Finite Group Databasebeta

← #25025766

Subgroups — #25025766

Order 11008.

2070 conjugacy classes of subgroups.

The subgroup lattice has 1170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063310C211yesmaximal, characteristic
2C2×#14582801C211yesmaximal, characteristic
3C2×#14582777C211yesmaximal, characteristic
4#19132849C211yesmaximal, characteristic, complemented
5#19132848C211yesmaximal, characteristic, complemented
6#19132843C211yesmaximal, characteristic, complemented
7#19132843C211yesmaximal, characteristic, complemented
8#19132843C211yesmaximal, characteristic, complemented
9#19132843C211yesmaximal, characteristic, complemented
10#19132828C211yesmaximal, characteristic, complemented
11(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
12(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
13(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
15C43×#1436C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C2×#13063310—24no—
20C2×#13063310—24no—
21C2×#13063310C418yescomplemented
22C22×C4⋊Dic43C2211yescharacteristic
23C22×Dic43⋊C4C2211yescharacteristic
24C22×(C2×D43)⋊C4C2211yescharacteristic
25C22×(C2×D43)⋊C4C2211yescharacteristic
26C22×(C2×D43)⋊C4C2211yescharacteristic
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34#14582801—24no—
35#14582777—24no—
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
57C24×D43C2311yescharacteristic
58C22×D172—41no—
59C22×D172—41no—
60C22×D172—41no—
61C22×D172—41no—
62C22×D172C2×C414yes—
63C22×D172D414yes—
64C22×D172D414yes—
65C23×Dic43C2311yescharacteristic
66C23×Dic43C2311yescharacteristic
67C23×Dic43C2311yescharacteristic
68C23×Dic43C2311yescharacteristic
69C23×Dic43C2311yescharacteristic
70C23×Dic43C2311yescharacteristic
71C22×C4×D43—22no—
72C22×C4×D43—22no—
73C22×C4×D43—22no—
74C22×C4×D43—22no—
75C22×C4×D43—22no—
76C22×C4×D43—41no—
77C22×C4×D43—41no—
78C22×C4×D43—41no—
79C22×C4×D43—41no—
80C22×C4×D43—41no—
81C22×C4×D43—41no—
82C22×C4×D43—41no—
83C22×C4×D43—41no—
84C22×C4×D43C2×C414yescomplemented
85#13063310—232no—
86C2×C4⋊Dic43—22no—
87C2×C4⋊Dic43—41no—
88C2×C4⋊Dic43—41no—
89C2×Dic43⋊C4—22no—
90C2×Dic43⋊C4—22no—
91C2×Dic43⋊C4C2×C414yescomplemented
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)⋊C4—22no—
100C2×(C2×D43)⋊C4—22no—
101C2×(C2×D43)⋊C4—22no—
102C2×(C2×D43)⋊C4—22no—
103C2×(C2×D43)⋊C4—22no—
104C2×(C2×D43)⋊C4—22no—
105C2×(C2×D43)⋊C4—22no—
106C2×(C2×D43)⋊C4—22no—
107C2×(C2×D43)⋊C4—22no—
108C2×(C2×D43)⋊C4—22no—
109C2×(C2×D43)⋊C4—22no—
110C2×(C2×D43)⋊C4—22no—
111C2×(C2×D43)⋊C4—41no—
112C2×(C2×D43)⋊C4—41no—
113C2×(C2×D43)⋊C4—41no—
114C2×(C2×D43)⋊C4—41no—
115C2×(C2×D43)⋊C4—41no—
116C2×(C2×D43)⋊C4—41no—
117C2×(C2×D43)⋊C4—41no—
118C2×(C2×D43)⋊C4—41no—
119C2×(C2×D43)⋊C4C2×C414yes—
120C2×(C2×D43)⋊C4C2×C414yes—
121C2×(C2×D43)⋊C4C2×C414yescomplemented
122C43⋊#95—22no—
