Finite Group Databasebeta

← #25019963

Subgroups — #25019963

Order 11008.

2950 conjugacy classes of subgroups.

The subgroup lattice has 1252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D172C211yesmaximal, characteristic
2C22×C4⋊C4×D43C211yesmaximal, characteristic, complemented
3C2×#14582777C211yesmaximal, characteristic
4C2×#14582777C211yesmaximal, characteristic
5C2×#14582773C211yesmaximal, characteristic, complemented
6C2×#14582773C211yesmaximal, characteristic, complemented
7C2×#14582770C211yesmaximal, characteristic, complemented
8#19132860C211yesmaximal, characteristic, complemented
9#19132859C211yesmaximal, characteristic, complemented
10#19132841C211yesmaximal, characteristic, complemented
11#19132839C211yesmaximal, characteristic, complemented
12#19132828C211yesmaximal, 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
20C23×C4×D43C2211yescharacteristic
21C2×C4×D172—24no—
22C2×C4×D172—24no—
23C2×C4×D172—24no—
24C22×C4⋊Dic43C2211yescharacteristic
25C22×C4⋊Dic43C2211yescharacteristic
26C22×C4⋊Dic43C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
28C22×Dic43⋊C4C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30C2×C4⋊C4×D43—24no—
31C2×C4⋊C4×D43—24no—
32C2×C4⋊C4×D43—24no—
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×(C2×D43)⋊C4C2211yescharacteristic
35C22×(C2×D43)⋊C4C2211yescharacteristic
36C22×(C2×D43)⋊C4C2211yescharacteristic
37C22×(C2×D43)⋊C4C2211yescharacteristic
38C22×(C2×D43)⋊C4C2211yescharacteristic
39C22×(C2×D43)⋊C4C2211yescharacteristic
40C22×(C2×D43)⋊C4C2211yescharacteristic
41#14582777—24no—
42#14582777C418yescomplemented
43#14582773—24no—
44#14582773—24no—
45#14582770—24no—
46C2×C43⋊#95C2211yescharacteristic
47C2×C43⋊#95C2211yescharacteristic
48C2×C43⋊#95C2211yescharacteristic
49C2×C43⋊#95C2211yescharacteristic
50C2×C43⋊#95C2211yescharacteristic
51C2×C43⋊#95C2211yescharacteristic
52C2×C43⋊#95C2211yescharacteristic
53C2×C43⋊#95C2211yescharacteristic
54C2×C43⋊#95C2211yescharacteristic
55C22×C4⋊C4×C43C2211yescharacteristic
56C22×C42×C43C2211yescharacteristic
57C2×#95×C43C2211yescharacteristic
58C2×#95×C43C2211yescharacteristic
59C2×#95×C43C2211yescharacteristic
60C2×#95×C43C2211yescharacteristic
61C2×#95×C43C2211yescharacteristic
62C24×D43C2311yescharacteristic
63C24×D43C2311yescharacteristic
64C22×D172—22no—
65C22×D172—22no—
66C22×D172—22no—
67C22×D172—22no—
68C22×D172C2×C414yes—
69C22×D172D414yes—
70C22×D172Q814yes—
71C23×Dic43C2311yescharacteristic
72C23×Dic43C2311yescharacteristic
73C23×Dic43C2311yescharacteristic
74C23×Dic43C2311yescharacteristic
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
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—22no—
91C22×C4×D43—22no—
92C22×C4×D43—22no—
93C22×C4×D43—22no—
94C22×C4×D43—22no—
95C22×C4×D43—22no—
96C22×C4×D43—22no—
97C22×C4×D43—41no—
98C22×C4×D43—41no—
99C22×C4×D43—41no—
100C22×C4×D43—41no—
101C22×C4×D43—41no—
102C22×C4×D43—41no—
103C22×C4×D43C2×C414yescomplemented
104C22×C4×D43D414yes—
105C4×D172—232no—
106C2×C4⋊Dic43—22no—
107C2×C4⋊Dic43—22no—
108C2×C4⋊Dic43—22no—
109C2×C4⋊Dic43—22no—
110C2×C4⋊Dic43—22no—
111C2×C4⋊Dic43—22no—
