×D43—42no—
342C22×D43—42no—
343C22×D43—42no—
344C22×D43—42no—
345C22×D43—42no—
346C22×D43—42no—
347C22×D43—42no—
348C22×D43—42no—
349C22×D43—42no—
350C22×D43—42no—
351C22×D43—42no—
352C22×D43—42no—
353C22×D43—42no—
354C22×D43—42no—
355C22×D43—42no—
356C22×D43—42no—
357C22×D43—42no—
358C22×D43—81no—
359C22×D43—81no—
360C22×D43—81no—
361C22×D43—81no—
362C22×D43—81no—
363C22×D43—81no—
364C22×D43—81no—
365C22×D43—81no—
366C22×D43—81no—
367C22×D43—81no—
368C22×D43—81no—
369C22×D43—81no—
370C22×D43—81no—
371C22×D43—81no—
372C22×D43—81no—
373C22×D43—81no—
374C22×D43#10214yescomplemented
375C2×C4×C43—24no—
376C2×C4×C43—42no—
377C2×C4×C43—42no—
378C2×C4×C43—42no—
379C2×C4×C43—42no—
380C2×C4×C43—42no—
381C2×C4×C43—42no—
382C2×C4×C43—42no—
383C2×C4×C43—42no—
384C2×C4×C43—42no—
385C2×C4×C43—81no—
386C2×C4×C43—81no—
387C2×C4×C43—81no—
388C2×C4×C43—81no—
389C2×C4×C43C2×C22⋊C411yescharacteristic
390C2×C4×C43C2×C22⋊C411yescharacteristic
391C2×C4×C43C4×D411yescharacteristic
392C2×C4×C43C4×D411yescharacteristic
393C2×C4×C43C4×D411yescharacteristic
394C2×C4×C43C4×D411yescharacteristic
395C2×C4×C43#12011yescharacteristic
396C2×C4×C43#12011yescharacteristic
397C2×C4×C43#12011yescharacteristic
398C2×C4×C43#12011yescharacteristic
399C2×C4×C43#12011yescharacteristic
400C2×C4×C43#12111yescharacteristic
401C2×C4×C43#12111yescharacteristic
402C2×C4×C43#12111yescharacteristic
403C2×C4×C43#12111yescharacteristic
404C2×C4×C43#12111yescharacteristic
405C2×C4×C43#12111yescharacteristic
406C2×C4×C43#12111yescharacteristic
407C2×C4×C43#12111yescharacteristic
408C2×C4×C43#12111yescharacteristic
409C2×C4×C43#12111yescharacteristic
410C2×C4×C43#12311yescharacteristic
411C2×C4×C43#12311yescharacteristic
412C2×C4×C43#12311yescharacteristic
413C2×C4×C43#12411yescharacteristic
414C2×C4×C43#12411yescharacteristic
415C2×C4×C43#12711yescharacteristic
416C2×C4×C43#12711yescharacteristic
417C2×Dic43—22no—
418C2×Dic43—22no—
419C2×Dic43—22no—
420C2×Dic43—41no—
421C2×Dic43—41no—
422C2×Dic43—41no—
423C2×Dic43—41no—
424C2×Dic43—42no—
425C2×Dic43—42no—
426C2×Dic43—42no—
427C2×Dic43—81no—
428C2×Dic43—81no—
429C2×Dic43—81no—
430C2×Dic43—81no—
431D172—24no—
432D172—24no—
433D172—432no—
434D172—42no—
435D172—42no—
436D172—42no—
437D172—42no—
438D172—42no—
439D172—42no—
440C4×D43—42no—
441C4×D43—42no—
442C4×D43—42no—
443C4×D43—42no—
444C4×D43—42no—
445C4×D43—42no—
446C4×D43—42no—
447C4×D43—42no—
448C8×C43—42no—
449C43⋊C8—42no—
450#10969—431nomaximal, Sylow
451C22×C43#37911yescharacteristic
452C22×C43#38611yescharacteristic
453C22×C43#38611yescharacteristic
454C22×C43#39211yescharacteristic
455C22×C43#39211yescharacteristic
456C22×C43#39411yescharacteristic
457C22×C43#39411yescharacteristic
458C22×C43C2×#10211yescharacteristic
459C22×C43#41611yescharacteristic
460C22×C43#41711yescharacteristic
461C22×C43#41811yescharacteristic
462C22×C43#44711yescharacteristic
