Finite Group Databasebeta

← #25019382

Subgroups — #25019382

Order 11008.

2742 conjugacy classes of subgroups.

The subgroup lattice has 1224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063310C211yesmaximal, characteristic
2C22×C4×D172C211yesmaximal, characteristic
3C2×#14582777C211yesmaximal, characteristic
4C2×#14582761C211yesmaximal, characteristic, complemented
5C2×#95×D43C211yesmaximal, characteristic, complemented
6#19132849C211yesmaximal, characteristic, complemented
7#19132848C211yesmaximal, 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
19C23×C4×D43C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21C2×#13063310—24no—
22C2×#13063310—24no—
23C2×#13063310C418yescomplemented
24C2×C4×D172—24no—
25C2×C4×D172—24no—
26C2×C4×D172—24no—
27C22×C4⋊Dic43C2211yescharacteristic
28C22×Dic43⋊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×(C2×D43)⋊C4C2211yescharacteristic
37#14582777—24no—
38#14582761—24no—
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
49C2×C43⋊#95C2211yescharacteristic
50C2×C43⋊#95C2211yescharacteristic
51C2×C43⋊#95C2211yescharacteristic
52#95×D43—24no—
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×D172C2×C414yes—
67C22×D172D414yes—
68C22×D172D414yes—
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—22no—
94C22×C4×D43—22no—
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#13063310—232no—
104C4×D172—232no—
105C2×C4⋊Dic43—22no—
106C2×C4⋊Dic43—22no—
107C2×C4⋊Dic43—22no—
108C2×Dic43⋊C4—22no—
109C2×Dic43⋊C4—22no—
110C2×Dic43⋊C4C2×C414yescomplemented
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—22no—
127C2×(C2×D43)⋊C4—22no—
128C2×(C2×D43)⋊C4—22no—
129C2×(C2×D43)⋊C4—41no—
130C2×(C2×D43)⋊C4—41no—
131C2×(C2×D43)⋊C4C2×C414yescomplemented
132C2×(C2×D43)⋊C4C2×C414yescomplemented
133C2×(C2×D43)⋊C4C2×C414yescomplemented
134C2×(C2×D43)⋊C4D414yes—
135C43⋊#95—22no—
136C43⋊#95—22no—
137C43⋊#95—22no—
138C43⋊#95—22no—
139C43⋊#95—22no—
140C43⋊#95—22no—
141C43⋊#95—22no—
142C43⋊#95—22no—
143C43⋊#95—22no—
144C43⋊#95—41no—
145C43⋊#95—41no—
146C43⋊#95—41no—
147C43⋊#95—41no—
148C23×C4×C43C2311yescharacteristic
149C23×C4×C43C2311yescharacteristic
150C23×C4×C43C2311yescharacteristic
151C23×C4×C43C2311yescharacteristic
152C23×C4×C43C2311yescharacteristic
153C23×C4×C43C2311yescharacteristic
154C23×C4×C43C2311yescharacteristic
155C2×C4⋊C4×C43—22no—
156C2×C4⋊C4×C43—22no—
157C2×C4⋊C4×C43C2×C414yescomplemented
158C2×C42×C43—22no—
159C2×C42×C43—22no—
160C2×C42×C43—22no—
161#95×C43—22no—
162#95×C43—22no—
163#95×C43—22no—
164#95×C43—22no—
165#95×C43—22no—
166C24×C43C2411yescharacteristic
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×D43C22×C412yes—
188C23×D43C22×C412yes—
189C23×D43C2×D412yes—
190C23×D43C2×D412yes—
191C23×D43C2×D412yes—
192C23×D43C2×D412yes—
193C23×D43C2×D412yes—
194C23×D43C2×D412yes—
195C23×D43#4112yes—
196C23×D43#4112yes—
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×C43—21no—
236C22×C4×C43C22×C412yes—
237C22×C4×C43C22×C412yes—
238C22×C4×C43C22×C412yes—
