Finite Group Databasebeta

← #25025142

Subgroups — #25025142

Order 11008.

1450 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582757C211yesmaximal, characteristic
2#19132855C211yesmaximal, characteristic, complemented
3#19132855C211yesmaximal, characteristic, complemented
4#19132846C211yesmaximal, characteristic, complemented
5#19132845C211yesmaximal, characteristic, complemented
6#19132838C211yesmaximal, characteristic
7#19132832C211yesmaximal, characteristic
8#19132832C211yesmaximal, characteristic
9#19132830C211yesmaximal, characteristic, complemented
10#19132827C211yesmaximal, characteristic, complemented
11#19132826C211yesmaximal, characteristic, complemented
12#19132826C211yesmaximal, characteristic, complemented
13#19132817C211yesmaximal, characteristic
14#19132817C211yesmaximal, characteristic
15C43×#1439C211yesmaximal, characteristic
16C24×Dic43C2211yescharacteristic
17C22×Dic43⋊C4C2211yescharacteristic
18C22×Dic43⋊C4C2211yescharacteristic
19C22×Dic43⋊C4C2211yescharacteristic
20C22×C22⋊Dic43C2211yescharacteristic
21C22×C22⋊Dic43C2211yescharacteristic
22C22×C22⋊Dic43C2211yescharacteristic
23C22×C4×Dic43C2211yescharacteristic
24C22×C4×Dic43C2211yescharacteristic
25#14582757C418yescomplemented
26C2×C43⋊#95C2211yescharacteristic
27C2×C43⋊#95C2211yescharacteristic
28C2×C43⋊#95C2211yescharacteristic
29C2×C43⋊#95C2211yescharacteristic
30C2×C43⋊#95C2211yescharacteristic
31C2×C43⋊#95C2211yescharacteristic
32C2×C43⋊#95C2211yescharacteristic
33C2×C43⋊#95C2211yescharacteristic
34C2×C43⋊#95C2211yescharacteristic
35C2×C43⋊#95C2211yescharacteristic
36C2×C43⋊#95C2211yescharacteristic
37C2×C43⋊#95C2211yescharacteristic
38C2×C43⋊#95C2211yescharacteristic
39C2×C43⋊#95C2211yescharacteristic
40C2×C43⋊#95C2211yescharacteristic
41C2×C43⋊#95C2211yescharacteristic
42C2×C43⋊#95C2211yescharacteristic
43C2×C43⋊#95C2211yescharacteristic
44C2×C43⋊#95C2211yescharacteristic
45C22×C4⋊C4×C43C2211yescharacteristic
46C22×C22⋊C4×C43C2211yescharacteristic
47C22×C22⋊C4×C43C2211yescharacteristic
48C22×C22⋊C4×C43C2211yescharacteristic
49C2×#95×C43C2211yescharacteristic
50C2×#95×C43C2211yescharacteristic
51C2×#95×C43C2211yescharacteristic
52C23×Dic43—22no—
53C23×Dic43—22no—
54C23×Dic43—41no—
55C23×Dic43—41no—
56C23×Dic43—41no—
57C23×Dic43—41no—
58C23×Dic43C2×C414yes—
59C23×Dic43C2311yescharacteristic
60C23×Dic43C2311yescharacteristic
61C23×Dic43C2311yescharacteristic
62C23×Dic43C2311yescharacteristic
63C23×Dic43C2311yescharacteristic
64C23×Dic43C2311yescharacteristic
65C23×Dic43C2311yescharacteristic
66C23×Dic43C2311yescharacteristic
67C2×Dic43⋊C4—22no—
68C2×Dic43⋊C4—41no—
69C2×Dic43⋊C4—41no—
70C2×Dic43⋊C4—41no—
71C2×Dic43⋊C4—41no—
72C2×Dic43⋊C4—41no—