112C2×C4⋊Dic43—22no—
113C2×C4⋊Dic43—22no—
114C2×C4⋊Dic43—41no—
115C2×Dic43⋊C4—22no—
116C2×Dic43⋊C4—22no—
117C2×Dic43⋊C4—22no—
118C2×Dic43⋊C4—22no—
119C2×Dic43⋊C4—22no—
120C2×Dic43⋊C4—22no—
121C2×Dic43⋊C4—22no—
122C2×Dic43⋊C4—41no—
123C2×Dic43⋊C4D414yescomplemented
124C4⋊C4×D43—232no—
125C2×(C2×D43)⋊C4—22no—
126C2×(C2×D43)⋊C4—22no—
127C2×(C2×D43)⋊C4—22no—
128C2×(C2×D43)⋊C4—22no—
129C2×(C2×D43)⋊C4—22no—
130C2×(C2×D43)⋊C4—22no—
131C2×(C2×D43)⋊C4—22no—
132C2×(C2×D43)⋊C4—22no—
133C2×(C2×D43)⋊C4—22no—
134C2×(C2×D43)⋊C4—22no—
135C2×(C2×D43)⋊C4—22no—
136C2×(C2×D43)⋊C4—22no—
137C2×(C2×D43)⋊C4—22no—
138C2×(C2×D43)⋊C4—22no—
139C2×(C2×D43)⋊C4—22no—
140C2×(C2×D43)⋊C4—22no—
141C2×(C2×D43)⋊C4—22no—
142C2×(C2×D43)⋊C4—22no—
143C2×(C2×D43)⋊C4—41no—
144C2×(C2×D43)⋊C4—41no—
145C2×(C2×D43)⋊C4C2×C414yescomplemented
146C2×(C2×D43)⋊C4C2×C414yescomplemented
147C2×(C2×D43)⋊C4C2×C414yescomplemented
148C2×(C2×D43)⋊C4D414yes—
149C43⋊#95—22no—
150C43⋊#95—22no—
151C43⋊#95—22no—
152C43⋊#95—22no—
153C43⋊#95—22no—
154C43⋊#95—22no—
155C43⋊#95—41no—
156C43⋊#95—41no—
157C43⋊#95C2×C414yescomplemented
158C23×C4×C43C2311yescharacteristic
159C23×C4×C43C2311yescharacteristic
160C23×C4×C43C2311yescharacteristic
161C23×C4×C43C2311yescharacteristic
162C23×C4×C43C2311yescharacteristic
163C23×C4×C43C2311yescharacteristic
164C23×C4×C43C2311yescharacteristic
165C2×C4⋊C4×C43—22no—
166C2×C4⋊C4×C43—22no—
167C2×C4⋊C4×C43D414yescomplemented
168C2×C42×C43—22no—
169C2×C42×C43—22no—
170C2×C42×C43—22no—
171#95×C43—22no—
172#95×C43—22no—
173#95×C43—22no—
174#95×C43—22no—
175#95×C43C2×C414yescomplemented
176C24×C43C2411yescharacteristic
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×D43—21no—
189C23×D43—21no—
190C23×D43—21no—
191C23×D43—21no—
192C23×D43—21no—
193C23×D43—21no—
194C23×D43—21no—
195C23×D43—21no—
196C23×D43—21no—
197C23×D43C22×C412yes—
198C23×D43C22×C412yes—
199C23×D43C2×D412yes—
200C23×D43C2×D412yes—
201C23×D43C2×D412yes—
202C23×D43C2×D412yes—
203C23×D43C2×Q812yes—
204C23×D43C2×Q812yes—
205C23×D43#4112yes—
206C23×D43#4112yes—
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×C43—21no—
238C22×C4×C43—21no—
239C22×C4×C43—21no—
240C22×C4×C43—21no—
241C22×C4×C43—21no—
242C22×C4×C43—21no—
243C22×C4×C43—21no—
244C22×C4×C43C22×C412yes—
245C22×C4×C43C22×C412yes—
246C22×C4×C43C22×C412yes—
247C22×C4×C43C2×D412yes—
248C22×C4×C43C2×D412yes—
249C22×C4×C43C2×D412yes—
250C22×C4×C43C2×D412yes—
251C22×C4×C43C2×D412yes—
252C22×C4×C43C2×D412yes—
253C22×C4×C43C2×D412yes—
254C22×C4×C43C2×Q812yes—
255C22×C4×C43#4112yes—
256C22×Dic43—21no—
257C22×Dic43—21no—
258C22×Dic43—21no—
259C22×Dic43—21no—
260C22×Dic43—21no—
261C22×Dic43—21no—
262C22×Dic43—21no—
263C22×Dic43—21no—
264C22×Dic43—21no—
265C22×Dic43—21no—
266C22×Dic43—21no—
267C22×Dic43—21no—
268C22×Dic43—21no—
269C22×Dic43—21no—
270C22×Dic43—21no—
271C22×Dic43—21no—
272C22×Dic43—21no—
273C22×Dic43—21no—
274C22×Dic43—21no—
275C22×Dic43—21no—
276C22×Dic43—21no—
277C22×Dic43—21no—
278C22×Dic43—21no—
279C22×Dic43—21no—
280C22×Dic43—21no—
281C22×Dic43—21no—
282C22×Dic43—21no—
283C22×Dic43—21no—
284C22×Dic43—21no—
285C22×Dic43—21no—
