Finite Group Databasebeta

← #25003102

Subgroups — #25003102

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×#13063296C211yesmaximal, characteristic
2C22×#13063246C211yesmaximal, characteristic, complemented
3C22×(C2×D43)⋊C8C211yesmaximal, characteristic, complemented
4C2×#14582756C211yesmaximal, characteristic, complemented
5C2×#14582662C211yesmaximal, characteristic, complemented
6C2×#14582661C211yesmaximal, characteristic, complemented
7C22×#102×C43C211yesmaximal, characteristic, complemented
8C23×C22⋊D43—21no—
9C23×C4×D43C2211yescharacteristic
10C23×C43⋊C8C2211yescharacteristic
11C2×#13063296—22no—
12C2×#13063296—22no—
13C2×#13063296—22no—
14C2×#13063296—22no—
15C2×#13063296—22no—
16C2×#13063296C414yescomplemented
17C22×C4⋊Dic43C2211yescharacteristic
18C22×C4⋊Dic43C2211yescharacteristic
19C22×C22⋊Dic43—21no—
20C22×(C2×D43)⋊C4—21no—
21C2×#13063246—22no—
22C2×#13063246—22no—
23C2×#13063246—22no—
24C2×(C2×D43)⋊C8—22no—
25C2×(C2×D43)⋊C8—22no—
26C2×(C2×D43)⋊C8—22no—
27#14582756—22no—
28#14582756—22no—
29C2×C43⋊#95—21no—
30#14582662—22no—
31#14582661—22no—
32C23×D4×C43C2211yescharacteristic
33C23×C8×C43C2211yescharacteristic
34C22×C4⋊C4×C43C2211yescharacteristic
35C2×#102×C43—22no—
36C2×#102×C43—22no—
37C2×#102×C43—22no—
38C24×D43D411yescharacteristic
39C22×C22⋊D43—24no—
40C22×C22⋊D43—24no—
41C22×C22⋊D43—24no—
42C22×C22⋊D43—42no—
43C22×C22⋊D43—42no—
44C22×C22⋊D43—42no—
45C22×C22⋊D43—42no—
46C23×Dic43—21no—
47C23×Dic43—21no—
48C23×Dic43D411yescharacteristic
49C22×C4×D43—21no—
50C22×C4×D43—21no—
51C22×C4×D43—21no—
52C22×C4×D43—21no—
53C22×C4×D43—21no—
54C22×C4×D43—21no—
55C22×C4×D43—21no—
56C22×C4×D43—21no—
57C22×C4×D43—21no—
58C22×C4×D43—21no—
59C22×C4×D43—21no—
60C22×C4×D43—21no—
61C22×C4×D43C2×C412yes—
62C22×C4×D43D412yes—
63C22×C43⋊C8—21no—
64C22×C43⋊C8—21no—
65C22×C43⋊C8—21no—
66C22×C43⋊C8—21no—
67C22×C43⋊C8—21no—
68C22×C43⋊C8—21no—
69C22×C43⋊C8D412yescomplemented
70#13063296—28no—
71#13063296—28no—
72#13063296—28no—
73#13063296—28no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43—21no—
82C2×C4⋊Dic43C2×C412yes—
83C2×C4⋊Dic43D412yes—
84C2×C4⋊Dic43D412yes—
85C2×C4⋊Dic43D412yescomplemented
86C2×C22⋊Dic43—24no—
87C2×C22⋊Dic43—24no—
88C2×C22⋊Dic43—24no—
89C2×(C2×D43)⋊C4—24no—
90C2×(C2×D43)⋊C4—42no—
91C2×(C2×D43)⋊C4—42no—
92#13063246—28no—
93(C2×D43)⋊C8—28no—
94C43⋊#95—24no—
95C25×C43—21no—
96C22×D4×C43—21no—
97C22×D4×C43—21no—
98C22×D4×C43—21no—
99C22×D4×C43—21no—
100C22×D4×C43—21no—
101C22×D4×C43—21no—
102C22×D4×C43—21no—
103C22×D4×C43—21no—
104C22×D4×C43—21no—
105C22×D4×C43—21no—
106C22×D4×C43—21no—
107C22×D4×C43C2×C412yes—
108C22×D4×C43D412yes—
109C22×D4×C43D412yes—
110C23×C4×C43—21no—
111C23×C4×C43C2311yescharacteristic
112C22×C8×C43—21no—
113C22×C8×C43—21no—
114C22×C8×C43—21no—
115C22×C8×C43—21no—
116C22×C8×C43—21no—
117C22×C8×C43—21no—
118C22×C8×C43D412yescomplemented
119C2×C4⋊C4×C43—21no—
120C2×C4⋊C4×C43—21no—
121C2×C4⋊C4×C43—21no—
122C2×C4⋊C4×C43—21no—
123C2×C4⋊C4×C43—21no—
124C2×C4⋊C4×C43D412yescomplemented
