Finite Group Databasebeta

← #25023712

Subgroups — #25023712

Order 11008.

1290 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582821C211yesmaximal, characteristic
2#19132862C211yesmaximal, characteristic, complemented
3#19132861C211yesmaximal, characteristic, complemented
4#19132856C211yesmaximal, characteristic, complemented
5#19132843C211yesmaximal, characteristic
6#19132843C211yesmaximal, characteristic
7#19132843C211yesmaximal, characteristic
8#19132831C211yesmaximal, characteristic
9#19132831C211yesmaximal, characteristic
10#19132831C211yesmaximal, characteristic
11#19132829C211yesmaximal, characteristic, complemented
12#19132827C211yesmaximal, characteristic, complemented
13#19132826C211yesmaximal, characteristic, complemented
14#95×Dic43C211yesmaximal, characteristic, complemented
15C43×#1445C211yesmaximal, characteristic, complemented
16C22×C4⋊Dic43C2211yescharacteristic
17C22×Dic43⋊C4C2211yescharacteristic
18C22×(C2×D43)⋊C4C2211yescharacteristic
19C22×(C2×D43)⋊C4C2211yescharacteristic
20C22×(C2×D43)⋊C4C2211yescharacteristic
21C22×(C2×D43)⋊C4C2211yescharacteristic
22C22×(C2×D43)⋊C4C2211yescharacteristic
23C22×(C2×D43)⋊C4C2211yescharacteristic
24C22×(C2×D43)⋊C4C2211yescharacteristic
25C22×C4×Dic43C2211yescharacteristic
26C22×C4×Dic43C2211yescharacteristic
27C22×C4×Dic43C2211yescharacteristic
28#14582821C418yescomplemented
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
46C2×#95×C43C2211yescharacteristic
47C2×#95×C43C2211yescharacteristic
48C2×#95×C43C2211yescharacteristic
49C2×#95×C43C2211yescharacteristic
50C2×#95×C43C2211yescharacteristic
51C2×#95×C43C2211yescharacteristic
52C24×D43C2311yescharacteristic
53C23×Dic43C2311yescharacteristic
54C23×Dic43C2311yescharacteristic
55C23×Dic43C2311yescharacteristic
56C23×Dic43C2311yescharacteristic
57C23×Dic43C2311yescharacteristic
58C23×Dic43C2311yescharacteristic
59C23×Dic43C2311yescharacteristic
60C2×C4⋊Dic43—41no—
61C2×C4⋊Dic43—41no—
62C2×C4⋊Dic43C2×C414yes—
63C2×Dic43⋊C4—41no—
64C2×Dic43⋊C4—41no—
65C2×Dic43⋊C4C2×C414yes—
66C2×(C2×D43)⋊C4—22no—
67C2×(C2×D43)⋊C4—22no—
68C2×(C2×D43)⋊C4—22no—
69C2×(C2×D43)⋊C4—22no—
70C2×(C2×D43)⋊C4—22no—
71C2×(C2×D43)⋊C4—22no—
72C2×(C2×D43)⋊C4—41no—
73C2×(C2×D43)⋊C4—41no—
74C2×(C2×D43)⋊C4—41no—
75C2×(C2×D43)⋊C4—41no—
76C2×(C2×D43)⋊C4—41no—
77C2×(C2×D43)⋊C4—41no—
78C2×(C2×D43)⋊C4—41no—
79C2×(C2×D43)⋊C4—41no—
80C2×(C2×D43)⋊C4—41no—
81C2×(C2×D43)⋊C4—41no—
82C2×(C2×D43)⋊C4—41no—
83C2×(C2×D43)⋊C4—41no—
84C2×(C2×D43)⋊C4C2×C414yes—
85C2×(C2×D43)⋊C4C2×C414yes—
86C2×(C2×D43)⋊C4C2×C414yes—
87C2×C4×Dic43—22no—
88C2×C4×Dic43—22no—
89C2×C4×Dic43—22no—
90C2×C4×Dic43—41no—
91C2×C4×Dic43—41no—
92C2×C4×Dic43—41no—
93C2×C4×Dic43—41no—
94C2×C4×Dic43—41no—
95C2×C4×Dic43—41no—
96C43⋊#95—22no—
97C43⋊#95—22no—
98C43⋊#95—22no—
99C43⋊#95—22no—
