Finite Group Databasebeta

← #25019715

Subgroups — #25019715

Order 11008.

2474 conjugacy classes of subgroups.

The subgroup lattice has 1212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063310C211yesmaximal, characteristic
2C2×#14582777C211yesmaximal, characteristic
3C2×#14582777C211yesmaximal, characteristic
4C2×#14582773C211yesmaximal, characteristic, complemented
5C2×#14582761C211yesmaximal, characteristic, complemented
6C2×#14582746C211yesmaximal, characteristic, complemented
7C2×#95×D43C211yesmaximal, characteristic, complemented
8#19132861C211yesmaximal, characteristic, complemented
9#19132841C211yesmaximal, characteristic, complemented
10#19132839C211yesmaximal, characteristic, complemented
11#19132831C211yesmaximal, characteristic, complemented
12#19132831C211yesmaximal, characteristic, complemented
13#19132824C211yesmaximal, characteristic, complemented
14Dic43⋊#95C211yesmaximal, characteristic, complemented
15C43×#1445C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C2×#13063310—24no—
21C2×#13063310—24no—
22C2×#13063310C418yescomplemented
23C22×C4⋊Dic43C2211yescharacteristic
24C22×Dic43⋊C4C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×(C2×D43)⋊C4C2211yescharacteristic
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×(C2×D43)⋊C4C2211yescharacteristic
35C22×C4×Dic43C2211yescharacteristic
36C22×C4×Dic43C2211yescharacteristic
37#14582777—24no—
38#14582777—24no—
39#14582773—24no—
40#14582761—24no—
41#14582746—24no—
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
54C2×#95×C43C2211yescharacteristic
55C2×#95×C43C2211yescharacteristic
56C2×#95×C43C2211yescharacteristic
57C2×#95×C43C2211yescharacteristic
58C2×#95×C43C2211yescharacteristic
59C2×#95×C43C2211yescharacteristic
60C24×D43C2311yescharacteristic
61C24×D43C2311yescharacteristic
62C22×D172—22no—
63C22×D172—22no—
64C22×D172—22no—
65C22×D172—22no—
66C22×D172—22no—
67C22×D172—22no—
68C22×D172C2×C414yes—
69C23×Dic43C2311yescharacteristic
70C23×Dic43C2311yescharacteristic
71C23×Dic43C2311yescharacteristic
72C23×Dic43C2311yescharacteristic
73C23×Dic43C2311yescharacteristic
74C23×Dic43C2311yescharacteristic
75C22×C4×D43—22no—
76C22×C4×D43—22no—
77C22×C4×D43—22no—
78C22×C4×D43—22no—
79C22×C4×D43—22no—
80C22×C4×D43—22no—
81C22×C4×D43—22no—
82C22×C4×D43—22no—
83C22×C4×D43—22no—
84C22×C4×D43—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×C414yes—
95C22×C4×D43D414yes—
96#13063310—232no—
97C2×C4⋊Dic43—22no—
98C2×C4⋊Dic43—22no—
99C2×C4⋊Dic43—41no—
100C2×Dic43⋊C4—22no—
101C2×Dic43⋊C4—22no—
102C2×Dic43⋊C4—22no—
103C2×Dic43⋊C4—22no—
104C2×Dic43⋊C4—41no—
105C2×Dic43⋊C4C2×C414yescomplemented
106C2×(C2×D43)⋊C4—22no—
107C2×(C2×D43)⋊C4—22no—
108C2×(C2×D43)⋊C4—22no—
109C2×(C2×D43)⋊C4—22no—
