Finite Group Databasebeta

← #25019965

Subgroups — #25019965

Order 11008.

2590 conjugacy classes of subgroups.

The subgroup lattice has 1218 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063287C211yesmaximal, characteristic
2C2×#14582777C211yesmaximal, characteristic
3C2×#14582777C211yesmaximal, characteristic
4C2×#14582773C211yesmaximal, characteristic, complemented
5C2×#95×D43C211yesmaximal, characteristic, complemented
6#19132854C211yesmaximal, characteristic, complemented
7#19132841C211yesmaximal, characteristic, complemented
8#19132839C211yesmaximal, characteristic, complemented
9#19132829C211yesmaximal, characteristic, complemented
10#19132826C211yesmaximal, characteristic, complemented
11(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
12(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
13(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
15C43×#1442C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21C2×#13063287—24no—
22C2×#13063287—24no—
23C2×#13063287—24no—
24C22×C4⋊Dic43C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×(C2×D43)⋊C4C2211yescharacteristic
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×C4×Dic43C2211yescharacteristic
35#14582777—24no—
36#14582777C418yescomplemented
37#14582773—24no—
38C2×C43⋊#95C2211yescharacteristic
39C2×C43⋊#95C2211yescharacteristic
40C2×C43⋊#95C2211yescharacteristic
41C2×C43⋊#95C2211yescharacteristic
42C2×C43⋊#95C2211yescharacteristic
43C2×C43⋊#95C2211yescharacteristic
44C2×C43⋊#95C2211yescharacteristic
45C2×C43⋊#95C2211yescharacteristic
46C2×C43⋊#95C2211yescharacteristic
47C2×C43⋊#95C2211yescharacteristic
48C2×C43⋊#95C2211yescharacteristic
49C2×C43⋊#95C2211yescharacteristic
50#95×D43—24no—
51C22×C4⋊C4×C43C2211yescharacteristic
52C2×#95×C43C2211yescharacteristic
53C2×#95×C43C2211yescharacteristic
54C2×#95×C43C2211yescharacteristic
55C2×#95×C43C2211yescharacteristic
56C2×#95×C43C2211yescharacteristic
57C2×#95×C43C2211yescharacteristic
58C24×D43C2311yescharacteristic
59C24×D43C2311yescharacteristic
60C22×D172—22no—
61C22×D172—22no—
62C22×D172—22no—
63C22×D172—22no—
64C22×D172C2×C414yes—
65C22×D172D414yes—
66C22×D172Q814yes—
67C23×Dic43C2311yescharacteristic
68C23×Dic43C2311yescharacteristic
69C23×Dic43C2311yescharacteristic
70C23×Dic43C2311yescharacteristic
71C23×Dic43C2311yescharacteristic
72C23×Dic43C2311yescharacteristic
73C22×C4×D43—22no—
74C22×C4×D43—22no—
75C22×C4×D43—22no—
76C22×C4×D43—22no—
77C22×C4×D43—22no—
78C22×C4×D43—22no—
79C22×C4×D43—22no—
80C22×C4×D43—22no—
81C22×C4×D43—22no—
82C22×C4×D43—22no—
83C22×C4×D43—22no—
84C22×C4×D43—22no—
85C22×C4×D43—22no—
86C22×C4×D43—22no—
87C22×C4×D43—22no—
88C22×C4×D43—22no—
89C22×C4×D43—41no—
90C22×C4×D43—41no—
91C22×C4×D43—41no—
92C22×C4×D43—41no—
93C22×C4×D43—41no—
94C22×C4×D43—41no—
95C22×C4×D43—41no—
96C22×C4×D43—41no—
97C22×C4×D43—41no—
98C22×C4×D43—41no—
99C22×C4×D43C2×C414yescomplemented
100C22×C4×D43D414yes—
101#13063287—232no—
102C2×C4⋊Dic43—22no—
103C2×C4⋊Dic43—22no—
104C2×C4⋊Dic43—41no—
105C2×Dic43⋊C4—22no—
106C2×Dic43⋊C4—22no—
107C2×Dic43⋊C4—41no—
108C2×(C2×D43)⋊C4—22no—