100C43⋊#95—22no—
101C43⋊#95—22no—
102C43⋊#95—22no—
103C43⋊#95—41no—
104C43⋊#95—41no—
105C43⋊#95—41no—
106C43⋊#95—41no—
107C43⋊#95—41no—
108C43⋊#95—41no—
109C43⋊#95—41no—
110C43⋊#95—41no—
111C43⋊#95C2×C414yes—
112C23×C4×C43C2311yescharacteristic
113C23×C4×C43C2311yescharacteristic
114C23×C4×C43C2311yescharacteristic
115C23×C4×C43C2311yescharacteristic
116C23×C4×C43C2311yescharacteristic
117C23×C4×C43C2311yescharacteristic
118C23×C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43—41no—
120C2×C4⋊C4×C43—41no—
121C2×C4⋊C4×C43C2×C414yes—
122#95×C43—22no—
123#95×C43—22no—
124#95×C43—41no—
125#95×C43—41no—
126#95×C43—41no—
127#95×C43—41no—
128C24×C43C2411yescharacteristic
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—21no—
140C23×D43—21no—
141C23×D43—21no—
142C23×D43—21no—
143C23×D43C22×C412yes—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
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×C43—21no—
188C22×C4×C43C22×C412yes—
189C22×C4×C43C22×C412yes—
190C22×C4×C43C22×C412yes—
191C22×C4×C43#4112yes—
192C22×C4×C43#4112yes—
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×Dic43C22×C412yes—
236C22×Dic43C22×C412yes—
237C22×Dic43C22×C412yes—
238C22×Dic43#4112yes—
239C22×Dic43#4112yes—
240C22×Dic43#4112yes—
241C22×Dic43#4112yes—
242C4⋊C4×C43—44no—
243(C2×D43)⋊C4—44no—
244(C2×D43)⋊C4—44no—
245(C2×D43)⋊C4—44no—
246(C2×D43)⋊C4—44no—
247(C2×D43)⋊C4—44no—
248(C2×D43)⋊C4—44no—
249(C2×D43)⋊C4—44no—
250C4⋊Dic43—44no—
251Dic43⋊C4—44no—
252C4×Dic43—44no—
253C4×Dic43—44no—
254C4×Dic43—44no—
255C23×C43C23×C411yescharacteristic
256C23×C43C2×#4111yescharacteristic
257C23×C43C2×#4111yescharacteristic
258C23×C43C2×#4111yescharacteristic
259C23×C43C2×#4111yescharacteristic
260C23×C43C2×#4111yescharacteristic
261C23×C43C2×#4111yescharacteristic
262C23×C43H(5,𝔽2)11yescharacteristic
263C23×C43H(5,𝔽2)11yescharacteristic
264C23×C43H(5,𝔽2)11yescharacteristic
265C23×C43H(5,𝔽2)11yescharacteristic
266C23×C43H(5,𝔽2)11yescharacteristic
267C23×C43H(5,𝔽2)11yescharacteristic
268C23×C432−1+411yescharacteristic
269C23×C432−1+411yescharacteristic
270C22×D43—22no—
271C22×D43—22no—
272C22×D43—22no—
273C22×D43—22no—
274C22×D43—22no—
275C22×D43—22no—
276C22×D43—22no—
277C22×D43—41no—
278C22×D43—41no—
279C22×D43—41no—
280C22×D43—41no—
281C22×D43—41no—
282C22×D43—41no—
283C22×D43—41no—
284C22×D43—41no—
285C22×D43—41no—
286C22×D43—41no—
287C22×D43—41no—
288C22×D43—41no—
289C22×D43—41no—
290C22×D43—41no—
291C22×D43—41no—
292C22×D43—41no—
293C22×D43—41no—
294C22×D43—41no—
295C22×D43—41no—
296C22×D43—41no—
297C22×D43—41no—
298C22×D43—41no—
299C22×D43—41no—
300C22×D43—41no—
301C22×D43—41no—
302C22×D43—41no—
303C22×D43—41no—
304C22×D43—41no—
305C2×C4×C43—22no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—41no—
