Finite Group Databasebeta

← #25018604

Subgroups — #25018604

Order 11008.

1862 conjugacy classes of subgroups.

The subgroup lattice has 1026 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582758C211yesmaximal, characteristic
2C2×#14582746C211yesmaximal, characteristic
3C2×#95×D43C211yesmaximal, characteristic
4#19132857C211yesmaximal, characteristic, complemented
5#19132853C211yesmaximal, characteristic, complemented
6#19132850C211yesmaximal, characteristic, complemented
7#19132830C211yesmaximal, characteristic, complemented
8#19132826C211yesmaximal, characteristic, complemented
9#19132821C211yesmaximal, characteristic, complemented
10#19132819C211yesmaximal, characteristic, complemented
11(C2×D43)⋊#95C211yesmaximal, characteristic
12(C2×D43)⋊#95C211yesmaximal, characteristic
13(C2×D43)⋊#95C211yesmaximal, characteristic
14(C2×D43)⋊#95C211yesmaximal, characteristic
15C43×#1443C211yesmaximal, characteristic, complemented
16C23×C4×D43C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C22×Dic43⋊C4C2211yescharacteristic
20C22×Dic43⋊C4C2211yescharacteristic
21C22×(C2×D43)⋊C4C2211yescharacteristic
22C22×(C2×D43)⋊C4C2211yescharacteristic
23C22×(C2×D43)⋊C4C2211yescharacteristic
24C22×(C2×D43)⋊C4C2211yescharacteristic
25C22×C4×Dic43C2211yescharacteristic
26C22×C4×Dic43C2211yescharacteristic
27#14582758—24no—
28#14582746—24no—
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
45C2×C43⋊#95C2211yescharacteristic
46#95×D43C418yescomplemented
47C2×#95×C43C2211yescharacteristic
48C2×#95×C43C2211yescharacteristic
49C2×#95×C43C2211yescharacteristic
50C2×#95×C43C2211yescharacteristic
51C2×#95×C43C2211yescharacteristic
52C2×#95×C43C2211yescharacteristic
53C2×#95×C43C2211yescharacteristic
54C24×D43C2311yescharacteristic
55C23×Dic43C2311yescharacteristic
56C23×Dic43C2311yescharacteristic
57C23×Dic43C2311yescharacteristic
58C23×Dic43C2311yescharacteristic
59C23×Dic43C2311yescharacteristic
60C23×Dic43C2311yescharacteristic
61C23×Dic43C2311yescharacteristic
62C22×C4×D43—22no—
63C22×C4×D43—22no—
64C22×C4×D43—22no—
65C22×C4×D43—22no—
66C22×C4×D43—22no—
67C22×C4×D43—22no—
68C22×C4×D43—22no—
69C22×C4×D43—22no—
70C22×C4×D43—22no—
71C22×C4×D43—22no—
72C22×C4×D43—41no—
73C22×C4×D43—41no—
74C22×C4×D43—41no—
75C22×C4×D43—41no—
76C22×C4×D43—41no—
77C22×C4×D43—41no—
78C22×C4×D43—41no—
79C22×C4×D43—41no—
80C22×C4×D43C2×C414yes—
81C22×C4×D43C2×C414yes—
82C22×C4×D43C2×C414yes—
83C2×Dic43⋊C4—22no—
84C2×Dic43⋊C4—22no—
85C2×Dic43⋊C4—22no—
86C2×Dic43⋊C4—22no—
87C2×Dic43⋊C4—41no—
88C2×Dic43⋊C4—41no—
89C2×(C2×D43)⋊C4—22no—
90C2×(C2×D43)⋊C4—22no—
91C2×(C2×D43)⋊C4—22no—
92C2×(C2×D43)⋊C4—22no—
93C2×(C2×D43)⋊C4—22no—
94C2×(C2×D43)⋊C4—22no—
95C2×(C2×D43)⋊C4—22no—
96C2×(C2×D43)⋊C4—22no—
97C2×(C2×D43)⋊C4—22no—
