Finite Group Databasebeta

← #25020004

Subgroups — #25020004

Order 11008.

2538 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×C4⋊C4×D43C211yesmaximal, characteristic, complemented
2C2×#14582790C211yesmaximal, characteristic, complemented
3C2×#14582789C211yesmaximal, characteristic, complemented
4C2×#14582777C211yesmaximal, characteristic
5C2×#14582777C211yesmaximal, characteristic
6C2×#14582777C211yesmaximal, characteristic
7C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
8#19132852C211yesmaximal, characteristic, complemented
9#19132850C211yesmaximal, characteristic, complemented
10#19132841C211yesmaximal, characteristic, complemented
11#19132839C211yesmaximal, characteristic, complemented
12#19132830C211yesmaximal, characteristic, complemented
13(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
15C43×#1436C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C22×C4⋊Dic43C2211yescharacteristic
21C22×Dic43⋊C4C2211yescharacteristic
22C22×Dic43⋊C4C2211yescharacteristic
23C2×C4⋊C4×D43—24no—
24C2×C4⋊C4×D43—24no—
25C2×C4⋊C4×D43—24no—
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
36#14582790—24no—
37#14582789—24no—
38#14582777—24no—
39#14582777—24no—
40#14582777C418yescomplemented
41C4×(C2×D43)⋊C4—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
52C2×C43⋊#95C2211yescharacteristic
53C22×C4⋊C4×C43C2211yescharacteristic
54C22×C42×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—
96C2×C4⋊Dic43—22no—
97C2×C4⋊Dic43—22no—
98C2×C4⋊Dic43—22no—
99C2×Dic43⋊C4—22no—
100C2×Dic43⋊C4—22no—
101C2×Dic43⋊C4—22no—
102C2×Dic43⋊C4—22no—
103C2×Dic43⋊C4—22no—
104C2×Dic43⋊C4D414yescomplemented
105C4⋊C4×D43—232no—
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—22no—
124C2×(C2×D43)⋊C4—22no—
125C2×(C2×D43)⋊C4—41no—
126C2×(C2×D43)⋊C4—41no—
127C2×(C2×D43)⋊C4—41no—
128C2×(C2×D43)⋊C4—41no—
129C2×(C2×D43)⋊C4C2×C414yes—
130C2×(C2×D43)⋊C4C2×C414yescomplemented
131C2×(C2×D43)⋊C4C2×C414yescomplemented
132C2×(C2×D43)⋊C4D414yes—
133C2×C4×Dic43—22no—
134C2×C4×Dic43—22no—
135C2×C4×Dic43—41no—
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—
145C43⋊#95—41no—
146C43⋊#95C2×C414yescomplemented
147C23×C4×C43C2311yescharacteristic
148C23×C4×C43C2311yescharacteristic
149C23×C4×C43C2311yescharacteristic
150C23×C4×C43C2311yescharacteristic
151C23×C4×C43C2311yescharacteristic
152C23×C4×C43C2311yescharacteristic
153C23×C4×C43C2311yescharacteristic
154C2×C4⋊C4×C43—22no—
155C2×C4⋊C4×C43—22no—
156C2×C4⋊C4×C43D414yescomplemented
157C2×C42×C43—22no—
158C2×C42×C43—22no—
159C2×C42×C43—41no—
160#95×C43—22no—
161#95×C43—22no—
162#95×C43—22no—
163#95×C43—41no—
164#95×C43C2×C414yescomplemented
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×D43#4112yes—
193C23×D43#4112yes—
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×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×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—28no—
301C2×C4×D43—28no—
302C2×C4×D43—28no—
303C2×C4×D43—28no—
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—
316C42×C43—44no—
317(C2×D43)⋊C4—28no—
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—
326C4⋊Dic43—28no—
327Dic43⋊C4—28no—
328Dic43⋊C4—28no—
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×D43#11714yes—
409C22×D43C4×D414yes—
410C22×D43C4×D414yes—
411C22×D43#12114yes—
412C22×D43#12314yes—
413C22×D43#12414yes—
414C22×D43#12614yes—
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×C43C4×D414yes—
463C2×C4×C43#12014yes—
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×Dic43C4×D414yes—
506D172—416no—
507C4×D43—232no—
508C4×D43—416no—
509C4×D43—416no—
510#14019—431nomaximal, Sylow
511C22×C43C2×#11711yescharacteristic
512C22×C43C2×C4×D411yescharacteristic