321C2×C4×C43—41no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
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×Dic43—22no—
355C2×Dic43—22no—
356C2×Dic43—22no—
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—41no—
373C2×Dic43—41no—
374C2×Dic43—41no—
375C2×Dic43—41no—
376C2×Dic43—41no—
377C2×Dic43—41no—
378C2×Dic43—41no—
379C2×Dic43—41no—
380C2×Dic43—41no—
381C2×Dic43—41no—
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#12614yes—
403#14331—431nomaximal, Sylow
404C22×C43C4×#4111yescharacteristic
405C22×C43C4×#4111yescharacteristic
406C22×C43C4×#4111yescharacteristic
407C22×C43#51811yescharacteristic
408C22×C43#51811yescharacteristic
409C22×C43#51811yescharacteristic
410C22×C43#51911yescharacteristic
411C22×C43C2×#12611yescharacteristic
412C22×C43#52911yescharacteristic
413C22×C43#52911yescharacteristic
414C22×C43#52911yescharacteristic
415C22×C43#53811yescharacteristic
416C22×C43#53811yescharacteristic
417C22×C43#53811yescharacteristic
418C22×C43#53811yescharacteristic
419C22×C43#53811yescharacteristic
420C22×C43#53811yescharacteristic
421C22×C43#53911yescharacteristic
422C22×C43#53911yescharacteristic
423C22×C43#53911yescharacteristic
424C22×C43#53911yescharacteristic
425C22×C43#53911yescharacteristic
426C22×C43#53911yescharacteristic
427C22×C43#54011yescharacteristic
428C22×C43#54011yescharacteristic
429C22×C43#54011yescharacteristic
430C22×C43#54011yescharacteristic
431C22×C43#54011yescharacteristic
432C22×C43#54011yescharacteristic
433C22×C43#54211yescharacteristic
434C22×C43#54211yescharacteristic
435C22×C43#54211yescharacteristic
436C22×C43#54211yescharacteristic
437C22×C43#54211yescharacteristic
438C22×C43#54211yescharacteristic
439C2×D43—42no—
440C2×D43—42no—
441C2×D43—42no—
442C2×D43—42no—
443C2×D43—42no—
444C2×D43—42no—
445C2×D43—42no—
446C2×D43—81no—
447C2×D43—81no—
448C2×D43—81no—
449C2×D43—81no—
450C2×D43—81no—
451C2×D43—81no—
452C2×D43—81no—
453C2×D43—81no—
454C4×C43—42no—
455C4×C43—42no—
456C4×C43—42no—
457C4×C43—42no—
458C4×C43—42no—
459C4×C43—81no—
460C4×C43—81no—
461Dic43—24no—
462Dic43—42no—
463Dic43—42no—
464Dic43—42no—
465Dic43—42no—
466Dic43—81no—
467Dic43—81no—
468C2×#396—431no—
469#1445—431no—
470#1445—431no—
471#1445D4311yescharacteristic, complemented
472#1443—431no—
473#1440—431no—
474#1440—431no—
475#1440—431no—
476#1437—431no—
477#1437—431no—
478#1437—431no—
479#1436—431no—
480#1436—431no—
481#1436—431no—
482C4×#95—431no—
483C2×C43C4×#12611yescharacteristic
484C2×C43#233211yescharacteristic
485C2×C43#233211yescharacteristic
486C2×C43#233211yescharacteristic
487C2×C43#233311yescharacteristic
488C2×C43#233311yescharacteristic
489C2×C43#233311yescharacteristic
490C2×C43#264311yescharacteristic
491C2×C43#264411yescharacteristic
492C2×C43#264911yescharacteristic
493C2×C43#264911yescharacteristic