73C2×Dic43⋊C4—41no—
74C2×Dic43⋊C4C2×C414yes—
75C2×Dic43⋊C4C2×C414yes—
76C2×C22⋊Dic43—22no—
77C2×C22⋊Dic43—22no—
78C2×C22⋊Dic43—41no—
79C2×C22⋊Dic43—41no—
80C2×C22⋊Dic43—41no—
81C2×C22⋊Dic43—41no—
82C2×C22⋊Dic43—41no—
83C2×C22⋊Dic43C2×C414yes—
84C2×C22⋊Dic43Q814yes—
85C2×C4×Dic43—41no—
86C2×C4×Dic43—41no—
87C2×C4×Dic43—41no—
88C2×C4×Dic43—41no—
89C2×C4×Dic43—41no—
90C2×C4×Dic43—41no—
91C43⋊#95—22no—
92C43⋊#95—22no—
93C43⋊#95—22no—
94C43⋊#95—22no—
95C43⋊#95—22no—
96C43⋊#95—22no—
97C43⋊#95—41no—
98C43⋊#95—41no—
99C43⋊#95—41no—
100C43⋊#95—41no—
101C43⋊#95—41no—
102C43⋊#95—41no—
103C43⋊#95—41no—
104C43⋊#95—41no—
105C43⋊#95—41no—
106C43⋊#95—41no—
107C43⋊#95—41no—
108C43⋊#95C2×C414yes—
109C43⋊#95C2×C414yes—
110C25×C43C2311yescharacteristic
111C23×C4×C43C2311yescharacteristic
112C23×C4×C43C2311yescharacteristic
113C23×C4×C43C2311yescharacteristic
114C23×C4×C43C2311yescharacteristic
115C23×C4×C43C2311yescharacteristic
116C23×C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43—22no—
118C2×C4⋊C4×C43—41no—
119C2×C4⋊C4×C43—41no—
120C2×C22⋊C4×C43—22no—
121C2×C22⋊C4×C43—22no—
122C2×C22⋊C4×C43—22no—
123C2×C22⋊C4×C43—41no—
124C2×C22⋊C4×C43—41no—
125C2×C22⋊C4×C43—41no—
126C2×C22⋊C4×C43—41no—
127C2×C22⋊C4×C43—41no—
128C2×C22⋊C4×C43C2×C414yes—
129#95×C43—41no—
130#95×C43—41no—
131#95×C43—41no—
132C24×C43—21no—
133C24×C43—21no—
134C24×C43—21no—
135C24×C43—21no—
136C24×C43—21no—
137C24×C43—21no—
138C24×C43—21no—
139C24×C43—21no—
140C24×C43—21no—
141C24×C43—21no—
142C24×C43—21no—
143C24×C43—21no—
144C24×C43C22×C412yes—
145C24×C43C2×Q812yes—
146C24×C43#4112yes—
147C24×C43C2411yescharacteristic
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43C22×C412yes—
188C22×C4×C43C22×C412yes—
189C22×C4×C43#4112yes—
190C22×Dic43—28no—
191C22×Dic43—21no—
192C22×Dic43—21no—
193C22×Dic43—21no—
194C22×Dic43—21no—
195C22×Dic43—21no—
196C22×Dic43—21no—
197C22×Dic43—21no—
198C22×Dic43—21no—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205C22×Dic43—21no—
206C22×Dic43—21no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—21no—
216C22×Dic43—21no—
217C22×Dic43—21no—
218C22×Dic43—21no—
219C22×Dic43—21no—
220C22×Dic43—21no—
221C22×Dic43—21no—
222C22×Dic43—21no—
223C22×Dic43—21no—
224C22×Dic43—21no—
225C22×Dic43—21no—
226C22×Dic43—21no—
227C22×Dic43—21no—
228C22×Dic43—21no—
229C22×Dic43—21no—
230C22×Dic43—21no—
231C22×Dic43—21no—
232C22×Dic43—21no—
233C22×Dic43—21no—
234C22×Dic43—21no—
235C22×Dic43—21no—
236C22×Dic43—21no—
237C22×Dic43—21no—
238C22×Dic43—44no—
239C22×Dic43—44no—
240C22×Dic43—44no—
241C22×Dic43—44no—
242C22×Dic43—44no—
243C22×Dic43—44no—
244C22×Dic43C22×C412yes—
245C22×Dic43C22×C412yes—
246C22×Dic43C22×C412yes—
247C22×Dic43C22×C412yes—