286C22×Dic43—21no—
287C22×Dic43—21no—
288C22×Dic43—21no—
289C22×Dic43—21no—
290C22×Dic43—21no—
291C22×Dic43C22×C412yes—
292C22×Dic43C22×C412yes—
293C22×Dic43C2×D412yes—
294C22×Dic43C2×D412yes—
295C22×Dic43C2×D412yes—
296C22×Dic43C2×D412yes—
297C22×Dic43#4112yes—
298C2×D172—28no—
299C2×D172—28no—
300C2×D172—28no—
301C2×D172—28no—
302C2×D172—28no—
303C2×D172—28no—
304C2×D172C4⋊C4116yescomplemented
305C2×C4×D43—28no—
306C2×C4×D43—28no—
307C2×C4×D43—28no—
308C2×C4×D43—28no—
309C2×C4×D43—28no—
310C2×C4×D43—28no—
311C2×C4×D43—28no—
312C2×C4×D43—28no—
313C2×C4×D43—28no—
314C2×C4×D43—28no—
315C2×C4×D43—28no—
316C2×C4×D43—44no—
317C2×C4×D43—44no—
318C2×C4×D43—44no—
319C2×C4×D43—44no—
320C2×C4×D43—44no—
321C2×C4×D43—44no—
322C2×C4×D43—44no—
323C2×C4×D43—44no—
324C2×C4×D43—44no—
325C2×C4×D43—44no—
326C2×C4×D43—44no—
327C2×C4×D43—44no—
328C2×C4×D43—44no—
329C2×C4×D43—44no—
330C2×C4×D43—44no—
331C2×C4×D43—44no—
332C2×C4×D43—44no—
333C4⋊C4×C43—28no—
334C42×C43—28no—
335(C2×D43)⋊C4—28no—
336(C2×D43)⋊C4—28no—
337(C2×D43)⋊C4—28no—
338(C2×D43)⋊C4—28no—
339(C2×D43)⋊C4—28no—
340(C2×D43)⋊C4—44no—
341(C2×D43)⋊C4—44no—
342(C2×D43)⋊C4—44no—
343C4⋊Dic43—28no—
344C4⋊Dic43—28no—
345C4⋊Dic43—44no—
346Dic43⋊C4—28no—
347Dic43⋊C4—28no—
348Dic43⋊C4—44no—
349C23×C43C23×C411yescharacteristic
350C23×C43C22×D411yescharacteristic
351C23×C43C22×D411yescharacteristic
352C23×C43C22×D411yescharacteristic
353C23×C43C22×D411yescharacteristic
354C23×C43C22×D411yescharacteristic
355C23×C43C22×Q811yescharacteristic
356C23×C43C2×#4111yescharacteristic
357C23×C43C2×#4111yescharacteristic
358C23×C43C2×#4111yescharacteristic
359C23×C43C2×#4111yescharacteristic
360C23×C43H(5,𝔽2)11yescharacteristic
361C23×C43H(5,𝔽2)11yescharacteristic
362C23×C432−1+411yescharacteristic
363C23×C432−1+411yescharacteristic
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—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×D43—22no—
409C22×D43—22no—
410C22×D43—41no—
411C22×D43—41no—
412C22×D43—41no—
413C22×D43—41no—
414C22×D43—41no—
415C22×D43—41no—
416C22×D43—41no—
417C22×D43—41no—
418C22×D43—41no—
419C22×D43—41no—
420C22×D43—41no—
421C22×D43—41no—
422C22×D43—41no—
423C22×D43—41no—
424C22×D43—41no—
425C22×D43—41no—
426C22×D43C2×C4⋊C414yes—
427C22×D43C2×C4⋊C414yescomplemented
428C22×D43C4×D414yes—
429C22×D43C4×D414yes—
430C22×D43#12014yes—
431C22×D43C22⋊Q814yes—
432C22×D43C22⋊Q814yes—
433C22×D43#12314yes—
434C2×C4×C43—22no—
435C2×C4×C43—22no—
436C2×C4×C43—22no—
437C2×C4×C43—22no—
438C2×C4×C43—22no—
439C2×C4×C43—22no—
440C2×C4×C43—22no—
441C2×C4×C43—22no—
442C2×C4×C43—22no—
443C2×C4×C43—22no—
444C2×C4×C43—22no—
445C2×C4×C43—22no—
446C2×C4×C43—22no—
447C2×C4×C43—22no—
448C2×C4×C43—22no—
449C2×C4×C43—22no—
450C2×C4×C43—22no—
451C2×C4×C43—22no—
452C2×C4×C43—22no—
453C2×C4×C43—22no—
454C2×C4×C43—22no—
455C2×C4×C43—22no—
456C2×C4×C43—22no—
457C2×C4×C43—22no—
458C2×C4×C43—22no—
459C2×C4×C43—22no—
460C2×C4×C43—22no—
461C2×C4×C43—41no—
462C2×C4×C43—41no—
463C2×C4×C43—41no—
464C2×C4×C43—41no—
465C2×C4×C43—41no—
466C2×C4×C43—41no—
467C2×C4×C43—41no—
468C2×C4×C43—41no—
469C2×C4×C43—41no—
