Finite Group Databasebeta

← #25019450

Subgroups — #25019450

Order 11008.

2690 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063287C211yesmaximal, characteristic
2C2×#14582777C211yesmaximal, characteristic
3C2×#14582777C211yesmaximal, characteristic
4C2×#14582770C211yesmaximal, characteristic, complemented
5C2×#14582770C211yesmaximal, characteristic, complemented
6C2×#14582756C211yesmaximal, characteristic, complemented
7C2×#95×D43C211yesmaximal, characteristic, complemented
8#19132854C211yesmaximal, characteristic, complemented
9#19132841C211yesmaximal, characteristic, complemented
10#19132837C211yesmaximal, characteristic, complemented
11#19132829C211yesmaximal, characteristic, complemented
12#19132826C211yesmaximal, characteristic, complemented
13(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
15C43×#1444C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21C2×#13063287—24no—
22C2×#13063287—24no—
23C2×#13063287—24no—
24C22×C4⋊Dic43C2211yescharacteristic
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×C4×Dic43C2211yescharacteristic
35#14582777—24no—
36#14582777C418yescomplemented
37#14582770—24no—
38#14582770—24no—
39#14582756—24no—
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
49C2×C43⋊#95C2211yescharacteristic
50C2×C43⋊#95C2211yescharacteristic
51C2×C43⋊#95C2211yescharacteristic
52#95×D43—24no—
53C22×C4⋊C4×C43C2211yescharacteristic
54C22×C4⋊C4×C43C2211yescharacteristic
55C22×C4⋊C4×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×D172C2×C414yes—
67C22×D172D414yes—
68C22×D172Q814yes—
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—22no—
85C22×C4×D43—22no—
86C22×C4×D43—22no—
87C22×C4×D43—22no—
88C22×C4×D43—22no—
89C22×C4×D43—22no—
90C22×C4×D43—22no—
91C22×C4×D43—22no—
92C22×C4×D43—22no—
93C22×C4×D43—41no—
94C22×C4×D43—41no—
95C22×C4×D43—41no—
96C22×C4×D43—41no—
97C22×C4×D43—41no—
98C22×C4×D43—41no—
99C22×C4×D43—41no—
100C22×C4×D43—41no—
101C22×C4×D43C2×C414yescomplemented
102C22×C4×D43D414yes—
103#13063287—232no—
104C2×C4⋊Dic43—22no—
105C2×C4⋊Dic43—22no—
106C2×C4⋊Dic43—41no—
107C2×Dic43⋊C4—22no—
108C2×Dic43⋊C4—22no—
109C2×Dic43⋊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—22no—
124C2×(C2×D43)⋊C4—22no—
125C2×(C2×D43)⋊C4—22no—
126C2×(C2×D43)⋊C4—41no—
127C2×(C2×D43)⋊C4—41no—
128C2×(C2×D43)⋊C4—41no—
129C2×(C2×D43)⋊C4—41no—
130C2×(C2×D43)⋊C4C2×C414yescomplemented
131C2×(C2×D43)⋊C4C2×C414yescomplemented
132C2×(C2×D43)⋊C4C2×C414yescomplemented
133C2×(C2×D43)⋊C4D414yes—
134C2×C4×Dic43—22no—
135C2×C4×Dic43—22no—
136C2×C4×Dic43—22no—
137C43⋊#95—22no—
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⋊#95—41no—
147C43⋊#95C2×C414yescomplemented
148C43⋊#95D414yescomplemented
149C23×C4×C43C2311yescharacteristic
150C23×C4×C43C2311yescharacteristic
151C23×C4×C43C2311yescharacteristic
