Finite Group Databasebeta

← #25022069

Subgroups — #25022069

Order 11008.

2422 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063287C211yesmaximal, characteristic
2C2×#14582817C211yesmaximal, characteristic
3C2×#14582794C211yesmaximal, characteristic, complemented
4C2×#14582790C211yesmaximal, characteristic, complemented
5C2×#14582773C211yesmaximal, characteristic, complemented
6C2×#14582773C211yesmaximal, characteristic, complemented
7C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
8#19132843C211yesmaximal, characteristic, complemented
9#19132839C211yesmaximal, characteristic, complemented
10#19132835C211yesmaximal, characteristic
11#19132831C211yesmaximal, characteristic, complemented
12#19132830C211yesmaximal, characteristic, complemented
13#19132829C211yesmaximal, characteristic, complemented
14(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
15C43×#1436C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C2×#13063287—24no—
20C2×#13063287—24no—
21C2×#13063287—24no—
22C22×C4⋊Dic43C2211yescharacteristic
23C22×Dic43⋊C4C2211yescharacteristic
24C22×Dic43⋊C4C2211yescharacteristic
25C22×Dic43⋊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
34C22×(C2×D43)⋊C4C2211yescharacteristic
35C22×(C2×D43)⋊C4C2211yescharacteristic
36C22×C4×Dic43C2211yescharacteristic
37C22×C4×Dic43C2211yescharacteristic
38#14582817C418yescomplemented
39#14582794—24no—
40#14582790—24no—
41#14582773—24no—
42#14582773—24no—
43C4×(C2×D43)⋊C4—24no—
44C2×C43⋊#95C2211yescharacteristic
45C2×C43⋊#95C2211yescharacteristic
46C2×C43⋊#95C2211yescharacteristic
47C2×C43⋊#95C2211yescharacteristic
48C2×C43⋊#95C2211yescharacteristic
49C2×C43⋊#95C2211yescharacteristic
50C2×C43⋊#95C2211yescharacteristic
51C2×C43⋊#95C2211yescharacteristic
52C2×C43⋊#95C2211yescharacteristic
53C22×C4⋊C4×C43C2211yescharacteristic
54C22×C42×C43C2211yescharacteristic
55C2×#95×C43C2211yescharacteristic
56C2×#95×C43C2211yescharacteristic
57C2×#95×C43C2211yescharacteristic
58C2×#95×C43C2211yescharacteristic
59C2×#95×C43C2211yescharacteristic
60C24×D43C2311yescharacteristic
61C24×D43C2311yescharacteristic
62C22×D172—22no—
63C22×D172—22no—
64C22×D172—22no—
65C22×D172—22no—
66C22×D172—22no—
67C22×D172—22no—
68C22×D172C2×C414yes—
69C23×Dic43C2311yescharacteristic
70C23×Dic43C2311yescharacteristic
71C23×Dic43C2311yescharacteristic
72C23×Dic43C2311yescharacteristic
73C23×Dic43C2311yescharacteristic
74C23×Dic43C2311yescharacteristic
75C22×C4×D43—22no—
76C22×C4×D43—22no—
77C22×C4×D43—22no—
78C22×C4×D43—22no—
79C22×C4×D43—22no—
80C22×C4×D43—22no—
81C22×C4×D43—22no—
82C22×C4×D43—22no—
83C22×C4×D43—22no—
84C22×C4×D43—41no—
85C22×C4×D43—41no—
86C22×C4×D43—41no—
87C22×C4×D43—41no—
88C22×C4×D43D414yes—
89#13063287—232no—
90C2×C4⋊Dic43—22no—
91C2×C4⋊Dic43—22no—
92C2×C4⋊Dic43—22no—
93C2×Dic43⋊C4—22no—
94C2×Dic43⋊C4—22no—
95C2×Dic43⋊C4—22no—
96C2×Dic43⋊C4—22no—
97C2×Dic43⋊C4—22no—
98C2×Dic43⋊C4—22no—