109C2×(C2×D43)⋊C4—22no—
110C2×(C2×D43)⋊C4—22no—
111C2×(C2×D43)⋊C4—22no—
112C2×(C2×D43)⋊C4—22no—
113C2×(C2×D43)⋊C4—22no—
114C2×(C2×D43)⋊C4—22no—
115C2×(C2×D43)⋊C4—22no—
116C2×(C2×D43)⋊C4—22no—
117C2×(C2×D43)⋊C4—22no—
118C2×(C2×D43)⋊C4—22no—
119C2×(C2×D43)⋊C4—22no—
120C2×(C2×D43)⋊C4—22no—
121C2×(C2×D43)⋊C4—22no—
122C2×(C2×D43)⋊C4—41no—
123C2×(C2×D43)⋊C4—41no—
124C2×(C2×D43)⋊C4—41no—
125C2×(C2×D43)⋊C4—41no—
126C2×(C2×D43)⋊C4—41no—
127C2×(C2×D43)⋊C4—41no—
128C2×(C2×D43)⋊C4C2×C414yescomplemented
129C2×(C2×D43)⋊C4C2×C414yescomplemented
130C2×(C2×D43)⋊C4C2×C414yescomplemented
131C2×(C2×D43)⋊C4D414yes—
132C2×C4×Dic43—22no—
133C2×C4×Dic43—22no—
134C2×C4×Dic43—22no—
135C43⋊#95—22no—
136C43⋊#95—22no—
137C43⋊#95—22no—
138C43⋊#95—22no—
139C43⋊#95—22no—
140C43⋊#95—22no—
141C43⋊#95—22no—
142C43⋊#95—41no—
143C43⋊#95—41no—
144C43⋊#95—41no—
145C43⋊#95—41no—
146C43⋊#95C2×C414yescomplemented
147C23×C4×C43C2311yescharacteristic
148C23×C4×C43C2311yescharacteristic
149C23×C4×C43C2311yescharacteristic
150C23×C4×C43C2311yescharacteristic
151C23×C4×C43C2311yescharacteristic
152C23×C4×C43C2311yescharacteristic
153C23×C4×C43C2311yescharacteristic
154C2×C4⋊C4×C43—22no—
155C2×C4⋊C4×C43—22no—
156C2×C4⋊C4×C43—22no—
157#95×C43—22no—
158#95×C43—22no—
159#95×C43—22no—
160#95×C43—41no—
161#95×C43—41no—
162#95×C43C2×C414yescomplemented
163C24×C43C2411yescharacteristic
164C23×D43—21no—
165C23×D43—21no—
166C23×D43—21no—
167C23×D43—21no—
168C23×D43—21no—
169C23×D43—21no—
170C23×D43—21no—
171C23×D43—21no—
172C23×D43—21no—
173C23×D43—21no—
174C23×D43—21no—
175C23×D43—21no—
176C23×D43—21no—
177C23×D43—21no—
178C23×D43—21no—
179C23×D43—21no—
180C23×D43—21no—
181C23×D43—21no—
182C23×D43—21no—
183C23×D43—21no—
184C23×D43C22×C412yes—
185C23×D43C22×C412yes—
186C23×D43C2×D412yes—
187C23×D43C2×D412yes—
188C23×D43C2×D412yes—
189C23×D43C2×D412yes—
190C23×D43C2×Q812yes—
191C23×D43C2×Q812yes—
192C23×D43#4112yes—
193C23×D43#4112yes—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
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—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43—21no—
230C22×C4×C43—21no—
231C22×C4×C43—21no—
232C22×C4×C43—21no—
233C22×C4×C43—21no—
234C22×C4×C43—21no—
235C22×C4×C43C22×C412yes—
236C22×C4×C43C22×C412yes—
237C22×C4×C43C22×C412yes—
238C22×C4×C43C2×D412yes—
239C22×C4×C43C2×D412yes—
240C22×C4×C43C2×D412yes—
241C22×C4×C43C2×Q812yes—
242C22×C4×C43#4112yes—
243C22×Dic43—21no—
244C22×Dic43—21no—
245C22×Dic43—21no—
246C22×Dic43—21no—
247C22×Dic43—21no—
248C22×Dic43—21no—
249C22×Dic43—21no—
250C22×Dic43—21no—
251C22×Dic43—21no—
252C22×Dic43—21no—
253C22×Dic43—21no—
254C22×Dic43—21no—
255C22×Dic43—21no—
256C22×Dic43—21no—
257C22×Dic43—21no—
258C22×Dic43—21no—
259C22×Dic43—21no—
260C22×Dic43—21no—
261C22×Dic43—21no—
262C22×Dic43—21no—
263C22×Dic43—21no—
264C22×Dic43—21no—
265C22×Dic43—21no—
266C22×Dic43—21no—
267C22×Dic43—21no—
268C22×Dic43—21no—
269C22×Dic43—21no—
270C22×Dic43—21no—
271C22×Dic43—21no—
272C22×Dic43—21no—
273C22×Dic43—21no—
274C22×Dic43—21no—
275C22×Dic43—21no—
276C22×Dic43—21no—
277C22×Dic43—21no—
