Finite Group Databasebeta

← #25019717

Subgroups — #25019717

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×#14582770C211yesmaximal, characteristic, complemented
5C2×#14582761C211yesmaximal, characteristic, complemented
6C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
7C2×#95×D43C211yesmaximal, characteristic, complemented
8#19132863C211yesmaximal, characteristic, complemented
9#19132861C211yesmaximal, characteristic, complemented
10#19132839C211yesmaximal, characteristic, complemented
11#19132837C211yesmaximal, characteristic, complemented
12#19132833C211yesmaximal, characteristic, complemented
13#19132831C211yesmaximal, characteristic, complemented
14Dic43⋊#95C211yesmaximal, characteristic, complemented
15C43×C4⋊#95C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C2×#13063310—24no—
21C2×#13063310—24no—
22C2×#13063310C418yescomplemented
23C22×Dic43⋊C4C2211yescharacteristic
24C22×Dic43⋊C4C2211yescharacteristic
25C22×(C2×D43)⋊C4C2211yescharacteristic
26C22×(C2×D43)⋊C4C2211yescharacteristic
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×C4×Dic43C2211yescharacteristic
35#14582777—24no—
36#14582777—24no—
37#14582770—24no—
38#14582761—24no—
39C4×(C2×D43)⋊C4—24no—
40C2×C43⋊#95C2211yescharacteristic
41C2×C43⋊#95C2211yescharacteristic
42C2×C43⋊#95C2211yescharacteristic
43C2×C43⋊#95C2211yescharacteristic
44C2×C43⋊#95C2211yescharacteristic
45C2×C43⋊#95C2211yescharacteristic
46C2×C43⋊#95C2211yescharacteristic
47C2×C43⋊#95C2211yescharacteristic
48C2×C43⋊#95C2211yescharacteristic
49C2×C43⋊#95C2211yescharacteristic
50C2×C43⋊#95C2211yescharacteristic
51C2×C43⋊#95C2211yescharacteristic
52#95×D43—24no—
53C22×C4⋊C4×C43C2211yescharacteristic
54C22×C4⋊C4×C43C2211yescharacteristic
55C22×C42×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×Dic43⋊C4—22no—
98C2×Dic43⋊C4—22no—
99C2×Dic43⋊C4—22no—
100C2×Dic43⋊C4—22no—
101C2×Dic43⋊C4—41no—
102C2×Dic43⋊C4C2×C414yescomplemented
103C2×(C2×D43)⋊C4—22no—
104C2×(C2×D43)⋊C4—22no—
105C2×(C2×D43)⋊C4—22no—
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—41no—
121C2×(C2×D43)⋊C4—41no—
122C2×(C2×D43)⋊C4—41no—
123C2×(C2×D43)⋊C4—41no—
124C2×(C2×D43)⋊C4C2×C414yes—
125C2×(C2×D43)⋊C4C2×C414yescomplemented
126C2×(C2×D43)⋊C4C2×C414yescomplemented
127C2×(C2×D43)⋊C4D414yes—
128C2×(C2×D43)⋊C4D414yes—
129C2×(C2×D43)⋊C4D414yes—
130C2×C4×Dic43—22no—
131C2×C4×Dic43—22no—
132C2×C4×Dic43—41no—
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—22no—
144C43⋊#95—22no—
145C23×C4×C43C2311yescharacteristic
146C23×C4×C43C2311yescharacteristic
147C23×C4×C43C2311yescharacteristic
148C23×C4×C43C2311yescharacteristic
149C23×C4×C43C2311yescharacteristic
150C23×C4×C43C2311yescharacteristic
151C23×C4×C43C2311yescharacteristic
152C2×C4⋊C4×C43—22no—
153C2×C4⋊C4×C43—22no—
154C2×C4⋊C4×C43—22no—
155C2×C4⋊C4×C43—22no—
156C2×C4⋊C4×C43—41no—
157C2×C4⋊C4×C43C2×C414yescomplemented
158C2×C42×C43—22no—
159C2×C42×C43—22no—
160C2×C42×C43—41no—
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×C43C22×C412yes—
236C22×C4×C43C22×C412yes—
237C22×C4×C43C22×C412yes—
238C22×C4×C43C2×D412yes—
239C22×C4×C43C2×D412yes—
240C22×C4×C43C2×D412yes—
241C22×C4×C43C2×D412yes—
242C22×C4×C43#4112yes—
243C22×C4×C43#4112yes—
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×Dic43—21no—
279C22×Dic43—21no—
280C22×Dic43C22×C412yes—