99C2×Dic43⋊C4—22no—
100C2×Dic43⋊C4—41no—
101C2×Dic43⋊C4C2×C414yescomplemented
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—22no—
112C2×(C2×D43)⋊C4—22no—
113C2×(C2×D43)⋊C4—22no—
114C2×(C2×D43)⋊C4—22no—
115C2×(C2×D43)⋊C4—22no—
116C2×(C2×D43)⋊C4—22no—
117C2×(C2×D43)⋊C4—22no—
118C2×(C2×D43)⋊C4—22no—
119C2×(C2×D43)⋊C4—22no—
120C2×(C2×D43)⋊C4—22no—
121C2×(C2×D43)⋊C4—22no—
122C2×(C2×D43)⋊C4—22no—
123C2×(C2×D43)⋊C4—41no—
124C2×(C2×D43)⋊C4—41no—
125C2×(C2×D43)⋊C4—41no—
126C2×(C2×D43)⋊C4—41no—
127C2×(C2×D43)⋊C4C2×C414yescomplemented
128C2×(C2×D43)⋊C4C2×C414yescomplemented
129C2×(C2×D43)⋊C4C2×C414yescomplemented
130C2×(C2×D43)⋊C4C2×C414yescomplemented
131C2×(C2×D43)⋊C4D414yes—
132C2×C4×Dic43—22no—
133C2×C4×Dic43—22no—
134C2×C4×Dic43—22no—
135C2×C4×Dic43—22no—
136C2×C4×Dic43—22no—
137C2×C4×Dic43—41no—
138C43⋊#95—22no—
139C43⋊#95—22no—
140C43⋊#95—22no—
141C43⋊#95—22no—
142C43⋊#95—22no—
143C43⋊#95—22no—
144C43⋊#95—22no—
145C43⋊#95—22no—
146C43⋊#95D414yescomplemented
147C23×C4×C43C2311yescharacteristic
148C23×C4×C43C2311yescharacteristic
149C23×C4×C43C2311yescharacteristic
150C23×C4×C43C2311yescharacteristic
151C23×C4×C43C2311yescharacteristic
152C23×C4×C43C2311yescharacteristic
153C23×C4×C43C2311yescharacteristic
154C2×C4⋊C4×C43—22no—
155C2×C4⋊C4×C43—22no—
156C2×C4⋊C4×C43D414yes—
157C2×C42×C43—22no—
158C2×C42×C43—22no—
159C2×C42×C43—41no—
160#95×C43—22no—
161#95×C43—22no—
162#95×C43—22no—
163#95×C43—41no—
164#95×C43C2×C414yescomplemented
165C24×C43C2411yescharacteristic
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×D43—21no—
179C23×D43—21no—
180C23×D43—21no—
181C23×D43—21no—
182C23×D43—21no—
183C23×D43—21no—
184C23×D43—21no—
185C23×D43—21no—
186C23×D43—21no—
187C23×D43—21no—
188C23×D43—21no—
189C23×D43—21no—
190C23×D43C22×C412yes—
191C23×D43C22×C412yes—
192C23×D43C2×D412yes—
193C23×D43C2×D412yes—
194C23×D43#4112yes—
195C23×D43#4112yes—
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×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43—21no—
230C22×C4×C43—21no—
231C22×C4×C43—21no—
232C22×C4×C43—21no—
233C22×C4×C43—21no—
234C22×C4×C43—21no—
235C22×C4×C43C22×C412yes—
236C22×C4×C43C22×C412yes—
237C22×C4×C43C22×C412yes—
238C22×C4×C43C2×D412yes—
239C22×C4×C43C2×D412yes—
240C22×C4×C43C2×D412yes—
241C22×C4×C43C2×D412yes—
242C22×C4×C43C2×D412yes—
243C22×C4×C43C2×D412yes—
244C22×C4×C43#4112yes—
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×Dic43—21no—
273C22×Dic43—21no—
274C22×Dic43—21no—
275C22×Dic43—21no—
276C22×Dic43—21no—
277C22×Dic43—21no—
278C22×Dic43C22×C412yes—
279C22×Dic43C22×C412yes—
280C22×Dic43C2×D412yes—
281C22×Dic43C2×D412yes—
282C22×Dic43C2×D412yes—
283C22×Dic43C2×D412yes—
284C22×Dic43#4112yes—
285C22×Dic43#4112yes—
286C22×Dic43#4112yes—
287C2×D172—28no—
288C2×D172—28no—
289C2×D172—28no—
290C2×D172—28no—
291C2×D172—28no—
292C2×D172—28no—
293C2×D172—28no—
294C2×C4×D43—28no—
295C2×C4×D43—28no—
296C2×C4×D43—28no—
297C2×C4×D43—44no—