110C2×(C2×D43)⋊C4—22no—
111C2×(C2×D43)⋊C4—22no—
112C2×(C2×D43)⋊C4—22no—
113C2×(C2×D43)⋊C4—22no—
114C2×(C2×D43)⋊C4—22no—
115C2×(C2×D43)⋊C4—22no—
116C2×(C2×D43)⋊C4—22no—
117C2×(C2×D43)⋊C4—22no—
118C2×(C2×D43)⋊C4—22no—
119C2×(C2×D43)⋊C4—22no—
120C2×(C2×D43)⋊C4—22no—
121C2×(C2×D43)⋊C4—22no—
122C2×(C2×D43)⋊C4—22no—
123C2×(C2×D43)⋊C4—41no—
124C2×(C2×D43)⋊C4—41no—
125C2×(C2×D43)⋊C4—41no—
126C2×(C2×D43)⋊C4—41no—
127C2×(C2×D43)⋊C4C2×C414yes—
128C2×(C2×D43)⋊C4C2×C414yescomplemented
129C2×(C2×D43)⋊C4C2×C414yescomplemented
130C2×(C2×D43)⋊C4D414yes—
131C2×(C2×D43)⋊C4D414yes—
132C2×(C2×D43)⋊C4D414yes—
133C2×C4×Dic43—22no—
134C2×C4×Dic43—22no—
135C2×C4×Dic43—22no—
136C2×C4×Dic43—22no—
137C2×C4×Dic43—41no—
138C2×C4×Dic43—41no—
139C43⋊#95—22no—
140C43⋊#95—22no—
141C43⋊#95—22no—
142C43⋊#95—22no—
143C43⋊#95—22no—
144C43⋊#95—22no—
145C43⋊#95—22no—
146C43⋊#95—22no—
147C43⋊#95—22no—
148C43⋊#95—22no—
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×C43C2×C414yescomplemented
159#95×C43—22no—
160#95×C43—22no—
161#95×C43—22no—
162#95×C43—22no—
163#95×C43—22no—
164#95×C43—22no—
165C24×C43C2411yescharacteristic
166C23×D43—21no—
167C23×D43—21no—
168C23×D43—21no—
169C23×D43—21no—
170C23×D43—21no—
171C23×D43—21no—
172C23×D43—21no—
173C23×D43—21no—
174C23×D43—21no—
175C23×D43—21no—
176C23×D43—21no—
177C23×D43—21no—
178C23×D43—21no—
179C23×D43—21no—
180C23×D43—21no—
181C23×D43—21no—
182C23×D43—21no—
183C23×D43—21no—
184C23×D43—21no—
185C23×D43—21no—
186C23×D43—21no—
187C23×D43—21no—
188C23×D43C22×C412yes—
189C23×D43C22×C412yes—
190C23×D43C2×D412yes—
191C23×D43C2×D412yes—
192C23×D43C2×D412yes—
193C23×D43C2×D412yes—
194C23×D43#4112yes—
195C23×D43#4112yes—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43—21no—
230C22×C4×C43—21no—
231C22×C4×C43—21no—
232C22×C4×C43—21no—
233C22×C4×C43—21no—
234C22×C4×C43—21no—
235C22×C4×C43—21no—
236C22×C4×C43—21no—
237C22×C4×C43C22×C412yes—
238C22×C4×C43C22×C412yes—
239C22×C4×C43C22×C412yes—
240C22×C4×C43C2×D412yes—
241C22×C4×C43C2×D412yes—
242C22×C4×C43C2×D412yes—
243C22×C4×C43C2×D412yes—
244C22×C4×C43#4112yes—
245C22×Dic43—21no—
246C22×Dic43—21no—
247C22×Dic43—21no—
248C22×Dic43—21no—
249C22×Dic43—21no—
250C22×Dic43—21no—
251C22×Dic43—21no—
252C22×Dic43—21no—
253C22×Dic43—21no—
254C22×Dic43—21no—
255C22×Dic43—21no—
256C22×Dic43—21no—
257C22×Dic43—21no—
258C22×Dic43—21no—
259C22×Dic43—21no—
260C22×Dic43—21no—
261C22×Dic43—21no—
262C22×Dic43—21no—
263C22×Dic43—21no—
264C22×Dic43—21no—
265C22×Dic43—21no—
266C22×Dic43—21no—
267C22×Dic43—21no—
268C22×Dic43—21no—
269C22×Dic43—21no—
270C22×Dic43—21no—
271C22×Dic43—21no—
272C22×Dic43—21no—
273C22×Dic43—21no—
274C22×Dic43—21no—
275C22×Dic43—21no—
276C22×Dic43—21no—
277C22×Dic43—21no—
278C22×Dic43C22×C412yes—
279C22×Dic43C22×C412yes—