152C23×C4×C43C2311yescharacteristic
153C23×C4×C43C2311yescharacteristic
154C23×C4×C43C2311yescharacteristic
155C23×C4×C43C2311yescharacteristic
156C2×C4⋊C4×C43—22no—
157C2×C4⋊C4×C43—22no—
158C2×C4⋊C4×C43—22no—
159C2×C4⋊C4×C43—22no—
160C2×C4⋊C4×C43—22no—
161C2×C4⋊C4×C43—22no—
162C2×C4⋊C4×C43—41no—
163C2×C4⋊C4×C43—41no—
164C2×C4⋊C4×C43—41no—
165#95×C43—22no—
166#95×C43—22no—
167#95×C43—41no—
168#95×C43C2×C414yescomplemented
169C24×C43C2411yescharacteristic
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×D43C2×D412yes—
195C23×D43C2×D412yes—
196C23×D43C2×Q812yes—
197C23×D43C2×Q812yes—
198C23×D43#4112yes—
199C23×D43#4112yes—
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×C43—21no—
236C22×C4×C43—21no—
237C22×C4×C43—21no—
238C22×C4×C43—21no—
239C22×C4×C43C22×C412yes—
240C22×C4×C43C22×C412yes—
241C22×C4×C43C22×C412yes—
242C22×C4×C43C2×D412yes—
243C22×C4×C43C2×D412yes—
244C22×C4×C43C2×D412yes—
245C22×C4×C43C2×D412yes—
246C22×C4×C43C2×Q812yes—
247C22×C4×C43#4112yes—
248C22×C4×C43#4112yes—
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×Dic43—21no—
279C22×Dic43—21no—
280C22×Dic43—21no—
281C22×Dic43—21no—
282C22×Dic43—21no—
283C22×Dic43—21no—
284C22×Dic43C22×C412yes—
285C22×Dic43C22×C412yes—
286C22×Dic43C2×D412yes—
287C22×Dic43C2×D412yes—
288C22×Dic43C2×D412yes—
289C22×Dic43C2×D412yes—
290C22×Dic43#4112yes—
291C2×D172—28no—
292C2×D172—28no—
293C2×D172—28no—
294C2×D172—28no—
295C2×D172—28no—
296C2×D172—28no—
297C2×D172C4⋊C4116yescomplemented
298C2×C4×D43—28no—
299C2×C4×D43—28no—
300C2×C4×D43—28no—
301C2×C4×D43—28no—
302C2×C4×D43—28no—
303C2×C4×D43—28no—
304C2×C4×D43—44no—
305C2×C4×D43—44no—
306C2×C4×D43—44no—
307C2×C4×D43—44no—
308C2×C4×D43—44no—
309C2×C4×D43—44no—
310C2×C4×D43—44no—
311C2×C4×D43—44no—
312C2×C4×D43—44no—
313C2×C4×D43—44no—
314C2×C4×D43—44no—
315C2×C4×D43—44no—
316C2×C4×D43—44no—
317C2×C4×D43—44no—
318C2×C4×D43—44no—
319C2×C4×D43—44no—
320C2×C4×D43—44no—
321C2×C4×D43—44no—
322C2×C4×D43—44no—
323C2×C4×D43—44no—
324C2×C4×D43—44no—
325C2×C4×D43—44no—
326C4⋊C4×C43—28no—
327C4⋊C4×C43—44no—
328C4⋊C4×C43—44no—
329(C2×D43)⋊C4—28no—
330(C2×D43)⋊C4—28no—
331(C2×D43)⋊C4—28no—
332(C2×D43)⋊C4—28no—
333(C2×D43)⋊C4—44no—
334(C2×D43)⋊C4—44no—
335(C2×D43)⋊C4—44no—
336(C2×D43)⋊C4—44no—
337C4⋊Dic43—44no—
338Dic43⋊C4—44no—
339C4×Dic43—28no—
340C23×C43C23×C411yescharacteristic
341C23×C43C22×D411yescharacteristic
342C23×C43C22×D411yescharacteristic
343C23×C43C22×D411yescharacteristic
344C23×C43C22×D411yescharacteristic
345C23×C43C22×Q811yescharacteristic
346C23×C43C2×#4111yescharacteristic
347C23×C43C2×#4111yescharacteristic
348C23×C43C2×#4111yescharacteristic
349C23×C43C2×#4111yescharacteristic
350C23×C43C2×#4111yescharacteristic
351C23×C43H(5,𝔽2)11yescharacteristic
352C23×C43H(5,𝔽2)11yescharacteristic