298C2×C4×D43—44no—
299C2×C4×D43—44no—
300C2×C4×D43—44no—
301C2×C4×D43—44no—
302C2×C4×D43—44no—
303C2×C4×D43—44no—
304C2×C4×D43—44no—
305C2×C4×D43—44no—
306C2×C4×D43—44no—
307C2×C4×D43—44no—
308C4⋊C4×C43—28no—
309C42×C43—44no—
310(C2×D43)⋊C4—28no—
311(C2×D43)⋊C4—28no—
312(C2×D43)⋊C4—28no—
313(C2×D43)⋊C4—28no—
314(C2×D43)⋊C4—28no—
315(C2×D43)⋊C4—28no—
316(C2×D43)⋊C4—28no—
317(C2×D43)⋊C4—44no—
318(C2×D43)⋊C4—44no—
319(C2×D43)⋊C4—44no—
320C4⋊Dic43—44no—
321Dic43⋊C4—28no—
322Dic43⋊C4—44no—
323Dic43⋊C4—44no—
324C4×Dic43—28no—
325C4×Dic43—44no—
326C23×C43C23×C411yescharacteristic
327C23×C43C22×D411yescharacteristic
328C23×C43C22×D411yescharacteristic
329C23×C43C22×D411yescharacteristic
330C23×C43C22×D411yescharacteristic
331C23×C43C2×#4111yescharacteristic
332C23×C43C2×#4111yescharacteristic
333C23×C43C2×#4111yescharacteristic
334C23×C43C2×#4111yescharacteristic
335C23×C43C2×#4111yescharacteristic
336C23×C43C2×#4111yescharacteristic
337C23×C43H(5,𝔽2)11yescharacteristic
338C23×C43H(5,𝔽2)11yescharacteristic
339C23×C432−1+411yescharacteristic
340C23×C432−1+411yescharacteristic
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—22no—
362C22×D43—22no—
363C22×D43—22no—
364C22×D43—22no—
365C22×D43—22no—
366C22×D43—22no—
367C22×D43—22no—
368C22×D43—22no—
369C22×D43—22no—
370C22×D43—22no—
371C22×D43—22no—
372C22×D43—22no—
373C22×D43—22no—
374C22×D43—22no—
375C22×D43—22no—
376C22×D43—22no—
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×D43—41no—
394C22×D43—41no—
395C22×D43—41no—
396C22×D43—41no—
397C22×D43—41no—
398C22×D43—41no—
399C22×D43—41no—
400C22×D43—41no—
401C22×D43—41no—
402C22×D43—41no—
403C22×D43—41no—
404C22×D43—41no—
405C22×D43—41no—
406C22×D43—41no—
407C22×D43—41no—
408C22×D43—41no—
409C22×D43C4×D414yes—
410C22×D43C4×D414yes—
411C2×C4×C43—22no—
412C2×C4×C43—22no—
413C2×C4×C43—22no—
414C2×C4×C43—22no—
415C2×C4×C43—22no—
416C2×C4×C43—22no—
417C2×C4×C43—22no—
418C2×C4×C43—22no—
419C2×C4×C43—22no—
420C2×C4×C43—22no—
421C2×C4×C43—22no—
422C2×C4×C43—22no—
423C2×C4×C43—22no—
424C2×C4×C43—22no—
425C2×C4×C43—22no—
426C2×C4×C43—22no—
427C2×C4×C43—22no—
428C2×C4×C43—22no—
429C2×C4×C43—22no—
430C2×C4×C43—22no—
431C2×C4×C43—22no—
432C2×C4×C43—22no—
433C2×C4×C43—22no—
434C2×C4×C43—22no—
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×C43—41no—
444C2×C4×C43—41no—
445C2×C4×C43—41no—
446C2×C4×C43—41no—
447C2×C4×C43—41no—
448C2×C4×C43—41no—
449C2×C4×C43—41no—
450C2×C4×C43—41no—
451C2×C4×C43—41no—
452C2×C4×C43—41no—
453C2×C4×C43—41no—
454C2×C4×C43—41no—
455C2×C4×C43—41no—
456C2×C4×C43—41no—
457C2×C4×C43—41no—
458C2×C4×C43C4×D414yes—
459C2×C4×C43#12014yes—
460C2×Dic43—22no—
461C2×Dic43—22no—
462C2×Dic43—22no—
463C2×Dic43—22no—
464C2×Dic43—22no—
465C2×Dic43—22no—
466C2×Dic43—22no—
467C2×Dic43—22no—
468C2×Dic43—22no—
469C2×Dic43—22no—
470C2×Dic43—22no—
471C2×Dic43—22no—
472C2×Dic43—22no—
473C2×Dic43—22no—
474C2×Dic43—22no—
475C2×Dic43—22no—
476C2×Dic43—22no—