125#102×C43—28no—
126C24×C43—22no—
127C24×C43—22no—
128C24×C43—22no—
129C24×C43—41no—
130C24×C43—41no—
131C24×C43—41no—
132C24×C43—41no—
133C24×C43—41no—
134C24×C43—41no—
135C24×C43—41no—
136C24×C43—41no—
137C24×C43—41no—
138C24×C43—41no—
139C24×C43—41no—
140C24×C43—41no—
141C24×C43C2×D411yescharacteristic
142C23×D43—21no—
143C23×D43—21no—
144C23×D43—21no—
145C23×D43—21no—
146C23×D43—21no—
147C23×D43—21no—
148C23×D43—21no—
149C23×D43—21no—
150C23×D43—21no—
151C23×D43—21no—
152C23×D43—21no—
153C23×D43—21no—
154C23×D43C22⋊C412yes—
155C23×D43D812yes—
156C23×D43SD1612yes—
157C2×D4×C43—22no—
158C2×D4×C43—22no—
159C2×D4×C43—22no—
160C2×D4×C43—22no—
161C2×D4×C43—22no—
162C2×D4×C43—22no—
163C2×D4×C43—22no—
164C2×D4×C43—22no—
165C2×D4×C43—22no—
166C2×D4×C43—22no—
167C2×D4×C43—22no—
168C2×D4×C43—22no—
169C2×D4×C43—22no—
170C2×D4×C43—22no—
171C2×D4×C43—22no—
172C2×D4×C43—41no—
173C2×D4×C43—41no—
174C2×D4×C43—41no—
175C2×D4×C43—41no—
176C2×D4×C43—41no—
177C2×D4×C43—41no—
178C2×D4×C43—41no—
179C2×D4×C43—41no—
180C2×D4×C43—41no—
181C2×D4×C43—41no—
182C2×D4×C43—41no—
183C2×D4×C43—41no—
184C2×D4×C43C22⋊C414yescomplemented
185C22×C4×C43—22no—
186C22×C4×C43—41no—
187C22×C4×C43—41no—
188C22×C4×C43—41no—
189C22×C4×C43—41no—
190C22×C4×C43—41no—
191C22×C4×C43—41no—
192C22×C4×C43C22×C411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43#4111yescharacteristic
203C22×C4×C43#4111yescharacteristic
204C22×C4×C43#4111yescharacteristic
205C22×C4×C43#4111yescharacteristic
206C2×C22⋊D43—216no—
207C2×C22⋊D43—48no—
208C2×C22⋊D43—48no—
209C2×C22⋊D43—48no—
210C2×C22⋊D43—48no—
211C2×C22⋊D43—48no—
212C2×C22⋊D43—48no—
213C22×Dic43—22no—
214C22×Dic43—21no—
215C22×Dic43—21no—
216C22×Dic43—21no—
217C22×Dic43—22no—
218C22×Dic43—22no—
219C22×Dic43—22no—
220C22×Dic43—21no—
221C22×Dic43—21no—
222C22×Dic43—21no—
223C22×Dic43—41no—
224C22×Dic43—41no—
225C22×Dic43—41no—
226C22×Dic43—41no—
227C22×Dic43—41no—
228C22×Dic43—41no—
229C22×Dic43—41no—
230C22×Dic43—41no—
231C22×Dic43—41no—
232C22×Dic43—41no—
233C22×Dic43C22⋊C412yes—
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—41no—
272C4⋊C4×C43—41no—
273C22⋊Dic43—216no—
274(C2×D43)⋊C4—48no—
275C4⋊Dic43—22no—
276C4⋊Dic43—22no—
277C4⋊Dic43—22no—
278C4⋊Dic43—22no—
279C4⋊Dic43—22no—
280C4⋊Dic43—41no—
281C4⋊Dic43—41no—
282C4⋊Dic43C22⋊C414yescomplemented
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×C43—24no—
291C23×C43—42no—
292C23×C43—42no—
293C23×C43—42no—
294C23×C43—42no—
295C23×C43—42no—
296C23×C43—42no—
297C23×C43—42no—
298C23×C43—42no—
299C23×C43—42no—
300C23×C43—42no—
301C23×C43—42no—
302C23×C43—42no—
303C23×C43—42no—
304C23×C43—42no—
305C23×C43—42no—
306C23×C43—42no—
307C23×C43—42no—
308C23×C43—42no—
309C23×C43—81no—
310C23×C43—81no—
311C23×C43—81no—
312C23×C43—81no—
313C23×C43—81no—
314C23×C43—81no—
315C23×C43—81no—
316C23×C43—81no—
317C23×C43—81no—
318C23×C43—81no—
319C23×C43—81no—
320C23×C43—81no—
321C23×C43—81no—
322C23×C43—81no—
323C23×C43—81no—
324C23×C43—81no—
325C23×C43C2×C22⋊C411yescharacteristic