470C2×C4×C43—41no—
471C2×C4×C43—41no—
472C2×C4×C43—41no—
473C2×C4×C43—41no—
474C2×C4×C43—41no—
475C2×C4×C43—41no—
476C2×C4×C43—41no—
477C2×C4×C43—41no—
478C2×C4×C43—41no—
479C2×C4×C43—41no—
480C2×C4×C43C2×C4⋊C414yescomplemented
481C2×C4×C43C4×D414yescomplemented
482C2×C4×C43#12014yes—
483C2×Dic43—22no—
484C2×Dic43—22no—
485C2×Dic43—22no—
486C2×Dic43—22no—
487C2×Dic43—22no—
488C2×Dic43—22no—
489C2×Dic43—22no—
490C2×Dic43—22no—
491C2×Dic43—22no—
492C2×Dic43—22no—
493C2×Dic43—22no—
494C2×Dic43—22no—
495C2×Dic43—22no—
496C2×Dic43—22no—
497C2×Dic43—22no—
498C2×Dic43—22no—
499C2×Dic43—22no—
500C2×Dic43—22no—
501C2×Dic43—41no—
502C2×Dic43—41no—
503C2×Dic43—41no—
504C2×Dic43—41no—
505C2×Dic43—41no—
506C2×Dic43—41no—
507C2×Dic43—41no—
508C2×Dic43—41no—
509C2×Dic43—41no—
510C2×Dic43—41no—
511C2×Dic43—41no—
512C2×Dic43—41no—
513C2×Dic43—41no—
514C2×Dic43—41no—
515C2×Dic43—41no—
516C2×Dic43—41no—
517C2×Dic43—41no—
518C2×Dic43—41no—
519C2×Dic43—41no—
520C2×Dic43—41no—
521C2×Dic43—41no—
522C2×Dic43—41no—
523C2×Dic43—41no—
524C2×Dic43C4×D414yescomplemented
525D172—232no—
526C4×D43—232no—
527C4×D43—416no—
528C4×D43—416no—
529C4×D43—416no—
530#14015—431nomaximal, Sylow
531C22×C43C22×C4⋊C411yescharacteristic
532C22×C43C2×C4×D411yescharacteristic
533C22×C43C2×C4×D411yescharacteristic
534C22×C43C2×C4×D411yescharacteristic
535C22×C43C2×C4×D411yescharacteristic
536C22×C43#52011yescharacteristic
537C22×C43#52011yescharacteristic
538C22×C43C2×#12011yescharacteristic
539C22×C43C2×#12011yescharacteristic
540C22×C43C2×C22⋊Q811yescharacteristic
541C22×C43C2×C22⋊Q811yescharacteristic
542C22×C43C2×#12311yescharacteristic
543C22×C43#52511yescharacteristic
544C22×C43#52511yescharacteristic
545C22×C43#52511yescharacteristic
546C22×C43#53411yescharacteristic
547C22×C43#53611yescharacteristic
548C22×C43#53911yescharacteristic
549C22×C43#53911yescharacteristic
550C22×C43D4211yescharacteristic
551C22×C43D4211yescharacteristic
552C22×C43D4211yescharacteristic
553C22×C43D4211yescharacteristic
554C22×C43#54711yescharacteristic
555C22×C43#54711yescharacteristic
556C22×C43#54711yescharacteristic
557C22×C43#54711yescharacteristic
558C22×C43#54811yescharacteristic
559C22×C43#54811yescharacteristic
560C22×C43D4×Q811yescharacteristic
561C22×C43D4×Q811yescharacteristic
562C22×C43#55311yescharacteristic
563C22×C43#55311yescharacteristic
564C22×C43#55411yescharacteristic
565C22×C43#55411yescharacteristic
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—24no—
576C2×D43—24no—
577C2×D43—24no—
578C2×D43—24no—
579C2×D43—24no—
580C2×D43—24no—
581C2×D43—24no—
582C2×D43—24no—
583C2×D43—42no—
584C2×D43—42no—
585C2×D43—42no—
586C2×D43—42no—
587C2×D43—42no—
588C2×D43—42no—
589C2×D43—42no—
590C2×D43—42no—
591C2×D43—42no—
592C2×D43—42no—
593C2×D43—42no—
594C2×D43—42no—
595C2×D43#38518yescomplemented
596C4×C43—24no—
597C4×C43—24no—
598C4×C43—24no—
599C4×C43—42no—
600C4×C43—42no—
601C4×C43—42no—
602C4×C43—81no—
603Dic43—24no—
604Dic43—42no—
605Dic43—42no—
606Dic43—42no—
607Dic43—42no—
608Dic43—81no—
609C22×C4×D4—431no—
610C23×C4⋊C4—431no—
611C2×#386—431no—
612C2×#386—431no—
613C2×#385—431no—