353C23×C43H(5,𝔽2)11yescharacteristic
354C23×C432−1+411yescharacteristic
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—22no—
378C22×D43—22no—
379C22×D43—22no—
380C22×D43—22no—
381C22×D43—22no—
382C22×D43—22no—
383C22×D43—22no—
384C22×D43—22no—
385C22×D43—22no—
386C22×D43—22no—
387C22×D43—22no—
388C22×D43—22no—
389C22×D43—22no—
390C22×D43—22no—
391C22×D43—22no—
392C22×D43—22no—
393C22×D43—22no—
394C22×D43—22no—
395C22×D43—22no—
396C22×D43—22no—
397C22×D43—22no—
398C22×D43—22no—
399C22×D43—22no—
400C22×D43—22no—
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×D43—41no—
410C22×D43—41no—
411C22×D43—41no—
412C22×D43—41no—
413C22×D43—41no—
414C22×D43—41no—
415C22×D43—41no—
416C22×D43—41no—
417C22×D43C2×C4⋊C414yes—
418C22×D43C2×C4⋊C414yes—
419C22×D43C4×D414yes—
420C22×D43C4×D414yes—
421C22×D43#12014yes—
422C22×D43C22⋊Q814yes—
423C22×D43C22⋊Q814yes—
424C22×D43#12314yes—
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—22no—
436C2×C4×C43—22no—
437C2×C4×C43—22no—
438C2×C4×C43—22no—
439C2×C4×C43—22no—
440C2×C4×C43—22no—
441C2×C4×C43—22no—
442C2×C4×C43—22no—
443C2×C4×C43—22no—
444C2×C4×C43—22no—
445C2×C4×C43—22no—
446C2×C4×C43—22no—
447C2×C4×C43—22no—
448C2×C4×C43—22no—
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×C43—41no—
459C2×C4×C43—41no—
460C2×C4×C43—41no—
461C2×C4×C43—41no—
462C2×C4×C43—41no—
463C2×C4×C43—41no—
464C2×C4×C43—41no—
465C2×C4×C43—41no—
466C2×C4×C43—41no—
467C2×C4×C43—41no—
468C2×C4×C43—41no—
469C2×C4×C43—41no—
470C2×C4×C43—41no—
471C2×C4×C43—41no—
472C2×C4×C43C2×C4⋊C414yes—
473C2×C4×C43C4×D414yescomplemented
474C2×Dic43—22no—
475C2×Dic43—22no—
476C2×Dic43—22no—
477C2×Dic43—22no—
478C2×Dic43—22no—
479C2×Dic43—22no—
480C2×Dic43—22no—
481C2×Dic43—22no—
482C2×Dic43—22no—
483C2×Dic43—22no—
484C2×Dic43—22no—
485C2×Dic43—22no—
486C2×Dic43—22no—
487C2×Dic43—22no—
488C2×Dic43—22no—
489C2×Dic43—22no—
490C2×Dic43—22no—
491C2×Dic43—22no—
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×Dic43—41no—
501C2×Dic43—41no—
502C2×Dic43—41no—
503C2×Dic43—41no—
504C2×Dic43—41no—
505C2×Dic43—41no—
506C2×Dic43—41no—
507C2×Dic43—41no—
508C2×Dic43—41no—
509C2×Dic43—41no—
510C2×Dic43—41no—
511C2×Dic43—41no—
512C2×Dic43—41no—
513C2×Dic43—41no—
514C2×Dic43—41no—
515C2×Dic43#12114yes—
516D172—232no—
517C4×D43—416no—
518C4×D43—416no—
519C4×D43—416no—
520C4×D43—416no—
521#13975—431nomaximal, Sylow
522C22×C43C22×C4⋊C411yescharacteristic
523C22×C43C2×C4×D411yescharacteristic
524C22×C43C2×C4×D411yescharacteristic
525C22×C43C2×C4×D411yescharacteristic
526C22×C43C4×#4111yescharacteristic
527C22×C43#51811yescharacteristic
528C22×C43#52011yescharacteristic
529C22×C43C2×#12011yescharacteristic
530C22×C43C2×#12111yescharacteristic
531C22×C43C2×C22⋊Q811yescharacteristic
532C22×C43C2×C22⋊Q811yescharacteristic
533C22×C43C2×#12311yescharacteristic
