Finite Group Databasebeta

← #25019379

Subgroups — #25019379

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×#13063307C211yesmaximal, characteristic
2C22×(C22⋊D43)⋊C4C211yesmaximal, characteristic
3C2×#14582775C211yesmaximal, characteristic
4C2×#14582761C211yesmaximal, characteristic, complemented
5C2×#95×D43C211yesmaximal, characteristic, complemented
6#19132847C211yesmaximal, characteristic, complemented
7#19132846C211yesmaximal, characteristic, complemented
8#19132842C211yesmaximal, characteristic, complemented
9#19132829C211yesmaximal, characteristic, complemented
10#19132826C211yesmaximal, characteristic, complemented
11#19132817C211yesmaximal, characteristic, complemented
12#19132817C211yesmaximal, characteristic, complemented
13(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
15C43×#1440C211yesmaximal, characteristic, complemented
16C23×C22⋊D43C2211yescharacteristic
17C24×Dic43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21C2×#13063307—24no—
22C2×#13063307—24no—
23C2×#13063307C418yescomplemented
24C2×(C22⋊D43)⋊C4—24no—
25C2×(C22⋊D43)⋊C4—24no—
26C2×(C22⋊D43)⋊C4—24no—
27C22×C4⋊Dic43C2211yescharacteristic
28C22×Dic43⋊C4C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30C22×C22⋊Dic43C2211yescharacteristic
31C22×C22⋊Dic43C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×(C2×D43)⋊C4C2211yescharacteristic
35C22×C4×Dic43C2211yescharacteristic
36#14582775—24no—
37#14582761—24no—
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
49C2×C43⋊#95C2211yescharacteristic
50C2×C43⋊#95C2211yescharacteristic
51C2×C43⋊#95C2211yescharacteristic
52#95×D43—24no—
53C22×C22⋊C4×C43C2211yescharacteristic
54C22×C22⋊C4×C43C2211yescharacteristic
55C22×C22⋊C4×C43C2211yescharacteristic
56C2×#95×C43C2211yescharacteristic
57C2×#95×C43C2211yescharacteristic
58C2×#95×C43C2211yescharacteristic
59C2×#95×C43C2211yescharacteristic
60C24×D43C2311yescharacteristic
61C22×C22⋊D43—22no—
62C22×C22⋊D43—22no—
63C22×C22⋊D43—22no—
64C22×C22⋊D43—22no—
65C22×C22⋊D43C2×C414yes—
66C22×C22⋊D43D414yes—
67C22×C22⋊D43D414yes—
68C23×Dic43—22no—
69C23×Dic43—22no—
70C23×Dic43—22no—
71C23×Dic43—22no—
72C23×Dic43—22no—
73C23×Dic43—41no—
74C23×Dic43—41no—
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81C23×Dic43C2311yescharacteristic
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—22no—
96C22×C4×D43—22no—
97C22×C4×D43—41no—
98C22×C4×D43—41no—
99C22×C4×D43—41no—
100C22×C4×D43—41no—
101C22×C4×D43C2×C414yescomplemented
102C22×C4×D43D414yes—
103#13063307—232no—
104(C22⋊D43)⋊C4—232no—
105C2×C4⋊Dic43—22no—
106C2×C4⋊Dic43—22no—
107C2×C4⋊Dic43C2×C414yescomplemented
108C2×Dic43⋊C4—22no—
109C2×Dic43⋊C4—22no—
110C2×Dic43⋊C4—22no—
111C2×Dic43⋊C4—22no—
112C2×Dic43⋊C4—22no—
113C2×Dic43⋊C4C2×C414yescomplemented
114C2×C22⋊Dic43—22no—
115C2×C22⋊Dic43—22no—
116C2×C22⋊Dic43—22no—
117C2×C22⋊Dic43—22no—
118C2×C22⋊Dic43—41no—
119C2×C22⋊Dic43C2×C414yescomplemented