614C2×#385—431no—
615C2×#385—431no—
616#1444—431no—
617#1444—431no—
618#1439—431no—
619#1439—431no—
620#1436—431no—
621#1436D4311yescharacteristic, complemented
622C22⋊#95—431no—
623C22⋊#95—431no—
624C2×C43C2×#38511yescharacteristic
625C2×C43C4×#12011yescharacteristic
626C2×C43#232211yescharacteristic
627C2×C43D4×C4⋊C411yescharacteristic
628C2×C43D4×C4⋊C411yescharacteristic
629C2×C43#236111yescharacteristic
630C2×C43#236111yescharacteristic
631C2×C43#240311yescharacteristic
632C2×C43#240611yescharacteristic
633C2×C43#240911yescharacteristic
634C2×C43#244311yescharacteristic
635C2×C43#244311yescharacteristic
636C2×C43#244911yescharacteristic
637C2×C43#244911yescharacteristic
638C2×C43#257911yescharacteristic
639D43—28no—
640D43—44no—
641C23×D4—431no—
642C24×C4—431no—
643C24×C4—431no—
644C24×C4—431no—
645C24×C4—431no—
646C2×C4×D4—864no—
647C2×C4×D4—864no—
648C2×C4×D4—864no—
649C22×C4⋊C4—431no—
650C22×C4⋊C4—431no—
651C22×C4⋊C4—431no—
652C22×C4⋊C4—431no—
653C22×C4⋊C4—431no—
654C22×C4⋊C4—431no—
655C22×C4⋊C4—864no—
656C22×C4⋊C4—864no—
657C22×C4⋊C4—864no—
658C22×C4⋊C4C2×D4311yescharacteristic
659C22×C22⋊C4—431no—
660C22×C22⋊C4—431no—
661C22×C22⋊C4—431no—
662C22×C22⋊C4—431no—
663C22×C22⋊C4—431no—
664C22×C22⋊C4—431no—
665C22×C22⋊C4—431no—
666C22×C22⋊C4—431no—
667C22×C42C2×D4311yescharacteristic
668#386—438no—
669#386—864no—
670#385—864no—
671#385—864no—
672#385—864no—
673C2×#95—431no—
674C2×#95—431no—
675C2×#95—431no—
676C2×#95—431no—
677C2×#95—431no—
678C2×#95—431no—
679C2×#95—431no—
680C2×#95—431no—
681C2×#95—431no—
682C2×#95C2×D4311yescharacteristic
683C2×#95C2×D4311yescharacteristic
684C2×#95C2×D4311yescharacteristic
685C2×#95C2×D4311yescharacteristic
686C2×#95C2×D4311yescharacteristic
687C43#1401511yescharacteristic, complemented, Sylow
688C25—431no—
689C25—431no—
690C22×D4—434no—
691C22×D4—434no—
692C22×D4—434no—
693C22×D4—862no—
694C22×D4—862no—
695C22×D4—862no—
696C22×D4—862no—
697C23×C4—431no—
698C23×C4—431no—
699C23×C4—431no—
700C23×C4—431no—
701C23×C4—431no—
702C23×C4—434no—
703C23×C4—434no—
704C23×C4—431no—
705C23×C4—862no—
706C23×C4—862no—
707C23×C4—862no—
708C23×C4—862no—
709C23×C4—862no—
710C23×C4—862no—
711C23×C4—862no—
712C23×C4—862no—
713C23×C4—862no—
714C23×C4—862no—
715C23×C4—862no—
716C23×C4—862no—
717C23×C4—862no—
718C23×C4—862no—
719C23×C4—862no—
720C23×C4—862no—
721C23×C4—862no—
722C23×C4—862no—
723C23×C4—862no—
724C23×C4—862no—
725C23×C4—1721no—
726C23×C4—1721no—
727C23×C4—1721no—
728C23×C4—1721no—
729C23×C4—1721no—
730C23×C4—1721no—
731C23×C4C22×D4311yescharacteristic
732C23×C4C22×D4311yescharacteristic
733C23×C4C22×D4311yescharacteristic
734C23×C4C22×D4311yescharacteristic
735C23×C4C22×D4311yescharacteristic
736C23×C4C22×D4311yescharacteristic
737C23×C4C22×D4311yescharacteristic
738C4×D4—8632no—
739C2×C4⋊C4—22no—
740C2×C4⋊C4—22no—
741C2×C4⋊C4—434no—
742C2×C4⋊C4—8632no—
743C2×C4⋊C4—862no—
744C2×C4⋊C4—862no—
745C2×C4⋊C4—862no—
746C2×C4⋊C4—862no—
747C2×C4⋊C4—862no—
748C2×C4⋊C4—862no—
749C2×C4⋊C4—862no—
750C2×C4⋊C4—862no—
751C2×C4⋊C4—862no—
752C2×C4⋊C4—862no—
753C2×C4⋊C4—862no—
754C2×C4⋊C4—862no—
755C2×C4⋊C4—862no—