326C23×C43#12011yescharacteristic
327C23×C43#12011yescharacteristic
328C23×C43#12011yescharacteristic
329C23×C43#12111yescharacteristic
330C23×C43#12111yescharacteristic
331C23×C43#12311yescharacteristic
332C23×C43C2×D811yescharacteristic
333C23×C43C2×SD1611yescharacteristic
334C23×C43#13511yescharacteristic
335C23×C43#13511yescharacteristic
336C23×C43AGL(1,ℤ/8)11yescharacteristic
337C23×C43AGL(1,ℤ/8)11yescharacteristic
338C23×C43AGL(1,ℤ/8)11yescharacteristic
339C23×C43#13711yescharacteristic
340C22×D43—22no—
341C22×D43—22no—
342C22×D43—22no—
343C22×D43—22no—
344C22×D43—22no—
345C22×D43—22no—
346C22×D43—22no—
347C22×D43—22no—
348C22×D43—22no—
349C22×D43—22no—
350C22×D43—22no—
351C22×D43—22no—
352C22×D43—22no—
353C22×D43—22no—
354C22×D43—22no—
355C22×D43—22no—
356C22×D43—22no—
357C22×D43—22no—
358C22×D43—41no—
359C22×D43—41no—
360C22×D43—41no—
361C22×D43—41no—
362C22×D43—41no—
363C22×D43—41no—
364C22×D43—41no—
365C22×D43—41no—
366C22×D43—41no—
367C22×D43—41no—
368C22×D43—41no—
369C22×D43—41no—
370C22×D43—41no—
371C22×D43—41no—
372C22×D43—41no—
373C22×D43—41no—
374C22×D43#10214yescomplemented
375D4×C43—24no—
376D4×C43—24no—
377D4×C43—42no—
378D4×C43—42no—
379D4×C43—42no—
380D4×C43—42no—
381D4×C43—42no—
382D4×C43—42no—
383C2×C4×C43—42no—
384C2×C4×C43—42no—
385C2×C4×C43—42no—
386C2×C4×C43—81no—
387C2×C4×C43—81no—
388C2×C4×C43—81no—
389C2×C4×C43—81no—
390C2×C4×C43C2×C22⋊C411yescharacteristic
391C2×C4×C43C2×C22⋊C411yescharacteristic
392C2×C4×C43C4×D411yescharacteristic
393C2×C4×C43C4×D411yescharacteristic
394C2×C4×C43C4×D411yescharacteristic
395C2×C4×C43C4×D411yescharacteristic
396C2×C4×C43#12011yescharacteristic
397C2×C4×C43#12011yescharacteristic
398C2×C4×C43#12011yescharacteristic
399C2×C4×C43#12011yescharacteristic
400C2×C4×C43#12011yescharacteristic
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#12111yescharacteristic
411C2×C4×C43#12311yescharacteristic
412C2×C4×C43#12311yescharacteristic
413C2×C4×C43#12311yescharacteristic
414C2×C4×C43#12411yescharacteristic
415C2×C4×C43#12411yescharacteristic
416C2×C4×C43#12711yescharacteristic
417C2×C4×C43#12711yescharacteristic
418C22⋊D43—432no—
419C2×Dic43—24no—
420C2×Dic43—22no—
421C2×Dic43—22no—
422C2×Dic43—22no—
423C2×Dic43—41no—
424C2×Dic43—41no—
425C2×Dic43—41no—
426C2×Dic43—41no—
427C2×Dic43—42no—
428C2×Dic43—42no—
429C2×Dic43—42no—
430C2×Dic43—42no—
431C2×Dic43—42no—
432C2×Dic43—42no—
433C2×Dic43—42no—
434C2×Dic43—42no—
435C2×Dic43—42no—
436C2×Dic43—81no—
437C2×Dic43—81no—
438C2×Dic43—81no—
439C2×Dic43—81no—
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—44no—
452C22×C43—44no—
453C22×C43—44no—
454C22×C43—82no—
455C22×C43—82no—
456C22×C43—82no—
457C22×C43—82no—
458C22×C43—82no—
459C22×C43—82no—
460C22×C43—82no—
461C22×C43—82no—
462C22×C43—82no—
463C22×C43—82no—
464C22×C43—82no—
465C22×C43—82no—
466C22×C43#37911yescharacteristic
467C22×C43#38611yescharacteristic
468C22×C43#38611yescharacteristic
469C22×C43#39211yescharacteristic