280C22×Dic43C2×D412yes—
281C22×Dic43C2×D412yes—
282C22×Dic43C2×D412yes—
283C22×Dic43C2×D412yes—
284C22×Dic43#4112yes—
285C22×Dic43#4112yes—
286C22×Dic43#4112yes—
287C2×D172—28no—
288C2×D172—28no—
289C2×D172—28no—
290C2×D172—44no—
291C2×D172—44no—
292C2×D172—44no—
293C2×D172—44no—
294C2×C4×D43—28no—
295C2×C4×D43—28no—
296C2×C4×D43—28no—
297C2×C4×D43—28no—
298C2×C4×D43—28no—
299C2×C4×D43—28no—
300C2×C4×D43—44no—
301C2×C4×D43—44no—
302C2×C4×D43—44no—
303C2×C4×D43—44no—
304C2×C4×D43—44no—
305C2×C4×D43—44no—
306C2×C4×D43—44no—
307C2×C4×D43—44no—
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—
315C4⋊C4×C43—28no—
316(C2×D43)⋊C4—28no—
317(C2×D43)⋊C4—28no—
318(C2×D43)⋊C4—28no—
319(C2×D43)⋊C4—44no—
320(C2×D43)⋊C4—44no—
321(C2×D43)⋊C4—44no—
322(C2×D43)⋊C4—44no—
323(C2×D43)⋊C4—44no—
324(C2×D43)⋊C4C22⋊C4116yescomplemented
325C4⋊Dic43—44no—
326Dic43⋊C4—28no—
327Dic43⋊C4—44no—
328C4×Dic43—44no—
329C4×Dic43—44no—
330C23×C43C23×C411yescharacteristic
331C23×C43C22×D411yescharacteristic
332C23×C43C22×D411yescharacteristic
333C23×C43C22×D411yescharacteristic
334C23×C43C22×D411yescharacteristic
335C23×C43C2×#4111yescharacteristic
336C23×C43C2×#4111yescharacteristic
337C23×C43C2×#4111yescharacteristic
338C23×C43C2×#4111yescharacteristic
339C23×C43C2×#4111yescharacteristic
340C23×C43C2×#4111yescharacteristic
341C23×C43H(5,𝔽2)11yescharacteristic
342C23×C43H(5,𝔽2)11yescharacteristic
343C23×C432−1+411yescharacteristic
344C23×C432−1+411yescharacteristic
345C22×D43—22no—
346C22×D43—22no—
347C22×D43—22no—
348C22×D43—22no—
349C22×D43—22no—
350C22×D43—22no—
351C22×D43—22no—
352C22×D43—22no—
353C22×D43—22no—
354C22×D43—22no—
355C22×D43—22no—
356C22×D43—22no—
357C22×D43—22no—
358C22×D43—22no—
359C22×D43—22no—
360C22×D43—22no—
361C22×D43—22no—
362C22×D43—22no—
363C22×D43—22no—
364C22×D43—22no—
365C22×D43—22no—
366C22×D43—22no—
367C22×D43—22no—
368C22×D43—22no—
369C22×D43—22no—
370C22×D43—22no—
371C22×D43—22no—
372C22×D43—22no—
373C22×D43—22no—
374C22×D43—22no—
375C22×D43—22no—
376C22×D43—22no—
377C22×D43—22no—
378C22×D43—22no—
379C22×D43—22no—
380C22×D43—41no—
381C22×D43—41no—
382C22×D43—41no—
383C22×D43—41no—
384C22×D43—41no—
385C22×D43—41no—
386C22×D43—41no—
387C22×D43—41no—
388C22×D43—41no—
389C22×D43—41no—
390C22×D43—41no—
391C22×D43—41no—
392C22×D43—41no—
393C22×D43—41no—
394C22×D43—41no—
395C22×D43—41no—
396C22×D43—41no—
397C22×D43—41no—
398C22×D43—41no—
399C22×D43—41no—
400C22×D43—41no—
401C22×D43—41no—
402C22×D43—41no—
403C22×D43—41no—
404C22×D43—41no—
405C22×D43—41no—
406C22×D43—41no—
407C22×D43—41no—
408C22×D43C2×C22⋊C414yes—
409C22×D43C4×D414yes—
410C22×D43C4×D414yes—
411C22×D43#12114yes—
412C22×D43#12114yes—
413C22×D43#12414yes—
414C22×D43#12714yes—
415C2×C4×C43—22no—
