Finite Group Databasebeta

← #25019719

Subgroups — #25019719

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×#13063307C211yesmaximal, characteristic
2C2×#14582775C211yesmaximal, characteristic
3C2×#14582775C211yesmaximal, characteristic
4C2×#14582773C211yesmaximal, characteristic, complemented
5C2×#14582761C211yesmaximal, characteristic, complemented
6C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
7C2×#95×D43C211yesmaximal, characteristic, complemented
8#19132864C211yesmaximal, characteristic, complemented
9#19132861C211yesmaximal, characteristic, complemented
10#19132840C211yesmaximal, characteristic, complemented
11#19132838C211yesmaximal, characteristic, complemented
12#19132832C211yesmaximal, characteristic, complemented
13#19132825C211yesmaximal, characteristic, complemented
14Dic43⋊#95C211yesmaximal, characteristic, complemented
15C43×#1437C211yesmaximal, characteristic, complemented
16C23×C22⋊D43C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C2×#13063307—24no—
21C2×#13063307—24no—
22C2×#13063307C418yescomplemented
23C22×C4⋊Dic43C2211yescharacteristic
24C22×C4⋊Dic43C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×Dic43⋊C4C2211yescharacteristic
27C22×C22⋊Dic43C2211yescharacteristic
28C22×C22⋊Dic43C2211yescharacteristic
29C22×C22⋊Dic43C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×C4×Dic43C2211yescharacteristic
34#14582775—24no—
35#14582775—24no—
36#14582773—24no—
37#14582761—24no—
38C4×(C2×D43)⋊C4—24no—
39C2×C43⋊#95C2211yescharacteristic
40C2×C43⋊#95C2211yescharacteristic
41C2×C43⋊#95C2211yescharacteristic
42C2×C43⋊#95C2211yescharacteristic
43C2×C43⋊#95C2211yescharacteristic
44C2×C43⋊#95C2211yescharacteristic
45C2×C43⋊#95C2211yescharacteristic
46C2×C43⋊#95C2211yescharacteristic
47C2×C43⋊#95C2211yescharacteristic
48C2×C43⋊#95C2211yescharacteristic
49C2×C43⋊#95C2211yescharacteristic
50C2×C43⋊#95C2211yescharacteristic
51C2×C43⋊#95C2211yescharacteristic
52#95×D43—24no—
53C22×C22⋊C4×C43C2211yescharacteristic
54C22×C22⋊C4×C43C2211yescharacteristic
55C22×C22⋊C4×C43C2211yescharacteristic
56C22×C42×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⋊D43—22no—
66C22×C22⋊D43—22no—
67C22×C22⋊D43C2×C414yes—
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×C414yes—
95C22×C4×D43D414yes—
96#13063307—232no—
97C2×C4⋊Dic43—22no—
98C2×C4⋊Dic43—22no—
99C2×C4⋊Dic43—22no—
100C2×C4⋊Dic43—22no—
101C2×C4⋊Dic43—41no—
102C2×C4⋊Dic43C2×C414yescomplemented
103C2×Dic43⋊C4—22no—
104C2×Dic43⋊C4—22no—
105C2×Dic43⋊C4—22no—
106C2×Dic43⋊C4—22no—
107C2×Dic43⋊C4—41no—
108C2×Dic43⋊C4C2×C414yescomplemented
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⋊Dic43—41no—
116C2×C22⋊Dic43—41no—
117C2×C22⋊Dic43C2×C414yescomplemented
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×C414yes—
124C2×(C2×D43)⋊C4D414yes—
125C2×(C2×D43)⋊C4D414yes—
126C2×(C2×D43)⋊C4D414yes—
127C2×C4×Dic43—22no—
128C2×C4×Dic43—22no—
129C2×C4×Dic43—41no—
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—22no—
140C43⋊#95—22no—
141C43⋊#95—22no—
142C43⋊#95—22no—
143C25×C43C2311yescharacteristic
144C23×C4×C43C2311yescharacteristic
145C23×C4×C43C2311yescharacteristic
146C23×C4×C43C2311yescharacteristic
147C23×C4×C43C2311yescharacteristic
148C23×C4×C43C2311yescharacteristic
149C23×C4×C43C2311yescharacteristic
150C2×C22⋊C4×C43—22no—
151C2×C22⋊C4×C43—22no—
152C2×C22⋊C4×C43—22no—
153C2×C22⋊C4×C43—22no—
154C2×C22⋊C4×C43—22no—