98C2×(C2×D43)⋊C4—22no—
99C2×(C2×D43)⋊C4D414yes—
100C2×(C2×D43)⋊C4Q814yes—
101C2×C4×Dic43—22no—
102C2×C4×Dic43—22no—
103C2×C4×Dic43—22no—
104C2×C4×Dic43—22no—
105C2×C4×Dic43—41no—
106C2×C4×Dic43—41no—
107C43⋊#95—22no—
108C43⋊#95—22no—
109C43⋊#95—22no—
110C43⋊#95—22no—
111C43⋊#95—22no—
112C43⋊#95—22no—
113C43⋊#95—41no—
114C43⋊#95—41no—
115C43⋊#95—41no—
116C43⋊#95—41no—
117C43⋊#95—41no—
118C43⋊#95—41no—
119C43⋊#95—41no—
120C43⋊#95—41no—
121C43⋊#95C2×C414yes—
122C43⋊#95C2×C414yes—
123C43⋊#95C2×C414yes—
124C23×C4×C43C2311yescharacteristic
125C23×C4×C43C2311yescharacteristic
126C23×C4×C43C2311yescharacteristic
127C23×C4×C43C2311yescharacteristic
128C23×C4×C43C2311yescharacteristic
129C23×C4×C43C2311yescharacteristic
130C23×C4×C43C2311yescharacteristic
131#95×C43—22no—
132#95×C43—22no—
133#95×C43—41no—
134#95×C43—41no—
135#95×C43—41no—
136#95×C43—41no—
137#95×C43C2×C414yes—
138C24×C43C2411yescharacteristic
139C23×D43—21no—
140C23×D43—21no—
141C23×D43—21no—
142C23×D43—21no—
143C23×D43—21no—
144C23×D43—21no—
145C23×D43—21no—
146C23×D43—21no—
147C23×D43C22×C412yes—
148C23×D43C2×D412yes—
149C23×D43C2×Q812yes—
150C23×D43#4112yes—
151C23×D43#4112yes—
152C23×D43#4112yes—
153C23×D43#4112yes—
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×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43C22×C412yes—
199C22×C4×C43C22×C412yes—
200C22×C4×C43C22×C412yes—
201C22×C4×C43C2×D412yes—
202C22×C4×C43C2×Q812yes—
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—21no—
239C22×Dic43—21no—
240C22×Dic43—21no—
241C22×Dic43—21no—
242C22×Dic43—21no—
243C22×Dic43C22×C412yes—
244C22×Dic43C22×C412yes—
245C22×Dic43C22×C412yes—
246C22×Dic43C2×D412yes—
247C22×Dic43C2×Q812yes—
248C22×Dic43#4112yes—
249C22×Dic43#4112yes—
250C22×Dic43#4112yes—
251C22×Dic43#4112yes—
252C2×C4×D43—28no—
253C2×C4×D43—28no—
254C2×C4×D43—28no—
255C2×C4×D43—28no—
256C2×C4×D43—28no—
257C2×C4×D43—44no—
258C2×C4×D43—44no—
259C2×C4×D43—44no—
260C2×C4×D43—44no—
261C2×C4×D43—44no—
262C2×C4×D43—44no—
263C2×C4×D43—44no—
264C2×C4×D43—44no—
265C2×C4×D43—44no—
266C2×C4×D43—44no—
267C2×C4×D43—44no—
268C2×C4×D43—44no—
269C2×C4×D43—44no—
270C2×C4×D43—44no—
271C2×C4×D43—44no—
272C2×C4×D43—44no—
273(C2×D43)⋊C4—28no—
274(C2×D43)⋊C4—28no—
275(C2×D43)⋊C4—44no—
276(C2×D43)⋊C4—44no—
277Dic43⋊C4—44no—
278Dic43⋊C4—44no—
279C4×Dic43—44no—
280C4×Dic43—44no—
281C23×C43C23×C411yescharacteristic
282C23×C43C22×D411yescharacteristic
283C23×C43C22×Q811yescharacteristic
284C23×C43C2×#4111yescharacteristic
285C23×C43C2×#4111yescharacteristic
286C23×C43C2×#4111yescharacteristic
287C23×C43C2×#4111yescharacteristic
288C23×C43C2×#4111yescharacteristic
289C23×C43C2×#4111yescharacteristic
290C23×C43C2×#4111yescharacteristic
291C23×C43C2×#4111yescharacteristic
292C23×C43H(5,𝔽2)11yescharacteristic