494C2×C43#264911yescharacteristic
495C2×C43#265111yescharacteristic
496C2×C43#265111yescharacteristic
497C2×C43#265111yescharacteristic
498D43—82no—
499C22×C4⋊C4—431no—
500C22×C4⋊C4—431no—
501C22×C4⋊C4C2×D4311yescharacteristic
502C22×C22⋊C4—431no—
503C22×C22⋊C4—431no—
504C22×C22⋊C4—431no—
505C22×C22⋊C4—431no—
506C22×C22⋊C4—431no—
507C22×C22⋊C4—431no—
508C22×C22⋊C4—431no—
509C22×C42—431no—
510C22×C42—431no—
511C22×C42—431no—
512#396—438no—
513C2×#95—431no—
514C2×#95—431no—
515C2×#95—431no—
516C2×#95—431no—
517C2×#95—431no—
518C2×#95—431no—
519C2×#95—431no—
520C2×#95—431no—
521C2×#95—431no—
522C2×#95—431no—
523C2×#95—431no—
524C2×#95—431no—
525C2×#95—431no—
526C2×#95—431no—
527C2×#95—431no—
528C2×#95—431no—
529C2×#95C2×D4311yescharacteristic
530C2×#95C2×D4311yescharacteristic
531C2×#95C2×D4311yescharacteristic
532C2×#95C2×D4311yescharacteristic
533C2×#95C2×D4311yescharacteristic
534C2×#95C2×D4311yescharacteristic
535C43#1433111yescharacteristic, complemented, Sylow
536C25—431no—
537C23×C4—431no—
538C23×C4—431no—
539C23×C4—431no—
540C23×C4—431no—
541C23×C4—431no—
542C23×C4—431no—
543C23×C4—431no—
544C23×C4C22×D4311yescharacteristic
545C23×C4C22×D4311yescharacteristic
546C23×C4C22×D4311yescharacteristic
547C23×C4C22×D4311yescharacteristic
548C23×C4C22×D4311yescharacteristic
549C23×C4C22×D4311yescharacteristic
550C23×C4C22×D4311yescharacteristic
551C2×C4⋊C4—41no—
552C2×C4⋊C4—41no—
553C2×C4⋊C4—434no—
554C2×C4⋊C4—434no—
555C2×C4⋊C4—1721no—
556C2×C4⋊C4—1721no—
557C2×C4⋊C4—1721no—
558C2×C4⋊C4—1721no—
559C2×C4⋊C4C4×D4314yes—
560C2×C22⋊C4—434no—
561C2×C22⋊C4—434no—
562C2×C22⋊C4—434no—
563C2×C22⋊C4—862no—
564C2×C22⋊C4—862no—
565C2×C22⋊C4—862no—
566C2×C22⋊C4—862no—
567C2×C22⋊C4—862no—
568C2×C22⋊C4—862no—
569C2×C22⋊C4—1721no—
570C2×C22⋊C4—1721no—
571C2×C22⋊C4—1721no—
572C2×C22⋊C4—1721no—
573C2×C22⋊C4—1721no—
574C2×C22⋊C4—1721no—
575C2×C22⋊C4—1721no—
576C2×C22⋊C4—1721no—
577C2×C22⋊C4—1721no—
578C2×C22⋊C4—1721no—
579C2×C22⋊C4—1721no—
580C2×C22⋊C4—1721no—
581C2×C42—862no—
582C2×C42—862no—
583C2×C42—862no—
584C2×C42—1721no—
585C2×C42—1721no—
586C2×C42—1721no—
587C2×C42—1721no—
588C2×C42—1721no—
589C2×C42—1721no—
590#95—22no—
591#95—22no—
592#95—41no—
593#95—41no—
594#95—41no—
595#95—41no—
596#95—434no—
597#95—862no—
598#95—862no—
599#95—862no—
600#95—862no—
601#95—862no—
602#95—862no—
603#95—862no—
604#95—1721no—
605#95—1721no—
606#95—1721no—
607#95—1721no—
608#95—1721no—
609#95—1721no—
610#95—1721no—
611#95—1721no—
612C24—432no—
613C24—861no—
614C24—861no—
615C24—861no—
616C24—861no—
617C24—861no—
618C24—861no—
619C24—861no—
620C24—861no—
621C24—861no—
622C24—861no—
623C24—861no—
624C24—861no—
625C24—861no—
626C24—861no—
627C24C23×D4311yescharacteristic
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
