Finite Group Databasebeta

← #25019164

Subgroups — #25019164

Order 11008.

1846 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063283C211yesmaximal, characteristic
2C2×#14582790C211yesmaximal, characteristic
3C2×#14582788C211yesmaximal, characteristic
4#19132847C211yesmaximal, characteristic, complemented
5#19132847C211yesmaximal, characteristic, complemented
6#19132843C211yesmaximal, characteristic
7#19132843C211yesmaximal, characteristic
8#19132827C211yesmaximal, characteristic, complemented
9Dic43⋊#95C211yesmaximal, characteristic, complemented
10#19132820C211yesmaximal, characteristic, complemented
11#19132819C211yesmaximal, characteristic, complemented
12(C2×D43)⋊#95C211yesmaximal, characteristic
13(C2×D43)⋊#95C211yesmaximal, characteristic
14C4×C43⋊#95C211yesmaximal, characteristic, complemented
15C43×#1436C211yesmaximal, characteristic, complemented
16C23×C4×D43C2211yescharacteristic
17C2×#13063283—24no—
18C2×#13063283—24no—
19C2×#13063283C418yescomplemented
20C22×C4⋊Dic43C2211yescharacteristic
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
31C22×C4×Dic43C2211yescharacteristic
32#14582790—24no—
33#14582788—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×C43⋊#95C2211yescharacteristic
48C2×C43⋊#95C2211yescharacteristic
49C22×C4⋊C4×C43C2211yescharacteristic
50C22×C42×C43C2211yescharacteristic
51C2×#95×C43C2211yescharacteristic
52C2×#95×C43C2211yescharacteristic
53C2×#95×C43C2211yescharacteristic
54C2×#95×C43C2211yescharacteristic
55C2×#95×C43C2211yescharacteristic
56C24×D43C2311yescharacteristic
57C23×Dic43C2311yescharacteristic
58C23×Dic43C2311yescharacteristic
59C23×Dic43C2311yescharacteristic
60C23×Dic43C2311yescharacteristic
61C23×Dic43C2311yescharacteristic
62C23×Dic43C2311yescharacteristic
63C23×Dic43C2311yescharacteristic
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×D43C2×C414yes—
71#13063283—232no—
72C2×C4⋊Dic43—22no—
73C2×C4⋊Dic43—22no—
74C2×C4⋊Dic43C2×C414yes—
75C2×Dic43⋊C4—22no—
76C2×Dic43⋊C4—22no—
77C2×Dic43⋊C4—22no—
78C2×Dic43⋊C4—22no—
79C2×Dic43⋊C4—41no—
80C2×Dic43⋊C4—41no—
81C2×(C2×D43)⋊C4—22no—
82C2×(C2×D43)⋊C4—22no—
83C2×(C2×D43)⋊C4—22no—
84C2×(C2×D43)⋊C4—22no—
85C2×(C2×D43)⋊C4—22no—
86C2×(C2×D43)⋊C4—22no—
87C2×(C2×D43)⋊C4—22no—
88C2×(C2×D43)⋊C4—22no—
89C2×(C2×D43)⋊C4—22no—
90C2×(C2×D43)⋊C4—22no—
91C2×(C2×D43)⋊C4—41no—
92C2×(C2×D43)⋊C4—41no—
93C2×(C2×D43)⋊C4—41no—
94C2×(C2×D43)⋊C4—41no—
95C2×(C2×D43)⋊C4C2×C414yes—
96C2×(C2×D43)⋊C4C2×C414yes—
97C2×(C2×D43)⋊C4D414yes—
98C2×(C2×D43)⋊C4D414yes—
99C2×C4×Dic43—22no—
100C2×C4×Dic43—22no—
101C2×C4×Dic43—22no—
102C2×C4×Dic43—22no—
103C2×C4×Dic43—22no—
104C2×C4×Dic43—22no—
105C2×C4×Dic43—41no—
106C2×C4×Dic43C2×C414yes—
107C2×C4×Dic43C2×C414yes—
108C43⋊#95—22no—
109C43⋊#95—22no—
110C43⋊#95—22no—
111C43⋊#95—22no—
112C43⋊#95—22no—
113C43⋊#95—22no—
114C43⋊#95—22no—
115C43⋊#95—22no—
116C43⋊#95—22no—
117C43⋊#95—22no—
118C43⋊#95—22no—
119C43⋊#95—22no—
120C43⋊#95—41no—
121C43⋊#95—41no—
122C43⋊#95—41no—
123C23×C4×C43C2311yescharacteristic
124C23×C4×C43C2311yescharacteristic
125C23×C4×C43C2311yescharacteristic
126C23×C4×C43C2311yescharacteristic
127C23×C4×C43C2311yescharacteristic
128C23×C4×C43C2311yescharacteristic
129C23×C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43—22no—