248C22×Dic43C2×Q812yes—
249C22×Dic43C2×Q812yes—
250C22×Dic43#4112yes—
251C22×Dic43#4112yes—
252C22×Dic43#4112yes—
253C4⋊C4×C43—44no—
254C22⋊C4×C43—44no—
255C22⋊C4×C43—44no—
256C22⋊C4×C43—44no—
257C22⋊Dic43—44no—
258C22⋊Dic43—44no—
259C22⋊Dic43—44no—
260Dic43⋊C4—44no—
261Dic43⋊C4—44no—
262Dic43⋊C4—44no—
263C4×Dic43—44no—
264C4×Dic43—44no—
265C23×C43—22no—
266C23×C43—22no—
267C23×C43—22no—
268C23×C43—22no—
269C23×C43—22no—
270C23×C43—22no—
271C23×C43—22no—
272C23×C43—22no—
273C23×C43—22no—
274C23×C43—22no—
275C23×C43—22no—
276C23×C43—22no—
277C23×C43—22no—
278C23×C43—22no—
279C23×C43—22no—
280C23×C43—22no—
281C23×C43—22no—
282C23×C43—22no—
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—41no—
292C23×C43—41no—
293C23×C43—41no—
294C23×C43—41no—
295C23×C43—41no—
296C23×C43—41no—
297C23×C43—41no—
298C23×C43—41no—
299C23×C43C4×Q814yes—
300C23×C43C23×C411yescharacteristic
301C23×C43C22×Q811yescharacteristic
302C23×C43C2×#4111yescharacteristic
303C23×C43C2×#4111yescharacteristic
304C23×C43C2×#4111yescharacteristic
305C23×C43C2×#4111yescharacteristic
306C23×C43C2×#4111yescharacteristic
307C23×C43H(5,𝔽2)11yescharacteristic
308C23×C43H(5,𝔽2)11yescharacteristic
309C23×C43H(5,𝔽2)11yescharacteristic
310C23×C43H(5,𝔽2)11yescharacteristic
311C23×C43H(5,𝔽2)11yescharacteristic
312C23×C43H(5,𝔽2)11yescharacteristic
313C23×C43H(5,𝔽2)11yescharacteristic
314C23×C432−1+411yescharacteristic
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43—41no—
342C2×C4×C43—41no—
343C2×C4×C43—41no—
344C2×C4×C43—41no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43—41no—
350C2×C4×C43—41no—
351C2×C4×C43—41no—
352C2×C4×C43—41no—
353C2×C4×C43—41no—
354C2×C4×C43—41no—
355C2×C4×C43—41no—
356C2×C4×C43—41no—
357C2×Dic43—22no—
358C2×Dic43—22no—
359C2×Dic43—22no—
360C2×Dic43—22no—
361C2×Dic43—22no—
362C2×Dic43—22no—
363C2×Dic43—22no—
364C2×Dic43—22no—
365C2×Dic43—22no—
366C2×Dic43—22no—
367C2×Dic43—22no—
368C2×Dic43—22no—
369C2×Dic43—22no—
370C2×Dic43—22no—
371C2×Dic43—22no—
372C2×Dic43—22no—
373C2×Dic43—22no—
374C2×Dic43—22no—
375C2×Dic43—22no—
376C2×Dic43—22no—
377C2×Dic43—22no—
378C2×Dic43—22no—
379C2×Dic43—22no—
380C2×Dic43—22no—
381C2×Dic43—416no—
382C2×Dic43—41no—
383C2×Dic43—41no—
384C2×Dic43—41no—
385C2×Dic43—41no—
386C2×Dic43—41no—
387C2×Dic43—41no—
388C2×Dic43—41no—
389C2×Dic43—41no—
390C2×Dic43—41no—
391C2×Dic43—41no—
392C2×Dic43—41no—
393C2×Dic43—41no—
394C2×Dic43—41no—
395C2×Dic43—41no—
396C2×Dic43—41no—
397C2×Dic43—41no—
398C2×Dic43—41no—
399C2×Dic43—41no—
400C2×Dic43—41no—
401C2×Dic43—41no—
402C2×Dic43—41no—
403C2×Dic43—41no—
404C2×Dic43—41no—
405C2×Dic43—41no—
406C2×Dic43—41no—
407C2×Dic43—41no—
408C2×Dic43—41no—
409C2×Dic43—41no—
410C2×Dic43—41no—