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)⋊C4C2×C414yescomplemented
128C2×(C2×D43)⋊C4D414yes—
129C2×C4×Dic43—22no—
130C2×C4×Dic43—22no—
131C2×C4×Dic43—22no—
132C43⋊#95—22no—
133C43⋊#95—22no—
134C43⋊#95—22no—
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—41no—
144C43⋊#95—41no—
145C43⋊#95—41no—
146C25×C43C2311yescharacteristic
147C23×C4×C43C2311yescharacteristic
148C23×C4×C43C2311yescharacteristic
149C23×C4×C43C2311yescharacteristic
150C23×C4×C43C2311yescharacteristic
151C23×C4×C43C2311yescharacteristic
152C23×C4×C43C2311yescharacteristic
153C2×C22⋊C4×C43—22no—
154C2×C22⋊C4×C43—22no—
155C2×C22⋊C4×C43—22no—
156C2×C22⋊C4×C43—22no—
157C2×C22⋊C4×C43—22no—
158C2×C22⋊C4×C43—22no—
159C2×C22⋊C4×C43—22no—
160C2×C22⋊C4×C43—41no—
161C2×C22⋊C4×C43C2×C414yescomplemented
162#95×C43—22no—
163#95×C43—22no—
164#95×C43—22no—
165#95×C43—41no—
166C24×C43—21no—
167C24×C43—21no—
168C24×C43—21no—
169C24×C43—21no—
170C24×C43—21no—
171C24×C43—21no—
172C24×C43—21no—
173C24×C43—21no—
174C24×C43—21no—
175C24×C43—21no—
176C24×C43—21no—
177C24×C43—21no—
178C24×C43C22×C412yes—
179C24×C43C2×D412yes—
180C24×C43C2×D412yes—
181C24×C43C2411yescharacteristic
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×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×C43C22×C412yes—
235C22×C4×C43C22×C412yes—
236C22×C4×C43C2×D412yes—
237C22×C4×C43C2×D412yes—
238C22×C4×C43#4112yes—
239C2×C22⋊D43—28no—
240C2×C22⋊D43—28no—
241C2×C22⋊D43—28no—
242C2×C22⋊D43—28no—
243C2×C22⋊D43—28no—
244C2×C22⋊D43—28no—
245C2×C22⋊D43C22⋊C4116yes—
246C22×Dic43—28no—
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×Dic43—21no—
284C22×Dic43—21no—
285C22×Dic43—21no—
286C22×Dic43—44no—
287C22×Dic43—44no—
288C22×Dic43—44no—
289C22×Dic43—44no—
290C22×Dic43—44no—
291C22×Dic43—44no—
292C22×Dic43C22×C412yes—
293C22×Dic43C22×C412yes—
294C22×Dic43C22×C412yes—
295C22×Dic43C2×D412yes—
296C22×Dic43C2×D412yes—
297C22×Dic43C2×D412yes—
298C22×Dic43C2×D412yes—
299C22×Dic43#4112yes—
300C22×Dic43#4112yes—
301C22×Dic43#4112yes—
302C2×C4×D43—28no—
303C2×C4×D43—28no—
304C2×C4×D43—28no—
305C2×C4×D43—28no—
306C2×C4×D43—28no—
307C2×C4×D43—28no—
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—
323C22⋊C4×C43—28no—
324C22⋊C4×C43—28no—
325C22⋊C4×C43—44no—
326C22⋊Dic43—28no—
327C22⋊Dic43—44no—
328(C2×D43)⋊C4—28no—
329(C2×D43)⋊C4—28no—
330(C2×D43)⋊C4—44no—
331C4⋊Dic43—28no—
332Dic43⋊C4—28no—
333Dic43⋊C4—28no—
334C4×Dic43—28no—
335C23×C43—22no—
336C23×C43—22no—
337C23×C43—22no—
338C23×C43—22no—
339C23×C43—22no—
340C23×C43—22no—
341C23×C43—22no—
342C23×C43—22no—
343C23×C43—22no—
344C23×C43—22no—
345C23×C43—22no—
346C23×C43—22no—
347C23×C43—22no—
348C23×C43—22no—
349C23×C43—22no—
350C23×C43—22no—
351C23×C43—22no—
352C23×C43—22no—
353C23×C43—41no—
354C23×C43—41no—
355C23×C43—41no—
356C23×C43—41no—
357C23×C43—41no—
358C23×C43—41no—
359C23×C43—41no—
360C23×C43—41no—
361C23×C43—41no—
362C23×C43—41no—
363C23×C43—41no—
364C23×C43—41no—
365C23×C43—41no—
366C23×C43—41no—