463C22×C43#44711yescharacteristic
464C22×C43#44711yescharacteristic
465C22×C43#44811yescharacteristic
466C22×C43#44911yescharacteristic
467C22×C43#44911yescharacteristic
468C22×C43#44911yescharacteristic
469C22×C43#44911yescharacteristic
470C22×C43#45011yescharacteristic
471C22×C43#45011yescharacteristic
472C22×C43#45211yescharacteristic
473C22×C43#45211yescharacteristic
474C22×C43#46511yescharacteristic
475C22×C43#46511yescharacteristic
476C22×C43#46611yescharacteristic
477C22×C43#46611yescharacteristic
478C22×C43#46811yescharacteristic
479C22×C43#46811yescharacteristic
480C22×C43#46911yescharacteristic
481C22×C43#46911yescharacteristic
482C22×C43#48011yescharacteristic
483C22×C43#48111yescharacteristic
484C22×C43#48211yescharacteristic
485C22×C43#48211yescharacteristic
486C2×D43—24no—
487C2×D43—24no—
488C2×D43—24no—
489C2×D43—42no—
490C2×D43—42no—
491C2×D43—42no—
492C2×D43—42no—
493C2×D43—42no—
494C2×D43—42no—
495C2×D43—42no—
496C2×D43—42no—
497C2×D43—42no—
498C2×D43—42no—
499C2×D43—42no—
500C2×D43—42no—
501C2×D43—44no—
502C2×D43—44no—
503C2×D43—44no—
504C2×D43—82no—
505C2×D43—82no—
506C2×D43—82no—
507C2×D43—82no—
508C2×D43—82no—
509C2×D43—82no—
510C2×D43—82no—
511C2×D43—82no—
512C2×D43—82no—
513C2×D43—82no—
514C2×D43—82no—
515C2×D43—82no—
516C4×C43—44no—
517C4×C43—82no—
518C4×C43#38611yescharacteristic
519C4×C43#38611yescharacteristic
520C4×C43#39011yescharacteristic
521C4×C43#39011yescharacteristic
522C4×C43#39211yescharacteristic
523C4×C43#39211yescharacteristic
524C4×C43#39411yescharacteristic
525C4×C43#39411yescharacteristic
526Dic43—42no—
527Dic43—82no—
528C22×#121—431no—
529C22×#102—431no—
530C22×#102—431no—
531C22×C22⋊C8—431no—
532C2×#380—431no—
533C2×#340—431no—
534C2×#340D4311yescharacteristic, complemented
535C2×C43#143811yescharacteristic
536C2×C43#178611yescharacteristic
537C2×C43#178811yescharacteristic
538C2×C43#187411yescharacteristic
539C2×C43#187511yescharacteristic
540C2×C43#189311yescharacteristic
541C2×C43#189511yescharacteristic
542C2×C43#199911yescharacteristic
543C2×C43#199911yescharacteristic
544C2×C43#200011yescharacteristic
545C2×C43#200011yescharacteristic
546C2×C43#203311yescharacteristic
547C2×C43#203311yescharacteristic
548C2×C43#203411yescharacteristic
549C2×C43#203411yescharacteristic
550D43—44no—
551D43—84no—
552C23×D4—431no—
553C23×D4—861no—
554C24×C4—431no—
555C23×C8—431no—
556C23×C8C2×D4311yescharacteristic
557C2×#121—434no—
558C2×#121—862no—
559C2×#121—862no—
560C2×#121—862no—
561C2×#121—862no—
562C2×#121—862no—
563C22×C4⋊C4—431no—
564C22×C4⋊C4C2×D4311yescharacteristic
565C22×C4⋊C4C2×D4311yescharacteristic
566C22×C22⋊C4—861no—
567C22×C22⋊C4—861no—
568C2×#102—862no—
569C2×#102—862no—
570C2×#102—862no—
571C2×#102—862no—
572C2×#102—862no—
573C2×#102—862no—
574C2×C22⋊C8—862no—
575C2×C22⋊C8—862no—
576C2×C22⋊C8—862no—
577#380—862no—
578#380—862no—
579C2×#95—861no—
