Finite Group Databasebeta

← #25024475

Subgroups — #25024475

Order 11008.

1550 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582782C211yesmaximal, characteristic, complemented
2C2×#14582773C211yesmaximal, characteristic
3C2×#14582758C211yesmaximal, characteristic
4#19132859C211yesmaximal, characteristic, complemented
5#19132852C211yesmaximal, characteristic, complemented
6#19132847C211yesmaximal, characteristic, complemented
7#19132841C211yesmaximal, characteristic
8#19132839C211yesmaximal, characteristic
9#19132831C211yesmaximal, characteristic
10#19132831C211yesmaximal, characteristic
11#19132830C211yesmaximal, characteristic, complemented
12#19132826C211yesmaximal, characteristic, complemented
13Dic43⋊#95C211yesmaximal, characteristic, complemented
14(C2×D43)⋊#95C211yesmaximal, characteristic
15C43×#1443C211yesmaximal, characteristic, complemented
16C23×C4×D43C2211yescharacteristic
17C22×C4⋊Dic43C2211yescharacteristic
18C22×C4⋊Dic43C2211yescharacteristic
19C22×Dic43⋊C4C2211yescharacteristic
20C22×Dic43⋊C4C2211yescharacteristic
21C22×Dic43⋊C4C2211yescharacteristic
22C22×Dic43⋊C4C2211yescharacteristic
23C22×(C2×D43)⋊C4C2211yescharacteristic
24C22×(C2×D43)⋊C4C2211yescharacteristic
25C22×(C2×D43)⋊C4C2211yescharacteristic
26C22×(C2×D43)⋊C4C2211yescharacteristic
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×C4×Dic43C2211yescharacteristic
30C22×C4×Dic43C2211yescharacteristic
31#14582782—24no—
32#14582773C418yescomplemented
33#14582758—24no—
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
46C2×C43⋊#95C2211yescharacteristic
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—41no—
65C22×C4×D43—41no—
66C22×C4×D43—41no—
67C22×C4×D43—41no—
68C22×C4×D43C2×C414yes—
69C2×C4⋊Dic43—22no—
70C2×C4⋊Dic43—22no—
71C2×C4⋊Dic43—41no—
72C2×C4⋊Dic43—41no—
73C2×C4⋊Dic43—41no—
74C2×C4⋊Dic43C2×C414yes—
75C2×Dic43⋊C4—22no—
76C2×Dic43⋊C4—22no—
77C2×Dic43⋊C4—41no—
78C2×Dic43⋊C4—41no—
79C2×Dic43⋊C4—41no—
80C2×Dic43⋊C4—41no—
81C2×Dic43⋊C4—41no—
82C2×Dic43⋊C4—41no—
83C2×Dic43⋊C4—41no—
84C2×Dic43⋊C4—41no—
85C2×Dic43⋊C4C2×C414yes—
86C2×Dic43⋊C4D414yes—
87C2×(C2×D43)⋊C4—22no—
88C2×(C2×D43)⋊C4—22no—
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—41no—
95C2×(C2×D43)⋊C4—41no—
96C2×(C2×D43)⋊C4—41no—
97C2×(C2×D43)⋊C4—41no—
98C2×(C2×D43)⋊C4—41no—
99C2×(C2×D43)⋊C4—41no—
100C2×(C2×D43)⋊C4—41no—
101C2×(C2×D43)⋊C4—41no—
102C2×(C2×D43)⋊C4C2×C414yes—
103C2×(C2×D43)⋊C4C2×C414yes—
104C2×(C2×D43)⋊C4Q814yes—
105C2×C4×Dic43—22no—
106C2×C4×Dic43—22no—
107C2×C4×Dic43—41no—
108C2×C4×Dic43—41no—
109C2×C4×Dic43—41no—
110C2×C4×Dic43—41no—
111C43⋊#95—22no—
112C43⋊#95—22no—
113C43⋊#95—22no—
114C43⋊#95—22no—
115C43⋊#95—22no—
116C43⋊#95—22no—
117C43⋊#95—22no—
118C43⋊#95—41no—
119C43⋊#95—41no—
120C43⋊#95—41no—
121C43⋊#95—41no—
122C43⋊#95—41no—
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×D43—21no—
148C23×D43—21no—
149C23×D43—21no—
150C23×D43—21no—
151C23×D43C22×C412yes—
152C23×D43C2×Q812yes—
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×D412yes—
248C22×Dic43C2×Q812yes—
249C22×Dic43#4112yes—
250C22×Dic43#4112yes—
251C22×Dic43#4112yes—
252C2×C4×D43—28no—
253C2×C4×D43—44no—
254C2×C4×D43—44no—
255C2×C4×D43—44no—
256C2×C4×D43—44no—
257C2×C4×D43—44no—