131C2×C4⋊C4×C43—22no—
132C2×C4⋊C4×C43C2×C414yes—
133C2×C42×C43—22no—
134C2×C42×C43—22no—
135C2×C42×C43—41no—
136#95×C43—22no—
137#95×C43—22no—
138#95×C43—22no—
139#95×C43—22no—
140#95×C43—41no—
141C24×C43C2411yescharacteristic
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×D43—21no—
152C23×D43—21no—
153C23×D43—21no—
154C23×D43C22×C412yes—
155C23×D43C2×D412yes—
156C23×D43C2×D412yes—
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×C43C22×C412yes—
198C22×C4×C43C22×C412yes—
199C22×C4×C43C22×C412yes—
200C22×C4×C43C2×D412yes—
201C22×C4×C43C2×D412yes—
202C22×C4×C43#4112yes—
203C22×C4×C43#4112yes—
204C22×C4×C43#4112yes—
205C22×C4×C43#4112yes—
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×Dic43—21no—
244C22×Dic43—21no—
245C22×Dic43—21no—
246C22×Dic43C22×C412yes—
247C22×Dic43C22×C412yes—
248C22×Dic43C22×C412yes—
249C22×Dic43C2×D412yes—
250C22×Dic43C2×D412yes—
251C22×Dic43#4112yes—
252C22×Dic43#4112yes—
253C22×Dic43#4112yes—
254C22×Dic43#4112yes—
255C2×C4×D43—28no—
256C2×C4×D43—28no—
257C2×C4×D43—28no—
258C2×C4×D43—28no—
259C2×C4×D43—28no—
260C2×C4×D43—28no—
261C2×C4×D43—28no—
262C4⋊C4×C43—28no—
263C42×C43—44no—
264(C2×D43)⋊C4—28no—
265(C2×D43)⋊C4—44no—
266(C2×D43)⋊C4—44no—
267(C2×D43)⋊C4—44no—
268(C2×D43)⋊C4—44no—
269(C2×D43)⋊C4C22⋊C4116yes—
270C4⋊Dic43—28no—
271Dic43⋊C4—44no—
272Dic43⋊C4—44no—
273C4×Dic43—28no—
274C4×Dic43—28no—
275C4×Dic43—44no—
276C23×C43C23×C411yescharacteristic
277C23×C43C22×D411yescharacteristic
278C23×C43C22×D411yescharacteristic
279C23×C43C2×#4111yescharacteristic
280C23×C43C2×#4111yescharacteristic
281C23×C43C2×#4111yescharacteristic
282C23×C43C2×#4111yescharacteristic
283C23×C43C2×#4111yescharacteristic
284C23×C43C2×#4111yescharacteristic
285C23×C43C2×#4111yescharacteristic
286C23×C43C2×#4111yescharacteristic
287C23×C43H(5,𝔽2)11yescharacteristic
288C23×C43H(5,𝔽2)11yescharacteristic
289C23×C432−1+411yescharacteristic
290C23×C432−1+411yescharacteristic
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—22no—
307C22×D43—22no—
308C22×D43—22no—
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×D43—41no—
323C22×D43—41no—
324C22×D43—41no—
325C22×D43C2×C22⋊C414yes—
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—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—22no—
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×C43C2×C22⋊C414yes—
374C2×C4×C43#11714yes—
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—22no—
394C2×Dic43—22no—
395C2×Dic43—22no—
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—41no—
420C2×Dic43—41no—
421C2×Dic43—41no—
422C2×Dic43C2×C22⋊C414yes—
423C2×Dic43#11714yes—
424C4×D43—232no—
425#13943—431nomaximal, Sylow
426C22×C43C22×C22⋊C411yescharacteristic
427C22×C43C2×#11711yescharacteristic
428C22×C43C2×#11711yescharacteristic
429C22×C43C4×#4111yescharacteristic
430C22×C43C4×#4111yescharacteristic
431C22×C43#52011yescharacteristic
432C22×C43#52011yescharacteristic
433C22×C43#52511yescharacteristic
434C22×C43#52511yescharacteristic
435C22×C43#52511yescharacteristic
436C22×C43#52511yescharacteristic
437C22×C43#52911yescharacteristic
438C22×C43#52911yescharacteristic
439C22×C43#52911yescharacteristic
440C22×C43#52911yescharacteristic
441C22×C43#54011yescharacteristic