534C22×C43#52511yescharacteristic
535C22×C43#52911yescharacteristic
536C22×C43#53211yescharacteristic
537C22×C43#53411yescharacteristic
538C22×C43#53711yescharacteristic
539C22×C43#53811yescharacteristic
540C22×C43#53911yescharacteristic
541C22×C43D4211yescharacteristic
542C22×C43D4211yescharacteristic
543C22×C43#54611yescharacteristic
544C22×C43#54611yescharacteristic
545C22×C43#54611yescharacteristic
546C22×C43#54611yescharacteristic
547C22×C43#54611yescharacteristic
548C22×C43#54711yescharacteristic
549C22×C43#54711yescharacteristic
550C22×C43D4×Q811yescharacteristic
551C22×C43#55111yescharacteristic
552C22×C43#55111yescharacteristic
553C22×C43#55211yescharacteristic
554C22×C43#55411yescharacteristic
555C22×C43#55411yescharacteristic
556C22×C43#55411yescharacteristic
557C2×D43—24no—
558C2×D43—24no—
559C2×D43—24no—
560C2×D43—24no—
561C2×D43—24no—
562C2×D43—24no—
563C2×D43—24no—
564C2×D43—24no—
565C2×D43—24no—
566C2×D43—24no—
567C2×D43—24no—
568C2×D43—24no—
569C2×D43—24no—
570C2×D43—24no—
571C2×D43—24no—
572C2×D43—24no—
573C2×D43—24no—
574C2×D43—42no—
575C2×D43—42no—
576C2×D43—42no—
577C2×D43—42no—
578C2×D43—42no—
579C2×D43—42no—
580C2×D43—42no—
581C2×D43—42no—
582C2×D43—42no—
583C2×D43—42no—
584C2×D43—42no—
585C2×D43—42no—
586C2×D43#38518yescomplemented
587C4×C43—24no—
588C4×C43—24no—
589C4×C43—42no—
590C4×C43—42no—
591C4×C43—42no—
592C4×C43—42no—
593C4×C43—81no—
594Dic43—24no—
595Dic43—42no—
596Dic43—42no—
597Dic43—42no—
598Dic43—42no—
599Dic43—81no—
600C22×C4×D4—431no—
601C2×#386—431no—
602C2×#386—431no—
603C2×#385—431no—
604C2×#385—431no—
605C2×#380—431no—
606C22×#95—431no—
607#1444D4311yescharacteristic, complemented
608#1442—431no—
609#1439—431no—
610#1439—431no—
611#1436—431no—
612#1436—431no—
613C22⋊#95—431no—
614C22⋊#95—431no—
615C2×C43C2×#38511yescharacteristic
616C2×C43C4×#12111yescharacteristic
617C2×C43#232511yescharacteristic
618C2×C43D4×C4⋊C411yescharacteristic
619C2×C43#234911yescharacteristic
620C2×C43#235811yescharacteristic
621C2×C43#235911yescharacteristic
622C2×C43#241011yescharacteristic
623C2×C43#241711yescharacteristic
624C2×C43#241811yescharacteristic
625C2×C43#241911yescharacteristic
626C2×C43#243011yescharacteristic
627C2×C43#244911yescharacteristic
628C2×C43#245011yescharacteristic
629C2×C43#256411yescharacteristic
630D43—28no—
631D43—44no—
632C23×D4—431no—
633C24×C4—431no—
634C24×C4—431no—
635C24×C4—431no—
636C24×C4—431no—
637C2×C4×D4—864no—
638C2×C4×D4—864no—
639C2×C4×D4—864no—
640C22×C4⋊C4—431no—
641C22×C4⋊C4—431no—
642C22×C4⋊C4C2×D4311yescharacteristic
643C22×C4⋊C4C2×D4311yescharacteristic
644C22×C4⋊C4C2×D4311yescharacteristic
645C22×C22⋊C4—431no—
646C22×C22⋊C4—431no—
647C22×C22⋊C4—431no—
648C22×C22⋊C4—431no—
649C22×C22⋊C4—431no—
650C22×C22⋊C4—431no—
651C22×C22⋊C4—431no—