278C22×Dic43C22×C412yes—
279C22×Dic43C22×C412yes—
280C22×Dic43C2×D412yes—
281C22×Dic43C2×D412yes—
282C22×Dic43#4112yes—
283C22×Dic43#4112yes—
284C22×Dic43#4112yes—
285C2×D172—28no—
286C2×D172—28no—
287C2×D172—28no—
288C2×D172—28no—
289C2×D172—28no—
290C2×D172—28no—
291C2×D172C4⋊C4116yescomplemented
292C2×C4×D43—28no—
293C2×C4×D43—28no—
294C2×C4×D43—28no—
295C2×C4×D43—28no—
296C2×C4×D43—28no—
297C2×C4×D43—44no—
298C2×C4×D43—44no—
299C2×C4×D43—44no—
300C2×C4×D43—44no—
301C2×C4×D43—44no—
302C2×C4×D43—44no—
303C2×C4×D43—44no—
304C2×C4×D43—44no—
305C2×C4×D43—44no—
306C2×C4×D43—44no—
307C2×C4×D43—44no—
308C2×C4×D43—44no—
309C2×C4×D43—44no—
310C2×C4×D43—44no—
311C2×C4×D43—44no—
312C2×C4×D43—44no—
313C2×C4×D43—44no—
314C2×C4×D43—44no—
315C2×C4×D43—44no—
316C2×C4×D43—44no—
317C2×C4×D43—44no—
318C2×C4×D43—44no—
319C2×C4×D43—44no—
320C4⋊C4×C43—28no—
321(C2×D43)⋊C4—28no—
322(C2×D43)⋊C4—28no—
323(C2×D43)⋊C4—28no—
324(C2×D43)⋊C4—44no—
325(C2×D43)⋊C4—44no—
326(C2×D43)⋊C4—44no—
327(C2×D43)⋊C4—44no—
328(C2×D43)⋊C4—44no—
329C4⋊Dic43—44no—
330Dic43⋊C4—44no—
331C4×Dic43—28no—
332C23×C43C23×C411yescharacteristic
333C23×C43C22×D411yescharacteristic
334C23×C43C22×D411yescharacteristic
335C23×C43C22×D411yescharacteristic
336C23×C43C22×Q811yescharacteristic
337C23×C43C2×#4111yescharacteristic
338C23×C43C2×#4111yescharacteristic
339C23×C43C2×#4111yescharacteristic
340C23×C43C2×#4111yescharacteristic
341C23×C43C2×#4111yescharacteristic
342C23×C43C2×#4111yescharacteristic
343C23×C43H(5,𝔽2)11yescharacteristic
344C23×C43H(5,𝔽2)11yescharacteristic
345C23×C43H(5,𝔽2)11yescharacteristic
346C23×C43H(5,𝔽2)11yescharacteristic
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—22no—
359C22×D43—22no—
360C22×D43—22no—
361C22×D43—22no—
362C22×D43—22no—
363C22×D43—22no—
364C22×D43—22no—
365C22×D43—22no—
366C22×D43—22no—
367C22×D43—22no—
368C22×D43—22no—
369C22×D43—22no—
370C22×D43—22no—
371C22×D43—22no—
372C22×D43—22no—
373C22×D43—22no—
374C22×D43—22no—
375C22×D43—22no—
376C22×D43—22no—
377C22×D43—22no—
378C22×D43—22no—
379C22×D43—22no—
380C22×D43—22no—
381C22×D43—22no—
382C22×D43—22no—
383C22×D43—22no—
384C22×D43—22no—
385C22×D43—22no—
386C22×D43—22no—
387C22×D43—22no—
388C22×D43—22no—
389C22×D43—22no—
390C22×D43—22no—
391C22×D43—22no—
392C22×D43—22no—
393C22×D43—41no—
394C22×D43—41no—
395C22×D43—41no—
396C22×D43—41no—
397C22×D43—41no—
398C22×D43—41no—
399C22×D43—41no—
400C22×D43—41no—
401C22×D43—41no—
402C22×D43—41no—
403C22×D43—41no—
404C22×D43—41no—
405C22×D43—41no—
406C22×D43—41no—
407C22×D43—41no—
408C22×D43—41no—
409C22×D43C2×C4⋊C414yes—
410C22×D43C2×C4⋊C414yes—
411C22×D43C4×D414yes—
412C22×D43C4×D414yes—
413C22×D43#12014yes—
414C22×D43C22⋊Q814yes—
415C22×D43C22⋊Q814yes—
416C22×D43#12314yes—
417C2×C4×C43—22no—
418C2×C4×C43—22no—
419C2×C4×C43—22no—
420C2×C4×C43—22no—
421C2×C4×C43—22no—
422C2×C4×C43—22no—
423C2×C4×C43—22no—
424C2×C4×C43—22no—
425C2×C4×C43—22no—
426C2×C4×C43—22no—
427C2×C4×C43—22no—
428C2×C4×C43—22no—
429C2×C4×C43—22no—
430C2×C4×C43—22no—
431C2×C4×C43—22no—
432C2×C4×C43—22no—
433C2×C4×C43—22no—
434C2×C4×C43—22no—