477C2×Dic43—22no—
478C2×Dic43—22no—
479C2×Dic43—22no—
480C2×Dic43—22no—
481C2×Dic43—41no—
482C2×Dic43—41no—
483C2×Dic43—41no—
484C2×Dic43—41no—
485C2×Dic43—41no—
486C2×Dic43—41no—
487C2×Dic43—41no—
488C2×Dic43—41no—
489C2×Dic43—41no—
490C2×Dic43—41no—
491C2×Dic43—41no—
492C2×Dic43—41no—
493C2×Dic43—41no—
494C2×Dic43—41no—
495C2×Dic43—41no—
496C2×Dic43—41no—
497C2×Dic43—41no—
498C2×Dic43—41no—
499C2×Dic43—41no—
500C2×Dic43C4×D414yescomplemented
501C2×Dic43#12114yes—
502D172—232no—
503C4×D43—416no—
504C4×D43—416no—
505#14185—431nomaximal, Sylow
506C22×C43C2×C4×D411yescharacteristic
507C22×C43C2×C4×D411yescharacteristic
508C22×C43C2×C4×D411yescharacteristic
509C22×C43C2×C4×D411yescharacteristic
510C22×C43C4×#4111yescharacteristic
511C22×C43#52011yescharacteristic
512C22×C43#52011yescharacteristic
513C22×C43C2×#12011yescharacteristic
514C22×C43C2×#12111yescharacteristic
515C22×C43#52511yescharacteristic
516C22×C43#52511yescharacteristic
517C22×C43#52511yescharacteristic
518C22×C43#52511yescharacteristic
519C22×C43#52911yescharacteristic
520C22×C43#53211yescharacteristic
521C22×C43#53411yescharacteristic
522C22×C43#53611yescharacteristic
523C22×C43#53911yescharacteristic
524C22×C43#53911yescharacteristic
525C22×C43D4211yescharacteristic
526C22×C43D4211yescharacteristic
527C22×C43#54611yescharacteristic
528C22×C43#54611yescharacteristic
529C22×C43#54711yescharacteristic
530C22×C43#54711yescharacteristic
531C22×C43#54711yescharacteristic
532C22×C43#54811yescharacteristic
533C22×C43#54811yescharacteristic
534C22×C43#54811yescharacteristic
535C22×C43#55111yescharacteristic
536C22×C43#55211yescharacteristic
537C22×C43#55311yescharacteristic
538C22×C43#55311yescharacteristic
539C22×C43#55611yescharacteristic
540C22×C43#55911yescharacteristic
541C2×D43—24no—
542C2×D43—24no—
543C2×D43—24no—
544C2×D43—24no—
545C2×D43—24no—
546C2×D43—24no—
547C2×D43—42no—
548C2×D43—42no—
549C2×D43—42no—
550C2×D43—42no—
551C2×D43—42no—
552C2×D43—42no—
553C2×D43—42no—
554C2×D43—42no—
555C2×D43—42no—
556C2×D43—42no—
557C2×D43—42no—
558C2×D43—42no—
559C2×D43—42no—
560C2×D43—42no—
561C2×D43—42no—
562C2×D43—42no—
563C2×D43—42no—
564C2×D43—42no—
565C2×D43—42no—
566C2×D43—42no—
567C2×D43—42no—
568C2×D43—42no—
569C2×D43—42no—
570C2×D43—42no—
571C4×C43—24no—
572C4×C43—24no—
573C4×C43—42no—
574C4×C43—42no—
575C4×C43—42no—
576C4×C43—42no—
577C4×C43—81no—
578Dic43—24no—
579Dic43—24no—
580Dic43—42no—
581Dic43—42no—
582Dic43—42no—
583Dic43—81no—
584C22×C4×D4—431no—
585C2×#394—431no—
586C2×#389—431no—
587C2×#388—431no—
588C2×#385—431no—
589C2×#385—431no—
590C2×C4×C22⋊C4—431no—
591#1440—431no—
592#1439—431no—
593#1438—431no—
594#1437—431no—
595#1436—431no—
596#1436—431no—
597#1436D4311yescharacteristic, complemented
598C22⋊#95—431no—
599C2×C43C4×#12011yescharacteristic
600C2×C43C4×#12111yescharacteristic
601C2×C43#232211yescharacteristic
602C2×C43#235911yescharacteristic
603C2×C43#236111yescharacteristic