652C22×C22⋊C4—431no—
653C22×C42—431no—
654#386—438no—
655#386—864no—
656#385—864no—
657#385—864no—
658#380—864no—
659C2×#95—431no—
660C2×#95—431no—
661C2×#95—431no—
662C2×#95—431no—
663C2×#95—431no—
664C2×#95—431no—
665C2×#95—431no—
666C2×#95—431no—
667C2×#95—431no—
668C2×#95—431no—
669C2×#95—431no—
670C2×#95—431no—
671C2×#95—864no—
672C2×#95C2×D4311yescharacteristic
673C2×#95C2×D4311yescharacteristic
674C2×#95C2×D4311yescharacteristic
675C2×#95C2×D4311yescharacteristic
676C43#1397511yescharacteristic, complemented, Sylow
677C25—431no—
678C25—431no—
679C22×D4—434no—
680C22×D4—434no—
681C22×D4—434no—
682C22×D4—862no—
683C22×D4—862no—
684C22×D4—862no—
685C22×D4—862no—
686C23×C4—431no—
687C23×C4—431no—
688C23×C4—431no—
689C23×C4—431no—
690C23×C4—431no—
691C23×C4—434no—
692C23×C4—434no—
693C23×C4—431no—
694C23×C4—862no—
695C23×C4—862no—
696C23×C4—862no—
697C23×C4—862no—
698C23×C4—862no—
699C23×C4—862no—
700C23×C4—862no—
701C23×C4—862no—
702C23×C4—862no—
703C23×C4—862no—
704C23×C4—862no—
705C23×C4—862no—
706C23×C4—862no—
707C23×C4—862no—
708C23×C4—862no—
709C23×C4—862no—
710C23×C4—862no—
711C23×C4—862no—
712C23×C4—1721no—
713C23×C4—1721no—
714C23×C4—1721no—
715C23×C4—1721no—
716C23×C4—1721no—
717C23×C4—1721no—
718C23×C4—1721no—
719C23×C4—1721no—
720C23×C4C22×D4311yescharacteristic
721C23×C4C22×D4311yescharacteristic
722C23×C4C22×D4311yescharacteristic
723C23×C4C22×D4311yescharacteristic
724C23×C4C22×D4311yescharacteristic
725C23×C4C22×D4311yescharacteristic
726C23×C4C22×D4311yescharacteristic
727C4×D4—8632no—
728C2×C4⋊C4—22no—
729C2×C4⋊C4—22no—
730C2×C4⋊C4—22no—
731C2×C4⋊C4—22no—
732C2×C4⋊C4—22no—
733C2×C4⋊C4—22no—
734C2×C4⋊C4—41no—
735C2×C4⋊C4—41no—
736C2×C4⋊C4—41no—
737C2×C4⋊C4—862no—
738C2×C4⋊C4—862no—
739C2×C4⋊C4—862no—
740C2×C4⋊C4—862no—
741C2×C4⋊C4—862no—
742C2×C4⋊C4—1721no—
743C2×C22⋊C4—434no—
744C2×C22⋊C4—434no—
745C2×C22⋊C4—434no—
746C2×C22⋊C4—434no—
747C2×C22⋊C4—862no—
748C2×C22⋊C4—862no—
749C2×C22⋊C4—862no—
750C2×C22⋊C4—862no—
751C2×C22⋊C4—862no—
752C2×C22⋊C4—862no—
753C2×C22⋊C4—862no—
754C2×C22⋊C4—862no—
755C2×C22⋊C4—862no—
756C2×C22⋊C4—862no—
757C2×C22⋊C4—862no—
758C2×C22⋊C4—862no—
759C2×C22⋊C4—862no—
760C2×C22⋊C4—862no—
761C2×C22⋊C4—862no—
762C2×C22⋊C4—862no—
763C2×C22⋊C4—1721no—
764C2×C22⋊C4—1721no—
765C2×C22⋊C4—1721no—
766C2×C22⋊C4—1721no—
767C2×C42—862no—
768C2×C42—862no—
769C2×C42—862no—
770#95—22no—
771#95—22no—
772#95—41no—
773#95—434no—
774#95—434no—
775#95—862no—
776#95—862no—
777#95—862no—
778#95—862no—
779#95—862no—
780#95—862no—
781#95—862no—
782#95—862no—
783#95—862no—
784#95—1721no—
785#95C4×D4314yescomplemented
786C24—432no—
787C24—432no—
788C24—432no—
789C24—432no—
790C24—432no—
791C24—432no—
792C24—432no—
793C24—432no—
794C24—432no—
795C24—432no—
796C24—861no—
797C24—861no—
798C24—861no—
