Finite Group Databasebeta

← #25019376

Subgroups — #25019376

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×C4×C22⋊D43C211yesmaximal, characteristic
3C2×#14582775C211yesmaximal, characteristic
4C2×#14582761C211yesmaximal, characteristic, complemented
5C2×#95×D43C211yesmaximal, characteristic, complemented
6#19132847C211yesmaximal, characteristic, complemented
7#19132846C211yesmaximal, characteristic, complemented
8#19132844C211yesmaximal, characteristic, complemented
9#19132842C211yesmaximal, characteristic, complemented
10#19132829C211yesmaximal, characteristic, complemented
11#19132826C211yesmaximal, characteristic, complemented
12#19132818C211yesmaximal, characteristic, complemented
13(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
15C43×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×C22⋊D43C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C2×#13063307—24no—
21C2×#13063307—24no—
22C2×#13063307C418yescomplemented
23C2×C4×C22⋊D43—24no—
24C2×C4×C22⋊D43—24no—
25C2×C4×C22⋊D43—24no—
26C22×C4⋊Dic43C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
28C22×Dic43⋊C4C2211yescharacteristic
29C22×C22⋊Dic43C2211yescharacteristic
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—
53C24×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×Dic43C2311yescharacteristic
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—41no—
91C22×C4×D43—41no—
92C22×C4×D43—41no—
93C22×C4×D43—41no—
94C22×C4×D43C2×C414yescomplemented
95C22×C4×D43D414yes—
96#13063307—232no—
97C4×C22⋊D43—232no—
98C2×C4⋊Dic43—22no—
99C2×C4⋊Dic43—22no—
100C2×C4⋊Dic43C2×C414yescomplemented
101C2×Dic43⋊C4—22no—
102C2×Dic43⋊C4—22no—
103C2×Dic43⋊C4—22no—
104C2×Dic43⋊C4—22no—
105C2×Dic43⋊C4—22no—
106C2×Dic43⋊C4C2×C414yescomplemented
107C2×C22⋊Dic43—22no—
108C2×C22⋊Dic43—22no—
109C2×C22⋊Dic43—22no—
110C2×C22⋊Dic43—22no—
111C2×C22⋊Dic43—22no—
112C2×C22⋊Dic43—22no—
113C2×C22⋊Dic43—22no—
114C2×C22⋊Dic43—41no—
115C2×C22⋊Dic43C2×C414yescomplemented
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)⋊C4C2×C414yescomplemented
124C2×(C2×D43)⋊C4D414yes—
125C2×C4×Dic43—22no—
126C2×C4×Dic43—22no—
127C2×C4×Dic43—22no—
128C43⋊#95—22no—
129C43⋊#95—22no—
130C43⋊#95—22no—
131C43⋊#95—22no—
132C43⋊#95—22no—
133C43⋊#95—22no—
134C43⋊#95—22no—
135C43⋊#95—22no—
136C43⋊#95—22no—
137C43⋊#95—22no—
138C43⋊#95—22no—
139C43⋊#95—41no—
140C43⋊#95—41no—
141C43⋊#95—41no—
142C25×C43C2311yescharacteristic
143C23×C4×C43—22no—
144C23×C4×C43—22no—
145C23×C4×C43—22no—
146C23×C4×C43—22no—
147C23×C4×C43—22no—
148C23×C4×C43—41no—
149C23×C4×C43—41no—
150C23×C4×C43C2311yescharacteristic
151C23×C4×C43C2311yescharacteristic
152C23×C4×C43C2311yescharacteristic
153C23×C4×C43C2311yescharacteristic
154C23×C4×C43C2311yescharacteristic
155C23×C4×C43C2311yescharacteristic
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—28no—
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—44no—
234C22×C4×C43—44no—
235C22×C4×C43—44no—
236C22×C4×C43—44no—
237C22×C4×C43—44no—
238C22×C4×C43—44no—
239C22×C4×C43C22×C412yes—
240C22×C4×C43C22×C412yes—
241C22×C4×C43C2×D412yes—
242C22×C4×C43C2×D412yes—
243C22×C4×C43#4112yes—
244C22×C4×C43#4112yes—
245C22×C4×C43#4112yes—
246C2×C22⋊D43—28no—
247C2×C22⋊D43—28no—
248C2×C22⋊D43—28no—
249C2×C22⋊D43—28no—
250C2×C22⋊D43—28no—
251C2×C22⋊D43—28no—
252C2×C22⋊D43C22⋊C4116yes—
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—21no—
287C22×Dic43—21no—
288C22×Dic43—21no—
289C22×Dic43—21no—
290C22×Dic43—21no—
291C22×Dic43—21no—
292C22×Dic43—21no—
293C22×Dic43—21no—
294C22×Dic43C22×C412yes—
295C22×Dic43C22×C412yes—
296C22×Dic43C22×C412yes—
297C22×Dic43C2×D412yes—
298C22×Dic43C2×D412yes—
299C22×Dic43C2×D412yes—
300C22×Dic43C2×D412yes—
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—44no—
325C22⋊Dic43—28no—
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—22no—
436C2×C4×C43—22no—
437C2×C4×C43—22no—
438C2×C4×C43—416no—
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—
462C2×C4×C43#12314yescomplemented
463C22⋊D43—232no—
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—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—
511C2×Dic43—41no—
512C2×Dic43C2×C22⋊C414yes—
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—24no—
583C4×C43—42no—
584C4×C43—42no—
585C4×C43—42no—
586C4×C43—42no—
587C4×C43—81no—
588Dic43—24no—
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#1436—431no—
606C22⋊#95—431no—
607C22⋊#95—431no—
608C22⋊#95—431no—
609C22⋊#95D4311yescharacteristic, complemented
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×C4C2×D4311yescharacteristic
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⋊C4—431no—
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—22no—
682C23×C4—22no—
683C23×C4—22no—
684C23×C4—22no—
685C23×C4—22no—
686C23×C4—41no—
687C23×C4—41no—
688C23×C4—431no—
689C23×C4—431no—
690C23×C4—431no—
691C23×C4—431no—