580#340—22no—
581#340—862no—
582C43#1096911yescharacteristic, complemented, Sylow
583C25—431no—
584C25—861no—
585C22×D4—432no—
586C22×D4—432no—
587C22×D4—432no—
588C22×D4—864no—
589C22×D4—864no—
590C22×D4—864no—
591C22×D4—861no—
592C22×D4—861no—
593C22×D4—861no—
594C22×D4—861no—
595C22×D4—861no—
596C22×D4—861no—
597C22×D4—861no—
598C22×D4—861no—
599C22×D4—861no—
600C22×D4—861no—
601C22×D4—861no—
602C22×D4—1722no—
603C22×D4—1722no—
604C22×D4—1722no—
605C22×D4—1722no—
606C23×C4—21no—
607C23×C4—21no—
608C23×C4—431no—
609C23×C4—432no—
610C23×C4—432no—
611C23×C4—861no—
612C23×C4—861no—
613C23×C4—861no—
614C23×C4—861no—
615C23×C4—861no—
616C23×C4—861no—
617C23×C4—861no—
618C23×C4—861no—
619C23×C4—861no—
620C23×C4—861no—
621C23×C4—861no—
622C23×C4—861no—
623C23×C4—861no—
624C23×C4C22×D4311yescharacteristic
625C22×C8—21no—
626C22×C8—21no—
627C22×C8—21no—
628C22×C8—21no—
629C22×C8—21no—
630C22×C8—21no—
631C22×C8—432no—
632C22×C8—861no—
633C22×C8—861no—
634C22×C8—861no—
635C22×C8—861no—
636C22×C8—861no—
637C22×C8—861no—
638C22×C8D17212yescomplemented
639#121—868no—
640#121—868no—
641#121—868no—
642#121—868no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—432no—
652C2×C4⋊C4—861no—
653C2×C4⋊C4—861no—
654C2×C4⋊C4—861no—
655C2×C4⋊C4—861no—
656C2×C4⋊C4—861no—
657C2×C4⋊C4C4×D4312yes—
658C2×C4⋊C4D17212yes—
659C2×C4⋊C4D17212yescomplemented
660C2×C4⋊C4C22⋊D4312yes—
661C2×C22⋊C4—864no—
662C2×C22⋊C4—864no—
663C2×C22⋊C4—864no—
664C2×C22⋊C4—864no—
665C2×C22⋊C4—1722no—
666C2×C22⋊C4—1722no—
667#102—868no—
668#102—868no—
669C22⋊C8—868no—
670#95—864no—
671C24—432no—
672C24—432no—
673C24—432no—
674C24—861no—
675C24—861no—
676C24—861no—
677C24—861no—
678C24—861no—
679C24—861no—
680C24—861no—
681C24—861no—
682C24—861no—
683C24—861no—
684C24—861no—
685C24—861no—
686C24—862no—
687C24—862no—
688C24—862no—
689C24—1721no—
690C24—1721no—
691C24—1721no—
692C24—1721no—
693C24—1721no—
694C24—1721no—
695C24—1721no—
696C24—1721no—
697C24—1721no—
698C24—1721no—
699C24—1721no—
700C24—1721no—
701C24D4×D4311yescharacteristic
702C2×D4—434no—
703C2×D4—8616no—
704C2×D4—862no—
705C2×D4—862no—
706C2×D4—862no—
707C2×D4—862no—
708C2×D4—862no—
709C2×D4—862no—
710C2×D4—862no—
711C2×D4—862no—
712C2×D4—862no—
713C2×D4—862no—
714C2×D4—862no—
715C2×D4—862no—
716C2×D4—862no—
717C2×D4—862no—
718C2×D4—862no—
719C2×D4—1728no—
720C2×D4—1728no—
721C2×D4—1728no—
722C2×D4—1728no—
723C2×D4—1728no—
724C2×D4—1728no—
725C2×D4—1721no—
726C2×D4—1721no—
727C2×D4—1721no—
728C2×D4—1721no—
729C2×D4—1721no—
730C2×D4—1721no—
731C2×D4—1721no—
732C2×D4—1721no—
733C2×D4—1721no—
734C2×D4—1721no—
735C2×D4—1721no—
736C2×D4—1721no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—41no—
742C22×C4—41no—
743C22×C4—41no—
744C22×C4—41no—
745C22×C4—41no—
746C22×C4—41no—
747C22×C4—41no—
748C22×C4—41no—
749C22×C4—41no—
750C22×C4—41no—
751C22×C4—432no—
752C22×C4—861no—
753C22×C4—861no—