416C2×C4×C43—22no—
417C2×C4×C43—22no—
418C2×C4×C43—22no—
419C2×C4×C43—22no—
420C2×C4×C43—22no—
421C2×C4×C43—22no—
422C2×C4×C43—22no—
423C2×C4×C43—22no—
424C2×C4×C43—22no—
425C2×C4×C43—22no—
426C2×C4×C43—22no—
427C2×C4×C43—22no—
428C2×C4×C43—22no—
429C2×C4×C43—22no—
430C2×C4×C43—22no—
431C2×C4×C43—22no—
432C2×C4×C43—22no—
433C2×C4×C43—22no—
434C2×C4×C43—22no—
435C2×C4×C43—22no—
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—
462C2×C4×C43—41no—
463C2×C4×C43C2×C22⋊C414yes—
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×Dic43C2×C22⋊C414yes—
505C2×Dic43#12314yescomplemented
506D172—416no—
507C4×D43—416no—
508C4×D43—416no—
509C4×D43—416no—
510#13996—431nomaximal, Sylow
511C22×C43C22×C22⋊C411yescharacteristic
512C22×C43C2×C4×D411yescharacteristic
513C22×C43C2×C4×D411yescharacteristic
514C22×C43C4×#4111yescharacteristic
515C22×C43C4×#4111yescharacteristic
516C22×C43#52011yescharacteristic
517C22×C43#52011yescharacteristic
518C22×C43C2×#12111yescharacteristic
519C22×C43C2×#12111yescharacteristic
520C22×C43C2×#12311yescharacteristic
521C22×C43#52511yescharacteristic
522C22×C43C2×#12411yescharacteristic
523C22×C43#52911yescharacteristic
524C22×C43#52911yescharacteristic
525C22×C43C2×#12711yescharacteristic
526C22×C43#53411yescharacteristic
527C22×C43#53611yescharacteristic
528C22×C43#53911yescharacteristic
529C22×C43#53911yescharacteristic
530C22×C43#54611yescharacteristic
531C22×C43#54611yescharacteristic
532C22×C43#54611yescharacteristic
533C22×C43#54611yescharacteristic
534C22×C43#54611yescharacteristic
535C22×C43#54611yescharacteristic
536C22×C43#54711yescharacteristic
537C22×C43#54711yescharacteristic
538C22×C43#54711yescharacteristic
539C22×C43#54711yescharacteristic
540C22×C43#54711yescharacteristic
541C22×C43#54711yescharacteristic
542C22×C43#55111yescharacteristic
543C22×C43#55111yescharacteristic
544C22×C43#55211yescharacteristic
545C22×C43#55211yescharacteristic
546C2×D43—24no—
547C2×D43—24no—
548C2×D43—24no—
549C2×D43—24no—
550C2×D43—24no—
551C2×D43—24no—
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—42no—
561C2×D43—42no—
562C2×D43—42no—
563C2×D43—42no—
564C2×D43—42no—
565C2×D43—42no—
566C2×D43—42no—
567C2×D43—81no—
568C2×D43—81no—
569C2×D43—81no—
570C2×D43—81no—
571C2×D43—81no—
572C2×D43—81no—
573C2×D43—81no—
574C2×D43—81no—
575C2×D43#39018yes—
576C4×C43—24no—
577C4×C43—42no—
578C4×C43—42no—
579C4×C43—42no—
580C4×C43—42no—
581C4×C43—42no—
582C4×C43—81no—
583Dic43—24no—
584Dic43—24no—
585Dic43—42no—
586Dic43—42no—
587Dic43—42no—
588Dic43—81no—
589C22×#123—431no—
590C2×#386—431no—
591C2×#386—431no—
592C2×#385—431no—
593C2×#381—431no—
594C2×C4×C22⋊C4—431no—
595C22×#95—431no—
596#1445—431no—
597#1445D4311yescharacteristic, complemented
598#1439—431no—
599#1439—431no—