799C24—861no—
800C24—861no—
801C24—861no—
802C24—861no—
803C24—861no—
804C24—861no—
805C24—861no—
806C24—861no—
807C24—861no—
808C24—861no—
809C24—861no—
810C24—861no—
811C24—861no—
812C24—861no—
813C24—861no—
814C24—861no—
815C24—861no—
816C24C23×D4311yescharacteristic
817C2×D4—4316no—
818C2×D4—868no—
819C2×D4—868no—
820C2×D4—868no—
821C2×D4—868no—
822C2×D4—868no—
823C2×D4—868no—
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—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—432no—
864C22×C4—432no—
865C22×C4—432no—
866C22×C4—432no—
867C22×C4—432no—
868C22×C4—432no—
869C22×C4—432no—
870C22×C4—868no—
871C22×C4—868no—
872C22×C4—868no—
873C22×C4—868no—
874C22×C4—868no—
875C22×C4—861no—
876C22×C4—861no—
877C22×C4—861no—
878C22×C4—861no—
879C22×C4—861no—
880C22×C4—861no—
881C22×C4—861no—
882C22×C4—861no—
883C22×C4—861no—
884C22×C4—861no—
885C22×C4—861no—
886C22×C4—861no—
887C22×C4—861no—
888C22×C4—861no—
889C22×C4—861no—
890C22×C4—861no—
891C22×C4—861no—
892C22×C4—861no—
893C22×C4—861no—
894C22×C4—861no—
895C22×C4—861no—
896C22×C4—861no—
897C22×C4—861no—
898C22×C4—861no—
899C22×C4—861no—
900C22×C4—861no—
901C22×C4—861no—
902C22×C4—861no—
903C22×C4—868no—
904C22×C4—861no—
905C22×C4—861no—
906C22×C4—861no—
907C22×C4—861no—
908C22×C4—861no—
909C22×C4—861no—
910C22×C4—861no—
911C22×C4—1724no—
912C22×C4—1724no—
913C22×C4—1724no—
914C22×C4—1724no—
915C22×C4—1724no—
916C22×C4—1724no—
917C22×C4—1724no—
918C22×C4—1724no—
919C22×C4—1724no—
920C22×C4—1724no—
921C22×C4—1724no—
922C22×C4—1724no—
923C22×C4—1724no—
924C22×C4—1724no—
925C22×C4—1724no—
926C22×C4—1724no—
927C22×C4—1724no—
928C22×C4—1724no—
929C22×C4—1724no—
930C22×C4—1724no—
931C22×C4—1724no—
932C22×C4—1724no—
933C22×C4C2×C4×D4312yes—
934C22×C4C2×C4×D4312yes—
935C22×C4C2×C4×D4312yes—
936C22×C4D4×D4312yes—
937C22×C4D4×D4312yes—
938C22×C4D4×D4312yes—
939C22×C4D4×D4312yes—
940C22×C4Q8×D4312yes—
941C22×C4#1062190212yes—
942C22×C4#1062190212yes—
943C4⋊C4—28no—
944C4⋊C4—44no—
945C4⋊C4—44no—
946C4⋊C4—1724no—
947C4⋊C4—1724no—
948C22⋊C4—868no—
949C22⋊C4—868no—
950C22⋊C4—868no—
951C22⋊C4—868no—
952C22⋊C4—1724no—
953C22⋊C4—1724no—
954C22⋊C4—1724no—
955C22⋊C4—1724no—
956C42—868no—
957C23—434no—
958C23—434no—
959C23—434no—
960C23—434no—
961C23—434no—
962C23—434no—
963C23—434no—
964C23—434no—
965C23—862no—
966C23—862no—
967C23—862no—
968C23—862no—
969C23—862no—
970C23—862no—
971C23—862no—
972C23—862no—
973C23—862no—
974C23—862no—
975C23—862no—
976C23—862no—
977C23—862no—
978C23—862no—
979C23—862no—
980C23—862no—
981C23—862no—
982C23—862no—
983C23—862no—
984C23—862no—
985C23—862no—
986C23—862no—
987C23—862no—
988C23—862no—
989C23—862no—
990C23—862no—
991C23—862no—
992C23—862no—
993C23—862no—
994C23—862no—
995C23—862no—
996C23—862no—
997C23—862no—
998C23—862no—
999C23—862no—