155C2×C22⋊C4×C43—22no—
156C2×C22⋊C4×C43—22no—
157C2×C22⋊C4×C43—41no—
158C2×C22⋊C4×C43C2×C414yescomplemented
159C2×C42×C43—22no—
160C2×C42×C43—22no—
161C2×C42×C43—41no—
162#95×C43—22no—
163#95×C43—22no—
164#95×C43—22no—
165C24×C43—21no—
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×C43—21no—
179C24×C43C22×C412yes—
180C24×C43C2411yescharacteristic
181C23×D43—21no—
182C23×D43—21no—
183C23×D43—21no—
184C23×D43—21no—
185C23×D43—21no—
186C23×D43—21no—
187C23×D43—21no—
188C23×D43—21no—
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×C43C22×C412yes—
230C22×C4×C43C22×C412yes—
231C22×C4×C43C2×D412yes—
232C22×C4×C43C2×D412yes—
233C22×C4×C43C2×D412yes—
234C22×C4×C43C2×D412yes—
235C22×C4×C43#4112yes—
236C22×C4×C43#4112yes—
237C22×C4×C43#4112yes—
238C2×C22⋊D43—28no—
239C2×C22⋊D43—28no—
240C2×C22⋊D43—28no—
241C2×C22⋊D43—44no—
242C2×C22⋊D43—44no—
243C2×C22⋊D43—44no—
244C2×C22⋊D43—44no—
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×Dic43—21no—
281C22×Dic43—21no—
282C22×Dic43—21no—
283C22×Dic43—21no—
284C22×Dic43—21no—
285C22×Dic43—21no—
286C22×Dic43C22×C412yes—
287C22×Dic43C22×C412yes—
288C22×Dic43C22×C412yes—
289C22×Dic43C2×D412yes—
290C22×Dic43C2×D412yes—
291C22×Dic43C2×D412yes—
292C22×Dic43C2×D412yes—
293C22×Dic43#4112yes—
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—
315C22⋊C4×C43—28no—
316C22⋊C4×C43—44no—
317C22⋊C4×C43—44no—
318C42×C43—44no—
319C22⋊Dic43—28no—
320C22⋊Dic43—44no—
321C22⋊Dic43—44no—
322(C2×D43)⋊C4—28no—
323(C2×D43)⋊C4—44no—
324(C2×D43)⋊C4C22⋊C4116yescomplemented
325C4⋊Dic43—28no—
326C4⋊Dic43—44no—
327Dic43⋊C4—28no—
328Dic43⋊C4—44no—
329C4×Dic43—44no—
330C23×C43—22no—
331C23×C43—22no—
332C23×C43—22no—
333C23×C43—22no—
334C23×C43—22no—
335C23×C43—22no—
336C23×C43—22no—
337C23×C43—41no—
338C23×C43—41no—
339C23×C43—41no—
340C23×C43—41no—
341C23×C43—41no—
342C23×C43—41no—
343C23×C43—41no—
344C23×C43—41no—
345C23×C43—41no—
346C23×C43—41no—
347C23×C43—41no—
348C23×C43—41no—
349C23×C43—41no—
350C23×C43—41no—
351C23×C43—41no—
352C23×C43—41no—
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×C43C23×C411yescharacteristic
366C23×C43C22×D411yescharacteristic
367C23×C43C22×D411yescharacteristic
368C23×C43C22×D411yescharacteristic
369C23×C43C22×D411yescharacteristic
370C23×C43C2×#4111yescharacteristic
371C23×C43C2×#4111yescharacteristic
372C23×C43C2×#4111yescharacteristic
373C23×C43C2×#4111yescharacteristic
374C23×C43C2×#4111yescharacteristic
375C23×C43C2×#4111yescharacteristic
376C23×C43H(5,𝔽2)11yescharacteristic
377C23×C43H(5,𝔽2)11yescharacteristic
378C23×C432−1+411yescharacteristic
379C23×C432−1+411yescharacteristic
380C22×D43—22no—
381C22×D43—22no—
382C22×D43—22no—
383C22×D43—22no—
384C22×D43—22no—
385C22×D43—22no—
386C22×D43—22no—
387C22×D43—22no—
388C22×D43—22no—
389C22×D43—22no—
390C22×D43—22no—
391C22×D43—22no—
392C22×D43—22no—
393C22×D43—22no—
394C22×D43—22no—
395C22×D43—22no—
396C22×D43—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×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×C43C2×C22⋊C414yes—
456C2×C4×C43#12314yescomplemented
457C22⋊D43—416no—
458C2×Dic43—22no—
459C2×Dic43—22no—
460C2×Dic43—22no—
461C2×Dic43—22no—
462C2×Dic43—22no—
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—41no—
480C2×Dic43—41no—
481C2×Dic43—41no—
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×Dic43—41no—
506C2×Dic43C2×C22⋊C414yes—
507C4×D43—416no—