411C2×Dic43—41no—
412C2×Dic43—41no—
413C2×Dic43#11714yes—
414#14453—431nomaximal, Sylow
415C22×C43—24no—
416C22×C43—24no—
417C22×C43—24no—
418C22×C43—42no—
419C22×C43—42no—
420C22×C43—42no—
421C22×C43—42no—
422C22×C43—42no—
423C22×C43—42no—
424C22×C43—42no—
425C22×C43—42no—
426C22×C43—42no—
427C22×C43—42no—
428C22×C43—42no—
429C22×C43—42no—
430C22×C43C2×#11711yescharacteristic
431C22×C43C2×C4×Q811yescharacteristic
432C22×C43C4×#4111yescharacteristic
433C22×C43#51811yescharacteristic
434C22×C43#51811yescharacteristic
435C22×C43#51811yescharacteristic
436C22×C43#52011yescharacteristic
437C22×C43#53811yescharacteristic
438C22×C43#53811yescharacteristic
439C22×C43#53811yescharacteristic
440C22×C43#53811yescharacteristic
441C22×C43#53811yescharacteristic
442C22×C43#53811yescharacteristic
443C22×C43#53811yescharacteristic
444C22×C43#53911yescharacteristic
445C22×C43#54011yescharacteristic
446C22×C43#54011yescharacteristic
447C22×C43#54311yescharacteristic
448C22×C43#54411yescharacteristic
449C22×C43#55111yescharacteristic
450C22×C43#55111yescharacteristic
451C22×C43#55311yescharacteristic
452C22×C43#55311yescharacteristic
453C22×C43#55311yescharacteristic
454C22×C43#55311yescharacteristic
455C22×C43#55411yescharacteristic
456C22×C43#55411yescharacteristic
457C22×C43#55411yescharacteristic
458C22×C43#55411yescharacteristic
459C22×C43#55611yescharacteristic
460C22×C43#55611yescharacteristic
461C22×C43#56011yescharacteristic
462C22×C43#56011yescharacteristic
463C22×C43#56211yescharacteristic
464C22×C43#56211yescharacteristic
465C4×C43—42no—
466C4×C43—42no—
467C4×C43—42no—
468C4×C43—81no—
469C4×C43—81no—
470C4×C43—81no—
471Dic43—24no—
472Dic43—42no—
473Dic43—42no—
474Dic43—42no—
475Dic43—42no—
476Dic43—42no—
477Dic43—42no—
478Dic43—81no—
479C2×#380—431no—
480#1443—431no—
481#1443—431no—
482#1441—431no—
483#1441—431no—
484#1439—431no—
485#1439D4311yescharacteristic
486#1437—431no—
487#1437—431no—
488#1436—431no—
489#1436—431no—
490#1436—431no—
491#1436—431no—
492C22⋊#95—431no—
493C22⋊#95—431no—
494C2×C43—44no—
495C2×C43#231211yescharacteristic
496C2×C43#232911yescharacteristic
497C2×C43#233311yescharacteristic
498C2×C43#234511yescharacteristic
499C2×C43#234711yescharacteristic
500C2×C43#236811yescharacteristic
501C2×C43#237711yescharacteristic
502C2×C43#277811yescharacteristic
503C2×C43#277811yescharacteristic
504C2×C43#278011yescharacteristic
505C2×C43#278011yescharacteristic
506C2×C43#278611yescharacteristic
507C2×C43#278611yescharacteristic
508C2×C43#278811yescharacteristic
509C2×C43#278811yescharacteristic
510C24×C4—431no—
511C22×C4⋊C4—431no—
512C22×C4⋊C4—431no—
513C22×C4⋊C4—431no—
514C22×C4⋊C4C2×D4311yescharacteristic
515C22×C22⋊C4—431no—