123C43⋊#95—22no—
124C43⋊#95—22no—
125C43⋊#95—41no—
126C43⋊#95—41no—
127C43⋊#95—41no—
128C43⋊#95—41no—
129C43⋊#95—41no—
130C43⋊#95—41no—
131C43⋊#95—41no—
132C43⋊#95—41no—
133C43⋊#95—41no—
134C43⋊#95—41no—
135C23×C4×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C23×C4×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142C2×C4⋊C4×C43—22no—
143C2×C4⋊C4×C43—22no—
144C2×C4⋊C4×C43C2×C414yescomplemented
145C2×C42×C43—22no—
146C2×C42×C43—41no—
147C2×C42×C43—41no—
148#95×C43—22no—
149#95×C43—22no—
150#95×C43—22no—
151#95×C43—41no—
152#95×C43—41no—
153C24×C43C2411yescharacteristic
154C23×D43—21no—
155C23×D43—21no—
156C23×D43—21no—
157C23×D43—21no—
158C23×D43—21no—
159C23×D43—21no—
160C23×D43—21no—
161C23×D43—21no—
162C23×D43—21no—
163C23×D43—21no—
164C23×D43—21no—
165C23×D43—21no—
166C23×D43—21no—
167C23×D43—21no—
168C23×D43—21no—
169C23×D43—21no—
170C23×D43—21no—
171C23×D43—21no—
172C23×D43—21no—
173C23×D43—21no—
174C23×D43—21no—
175C23×D43—21no—
176C23×D43—21no—
177C23×D43—21no—
178C23×D43C22×C412yes—
179C23×D43C22×C412yes—
180C23×D43C2×D412yes—
181C23×D43C2×D412yes—
182C23×D43C2×D412yes—
183C23×D43C2×D412yes—
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×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43C22×C412yes—
226C22×C4×C43C22×C412yes—
227C22×C4×C43C22×C412yes—
228C22×C4×C43C2×D412yes—
229C22×C4×C43C2×D412yes—
230C22×C4×C43#4112yes—
231C22×C4×C43#4112yes—
232C22×C4×C43#4112yes—
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×Dic43—21no—
247C22×Dic43—21no—
248C22×Dic43—21no—
249C22×Dic43—21no—
250C22×Dic43—21no—
251C22×Dic43—21no—
252C22×Dic43—21no—
253C22×Dic43—21no—
254C22×Dic43—21no—
255C22×Dic43—21no—
256C22×Dic43—21no—
257C22×Dic43—21no—
258C22×Dic43—21no—
259C22×Dic43—21no—
260C22×Dic43—21no—
261C22×Dic43—21no—
262C22×Dic43—21no—
263C22×Dic43—21no—
264C22×Dic43—21no—
265C22×Dic43—21no—
266C22×Dic43—21no—
267C22×Dic43—21no—
268C22×Dic43—21no—
269C22×Dic43—21no—
270C22×Dic43—21no—
271C22×Dic43—21no—
272C22×Dic43C22×C412yes—
273C22×Dic43C22×C412yes—
274C22×Dic43#4112yes—
275C2×D172—44no—
276C2×D172—44no—
277C2×D172—44no—
278C2×D172—44no—
279C2×D172—44no—
280C2×D172—44no—
281C2×D172C22⋊C4116yes—
282C2×C4×D43—28no—
283C2×C4×D43—44no—
284C2×C4×D43—44no—
285C2×C4×D43—44no—
286C2×C4×D43—44no—
287C2×C4×D43—44no—
288C2×C4×D43—44no—
289C2×C4×D43—44no—
290C2×C4×D43—44no—
291C2×C4×D43—44no—
292C2×C4×D43—44no—
293C2×C4×D43—44no—
294C2×C4×D43—44no—
295C2×C4×D43—44no—
296C4⋊C4×C43—28no—
297C42×C43—44no—
298(C2×D43)⋊C4—28no—
299(C2×D43)⋊C4—28no—
300(C2×D43)⋊C4—28no—
301(C2×D43)⋊C4—44no—
302(C2×D43)⋊C4—44no—
303(C2×D43)⋊C4—44no—
304(C2×D43)⋊C4—44no—
305(C2×D43)⋊C4—44no—
306(C2×D43)⋊C4—44no—
307(C2×D43)⋊C4—44no—
308C4⋊Dic43—44no—
309Dic43⋊C4—28no—
310C23×C43C23×C411yescharacteristic
311C23×C43C22×D411yescharacteristic