508C4×D43—416no—
509C4×D43—416no—
510#13996—431nomaximal, Sylow
511C22×C43—42no—
512C22×C43—42no—
513C22×C43—42no—
514C22×C43—42no—
515C22×C43—42no—
516C22×C43—42no—
517C22×C43—42no—
518C22×C43—81no—
519C22×C43—81no—
520C22×C43—81no—
521C22×C43—81no—
522C22×C43—81no—
523C22×C43—81no—
524C22×C43—81no—
525C22×C43—81no—
526C22×C43C22×C22⋊C411yescharacteristic
527C22×C43C2×C4×D411yescharacteristic
528C22×C43C2×C4×D411yescharacteristic
529C22×C43C4×#4111yescharacteristic
530C22×C43C4×#4111yescharacteristic
531C22×C43#52011yescharacteristic
532C22×C43#52011yescharacteristic
533C22×C43C2×#12111yescharacteristic
534C22×C43C2×#12111yescharacteristic
535C22×C43C2×#12311yescharacteristic
536C22×C43#52511yescharacteristic
537C22×C43C2×#12411yescharacteristic
538C22×C43#52911yescharacteristic
539C22×C43#52911yescharacteristic
540C22×C43C2×#12711yescharacteristic
541C22×C43#53411yescharacteristic
542C22×C43#53611yescharacteristic
543C22×C43#53911yescharacteristic
544C22×C43#53911yescharacteristic
545C22×C43#54611yescharacteristic
546C22×C43#54611yescharacteristic
547C22×C43#54611yescharacteristic
548C22×C43#54611yescharacteristic
549C22×C43#54611yescharacteristic
550C22×C43#54611yescharacteristic
551C22×C43#54711yescharacteristic
552C22×C43#54711yescharacteristic
553C22×C43#54711yescharacteristic
554C22×C43#54711yescharacteristic
555C22×C43#54711yescharacteristic
556C22×C43#54711yescharacteristic
557C22×C43#55111yescharacteristic
558C22×C43#55111yescharacteristic
559C22×C43#55211yescharacteristic
560C22×C43#55211yescharacteristic
561C2×D43—24no—
562C2×D43—24no—
563C2×D43—24no—
564C2×D43—24no—
565C2×D43—24no—
566C2×D43—24no—
567C2×D43—24no—
568C2×D43—24no—
569C2×D43—24no—
570C2×D43—24no—
571C2×D43—24no—
572C2×D43—24no—
573C2×D43—24no—
574C2×D43—24no—
575C2×D43#39018yes—
576C4×C43—24no—
577C4×C43—24no—
578C4×C43—42no—
579C4×C43—42no—
580C4×C43—42no—
581C4×C43—81no—
582Dic43—24no—
583Dic43—42no—
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#1437D4311yescharacteristic, complemented
602C4⋊#95—431no—
603C4⋊#95—431no—
604C2×C43—82no—
605C2×C43C2×#39011yescharacteristic
606C2×C43C4×#12311yescharacteristic
607C2×C43#232211yescharacteristic
608C2×C43#233911yescharacteristic
609C2×C43#233911yescharacteristic
610C2×C43#235911yescharacteristic
611C2×C43#235911yescharacteristic
612C2×C43#241211yescharacteristic
613C2×C43#241311yescharacteristic
614C2×C43#242511yescharacteristic
615C2×C43#242511yescharacteristic
616C2×C43#248811yescharacteristic
617C2×C43#248811yescharacteristic
618C2×C43#250111yescharacteristic
619C2×C43#253911yescharacteristic
620D43—28no—
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⋊C4—431no—
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⋊C4C2×D4311yescharacteristic
639C22×C22⋊C4C2×D4311yescharacteristic
640C22×C22⋊C4C2×D4311yescharacteristic
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—431no—
661C2×#95—864no—
662C2×#95C2×D4311yescharacteristic
663C2×#95C2×D4311yescharacteristic
664C2×#95C2×D4311yescharacteristic
665C43#1399611yescharacteristic, complemented, Sylow
666C25—431no—
667C25C22×D4311yescharacteristic
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—431no—
681C23×C4—434no—
682C23×C4—434no—
683C23×C4—431no—
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—862no—
699C23×C4—1721no—
700C23×C4—1721no—
701C23×C4—1721no—
702C23×C4—1721no—
703C23×C4C22×D4311yescharacteristic