516C22×C22⋊C4—431no—
517C22×C22⋊C4—431no—
518C22×C22⋊C4C2×D4311yescharacteristic
519C22×C22⋊C4C2×D4311yescharacteristic
520C22×C22⋊C4C2×D4311yescharacteristic
521C22×C42—431no—
522C22×C42—431no—
523#380—438no—
524C2×#95—431no—
525C2×#95—431no—
526C2×#95—431no—
527C2×#95—431no—
528C2×#95—431no—
529C2×#95—431no—
530C2×#95—431no—
531C2×#95—431no—
532C2×#95—431no—
533C2×#95—431no—
534C2×#95—431no—
535C2×#95—431no—
536C2×#95—431no—
537C2×#95—431no—
538C2×#95—431no—
539C2×#95—431no—
540C2×#95—431no—
541C2×#95—431no—
542C2×#95—431no—
543C2×#95C2×D4311yescharacteristic
544C2×#95C2×D4311yescharacteristic
545C2×#95C2×D4311yescharacteristic
546C43#1445311yescharacteristic, complemented, Sylow
547C25C22×D4311yescharacteristic
548C23×C4—431no—
549C23×C4—431no—
550C23×C4—431no—
551C23×C4—431no—
552C23×C4—431no—
553C23×C4—431no—
554C23×C4—431no—
555C23×C4—434no—
556C23×C4—431no—
557C23×C4—862no—
558C23×C4—862no—
559C23×C4—1721no—
560C23×C4—1721no—
561C23×C4—1721no—
562C23×C4—1721no—
563C23×C4C22×D4311yescharacteristic
564C23×C4C22×D4311yescharacteristic
565C23×C4C22×D4311yescharacteristic
566C23×C4C22×D4311yescharacteristic
567C23×C4C22×D4311yescharacteristic
568C23×C4C22×D4311yescharacteristic
569C2×C4⋊C4—22no—
570C2×C4⋊C4—41no—
571C2×C4⋊C4—41no—
572C2×C4⋊C4—434no—
573C2×C4⋊C4—434no—
574C2×C4⋊C4—862no—
575C2×C4⋊C4—1721no—
576C2×C4⋊C4—1721no—
577C2×C4⋊C4—1721no—
578C2×C4⋊C4—1721no—
579C2×C4⋊C4—1721no—
580C2×C4⋊C4—1721no—
581C2×C22⋊C4—22no—
582C2×C22⋊C4—22no—
583C2×C22⋊C4—22no—
584C2×C22⋊C4—41no—
585C2×C22⋊C4—41no—
586C2×C22⋊C4—41no—
587C2×C22⋊C4—41no—
588C2×C22⋊C4—41no—
589C2×C22⋊C4—434no—
590C2×C22⋊C4—434no—
591C2×C22⋊C4—862no—
592C2×C22⋊C4—862no—
593C2×C22⋊C4—1721no—
594C2×C22⋊C4—1721no—
595C2×C22⋊C4—1721no—
596C2×C22⋊C4—1721no—
597C2×C22⋊C4—1721no—
598C2×C22⋊C4C4×D4314yes—
599C2×C42—1721no—
600C2×C42—1721no—
601C2×C42—1721no—
602C2×C42—1721no—
603C2×C42—1721no—
604C2×C42—1721no—
605#95—41no—
606#95—41no—
607#95—41no—
608#95—434no—
609#95—434no—
610#95—862no—
611#95—862no—
612#95—862no—
613#95—862no—
614#95—862no—
615#95—862no—
616#95—1721no—
617#95—1721no—
618#95—1721no—
619#95—1721no—
620#95—1721no—
621#95—1721no—
622#95—1721no—
623#95—1721no—
624#95—1721no—
625#95—1721no—
626#95—1721no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24C2×C4×D4312yes—
640C24#1062190012yes—
641C24Q8×D4312yes—
642C24C23×D4311yescharacteristic
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—432no—
683C22×C4—432no—
684C22×C4—432no—
685C22×C4—432no—
686C22×C4—432no—
687C22×C4—432no—
688C22×C4—432no—
689C22×C4—432no—
690C22×C4—432no—
691C22×C4—868no—
692C22×C4—861no—
693C22×C4—861no—
694C22×C4—861no—
695C22×C4—861no—
696C22×C4—861no—
697C22×C4—861no—