312C23×C43C22×D411yescharacteristic
313C23×C43C2×#4111yescharacteristic
314C23×C43C2×#4111yescharacteristic
315C23×C43C2×#4111yescharacteristic
316C23×C43C2×#4111yescharacteristic
317C23×C43H(5,𝔽2)11yescharacteristic
318C23×C43H(5,𝔽2)11yescharacteristic
319C23×C43H(5,𝔽2)11yescharacteristic
320C23×C43H(5,𝔽2)11yescharacteristic
321C23×C43H(5,𝔽2)11yescharacteristic
322C23×C43H(5,𝔽2)11yescharacteristic
323C23×C432−1+411yescharacteristic
324C23×C432−1+411yescharacteristic
325C22×D43—22no—
326C22×D43—22no—
327C22×D43—22no—
328C22×D43—22no—
329C22×D43—22no—
330C22×D43—22no—
331C22×D43—22no—
332C22×D43—22no—
333C22×D43—22no—
334C22×D43—22no—
335C22×D43—22no—
336C22×D43—22no—
337C22×D43—22no—
338C22×D43—22no—
339C22×D43—22no—
340C22×D43—22no—
341C22×D43—22no—
342C22×D43—22no—
343C22×D43—22no—
344C22×D43—22no—
345C22×D43—22no—
346C22×D43—22no—
347C22×D43—22no—
348C22×D43—22no—
349C22×D43—22no—
350C22×D43—22no—
351C22×D43—22no—
352C22×D43—22no—
353C22×D43—22no—
354C22×D43—22no—
355C22×D43—22no—
356C22×D43—22no—
357C22×D43—22no—
358C22×D43—22no—
359C22×D43—22no—
360C22×D43—22no—
361C22×D43—41no—
362C22×D43—41no—
363C22×D43—41no—
364C22×D43—41no—
365C22×D43—41no—
366C22×D43—41no—
367C22×D43—41no—
368C22×D43—41no—
369C22×D43—41no—
370C22×D43—41no—
371C22×D43—41no—
372C22×D43—41no—
373C22×D43—41no—
374C22×D43—41no—
375C22×D43—41no—
376C22×D43—41no—
377C22×D43—41no—
378C22×D43—41no—
379C22×D43—41no—
380C22×D43—41no—
381C22×D43—41no—
382C22×D43—41no—
383C22×D43—41no—
384C22×D43—41no—
385C22×D43—41no—
386C22×D43—41no—
387C22×D43—41no—
388C22×D43—41no—
389C22×D43—41no—
390C22×D43—41no—
391C22×D43—41no—
392C22×D43—41no—
393C22×D43C2×C22⋊C414yes—
394C22×D43C2×C22⋊C414yes—
395C2×C4×C43—22no—
396C2×C4×C43—22no—
397C2×C4×C43—22no—
398C2×C4×C43—22no—
399C2×C4×C43—22no—
400C2×C4×C43—22no—
401C2×C4×C43—22no—
402C2×C4×C43—22no—
403C2×C4×C43—22no—
404C2×C4×C43—22no—
405C2×C4×C43—22no—
406C2×C4×C43—22no—
407C2×C4×C43—22no—
408C2×C4×C43—22no—
409C2×C4×C43—22no—
410C2×C4×C43—22no—
411C2×C4×C43—22no—
412C2×C4×C43—22no—
413C2×C4×C43—22no—
414C2×C4×C43—22no—
415C2×C4×C43—22no—
416C2×C4×C43—41no—
417C2×C4×C43—41no—
418C2×C4×C43—41no—
419C2×C4×C43—41no—
420C2×C4×C43—41no—
421C2×C4×C43—41no—
422C2×C4×C43—41no—
423C2×C4×C43—41no—
424C2×C4×C43—41no—
425C2×C4×C43—41no—
426C2×C4×C43—41no—
427C2×C4×C43—41no—
428C2×C4×C43—41no—
429C2×C4×C43—41no—
430C2×C4×C43—41no—
431C2×C4×C43—41no—
432C2×C4×C43—41no—
433C2×C4×C43—41no—
434C2×C4×C43—41no—
435C2×C4×C43—41no—
436C2×C4×C43—41no—
437C2×C4×C43—41no—
438C2×C4×C43—41no—
439C2×C4×C43—41no—
440C2×C4×C43—41no—
441C2×C4×C43—41no—
442C2×C4×C43—41no—
443C2×C4×C43C2×C22⋊C414yes—
444C2×Dic43—22no—
445C2×Dic43—22no—
446C2×Dic43—22no—
447C2×Dic43—22no—
448C2×Dic43—22no—
449C2×Dic43—22no—
450C2×Dic43—22no—
451C2×Dic43—22no—
452C2×Dic43—22no—
453C2×Dic43—41no—