435C2×C4×C43—22no—
436C2×C4×C43—22no—
437C2×C4×C43—22no—
438C2×C4×C43—41no—
439C2×C4×C43—41no—
440C2×C4×C43—41no—
441C2×C4×C43—41no—
442C2×C4×C43—41no—
443C2×C4×C43—41no—
444C2×C4×C43—41no—
445C2×C4×C43—41no—
446C2×C4×C43—41no—
447C2×C4×C43—41no—
448C2×C4×C43—41no—
449C2×C4×C43—41no—
450C2×C4×C43—41no—
451C2×C4×C43—41no—
452C2×C4×C43—41no—
453C2×C4×C43—41no—
454C2×C4×C43—41no—
455C2×C4×C43—41no—
456C2×C4×C43—41no—
457C2×C4×C43—41no—
458C2×C4×C43—41no—
459C2×C4×C43—41no—
460C2×C4×C43—41no—
461C2×C4×C43—41no—
462C2×C4×C43—41no—
463C2×C4×C43—41no—
464C2×C4×C43—41no—
465C2×C4×C43C2×C4⋊C414yes—
466C2×Dic43—22no—
467C2×Dic43—22no—
468C2×Dic43—22no—
469C2×Dic43—22no—
470C2×Dic43—22no—
471C2×Dic43—22no—
472C2×Dic43—22no—
473C2×Dic43—22no—
474C2×Dic43—22no—
475C2×Dic43—22no—
476C2×Dic43—22no—
477C2×Dic43—22no—
478C2×Dic43—22no—
479C2×Dic43—22no—
480C2×Dic43—22no—
481C2×Dic43—22no—
482C2×Dic43—22no—
483C2×Dic43—22no—
484C2×Dic43—41no—
485C2×Dic43—41no—
486C2×Dic43—41no—
487C2×Dic43—41no—
488C2×Dic43—41no—
489C2×Dic43—41no—
490C2×Dic43—41no—
491C2×Dic43—41no—
492C2×Dic43—41no—
493C2×Dic43—41no—
494C2×Dic43—41no—
495C2×Dic43—41no—
496C2×Dic43—41no—
497C2×Dic43—41no—
498C2×Dic43—41no—
499C2×Dic43—41no—
500C2×Dic43—41no—
501C2×Dic43—41no—
502C2×Dic43—41no—
503C2×Dic43—41no—
504C2×Dic43—41no—
505C2×Dic43—41no—
506C2×Dic43—41no—
507C2×Dic43#12314yes—
508D172—232no—
509C4×D43—416no—
510C4×D43—416no—
511C4×D43—416no—
512C4×D43—416no—
513#14016—431nomaximal, Sylow
514C22×C43C22×C4⋊C411yescharacteristic
515C22×C43C2×C4×D411yescharacteristic
516C22×C43C2×C4×D411yescharacteristic
517C22×C43C4×#4111yescharacteristic
518C22×C43C4×#4111yescharacteristic
519C22×C43#51811yescharacteristic
520C22×C43#51811yescharacteristic
521C22×C43C2×#12011yescharacteristic
522C22×C43C2×C22⋊Q811yescharacteristic
523C22×C43C2×C22⋊Q811yescharacteristic
524C22×C43C2×#12311yescharacteristic
525C22×C43C2×#12311yescharacteristic
526C22×C43#52511yescharacteristic
527C22×C43#52911yescharacteristic
528C22×C43#52911yescharacteristic
529C22×C43#53411yescharacteristic
530C22×C43#53511yescharacteristic
531C22×C43#53811yescharacteristic
532C22×C43#53811yescharacteristic
533C22×C43#54611yescharacteristic
534C22×C43#54611yescharacteristic
535C22×C43#54611yescharacteristic
536C22×C43#54611yescharacteristic
537C22×C43#54611yescharacteristic
538C22×C43#54611yescharacteristic
539C22×C43#54611yescharacteristic
540C22×C43#54611yescharacteristic
541C22×C43#55311yescharacteristic
542C22×C43#55311yescharacteristic
543C22×C43#55311yescharacteristic
544C22×C43#55311yescharacteristic
545C22×C43#55411yescharacteristic
546C22×C43#55411yescharacteristic
547C22×C43#55411yescharacteristic
548C22×C43#55411yescharacteristic
549C2×D43—24no—
550C2×D43—24no—
551C2×D43—24no—
552C2×D43—24no—
553C2×D43—24no—
554C2×D43—24no—
555C2×D43—24no—
556C2×D43—24no—
557C2×D43—24no—
558C2×D43—24no—
559C2×D43—24no—
560C2×D43—24no—
561C2×D43—24no—
562C2×D43—24no—
563C2×D43—24no—
564C2×D43—24no—
565C2×D43—24no—
566C2×D43—42no—
567C2×D43—42no—
568C2×D43—42no—
569C2×D43—42no—
570C2×D43—42no—
571C2×D43—42no—