513C22×C43C2×C4×D411yescharacteristic
514C22×C43C2×C4×D411yescharacteristic
515C22×C43C2×C4×D411yescharacteristic
516C22×C43#52011yescharacteristic
517C22×C43#52011yescharacteristic
518C22×C43C2×#12011yescharacteristic
519C22×C43C2×#12111yescharacteristic
520C22×C43C2×#12311yescharacteristic
521C22×C43#52511yescharacteristic
522C22×C43#52511yescharacteristic
523C22×C43#52511yescharacteristic
524C22×C43C2×#12411yescharacteristic
525C22×C43C2×#12611yescharacteristic
526C22×C43#53411yescharacteristic
527C22×C43#53611yescharacteristic
528C22×C43#53911yescharacteristic
529C22×C43#53911yescharacteristic
530C22×C43D4211yescharacteristic
531C22×C43D4211yescharacteristic
532C22×C43#54611yescharacteristic
533C22×C43#54611yescharacteristic
534C22×C43#54711yescharacteristic
535C22×C43#54711yescharacteristic
536C22×C43#54811yescharacteristic
537C22×C43#54811yescharacteristic
538C22×C43#54811yescharacteristic
539C22×C43#54811yescharacteristic
540C22×C43#55211yescharacteristic
541C22×C43#55211yescharacteristic
542C22×C43#55311yescharacteristic
543C22×C43#55311yescharacteristic
544C22×C43#55311yescharacteristic
545C22×C43#55311yescharacteristic
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#38818yescomplemented
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—
589C23×C4⋊C4—431no—
590C2×#388—431no—
591C2×#388—431no—
592C2×#386—431no—
593C2×#386—431no—
594C2×#386—431no—
595C2×C4×C22⋊C4—431no—
596#1442—431no—
597#1442—431no—
598#1439—431no—
599#1439—431no—
600#1436—431no—
601#1436D4311yescharacteristic, complemented
602C22⋊#95—431no—
603C22⋊#95—431no—
604C2×C43C2×#38811yescharacteristic
605C2×C43C4×#12011yescharacteristic
606C2×C43#232211yescharacteristic
607C2×C43#235211yescharacteristic
608C2×C43#235211yescharacteristic
609C2×C43#236111yescharacteristic
610C2×C43#236111yescharacteristic
611C2×C43#241011yescharacteristic
612C2×C43#241311yescharacteristic
613C2×C43#243611yescharacteristic
614C2×C43#244311yescharacteristic
615C2×C43#244311yescharacteristic
616C2×C43#248111yescharacteristic
617C2×C43#248111yescharacteristic
618C2×C43#259111yescharacteristic
619D43—28no—
620D43—82no—
621C23×D4—431no—
622C24×C4—431no—
623C24×C4—431no—
624C24×C4—431no—
625C22×C4⋊C4—431no—
626C22×C4⋊C4—431no—
627C22×C4⋊C4—431no—
628C22×C4⋊C4—864no—
629C22×C4⋊C4—864no—
630C22×C4⋊C4—864no—
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#388—864no—
644#388—864no—
645#386—438no—
646#386—864no—
647#386—864no—
648C4×C22⋊C4—864no—
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×#95C2×D4311yescharacteristic
661C2×#95C2×D4311yescharacteristic
662C2×#95C2×D4311yescharacteristic
663C2×#95C2×D4311yescharacteristic
664C2×#95C2×D4311yescharacteristic
665C43#1401911yescharacteristic, 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
709C2×C4⋊C4—22no—
710C2×C4⋊C4—22no—
711C2×C4⋊C4—434no—
712C2×C4⋊C4—8632no—
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—862no—
721C2×C4⋊C4D17214yescomplemented
722C2×C22⋊C4—434no—
723C2×C22⋊C4—434no—
724C2×C22⋊C4—434no—
725C2×C22⋊C4—434no—
726C2×C22⋊C4—862no—
727C2×C22⋊C4—862no—
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—41no—
759#95—434no—
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—1721no—
770#95C4×D4314yescomplemented
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—868no—
861C22×C4—868no—
862C22×C4—868no—
863C22×C4—861no—
864C22×C4—861no—
865C22×C4—861no—
866C22×C4—861no—
867C22×C4—868no—
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—868no—
893C22×C4—861no—
894C22×C4—861no—
895C22×C4—861no—
896C22×C4—861no—
897C22×C4—861no—
898C22×C4—861no—
899C22×C4—861no—
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×C4C2×D17212yes—