442C22×C43#54111yescharacteristic
443C22×C43#54211yescharacteristic
444C22×C43#54211yescharacteristic
445C22×C43#54611yescharacteristic
446C22×C43#54611yescharacteristic
447C22×C43#54611yescharacteristic
448C22×C43#54611yescharacteristic
449C22×C43#54711yescharacteristic
450C22×C43#54711yescharacteristic
451C22×C43#54711yescharacteristic
452C22×C43#54711yescharacteristic
453C22×C43#55211yescharacteristic
454C22×C43#55211yescharacteristic
455C22×C43#55311yescharacteristic
456C22×C43#55311yescharacteristic
457C22×C43#55511yescharacteristic
458C22×C43#55511yescharacteristic
459C22×C43#55611yescharacteristic
460C22×C43#55611yescharacteristic
461C2×D43—24no—
462C2×D43—24no—
463C2×D43—24no—
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—
473C2×D43—42no—
474C2×D43—42no—
475C2×D43—42no—
476C4×C43—24no—
477C4×C43—24no—
478C4×C43—42no—
479C4×C43—42no—
480C4×C43—42no—
481C4×C43—81no—
482C4×C43—81no—
483Dic43—24no—
484Dic43—24no—
485Dic43—42no—
486Dic43—42no—
487Dic43—42no—
488Dic43—81no—
489Dic43—81no—
490C22×#117—431no—
491C2×#388—431no—
492C2×#388—431no—
493#1441—431no—
494#1441—431no—
495#1440—431no—
496#1440—431no—
497#1436—431no—
498#1436D4311yescharacteristic, complemented
499C4⋊#95—431no—
500#1434—431no—
501#1434—431no—
502C22⋊#95—431no—
503C22⋊#95—431no—
504C4×#95—431no—
505C2×C43#228011yescharacteristic
506C2×C43#229811yescharacteristic
507C2×C43#231411yescharacteristic
508C2×C43#233911yescharacteristic
509C2×C43#233911yescharacteristic
510C2×C43#234611yescharacteristic
511C2×C43#234711yescharacteristic
512C2×C43#247011yescharacteristic
513C2×C43#247011yescharacteristic
514C2×C43#247411yescharacteristic
515C2×C43#247411yescharacteristic
516C2×C43#247611yescharacteristic
517C2×C43#247611yescharacteristic
518C2×C43#247811yescharacteristic
519C2×C43#247811yescharacteristic
520D43—44no—
521C24×C4—431no—
522C2×#117—438no—
523C2×#117—864no—
524C2×#117—864no—
525C22×C4⋊C4—431no—
526C22×C4⋊C4—431no—
527C22×C4⋊C4—431no—
528C22×C4⋊C4C2×D4311yescharacteristic
529C22×C22⋊C4—431no—
530C22×C22⋊C4—431no—
531C22×C22⋊C4—431no—
532C22×C22⋊C4—431no—
533C22×C22⋊C4—431no—
534C22×C22⋊C4—431no—
535C22×C42—431no—
536C22×C42—431no—
537C22×C42—431no—
538C22×C42C2×D4311yescharacteristic
539#388—864no—
540#388—864no—
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×#95—431no—
550C2×#95—431no—
551C2×#95—431no—
552C2×#95—431no—
553C2×#95—431no—
554C2×#95—431no—
555C2×#95—431no—
556C2×#95C2×D4311yescharacteristic
557C2×#95C2×D4311yescharacteristic
558C2×#95C2×D4311yescharacteristic
559C2×#95C2×D4311yescharacteristic
560C2×#95C2×D4311yescharacteristic
561C43#1394311yescharacteristic, complemented, Sylow
562C25—431no—
563C23×C4—431no—
564C23×C4—431no—
565C23×C4—431no—
566C23×C4—431no—
567C23×C4—431no—
568C23×C4—434no—
569C23×C4—431no—
570C23×C4—431no—
571C23×C4—862no—
572C23×C4—862no—
573C23×C4—862no—
574C23×C4—862no—
575C23×C4—862no—
576C23×C4—862no—
577C23×C4C22×D4311yescharacteristic
578C23×C4C22×D4311yescharacteristic
579C23×C4C22×D4311yescharacteristic
580C23×C4C22×D4311yescharacteristic
581C23×C4C22×D4311yescharacteristic
582C23×C4C22×D4311yescharacteristic
583C23×C4C22×D4311yescharacteristic
584#117—8632no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—434no—
588C2×C4⋊C4—862no—