698C22×C4—861no—
699C22×C4—861no—
700C22×C4—861no—
701C22×C4—861no—
702C22×C4—861no—
703C22×C4—861no—
704C22×C4—861no—
705C22×C4—861no—
706C22×C4—861no—
707C22×C4—861no—
708C22×C4—861no—
709C22×C4—861no—
710C22×C4—861no—
711C22×C4—861no—
712C22×C4—861no—
713C22×C4—861no—
714C22×C4—861no—
715C22×C4—861no—
716C22×C4—861no—
717C22×C4—861no—
718C22×C4—861no—
719C22×C4—861no—
720C22×C4—861no—
721C22×C4—861no—
722C22×C4—861no—
723C22×C4—861no—
724C22×C4—861no—
725C22×C4—861no—
726C22×C4—861no—
727C22×C4—861no—
728C22×C4—861no—
729C22×C4—861no—
730C22×C4—861no—
731C22×C4—861no—
732C22×C4—861no—
733C22×C4—861no—
734C22×C4—861no—
735C22×C4—861no—
736C22×C4—861no—
737C22×C4—861no—
738C22×C4—861no—
739C22×C4—1724no—
740C22×C4—1724no—
741C22×C4—1724no—
742C22×C4—1724no—
743C22×C4—1724no—
744C22×C4—1724no—
745C22×C4C2×C4×D4312yes—
746C22×C4C2×C4×D4312yes—
747C22×C4#1062190012yes—
748C4⋊C4—44no—
749C4⋊C4—1724no—
750C4⋊C4—1724no—
751C4⋊C4—1724no—
752C22⋊C4—44no—
753C22⋊C4—44no—
754C22⋊C4—44no—
755C22⋊C4—1724no—
756C22⋊C4—1724no—
757C22⋊C4—1724no—
758C42—1724no—
759C42—1724no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23#1306329014yes—
795C23C22×C4×D4311yescharacteristic
796C23C2×Q8×D4311yescharacteristic
797C23#41×D4311yescharacteristic
798C23#41×D4311yescharacteristic
799C23#41×D4311yescharacteristic
800C23C2×#1062190011yescharacteristic
801C23C2×#1062190011yescharacteristic
802C23#1306337011yescharacteristic
803C23#1306337011yescharacteristic
804C23#1306337011yescharacteristic
805C23#1306337011yescharacteristic
806C23#1306337011yescharacteristic
807C23#1306337111yescharacteristic
808C23#1306337111yescharacteristic
809C23#1306337211yescharacteristic
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—434no—
853C2×C4—862no—
854C2×C4—862no—
855C2×C4—862no—
856C2×C4—862no—
857C2×C4—862no—
858C2×C4—862no—
859C2×C4—862no—
860C2×C4—862no—
861C2×C4—862no—
862C2×C4—862no—
863C2×C4—862no—
864C2×C4—862no—
865C2×C4—862no—
866C2×C4—862no—
867C2×C4—862no—
868C2×C4—862no—
869C2×C4—862no—
870C2×C4—862no—
871C2×C4—862no—
872C2×C4—862no—
873C2×C4—862no—
874C2×C4—862no—
875C2×C4—862no—
876C2×C4—862no—
877C2×C4—17216no—
878C2×C4—1721no—
879C2×C4—1721no—
880C2×C4—1721no—
881C2×C4—1721no—
882C2×C4—1721no—
883C2×C4—1721no—
884C2×C4—1721no—
885C2×C4—1721no—
886C2×C4—1721no—
887C2×C4—1721no—
888C2×C4—1721no—
889C2×C4—1721no—
890C2×C4—1721no—
891C2×C4—1721no—
892C2×C4—1721no—
893C2×C4—1721no—
894C2×C4—1721no—
895C2×C4—1721no—
896C2×C4—1721no—
897C2×C4—1721no—
898C2×C4—1721no—
899C2×C4—1721no—
900C2×C4—1721no—
901C2×C4—1721no—
902C2×C4—1721no—
903C2×C4—1721no—
904C2×C4—1721no—
905C2×C4—1721no—
906C2×C4—1721no—
907C2×C4—1721no—
908C2×C4—1721no—