239C22×C4×C43C2×D412yes—
240C22×C4×C43C2×D412yes—
241C22×C4×C43C2×D412yes—
242C22×C4×C43C2×D412yes—
243C22×C4×C43#4112yes—
244C22×C4×C43#4112yes—
245C22×C4×C43#4112yes—
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×Dic43—21no—
279C22×Dic43—21no—
280C22×Dic43—21no—
281C22×Dic43—21no—
282C22×Dic43—21no—
283C22×Dic43C22×C412yes—
284C22×Dic43C22×C412yes—
285C22×Dic43C2×D412yes—
286C22×Dic43C2×D412yes—
287C22×Dic43#4112yes—
288C2×D172—28no—
289C2×D172—28no—
290C2×D172—28no—
291C2×D172—28no—
292C2×D172—28no—
293C2×D172—28no—
294C2×D172C22⋊C4116yes—
295C2×C4×D43—28no—
296C2×C4×D43—28no—
297C2×C4×D43—28no—
298C2×C4×D43—28no—
299C2×C4×D43—28no—
300C2×C4×D43—28no—
301C2×C4×D43—28no—
302C2×C4×D43—44no—
303C2×C4×D43—44no—
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—
323C4⋊C4×C43—28no—
324C42×C43—28no—
325(C2×D43)⋊C4—28no—
326(C2×D43)⋊C4—28no—
327(C2×D43)⋊C4—28no—
328(C2×D43)⋊C4—28no—
329(C2×D43)⋊C4—28no—
330(C2×D43)⋊C4—44no—
331(C2×D43)⋊C4—44no—
332(C2×D43)⋊C4—44no—
333C4⋊Dic43—28no—
334Dic43⋊C4—28no—
335C23×C43C23×C411yescharacteristic
336C23×C43C22×D411yescharacteristic
337C23×C43C22×D411yescharacteristic
338C23×C43C22×D411yescharacteristic
339C23×C43C22×D411yescharacteristic
340C23×C43C2×#4111yescharacteristic
341C23×C43C2×#4111yescharacteristic
342C23×C43C2×#4111yescharacteristic
343C23×C43C2×#4111yescharacteristic
344C23×C43C2×#4111yescharacteristic
345C23×C43C2×#4111yescharacteristic
346C23×C43H(5,𝔽2)11yescharacteristic
347C23×C43H(5,𝔽2)11yescharacteristic
348C23×C432−1+411yescharacteristic
349C23×C432−1+411yescharacteristic
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—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—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×D43—41no—
410C22×D43—41no—
411C22×D43—41no—
412C22×D43C2×C22⋊C414yes—
413C22×D43C2×C22⋊C414yes—
414C22×D43C4×D414yes—
415C22×D43C4×D414yes—
416C22×D43#12014yes—
417C22×D43#12114yes—
418C22×D43#12114yes—
419C22×D43#12314yes—
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—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—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×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×C43C2×C22⋊C414yes—
468C2×C4×C43#12314yescomplemented
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—22no—
482C2×Dic43—22no—
483C2×Dic43—22no—
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×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—
511D172—232no—
512C4×D43—416no—
513C4×D43—416no—
514C4×D43—416no—
515C4×D43—416no—
516#13968—431nomaximal, Sylow
517C22×C43C22×C22⋊C411yescharacteristic
518C22×C43C2×C4×D411yescharacteristic
519C22×C43C2×C4×D411yescharacteristic
520C22×C43C4×#4111yescharacteristic
521C22×C43C4×#4111yescharacteristic
522C22×C43#52011yescharacteristic
523C22×C43#52011yescharacteristic
524C22×C43C2×#12011yescharacteristic
525C22×C43C2×#12111yescharacteristic
526C22×C43C2×#12111yescharacteristic
527C22×C43C2×#12311yescharacteristic
528C22×C43C2×#12311yescharacteristic