293C23×C43H(5,𝔽2)11yescharacteristic
294C23×C43H(5,𝔽2)11yescharacteristic
295C23×C43H(5,𝔽2)11yescharacteristic
296C22×D43—22no—
297C22×D43—22no—
298C22×D43—22no—
299C22×D43—22no—
300C22×D43—22no—
301C22×D43—22no—
302C22×D43—22no—
303C22×D43—22no—
304C22×D43—22no—
305C22×D43—22no—
306C22×D43—22no—
307C22×D43—22no—
308C22×D43—22no—
309C22×D43—22no—
310C22×D43—22no—
311C22×D43—22no—
312C22×D43—22no—
313C22×D43—22no—
314C22×D43—22no—
315C22×D43—22no—
316C22×D43—22no—
317C22×D43—22no—
318C22×D43—22no—
319C22×D43—22no—
320C22×D43—22no—
321C22×D43—22no—
322C22×D43—22no—
323C22×D43—22no—
324C22×D43#11714yes—
325C22×D43C4×D414yes—
326C22×D43C4×Q814yes—
327C22×D43C22⋊Q814yes—
328C22×D43#12314yes—
329C22×D43#12514yes—
330C22×D43#12614yes—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—22no—
335C2×C4×C43—22no—
336C2×C4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43—22no—
339C2×C4×C43—22no—
340C2×C4×C43—22no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—22no—
344C2×C4×C43—22no—
345C2×C4×C43—22no—
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×C4×C43—41no—
358C2×C4×C43—41no—
359C2×C4×C43—41no—
360C2×C4×C43—41no—
361C2×C4×C43—41no—
362C2×C4×C43—41no—
363C2×C4×C43—41no—
364C2×C4×C43—41no—
365C2×C4×C43—41no—
366C2×C4×C43—41no—
367C2×C4×C43—41no—
368C2×C4×C43—41no—
369C2×C4×C43—41no—
370C2×C4×C43—41no—
371C2×C4×C43—41no—
372C2×C4×C43—41no—
373C2×C4×C43—41no—
374C2×C4×C43—41no—
375C2×C4×C43—41no—
376C2×C4×C43—41no—
377C2×C4×C43—41no—
378C2×C4×C43—41no—
379C2×C4×C43—41no—
380C2×Dic43—22no—
381C2×Dic43—22no—
382C2×Dic43—22no—
383C2×Dic43—22no—
384C2×Dic43—22no—
385C2×Dic43—22no—
386C2×Dic43—22no—
387C2×Dic43—22no—
388C2×Dic43—22no—
389C2×Dic43—22no—
390C2×Dic43—22no—
391C2×Dic43—22no—
392C2×Dic43—22no—
393C2×Dic43—22no—
394C2×Dic43—22no—
395C2×Dic43—22no—
396C2×Dic43—22no—
397C2×Dic43—22no—
398C2×Dic43—22no—
399C2×Dic43—22no—
400C2×Dic43—22no—
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—41no—
414C2×Dic43—41no—
415C2×Dic43—41no—
416C2×Dic43—41no—
417C2×Dic43—41no—
418C2×Dic43—41no—
419C2×Dic43—41no—
420C2×Dic43—41no—
421C2×Dic43—41no—
422C2×Dic43—41no—
423C2×Dic43—41no—
424C2×Dic43—41no—
425C2×Dic43—41no—
426C2×Dic43—41no—
427C2×Dic43#11714yes—
428C2×Dic43#11714yes—
429C4×D43—416no—
430C4×D43—416no—
431C4×D43—416no—
432#13883—431nomaximal, Sylow
433C22×C43C2×#11711yescharacteristic
434C22×C43C2×#11711yescharacteristic
435C22×C43C2×#11711yescharacteristic
436C22×C43C2×C4×D411yescharacteristic
437C22×C43C2×C4×Q811yescharacteristic
438C22×C43#51811yescharacteristic
439C22×C43#51811yescharacteristic
440C22×C43C2×C22⋊Q811yescharacteristic
441C22×C43C2×#12311yescharacteristic
442C22×C43C2×#12511yescharacteristic
443C22×C43C2×#12611yescharacteristic