454C2×Dic43—41no—
455C2×Dic43—41no—
456C2×Dic43—41no—
457C2×Dic43—41no—
458C2×Dic43—41no—
459C2×Dic43—41no—
460C2×Dic43—41no—
461C2×Dic43—41no—
462C2×Dic43—41no—
463C2×Dic43—41no—
464C2×Dic43—41no—
465C2×Dic43—41no—
466C2×Dic43—41no—
467C2×Dic43—41no—
468C2×Dic43—41no—
469C2×Dic43—41no—
470C2×Dic43—41no—
471C2×Dic43—41no—
472C2×Dic43—41no—
473C2×Dic43—41no—
474C2×Dic43—41no—
475C2×Dic43—41no—
476C2×Dic43—41no—
477C2×Dic43—41no—
478C2×Dic43—41no—
479C2×Dic43—41no—
480C2×Dic43—41no—
481C2×Dic43—41no—
482C2×Dic43—41no—
483C2×Dic43—41no—
484C2×Dic43—41no—
485C2×Dic43—41no—
486D172—416no—
487C4×D43—416no—
488C4×D43—416no—
489#14505—431nomaximal, Sylow
490C22×C43C22×C22⋊C411yescharacteristic
491C22×C43C4×#4111yescharacteristic
492C22×C43C4×#4111yescharacteristic
493C22×C43#51811yescharacteristic
494C22×C43#51811yescharacteristic
495C22×C43#52011yescharacteristic
496C22×C43#52011yescharacteristic
497C22×C43#53411yescharacteristic
498C22×C43#53411yescharacteristic
499C22×C43#53411yescharacteristic
500C22×C43#53411yescharacteristic
501C22×C43#53811yescharacteristic
502C22×C43#53811yescharacteristic
503C22×C43#53911yescharacteristic
504C22×C43#53911yescharacteristic
505C22×C43#54011yescharacteristic
506C22×C43#54011yescharacteristic
507C22×C43#54211yescharacteristic
508C22×C43#54211yescharacteristic
509C22×C43#54611yescharacteristic
510C22×C43#54611yescharacteristic
511C22×C43#54611yescharacteristic
512C22×C43#54611yescharacteristic
513C22×C43#54711yescharacteristic
514C22×C43#54711yescharacteristic
515C22×C43#54711yescharacteristic
516C22×C43#54711yescharacteristic
517C22×C43#55111yescharacteristic
518C22×C43#55311yescharacteristic
519C22×C43#55311yescharacteristic
520C22×C43#55911yescharacteristic
521C22×C43#56011yescharacteristic
522C22×C43#56211yescharacteristic
523C22×C43#56211yescharacteristic
524C22×C43#56311yescharacteristic
525C2×D43—24no—
526C2×D43—24no—
527C2×D43—24no—
528C2×D43—24no—
529C2×D43—24no—
530C2×D43—24no—
531C2×D43—42no—
532C2×D43—42no—
533C2×D43—42no—
534C2×D43—42no—
535C2×D43—42no—
536C2×D43—42no—
537C2×D43—42no—
538C2×D43—42no—
539C2×D43—42no—
540C2×D43—42no—
541C2×D43—42no—
542C2×D43—42no—
543C2×D43—42no—
544C2×D43—42no—
545C2×D43—42no—
546C2×D43—42no—
547C2×D43—42no—
548C2×D43—42no—
549C2×D43—42no—
550C2×D43—42no—
551C2×D43—42no—
552C2×D43—42no—
553C2×D43—42no—
554C2×D43—42no—
555C4×C43—24no—
556C4×C43—42no—
557C4×C43—42no—
558C4×C43—42no—
559C4×C43—42no—
560C4×C43—42no—
561C4×C43—81no—
562Dic43—42no—
563Dic43—42no—
564Dic43—42no—
565Dic43—81no—
566Dic43—81no—
567Dic43—81no—
568C22×#123—431no—
569C2×#390—431no—
570C2×#386—431no—
571#1441—431no—
572#1441—431no—
573#1440—431no—
574#1440—431no—
575#1440—431no—
576#1440—431no—
577#1436—431no—
578#1436D4311yescharacteristic, complemented
579C22⋊#95—431no—
580C22⋊#95—431no—