367C23×C43—41no—
368C23×C43—41no—
369C23×C43C2×C22⋊C414yes—
370C23×C43C23×C411yescharacteristic
371C23×C43C22×D411yescharacteristic
372C23×C43C22×D411yescharacteristic
373C23×C43C22×D411yescharacteristic
374C23×C43C22×D411yescharacteristic
375C23×C43C2×#4111yescharacteristic
376C23×C43C2×#4111yescharacteristic
377C23×C43C2×#4111yescharacteristic
378C23×C43C2×#4111yescharacteristic
379C23×C43C2×#4111yescharacteristic
380C23×C43C2×#4111yescharacteristic
381C23×C43H(5,𝔽2)11yescharacteristic
382C23×C43H(5,𝔽2)11yescharacteristic
383C23×C432−1+411yescharacteristic
384C23×C432−1+411yescharacteristic
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—22no—
402C22×D43—22no—
403C22×D43—22no—
404C22×D43—22no—
405C22×D43—22no—
406C22×D43—22no—
407C22×D43—22no—
408C22×D43—22no—
409C22×D43—22no—
410C22×D43—22no—
411C22×D43—22no—
412C22×D43—22no—
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—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×C43—41no—
459C2×C4×C43—41no—
460C2×C4×C43—41no—
461C2×C4×C43—41no—
462C22⋊D43—232no—
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—22no—
482C2×Dic43—22no—
483C2×Dic43—22no—
484C2×Dic43—22no—
485C2×Dic43—22no—
486C2×Dic43—22no—
487C2×Dic43—416no—
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—
511C2×Dic43C2×C22⋊C414yes—
512C2×Dic43#12314yescomplemented
513C4×D43—416no—
514C4×D43—416no—
515C4×D43—416no—
516#13968—431nomaximal, Sylow
517C22×C43—24no—
518C22×C43—24no—
519C22×C43—24no—
520C22×C43—42no—
521C22×C43—42no—
522C22×C43—42no—
523C22×C43—42no—
524C22×C43—42no—
525C22×C43—42no—
526C22×C43—42no—
527C22×C43—42no—
528C22×C43—42no—
529C22×C43—42no—
530C22×C43—42no—
531C22×C43—42no—
532C22×C43C22×C22⋊C411yescharacteristic
533C22×C43C2×C4×D411yescharacteristic
534C22×C43C2×C4×D411yescharacteristic
535C22×C43C4×#4111yescharacteristic
536C22×C43C4×#4111yescharacteristic
537C22×C43#52011yescharacteristic
538C22×C43#52011yescharacteristic
539C22×C43C2×#12011yescharacteristic
540C22×C43C2×#12111yescharacteristic
541C22×C43C2×#12111yescharacteristic
542C22×C43C2×#12311yescharacteristic
543C22×C43C2×#12311yescharacteristic
544C22×C43#52511yescharacteristic
545C22×C43#52911yescharacteristic
546C22×C43#52911yescharacteristic
547C22×C43#53411yescharacteristic
548C22×C43#53611yescharacteristic
549C22×C43#53911yescharacteristic
550C22×C43#53911yescharacteristic
551C22×C43#54611yescharacteristic
552C22×C43#54611yescharacteristic
553C22×C43#54611yescharacteristic
554C22×C43#54611yescharacteristic
555C22×C43#54611yescharacteristic
556C22×C43#54611yescharacteristic
557C22×C43#54711yescharacteristic
558C22×C43#54711yescharacteristic
559C22×C43#54711yescharacteristic
560C22×C43#54711yescharacteristic
561C22×C43#54711yescharacteristic
562C22×C43#54711yescharacteristic
563C22×C43#55111yescharacteristic
564C22×C43#55111yescharacteristic
565C22×C43#55211yescharacteristic
566C22×C43#55211yescharacteristic
567C2×D43—24no—
568C2×D43—24no—