258C2×C4×D43—44no—
259(C2×D43)⋊C4—28no—
260(C2×D43)⋊C4—44no—
261(C2×D43)⋊C4—44no—
262(C2×D43)⋊C4—44no—
263(C2×D43)⋊C4—44no—
264(C2×D43)⋊C4—44no—
265C4⋊Dic43—28no—
266C4⋊Dic43—44no—
267Dic43⋊C4—44no—
268Dic43⋊C4—44no—
269Dic43⋊C4—44no—
270Dic43⋊C4—44no—
271C4×Dic43—44no—
272C4×Dic43—44no—
273C23×C43C23×C411yescharacteristic
274C23×C43C22×D411yescharacteristic
275C23×C43C22×Q811yescharacteristic
276C23×C43C2×#4111yescharacteristic
277C23×C43C2×#4111yescharacteristic
278C23×C43C2×#4111yescharacteristic
279C23×C43C2×#4111yescharacteristic
280C23×C43H(5,𝔽2)11yescharacteristic
281C23×C43H(5,𝔽2)11yescharacteristic
282C23×C43H(5,𝔽2)11yescharacteristic
283C23×C43H(5,𝔽2)11yescharacteristic
284C23×C43H(5,𝔽2)11yescharacteristic
285C23×C43H(5,𝔽2)11yescharacteristic
286C23×C432−1+411yescharacteristic
287C23×C432−1+411yescharacteristic
288C22×D43—22no—
289C22×D43—22no—
290C22×D43—22no—
291C22×D43—22no—
292C22×D43—22no—
293C22×D43—22no—
294C22×D43—22no—
295C22×D43—22no—
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—41no—
307C22×D43—41no—
308C22×D43—41no—
309C22×D43—41no—
310C22×D43—41no—
311C22×D43—41no—
312C22×D43—41no—
313C22×D43—41no—
314C22×D43—41no—
315C22×D43—41no—
316C22×D43—41no—
317C22×D43—41no—
318C22×D43—41no—
319C22×D43—41no—
320C22×D43—41no—
321C22×D43—41no—
322C22×D43C4×Q814yes—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
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—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×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×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—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—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—41no—
414C2×Dic43—41no—
415C2×Dic43—41no—
416C2×Dic43—41no—
417C2×Dic43—41no—
418C2×Dic43—41no—
419C2×Dic43#11714yes—
420C2×Dic43C4×D414yes—
421C4×D43—416no—
422#14398—431nomaximal, Sylow
423C22×C43C2×#11711yescharacteristic
424C22×C43C2×C4×D411yescharacteristic
425C22×C43C2×C4×Q811yescharacteristic
426C22×C43#51811yescharacteristic
427C22×C43#51811yescharacteristic
428C22×C43#52011yescharacteristic
429C22×C43#52011yescharacteristic
430C22×C43#53411yescharacteristic
431C22×C43#53511yescharacteristic
432C22×C43#53811yescharacteristic
433C22×C43#53811yescharacteristic
434C22×C43#53811yescharacteristic
435C22×C43#53811yescharacteristic
436C22×C43#53811yescharacteristic
437C22×C43#53911yescharacteristic
438C22×C43#53911yescharacteristic
439C22×C43#53911yescharacteristic
440C22×C43#54311yescharacteristic
441C22×C43#54411yescharacteristic
442C22×C43#54611yescharacteristic
443C22×C43#54711yescharacteristic
444C22×C43D4×Q811yescharacteristic
445C22×C43#55011yescharacteristic
446C22×C43#55211yescharacteristic
447C22×C43#55311yescharacteristic
448C22×C43#55311yescharacteristic
449C22×C43#55411yescharacteristic
450C22×C43#55411yescharacteristic
451C22×C43#55411yescharacteristic
452C22×C43#55511yescharacteristic
453C22×C43#55611yescharacteristic
454C22×C43#56011yescharacteristic
455C22×C43#56211yescharacteristic
456C22×C43#56211yescharacteristic
457C22×C43#56311yescharacteristic
458C2×D43—24no—
459C2×D43—24no—
460C2×D43—24no—
461C2×D43—42no—
462C2×D43—42no—
463C2×D43—42no—
464C2×D43—42no—
465C2×D43—42no—