754C22×C4—861no—
755C22×C4—861no—
756C22×C4—861no—
757C22×C4—861no—
758C22×C4—862no—
759C22×C4—862no—
760C22×C4—862no—
761C22×C4—862no—
762C22×C4—862no—
763C22×C4—862no—
764C22×C4—862no—
765C22×C4—862no—
766C22×C4—862no—
767C22×C4—862no—
768C22×C4—862no—
769C22×C4—862no—
770C22×C4—862no—
771C22×C4—1721no—
772C22×C4—1721no—
773C22×C4—1721no—
774C22×C4—1721no—
775C22×C4—1721no—
776C22×C4—1721no—
777C22×C4—1721no—
778C22×C4—1721no—
779C22×C4—1721no—
780C22×C4—1721no—
781C22×C4—1721no—
782C22×C4—1721no—
783C22×C4—1721no—
784C22×C4—1721no—
785C22×C4—1721no—
786C22×C4—1721no—
787C22×C4—1721no—
788C22×C4—1721no—
789C22×C4—1721no—
790C22×C4—1721no—
791C22×C4—1721no—
792C22×C4—1721no—
793C22×C4C2×C4×D4311yescharacteristic
794C22×C4C2×D17211yescharacteristic
795C22×C4C2×D17211yescharacteristic
796C22×C4C2×D17211yescharacteristic
797C22×C4#1062189811yescharacteristic
798C22×C4#1062189811yescharacteristic
799C22×C4D4×D4311yescharacteristic
800C22×C4D4×D4311yescharacteristic
801C22×C4D4×D4311yescharacteristic
802C22×C4D4×D4311yescharacteristic
803C22×C4D4×D4311yescharacteristic
804C22×C4#1062190211yescharacteristic
805C22×C4#1062190211yescharacteristic
806C22×C4C2×C22⋊D4311yescharacteristic
807C2×C8—22no—
808C2×C8—22no—
809C2×C8—22no—
810C2×C8—41no—
811C2×C8—41no—
812C2×C8—41no—
813C2×C8—41no—
814C2×C8—862no—
815C2×C8—862no—
816C2×C8—862no—
817C2×C8—1721no—
818C2×C8—1721no—
819C2×C8—1721no—
820C2×C8—1721no—
821C4⋊C4—22no—
822C4⋊C4—22no—
823C4⋊C4—22no—
824C4⋊C4—22no—
825C4⋊C4—22no—
826C4⋊C4—41no—
827C4⋊C4—41no—
828C4⋊C4—862no—
829C4⋊C4—862no—
830C4⋊C4—1721no—
831C4⋊C4—1721no—
832C4⋊C4(C2×D43)⋊C414yescomplemented
833C22⋊C4—8616no—
834C22⋊C4—1728no—
835C23—434no—
836C23—862no—
837C23—862no—
838C23—862no—
839C23—862no—
840C23—862no—
841C23—862no—
842C23—862no—
843C23—862no—
844C23—862no—
845C23—862no—
846C23—862no—
847C23—862no—
848C23—862no—
849C23—862no—
850C23—862no—
851C23—862no—
852C23—862no—
853C23—862no—
854C23—864no—
855C23—3441no—
856C23—3441no—
857C23—3441no—
858C23—3441no—
859C23—3441no—
860C23—3441no—
861C23—3441no—
862C23—3441no—
863C23—3441no—
864C23—3441no—
865C23—3441no—
866C23—3441no—
867C23—3441no—
868C23—3441no—
869C23—3441no—
870C23—3441no—
871C23—1722no—
872C23—1722no—
873C23—1722no—
874C23—1722no—
875C23—1722no—
876C23—1722no—
877C23—1722no—
878C23—1722no—
879C23—1722no—
880C23—1722no—
881C23—1722no—
882C23—1722no—
883C23—1722no—
884C23—1722no—
885C23—1722no—
886C23—1722no—
887C23—1722no—
888C23—1722no—
889C23—1721no—
890C23—1721no—
891C23—1721no—
892C23—1721no—
893C23—1721no—
894C23—1721no—
895C23—1721no—
896C23—1721no—
897C23—1721no—
898C23—1721no—
899C23—1721no—
900C23—1721no—
901C23—1721no—
902C23—1721no—
903C23—1721no—
904C23—1721no—
905C23C22⋊C4×D4311yescharacteristic
906C23#1306329311yescharacteristic
907C23#1306329511yescharacteristic
908C23#1306329511yescharacteristic
909C23#1306329811yescharacteristic