281C22×Dic43C22×C412yes—
282C22×Dic43C2×D412yes—
283C22×Dic43C2×D412yes—
284C22×Dic43C2×D412yes—
285C22×Dic43C2×D412yes—
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—
316C4⋊C4×C43—44no—
317C42×C43—44no—
318(C2×D43)⋊C4—28no—
319(C2×D43)⋊C4—28no—
320(C2×D43)⋊C4—28no—
321(C2×D43)⋊C4—44no—
322(C2×D43)⋊C4—44no—
323(C2×D43)⋊C4—44no—
324(C2×D43)⋊C4—44no—
325(C2×D43)⋊C4—44no—
326(C2×D43)⋊C4C22⋊C4116yescomplemented
327Dic43⋊C4—28no—
328Dic43⋊C4—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—22no—
437C2×C4×C43—22no—
438C2×C4×C43—22no—
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×C43C2×C22⋊C414yes—
463C2×C4×C43#12314yescomplemented
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—41no—
483C2×Dic43—41no—
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×Dic43C2×C22⋊C414yes—
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—24no—
578C4×C43—42no—
579C4×C43—42no—
580C4×C43—42no—
581C4×C43—42no—
582C4×C43—81no—
583Dic43—24no—
584Dic43—42no—
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#1445—431no—
598#1439—431no—
599#1439—431no—
600#1437—431no—
601#1437—431no—
602C4⋊#95—431no—
603C4⋊#95D4311yescharacteristic, complemented
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⋊C4C2×D4311yescharacteristic
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×C42C2×D4311yescharacteristic
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—431no—
659C2×#95—431no—
660C2×#95—864no—
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—22no—
713C2×C4⋊C4—22no—
714C2×C4⋊C4—41no—
715C2×C4⋊C4—434no—
716C2×C4⋊C4—862no—
717C2×C4⋊C4—862no—
718C2×C4⋊C4—862no—
719C2×C4⋊C4—862no—
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—22no—
750C2×C42—22no—
751C2×C42—41no—
752C2×C42—862no—
753C2×C42—862no—
754C2×C42—1721no—
755#95—22no—
756#95—22no—
757#95—22no—
758#95—22no—
759#95—862no—
760#95—862no—
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—432no—
849C22×C4—432no—
850C22×C4—432no—
851C22×C4—432no—
852C22×C4—432no—
853C22×C4—432no—
854C22×C4—432no—
855C22×C4—868no—
856C22×C4—868no—
857C22×C4—868no—
858C22×C4—868no—
859C22×C4—868no—
860C22×C4—861no—
861C22×C4—861no—
862C22×C4—861no—
863C22×C4—861no—
864C22×C4—861no—
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—868no—
889C22×C4—861no—
890C22×C4—861no—
891C22×C4—861no—
892C22×C4—861no—
893C22×C4—861no—
894C22×C4—861no—
895C22×C4—861no—
896C22×C4—1724no—
897C22×C4—1724no—
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×C4C2×C4×D4312yes—
912C22×C4C2×C4×D4312yes—
913C22×C4C2×C4×D4312yes—
914C22×C4#1062189812yes—
915C22×C4#1062189812yes—
916C22×C4D4×D4312yes—
917C22×C4D4×D4312yes—
918C22×C4D4×D4312yes—
919C22×C4D4×D4312yes—
920C22×C4#1062190212yes—
921C4⋊C4—28no—
922C4⋊C4—44no—
923C4⋊C4—868no—
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—44no—
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
1014C23C2×#1062189811yescharacteristic
1015C23C2×#1062189811yescharacteristic
1016C23C2×#1062190211yescharacteristic
1017C23#1306337011yescharacteristic
1018C23#1306337111yescharacteristic
1019C23#1306337311yescharacteristic
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—22no—
1044C2×C4—22no—
1045C2×C4—22no—
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—434no—
1070C2×C4—862no—
1071C2×C4—862no—