756C2×C4⋊C4—862no—
757C2×C4⋊C4—862no—
758C2×C4⋊C4—1721no—
759C2×C4⋊C4—1721no—
760C2×C4⋊C4D17214yescomplemented
761C2×C22⋊C4—434no—
762C2×C22⋊C4—434no—
763C2×C22⋊C4—434no—
764C2×C22⋊C4—434no—
765C2×C22⋊C4—862no—
766C2×C22⋊C4—862no—
767C2×C22⋊C4—862no—
768C2×C22⋊C4—862no—
769C2×C22⋊C4—862no—
770C2×C22⋊C4—862no—
771C2×C22⋊C4—862no—
772C2×C22⋊C4—862no—
773C2×C22⋊C4—862no—
774C2×C22⋊C4—862no—
775C2×C22⋊C4—862no—
776C2×C22⋊C4—862no—
777C2×C22⋊C4—862no—
778C2×C22⋊C4—862no—
779C2×C22⋊C4—862no—
780C2×C22⋊C4—862no—
781C2×C22⋊C4—862no—
782C2×C22⋊C4—862no—
783C2×C22⋊C4—1721no—
784C2×C22⋊C4—1721no—
785C2×C42—22no—
786C2×C42—22no—
787C2×C42—22no—
788#95—22no—
789#95—22no—
790#95—22no—
791#95—22no—
792#95—434no—
793#95—862no—
794#95—862no—
795#95—862no—
796#95—862no—
797#95—862no—
798#95—862no—
799#95—1721no—
800#95—1721no—
801#95C4×D4314yescomplemented
802C24—432no—
803C24—432no—
804C24—432no—
805C24—432no—
806C24—432no—
807C24—432no—
808C24—432no—
809C24—432no—
810C24—432no—
811C24—432no—
812C24—861no—
813C24—861no—
814C24—861no—
815C24—861no—
816C24—861no—
817C24—861no—
818C24—861no—
819C24—861no—
820C24—861no—
821C24—861no—
822C24—861no—
823C24—861no—
824C24—861no—
825C24—861no—
826C24—861no—
827C24—861no—
828C24—861no—
829C24—861no—
830C24—861no—
831C24—861no—
832C24C23×D4311yescharacteristic
833C2×D4—4316no—
834C2×D4—868no—
835C2×D4—868no—
836C2×D4—868no—
837C2×D4—868no—
838C2×D4—868no—
839C2×D4—868no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—432no—
878C22×C4—432no—
879C22×C4—432no—
880C22×C4—432no—
881C22×C4—432no—
882C22×C4—432no—
883C22×C4—432no—
884C22×C4—868no—
885C22×C4—868no—
886C22×C4—868no—
887C22×C4—868no—
888C22×C4—868no—
889C22×C4—868no—
890C22×C4—868no—
891C22×C4—868no—
892C22×C4—868no—
893C22×C4—861no—
894C22×C4—861no—
895C22×C4—861no—
896C22×C4—861no—
897C22×C4—868no—
898C22×C4—861no—
899C22×C4—861no—
900C22×C4—861no—
901C22×C4—861no—
902C22×C4—861no—
903C22×C4—861no—
904C22×C4—861no—
905C22×C4—861no—
906C22×C4—861no—
907C22×C4—861no—
908C22×C4—861no—
909C22×C4—861no—
910C22×C4—861no—
911C22×C4—861no—
912C22×C4—861no—
913C22×C4—861no—
914C22×C4—861no—
915C22×C4—861no—
916C22×C4—861no—
917C22×C4—861no—
918C22×C4—861no—
919C22×C4—861no—
920C22×C4—861no—
921C22×C4—861no—
922C22×C4—868no—
923C22×C4—861no—
924C22×C4—861no—
925C22×C4—861no—
926C22×C4—861no—
927C22×C4—861no—
928C22×C4—861no—
929C22×C4—861no—
930C22×C4—1724no—
931C22×C4—1724no—
932C22×C4—1724no—
933C22×C4—1724no—
934C22×C4—1724no—
935C22×C4—1724no—
936C22×C4—1724no—
937C22×C4—1724no—
938C22×C4—1724no—
939C22×C4—1724no—
940C22×C4—1724no—
941C22×C4—1724no—
942C22×C4—1724no—
943C22×C4—1724no—
944C22×C4—1724no—
945C22×C4—1724no—
946C22×C4—1724no—
947C22×C4C2×C4×D4312yes—
948C22×C4C2×C4×D4312yes—
949C22×C4C2×C4×D4312yes—
950C22×C4C2×D17212yes—
951C22×C4C2×D17212yes—
952C22×C4C2×D17212yes—
953C22×C4#1062189812yes—
954C22×C4D4×D4312yes—
955C22×C4D4×D4312yes—
956C22×C4D4×D4312yes—
957C22×C4D4×D4312yes—
958C22×C4Q8×D4312yes—
959C4⋊C4—28no—
960C4⋊C4—868no—
961C4⋊C4—868no—
962C4⋊C4—868no—
963C4⋊C4—868no—
964C4⋊C4—1724no—
965C4⋊C4—1724no—
966C22⋊C4—868no—