529C22×C43#52511yescharacteristic
530C22×C43#52911yescharacteristic
531C22×C43#52911yescharacteristic
532C22×C43#53411yescharacteristic
533C22×C43#53611yescharacteristic
534C22×C43#53911yescharacteristic
535C22×C43#53911yescharacteristic
536C22×C43#54611yescharacteristic
537C22×C43#54611yescharacteristic
538C22×C43#54611yescharacteristic
539C22×C43#54611yescharacteristic
540C22×C43#54611yescharacteristic
541C22×C43#54611yescharacteristic
542C22×C43#54711yescharacteristic
543C22×C43#54711yescharacteristic
544C22×C43#54711yescharacteristic
545C22×C43#54711yescharacteristic
546C22×C43#54711yescharacteristic
547C22×C43#54711yescharacteristic
548C22×C43#55111yescharacteristic
549C22×C43#55111yescharacteristic
550C22×C43#55211yescharacteristic
551C22×C43#55211yescharacteristic
552C2×D43—24no—
553C2×D43—24no—
554C2×D43—24no—
555C2×D43—24no—
556C2×D43—24no—
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—42no—
570C2×D43—42no—
571C2×D43—42no—
572C2×D43—42no—
573C2×D43—42no—
574C2×D43—42no—
575C2×D43—42no—
576C2×D43—42no—
577C2×D43—42no—
578C2×D43—42no—
579C2×D43—42no—
580C2×D43—42no—
581C2×D43#38618yes—
582C4×C43—24no—
583C4×C43—24no—
584C4×C43—42no—
585C4×C43—42no—
586C4×C43—42no—
587C4×C43—42no—
588C4×C43—81no—
589Dic43—42no—
590Dic43—42no—
591Dic43—42no—
592Dic43—42no—
593Dic43—42no—
594Dic43—81no—
595C22×#123—431no—
596C22×C4×D4—431no—
597C2×#386—431no—
598C2×#381—431no—
599C22×#95—431no—
600#1441—431no—
601#1441—431no—
602#1440—431no—
603#1440—431no—
604#1436—431no—
605#1436D4311yescharacteristic, complemented
606C22⋊#95—431no—
607C22⋊#95—431no—
608C22⋊#95—431no—
609C22⋊#95—431no—
610C2×C43C2×#38611yescharacteristic
611C2×C43C4×#12311yescharacteristic
612C2×C43#232211yescharacteristic
613C2×C43#233911yescharacteristic
614C2×C43#233911yescharacteristic
615C2×C43#235911yescharacteristic
616C2×C43#235911yescharacteristic
617C2×C43#240511yescharacteristic
618C2×C43#240611yescharacteristic
619C2×C43#241911yescharacteristic
620C2×C43#241911yescharacteristic
621C2×C43#242511yescharacteristic
622C2×C43#242511yescharacteristic
623C2×C43#248611yescharacteristic
624C2×C43#253411yescharacteristic
625D43—28no—
626D43—44no—
627C23×D4—431no—
628C24×C4—431no—
629C24×C4—431no—
630C24×C4—431no—
631C24×C4—431no—
632C2×#123—438no—
633C2×#123—864no—
634C2×#123—864no—
635C2×C4×D4—864no—
636C2×C4×D4—864no—
637C2×C4×D4—864no—
638C22×C4⋊C4—431no—
639C22×C4⋊C4—431no—
640C22×C4⋊C4C2×D4311yescharacteristic
641C22×C22⋊C4—431no—
642C22×C22⋊C4—431no—
643C22×C22⋊C4—431no—
644C22×C22⋊C4—431no—
645C22×C22⋊C4—431no—
646C22×C22⋊C4—431no—
647C22×C22⋊C4—431no—
648C22×C22⋊C4—431no—
649C22×C42C2×D4311yescharacteristic
650#386—864no—
651#381—864no—
652C2×#95—431no—
653C2×#95—431no—
654C2×#95—431no—
655C2×#95—431no—
656C2×#95—431no—
657C2×#95—431no—
658C2×#95—431no—
659C2×#95—431no—
660C2×#95—431no—
661C2×#95—431no—
662C2×#95—431no—
663C2×#95—431no—
664C2×#95—431no—
665C2×#95—864no—
666C2×#95C2×D4311yescharacteristic
667C2×#95C2×D4311yescharacteristic