572C2×D43—42no—
573C2×D43—42no—
574C2×D43—42no—
575C2×D43—42no—
576C2×D43—42no—
577C2×D43—42no—
578C2×D43#38518yes—
579C4×C43—24no—
580C4×C43—42no—
581C4×C43—42no—
582C4×C43—42no—
583C4×C43—42no—
584C4×C43—42no—
585C4×C43—81no—
586Dic43—24no—
587Dic43—42no—
588Dic43—42no—
589Dic43—42no—
590Dic43—42no—
591Dic43—81no—
592C22×C4×D4—431no—
593C2×#386—431no—
594C2×#386—431no—
595C2×#385—431no—
596C22×#95—431no—
597#1442—431no—
598#1442D4311yescharacteristic, complemented
599#1439—431no—
600#1439—431no—
601#1436—431no—
602#1436—431no—
603C22⋊#95—431no—
604C22⋊#95—431no—
605C22⋊#95—431no—
606C22⋊#95—431no—
607C2×C43C2×#38511yescharacteristic
608C2×C43C4×#12311yescharacteristic
609C2×C43#232111yescharacteristic
610C2×C43#234911yescharacteristic
611C2×C43#234911yescharacteristic
612C2×C43#236411yescharacteristic
613C2×C43#236411yescharacteristic
614C2×C43#240411yescharacteristic
615C2×C43#240511yescharacteristic
616C2×C43#244411yescharacteristic
617C2×C43#244411yescharacteristic
618C2×C43#245011yescharacteristic
619C2×C43#245011yescharacteristic
620C2×C43#248711yescharacteristic
621C2×C43#257911yescharacteristic
622D43—28no—
623D43—44no—
624C23×D4—431no—
625C24×C4—431no—
626C24×C4—431no—
627C24×C4—431no—
628C24×C4—431no—
629C2×C4×D4—864no—
630C2×C4×D4—864no—
631C2×C4×D4—864no—
632C22×C4⋊C4—431no—
633C22×C4⋊C4—431no—
634C22×C4⋊C4C2×D4311yescharacteristic
635C22×C22⋊C4—431no—
636C22×C22⋊C4—431no—
637C22×C22⋊C4—431no—
638C22×C22⋊C4—431no—
639C22×C22⋊C4—431no—
640C22×C22⋊C4—431no—
641C22×C22⋊C4—431no—
642C22×C22⋊C4—431no—
643C22×C42—431no—
644#386—438no—
645#386—864no—
646#385—864no—
647C2×#95—431no—
648C2×#95—431no—
649C2×#95—431no—
650C2×#95—431no—
651C2×#95—431no—
652C2×#95—431no—
653C2×#95—431no—
654C2×#95—431no—
655C2×#95—431no—
656C2×#95—431no—
657C2×#95—431no—
658C2×#95—431no—
659C2×#95—864no—
660C2×#95C2×D4311yescharacteristic
661C2×#95C2×D4311yescharacteristic
662C2×#95C2×D4311yescharacteristic
663C2×#95C2×D4311yescharacteristic
664C2×#95C2×D4311yescharacteristic
665C2×#95C2×D4311yescharacteristic
666C43#1401611yescharacteristic, complemented, Sylow
667C25—431no—
668C25—431no—
669C22×D4—434no—
670C22×D4—434no—
671C22×D4—434no—
672C22×D4—862no—
673C22×D4—862no—
674C22×D4—862no—
675C22×D4—862no—
676C23×C4—431no—
677C23×C4—431no—
678C23×C4—431no—
679C23×C4—431no—
680C23×C4—431no—
681C23×C4—434no—
682C23×C4—434no—
683C23×C4—431no—
684C23×C4—862no—
685C23×C4—862no—
686C23×C4—862no—
687C23×C4—862no—
688C23×C4—862no—
689C23×C4—862no—
690C23×C4—862no—
691C23×C4—862no—
692C23×C4—862no—
693C23×C4—862no—
694C23×C4—862no—
695C23×C4—862no—
696C23×C4—862no—
697C23×C4—862no—
698C23×C4—862no—
699C23×C4—862no—
700C23×C4—1721no—
701C23×C4—1721no—
702C23×C4—1721no—
703C23×C4—1721no—
704C23×C4—1721no—
705C23×C4—1721no—
706C23×C4—1721no—
707C23×C4—1721no—
708C23×C4—1721no—
709C23×C4—1721no—
710C23×C4C22×D4311yescharacteristic
711C23×C4C22×D4311yescharacteristic
712C23×C4C22×D4311yescharacteristic
713C23×C4C22×D4311yescharacteristic
714C23×C4C22×D4311yescharacteristic
715C23×C4C22×D4311yescharacteristic
716C23×C4C22×D4311yescharacteristic