589C2×C4⋊C4—862no—
590C2×C4⋊C4—862no—
591C2×C4⋊C4—862no—
592C2×C4⋊C4—862no—
593C2×C4⋊C4—862no—
594C2×C4⋊C4—1721no—
595C2×C4⋊C4—1721no—
596C2×C4⋊C4C4×D4314yes—
597C2×C22⋊C4—434no—
598C2×C22⋊C4—434no—
599C2×C22⋊C4—434no—
600C2×C22⋊C4—434no—
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—862no—
608C2×C22⋊C4—862no—
609C2×C22⋊C4—862no—
610C2×C22⋊C4—862no—
611C2×C22⋊C4—1721no—
612C2×C22⋊C4—1721no—
613C2×C22⋊C4—1721no—
614C2×C22⋊C4—1721no—
615C2×C42—22no—
616C2×C42—22no—
617C2×C42—41no—
618C2×C42—434no—
619C2×C42—434no—
620C2×C42—862no—
621C2×C42—862no—
622C2×C42—862no—
623C2×C42—862no—
624C2×C42—862no—
625C2×C42—862no—
626C2×C42—1721no—
627#95—22no—
628#95—22no—
629#95—22no—
630#95—22no—
631#95—41no—
632#95—862no—
633#95—862no—
634#95—862no—
635#95—862no—
636#95—862no—
637#95—862no—
638#95—862no—
639#95—862no—
640#95—862no—
641#95—862no—
642#95—862no—
643#95—862no—
644#95—1721no—
645#95—1721no—
646#95—1721no—
647C24—432no—
648C24—432no—
649C24—432no—
650C24—861no—
651C24—861no—
652C24—861no—
653C24—861no—
654C24—861no—
655C24—861no—
656C24—861no—
657C24—861no—
658C24—861no—
659C24—861no—
660C24—861no—
661C24—861no—
662C24C23×D4311yescharacteristic
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—21no—
702C22×C4—21no—
703C22×C4—432no—
704C22×C4—432no—
705C22×C4—432no—
706C22×C4—432no—
707C22×C4—432no—
708C22×C4—432no—
709C22×C4—432no—
710C22×C4—432no—
711C22×C4—432no—
712C22×C4—868no—
713C22×C4—868no—
714C22×C4—868no—
715C22×C4—868no—
716C22×C4—868no—
717C22×C4—868no—
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—868no—
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×C4C2×C4×D4312yes—
760C22×C4C2×C4×D4312yes—
761C22×C4C2×C4×D4312yes—
762C22×C4#1062189812yes—
763C22×C4#1062189812yes—
764C22×C4D4×D4312yes—
765C22×C4D4×D4312yes—
766C22×C4#1062190012yes—
767C22×C4#1062190212yes—
768C4⋊C4—28no—
769C4⋊C4—868no—
770C4⋊C4—1724no—
771C4⋊C4—1724no—
772C22⋊C4—4316no—
773C22⋊C4—868no—
774C22⋊C4—1724no—
775C22⋊C4—1724no—
776C22⋊C4—1724no—
777C22⋊C4—1724no—
778C42—44no—
779C42—868no—
780C42—868no—
781C42—1724no—
782C23—434no—
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—862no—
796C23—862no—
797C23—862no—
798C23—862no—
799C23—862no—
800C23—862no—
801C23—1721no—
802C23—1721no—
803C23—1721no—
804C23—1721no—
805C23—1721no—
806C23—1721no—
807C23—1721no—
808C23—1721no—
809C23—1721no—
810C23—1721no—
811C23—1721no—
812C23—1721no—
813C23—1721no—
814C23—1721no—
815C23—1721no—
816C23—1721no—
817C23C22×C4×D4311yescharacteristic
818C23C2×D4×D4311yescharacteristic
819C23C2×D4×D4311yescharacteristic
820C23#41×D4311yescharacteristic
821C23#41×D4311yescharacteristic
822C23#41×D4311yescharacteristic
823C23#41×D4311yescharacteristic
824C23C2×#1062190011yescharacteristic
825C23C2×#1062189811yescharacteristic
826C23C2×#1062189811yescharacteristic
827C23C2×#1062190211yescharacteristic
828C23#1306337011yescharacteristic
829C23#1306337111yescharacteristic
830C23#1306337211yescharacteristic
831C23#1306337311yescharacteristic
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—22no—
842C2×C4—22no—
843C2×C4—22no—
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—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—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—434no—