604C2×C43#236111yescharacteristic
605C2×C43#236711yescharacteristic
606C2×C43#241011yescharacteristic
607C2×C43#241511yescharacteristic
608C2×C43#243211yescharacteristic
609C2×C43#245511yescharacteristic
610C2×C43#246011yescharacteristic
611C2×C43#246311yescharacteristic
612C2×C43#246611yescharacteristic
613C2×C43#260211yescharacteristic
614D43—44no—
615D43—44no—
616C23×D4—431no—
617C24×C4—431no—
618C24×C4—431no—
619C2×C4×D4—864no—
620C2×C4×D4—864no—
621C2×C4×D4—864no—
622C22×C4⋊C4—431no—
623C22×C4⋊C4—431no—
624C22×C4⋊C4—431no—
625C22×C4⋊C4—431no—
626C22×C4⋊C4C2×D4311yescharacteristic
627C22×C22⋊C4—431no—
628C22×C22⋊C4—431no—
629C22×C22⋊C4—431no—
630C22×C22⋊C4—431no—
631C22×C22⋊C4—431no—
632C22×C22⋊C4—431no—
633C22×C22⋊C4—431no—
634C22×C22⋊C4—431no—
635C22×C22⋊C4—431no—
636C22×C22⋊C4—431no—
637C22×C42—431no—
638C22×C42—431no—
639C22×C42C2×D4311yescharacteristic
640#394—438no—
641#389—864no—
642#388—864no—
643#385—864no—
644#385—864no—
645C4×C22⋊C4—864no—
646C2×#95—431no—
647C2×#95—431no—
648C2×#95—431no—
649C2×#95—431no—
650C2×#95—431no—
651C2×#95—431no—
652C2×#95—431no—
653C2×#95—431no—
654C2×#95—431no—
655C2×#95C2×D4311yescharacteristic
656C2×#95C2×D4311yescharacteristic
657C2×#95C2×D4311yescharacteristic
658C2×#95C2×D4311yescharacteristic
659C2×#95C2×D4311yescharacteristic
660C43#1418511yescharacteristic, complemented, Sylow
661C25—431no—
662C25—431no—
663C22×D4—434no—
664C22×D4—862no—
665C22×D4—862no—
666C22×D4—862no—
667C22×D4—862no—
668C22×D4—862no—
669C22×D4—862no—
670C23×C4—431no—
671C23×C4—431no—
672C23×C4—431no—
673C23×C4—431no—
674C23×C4—431no—
675C23×C4—434no—
676C23×C4—431no—
677C23×C4—862no—
678C23×C4—862no—
679C23×C4—862no—
680C23×C4—862no—
681C23×C4—862no—
682C23×C4—862no—
683C23×C4—862no—
684C23×C4—862no—
685C23×C4—862no—
686C23×C4—1721no—
687C23×C4—1721no—
688C23×C4—1721no—
689C23×C4—1721no—
690C23×C4C22×D4311yescharacteristic
691C23×C4C22×D4311yescharacteristic
692C23×C4C22×D4311yescharacteristic
693C23×C4C22×D4311yescharacteristic
694C23×C4C22×D4311yescharacteristic
695C23×C4C22×D4311yescharacteristic
696C23×C4C22×D4311yescharacteristic
697C4×D4—8632no—
698C2×C4⋊C4—22no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4—434no—
701C2×C4⋊C4—862no—
702C2×C4⋊C4—862no—
703C2×C4⋊C4—862no—
704C2×C4⋊C4—862no—
705C2×C4⋊C4—862no—
706C2×C4⋊C4—862no—
707C2×C4⋊C4—862no—
708C2×C4⋊C4—862no—
709C2×C4⋊C4—862no—
710C2×C4⋊C4—862no—
711C2×C4⋊C4—1721no—
712C2×C4⋊C4D17214yes—
713C2×C22⋊C4—434no—
714C2×C22⋊C4—434no—
715C2×C22⋊C4—434no—
716C2×C22⋊C4—434no—
717C2×C22⋊C4—434no—
718C2×C22⋊C4—862no—
719C2×C22⋊C4—862no—
720C2×C22⋊C4—862no—
721C2×C22⋊C4—862no—
722C2×C22⋊C4—862no—
723C2×C22⋊C4—862no—
724C2×C22⋊C4—862no—
725C2×C22⋊C4—862no—
726C2×C22⋊C4—862no—
727C2×C22⋊C4—862no—
728C2×C22⋊C4—862no—
729C2×C22⋊C4—862no—
730C2×C22⋊C4—862no—
731C2×C22⋊C4—862no—
732C2×C22⋊C4—862no—
733C2×C22⋊C4—862no—
734C2×C22⋊C4—862no—
735C2×C22⋊C4—862no—