668C2×#95C2×D4311yescharacteristic
669C2×#95C2×D4311yescharacteristic
670C2×#95C2×D4311yescharacteristic
671C43#1396811yescharacteristic, complemented, Sylow
672C25—431no—
673C25—431no—
674C22×D4—434no—
675C22×D4—434no—
676C22×D4—434no—
677C22×D4—862no—
678C22×D4—862no—
679C22×D4—862no—
680C22×D4—862no—
681C23×C4—431no—
682C23×C4—431no—
683C23×C4—431no—
684C23×C4—431no—
685C23×C4—431no—
686C23×C4—434no—
687C23×C4—434no—
688C23×C4—431no—
689C23×C4—862no—
690C23×C4—862no—
691C23×C4—862no—
692C23×C4—862no—
693C23×C4—862no—
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—1721no—
710C23×C4—1721no—
711C23×C4—1721no—
712C23×C4—1721no—
713C23×C4—1721no—
714C23×C4—1721no—
715C23×C4C22×D4311yescharacteristic
716C23×C4C22×D4311yescharacteristic
717C23×C4C22×D4311yescharacteristic
718C23×C4C22×D4311yescharacteristic
719C23×C4C22×D4311yescharacteristic
720C23×C4C22×D4311yescharacteristic
721C23×C4C22×D4311yescharacteristic
722#123—8632no—
723C4×D4—8632no—
724C2×C4⋊C4—22no—
725C2×C4⋊C4—22no—
726C2×C4⋊C4—434no—
727C2×C4⋊C4—862no—
728C2×C4⋊C4—862no—
729C2×C4⋊C4—862no—
730C2×C4⋊C4—862no—
731C2×C4⋊C4—862no—
732C2×C4⋊C4C4×D4314yescomplemented
733C2×C22⋊C4—434no—
734C2×C22⋊C4—434no—
735C2×C22⋊C4—434no—
736C2×C22⋊C4—434no—
737C2×C22⋊C4—862no—
738C2×C22⋊C4—862no—
739C2×C22⋊C4—862no—
740C2×C22⋊C4—862no—
741C2×C22⋊C4—862no—
742C2×C22⋊C4—862no—
743C2×C22⋊C4—862no—
744C2×C22⋊C4—862no—
745C2×C22⋊C4—862no—
746C2×C22⋊C4—862no—
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—1721no—
756C2×C22⋊C4—1721no—
757C2×C42—22no—
758C2×C42—22no—
759C2×C42—22no—
760#95—22no—
761#95—22no—
762#95—22no—
763#95—22no—
764#95—22no—
765#95—862no—
766#95—862no—
767#95—862no—
768#95—862no—
769#95—862no—
770#95—862no—
771#95—862no—
772#95—862no—
773#95—862no—
774#95—1721no—
775#95—1721no—
776#95—1721no—
777#95—1721no—
778C24—432no—
779C24—432no—
780C24—432no—
781C24—432no—
782C24—432no—
783C24—432no—
784C24—432no—
785C24—432no—
786C24—432no—
787C24—432no—
788C24—861no—
789C24—861no—
790C24—861no—
791C24—861no—
792C24—861no—
793C24—861no—
794C24—861no—
795C24—861no—
796C24—861no—
797C24—861no—
798C24—861no—
799C24—861no—
800C24—861no—
801C24—861no—
802C24—861no—
803C24—861no—
804C24—861no—
805C24—861no—
806C24—861no—
807C24—861no—
808C24C23×D4311yescharacteristic
809C2×D4—4316no—
810C2×D4—868no—
811C2×D4—868no—
812C2×D4—868no—
813C2×D4—868no—
814C2×D4—868no—
815C2×D4—868no—
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—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—432no—
856C22×C4—432no—
857C22×C4—432no—
858C22×C4—432no—
859C22×C4—432no—
860C22×C4—868no—
861C22×C4—868no—
862C22×C4—868no—
863C22×C4—868no—
864C22×C4—868no—
865C22×C4—868no—
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—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—868no—
897C22×C4—861no—
898C22×C4—861no—
899C22×C4—861no—
900C22×C4—861no—
901C22×C4—861no—
902C22×C4—861no—
903C22×C4—861no—
904C22×C4—1724no—
905C22×C4—1724no—
906C22×C4—1724no—
907C22×C4—1724no—
908C22×C4—1724no—