600#1437—431no—
601#1437—431no—
602C4⋊#95—431no—
603C4⋊#95—431no—
604C2×C43C2×#39011yescharacteristic
605C2×C43C4×#12311yescharacteristic
606C2×C43#232211yescharacteristic
607C2×C43#233911yescharacteristic
608C2×C43#233911yescharacteristic
609C2×C43#235911yescharacteristic
610C2×C43#235911yescharacteristic
611C2×C43#241211yescharacteristic
612C2×C43#241311yescharacteristic
613C2×C43#242511yescharacteristic
614C2×C43#242511yescharacteristic
615C2×C43#248811yescharacteristic
616C2×C43#248811yescharacteristic
617C2×C43#250111yescharacteristic
618C2×C43#253911yescharacteristic
619D43—28no—
620D43—82no—
621C23×D4—431no—
622C24×C4—431no—
623C24×C4—431no—
624C24×C4—431no—
625C2×#123—438no—
626C2×#123—864no—
627C2×#123—864no—
628C22×C4⋊C4—431no—
629C22×C4⋊C4—431no—
630C22×C4⋊C4—431no—
631C22×C4⋊C4C2×D4311yescharacteristic
632C22×C22⋊C4—431no—
633C22×C22⋊C4—431no—
634C22×C22⋊C4—431no—
635C22×C22⋊C4—431no—
636C22×C22⋊C4—431no—
637C22×C22⋊C4—431no—
638C22×C22⋊C4—431no—
639C22×C22⋊C4—431no—
640C22×C22⋊C4—431no—
641C22×C42—431no—
642C22×C42—431no—
643#386—864no—
644#386—864no—
645#385—864no—
646#381—864no—
647C4×C22⋊C4—864no—
648C2×#95—431no—
649C2×#95—431no—
650C2×#95—431no—
651C2×#95—431no—
652C2×#95—431no—
653C2×#95—431no—
654C2×#95—431no—
655C2×#95—431no—
656C2×#95—431no—
657C2×#95—431no—
658C2×#95—864no—
659C2×#95C2×D4311yescharacteristic
660C2×#95C2×D4311yescharacteristic
661C2×#95C2×D4311yescharacteristic
662C2×#95C2×D4311yescharacteristic
663C2×#95C2×D4311yescharacteristic
664C2×#95C2×D4311yescharacteristic
665C43#1399611yescharacteristic, complemented, Sylow
666C25—431no—
667C25—431no—
668C22×D4—434no—
669C22×D4—862no—
670C22×D4—862no—
671C22×D4—862no—
672C22×D4—862no—
673C22×D4—862no—
674C22×D4—862no—
675C23×C4—431no—
676C23×C4—431no—
677C23×C4—431no—
678C23×C4—431no—
679C23×C4—431no—
680C23×C4—434no—
681C23×C4—434no—
682C23×C4—431no—
683C23×C4—862no—
684C23×C4—862no—
685C23×C4—862no—
686C23×C4—862no—
687C23×C4—862no—
688C23×C4—862no—
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—1721no—
699C23×C4—1721no—
700C23×C4—1721no—
701C23×C4—1721no—
702C23×C4C22×D4311yescharacteristic
703C23×C4C22×D4311yescharacteristic
704C23×C4C22×D4311yescharacteristic
705C23×C4C22×D4311yescharacteristic
706C23×C4C22×D4311yescharacteristic
707C23×C4C22×D4311yescharacteristic
708C23×C4C22×D4311yescharacteristic
709#123—8632no—
710C2×C4⋊C4—22no—
711C2×C4⋊C4—22no—
712C2×C4⋊C4—434no—
713C2×C4⋊C4—862no—
714C2×C4⋊C4—862no—
715C2×C4⋊C4—862no—
716C2×C4⋊C4—862no—
717C2×C4⋊C4—862no—
718C2×C4⋊C4—862no—
719C2×C4⋊C4—1721no—
720C2×C4⋊C4—1721no—
721C2×C4⋊C4C4×D4314yescomplemented
722C2×C22⋊C4—434no—
723C2×C22⋊C4—434no—
724C2×C22⋊C4—434no—
725C2×C22⋊C4—434no—
726C2×C22⋊C4—434no—
727C2×C22⋊C4—434no—