444C22×C43#52911yescharacteristic
445C22×C43#52911yescharacteristic
446C22×C43#52911yescharacteristic
447C22×C43#52911yescharacteristic
448C22×C43#53811yescharacteristic
449C22×C43#53811yescharacteristic
450C22×C43#53811yescharacteristic
451C22×C43#53811yescharacteristic
452C22×C43#54611yescharacteristic
453C22×C43#54611yescharacteristic
454C22×C43#54611yescharacteristic
455C22×C43#54611yescharacteristic
456C22×C43#55111yescharacteristic
457C22×C43#55111yescharacteristic
458C22×C43#55111yescharacteristic
459C22×C43#55111yescharacteristic
460C22×C43#55311yescharacteristic
461C22×C43#55311yescharacteristic
462C22×C43#55311yescharacteristic
463C22×C43#55311yescharacteristic
464C22×C43#55411yescharacteristic
465C22×C43#55411yescharacteristic
466C22×C43#55411yescharacteristic
467C22×C43#55411yescharacteristic
468C2×D43—24no—
469C2×D43—24no—
470C2×D43—24no—
471C2×D43—24no—
472C2×D43—24no—
473C2×D43—24no—
474C2×D43—24no—
475C2×D43—24no—
476C2×D43—24no—
477C2×D43—24no—
478C2×D43—24no—
479C2×D43—24no—
480C2×D43—24no—
481C2×D43—24no—
482C2×D43#38718yes—
483C4×C43—42no—
484C4×C43—42no—
485C4×C43—42no—
486C4×C43—42no—
487C4×C43—42no—
488C4×C43—81no—
489C4×C43—81no—
490Dic43—24no—
491Dic43—24no—
492Dic43—42no—
493Dic43—42no—
494Dic43—42no—
495Dic43—81no—
496Dic43—81no—
497C2×#380—431no—
498C2×C4×C22⋊C4—431no—
499C22×#95—431no—
500#1443—431no—
501#1443D4311yescharacteristic, complemented
502#1442—431no—
503#1442—431no—
504#1436—431no—
505#1436—431no—
506#1434—431no—
507#1434—431no—
508C22⋊#95—431no—
509C22⋊#95—431no—
510C22⋊#95—431no—
511C22⋊#95—431no—
512C2×C43#228311yescharacteristic
513C2×C43C2×#38711yescharacteristic
514C2×C43#231211yescharacteristic
515C2×C43#234211yescharacteristic
516C2×C43#234211yescharacteristic
517C2×C43#234511yescharacteristic
518C2×C43#234511yescharacteristic
519C2×C43#244411yescharacteristic
520C2×C43#244411yescharacteristic
521C2×C43#245011yescharacteristic
522C2×C43#245011yescharacteristic
523C2×C43#250511yescharacteristic
524C2×C43#250511yescharacteristic
525C2×C43#251011yescharacteristic
526C2×C43#251011yescharacteristic
527D43—28no—
528C24×C4—431no—
529C24×C4—431no—
530C24×C4—431no—
531C22×C4⋊C4—431no—
532C22×C4⋊C4—431no—
533C22×C22⋊C4—431no—
534C22×C22⋊C4—431no—
535C22×C22⋊C4—431no—
536C22×C22⋊C4—431no—
537C22×C42—431no—
538C22×C42—431no—
539#380—864no—
540C4×C22⋊C4—864no—
541C2×#95—431no—
542C2×#95—431no—
543C2×#95—431no—
544C2×#95—438no—
545C2×#95—431no—
546C2×#95—431no—
547C2×#95—431no—
548C2×#95—431no—
549C2×#95—431no—
550C2×#95—431no—
551C2×#95—431no—
552C2×#95—431no—
553C2×#95—431no—
554C2×#95—431no—
555C2×#95—431no—
556C2×#95—431no—
557C2×#95—431no—
558C2×#95—431no—
559C2×#95C2×D4311yescharacteristic
560C2×#95C2×D4311yescharacteristic
561C2×#95C2×D4311yescharacteristic