736C2×C22⋊C4—862no—
737C2×C22⋊C4—862no—
738C2×C22⋊C4—862no—
739C2×C22⋊C4—1721no—
740C2×C22⋊C4—1721no—
741C2×C22⋊C4—1721no—
742C2×C22⋊C4—1721no—
743C2×C42—22no—
744C2×C42—22no—
745C2×C42—41no—
746C2×C42—862no—
747C2×C42—862no—
748C2×C42—862no—
749C2×C42—862no—
750C2×C42—862no—
751C2×C42—1721no—
752#95—22no—
753#95—22no—
754#95—22no—
755#95—41no—
756#95—434no—
757#95—862no—
758#95—862no—
759#95—862no—
760#95—862no—
761#95—862no—
762#95—862no—
763#95—862no—
764#95—862no—
765#95C4×D4314yescomplemented
766C24—432no—
767C24—432no—
768C24—432no—
769C24—432no—
770C24—432no—
771C24—432no—
772C24—861no—
773C24—861no—
774C24—861no—
775C24—861no—
776C24—861no—
777C24—861no—
778C24—861no—
779C24—861no—
780C24—861no—
781C24—861no—
782C24—861no—
783C24—861no—
784C24—861no—
785C24—861no—
786C24—861no—
787C24—861no—
788C24—861no—
789C24—861no—
790C24—861no—
791C24—861no—
792C24—861no—
793C24—861no—
794C24—861no—
795C24—861no—
796C24C23×D4311yescharacteristic
797C2×D4—868no—
798C2×D4—868no—
799C2×D4—868no—
800C2×D4—868no—
801C2×D4—868no—
802C2×D4—868no—
803C2×D4—868no—
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—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—432no—
844C22×C4—432no—
845C22×C4—432no—
846C22×C4—432no—
847C22×C4—432no—
848C22×C4—432no—
849C22×C4—432no—
850C22×C4—432no—
851C22×C4—432no—
852C22×C4—868no—
853C22×C4—868no—
854C22×C4—861no—
855C22×C4—861no—
856C22×C4—861no—
857C22×C4—861no—
858C22×C4—861no—
859C22×C4—861no—
860C22×C4—861no—
861C22×C4—861no—
862C22×C4—861no—
863C22×C4—861no—
864C22×C4—861no—
865C22×C4—861no—
866C22×C4—861no—
867C22×C4—861no—
868C22×C4—861no—
869C22×C4—861no—
870C22×C4—861no—
871C22×C4—861no—
872C22×C4—861no—
873C22×C4—861no—
874C22×C4—861no—
875C22×C4—861no—
876C22×C4—861no—
877C22×C4—861no—
878C22×C4—861no—
879C22×C4—861no—
880C22×C4—868no—
881C22×C4—861no—
882C22×C4—861no—
883C22×C4—861no—
884C22×C4—861no—
885C22×C4—861no—
886C22×C4—861no—
887C22×C4—861no—
888C22×C4—1724no—
889C22×C4—1724no—
890C22×C4—1724no—
891C22×C4—1724no—
892C22×C4—1724no—
893C22×C4—1724no—
894C22×C4—1724no—
895C22×C4—1724no—
896C22×C4—1724no—
897C22×C4—1724no—
898C22×C4—1724no—
899C22×C4C2×C4×D4312yes—
900C22×C4C2×C4×D4312yes—
901C22×C4C2×C4×D4312yes—
902C22×C4C2×D17212yes—
903C22×C4C2×D17212yes—
904C22×C4C2×D17212yes—
905C22×C4#1062189812yes—
906C22×C4D4×D4312yes—
907C22×C4D4×D4312yes—
908C22×C4D4×D4312yes—
909C4⋊C4—28no—
910C4⋊C4—868no—
911C4⋊C4—1724no—
912C4⋊C4—1724no—
913C4⋊C4—1724no—
914C22⋊C4—868no—
915C22⋊C4—868no—
916C22⋊C4—868no—
917C22⋊C4—868no—
918C22⋊C4—868no—
919C22⋊C4—868no—
920C22⋊C4—868no—
921C22⋊C4—1724no—
922C22⋊C4—1724no—
923C22⋊C4—1724no—
924C42—44no—
925C42—868no—
926C42—1724no—
927C23—434no—
928C23—434no—
929C23—862no—
930C23—862no—
931C23—862no—
932C23—862no—
933C23—862no—
934C23—862no—
935C23—862no—
936C23—862no—
937C23—862no—
938C23—862no—
939C23—862no—
940C23—862no—
941C23—862no—
942C23—862no—
943C23—862no—