717C4×D4—8632no—
718C2×C4⋊C4—22no—
719C2×C4⋊C4—22no—
720C2×C4⋊C4—22no—
721C2×C4⋊C4—862no—
722C2×C4⋊C4—862no—
723C2×C4⋊C4—862no—
724C2×C4⋊C4—862no—
725C2×C4⋊C4—1721no—
726C2×C4⋊C4—1721no—
727C2×C22⋊C4—434no—
728C2×C22⋊C4—434no—
729C2×C22⋊C4—434no—
730C2×C22⋊C4—434no—
731C2×C22⋊C4—862no—
732C2×C22⋊C4—862no—
733C2×C22⋊C4—862no—
734C2×C22⋊C4—862no—
735C2×C22⋊C4—862no—
736C2×C22⋊C4—862no—
737C2×C22⋊C4—862no—
738C2×C22⋊C4—862no—
739C2×C22⋊C4—862no—
740C2×C22⋊C4—862no—
741C2×C22⋊C4—862no—
742C2×C22⋊C4—862no—
743C2×C22⋊C4—862no—
744C2×C22⋊C4—862no—
745C2×C22⋊C4—1721no—
746C2×C22⋊C4—1721no—
747C2×C22⋊C4—1721no—
748C2×C22⋊C4—1721no—
749C2×C22⋊C4—1721no—
750C2×C22⋊C4—1721no—
751C2×C42—862no—
752C2×C42—862no—
753C2×C42—862no—
754#95—22no—
755#95—22no—
756#95—22no—
757#95—41no—
758#95—41no—
759#95—434no—
760#95—862no—
761#95—862no—
762#95—862no—
763#95—862no—
764#95—862no—
765#95—862no—
766#95—862no—
767#95—1721no—
768#95—1721no—
769#95—1721no—
770#95—1721no—
771#95C4×D4314yescomplemented
772C24—432no—
773C24—432no—
774C24—432no—
775C24—432no—
776C24—432no—
777C24—432no—
778C24—432no—
779C24—432no—
780C24—432no—
781C24—432no—
782C24—861no—
783C24—861no—
784C24—861no—
785C24—861no—
786C24—861no—
787C24—861no—
788C24—861no—
789C24—861no—
790C24—861no—
791C24—861no—
792C24—861no—
793C24—861no—
794C24—861no—
795C24—861no—
796C24—861no—
797C24—861no—
798C24—861no—
799C24—861no—
800C24—861no—
801C24—861no—
802C24C23×D4311yescharacteristic
803C2×D4—4316no—
804C2×D4—868no—
805C2×D4—868no—
806C2×D4—868no—
807C2×D4—868no—
808C2×D4—868no—
809C2×D4—868no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—432no—
852C22×C4—432no—
853C22×C4—432no—
854C22×C4—432no—
855C22×C4—432no—
856C22×C4—432no—
857C22×C4—432no—
858C22×C4—868no—
859C22×C4—868no—
860C22×C4—868no—
861C22×C4—868no—
862C22×C4—868no—
863C22×C4—861no—
864C22×C4—861no—
865C22×C4—861no—
866C22×C4—861no—
867C22×C4—861no—
868C22×C4—861no—
869C22×C4—861no—
870C22×C4—861no—
871C22×C4—861no—
872C22×C4—861no—
873C22×C4—861no—
874C22×C4—861no—
875C22×C4—861no—
876C22×C4—861no—
877C22×C4—861no—
878C22×C4—861no—
879C22×C4—861no—
880C22×C4—861no—
881C22×C4—861no—
882C22×C4—861no—
883C22×C4—861no—
884C22×C4—861no—
885C22×C4—861no—
886C22×C4—861no—
887C22×C4—861no—
888C22×C4—861no—
889C22×C4—861no—
890C22×C4—861no—
891C22×C4—861no—
892C22×C4—861no—
893C22×C4—861no—
894C22×C4—861no—
895C22×C4—861no—
896C22×C4—861no—
897C22×C4—861no—
898C22×C4—1724no—
899C22×C4—1724no—
900C22×C4—1724no—
901C22×C4—1724no—
902C22×C4—1724no—
903C22×C4—1724no—
904C22×C4—1724no—
905C22×C4—1724no—
906C22×C4—1724no—
907C22×C4—1724no—
908C22×C4—1724no—
909C22×C4—1724no—
910C22×C4—1724no—
911C22×C4—1724no—
912C22×C4—1724no—
913C22×C4—1724no—
914C22×C4—1724no—
915C22×C4—1724no—
916C22×C4—1724no—
917C22×C4—1724no—
918C22×C4—1724no—
919C22×C4—1724no—
920C22×C4—1724no—
921C22×C4C2×C4×D4312yes—
922C22×C4C2×C4×D4312yes—
923C22×C4C2×C4×D4312yes—
924C22×C4D4×D4312yes—
925C22×C4D4×D4312yes—
926C22×C4D4×D4312yes—
927C22×C4Q8×D4312yes—
928C22×C4#1062190212yes—
929C4⋊C4—28no—
930C4⋊C4—1724no—
931C4⋊C4—1724no—