562C2×#95C2×D4311yescharacteristic
563C2×#95C2×D4311yescharacteristic
564C2×#95C2×D4311yescharacteristic
565C2×#95C2×D4311yescharacteristic
566C43#1388311yescharacteristic, complemented, Sylow
567C25—431no—
568C23×C4—431no—
569C23×C4—431no—
570C23×C4—431no—
571C23×C4—431no—
572C23×C4—431no—
573C23×C4—434no—
574C23×C4—434no—
575C23×C4—434no—
576C23×C4—431no—
577C23×C4—431no—
578C23×C4—862no—
579C23×C4—862no—
580C23×C4—862no—
581C23×C4—862no—
582C23×C4—862no—
583C23×C4—862no—
584C23×C4—862no—
585C23×C4—862no—
586C23×C4—862no—
587C23×C4—862no—
588C23×C4—1721no—
589C23×C4—1721no—
590C23×C4—1721no—
591C23×C4—1721no—
592C23×C4—1721no—
593C23×C4—1721no—
594C23×C4—1721no—
595C23×C4—1721no—
596C23×C4C22×D4311yescharacteristic
597C23×C4C22×D4311yescharacteristic
598C23×C4C22×D4311yescharacteristic
599C23×C4C22×D4311yescharacteristic
600C23×C4C22×D4311yescharacteristic
601C23×C4C22×D4311yescharacteristic
602C23×C4C22×D4311yescharacteristic
603C2×C4⋊C4—862no—
604C2×C4⋊C4—862no—
605C2×C4⋊C4—862no—
606C2×C4⋊C4—862no—
607C2×C4⋊C4—1721no—
608C2×C4⋊C4—1721no—
609C2×C22⋊C4—434no—
610C2×C22⋊C4—434no—
611C2×C22⋊C4—862no—
612C2×C22⋊C4—862no—
613C2×C22⋊C4—862no—
614C2×C22⋊C4—862no—
615C2×C22⋊C4—862no—
616C2×C22⋊C4—862no—
617C2×C22⋊C4—862no—
618C2×C22⋊C4—862no—
619C2×C22⋊C4—862no—
620C2×C22⋊C4—862no—
621C2×C42—862no—
622C2×C42—862no—
623C2×C42—862no—
624C2×C42—862no—
625C2×C42—1721no—
626C2×C42—1721no—
627#95—22no—
628#95—22no—
629#95—41no—
630#95—41no—
631#95—41no—
632#95—41no—
633#95—434no—
634#95—434no—
635#95—434no—
636#95—862no—
637#95—862no—
638#95—862no—
639#95—862no—
640#95—862no—
641#95—862no—
642#95—1721no—
643#95—1721no—
644#95—1721no—
645#95—1721no—
646#95—1721no—
647#95—1721no—
648#95—1721no—
649#95—1721no—
650#95C4×D4314yes—
651C24—432no—
652C24—432no—
653C24—432no—
654C24—432no—
655C24—432no—
656C24—432no—
657C24—432no—
658C24—861no—
659C24—861no—
660C24—861no—
661C24—861no—
662C24—861no—
663C24—861no—
664C24—861no—
665C24—861no—
666C24C23×D4311yescharacteristic
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—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—432no—
712C22×C4—432no—
713C22×C4—432no—
714C22×C4—432no—
715C22×C4—432no—
716C22×C4—432no—
717C22×C4—432no—
718C22×C4—432no—
719C22×C4—432no—
720C22×C4—868no—
721C22×C4—868no—
722C22×C4—868no—
723C22×C4—868no—
724C22×C4—868no—
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—861no—
740C22×C4—861no—
741C22×C4—861no—
742C22×C4—861no—
743C22×C4—861no—
744C22×C4—861no—
745C22×C4—861no—
746C22×C4—861no—
747C22×C4—861no—
748C22×C4—861no—
749C22×C4—861no—
750C22×C4—861no—
751C22×C4—861no—
752C22×C4—861no—
753C22×C4—861no—
754C22×C4—861no—
755C22×C4—861no—
756C22×C4—861no—
757C22×C4—861no—
758C22×C4—861no—
759C22×C4—861no—