581C22⋊#95—431no—
582C22⋊#95—431no—
583C2×C43#230811yescharacteristic
584C2×C43#233511yescharacteristic
585C2×C43#233511yescharacteristic
586C2×C43#233911yescharacteristic
587C2×C43#233911yescharacteristic
588C2×C43#237411yescharacteristic
589C2×C43#237611yescharacteristic
590C2×C43#269711yescharacteristic
591C2×C43#270111yescharacteristic
592C2×C43#270111yescharacteristic
593C2×C43#270811yescharacteristic
594C2×C43#270811yescharacteristic
595C2×C43#270911yescharacteristic
596C2×C43#271711yescharacteristic
597C2×C43#272411yescharacteristic
598D43—44no—
599D43—44no—
600C23×D4—431no—
601C24×C4—431no—
602C24×C4—431no—
603C2×#123—438no—
604C2×#123—864no—
605C2×#123—864no—
606C22×C4⋊C4—431no—
607C22×C4⋊C4—431no—
608C22×C4⋊C4C2×D4311yescharacteristic
609C22×C22⋊C4—431no—
610C22×C22⋊C4—431no—
611C22×C22⋊C4—431no—
612C22×C22⋊C4—431no—
613C22×C22⋊C4—431no—
614C22×C22⋊C4—431no—
615C22×C22⋊C4—431no—
616C22×C22⋊C4—431no—
617C22×C22⋊C4—431no—
618C22×C22⋊C4—431no—
619C22×C42C2×D4311yescharacteristic
620#390—864no—
621#386—864no—
622C2×#95—431no—
623C2×#95—431no—
624C2×#95—431no—
625C2×#95—431no—
626C2×#95—431no—
627C2×#95—431no—
628C2×#95—431no—
629C2×#95—431no—
630C2×#95—431no—
631C2×#95—431no—
632C2×#95—431no—
633C2×#95—431no—
634C2×#95—431no—
635C2×#95C2×D4311yescharacteristic
636C2×#95C2×D4311yescharacteristic
637C2×#95C2×D4311yescharacteristic
638C2×#95C2×D4311yescharacteristic
639C2×#95C2×D4311yescharacteristic
640C43#1450511yescharacteristic, complemented, Sylow
641C25—431no—
642C25—431no—
643C22×D4—434no—
644C22×D4—434no—
645C22×D4—434no—
646C22×D4—1721no—
647C22×D4—1721no—
648C22×D4—1721no—
649C22×D4—1721no—
650C23×C4—431no—
651C23×C4—431no—
652C23×C4—431no—
653C23×C4—434no—
654C23×C4—431no—
655C23×C4—431no—
656C23×C4—431no—
657C23×C4—862no—
658C23×C4—862no—
659C23×C4—862no—
660C23×C4—862no—
661C23×C4—862no—
662C23×C4—1721no—
663C23×C4—1721no—
664C23×C4—1721no—
665C23×C4—1721no—
666C23×C4—1721no—
667C23×C4—1721no—
668C23×C4—1721no—
669C23×C4—1721no—
670C23×C4C22×D4311yescharacteristic
671C23×C4C22×D4311yescharacteristic
672C23×C4C22×D4311yescharacteristic
673C23×C4C22×D4311yescharacteristic
674C23×C4C22×D4311yescharacteristic
675C23×C4C22×D4311yescharacteristic
676C23×C4C22×D4311yescharacteristic
677#123—8632no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—434no—
681C2×C4⋊C4—862no—
682C2×C4⋊C4—862no—
683C2×C4⋊C4—862no—
684C2×C4⋊C4—1721no—
685C2×C4⋊C4—1721no—
686C2×C4⋊C4C4×D4314yescomplemented
687C2×C22⋊C4—434no—
688C2×C22⋊C4—434no—
689C2×C22⋊C4—434no—
690C2×C22⋊C4—862no—
691C2×C22⋊C4—862no—
692C2×C22⋊C4—862no—
693C2×C22⋊C4—862no—
694C2×C22⋊C4—862no—
695C2×C22⋊C4—862no—
696C2×C22⋊C4—862no—
697C2×C22⋊C4—862no—
698C2×C22⋊C4—862no—
699C2×C22⋊C4—862no—
700C2×C22⋊C4—862no—
701C2×C22⋊C4—862no—
702C2×C22⋊C4—862no—
703C2×C22⋊C4—862no—