932C22⋊C4—868no—
933C22⋊C4—868no—
934C22⋊C4—868no—
935C22⋊C4—1724no—
936C22⋊C4—1724no—
937C22⋊C4—1724no—
938C22⋊C4—1724no—
939C22⋊C4—1724no—
940C42—868no—
941C23—434no—
942C23—434no—
943C23—434no—
944C23—434no—
945C23—434no—
946C23—434no—
947C23—434no—
948C23—434no—
949C23—862no—
950C23—862no—
951C23—862no—
952C23—862no—
953C23—862no—
954C23—862no—
955C23—862no—
956C23—862no—
957C23—862no—
958C23—862no—
959C23—862no—
960C23—862no—
961C23—862no—
962C23—862no—
963C23—862no—
964C23—862no—
965C23—862no—
966C23—862no—
967C23—862no—
968C23—862no—
969C23—862no—
970C23—862no—
971C23—862no—
972C23—862no—
973C23—862no—
974C23—862no—
975C23—862no—
976C23—862no—
977C23—862no—
978C23—862no—
979C23—862no—
980C23—862no—
981C23—862no—
982C23—862no—
983C23—862no—
984C23—862no—
985C23—862no—
986C23—862no—
987C23—862no—
988C23—862no—
989C23—862no—
990C23—862no—
991C23—862no—
992C23—862no—
993C23—862no—
994C23—862no—
995C23—1721no—
996C23—1721no—
997C23—1721no—
998C23—1721no—
999C23—1721no—
1000C23—1721no—
1001C23—1721no—
1002C23—1721no—
1003C23—1721no—
1004C23—1721no—
1005C23—1721no—
1006C23—1721no—
1007C23—1721no—
1008C23—1721no—
1009C23—1721no—
1010C23—1721no—
1011C23C22×C4×D4311yescharacteristic
1012C23C2×D4×D4311yescharacteristic
1013C23C2×D4×D4311yescharacteristic
1014C23C2×D4×D4311yescharacteristic
1015C23C2×Q8×D4311yescharacteristic
1016C23#41×D4311yescharacteristic
1017C23#41×D4311yescharacteristic
1018C23#41×D4311yescharacteristic
1019C23#41×D4311yescharacteristic
1020C23#41×D4311yescharacteristic
1021C23C2×#1062190211yescharacteristic
1022C23#1306337011yescharacteristic
1023C23#1306337111yescharacteristic
1024C23#1306337111yescharacteristic
1025C23#1306337111yescharacteristic
1026D4—8632no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—434no—
1076C2×C4—862no—
1077C2×C4—862no—
1078C2×C4—862no—
1079C2×C4—862no—
1080C2×C4—862no—
1081C2×C4—862no—
1082C2×C4—862no—
1083C2×C4—862no—
1084C2×C4—862no—
1085C2×C4—862no—
1086C2×C4—862no—
1087C2×C4—862no—
1088C2×C4—862no—
1089C2×C4—862no—
1090C2×C4—862no—
1091C2×C4—862no—
1092C2×C4—862no—
1093C2×C4—862no—
1094C2×C4—17216no—
1095C2×C4—17216no—
1096C2×C4—17216no—
1097C2×C4—17216no—
1098C2×C4—1721no—
1099C2×C4—1721no—
1100C2×C4—1721no—
1101C2×C4—1721no—
1102C2×C4—1721no—
1103C2×C4—1721no—
1104C2×C4—1721no—
1105C2×C4—1721no—
1106C2×C4—1721no—
1107C2×C4—1721no—
1108C2×C4—1721no—
1109C2×C4—1721no—
1110C2×C4—1721no—
1111C2×C4—1721no—
1112C2×C4—1721no—
1113C2×C4—1721no—
1114C2×C4—1721no—
1115C2×C4—1721no—
1116C2×C4—1721no—
1117C2×C4—1721no—
1118C2×C4—1721no—
1119C2×C4—1721no—
1120C2×C4—1721no—
1121C2×C4C4⋊C4×D4314yes—
1122C22—438no—
1123C22—864no—
1124C22—864no—
1125C22—864no—
1126C22—864no—
1127C22—864no—
1128C22—864no—
1129C22—864no—
1130C22—864no—
1131C22—864no—
1132C22—864no—
1133C22—864no—
1134C22—864no—
1135C22—864no—
1136C22—864no—
1137C22—864no—
1138C22—864no—
1139C22—864no—
1140C22—1722no—
1141C22—1722no—
1142C22—1722no—
1143C22—1722no—
1144C22—1722no—
1145C22—1722no—
1146C22—1722no—
1147C22—1722no—
1148C22—1722no—
1149C22—1722no—
1150C22—1722no—
1151C22—1722no—