760C22×C4—861no—
761C22×C4—861no—
762C22×C4—861no—
763C22×C4—861no—
764C22×C4—861no—
765C22×C4—1724no—
766C22×C4—1724no—
767C22×C4—1724no—
768C22×C4—1724no—
769C22×C4—1724no—
770C22×C4—1724no—
771C22×C4—1724no—
772C22×C4—1724no—
773C22×C4—1724no—
774C22×C4—1724no—
775C22×C4—1724no—
776C22×C4—1724no—
777C22×C4—1724no—
778C22×C4—1724no—
779C22×C4—1724no—
780C22×C4—1724no—
781C22×C4C2×C4×D4312yes—
782C22×C4C2×C4×D4312yes—
783C22×C4C2×C4×D4312yes—
784C22×C4D4×D4312yes—
785C22×C4Q8×D4312yes—
786C4⋊C4—1724no—
787C4⋊C4—1724no—
788C22⋊C4—868no—
789C22⋊C4—868no—
790C22⋊C4—1724no—
791C22⋊C4—1724no—
792C42—1724no—
793C42—1724no—
794C23—434no—
795C23—434no—
796C23—434no—
797C23—434no—
798C23—434no—
799C23—434no—
800C23—434no—
801C23—862no—
802C23—862no—
803C23—862no—
804C23—862no—
805C23—862no—
806C23—862no—
807C23—862no—
808C23—862no—
809C23—862no—
810C23—862no—
811C23—862no—
812C23—862no—
813C23—862no—
814C23—862no—
815C23—862no—
816C23—862no—
817C23—862no—
818C23—862no—
819C23—862no—
820C23—862no—
821C23—862no—
822C23—862no—
823C23—862no—
824C23—862no—
825C23—862no—
826C23—862no—
827C23—862no—
828C23—862no—
829C23C22×C4×D4311yescharacteristic
830C23C2×D4×D4311yescharacteristic
831C23C2×Q8×D4311yescharacteristic
832C23#41×D4311yescharacteristic
833C23#41×D4311yescharacteristic
834C23#41×D4311yescharacteristic
835C23#41×D4311yescharacteristic
836C23#41×D4311yescharacteristic
837C23#41×D4311yescharacteristic
838C23#41×D4311yescharacteristic
839C23#41×D4311yescharacteristic
840C23#1306337011yescharacteristic
841C23#1306337011yescharacteristic
842C23#1306337111yescharacteristic
843C23#1306337111yescharacteristic
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—434no—
894C2×C4—434no—
895C2×C4—862no—
896C2×C4—862no—
897C2×C4—862no—
898C2×C4—862no—
899C2×C4—862no—
900C2×C4—862no—
901C2×C4—862no—
902C2×C4—862no—
903C2×C4—862no—
904C2×C4—862no—
905C2×C4—862no—
906C2×C4—862no—
907C2×C4—862no—
908C2×C4—862no—
909C2×C4—862no—
910C2×C4—862no—
911C2×C4—862no—
912C2×C4—862no—
913C2×C4—862no—
914C2×C4—862no—
915C2×C4—862no—
916C2×C4—17216no—
917C2×C4—17216no—
918C2×C4—17216no—
919C2×C4—1721no—
920C2×C4—1721no—
921C2×C4—1721no—
922C2×C4—1721no—
923C2×C4—1721no—
924C2×C4—1721no—
925C2×C4—1721no—
926C2×C4—1721no—
927C2×C4—1721no—
928C2×C4—1721no—
929C2×C4—1721no—
930C2×C4—1721no—
931C2×C4—1721no—
932C2×C4—1721no—
933C2×C4—1721no—
934C2×C4—1721no—
935C2×C4—1721no—
936C2×C4—1721no—
937C2×C4—1721no—
938C2×C4—1721no—
939C2×C4—1721no—
940C2×C4—1721no—
941C2×C4—1721no—
942C2×C4—1721no—
943C2×C4—1721no—
944C2×C4—1721no—
945C22—438no—
946C22—864no—
947C22—864no—
948C22—864no—
949C22—864no—
950C22—864no—
951C22—864no—
952C22—864no—
953C22—864no—
954C22—864no—
955C22—864no—
956C22—864no—
957C22—864no—
958C22—864no—