704C2×C22⋊C4—862no—
705C2×C22⋊C4—862no—
706C2×C22⋊C4—862no—
707C2×C22⋊C4—862no—
708C2×C22⋊C4—862no—
709C2×C22⋊C4—1721no—
710C2×C22⋊C4—1721no—
711C2×C22⋊C4—1721no—
712C2×C22⋊C4—1721no—
713C2×C22⋊C4—1721no—
714C2×C22⋊C4—1721no—
715C2×C22⋊C4—1721no—
716C2×C22⋊C4—1721no—
717C2×C42—22no—
718C2×C42—41no—
719C2×C42—41no—
720#95—22no—
721#95—22no—
722#95—22no—
723#95—41no—
724#95—41no—
725#95—862no—
726#95—862no—
727#95—862no—
728#95—1721no—
729#95—1721no—
730#95—1721no—
731#95—1721no—
732#95—1721no—
733#95—1721no—
734#95—1721no—
735#95—1721no—
736#95—1721no—
737#95—1721no—
738C24—432no—
739C24—432no—
740C24—432no—
741C24—432no—
742C24—432no—
743C24—432no—
744C24—861no—
745C24—861no—
746C24—861no—
747C24—861no—
748C24—861no—
749C24—861no—
750C24—861no—
751C24—861no—
752C24—861no—
753C24—861no—
754C24—861no—
755C24—861no—
756C24—861no—
757C24—861no—
758C24—861no—
759C24—861no—
760C24—861no—
761C24—861no—
762C24—861no—
763C24—861no—
764C24—861no—
765C24—861no—
766C24—861no—
767C24—861no—
768C24C23×D4311yescharacteristic
769C2×D4—4316no—
770C2×D4—1724no—
771C2×D4—1724no—
772C2×D4—1724no—
773C2×D4—1724no—
774C2×D4—1724no—
775C2×D4—1724no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—432no—
818C22×C4—432no—
819C22×C4—432no—
820C22×C4—868no—
821C22×C4—861no—
822C22×C4—861no—
823C22×C4—861no—
824C22×C4—861no—
825C22×C4—861no—
826C22×C4—861no—
827C22×C4—861no—
828C22×C4—861no—
829C22×C4—861no—
830C22×C4—861no—
831C22×C4—861no—
832C22×C4—861no—
833C22×C4—861no—
834C22×C4—861no—
835C22×C4—861no—
836C22×C4—861no—
837C22×C4—861no—
838C22×C4—861no—
839C22×C4—861no—
840C22×C4—861no—
841C22×C4—861no—
842C22×C4—861no—
843C22×C4—861no—
844C22×C4—861no—
845C22×C4—861no—
846C22×C4—861no—
847C22×C4—861no—
848C22×C4—861no—
849C22×C4—861no—
850C22×C4—861no—
851C22×C4—861no—
852C22×C4—861no—
853C22×C4—861no—
854C22×C4—861no—
855C22×C4—861no—
856C22×C4—861no—
857C22×C4—861no—
858C22×C4—861no—
859C22×C4—861no—
860C22×C4—1724no—
861C22×C4—1724no—
862C22×C4—1724no—
863C22×C4—1724no—
864C22×C4—1724no—
865C22×C4—1724no—
866C22×C4—1724no—
867C22×C4—1724no—
868C22×C4—1724no—
869C22×C4—1724no—
870C22×C4—1724no—
871C22×C4—1724no—
872C22×C4—1724no—
873C22×C4C2×C4×D4312yes—
874C22×C4C2×C4×D4312yes—
875C22×C4C2×C4×D4312yes—
876C22×C4#1062189812yes—
877C22×C4#1062189812yes—
878C22×C4D4×D4312yes—
879C22×C4D4×D4312yes—
880C22×C4#1062190212yes—
881C4⋊C4—28no—
882C4⋊C4—868no—
883C4⋊C4—1724no—
884C22⋊C4—868no—
885C22⋊C4—868no—
886C22⋊C4—868no—
887C22⋊C4—1724no—
888C22⋊C4—1724no—
889C22⋊C4—1724no—
890C22⋊C4—1724no—
891C22⋊C4—1724no—
892C22⋊C4—1724no—
893C22⋊C4—1724no—
894C42—44no—
895C23—434no—
896C23—434no—
897C23—862no—
898C23—862no—
899C23—862no—
900C23—862no—
901C23—862no—
902C23—862no—
903C23—862no—
904C23—862no—
905C23—862no—
906C23—862no—
907C23—862no—
908C23—862no—
909C23—862no—