1000C23—862no—
1001C23—862no—
1002C23—862no—
1003C23—862no—
1004C23—862no—
1005C23—862no—
1006C23—862no—
1007C23—862no—
1008C23—862no—
1009C23—862no—
1010C23—862no—
1011C23—1721no—
1012C23—1721no—
1013C23—1721no—
1014C23—1721no—
1015C23—1721no—
1016C23—1721no—
1017C23—1721no—
1018C23—1721no—
1019C23—1721no—
1020C23—1721no—
1021C23—1721no—
1022C23—1721no—
1023C23—1721no—
1024C23—1721no—
1025C23—1721no—
1026C23—1721no—
1027C23C22×C4×D4311yescharacteristic
1028C23C2×D4×D4311yescharacteristic
1029C23C2×D4×D4311yescharacteristic
1030C23C2×D4×D4311yescharacteristic
1031C23C2×D4×D4311yescharacteristic
1032C23C2×Q8×D4311yescharacteristic
1033C23#41×D4311yescharacteristic
1034C23#41×D4311yescharacteristic
1035C23#41×D4311yescharacteristic
1036C23C2×#1062190211yescharacteristic
1037C23C2×#1062190211yescharacteristic
1038C23#1306337011yescharacteristic
1039C23#1306337011yescharacteristic
1040C23#1306337111yescharacteristic
1041C23#1306337311yescharacteristic
1042D4—8632no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—434no—
1091C2×C4—862no—
1092C2×C4—862no—
1093C2×C4—862no—
1094C2×C4—862no—
1095C2×C4—862no—
1096C2×C4—862no—
1097C2×C4—862no—
1098C2×C4—862no—
1099C2×C4—862no—
1100C2×C4—862no—
1101C2×C4—862no—
1102C2×C4—862no—
1103C2×C4—862no—
1104C2×C4—862no—
1105C2×C4—862no—
1106C2×C4—862no—
1107C2×C4—862no—
1108C2×C4—862no—
1109C2×C4—17216no—
1110C2×C4—17216no—
1111C2×C4—17216no—
1112C2×C4—17216no—
1113C2×C4—1721no—
1114C2×C4—1721no—
1115C2×C4—1721no—
1116C2×C4—1721no—
1117C2×C4—1721no—
1118C2×C4—1721no—
1119C2×C4—1721no—
1120C2×C4—1721no—
1121C2×C4—1721no—
1122C2×C4—1721no—
1123C2×C4—1721no—
1124C2×C4—1721no—
1125C2×C4—1721no—
1126C2×C4—1721no—
1127C2×C4—1721no—
1128C2×C4—1721no—
1129C2×C4—1721no—
1130C2×C4—1721no—
1131C2×C4—1721no—
1132C2×C4—1721no—
1133C2×C4—1721no—
1134C2×C4—1721no—
1135C2×C4—1721no—
1136C2×C4C4⋊C4×D4314yes—
1137C2×C4#1306328714yescomplemented
1138C22—438no—
1139C22—864no—
1140C22—864no—
1141C22—864no—
1142C22—864no—
1143C22—864no—
1144C22—864no—
1145C22—864no—
1146C22—864no—
1147C22—864no—
1148C22—864no—
1149C22—864no—
1150C22—864no—
1151C22—864no—
1152C22—864no—
1153C22—864no—
1154C22—864no—
1155C22—864no—
1156C22—1722no—
1157C22—1722no—
1158C22—1722no—
1159C22—1722no—
1160C22—1722no—
1161C22—1722no—
1162C22—1722no—
1163C22—1722no—
1164C22—1722no—
1165C22—1722no—
1166C22—1722no—
1167C22—1722no—
1168C22C2×C4⋊C4×D4311yescharacteristic
1169C22C4×D4×D4311yescharacteristic
1170C22C4×D4×D4311yescharacteristic
1171C22C2×#1306328711yescharacteristic
1172C22C4×#1062190211yescharacteristic
1173C22#1458337111yescharacteristic
1174C22#1458338011yescharacteristic
1175C22#120×D4311yescharacteristic
1176C22#121×D4311yescharacteristic
1177C22C22⋊Q8×D4311yescharacteristic
1178C22C22⋊Q8×D4311yescharacteristic