1152C22C2×C4⋊C4×D4311yescharacteristic
1153C22C4×D4×D4311yescharacteristic
1154C22C4×D4×D4311yescharacteristic
1155C22#1458336711yescharacteristic
1156C22C4×#1062190211yescharacteristic
1157C22#1458337111yescharacteristic
1158C22#1458337311yescharacteristic
1159C22#120×D4311yescharacteristic
1160C22C22⋊Q8×D4311yescharacteristic
1161C22C22⋊Q8×D4311yescharacteristic
1162C22#123×D4311yescharacteristic
1163C22#123×D4311yescharacteristic
1164C22#1458341211yescharacteristic
1165C22#1458343211yescharacteristic
1166C22#1458343411yescharacteristic
1167C22#1458345711yescharacteristic
1168C22#1458346711yescharacteristic
1169C22#1458348511yescharacteristic
1170C22#1458348811yescharacteristic
1171C22#1458353811yescharacteristic
1172C22#1458354011yescharacteristic
1173C22#1458354011yescharacteristic
1174C22#1458354111yescharacteristic
1175C22#1458354211yescharacteristic
1176C22#1458354211yescharacteristic
1177C22#1458354211yescharacteristic
1178C22#1458354611yescharacteristic
1179C22#1458359411yescharacteristic
1180C22#1458360011yescharacteristic
1181C22#1458360011yescharacteristic
1182C22#1458360211yescharacteristic
1183C22#1458360511yescharacteristic
1184C22#1458360511yescharacteristic
1185C22#1458360511yescharacteristic
1186C22#1458361011yescharacteristic
1187C4—24no—
1188C4—42no—
1189C4—42no—
1190C4—42no—
1191C4—42no—
1192C4—42no—
1193C4—81no—
1194C4—864no—
1195C4—3441no—
1196C4—1722no—
1197C4—1722no—
1198C4—1722no—
1199C4—1722no—
1200C2—868no—
1201C2—1724no—
1202C2#385×D4311yescharacteristic
1203C2#1913711611yescharacteristic
1204C2#1913724811yescharacteristic
1205C2#1913750311yescharacteristic
1206C2#1913750411yescharacteristic
1207C2#1913763911yescharacteristic
1208C2#1913764111yescharacteristic
1209C2#1913791511yescharacteristic
1210C2#1913791711yescharacteristic
1211C2#1913834611yescharacteristic
1212C2#1913834811yescharacteristic
1213C2#1913842011yescharacteristic
1214C2#1913842211yescharacteristic
1215C2#1913890711yescharacteristic
1216C2#1913994311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1442C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenter#1442D43
hypocenterC43#14016
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
4. C2×#14582773C2semidirect
5. C2×#95×D43C2semidirect
6. #19132854C2semidirect
7. #19132841C2semidirect
8. #19132839C2semidirect
9. #19132829C2semidirect
10. #19132826C2semidirect
11. (C2×D43)⋊#95C2semidirect
12. (C2×D43)⋊#95C2semidirect
13. (C2×D43)⋊#95C2semidirect
14. (C2×D43)⋊#95C2semidirect
15. C43×#1442C2semidirect
36. #14582777C4semidirect
99. C22×C4×D43C2×C4semidirect
128. C2×(C2×D43)⋊C4C2×C4semidirect
129. C2×(C2×D43)⋊C4C2×C4semidirect
130. C2×(C2×D43)⋊C4C2×C4semidirect
146. C43⋊#95C2×C4semidirect
162. #95×C43C2×C4semidirect
291. C2×D172C4⋊C4semidirect
598. #1442D43semidirect
666. C43#14016semidirect
771. #95C4×D43semidirect

Maximal subgroups

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

subgroupindex
C22×#130632872
C2×#145827772
C2×#145827732
C2×#95×D432
#191328542
#191328412
#191328392
#191328292
#191328262
(C2×D43)⋊#952
C43×#14422
#1401643