692C23×C4—431no—
693C23×C4—431no—
694C23×C4—434no—
695C23×C4—434no—
696C23×C4—431no—
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×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—41no—
738C2×C22⋊C4—434no—
739C2×C22⋊C4—434no—
740C2×C22⋊C4—434no—
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⋊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—28no—
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—44no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—432no—
859C22×C4—432no—
860C22×C4—432no—
861C22×C4—432no—
862C22×C4—432no—
863C22×C4—432no—
864C22×C4—432no—
865C22×C4—432no—
866C22×C4—868no—
867C22×C4—868no—
868C22×C4—868no—
869C22×C4—868no—
870C22×C4—868no—
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—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—868no—
906C22×C4—861no—
907C22×C4—861no—
908C22×C4—861no—
909C22×C4—861no—
910C22×C4—861no—
911C22×C4—861no—
912C22×C4—861no—
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×C4C2×C4×D4312yes—
929C22×C4C2×C4×D4312yes—
930C22×C4#1062189812yes—
931C22×C4#1062189812yes—
932C22×C4D4×D4312yes—
933C22×C4D4×D4312yes—
934C22×C4#1062190012yes—
935C4⋊C4—868no—
936C4⋊C4—868no—
937C4⋊C4—868no—
938C22⋊C4—28no—
939C22⋊C4—44no—
940C22⋊C4—868no—
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
1025C23C2×#1062190011yescharacteristic
1026C23C2×#1062189811yescharacteristic
1027C23C2×#1062189811yescharacteristic
1028C23#1306337011yescharacteristic
1029C23#1306337011yescharacteristic
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—416no—
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—862no—
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—17216no—
1098C2×C4—17216no—
1099C2×C4—17216no—
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×C4—1721no—
1127C2×C4#1306330714yescomplemented
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
1162C22C4×#1062189811yescharacteristic
1163C22#1458337811yescharacteristic
1164C22#1458338011yescharacteristic
1165C22#120×D4311yescharacteristic
1166C22#121×D4311yescharacteristic
1167C22#121×D4311yescharacteristic
1168C22#123×D4311yescharacteristic
1169C22C2×#1306330711yescharacteristic
1170C22#1458340811yescharacteristic
1171C22#1458342711yescharacteristic
1172C22#1458343111yescharacteristic
1173C22#1458345911yescharacteristic
1174C22#1458347211yescharacteristic
1175C22#1458349211yescharacteristic
1176C22#1458349511yescharacteristic
1177C22#1458353611yescharacteristic
1178C22#1458353611yescharacteristic
1179C22#1458353811yescharacteristic
1180C22#1458353911yescharacteristic
1181C22#1458353911yescharacteristic
1182C22#1458353911yescharacteristic
1183C22#1458354711yescharacteristic
1184C22#1458354911yescharacteristic
1185C22#1458355011yescharacteristic
1186C22#1458355011yescharacteristic
1187C22#1458355111yescharacteristic
1188C22#1458355411yescharacteristic
1189C22#1458357711yescharacteristic
1190C22#1458357811yescharacteristic
1191C22#1458358311yescharacteristic
1192C22#1458358811yescharacteristic
1193C4—24no—
1194C4—42no—
1195C4—42no—
1196C4—42no—
1197C4—42no—
1198C4—81no—
1199C4—864no—
1200C4—3441no—
1201C4—1722no—
1202C4—1722no—
1203C4—1722no—
1204C4—1722no—
1205C4—1722no—
1206C2—44no—
1207C2—868no—
1208C2#386×D4311yescharacteristic
1209C2C4×#1306330711yescharacteristic
1210C2#1913726211yescharacteristic
1211C2#1913742111yescharacteristic
1212C2#1913742211yescharacteristic
1213C2#1913758811yescharacteristic
1214C2#1913759011yescharacteristic
1215C2#1913792011yescharacteristic
1216C2#1913792811yescharacteristic
1217C2#1913806911yescharacteristic
1218C2#1913807111yescharacteristic
1219C2#1913814311yescharacteristic
1220C2#1913814511yescharacteristic
1221C2#1913889911yescharacteristic
1222C2#1913948311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×C22⋊#95C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenterC22⋊#95D43
hypocenterC43#13968
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22⋊#95

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. #19132844C2semidirect
9. #19132842C2semidirect
10. #19132829C2semidirect
11. #19132826C2semidirect
12. #19132818C2semidirect
13. (C2×D43)⋊#95C2semidirect
14. (C2×D43)⋊#95C2semidirect
15. C43×C22⋊#95C2semidirect
22. C2×#13063307C4semidirect
94. C22×C4×D43C2×C4semidirect
100. C2×C4⋊Dic43C2×C4semidirect
106. C2×Dic43⋊C4C2×C4semidirect
115. C2×C22⋊Dic43C2×C4semidirect
123. C2×(C2×D43)⋊C4C2×C4semidirect
161. C2×C22⋊C4×C43C2×C4semidirect
462. C2×C4×C43#123semidirect
609. C22⋊#95D43semidirect
671. C43#13968semidirect
756. C2×C22⋊C4C4×D43semidirect
1127. C2×C4#13063307semidirect

Maximal subgroups

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

subgroupindex
C22×#130633072
C22×C4×C22⋊D432
C2×#145827752
C2×#145827612
C2×#95×D432
#191328472
#191328462
#191328442
#191328422
#191328292
#191328262
#191328182
(C2×D43)⋊#952
C43×C22⋊#952
#1396843