569C2×D43—24no—
570C2×D43—24no—
571C2×D43—24no—
572C2×D43—24no—
573C2×D43—24no—
574C2×D43—24no—
575C2×D43—24no—
576C2×D43—24no—
577C2×D43—24no—
578C2×D43—24no—
579C2×D43—24no—
580C2×D43—24no—
581C2×D43#38618yes—
582C4×C43—42no—
583C4×C43—42no—
584C4×C43—42no—
585C4×C43—42no—
586C4×C43—42no—
587C4×C43—81no—
588Dic43—24no—
589Dic43—24no—
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#1440D4311yescharacteristic, complemented
604#1436—431no—
605#1436—431no—
606C22⋊#95—431no—
607C22⋊#95—431no—
608C22⋊#95—431no—
609C22⋊#95—431no—
610C2×C43—44no—
611C2×C43C2×#38611yescharacteristic
612C2×C43C4×#12311yescharacteristic
613C2×C43#232211yescharacteristic
614C2×C43#233911yescharacteristic
615C2×C43#233911yescharacteristic
616C2×C43#235911yescharacteristic
617C2×C43#235911yescharacteristic
618C2×C43#240511yescharacteristic
619C2×C43#240611yescharacteristic
620C2×C43#241911yescharacteristic
621C2×C43#241911yescharacteristic
622C2×C43#242511yescharacteristic
623C2×C43#242511yescharacteristic
624C2×C43#248611yescharacteristic
625C2×C43#253411yescharacteristic
626D43—28no—
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⋊C4—431no—
641C22×C22⋊C4—431no—
642C22×C22⋊C4—431no—
643C22×C22⋊C4—431no—
644C22×C22⋊C4—431no—
645C22×C22⋊C4—431no—
646C22×C22⋊C4C2×D4311yescharacteristic
647C22×C22⋊C4C2×D4311yescharacteristic
648C22×C22⋊C4C2×D4311yescharacteristic
649C22×C42—431no—
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—431no—
666C2×#95—864no—
667C2×#95C2×D4311yescharacteristic
668C2×#95C2×D4311yescharacteristic
669C2×#95C2×D4311yescharacteristic
670C2×#95C2×D4311yescharacteristic
671C43#1396811yescharacteristic, complemented, Sylow
672C25—431no—
673C25C22×D4311yescharacteristic
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—431no—
687C23×C4—434no—
688C23×C4—434no—
689C23×C4—431no—
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—862no—
710C23×C4—1721no—
711C23×C4—1721no—
712C23×C4—1721no—
713C23×C4—1721no—
714C23×C4—1721no—
715C23×C4—1721no—
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—434no—
725C2×C4⋊C4—434no—
726C2×C4⋊C4—862no—
727C2×C4⋊C4—862no—
728C2×C4⋊C4—862no—
729C2×C4⋊C4—862no—
730C2×C4⋊C4—862no—
731C2×C4⋊C4—862no—
732C2×C4⋊C4—862no—
733C2×C22⋊C4—22no—
734C2×C22⋊C4—22no—
735C2×C22⋊C4—22no—
736C2×C22⋊C4—22no—
737C2×C22⋊C4—22no—
738C2×C22⋊C4—22no—
739C2×C22⋊C4—22no—
740C2×C22⋊C4—41no—
741C2×C22⋊C4—434no—
742C2×C22⋊C4—434no—
743C2×C22⋊C4—434no—
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⋊C4C4×D4314yescomplemented
757C2×C42—862no—
758C2×C42—862no—
759C2×C42—862no—
760#95—22no—
761#95—22no—
762#95—22no—
763#95—41no—
764#95—862no—
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—862no—
775#95—1721no—
776#95—1721no—
777#95—1721no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—21no—
785C24—21no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—432no—
791C24—432no—
792C24—432no—
793C24—432no—
794C24—432no—
795C24—432no—
796C24—432no—