704C23×C4C22×D4311yescharacteristic
705C23×C4C22×D4311yescharacteristic
706C23×C4C22×D4311yescharacteristic
707C23×C4C22×D4311yescharacteristic
708C23×C4C22×D4311yescharacteristic
709#123—8632no—
710C2×C4⋊C4—434no—
711C2×C4⋊C4—434no—
712C2×C4⋊C4—862no—
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—862no—
720C2×C4⋊C4—1721no—
721C2×C4⋊C4—1721no—
722C2×C22⋊C4—22no—
723C2×C22⋊C4—22no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—22no—
728C2×C22⋊C4—22no—
729C2×C22⋊C4—41no—
730C2×C22⋊C4—434no—
731C2×C22⋊C4—434no—
732C2×C22⋊C4—434no—
733C2×C22⋊C4—434no—
734C2×C22⋊C4—434no—
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⋊C4C4×D4314yescomplemented
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—862no—
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—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—21no—
785C24—432no—
786C24—432no—
787C24—432no—
788C24—432no—
789C24—432no—
790C24—432no—
791C24—432no—
792C24—861no—
793C24—861no—
794C24—861no—
795C24—861no—
796C24—861no—
797C24—861no—
798C24—861no—
799C24—861no—
800C24C2×C4×D4312yes—
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—432no—
843C22×C4—432no—
844C22×C4—432no—
845C22×C4—432no—
846C22×C4—432no—
847C22×C4—432no—
848C22×C4—432no—
849C22×C4—432no—
850C22×C4—868no—
851C22×C4—868no—
852C22×C4—868no—
853C22×C4—868no—
854C22×C4—868no—
855C22×C4—861no—
856C22×C4—861no—
857C22×C4—861no—
858C22×C4—861no—
859C22×C4—861no—
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—861no—
889C22×C4—868no—
890C22×C4—861no—
891C22×C4—861no—
892C22×C4—861no—
893C22×C4—861no—
894C22×C4—861no—
895C22×C4—861no—
896C22×C4—861no—
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×C4—1724no—
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#1062190012yes—
921C4⋊C4—868no—
922C4⋊C4—868no—
923C4⋊C4—1724no—
924C4⋊C4—1724no—
925C22⋊C4—28no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—4316no—
929C22⋊C4—868no—
930C22⋊C4—868no—
931C22⋊C4—1724no—
932C22⋊C4—1724no—
933C22⋊C4—1724no—
934C42—44no—
935C42—1724no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—434no—
972C23—434no—
973C23—434no—
974C23—434no—
975C23—434no—
976C23—434no—
977C23—434no—
978C23—862no—
979C23—862no—
980C23—862no—
981C23—862no—
982C23—862no—
983C23—862no—
984C23—862no—
985C23—862no—
986C23—862no—
987C23—862no—
988C23—862no—
989C23—862no—
990C23—862no—
991C23—862no—
992C23—862no—
993C23—862no—
994C23—862no—
995C23—862no—
996C23—862no—
997C23—862no—
998C23—862no—
999C23—862no—
1000C23—862no—
1001C23—862no—
1002C23—862no—
1003C23—862no—
1004C23—862no—
1005C23—862no—
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×#1062190011yescharacteristic
1015C23C2×#1062189811yescharacteristic
1016C23C2×#1062189811yescharacteristic
1017C23#1306337011yescharacteristic
1018C23#1306337111yescharacteristic
1019C23#1306337211yescharacteristic
1020C23#1306337211yescharacteristic
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—434no—
1063C2×C4—862no—
1064C2×C4—862no—
1065C2×C4—862no—
1066C2×C4—862no—
1067C2×C4—862no—
1068C2×C4—862no—
1069C2×C4—862no—
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—17216no—
1085C2×C4—17216no—
1086C2×C4—17216no—
1087C2×C4—1721no—
1088C2×C4—1721no—
1089C2×C4—1721no—
1090C2×C4—1721no—
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#1306330714yescomplemented
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—81no—