880C2×C4—434no—
881C2×C4—8632no—
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—862no—
899C2×C4—862no—
900C2×C4—862no—
901C2×C4—862no—
902C2×C4—862no—
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—
925C2×C4—1721no—
926C2×C4—1721no—
927C2×C4—1721no—
928C2×C4—1721no—
929C2×C4C22⋊C4×D4314yes—
930C2×C4#1306328214yes—
931C22—864no—
932C22—864no—
933C22—864no—
934C22—1722no—
935C22—1722no—
936C22—1722no—
937C22—1722no—
938C22—1722no—
939C22—1722no—
940C22—1722no—
941C22—1722no—
942C22—1722no—
943C22—1722no—
944C22—1722no—
945C22—1722no—
946C22C2×C22⋊C4×D4311yescharacteristic
947C22#117×D4311yescharacteristic
948C22C2×#1306328211yescharacteristic
949C22C4×#1062190011yescharacteristic
950C22C4×#1062190211yescharacteristic
951C22#1458337811yescharacteristic
952C22#1458338111yescharacteristic
953C22#1458340811yescharacteristic
954C22#1458340811yescharacteristic
955C22#1458340811yescharacteristic
956C22#1458340811yescharacteristic
957C22#1458342611yescharacteristic
958C22#1458343211yescharacteristic
959C22#1458343411yescharacteristic
960C22#1458343511yescharacteristic
961C22#1458350111yescharacteristic
962C22#1458350811yescharacteristic
963C22#1458351511yescharacteristic
964C22#1458351911yescharacteristic
965C22#1458353611yescharacteristic
966C22#1458353811yescharacteristic
967C22#1458354011yescharacteristic
968C22#1458354211yescharacteristic
969C22#1458354711yescharacteristic
970C22#1458354911yescharacteristic
971C22#1458355111yescharacteristic
972C22#1458355211yescharacteristic
973C22#1458358411yescharacteristic
974C22#1458359011yescharacteristic
975C22#1458359711yescharacteristic
976C22#1458359911yescharacteristic
977C22#1458361211yescharacteristic
978C22#1458361411yescharacteristic
979C22#1458361711yescharacteristic
980C22#1458362211yescharacteristic
981C4—24no—
982C4—24no—
983C4—42no—
984C4—42no—
985C4—42no—
986C4—81no—
987C4—81no—
988C4—864no—
989C4—864no—
990C4—3441no—
991C4—3441no—
992C4—1722no—
993C4—1722no—
994C4—1722no—
995C2—1724no—
996C2#1913697611yescharacteristic
997C2#1913708711yescharacteristic
998C2#1913720111yescharacteristic
999C2#1913742111yescharacteristic
1000C2#1913742411yescharacteristic
1001C2#1913747611yescharacteristic
1002C2#1913748411yescharacteristic
1003C2#1913869511yescharacteristic
1004C2#1913869711yescharacteristic
1005C2#1913875511yescharacteristic
1006C2#1913875711yescharacteristic
1007C2#1913878511yescharacteristic
1008C2#1913878711yescharacteristic
1009C2#1913881511yescharacteristic
1010C2#1913881711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1436C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenter#1436D43
hypocenterC43#13943
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
4. #19132847C2semidirect
5. #19132847C2semidirect
8. #19132827C2semidirect
9. Dic43⋊#95C2semidirect
10. #19132820C2semidirect
11. #19132819C2semidirect
14. C4×C43⋊#95C2semidirect
15. C43×#1436C2semidirect
19. C2×#13063283C4semidirect
498. #1436D43semidirect
561. C43#13943semidirect

Maximal subgroups

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

subgroupindex
C22×#130632832
C2×#145827902
C2×#145827882
#191328472
#191328432
#191328272
Dic43⋊#952
#191328202
#191328192
(C2×D43)⋊#952
C4×C43⋊#952
C43×#14362
#1394343