466C2×D43—42no—
467C2×D43—42no—
468C2×D43—42no—
469C2×D43—42no—
470C2×D43—42no—
471C2×D43—42no—
472C2×D43—42no—
473C4×C43—42no—
474C4×C43—42no—
475C4×C43—42no—
476C4×C43—42no—
477C4×C43—42no—
478C4×C43—81no—
479C4×C43—81no—
480Dic43—24no—
481Dic43—24no—
482Dic43—42no—
483Dic43—42no—
484Dic43—42no—
485Dic43—81no—
486Dic43—81no—
487C2×#387—431no—
488C2×#385—431no—
489C2×#380—431no—
490#1444—431no—
491#1443D4311yescharacteristic, complemented
492#1442—431no—
493#1441—431no—
494#1439—431no—
495#1439—431no—
496#1437—431no—
497#1437—431no—
498#1436—431no—
499#1436—431no—
500C4⋊#95—431no—
501C22⋊#95—431no—
502C2×C43#231811yescharacteristic
503C2×C43#232111yescharacteristic
504C2×C43#232911yescharacteristic
505C2×C43#234511yescharacteristic
506C2×C43#235411yescharacteristic
507C2×C43#236011yescharacteristic
508C2×C43#237611yescharacteristic
509C2×C43#270811yescharacteristic
510C2×C43#271411yescharacteristic
511C2×C43#272011yescharacteristic
512C2×C43#273211yescharacteristic
513C2×C43#278111yescharacteristic
514C2×C43#278411yescharacteristic
515C2×C43#278711yescharacteristic
516C2×C43#278811yescharacteristic
517D43—44no—
518C24×C4—431no—
519C22×C4⋊C4—431no—
520C22×C4⋊C4—431no—
521C22×C4⋊C4—431no—
522C22×C4⋊C4—431no—
523C22×C4⋊C4—431no—
524C22×C4⋊C4—431no—
525C22×C22⋊C4—431no—
526C22×C22⋊C4—431no—
527C22×C22⋊C4—431no—
528C22×C22⋊C4—431no—
529C22×C22⋊C4—431no—
530C22×C22⋊C4—431no—
531C22×C42—431no—
532C22×C42—431no—
533#387—864no—
534#385—438no—
535#380—864no—
536C2×#95—431no—
537C2×#95—431no—
538C2×#95—431no—
539C2×#95—431no—
540C2×#95—431no—
541C2×#95—431no—
542C2×#95—431no—
543C2×#95—431no—
544C2×#95—431no—
545C2×#95—431no—
546C2×#95—431no—
547C2×#95—431no—
548C2×#95—431no—
549C2×#95C2×D4311yescharacteristic
550C2×#95C2×D4311yescharacteristic
551C2×#95C2×D4311yescharacteristic
552C2×#95C2×D4311yescharacteristic
553C2×#95C2×D4311yescharacteristic
554C2×#95C2×D4311yescharacteristic
555C2×#95C2×D4311yescharacteristic
556C43#1439811yescharacteristic, complemented, Sylow
557C25—431no—
558C23×C4—431no—
559C23×C4—431no—
560C23×C4—431no—
561C23×C4—431no—
562C23×C4—431no—
563C23×C4—434no—
564C23×C4—431no—
565C23×C4—431no—
566C23×C4—862no—
567C23×C4—862no—
568C23×C4—1721no—
569C23×C4—1721no—
570C23×C4—1721no—
571C23×C4—1721no—
572C23×C4C22×D4311yescharacteristic
573C23×C4C22×D4311yescharacteristic
574C23×C4C22×D4311yescharacteristic
575C23×C4C22×D4311yescharacteristic
576C23×C4C22×D4311yescharacteristic
577C23×C4C22×D4311yescharacteristic
578C23×C4C22×D4311yescharacteristic
579C2×C4⋊C4—434no—
580C2×C4⋊C4—434no—
581C2×C4⋊C4—434no—
582C2×C4⋊C4—862no—
583C2×C4⋊C4—862no—
584C2×C4⋊C4—862no—
585C2×C4⋊C4—862no—
586C2×C4⋊C4—1721no—
587C2×C4⋊C4—1721no—
588C2×C4⋊C4—1721no—
589C2×C4⋊C4—1721no—
590C2×C4⋊C4—1721no—
591C2×C4⋊C4—1721no—
592C2×C4⋊C4—1721no—
593C2×C4⋊C4—1721no—
594C2×C4⋊C4—1721no—
595C2×C4⋊C4—1721no—
596C2×C4⋊C4—1721no—
597C2×C22⋊C4—434no—
598C2×C22⋊C4—434no—
599C2×C22⋊C4—434no—
600C2×C22⋊C4—862no—
601C2×C22⋊C4—862no—
602C2×C22⋊C4—862no—
603C2×C22⋊C4—862no—
604C2×C22⋊C4—862no—
605C2×C22⋊C4—862no—
606C2×C22⋊C4—862no—
607C2×C22⋊C4—1721no—
608C2×C22⋊C4—1721no—
609C2×C22⋊C4—1721no—
610C2×C22⋊C4—1721no—
611C2×C22⋊C4—1721no—
612C2×C22⋊C4—1721no—
613C2×C22⋊C4—1721no—