967C22⋊C4—868no—
968C22⋊C4—868no—
969C22⋊C4—868no—
970C22⋊C4—868no—
971C22⋊C4—1724no—
972C22⋊C4—1724no—
973C22⋊C4—1724no—
974C42—28no—
975C23—434no—
976C23—434no—
977C23—434no—
978C23—434no—
979C23—434no—
980C23—434no—
981C23—434no—
982C23—434no—
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—
1006C23—862no—
1007C23—862no—
1008C23—862no—
1009C23—862no—
1010C23—862no—
1011C23—862no—
1012C23—862no—
1013C23—862no—
1014C23—862no—
1015C23—862no—
1016C23—862no—
1017C23—862no—
1018C23—862no—
1019C23—862no—
1020C23—862no—
1021C23—862no—
1022C23—862no—
1023C23—862no—
1024C23—862no—
1025C23—862no—
1026C23—862no—
1027C23—862no—
1028C23—862no—
1029C23—1721no—
1030C23—1721no—
1031C23—1721no—
1032C23—1721no—
1033C23—1721no—
1034C23—1721no—
1035C23—1721no—
1036C23—1721no—
1037C23—1721no—
1038C23—1721no—
1039C23—1721no—
1040C23—1721no—
1041C23—1721no—
1042C23—1721no—
1043C23—1721no—
1044C23—1721no—
1045C23C22×C4×D4311yescharacteristic
1046C23C2×D4×D4311yescharacteristic
1047C23C2×D4×D4311yescharacteristic
1048C23C2×D4×D4311yescharacteristic
1049C23C2×D4×D4311yescharacteristic
1050C23C22×D17211yescharacteristic
1051C23C2×Q8×D4311yescharacteristic
1052C23#41×D4311yescharacteristic
1053C23#41×D4311yescharacteristic
1054C23#41×D4311yescharacteristic
1055C23C2×#1062189811yescharacteristic
1056C23#1306337111yescharacteristic
1057C23#1306337111yescharacteristic
1058C23#1306337211yescharacteristic
1059C23#1306337311yescharacteristic
1060D4—8632no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—434no—
1108C2×C4—8632no—
1109C2×C4—862no—
1110C2×C4—862no—
1111C2×C4—862no—
1112C2×C4—862no—
1113C2×C4—862no—
1114C2×C4—862no—
1115C2×C4—862no—
1116C2×C4—862no—
1117C2×C4—862no—
1118C2×C4—862no—
1119C2×C4—862no—
1120C2×C4—862no—
1121C2×C4—862no—
1122C2×C4—862no—
1123C2×C4—862no—
1124C2×C4—862no—
1125C2×C4—862no—
1126C2×C4—862no—
1127C2×C4—17216no—
1128C2×C4—17216no—
1129C2×C4—17216no—
1130C2×C4—1721no—
1131C2×C4—1721no—
1132C2×C4—1721no—
1133C2×C4—1721no—
1134C2×C4—1721no—
1135C2×C4—1721no—
1136C2×C4—1721no—
1137C2×C4—1721no—
1138C2×C4—1721no—
1139C2×C4—1721no—
1140C2×C4—1721no—
1141C2×C4—1721no—
1142C2×C4—1721no—
1143C2×C4—1721no—
1144C2×C4—1721no—
1145C2×C4—1721no—
1146C2×C4—1721no—
1147C2×C4—1721no—
1148C2×C4—1721no—
1149C2×C4—1721no—
1150C2×C4—1721no—
1151C2×C4—1721no—
1152C2×C4—1721no—
1153C2×C4C4⋊C4×D4314yescomplemented
1154C2×C4C4×D17214yescomplemented
1155C2×C4#1306329514yes—
1156C22—438no—
1157C22—864no—
1158C22—864no—
1159C22—864no—
1160C22—864no—
1161C22—864no—
1162C22—864no—
1163C22—864no—
1164C22—864no—
1165C22—864no—
1166C22—864no—
1167C22—864no—
1168C22—864no—
1169C22—864no—
1170C22—864no—
1171C22—864no—
1172C22—864no—
1173C22—864no—
1174C22—1722no—
1175C22—1722no—
1176C22—1722no—
1177C22—1722no—
1178C22—1722no—
1179C22—1722no—
1180C22—1722no—
1181C22—1722no—
1182C22—1722no—
1183C22—1722no—
1184C22—1722no—
1185C22—1722no—
1186C22C2×C4⋊C4×D4311yescharacteristic
1187C22C4×D4×D4311yescharacteristic
1188C22C4×D4×D4311yescharacteristic
1189C22C4×D4×D4311yescharacteristic
1190C22C2×C4×D17211yescharacteristic
1191C22#1458337911yescharacteristic