470C22×C43#39211yescharacteristic
471C22×C43#39411yescharacteristic
472C22×C43#39411yescharacteristic
473C22×C43C2×#10211yescharacteristic
474C22×C43#41611yescharacteristic
475C22×C43#41711yescharacteristic
476C22×C43#41811yescharacteristic
477C22×C43#44711yescharacteristic
478C22×C43#44711yescharacteristic
479C22×C43#44711yescharacteristic
480C22×C43#44811yescharacteristic
481C22×C43#44911yescharacteristic
482C22×C43#44911yescharacteristic
483C22×C43#44911yescharacteristic
484C22×C43#44911yescharacteristic
485C22×C43#45011yescharacteristic
486C22×C43#45011yescharacteristic
487C22×C43#45211yescharacteristic
488C22×C43#45211yescharacteristic
489C22×C43#46511yescharacteristic
490C22×C43#46511yescharacteristic
491C22×C43#46611yescharacteristic
492C22×C43#46611yescharacteristic
493C22×C43#46811yescharacteristic
494C22×C43#46811yescharacteristic
495C22×C43#46911yescharacteristic
496C22×C43#46911yescharacteristic
497C22×C43#48011yescharacteristic
498C22×C43#48111yescharacteristic
499C22×C43#48211yescharacteristic
500C22×C43#48211yescharacteristic
501C2×D43—24no—
502C2×D43—24no—
503C2×D43—24no—
504C2×D43—42no—
505C2×D43—42no—
506C2×D43—42no—
507C2×D43—42no—
508C2×D43—42no—
509C2×D43—42no—
510C2×D43—42no—
511C2×D43—42no—
512C2×D43—42no—
513C2×D43—42no—
514C2×D43—42no—
515C2×D43—42no—
516C4×C43—82no—
517C4×C43#38611yescharacteristic
518C4×C43#38611yescharacteristic
519C4×C43#39011yescharacteristic
520C4×C43#39011yescharacteristic
521C4×C43#39211yescharacteristic
522C4×C43#39211yescharacteristic
523C4×C43#39411yescharacteristic
524C4×C43#39411yescharacteristic
525Dic43—42no—
526Dic43—44no—
527Dic43—82no—
528C22×#121—431no—
529C22×#102—431no—
530C22×#102D4311yescharacteristic, complemented
531C22×C22⋊C8—431no—
532C2×#380—431no—
533C2×#340—431no—
534C2×#340—431no—
535C2×C43—84no—
536C2×C43#143811yescharacteristic
537C2×C43#178611yescharacteristic
538C2×C43#178811yescharacteristic
539C2×C43#187411yescharacteristic
540C2×C43#187511yescharacteristic
541C2×C43#189311yescharacteristic
542C2×C43#189511yescharacteristic
543C2×C43#199911yescharacteristic
544C2×C43#199911yescharacteristic
545C2×C43#200011yescharacteristic
546C2×C43#200011yescharacteristic
547C2×C43#203311yescharacteristic
548C2×C43#203311yescharacteristic
549C2×C43#203411yescharacteristic
550C2×C43#203411yescharacteristic
551D43—44no—
552C23×D4—861no—
553C23×D4C2×D4311yescharacteristic
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⋊C4—431no—
565C22×C4⋊C4C2×D4311yescharacteristic
566C22×C22⋊C4—861no—
567C22×C22⋊C4—861no—
568C2×#102—22no—
569C2×#102—22no—
570C2×#102—22no—
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—862no—
581#340—862no—
582C43#1096911yescharacteristic, complemented, Sylow
583C25—21no—
584C25—431no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4—21no—
588C22×D4—21no—
589C22×D4—21no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4—21no—
593C22×D4—21no—
594C22×D4—21no—
595C22×D4—21no—
596C22×D4—864no—
597C22×D4—864no—
598C22×D4—864no—
599C22×D4—1722no—