614C2×C22⋊C4—1721no—
615C2×C42—862no—
616C2×C42—862no—
617C2×C42—1721no—
618C2×C42—1721no—
619C2×C42—1721no—
620C2×C42—1721no—
621#95—22no—
622#95—22no—
623#95—41no—
624#95—41no—
625#95—41no—
626#95—41no—
627#95—434no—
628#95—862no—
629#95—862no—
630#95—862no—
631#95—862no—
632#95—862no—
633#95—862no—
634#95—862no—
635#95—1721no—
636#95—1721no—
637#95—1721no—
638#95—1721no—
639#95—1721no—
640#95C4×D4314yes—
641C24—432no—
642C24—432no—
643C24—432no—
644C24—861no—
645C24—861no—
646C24—861no—
647C24—861no—
648C24—861no—
649C24—861no—
650C24—861no—
651C24—861no—
652C24—861no—
653C24—861no—
654C24—861no—
655C24—861no—
656C24C23×D4311yescharacteristic
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—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—432no—
702C22×C4—432no—
703C22×C4—432no—
704C22×C4—432no—
705C22×C4—432no—
706C22×C4—432no—
707C22×C4—432no—
708C22×C4—432no—
709C22×C4—432no—
710C22×C4—868no—
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—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—1724no—
752C22×C4—1724no—
753C22×C4—1724no—
754C22×C4—1724no—
755C22×C4—1724no—
756C22×C4—1724no—
757C22×C4C2×C4×D4312yes—
758C22×C4C2×C4×D4312yes—
759C22×C4C2×C4×D4312yes—
760C22×C4D4×D4312yes—
761C22×C4Q8×D4312yes—
762C4⋊C4—868no—
763C4⋊C4—1724no—
764C4⋊C4—1724no—
765C4⋊C4—1724no—
766C4⋊C4—1724no—
767C4⋊C4—1724no—
768C22⋊C4—868no—
769C22⋊C4—1724no—
770C22⋊C4—1724no—
771C22⋊C4—1724no—
772C22⋊C4—1724no—
773C22⋊C4—1724no—
774C42—1724no—
775C42—1724no—
776C23—434no—
777C23—862no—
778C23—862no—
779C23—862no—
780C23—862no—
781C23—862no—
782C23—862no—
783C23—862no—
784C23—862no—
785C23—862no—
786C23—862no—
787C23—862no—
788C23—862no—
789C23—862no—
790C23—862no—
791C23—862no—
792C23—862no—
793C23—862no—
794C23—862no—
795C23—1721no—
796C23—1721no—
797C23—1721no—
798C23—1721no—
799C23—1721no—
800C23—1721no—
801C23—1721no—
802C23—1721no—
803C23—1721no—
804C23—1721no—
805C23—1721no—
806C23—1721no—
807C23—1721no—
808C23—1721no—
809C23—1721no—
810C23—1721no—
811C23C22×C4×D4311yescharacteristic
812C23C2×D4×D4311yescharacteristic
813C23C2×Q8×D4311yescharacteristic
814C23#41×D4311yescharacteristic
815C23#41×D4311yescharacteristic
816C23#41×D4311yescharacteristic
817C23#41×D4311yescharacteristic
818C23#1306337011yescharacteristic
819C23#1306337011yescharacteristic
820C23#1306337111yescharacteristic
821C23#1306337111yescharacteristic
822C23#1306337111yescharacteristic
823C23#1306337111yescharacteristic
824C23#1306337211yescharacteristic
825C23#1306337211yescharacteristic
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
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—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
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—434no—
876C2×C4—434no—
877C2×C4—862no—
878C2×C4—862no—
879C2×C4—862no—
880C2×C4—862no—
881C2×C4—862no—
882C2×C4—862no—
883C2×C4—862no—
884C2×C4—862no—
885C2×C4—862no—
886C2×C4—862no—
887C2×C4—862no—
888C2×C4—862no—
889C2×C4—862no—
890C2×C4—862no—
891C2×C4—862no—
892C2×C4—862no—
893C2×C4—862no—
894C2×C4—862no—
895C2×C4—862no—
896C2×C4—862no—
897C2×C4—862no—
898C2×C4—17216no—
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—
909C2×C4—1721no—
910C2×C4—1721no—
911C2×C4—1721no—