728C2×C22⋊C4—862no—
729C2×C22⋊C4—862no—
730C2×C22⋊C4—862no—
731C2×C22⋊C4—862no—
732C2×C22⋊C4—862no—
733C2×C22⋊C4—862no—
734C2×C22⋊C4—862no—
735C2×C22⋊C4—862no—
736C2×C22⋊C4—862no—
737C2×C22⋊C4—862no—
738C2×C22⋊C4—862no—
739C2×C22⋊C4—862no—
740C2×C22⋊C4—862no—
741C2×C22⋊C4—862no—
742C2×C22⋊C4—862no—
743C2×C22⋊C4—862no—
744C2×C22⋊C4—862no—
745C2×C22⋊C4—1721no—
746C2×C22⋊C4—1721no—
747C2×C22⋊C4—1721no—
748C2×C22⋊C4—1721no—
749C2×C42—862no—
750C2×C42—862no—
751C2×C42—862no—
752C2×C42—862no—
753C2×C42—1721no—
754C2×C42—1721no—
755#95—22no—
756#95—22no—
757#95—22no—
758#95—22no—
759#95—22no—
760#95—22no—
761#95—862no—
762#95—862no—
763#95—862no—
764#95—862no—
765#95—862no—
766#95—862no—
767#95—862no—
768#95—862no—
769#95—862no—
770#95—862no—
771C24—432no—
772C24—432no—
773C24—432no—
774C24—432no—
775C24—432no—
776C24—432no—
777C24—432no—
778C24—432no—
779C24—861no—
780C24—861no—
781C24—861no—
782C24—861no—
783C24—861no—
784C24—861no—
785C24—861no—
786C24—861no—
787C24—861no—
788C24—861no—
789C24—861no—
790C24—861no—
791C24—861no—
792C24—861no—
793C24—861no—
794C24—861no—
795C24—861no—
796C24—861no—
797C24—861no—
798C24—861no—
799C24—861no—
800C24—861no—
801C24C23×D4311yescharacteristic
802C2×D4—868no—
803C2×D4—868no—
804C2×D4—868no—
805C2×D4—1724no—
806C2×D4—1724no—
807C2×D4—1724no—
808C2×D4—1724no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—432no—
851C22×C4—432no—
852C22×C4—432no—
853C22×C4—432no—
854C22×C4—432no—
855C22×C4—432no—
856C22×C4—432no—
857C22×C4—432no—
858C22×C4—432no—
859C22×C4—868no—
860C22×C4—868no—
861C22×C4—868no—
862C22×C4—868no—
863C22×C4—868no—
864C22×C4—868no—
865C22×C4—861no—
866C22×C4—861no—
867C22×C4—861no—
868C22×C4—861no—
869C22×C4—861no—
870C22×C4—861no—
871C22×C4—861no—
872C22×C4—861no—
873C22×C4—861no—
874C22×C4—861no—
875C22×C4—861no—
876C22×C4—861no—
877C22×C4—861no—
878C22×C4—861no—
879C22×C4—861no—
880C22×C4—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—1724no—
899C22×C4—1724no—
900C22×C4—1724no—
901C22×C4—1724no—
902C22×C4—1724no—
903C22×C4—1724no—
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×C4C2×C4×D4312yes—
914C22×C4C2×C4×D4312yes—
915C22×C4C2×C4×D4312yes—
916C22×C4D4×D4312yes—
917C22×C4D4×D4312yes—
918C22×C4D4×D4312yes—
919C22×C4D4×D4312yes—
920C22×C4#1062190212yes—
921C4⋊C4—28no—
922C4⋊C4—868no—
923C4⋊C4—1724no—
924C4⋊C4—1724no—
925C22⋊C4—4316no—
926C22⋊C4—868no—
927C22⋊C4—868no—
928C22⋊C4—868no—
929C22⋊C4—1724no—
930C22⋊C4—1724no—
931C22⋊C4—1724no—
932C22⋊C4—1724no—
933C22⋊C4—1724no—
934C42—1724no—
935C42—1724no—
936C23—434no—
937C23—434no—
938C23—434no—
939C23—434no—
940C23—434no—
941C23—434no—
942C23—434no—
943C23—862no—
944C23—862no—
945C23—862no—
946C23—862no—
947C23—862no—
948C23—862no—
949C23—862no—