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—17216no—
1089C2×C4—17216no—
1090C2×C4—17216no—
1091C2×C4—1721no—
1092C2×C4—1721no—
1093C2×C4—1721no—
1094C2×C4—1721no—
1095C2×C4—1721no—
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×C4C22⋊C4×D4314yes—
1115C2×C4#1306331014yescomplemented
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
1149C22C4×#1062189811yescharacteristic
1150C22C4×#1062190211yescharacteristic
1151C22#1458338011yescharacteristic
1152C22#1458338111yescharacteristic
1153C22#121×D4311yescharacteristic
1154C22#121×D4311yescharacteristic
1155C22C2×#1306331011yescharacteristic
1156C22#1458340811yescharacteristic
1157C22#124×D4311yescharacteristic
1158C22#1458342711yescharacteristic
1159C22#1458343611yescharacteristic
1160C22#127×D4311yescharacteristic
1161C22#1458345711yescharacteristic
1162C22#1458347411yescharacteristic
1163C22#1458349511yescharacteristic
1164C22#1458349711yescharacteristic
1165C22#1458353811yescharacteristic
1166C22#1458353911yescharacteristic
1167C22#1458353911yescharacteristic
1168C22#1458354011yescharacteristic
1169C22#1458354211yescharacteristic
1170C22#1458354511yescharacteristic
1171C22#1458355011yescharacteristic
1172C22#1458355011yescharacteristic
1173C22#1458355011yescharacteristic
1174C22#1458355111yescharacteristic
1175C22#1458355211yescharacteristic
1176C22#1458355211yescharacteristic
1177C22#1458357311yescharacteristic
1178C22#1458357611yescharacteristic
1179C22#1458358111yescharacteristic
1180C22#1458359011yescharacteristic
1181C4—24no—
1182C4—24no—
1183C4—42no—
1184C4—42no—
1185C4—42no—
1186C4—42no—
1187C4—81no—
1188C4—864no—
1189C4—3441no—
1190C4—1722no—
1191C4—1722no—
1192C4—1722no—
1193C4—1722no—
1194C2—868no—
1195C2—3442no—
1196C2#390×D4311yescharacteristic
1197C2C4×#1306331011yescharacteristic
1198C2#1913725911yescharacteristic
1199C2#1913742211yescharacteristic
1200C2#1913742411yescharacteristic
1201C2#1913758211yescharacteristic
1202C2#1913759211yescharacteristic
1203C2#1913798811yescharacteristic
1204C2#1913799911yescharacteristic
1205C2#1913814311yescharacteristic
1206C2#1913815311yescharacteristic
1207C2#1913891811yescharacteristic
1208C2#1913892811yescharacteristic
1209C2#1913906311yescharacteristic
1210C2#1913952411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×C4⋊#95C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenterC4⋊#95D43
hypocenterC43#13996
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#14582770C2semidirect
5. C2×#14582761C2semidirect
6. C2×C4×(C2×D43)⋊C4C2semidirect
7. C2×#95×D43C2semidirect
8. #19132863C2semidirect
9. #19132861C2semidirect
10. #19132839C2semidirect
11. #19132837C2semidirect
12. #19132833C2semidirect
13. #19132831C2semidirect
14. Dic43⋊#95C2semidirect
15. C43×C4⋊#95C2semidirect
22. C2×#13063310C4semidirect
102. C2×Dic43⋊C4C2×C4semidirect
125. C2×(C2×D43)⋊C4C2×C4semidirect
126. C2×(C2×D43)⋊C4C2×C4semidirect
157. C2×C4⋊C4×C43C2×C4semidirect
326. (C2×D43)⋊C4C22⋊C4semidirect
463. C2×C4×C43#123semidirect
603. C4⋊#95D43semidirect
665. C43#13996semidirect
721. C2×C4⋊C4C4×D43semidirect
1115. 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
C2×#145827772
C2×#145827702
C2×#145827612
C2×C4×(C2×D43)⋊C42
C2×#95×D432
#191328632
#191328612
#191328392
#191328372
#191328332
#191328312
Dic43⋊#952
C43×C4⋊#952
#1399643