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—432no—
673C22×C4—432no—
674C22×C4—432no—
675C22×C4—432no—
676C22×C4—432no—
677C22×C4—432no—
678C22×C4—432no—
679C22×C4—861no—
680C22×C4—861no—
681C22×C4—861no—
682C22×C4—861no—
683C22×C4—861no—
684C22×C4—861no—
685C22×C4—861no—
686C22×C4—861no—
687C22×C4—861no—
688C22×C4—861no—
689C22×C4—861no—
690C22×C4—861no—
691C22×C4—861no—
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×C4C2×C4×D4312yes—
722C22×C4C2×C4×D4312yes—
723C22×C4C2×C4×D4312yes—
724C22×C4#1062190012yes—
725C22×C4#1062190212yes—
726C4⋊C4—44no—
727C4⋊C4—1724no—
728C4⋊C4—1724no—
729C22⋊C4—1724no—
730C22⋊C4—1724no—
731C22⋊C4—1724no—
732C22⋊C4—1724no—
733C22⋊C4—1724no—
734C22⋊C4—1724no—
735C22⋊C4—1724no—
736C42—1724no—
737C42—1724no—
738C42—1724no—
739C23—862no—
740C23—862no—
741C23—862no—
742C23—862no—
743C23—862no—
744C23—862no—
745C23—862no—
746C23—1721no—
747C23—1721no—
748C23—1721no—
749C23—1721no—
750C23—1721no—
751C23—1721no—
752C23—1721no—
753C23—1721no—
754C23—1721no—
755C23—1721no—
756C23—1721no—
757C23—1721no—
758C23—1721no—
759C23—1721no—
760C23—1721no—
761C23—1721no—
762C23—1721no—
763C23—1721no—
764C23—1721no—
765C23—1721no—
766C23—1721no—
767C23—1721no—
768C23—1721no—
769C23—1721no—
770C23—1721no—
771C23—1721no—
772C23—1721no—
773C23—1721no—
774C23C22×C4×D4311yescharacteristic
775C23#41×D4311yescharacteristic
776C23#41×D4311yescharacteristic
777C23#41×D4311yescharacteristic
778C23#41×D4311yescharacteristic
779C23C2×#1062190011yescharacteristic
780C23C2×#1062190211yescharacteristic
781C23#1306337011yescharacteristic
782C23#1306337011yescharacteristic
783C23#1306337011yescharacteristic
784C23#1306337111yescharacteristic
785C23#1306337111yescharacteristic
786C23#1306337111yescharacteristic
787C23#1306337211yescharacteristic
788C23#1306337311yescharacteristic
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
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—434no—
839C2×C4—862no—
840C2×C4—862no—
841C2×C4—862no—
842C2×C4—862no—
843C2×C4—862no—
844C2×C4—862no—
845C2×C4—862no—
846C2×C4—862no—
847C2×C4—862no—
848C2×C4—862no—
849C2×C4—862no—
850C2×C4—862no—
851C2×C4—862no—
852C2×C4—862no—
853C2×C4—862no—
854C2×C4—862no—
855C2×C4—862no—
856C2×C4—862no—
857C2×C4—1721no—
858C2×C4—1721no—
859C2×C4—1721no—
860C2×C4—1721no—
861C2×C4—1721no—
862C2×C4—1721no—
863C2×C4—1721no—
864C2×C4—1721no—
865C2×C4—1721no—
866C2×C4—1721no—
867C2×C4—1721no—
868C2×C4—1721no—
869C2×C4—1721no—
870C2×C4—1721no—
871C2×C4—1721no—
872C2×C4—1721no—
873C2×C4—1721no—
874C2×C4—1721no—
875C2×C4—1721no—
876C2×C4—1721no—
877C2×C4—1721no—
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—
887C22—3441no—
888C22—3441no—
889C22—3441no—
890C22—3441no—
891C22—3441no—
892C22—3441no—
893C22—3441no—
894C22—3441no—
895C22—1722no—
896C22—1722no—
897C22—1722no—