944C23—862no—
945C23—862no—
946C23—862no—
947C23—862no—
948C23—862no—
949C23—862no—
950C23—862no—
951C23—862no—
952C23—862no—
953C23—862no—
954C23—862no—
955C23—862no—
956C23—862no—
957C23—862no—
958C23—862no—
959C23—862no—
960C23—862no—
961C23—862no—
962C23—862no—
963C23—862no—
964C23—862no—
965C23—1721no—
966C23—1721no—
967C23—1721no—
968C23—1721no—
969C23—1721no—
970C23—1721no—
971C23—1721no—
972C23—1721no—
973C23—1721no—
974C23—1721no—
975C23—1721no—
976C23—1721no—
977C23—1721no—
978C23—1721no—
979C23—1721no—
980C23—1721no—
981C23—1721no—
982C23—1721no—
983C23—1721no—
984C23—1721no—
985C23—1721no—
986C23—1721no—
987C23—1721no—
988C23—1721no—
989C23—1721no—
990C23—1721no—
991C23—1721no—
992C23—1721no—
993C23—1721no—
994C23—1721no—
995C23—1721no—
996C23—1721no—
997C23C22×C4×D4311yescharacteristic
998C23C2×D4×D4311yescharacteristic
999C23C2×D4×D4311yescharacteristic
1000C23C2×D4×D4311yescharacteristic
1001C23C22×D17211yescharacteristic
1002C23#41×D4311yescharacteristic
1003C23#41×D4311yescharacteristic
1004C23#41×D4311yescharacteristic
1005C23#41×D4311yescharacteristic
1006C23#41×D4311yescharacteristic
1007C23C2×#1062189811yescharacteristic
1008C23#1306337011yescharacteristic
1009C23#1306337111yescharacteristic
1010C23#1306337311yescharacteristic
1011C23#1306337311yescharacteristic
1012D4—8632no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—434no—
1061C2×C4—434no—
1062C2×C4—862no—
1063C2×C4—862no—
1064C2×C4—862no—
1065C2×C4—862no—
1066C2×C4—862no—
1067C2×C4—862no—
1068C2×C4—862no—
1069C2×C4—862no—
1070C2×C4—862no—
1071C2×C4—862no—
1072C2×C4—862no—
1073C2×C4—862no—
1074C2×C4—862no—
1075C2×C4—862no—
1076C2×C4—862no—
1077C2×C4—862no—
1078C2×C4—862no—
1079C2×C4—862no—
1080C2×C4—862no—
1081C2×C4—862no—
1082C2×C4—862no—
1083C2×C4—17216no—
1084C2×C4—17216no—
1085C2×C4—1721no—
1086C2×C4—1721no—
1087C2×C4—1721no—
1088C2×C4—1721no—
1089C2×C4—1721no—
1090C2×C4—1721no—
1091C2×C4—1721no—
1092C2×C4—1721no—
1093C2×C4—1721no—
1094C2×C4—1721no—
1095C2×C4—1721no—
1096C2×C4—1721no—
1097C2×C4—1721no—
1098C2×C4—1721no—
1099C2×C4—1721no—
1100C2×C4—1721no—
1101C2×C4—1721no—
1102C2×C4—1721no—
1103C2×C4—1721no—
1104C2×C4C4×D17214yes—
1105C2×C4#1306329514yes—
1106C22—864no—
1107C22—864no—
1108C22—864no—
1109C22—864no—
1110C22—864no—
1111C22—864no—
1112C22—1722no—
1113C22—1722no—
1114C22—1722no—
1115C22—1722no—
1116C22—1722no—
1117C22—1722no—
1118C22—1722no—
1119C22—1722no—
1120C22—1722no—
1121C22—1722no—
1122C22—1722no—
1123C22—1722no—
1124C22—1722no—
1125C22—1722no—
1126C22—1722no—
1127C22—1722no—
1128C22—1722no—
1129C22—1722no—
1130C22—1722no—
1131C22—1722no—
1132C22—1722no—
1133C22—1722no—
1134C22—1722no—
1135C22—1722no—
1136C22C4×D4×D4311yescharacteristic
1137C22C4×D4×D4311yescharacteristic
1138C22C4×D4×D4311yescharacteristic
1139C22C2×C4×D17211yescharacteristic
1140C22#1458336711yescharacteristic
1141C22#1458338011yescharacteristic
1142C22#1458338111yescharacteristic