1192C22#1458338111yescharacteristic
1193C22#120×D4311yescharacteristic
1194C22C2×#1306329511yescharacteristic
1195C22C22⋊Q8×D4311yescharacteristic
1196C22C22⋊Q8×D4311yescharacteristic
1197C22#123×D4311yescharacteristic
1198C22#1458340811yescharacteristic
1199C22#1458340811yescharacteristic
1200C22#1458341111yescharacteristic
1201C22#1458346011yescharacteristic
1202C22#1458347211yescharacteristic
1203C22#1458349011yescharacteristic
1204C22#1458349711yescharacteristic
1205C22#1458353311yescharacteristic
1206C22#1458353311yescharacteristic
1207C22D4×D17211yescharacteristic
1208C22D4×D17211yescharacteristic
1209C22#1458354711yescharacteristic
1210C22#1458355011yescharacteristic
1211C22#1458355111yescharacteristic
1212C22#1458355411yescharacteristic
1213C22#1458355711yescharacteristic
1214C22#1458356111yescharacteristic
1215C22#1458356411yescharacteristic
1216C22Q8×D17211yescharacteristic
1217C22#1458359311yescharacteristic
1218C22#1458360011yescharacteristic
1219C22#1458360511yescharacteristic
1220C22#1458360911yescharacteristic
1221C4—24no—
1222C4—24no—
1223C4—24no—
1224C4—42no—
1225C4—42no—
1226C4—42no—
1227C4—81no—
1228C4—864no—
1229C4—3441no—
1230C4—1722no—
1231C4—1722no—
1232C4—1722no—
1233C4—1722no—
1234C2—868no—
1235C2—1724no—
1236C2#385×D4311yescharacteristic
1237C2C4×#1306329511yescharacteristic
1238C2#1913726811yescharacteristic
1239C2#1913749611yescharacteristic
1240C2C4⋊C4×D17211yescharacteristic
1241C2#1913760811yescharacteristic
1242C2#1913761311yescharacteristic
1243C2#1913790711yescharacteristic
1244C2#1913792811yescharacteristic
1245C2#1913795811yescharacteristic
1246C2#1913833511yescharacteristic
1247C2#1913833711yescharacteristic
1248C2#1913840911yescharacteristic
1249C2#1913841111yescharacteristic
1250C2#1913994611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1436C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenter#1436D43
hypocenterC43#14015
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D43C2semidirect
5. C2×#14582773C2semidirect
6. C2×#14582773C2semidirect
7. C2×#14582770C2semidirect
8. #19132860C2semidirect
9. #19132859C2semidirect
10. #19132841C2semidirect
11. #19132839C2semidirect
12. #19132828C2semidirect
13. (C2×D43)⋊#95C2semidirect
14. (C2×D43)⋊#95C2semidirect
15. C43×#1436C2semidirect
42. #14582777C4semidirect
103. C22×C4×D43C2×C4semidirect
123. C2×Dic43⋊C4D4semidirect
145. C2×(C2×D43)⋊C4C2×C4semidirect
146. C2×(C2×D43)⋊C4C2×C4semidirect
147. C2×(C2×D43)⋊C4C2×C4semidirect
157. C43⋊#95C2×C4semidirect
167. C2×C4⋊C4×C43D4semidirect
175. #95×C43C2×C4semidirect
304. C2×D172C4⋊C4semidirect
427. C22×D43C2×C4⋊C4semidirect
480. C2×C4×C43C2×C4⋊C4semidirect
481. C2×C4×C43C4×D4semidirect
524. C2×Dic43C4×D4semidirect
595. C2×D43#385semidirect
621. #1436D43semidirect
687. C43#14015semidirect
760. C2×C4⋊C4D172semidirect
801. #95C4×D43semidirect
1153. C2×C4C4⋊C4×D43semidirect
1154. C2×C4C4×D172semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D1722
C22×C4⋊C4×D432
C2×#145827772
C2×#145827732
C2×#145827702
#191328602
#191328592
#191328412
#191328392
#191328282
(C2×D43)⋊#952
C43×#14362
#1401543