950C23—862no—
951C23—862no—
952C23—862no—
953C23—862no—
954C23—862no—
955C23—862no—
956C23—862no—
957C23—862no—
958C23—862no—
959C23—862no—
960C23—862no—
961C23—862no—
962C23—862no—
963C23—862no—
964C23—862no—
965C23—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—1721no—
979C23—1721no—
980C23—1721no—
981C23—1721no—
982C23—1721no—
983C23—1721no—
984C23—1721no—
985C23—1721no—
986C23—1721no—
987C23—1721no—
988C23—1721no—
989C23—1721no—
990C23—1721no—
991C23—1721no—
992C23—1721no—
993C23—1721no—
994C23—1721no—
995C23—1721no—
996C23—1721no—
997C23—1721no—
998C23—1721no—
999C23—1721no—
1000C23—1721no—
1001C23—1721no—
1002C23—1721no—
1003C23—1721no—
1004C23—1721no—
1005C23—1721no—
1006C23C22×C4×D4311yescharacteristic
1007C23C2×D4×D4311yescharacteristic
1008C23C2×D4×D4311yescharacteristic
1009C23C2×D4×D4311yescharacteristic
1010C23C2×D4×D4311yescharacteristic
1011C23#41×D4311yescharacteristic
1012C23#41×D4311yescharacteristic
1013C23#41×D4311yescharacteristic
1014C23#41×D4311yescharacteristic
1015C23#41×D4311yescharacteristic
1016C23C2×#1062190211yescharacteristic
1017C23#1306337111yescharacteristic
1018C23#1306337111yescharacteristic
1019C23#1306337211yescharacteristic
1020C23#1306337311yescharacteristic
1021D4—17216no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—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—434no—
1071C2×C4—434no—
1072C2×C4—862no—
1073C2×C4—862no—
1074C2×C4—862no—
1075C2×C4—862no—
1076C2×C4—862no—
1077C2×C4—862no—
1078C2×C4—862no—
1079C2×C4—862no—
1080C2×C4—862no—
1081C2×C4—862no—
1082C2×C4—862no—
1083C2×C4—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—17216no—
1094C2×C4—17216no—
1095C2×C4—17216no—
1096C2×C4—1721no—
1097C2×C4—1721no—
1098C2×C4—1721no—
1099C2×C4—1721no—
1100C2×C4—1721no—
1101C2×C4—1721no—
1102C2×C4—1721no—
1103C2×C4—1721no—
1104C2×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×C4C22⋊C4×D4314yes—
1116C22—438no—
1117C22—864no—
1118C22—864no—
1119C22—864no—
1120C22—864no—
1121C22—864no—
1122C22—864no—
1123C22—864no—
1124C22—864no—
1125C22—864no—
1126C22—864no—
1127C22—864no—
1128C22—864no—
1129C22—864no—
1130C22—864no—
1131C22—3441no—
1132C22—3441no—
1133C22—3441no—
1134C22—3441no—
1135C22—3441no—
1136C22—3441no—
1137C22—3441no—
1138C22—3441no—
1139C22—1722no—
1140C22—1722no—
1141C22—1722no—
1142C22—1722no—
1143C22—1722no—
1144C22—1722no—
1145C22—1722no—
1146C22C2×C22⋊C4×D4311yescharacteristic
1147C22C4×D4×D4311yescharacteristic
1148C22C4×D4×D4311yescharacteristic
1149C22#1458336711yescharacteristic
1150C22C4×#1062190211yescharacteristic
1151C22#1458337911yescharacteristic
1152C22#1458338111yescharacteristic
1153C22#121×D4311yescharacteristic
1154C22#121×D4311yescharacteristic
1155C22#123×D4311yescharacteristic