910C23#1306330011yescharacteristic
911C23#1306331011yescharacteristic
912C23D8×D4311yescharacteristic
913C23SD16×D4311yescharacteristic
914C23#1306334611yescharacteristic
915C23#1306334811yescharacteristic
916C23#1306334911yescharacteristic
917C23#1306335211yescharacteristic
918C23#1306335211yescharacteristic
919C23#1306335711yescharacteristic
920D4—864no—
921D4—864no—
922D4—17232no—
923D4—1722no—
924D4—1722no—
925D4—1722no—
926D4—1722no—
927D4—1722no—
928D4—1722no—
929C2×C4—24no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—42no—
933C2×C4—42no—
934C2×C4—42no—
935C2×C4—42no—
936C2×C4—42no—
937C2×C4—42no—
938C2×C4—42no—
939C2×C4—81no—
940C2×C4—81no—
941C2×C4—81no—
942C2×C4—81no—
943C2×C4—862no—
944C2×C4—862no—
945C2×C4—862no—
946C2×C4—3441no—
947C2×C4—3441no—
948C2×C4—3441no—
949C2×C4—3441no—
950C2×C4—1722no—
951C2×C4—1722no—
952C2×C4—1722no—
953C2×C4—1721no—
954C2×C4—1721no—
955C2×C4—1721no—
956C2×C4—1721no—
957C2×C4—1722no—
958C2×C4—1722no—
959C2×C4—1722no—
960C2×C4—1722no—
961C2×C4—1722no—
962C2×C4—1722no—
963C2×C4—1722no—
964C2×C4—1722no—
965C2×C4C22⋊C4×D4311yescharacteristic
966C2×C4C2×(C2×D43)⋊C411yescharacteristic
967C2×C4#1306328711yescharacteristic
968C2×C4#1306328711yescharacteristic
969C2×C4C4×D17211yescharacteristic
970C2×C4C4×D17211yescharacteristic
971C2×C4#1306329311yescharacteristic
972C2×C4#1306329511yescharacteristic
973C2×C4#1306329511yescharacteristic
974C2×C4#1306329511yescharacteristic
975C2×C4#1306329511yescharacteristic
976C2×C4#1306329811yescharacteristic
977C2×C4#1306329811yescharacteristic
978C2×C4#1306329811yescharacteristic
979C2×C4#1306329911yescharacteristic
980C2×C4#1306329911yescharacteristic
981C2×C4#1306330011yescharacteristic
982C2×C4#1306330011yescharacteristic
983C2×C4#1306330011yescharacteristic
984C2×C4#1306330011yescharacteristic
985C2×C4#1306330011yescharacteristic
986C2×C4#1306331011yescharacteristic
987C2×C4#1306331011yescharacteristic
988C2×C4#1306331011yescharacteristic
989C2×C4#1306331311yescharacteristic
990C2×C4#1306331411yescharacteristic
991C2×C4#1306332111yescharacteristic
992C2×C4#1306332211yescharacteristic
993C8—42no—
994C8—1722no—
995C22—864no—
996C22—864no—
997C22—864no—
998C22—3442no—
999C22—3442no—
1000C22—3442no—
1001C22—3442no—
1002C22—3442no—
1003C22—3442no—
1004C22—3442no—
1005C22—3442no—
1006C22—3442no—
1007C22—3442no—
1008C22—3442no—
1009C22—3442no—
1010C22—1724no—
1011C22—1724no—
1012C22—1724no—
1013C22—1722no—
1014C22—1722no—
1015C22—1722no—
1016C22—1722no—
1017C22—1722no—
1018C22—1722no—
1019C22—1722no—
1020C22—1722no—
1021C22—1722no—
1022C22—1722no—
1023C22—1722no—
1024C22—1722no—
1025C22#1458275411yescharacteristic
1026C22#1458277711yescharacteristic
1027C22#1458277711yescharacteristic
1028C22#1458280811yescharacteristic
1029C22#1458280911yescharacteristic
1030C22#1458281611yescharacteristic