1143C22C2×#1306329511yescharacteristic
1144C22#121×D4311yescharacteristic
1145C22#1458340711yescharacteristic
1146C22#1458340811yescharacteristic
1147C22#1458340811yescharacteristic
1148C22#1458341111yescharacteristic
1149C22#1458343211yescharacteristic
1150C22#1458344811yescharacteristic
1151C22#1458345711yescharacteristic
1152C22#1458347411yescharacteristic
1153C22#1458349511yescharacteristic
1154C22#1458349711yescharacteristic
1155C22#1458353111yescharacteristic
1156C22D4×D17211yescharacteristic
1157C22#1458354111yescharacteristic
1158C22#1458354411yescharacteristic
1159C22#1458355011yescharacteristic
1160C22#1458355111yescharacteristic
1161C22#1458355111yescharacteristic
1162C22#1458355911yescharacteristic
1163C22#1458356111yescharacteristic
1164C22#1458356111yescharacteristic
1165C22#1458357411yescharacteristic
1166C22#1458358111yescharacteristic
1167C22#1458359311yescharacteristic
1168C22#1458359411yescharacteristic
1169C22#1458362111yescharacteristic
1170C22#1458363211yescharacteristic
1171C4—24no—
1172C4—24no—
1173C4—42no—
1174C4—42no—
1175C4—42no—
1176C4—42no—
1177C4—81no—
1178C4—864no—
1179C4—864no—
1180C4—3441no—
1181C4—1722no—
1182C4—1722no—
1183C4—1722no—
1184C2—1724no—
1185C2—1724no—
1186C2C4×#1306329511yescharacteristic
1187C2#1913710711yescharacteristic
1188C2#1913725911yescharacteristic
1189C2#1913758011yescharacteristic
1190C2#1913761311yescharacteristic
1191C2#1913761411yescharacteristic
1192C2#1913766611yescharacteristic
1193C2#1913796811yescharacteristic
1194C2#1913802311yescharacteristic
1195C2#1913822211yescharacteristic
1196C2#1913847611yescharacteristic
1197C2#1913854511yescharacteristic
1198C2#1913859011yescharacteristic
1199C2#1913863511yescharacteristic
1200C2#1914021411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1436C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenter#1436D43
hypocenterC43#14185
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
3. C2×#14582794C2semidirect
4. C2×#14582790C2semidirect
5. C2×#14582773C2semidirect
6. C2×#14582773C2semidirect
7. C2×C4×(C2×D43)⋊C4C2semidirect
8. #19132843C2semidirect
9. #19132839C2semidirect
11. #19132831C2semidirect
12. #19132830C2semidirect
13. #19132829C2semidirect
14. (C2×D43)⋊#95C2semidirect
15. C43×#1436C2semidirect
38. #14582817C4semidirect
101. C2×Dic43⋊C4C2×C4semidirect
127. C2×(C2×D43)⋊C4C2×C4semidirect
128. C2×(C2×D43)⋊C4C2×C4semidirect
129. C2×(C2×D43)⋊C4C2×C4semidirect
130. C2×(C2×D43)⋊C4C2×C4semidirect
146. C43⋊#95D4semidirect
164. #95×C43C2×C4semidirect
500. C2×Dic43C4×D4semidirect
597. #1436D43semidirect
660. C43#14185semidirect
765. #95C4×D43semidirect

Maximal subgroups

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

subgroupindex
C22×#130632872
C2×#145828172
C2×#145827942
C2×#145827902
C2×#145827732
C2×C4×(C2×D43)⋊C42
#191328432
#191328392
#191328352
#191328312
#191328302
#191328292
(C2×D43)⋊#952
C43×#14362
#1418543