600C22×D4—1722no—
601C22×D4—1722no—
602C22×D4—1722no—
603C22×D4C4×D4312yes—
604C22×D4D17212yes—
605C22×D4C22⋊D4312yes—
606C23×C4—21no—
607C23×C4—431no—
608C23×C4—432no—
609C23×C4—432no—
610C23×C4—861no—
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×C8C22⋊D4312yescomplemented
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—432no—
649C2×C4⋊C4—432no—
650C2×C4⋊C4—432no—
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⋊C4—861no—
658C2×C4⋊C4—861no—
659C2×C4⋊C4—861no—
660C2×C4⋊C4C22⋊D4312yescomplemented
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—28no—
668#102—868no—
669C22⋊C8—868no—
670#95—864no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—41no—
675C24—41no—
676C24—41no—
677C24—41no—
678C24—41no—
679C24—41no—
680C24—41no—
681C24—41no—
682C24—41no—
683C24—41no—
684C24—41no—
685C24—41no—
686C24—432no—
687C24—432no—
688C24—432no—
689C24—861no—
690C24—861no—
691C24—861no—
692C24—861no—
693C24—861no—
694C24—861no—
695C24—861no—
696C24—861no—
697C24—861no—
698C24—861no—
699C24—861no—
700C24—861no—
701C24D4×D4311yescharacteristic
702C2×D4—22no—
703C2×D4—22no—
704C2×D4—22no—
705C2×D4—22no—
706C2×D4—22no—
707C2×D4—22no—
708C2×D4—22no—
709C2×D4—22no—
710C2×D4—22no—
711C2×D4—22no—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—22no—
715C2×D4—22no—
716C2×D4—22no—
717C2×D4—41no—
718C2×D4—41no—
719C2×D4—41no—
720C2×D4—41no—
721C2×D4—41no—
722C2×D4—41no—
723C2×D4—41no—
724C2×D4—41no—
725C2×D4—41no—
726C2×D4—41no—
727C2×D4—41no—
728C2×D4—41no—
729C2×D4—8616no—
730C2×D4—1728no—
731C2×D4—1728no—
732C2×D4—1728no—
733C2×D4—1728no—
734C2×D4—1728no—
735C2×D4—1728no—
736C2×D4(C2×D43)⋊C414yescomplemented
737C22×C4—22no—
738C22×C4—41no—
739C22×C4—41no—
740C22×C4—41no—
741C22×C4—41no—
742C22×C4—41no—
743C22×C4—41no—
744C22×C4—432no—
745C22×C4—862no—
746C22×C4—861no—
747C22×C4—861no—
748C22×C4—862no—
749C22×C4—861no—
750C22×C4—862no—
751C22×C4—861no—
752C22×C4—861no—
753C22×C4—861no—
754C22×C4—862no—
755C22×C4—862no—
756C22×C4—862no—
757C22×C4—862no—
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—1721no—
768C22×C4—1721no—
769C22×C4—1721no—
770C22×C4—1721no—
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×C4#1062189811yescharacteristic
796C22×C4#1062189811yescharacteristic
797C22×C4D4×D4311yescharacteristic
798C22×C4D4×D4311yescharacteristic
799C22×C4D4×D4311yescharacteristic
800C22×C4D4×D4311yescharacteristic
801C22×C4D4×D4311yescharacteristic
802C22×C4#1062190011yescharacteristic
803C22×C4#1062190011yescharacteristic
804C22×C4C2×C22⋊D4311yescharacteristic
805C22×C4C2×C22⋊D4311yescharacteristic
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—41no—
824C4⋊C4—41no—
825C4⋊C4—434no—
826C4⋊C4—862no—
827C4⋊C4—862no—
828C4⋊C4—862no—
829C4⋊C4—862no—
830C4⋊C4—862no—
831C4⋊C4—1721no—
832C4⋊C4—1721no—
833C22⋊C4—8616no—
834C22⋊C4—1728no—
835C23—24no—
836C23—42no—
837C23—42no—
838C23—42no—
839C23—42no—
840C23—42no—
841C23—42no—
842C23—42no—
843C23—42no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—81no—