1031C22#1458281711yescharacteristic
1032C22#102×D4311yescharacteristic
1033C22#1458289411yescharacteristic
1034C22#1458289911yescharacteristic
1035C22#1458290211yescharacteristic
1036C22#1458303111yescharacteristic
1037C22#1458303411yescharacteristic
1038C22#1458303411yescharacteristic
1039C22#1458303911yescharacteristic
1040C22#1458304311yescharacteristic
1041C22#1458304511yescharacteristic
1042C22#1458304711yescharacteristic
1043C22#1458304711yescharacteristic
1044C22#1458304811yescharacteristic
1045C22#1458305111yescharacteristic
1046C22#1458306011yescharacteristic
1047C22#1458306411yescharacteristic
1048C22#1458312911yescharacteristic
1049C22#1458313111yescharacteristic
1050C22#1458313411yescharacteristic
1051C22#1458313611yescharacteristic
1052C22#1458314611yescharacteristic
1053C22#1458314811yescharacteristic
1054C22#1458315111yescharacteristic
1055C22#1458315311yescharacteristic
1056C22#1458321411yescharacteristic
1057C22#1458321911yescharacteristic
1058C22#1458322511yescharacteristic
1059C22#1458322611yescharacteristic
1060C4—44no—
1061C4—82no—
1062C4—3442no—
1063C4—1722no—
1064C4#1458277711yescharacteristic
1065C4#1458277711yescharacteristic
1066C4#1458280011yescharacteristic
1067C4#1458280111yescharacteristic
1068C4#1458280811yescharacteristic
1069C4#1458280911yescharacteristic
1070C4#1458281611yescharacteristic
1071C4#1458281711yescharacteristic
1072C2—3444no—
1073C2—1724no—
1074C2#1913283511yescharacteristic
1075C2#1913452411yescharacteristic
1076C2#1913453411yescharacteristic
1077C2#1913491111yescharacteristic
1078C2#1913491611yescharacteristic
1079C2#1913502211yescharacteristic
1080C2#1913503211yescharacteristic
1081C2#1913559211yescharacteristic
1082C2#1913559411yescharacteristic
1083C2#1913559711yescharacteristic
1084C2#1913560111yescharacteristic
1085C2#1913577911yescharacteristic
1086C2#1913578011yescharacteristic
1087C2#1913578611yescharacteristic
1088C2#1913578711yescharacteristic
subgroupG/H
centerC24D4×D43
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#340C2
socleC24×C43C2×D4
prime radicalC22×#13063300C2
cosocleC23×C4×C43C23
hypercenterC2×#340D43
hypocenterC43#10969
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
2. C22×#13063247C2semidirect
3. C22×#13063245C2semidirect
4. C22×(C2×D43)⋊C8C2semidirect
5. C2×#14582756C2semidirect
6. C2×#14582661C2semidirect
7. C2×C43×#340C2semidirect
17. C2×#13063300C4semidirect
83. C22×C43⋊C8D4semidirect
93. C2×C4⋊Dic43D4semidirect
113. C22×C8×C43D4semidirect
125. C2×C4⋊C4×C43D4semidirect
233. C2×D172C22⋊C4semidirect
276. C4⋊C4×C43C22⋊C4semidirect
374. C22×D43#102semidirect
534. C2×#340D43semidirect
582. C43#10969semidirect
638. C22×C8D172semidirect
659. C2×C4⋊C4D172semidirect
832. C4⋊C4(C2×D43)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#130633002
C22×#130632472
C22×#130632452
C22×(C2×D43)⋊C82
C2×#145827562
C2×#145826612
C2×C43×#3402
#1096943