909C22—24no—
910C22—24no—
911C22—24no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22#117×D4311yescharacteristic
925C22C2×#1306329011yescharacteristic
926C22C4×#1062190011yescharacteristic
927C22#1458337111yescharacteristic
928C22#1458337111yescharacteristic
929C22#1458337211yescharacteristic
930C22#1458337811yescharacteristic
931C22#1458348111yescharacteristic
932C22#1458348111yescharacteristic
933C22#1458348311yescharacteristic
934C22#1458348411yescharacteristic
935C22#1458348411yescharacteristic
936C22#1458348511yescharacteristic
937C22#1458348811yescharacteristic
938C22#1458349311yescharacteristic
939C22#1458350111yescharacteristic
940C22#1458350211yescharacteristic
941C22#1458352411yescharacteristic
942C22#1458352811yescharacteristic
943C22#1458357211yescharacteristic
944C22#1458358011yescharacteristic
945C22#1458359211yescharacteristic
946C22#1458359211yescharacteristic
947C22#1458359211yescharacteristic
948C22#1458359411yescharacteristic
949C22#1458360311yescharacteristic
950C22#1458360311yescharacteristic
951C22#1458360311yescharacteristic
952C22#1458360711yescharacteristic
953C22#1458361611yescharacteristic
954C22#1458361811yescharacteristic
955C22#1458363611yescharacteristic
956C22#1458363711yescharacteristic
957C22#1458364311yescharacteristic
958C22#1458364411yescharacteristic
959C4—42no—
960C4—42no—
961C4—42no—
962C4—81no—
963C4—81no—
964C4—81no—
965C4—864no—
966C4—3441no—
967C4—1722no—
968C4—1722no—
969C4—1722no—
970C4—1722no—
971C4—1722no—
972C4—1722no—
973C2—44no—
974C2#1913718911yescharacteristic
975C2#1913732611yescharacteristic
976C2#1913736111yescharacteristic
977C2#1913746711yescharacteristic
978C2#1913748511yescharacteristic
979C2#1913767611yescharacteristic
980C2#1913774611yescharacteristic
981C2#1914220611yescharacteristic
982C2#1914221811yescharacteristic
983C2#1914223611yescharacteristic
984C2#1914224811yescharacteristic
985C2#1914230411yescharacteristic
986C2#1914231611yescharacteristic
987C2#1914233411yescharacteristic
988C2#1914234611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1439C2
socle, cosocleC24×C43C24
prime radicalC25×C43C23
hypercenter#1439D43
hypocenterC43#14453
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. #19132855C2semidirect
3. #19132855C2semidirect
4. #19132846C2semidirect
5. #19132845C2semidirect
9. #19132830C2semidirect
10. #19132827C2semidirect
11. #19132826C2semidirect
12. #19132826C2semidirect
25. #14582757C4semidirect
546. C43#14453semidirect

Maximal subgroups

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

subgroupindex
C2×#145827572
#191328552
#191328462
#191328452
#191328382
#191328322
#191328302
#191328272
#191328262
#191328172
C43×#14392
#1445343