912C2×C4—1721no—
913C2×C4—1721no—
914C2×C4—1721no—
915C2×C4—1721no—
916C2×C4—1721no—
917C2×C4—1721no—
918C2×C4—1721no—
919C2×C4—1721no—
920C2×C4—1721no—
921C2×C4—1721no—
922C2×C4—1721no—
923C2×C4—1721no—
924C2×C4—1721no—
925C22—864no—
926C22—864no—
927C22—864no—
928C22—1722no—
929C22—1722no—
930C22—1722no—
931C22—1722no—
932C22—1722no—
933C22—1722no—
934C22—1722no—
935C22—1722no—
936C22—1722no—
937C22—1722no—
938C22—1722no—
939C22—1722no—
940C22#117×D4311yescharacteristic
941C22C4×D4×D4311yescharacteristic
942C22C4×Q8×D4311yescharacteristic
943C22#1458337111yescharacteristic
944C22#1458337311yescharacteristic
945C22#1458337811yescharacteristic
946C22#1458337911yescharacteristic
947C22#1458345711yescharacteristic
948C22#1458346711yescharacteristic
949C22#1458348511yescharacteristic
950C22#1458348511yescharacteristic
951C22#1458348811yescharacteristic
952C22#1458348811yescharacteristic
953C22#1458348811yescharacteristic
954C22#1458349011yescharacteristic
955C22#1458349011yescharacteristic
956C22#1458349011yescharacteristic
957C22#1458352411yescharacteristic
958C22#1458352911yescharacteristic
959C22#1458354111yescharacteristic
960C22#1458354711yescharacteristic
961C22#1458356211yescharacteristic
962C22#1458356711yescharacteristic
963C22#1458358511yescharacteristic
964C22#1458359411yescharacteristic
965C22#1458360011yescharacteristic
966C22#1458360311yescharacteristic
967C22#1458360511yescharacteristic
968C22#1458360511yescharacteristic
969C22#1458361111yescharacteristic
970C22#1458361611yescharacteristic
971C22#1458363911yescharacteristic
972C22#1458364311yescharacteristic
973C22#1458364411yescharacteristic
974C22#1458365111yescharacteristic
975C4—42no—
976C4—42no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—81no—
981C4—81no—
982C4—864no—
983C4—864no—
984C4—3441no—
985C4—3441no—
986C4—1722no—
987C4—1722no—
988C4—1722no—
989C2—1724no—
990C2#1913722611yescharacteristic
991C2#1913724811yescharacteristic
992C2#1913732411yescharacteristic
993C2#1913746911yescharacteristic
994C2#1913754111yescharacteristic
995C2#1913760311yescharacteristic
996C2#1913773711yescharacteristic
997C2#1914131211yescharacteristic
998C2#1914139011yescharacteristic
999C2#1914146811yescharacteristic
1000C2#1914160911yescharacteristic
1001C2#1914226311yescharacteristic
1002C2#1914229511yescharacteristic
1003C2#1914232511yescharacteristic
1004C2#1914234011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1443C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenter#1443D43
hypocenterC43#14398
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1443

Complements

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

NH ≅ G/Ntype
1. C2×#14582782C2semidirect
4. #19132859C2semidirect
5. #19132852C2semidirect
6. #19132847C2semidirect
11. #19132830C2semidirect
12. #19132826C2semidirect
13. Dic43⋊#95C2semidirect
15. C43×#1443C2semidirect
32. #14582773C4semidirect
491. #1443D43semidirect
556. C43#14398semidirect

Maximal subgroups

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

subgroupindex
C2×#145827822
C2×#145827732
C2×#145827582
#191328592
#191328522
#191328472
#191328412
#191328392
#191328312
#191328302
#191328262
Dic43⋊#952
(C2×D43)⋊#952
C43×#14432
#1439843