910C23—862no—
911C23—862no—
912C23—862no—
913C23—862no—
914C23—862no—
915C23—862no—
916C23—862no—
917C23—862no—
918C23—862no—
919C23—862no—
920C23—862no—
921C23—862no—
922C23—862no—
923C23—862no—
924C23—862no—
925C23—862no—
926C23—862no—
927C23—862no—
928C23—862no—
929C23—862no—
930C23—862no—
931C23—862no—
932C23—862no—
933C23—1721no—
934C23—1721no—
935C23—1721no—
936C23—1721no—
937C23—1721no—
938C23—1721no—
939C23—1721no—
940C23—1721no—
941C23—1721no—
942C23—1721no—
943C23—1721no—
944C23—1721no—
945C23—1721no—
946C23—1721no—
947C23—1721no—
948C23—1721no—
949C23—1721no—
950C23—1721no—
951C23—1721no—
952C23—1721no—
953C23—1721no—
954C23—1721no—
955C23—1721no—
956C23—1721no—
957C23—1721no—
958C23—1721no—
959C23—1721no—
960C23—1721no—
961C23—1721no—
962C23—1721no—
963C23—1721no—
964C23—1721no—
965C23C22×C4×D4311yescharacteristic
966C23C2×D4×D4311yescharacteristic
967C23C2×D4×D4311yescharacteristic
968C23#41×D4311yescharacteristic
969C23C2×#1062189811yescharacteristic
970C23C2×#1062189811yescharacteristic
971C23C2×#1062190211yescharacteristic
972C23#1306337011yescharacteristic
973C23#1306337011yescharacteristic
974C23#1306337111yescharacteristic
975C23#1306337111yescharacteristic
976C23#1306337111yescharacteristic
977C23#1306337111yescharacteristic
978C23#1306337211yescharacteristic
979C23#1306337311yescharacteristic
980D4—17216no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—862no—
1030C2×C4—862no—
1031C2×C4—862no—
1032C2×C4—862no—
1033C2×C4—862no—
1034C2×C4—862no—
1035C2×C4—862no—
1036C2×C4—862no—
1037C2×C4—862no—
1038C2×C4—17216no—
1039C2×C4—17216no—
1040C2×C4—1721no—
1041C2×C4—1721no—
1042C2×C4—1721no—
1043C2×C4—1721no—
1044C2×C4—1721no—
1045C2×C4—1721no—
1046C2×C4—1721no—
1047C2×C4—1721no—
1048C2×C4—1721no—
1049C2×C4—1721no—
1050C2×C4—1721no—
1051C2×C4—1721no—
1052C2×C4—1721no—
1053C2×C4—1721no—
1054C2×C4—1721no—
1055C2×C4—1721no—
1056C2×C4—1721no—
1057C2×C4—1721no—
1058C2×C4—1721no—
1059C2×C4—1721no—
1060C2×C4—1721no—
1061C2×C4—1721no—
1062C2×C4—1721no—
1063C2×C4—1721no—
1064C2×C4—1721no—
1065C2×C4—1721no—
1066C2×C4—1721no—
1067C2×C4—1721no—
1068C2×C4—1721no—
1069C2×C4—1721no—
1070C2×C4—1721no—
1071C2×C4—1721no—
1072C2×C4—1721no—
1073C2×C4C22⋊C4×D4314yes—
1074C22—864no—
1075C22—864no—
1076C22—864no—
1077C22—864no—
1078C22—864no—
1079C22—864no—
1080C22—1722no—
1081C22—1722no—
1082C22—1722no—
1083C22—1722no—
1084C22—1722no—
1085C22—1722no—
1086C22—1722no—
1087C22—1722no—
1088C22—1722no—
1089C22—1722no—
1090C22—1722no—
1091C22—1722no—
1092C22—1722no—
1093C22—1722no—
1094C22—1722no—
1095C22—1722no—
1096C22—1722no—
1097C22—1722no—
1098C22—1722no—
1099C22—1722no—
1100C22—1722no—
1101C22—1722no—
1102C22—1722no—
1103C22—1722no—
1104C22C2×C22⋊C4×D4311yescharacteristic
1105C22C4×#1062189811yescharacteristic
1106C22C4×#1062190211yescharacteristic