909C22×C4—1724no—
910C22×C4—1724no—
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×C4C2×C4×D4312yes—
926C22×C4C2×C4×D4312yes—
927C22×C4C2×C4×D4312yes—
928C22×C4#1062189812yes—
929C22×C4#1062189812yes—
930C22×C4D4×D4312yes—
931C22×C4D4×D4312yes—
932C22×C4D4×D4312yes—
933C22×C4D4×D4312yes—
934C22×C4#1062190212yes—
935C4⋊C4—28no—
936C4⋊C4—868no—
937C4⋊C4—868no—
938C22⋊C4—868no—
939C22⋊C4—868no—
940C22⋊C4—868no—
941C22⋊C4—868no—
942C22⋊C4—868no—
943C22⋊C4—1724no—
944C22⋊C4—1724no—
945C22⋊C4—1724no—
946C42—28no—
947C23—434no—
948C23—434no—
949C23—434no—
950C23—434no—
951C23—434no—
952C23—434no—
953C23—434no—
954C23—434no—
955C23—862no—
956C23—862no—
957C23—862no—
958C23—862no—
959C23—862no—
960C23—862no—
961C23—862no—
962C23—862no—
963C23—862no—
964C23—862no—
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—1721no—
1002C23—1721no—
1003C23—1721no—
1004C23—1721no—
1005C23—1721no—
1006C23—1721no—
1007C23—1721no—
1008C23—1721no—
1009C23—1721no—
1010C23—1721no—
1011C23—1721no—
1012C23—1721no—
1013C23—1721no—
1014C23—1721no—
1015C23—1721no—
1016C23—1721no—
1017C23C22×C4×D4311yescharacteristic
1018C23C2×D4×D4311yescharacteristic
1019C23C2×D4×D4311yescharacteristic
1020C23C2×D4×D4311yescharacteristic
1021C23C2×D4×D4311yescharacteristic
1022C23#41×D4311yescharacteristic
1023C23#41×D4311yescharacteristic
1024C23#41×D4311yescharacteristic
1025C23C2×#1062189811yescharacteristic
1026C23C2×#1062189811yescharacteristic
1027C23C2×#1062190211yescharacteristic
1028C23#1306337111yescharacteristic
1029C23#1306337111yescharacteristic
1030C23#1306337211yescharacteristic
1031C23#1306337311yescharacteristic
1032D4—8632no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
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—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
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—862no—
1081C2×C4—862no—
1082C2×C4—862no—
1083C2×C4—862no—
1084C2×C4—862no—
1085C2×C4—862no—
1086C2×C4—862no—
1087C2×C4—862no—
1088C2×C4—862no—
1089C2×C4—862no—
1090C2×C4—862no—
1091C2×C4—862no—
1092C2×C4—862no—
1093C2×C4—862no—
1094C2×C4—862no—
1095C2×C4—17216no—
1096C2×C4—17216no—
1097C2×C4—17216no—
1098C2×C4—17216no—
1099C2×C4—1721no—
1100C2×C4—1721no—
1101C2×C4—1721no—
1102C2×C4—1721no—
1103C2×C4—1721no—
1104C2×C4—1721no—
1105C2×C4—1721no—
1106C2×C4—1721no—
1107C2×C4—1721no—
1108C2×C4—1721no—
1109C2×C4—1721no—
1110C2×C4—1721no—
1111C2×C4—1721no—
1112C2×C4—1721no—
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×C4C22⋊C4×D4314yes—
1127C2×C4#1306331014yescomplemented
1128C22—438no—
1129C22—864no—
1130C22—864no—
1131C22—864no—
1132C22—864no—
1133C22—864no—
1134C22—864no—
1135C22—864no—
1136C22—864no—
1137C22—864no—
1138C22—864no—
1139C22—864no—
1140C22—864no—
1141C22—864no—
1142C22—864no—
1143C22—864no—
1144C22—864no—
1145C22—864no—
1146C22—1722no—
1147C22—1722no—
1148C22—1722no—
1149C22—1722no—
1150C22—1722no—
1151C22—1722no—
1152C22—1722no—
1153C22—1722no—
1154C22—1722no—
1155C22—1722no—