855C23—81no—
856C23—81no—
857C23—81no—
858C23—81no—
859C23—81no—
860C23—81no—
861C23—81no—
862C23—81no—
863C23—81no—
864C23—81no—
865C23—81no—
866C23—81no—
867C23—81no—
868C23—81no—
869C23—81no—
870C23—434no—
871C23—862no—
872C23—862no—
873C23—862no—
874C23—862no—
875C23—862no—
876C23—862no—
877C23—862no—
878C23—862no—
879C23—862no—
880C23—862no—
881C23—862no—
882C23—862no—
883C23—862no—
884C23—862no—
885C23—862no—
886C23—862no—
887C23—862no—
888C23—862no—
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#1306329311yescharacteristic
908C23#1306329511yescharacteristic
909C23#1306329611yescharacteristic
910C23#1306329811yescharacteristic
911C23#1306330711yescharacteristic
912C23D8×D4311yescharacteristic
913C23SD16×D4311yescharacteristic
914C23#1306334411yescharacteristic
915C23#1306334611yescharacteristic
916C23#1306334911yescharacteristic
917C23#1306334911yescharacteristic
918C23#1306335211yescharacteristic
919C23#1306335411yescharacteristic
920D4—24no—
921D4—24no—
922D4—42no—
923D4—42no—
924D4—42no—
925D4—42no—
926D4—42no—
927D4—42no—
928D4—17232no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—81no—
933C2×C4—81no—
934C2×C4—81no—
935C2×C4—81no—
936C2×C4—862no—
937C2×C4—864no—
938C2×C4—862no—
939C2×C4—862no—
940C2×C4—3441no—
941C2×C4—3441no—
942C2×C4—3441no—
943C2×C4—3441no—
944C2×C4—1722no—
945C2×C4—1722no—
946C2×C4—1722no—
947C2×C4—1722no—
948C2×C4—1722no—
949C2×C4—1721no—
950C2×C4—1721no—
951C2×C4—1721no—
952C2×C4—1721no—
953C2×C4—1722no—
954C2×C4—1722no—
955C2×C4—1722no—
956C2×C4—1722no—
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(C22⋊D43)⋊C411yescharacteristic
968C2×C4(C22⋊D43)⋊C411yescharacteristic
969C2×C4C4×C22⋊D4311yescharacteristic
970C2×C4C4×C22⋊D4311yescharacteristic
971C2×C4#1306329311yescharacteristic
972C2×C4#1306329311yescharacteristic
973C2×C4#1306329411yescharacteristic
974C2×C4#1306329511yescharacteristic
975C2×C4#1306329511yescharacteristic
976C2×C4#1306329611yescharacteristic
977C2×C4#1306329711yescharacteristic
978C2×C4#1306329711yescharacteristic
979C2×C4#1306329711yescharacteristic
980C2×C4#1306329711yescharacteristic
981C2×C4#1306329811yescharacteristic
982C2×C4#1306329811yescharacteristic
983C2×C4#1306329811yescharacteristic
984C2×C4#1306329911yescharacteristic
985C2×C4#1306329911yescharacteristic
986C2×C4#1306330711yescharacteristic
987C2×C4#1306330811yescharacteristic
988C2×C4#1306330911yescharacteristic
989C2×C4#1306331111yescharacteristic
990C2×C4#1306331111yescharacteristic
991C2×C4#1306332111yescharacteristic
992C2×C4#1306332111yescharacteristic
993C8—42no—
994C8—1722no—
995C22—44no—
996C22—44no—
997C22—44no—
998C22—82no—
999C22—82no—
1000C22—82no—
1001C22—82no—
1002C22—82no—
1003C22—82no—
1004C22—82no—
1005C22—82no—
1006C22—82no—
1007C22—82no—
1008C22—82no—
1009C22—82no—
1010C22—864no—
1011C22—864no—
1012C22—864no—
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#1458277511yescharacteristic
1027C22#1458277511yescharacteristic
1028C22#1458280711yescharacteristic