1107C22#1458337111yescharacteristic
1108C22#1458337111yescharacteristic
1109C22#1458337911yescharacteristic
1110C22#1458338111yescharacteristic
1111C22#1458345711yescharacteristic
1112C22#1458345711yescharacteristic
1113C22#1458345911yescharacteristic
1114C22#1458346011yescharacteristic
1115C22#1458348211yescharacteristic
1116C22#1458348511yescharacteristic
1117C22#1458349611yescharacteristic
1118C22#1458349811yescharacteristic
1119C22#1458350411yescharacteristic
1120C22#1458350511yescharacteristic
1121C22#1458351511yescharacteristic
1122C22#1458352111yescharacteristic
1123C22#1458354011yescharacteristic
1124C22#1458354211yescharacteristic
1125C22#1458354511yescharacteristic
1126C22#1458354511yescharacteristic
1127C22#1458355111yescharacteristic
1128C22#1458355211yescharacteristic
1129C22#1458355411yescharacteristic
1130C22#1458355411yescharacteristic
1131C22#1458357311yescharacteristic
1132C22#1458359711yescharacteristic
1133C22#1458359811yescharacteristic
1134C22#1458363411yescharacteristic
1135C22#1458364011yescharacteristic
1136C22#1458364511yescharacteristic
1137C22#1458364611yescharacteristic
1138C22#1458365311yescharacteristic
1139C4—24no—
1140C4—42no—
1141C4—42no—
1142C4—42no—
1143C4—42no—
1144C4—42no—
1145C4—81no—
1146C4—3441no—
1147C4—3441no—
1148C4—3441no—
1149C4—1722no—
1150C4—1722no—
1151C4—1722no—
1152C2—1724no—
1153C2—1724no—
1154C2#1913716911yescharacteristic
1155C2#1913737911yescharacteristic
1156C2#1913738411yescharacteristic
1157C2#1913742411yescharacteristic
1158C2#1913742611yescharacteristic
1159C2#1913772411yescharacteristic
1160C2#1913774211yescharacteristic
1161C2#1914115511yescharacteristic
1162C2#1914120311yescharacteristic
1163C2#1914120511yescharacteristic
1164C2#1914131411yescharacteristic
1165C2#1914131611yescharacteristic
1166C2#1914132711yescharacteristic
1167C2#1914143511yescharacteristic
1168C2#1914152411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1436C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenter#1436D43
hypocenterC43#14505
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
4. #19132849C2semidirect
5. #19132848C2semidirect
6. #19132843C2semidirect
7. #19132843C2semidirect
8. #19132843C2semidirect
9. #19132843C2semidirect
10. #19132828C2semidirect
11. (C2×D43)⋊#95C2semidirect
12. (C2×D43)⋊#95C2semidirect
13. (C2×D43)⋊#95C2semidirect
14. (C2×D43)⋊#95C2semidirect
15. C43×#1436C2semidirect
21. C2×#13063310C4semidirect
84. C22×C4×D43C2×C4semidirect
91. C2×Dic43⋊C4C2×C4semidirect
121. C2×(C2×D43)⋊C4C2×C4semidirect
144. C2×C4⋊C4×C43C2×C4semidirect
578. #1436D43semidirect
640. C43#14505semidirect
686. C2×C4⋊C4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C22×#130633102
C2×#145828012
C2×#145827772
#191328492
#191328482
#191328432
#191328282
(C2×D43)⋊#952
C43×#14362
#1450543