797C24—861no—
798C24—861no—
799C24—861no—
800C24—861no—
801C24—861no—
802C24—861no—
803C24—861no—
804C24—861no—
805C24C2×C4×D4312yes—
806C24D4×D4312yes—
807C24D4×D4312yes—
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—432no—
854C22×C4—432no—
855C22×C4—432no—
856C22×C4—432no—
857C22×C4—432no—
858C22×C4—432no—
859C22×C4—432no—
860C22×C4—432no—
861C22×C4—432no—
862C22×C4—432no—
863C22×C4—868no—
864C22×C4—868no—
865C22×C4—868no—
866C22×C4—868no—
867C22×C4—868no—
868C22×C4—868no—
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—868no—
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—861no—
904C22×C4—861no—
905C22×C4—861no—
906C22×C4—861no—
907C22×C4—861no—
908C22×C4—861no—
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×C4—1724no—
926C22×C4—1724no—
927C22×C4—1724no—
928C22×C4—1724no—
929C22×C4—1724no—
930C22×C4C2×C4×D4312yes—
931C22×C4C2×C4×D4312yes—
932C22×C4D4×D4312yes—
933C22×C4D4×D4312yes—
934C22×C4#1062190012yes—
935C4⋊C4—868no—
936C4⋊C4—868no—
937C4⋊C4—868no—
938C22⋊C4—28no—
939C22⋊C4—28no—
940C22⋊C4—44no—
941C22⋊C4—868no—
942C22⋊C4—868no—
943C22⋊C4—868no—
944C22⋊C4—1724no—
945C22⋊C4—1724no—
946C42—868no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—434no—
982C23—434no—
983C23—434no—
984C23—434no—
985C23—434no—
986C23—434no—
987C23—434no—
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—862no—
1012C23—862no—
1013C23—862no—
1014C23—862no—
1015C23—862no—
1016C23C22⋊C4×D4314yes—
1017C23C22×C4×D4311yescharacteristic
1018C23C2×D4×D4311yescharacteristic
1019C23C2×D4×D4311yescharacteristic
1020C23C2×D4×D4311yescharacteristic
1021C23C2×D4×D4311yescharacteristic
1022C23#41×D4311yescharacteristic
1023C23#41×D4311yescharacteristic
1024C23#41×D4311yescharacteristic
1025C23#41×D4311yescharacteristic
1026C23#41×D4311yescharacteristic
1027C23C2×#1062190011yescharacteristic
1028C23#1306337011yescharacteristic
1029C23#1306337111yescharacteristic
1030C23#1306337211yescharacteristic
1031C23#1306337211yescharacteristic
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—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—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—434no—
1076C2×C4—434no—
1077C2×C4—862no—
1078C2×C4—862no—
1079C2×C4—862no—
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—862no—
1096C2×C4—862no—
1097C2×C4—862no—
1098C2×C4—862no—
1099C2×C4—862no—
1100C2×C4—862no—
1101C2×C4—17216no—
1102C2×C4—17216no—
1103C2×C4—17216no—
1104C2×C4—17216no—
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×C4—1721no—
1127C2×C4—1721no—
1128C22—24no—
1129C22—24no—
1130C22—24no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22—42no—
1136C22—42no—
1137C22—42no—
1138C22—42no—
1139C22—42no—
1140C22—42no—
1141C22—42no—
1142C22—42no—
1143C22—438no—
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—864no—
1157C22—864no—
1158C22C2×C22⋊C4×D4311yescharacteristic
1159C22C4×D4×D4311yescharacteristic
1160C22C4×D4×D4311yescharacteristic