1029C22#1458280811yescharacteristic
1030C22#1458281411yescharacteristic
1031C22#1458281511yescharacteristic
1032C22#102×D4311yescharacteristic
1033C22#1458289211yescharacteristic
1034C22#1458289711yescharacteristic
1035C22#1458290211yescharacteristic
1036C22#1458303111yescharacteristic
1037C22#1458303111yescharacteristic
1038C22#1458303411yescharacteristic
1039C22#1458303611yescharacteristic
1040C22#1458304111yescharacteristic
1041C22#1458304111yescharacteristic
1042C22#1458304311yescharacteristic
1043C22#1458304511yescharacteristic
1044C22#1458304811yescharacteristic
1045C22#1458305111yescharacteristic
1046C22#1458305811yescharacteristic
1047C22#1458306211yescharacteristic
1048C22#1458312511yescharacteristic
1049C22#1458312711yescharacteristic
1050C22#1458313211yescharacteristic
1051C22#1458313411yescharacteristic
1052C22#1458314211yescharacteristic
1053C22#1458314411yescharacteristic
1054C22#1458314911yescharacteristic
1055C22#1458315111yescharacteristic
1056C22#1458321111yescharacteristic
1057C22#1458321611yescharacteristic
1058C22#1458322111yescharacteristic
1059C22#1458322211yescharacteristic
1060C4—82no—
1061C4—3442no—
1062C4—1724no—
1063C4—1722no—
1064C4#1458277611yescharacteristic
1065C4#1458277811yescharacteristic
1066C4#1458279911yescharacteristic
1067C4#1458279911yescharacteristic
1068C4#1458280711yescharacteristic
1069C4#1458280811yescharacteristic
1070C4#1458281411yescharacteristic
1071C4#1458281511yescharacteristic
1072C2—84no—
1073C2—1724no—
1074C2#1913283411yescharacteristic
1075C2#1913452411yescharacteristic
1076C2#1913453211yescharacteristic
1077C2#1913490911yescharacteristic
1078C2#1913491411yescharacteristic
1079C2#1913502011yescharacteristic
1080C2#1913503011yescharacteristic
1081C2#1913559011yescharacteristic
1082C2#1913559211yescharacteristic
1083C2#1913559511yescharacteristic
1084C2#1913559911yescharacteristic
1085C2#1913577511yescharacteristic
1086C2#1913577611yescharacteristic
1087C2#1913578211yescharacteristic
1088C2#1913578311yescharacteristic
subgroupG/H
centerC24D4×D43
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC22×#102×C43C2
socleC24×C43C2×D4
prime radicalC22×#13063296C2
cosocleC23×C4×C43C23
hypercenterC22×#102D43
hypocenterC43#10969
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C22×#13063246C2semidirect
3. C22×(C2×D43)⋊C8C2semidirect
4. C2×#14582756C2semidirect
5. C2×#14582662C2semidirect
6. C2×#14582661C2semidirect
7. C22×#102×C43C2semidirect
16. C2×#13063296C4semidirect
69. C22×C43⋊C8D4semidirect
85. C2×C4⋊Dic43D4semidirect
118. C22×C8×C43D4semidirect
124. C2×C4⋊C4×C43D4semidirect
184. C2×D4×C43C22⋊C4semidirect
282. C4⋊Dic43C22⋊C4semidirect
374. C22×D43#102semidirect
530. C22×#102D43semidirect
582. C43#10969semidirect
638. C22×C8C22⋊D43semidirect
660. C2×C4⋊C4C22⋊D43semidirect
736. C2×D4(C2×D43)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#130632962
C22×#130632462
C22×(C2×D43)⋊C82
C2×#145827562
C2×#145826622
C2×#145826612
C22×#102×C432
#1096943