1124C22—81no—
1125C22—81no—
1126C22—81no—
1127C22—81no—
1128C22—81no—
1129C22—81no—
1130C22—81no—
1131C22—438no—
1132C22—864no—
1133C22—864no—
1134C22—864no—
1135C22—864no—
1136C22—864no—
1137C22—864no—
1138C22—864no—
1139C22—864no—
1140C22—864no—
1141C22—864no—
1142C22—864no—
1143C22—864no—
1144C22—864no—
1145C22—864no—
1146C22C2×C22⋊C4×D4311yescharacteristic
1147C22C4×D4×D4311yescharacteristic
1148C22C4×D4×D4311yescharacteristic
1149C22C4×#1062190011yescharacteristic
1150C22C4×#1062189811yescharacteristic
1151C22#1458337811yescharacteristic
1152C22#1458337911yescharacteristic
1153C22#121×D4311yescharacteristic
1154C22#121×D4311yescharacteristic
1155C22C2×#1306330711yescharacteristic
1156C22#1458340811yescharacteristic
1157C22#124×D4311yescharacteristic
1158C22#1458342711yescharacteristic
1159C22#1458343111yescharacteristic
1160C22#127×D4311yescharacteristic
1161C22#1458345711yescharacteristic
1162C22#1458346911yescharacteristic
1163C22#1458349011yescharacteristic
1164C22#1458349211yescharacteristic
1165C22#1458353611yescharacteristic
1166C22#1458353811yescharacteristic
1167C22#1458353911yescharacteristic
1168C22#1458354211yescharacteristic
1169C22#1458354511yescharacteristic
1170C22#1458354511yescharacteristic
1171C22#1458354711yescharacteristic
1172C22#1458354911yescharacteristic
1173C22#1458354911yescharacteristic
1174C22#1458355411yescharacteristic
1175C22#1458355411yescharacteristic
1176C22#1458355411yescharacteristic
1177C22#1458357211yescharacteristic
1178C22#1458357811yescharacteristic
1179C22#1458358511yescharacteristic
1180C22#1458358811yescharacteristic
1181C4—24no—
1182C4—24no—
1183C4—42no—
1184C4—42no—
1185C4—42no—
1186C4—81no—
1187C4—864no—
1188C4—3441no—
1189C4—1722no—
1190C4—1722no—
1191C4—1722no—
1192C4—1722no—
1193C4—1722no—
1194C2—82no—
1195C2—868no—
1196C2#390×D4311yescharacteristic
1197C2C4×#1306330711yescharacteristic
1198C2#1913726511yescharacteristic
1199C2#1913742111yescharacteristic
1200C2#1913742611yescharacteristic
1201C2#1913758611yescharacteristic
1202C2#1913758811yescharacteristic
1203C2#1913799011yescharacteristic
1204C2#1913800111yescharacteristic
1205C2#1913814511yescharacteristic
1206C2#1913815111yescharacteristic
1207C2#1913892011yescharacteristic
1208C2#1913892611yescharacteristic
1209C2#1913906511yescharacteristic
1210C2#1913952411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1437C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenter#1437D43
hypocenterC43#13996
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
4. C2×#14582773C2semidirect
5. C2×#14582761C2semidirect
6. C2×C4×(C2×D43)⋊C4C2semidirect
7. C2×#95×D43C2semidirect
8. #19132864C2semidirect
9. #19132861C2semidirect
10. #19132840C2semidirect
11. #19132838C2semidirect
12. #19132832C2semidirect
13. #19132825C2semidirect
14. Dic43⋊#95C2semidirect
15. C43×#1437C2semidirect
22. C2×#13063307C4semidirect
102. C2×C4⋊Dic43C2×C4semidirect
108. C2×Dic43⋊C4C2×C4semidirect
117. C2×C22⋊Dic43C2×C4semidirect
158. C2×C22⋊C4×C43C2×C4semidirect
324. (C2×D43)⋊C4C22⋊C4semidirect
456. C2×C4×C43#123semidirect
601. #1437D43semidirect
665. C43#13996semidirect
748. C2×C22⋊C4C4×D43semidirect
1115. 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
C2×#145827752
C2×#145827732
C2×#145827612
C2×C4×(C2×D43)⋊C42
C2×#95×D432
#191328642
#191328612
#191328402
#191328382
#191328322
#191328252
Dic43⋊#952
C43×#14372
#1399643