1156C22—1722no—
1157C22—1722no—
1158C22C2×C22⋊C4×D4311yescharacteristic
1159C22C4×D4×D4311yescharacteristic
1160C22C4×D4×D4311yescharacteristic
1161C22C4×#1062189811yescharacteristic
1162C22C4×#1062190211yescharacteristic
1163C22#1458337911yescharacteristic
1164C22#1458338111yescharacteristic
1165C22#120×D4311yescharacteristic
1166C22#121×D4311yescharacteristic
1167C22#121×D4311yescharacteristic
1168C22#123×D4311yescharacteristic
1169C22C2×#1306331011yescharacteristic
1170C22#1458340811yescharacteristic
1171C22#1458342711yescharacteristic
1172C22#1458343611yescharacteristic
1173C22#1458346011yescharacteristic
1174C22#1458347211yescharacteristic
1175C22#1458349011yescharacteristic
1176C22#1458349711yescharacteristic
1177C22#1458354011yescharacteristic
1178C22#1458354011yescharacteristic
1179C22#1458354211yescharacteristic
1180C22#1458354511yescharacteristic
1181C22#1458354511yescharacteristic
1182C22#1458354511yescharacteristic
1183C22#1458354711yescharacteristic
1184C22#1458355011yescharacteristic
1185C22#1458355111yescharacteristic
1186C22#1458355211yescharacteristic
1187C22#1458355411yescharacteristic
1188C22#1458355411yescharacteristic
1189C22#1458357311yescharacteristic
1190C22#1458357411yescharacteristic
1191C22#1458358711yescharacteristic
1192C22#1458359011yescharacteristic
1193C4—24no—
1194C4—24no—
1195C4—42no—
1196C4—42no—
1197C4—42no—
1198C4—42no—
1199C4—81no—
1200C4—3441no—
1201C4—1722no—
1202C4—1722no—
1203C4—1722no—
1204C4—1722no—
1205C4—1722no—
1206C2—868no—
1207C2—1724no—
1208C2#386×D4311yescharacteristic
1209C2C4×#1306331011yescharacteristic
1210C2#1913726811yescharacteristic
1211C2#1913742411yescharacteristic
1212C2#1913742611yescharacteristic
1213C2#1913759211yescharacteristic
1214C2#1913759411yescharacteristic
1215C2#1913792411yescharacteristic
1216C2#1913792811yescharacteristic
1217C2#1913807711yescharacteristic
1218C2#1913807911yescharacteristic
1219C2#1913815111yescharacteristic
1220C2#1913815311yescharacteristic
1221C2#1913890111yescharacteristic
1222C2#1913948911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1436C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenter#1436D43
hypocenterC43#13968
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
4. C2×#14582761C2semidirect
5. C2×#95×D43C2semidirect
6. #19132849C2semidirect
7. #19132848C2semidirect
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
23. C2×#13063310C4semidirect
101. C22×C4×D43C2×C4semidirect
110. C2×Dic43⋊C4C2×C4semidirect
131. C2×(C2×D43)⋊C4C2×C4semidirect
132. C2×(C2×D43)⋊C4C2×C4semidirect
133. C2×(C2×D43)⋊C4C2×C4semidirect
157. C2×C4⋊C4×C43C2×C4semidirect
468. C2×C4×C43#123semidirect
605. #1436D43semidirect
671. C43#13968semidirect
732. C2×C4⋊C4C4×D43semidirect
1127. C2×C4#13063310semidirect

Maximal subgroups

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

subgroupindex
C22×#130633102
C22×C4×D1722
C2×#145827772
C2×#145827612
C2×#95×D432
#191328492
#191328482
#191328432
#191328282
(C2×D43)⋊#952
C43×#14362
#1396843