1161C22C4×#1062190011yescharacteristic
1162C22#1458336711yescharacteristic
1163C22#1458337811yescharacteristic
1164C22#1458337911yescharacteristic
1165C22#120×D4311yescharacteristic
1166C22#121×D4311yescharacteristic
1167C22#121×D4311yescharacteristic
1168C22#123×D4311yescharacteristic
1169C22#123×D4311yescharacteristic
1170C22#1458340911yescharacteristic
1171C22#1458342811yescharacteristic
1172C22#1458343211yescharacteristic
1173C22#1458345711yescharacteristic
1174C22#1458346911yescharacteristic
1175C22#1458349011yescharacteristic
1176C22#1458349211yescharacteristic
1177C22#1458353611yescharacteristic
1178C22#1458353811yescharacteristic
1179C22#1458354111yescharacteristic
1180C22#1458354111yescharacteristic
1181C22#1458354211yescharacteristic
1182C22#1458354611yescharacteristic
1183C22#1458354711yescharacteristic
1184C22#1458354711yescharacteristic
1185C22#1458354711yescharacteristic
1186C22#1458354711yescharacteristic
1187C22#1458354911yescharacteristic
1188C22#1458354911yescharacteristic
1189C22#1458357211yescharacteristic
1190C22#1458357911yescharacteristic
1191C22#1458358511yescharacteristic
1192C22#1458358511yescharacteristic
1193C4—42no—
1194C4—42no—
1195C4—42no—
1196C4—42no—
1197C4—42no—
1198C4—81no—
1199C4—864no—
1200C4—864no—
1201C4—3441no—
1202C4—1722no—
1203C4—1722no—
1204C4—1722no—
1205C4—1722no—
1206C2—44no—
1207C2—868no—
1208C2#386×D4311yescharacteristic
1209C2#1913712211yescharacteristic
1210C2#1913726511yescharacteristic
1211C2#1913741911yescharacteristic
1212C2#1913742111yescharacteristic
1213C2#1913758411yescharacteristic
1214C2#1913758611yescharacteristic
1215C2#1913791711yescharacteristic
1216C2#1913792511yescharacteristic
1217C2#1913806511yescharacteristic
1218C2#1913806711yescharacteristic
1219C2#1913814711yescharacteristic
1220C2#1913814911yescharacteristic
1221C2#1913889611yescharacteristic
1222C2#1913948011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1440C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenter#1440D43
hypocenterC43#13968
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
4. C2×#14582761C2semidirect
5. C2×#95×D43C2semidirect
6. #19132847C2semidirect
7. #19132846C2semidirect
8. #19132842C2semidirect
9. #19132829C2semidirect
10. #19132826C2semidirect
11. #19132817C2semidirect
12. #19132817C2semidirect
13. (C2×D43)⋊#95C2semidirect
14. (C2×D43)⋊#95C2semidirect
15. C43×#1440C2semidirect
23. C2×#13063307C4semidirect
101. C22×C4×D43C2×C4semidirect
107. C2×C4⋊Dic43C2×C4semidirect
113. C2×Dic43⋊C4C2×C4semidirect
119. C2×C22⋊Dic43C2×C4semidirect
127. C2×(C2×D43)⋊C4C2×C4semidirect
161. C2×C22⋊C4×C43C2×C4semidirect
512. C2×Dic43#123semidirect
603. #1440D43semidirect
671. C43#13968semidirect
756. C2×C22⋊C4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C22×#130633072
C22×(C22⋊D43)⋊C42
C2×#145827752
C2×#145827612
C2×#95×D432
#191328472
#191328462
#191328422
#191328292
#191328262
#191328172
(C2×D43)⋊#952
C43×#14402
#1396843