1179C22#123×D4311yescharacteristic
1180C22#1458341211yescharacteristic
1181C22#1458343411yescharacteristic
1182C22#1458345011yescharacteristic
1183C22#1458345911yescharacteristic
1184C22#1458347911yescharacteristic
1185C22#1458348511yescharacteristic
1186C22#1458349511yescharacteristic
1187C22#1458353111yescharacteristic
1188C22#1458353411yescharacteristic
1189C22#1458353811yescharacteristic
1190C22#1458354011yescharacteristic
1191C22#1458354011yescharacteristic
1192C22#1458354111yescharacteristic
1193C22#1458354611yescharacteristic
1194C22#1458355211yescharacteristic
1195C22#1458355211yescharacteristic
1196C22#1458356411yescharacteristic
1197C22#1458357611yescharacteristic
1198C22#1458357611yescharacteristic
1199C22#1458358111yescharacteristic
1200C22#1458360511yescharacteristic
1201C22#1458361011yescharacteristic
1202C22#1458361011yescharacteristic
1203C4—24no—
1204C4—24no—
1205C4—42no—
1206C4—42no—
1207C4—42no—
1208C4—42no—
1209C4—81no—
1210C4—864no—
1211C4—3441no—
1212C4—1722no—
1213C4—1722no—
1214C4—1722no—
1215C4—1722no—
1216C2—868no—
1217C2—1724no—
1218C2#385×D4311yescharacteristic
1219C2#1913710311yescharacteristic
1220C2#1913729211yescharacteristic
1221C2#1913749511yescharacteristic
1222C2#1913750411yescharacteristic
1223C2#1913757111yescharacteristic
1224C2#1913758211yescharacteristic
1225C2#1913796211yescharacteristic
1226C2#1913804111yescharacteristic
1227C2#1913806011yescharacteristic
1228C2#1913807311yescharacteristic
1229C2#1913820611yescharacteristic
1230C2#1913839711yescharacteristic
1231C2#1913842011yescharacteristic
1232C2#1913977611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1444C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenter#1444D43
hypocenterC43#13975
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
4. C2×#14582770C2semidirect
5. C2×#14582770C2semidirect
6. C2×#14582756C2semidirect
7. C2×#95×D43C2semidirect
8. #19132854C2semidirect
9. #19132841C2semidirect
10. #19132837C2semidirect
11. #19132829C2semidirect
12. #19132826C2semidirect
13. (C2×D43)⋊#95C2semidirect
14. (C2×D43)⋊#95C2semidirect
15. C43×#1444C2semidirect
36. #14582777C4semidirect
101. C22×C4×D43C2×C4semidirect
130. C2×(C2×D43)⋊C4C2×C4semidirect
131. C2×(C2×D43)⋊C4C2×C4semidirect
132. C2×(C2×D43)⋊C4C2×C4semidirect
147. C43⋊#95C2×C4semidirect
148. C43⋊#95D4semidirect
168. #95×C43C2×C4semidirect
297. C2×D172C4⋊C4semidirect
473. C2×C4×C43C4×D4semidirect
586. C2×D43#385semidirect
607. #1444D43semidirect
676. C43#13975semidirect
785. #95C4×D43semidirect
1137. C2×C4#13063287semidirect

Maximal subgroups

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

subgroupindex
C22×#130632872
C2×#145827772
C2×#145827702
C2×#145827562
C2×#95×D432
#191328542
#191328412
#191328372
#191328292
#191328262
(C2×D43)⋊#952
C43×#14442
#1397543