898C22—1722no—
899C22—1722no—
900C22—1722no—
901C22—1722no—
902C22C4×#1062190011yescharacteristic
903C22#1458336711yescharacteristic
904C22C4×#1062190211yescharacteristic
905C22#1458337111yescharacteristic
906C22#1458337211yescharacteristic
907C22#1458337311yescharacteristic
908C22#1458337511yescharacteristic
909C22#126×D4311yescharacteristic
910C22#1458342611yescharacteristic
911C22#1458343411yescharacteristic
912C22#1458343511yescharacteristic
913C22#1458348311yescharacteristic
914C22#1458348511yescharacteristic
915C22#1458348511yescharacteristic
916C22#1458348611yescharacteristic
917C22#1458348811yescharacteristic
918C22#1458348911yescharacteristic
919C22#1458349011yescharacteristic
920C22#1458349311yescharacteristic
921C22#1458349511yescharacteristic
922C22#1458349711yescharacteristic
923C22#1458349711yescharacteristic
924C22#1458349811yescharacteristic
925C22#1458349911yescharacteristic
926C22#1458350111yescharacteristic
927C22#1458350111yescharacteristic
928C22#1458350111yescharacteristic
929C22#1458350311yescharacteristic
930C22#1458350511yescharacteristic
931C22#1458351311yescharacteristic
932C22#1458351511yescharacteristic
933C22#1458351711yescharacteristic
934C22#1458351911yescharacteristic
935C22#1458352211yescharacteristic
936C22#1458352311yescharacteristic
937C4—42no—
938C4—42no—
939C4—42no—
940C4—42no—
941C4—42no—
942C4—81no—
943C4—81no—
944C4—864no—
945C4—3441no—
946C4—3441no—
947C4—1722no—
948C4—1722no—
949C4—1722no—
950C4—1722no—
951C2—3442no—
952C2#1913714511yescharacteristic
953C2#1913734711yescharacteristic
954C2#1913734911yescharacteristic
955C2#1913735011yescharacteristic
956C2#1913735411yescharacteristic
957C2#1913735711yescharacteristic
958C2#1913735911yescharacteristic
959C2#1914054911yescharacteristic
960C2#1914055411yescharacteristic
961C2#1914059311yescharacteristic
962C2#1914059711yescharacteristic
963C2#1914060111yescharacteristic
964C2#1914062111yescharacteristic
965C2#1914062711yescharacteristic
966C2#1914063111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1445C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenter#1445D43
hypocenterC43#14331
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1445

Complements

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

NH ≅ G/Ntype
2. #19132862C2semidirect
3. #19132861C2semidirect
4. #19132856C2semidirect
11. #19132829C2semidirect
12. #19132827C2semidirect
13. #19132826C2semidirect
14. #95×Dic43C2semidirect
15. C43×#1445C2semidirect
28. #14582821C4semidirect
471. #1445D43semidirect
535. C43#14331semidirect

Maximal subgroups

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

subgroupindex
C2×#145828212
#191328622
#191328612
#191328562
#191328432
#191328312
#191328292
#191328272
#191328262
#95×Dic432
C43×#14452
#1433143