1156C22#1458341211yescharacteristic
1157C22#124×D4311yescharacteristic
1158C22#1458343211yescharacteristic
1159C22#1458343411yescharacteristic
1160C22#127×D4311yescharacteristic
1161C22#1458346011yescharacteristic
1162C22#1458347211yescharacteristic
1163C22#1458349011yescharacteristic
1164C22#1458349711yescharacteristic
1165C22#1458354011yescharacteristic
1166C22#1458354011yescharacteristic
1167C22#1458354111yescharacteristic
1168C22#1458354111yescharacteristic
1169C22#1458354111yescharacteristic
1170C22#1458354211yescharacteristic
1171C22#1458354711yescharacteristic
1172C22#1458354711yescharacteristic
1173C22#1458354711yescharacteristic
1174C22#1458355111yescharacteristic
1175C22#1458355111yescharacteristic
1176C22#1458355211yescharacteristic
1177C22#1458357411yescharacteristic
1178C22#1458357411yescharacteristic
1179C22#1458358111yescharacteristic
1180C22#1458358711yescharacteristic
1181C4—24no—
1182C4—42no—
1183C4—42no—
1184C4—42no—
1185C4—42no—
1186C4—42no—
1187C4—81no—
1188C4—864no—
1189C4—864no—
1190C4—3441no—
1191C4—1722no—
1192C4—1722no—
1193C4—1722no—
1194C2—868no—
1195C2—3442no—
1196C2#390×D4311yescharacteristic
1197C2#1913711611yescharacteristic
1198C2#1913726811yescharacteristic
1199C2#1913741911yescharacteristic
1200C2#1913742411yescharacteristic
1201C2#1913758011yescharacteristic
1202C2#1913759411yescharacteristic
1203C2#1913798411yescharacteristic
1204C2#1913799511yescharacteristic
1205C2#1913813911yescharacteristic
1206C2#1913814911yescharacteristic
1207C2#1913891611yescharacteristic
1208C2#1913892211yescharacteristic
1209C2#1913906111yescharacteristic
1210C2#1913952211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1445C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenter#1445D43
hypocenterC43#13996
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1445

Complements

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

NH ≅ G/Ntype
4. C2×#14582773C2semidirect
5. C2×#14582761C2semidirect
6. C2×#14582746C2semidirect
7. C2×#95×D43C2semidirect
8. #19132861C2semidirect
9. #19132841C2semidirect
10. #19132839C2semidirect
11. #19132831C2semidirect
12. #19132831C2semidirect
13. #19132824C2semidirect
14. Dic43⋊#95C2semidirect
15. C43×#1445C2semidirect
22. C2×#13063310C4semidirect
105. C2×Dic43⋊C4C2×C4semidirect
128. C2×(C2×D43)⋊C4C2×C4semidirect
129. C2×(C2×D43)⋊C4C2×C4semidirect
158. C2×C4⋊C4×C43C2×C4semidirect
324. (C2×D43)⋊C4C22⋊C4semidirect
505. C2×Dic43#123semidirect
597. #1445D43semidirect
665. C43#13996semidirect
721. C2×C4⋊C4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C22×#130633102
C2×#145827772
C2×#145827732
C2×#145827612
C2×#145827462
C2×#95×D432
#191328612
#191328412
#191328392
#191328312
#191328242
Dic43⋊#952
C43×#14452
#1399643