915C22×C4C2×D17212yes—
916C22×C4C2×D17212yes—
917C22×C4#1062189812yes—
918C22×C4D4×D4312yes—
919C22×C4D4×D4312yes—
920C22×C4D4×D4312yes—
921C4⋊C4—28no—
922C4⋊C4—868no—
923C4⋊C4—868no—
924C4⋊C4—868no—
925C22⋊C4—868no—
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
1010C23C22×D17211yescharacteristic
1011C23#41×D4311yescharacteristic
1012C23#41×D4311yescharacteristic
1013C23#41×D4311yescharacteristic
1014C23#41×D4311yescharacteristic
1015C23#41×D4311yescharacteristic
1016C23C2×#1062189811yescharacteristic
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—8632no—
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—862no—
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×C4C4×D17214yes—
1115C2×C4#1306329514yes—
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—
1146C22#117×D4311yescharacteristic
1147C22C4×D4×D4311yescharacteristic
1148C22C4×D4×D4311yescharacteristic
1149C22C4×D4×D4311yescharacteristic
1150C22C2×C4×D17211yescharacteristic
1151C22#1458338011yescharacteristic
1152C22#1458338111yescharacteristic
1153C22C2×#1306329511yescharacteristic
1154C22#121×D4311yescharacteristic
1155C22#123×D4311yescharacteristic
1156C22#1458340811yescharacteristic
1157C22#1458340811yescharacteristic
1158C22#1458341111yescharacteristic
1159C22#124×D4311yescharacteristic
1160C22#126×D4311yescharacteristic
1161C22#1458345711yescharacteristic
1162C22#1458347411yescharacteristic
1163C22#1458349511yescharacteristic
1164C22#1458349711yescharacteristic
1165C22#1458353111yescharacteristic
1166C22D4×D17211yescharacteristic
1167C22#1458354111yescharacteristic
1168C22#1458354411yescharacteristic
1169C22#1458355011yescharacteristic
1170C22#1458355111yescharacteristic
1171C22#1458355911yescharacteristic
1172C22#1458355911yescharacteristic
1173C22#1458356111yescharacteristic
1174C22#1458356111yescharacteristic
1175C22#1458358111yescharacteristic
1176C22#1458359011yescharacteristic
1177C22#1458359311yescharacteristic
1178C22#1458359411yescharacteristic
1179C22#1458359911yescharacteristic
1180C22#1458360011yescharacteristic
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#388×D4311yescharacteristic
1197C2C4×#1306329511yescharacteristic
1198C2#1913725911yescharacteristic
1199C2#1913751911yescharacteristic
1200C2#1913752711yescharacteristic
1201C2#1913761311yescharacteristic
1202C2#1913761411yescharacteristic
1203C2#1913796811yescharacteristic
1204C2#1913799911yescharacteristic
1205C2#1913825211yescharacteristic
1206C2#1913832911yescharacteristic
1207C2#1913833511yescharacteristic
1208C2#1913885411yescharacteristic
1209C2#1913886011yescharacteristic
1210C2#1914007311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1436C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenter#1436D43
hypocenterC43#14019
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
1. C22×C4⋊C4×D43C2semidirect
2. C2×#14582790C2semidirect
3. C2×#14582789C2semidirect
7. C2×C4×(C2×D43)⋊C4C2semidirect
8. #19132852C2semidirect
9. #19132850C2semidirect
10. #19132841C2semidirect
11. #19132839C2semidirect
12. #19132830C2semidirect
13. (C2×D43)⋊#95C2semidirect
14. (C2×D43)⋊#95C2semidirect
15. C43×#1436C2semidirect
40. #14582777C4semidirect
104. C2×Dic43⋊C4D4semidirect
130. C2×(C2×D43)⋊C4C2×C4semidirect
131. C2×(C2×D43)⋊C4C2×C4semidirect
146. C43⋊#95C2×C4semidirect
156. C2×C4⋊C4×C43D4semidirect
164. #95×C43C2×C4semidirect
575. C2×D43#388semidirect
601. #1436D43semidirect
665. C43#14019semidirect
721. C2×C4⋊C4D172semidirect
770. #95C4×D43semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D432
C2×#145827902
C2×#145827892
C2×#145827772
C2×C4×(C2×D43)⋊C42
#191328522
#191328502
#191328412
#191328392
#191328302
(C2×D43)⋊#952
C43×#14362
#1401943