959C22—864no—
960C22#117×D4311yescharacteristic
961C22#117×D4311yescharacteristic
962C22#117×D4311yescharacteristic
963C22C4×D4×D4311yescharacteristic
964C22C4×Q8×D4311yescharacteristic
965C22#1458337111yescharacteristic
966C22#1458337111yescharacteristic
967C22C22⋊Q8×D4311yescharacteristic
968C22#123×D4311yescharacteristic
969C22#125×D4311yescharacteristic
970C22#126×D4311yescharacteristic
971C22#1458343211yescharacteristic
972C22#1458343211yescharacteristic
973C22#1458343211yescharacteristic
974C22#1458343211yescharacteristic
975C22#1458348111yescharacteristic
976C22#1458348311yescharacteristic
977C22#1458348511yescharacteristic
978C22#1458348811yescharacteristic
979C22#1458353811yescharacteristic
980C22#1458354111yescharacteristic
981C22#1458354211yescharacteristic
982C22#1458354611yescharacteristic
983C22#1458357411yescharacteristic
984C22#1458357411yescharacteristic
985C22#1458357711yescharacteristic
986C22#1458357911yescharacteristic
987C22#1458359411yescharacteristic
988C22#1458359411yescharacteristic
989C22#1458360011yescharacteristic
990C22#1458360011yescharacteristic
991C22#1458360311yescharacteristic
992C22#1458360311yescharacteristic
993C22#1458360511yescharacteristic
994C22#1458360511yescharacteristic
995C4—42no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—81no—
1001C4—81no—
1002C4—864no—
1003C4—864no—
1004C4—3441no—
1005C4—3441no—
1006C4—1722no—
1007C4—1722no—
1008C4—1722no—
1009C2—868no—
1010C2#1913699211yescharacteristic
1011C2#387×D4311yescharacteristic
1012C2#1913718911yescharacteristic
1013C2#1913743911yescharacteristic
1014C2#1913744311yescharacteristic
1015C2#1913746911yescharacteristic
1016C2#1913746911yescharacteristic
1017C2#1913834011yescharacteristic
1018C2#1913834811yescharacteristic
1019C2#1913841411yescharacteristic
1020C2#1913842211yescharacteristic
1021C2#1913909111yescharacteristic
1022C2#1913909911yescharacteristic
1023C2#1913915011yescharacteristic
1024C2#1913915811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1443C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenter#1443D43
hypocenterC43#13883
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1443

Complements

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

NH ≅ G/Ntype
4. #19132857C2semidirect
5. #19132853C2semidirect
6. #19132850C2semidirect
7. #19132830C2semidirect
8. #19132826C2semidirect
9. #19132821C2semidirect
10. #19132819C2semidirect
15. C43×#1443C2semidirect
46. #95×D43C4semidirect
501. #1443D43semidirect
566. C43#13883semidirect

Maximal subgroups

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

subgroupindex
C2×#145827582
C2×#145827462
C2×#95×D432
#191328572
#191328532
#191328502
#191328302
#191328262
#191328212
#191328192
(C2×D43)⋊#952
C43×#14432
#1388343