Finite Group Databasebeta

← #25019960

Subgroups — #25019960

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×(C22⋊D43)⋊C4C211yesmaximal, characteristic
2C22×C4⋊C4×D43C211yesmaximal, characteristic, complemented
3C2×#14582775C211yesmaximal, characteristic
4C2×#14582775C211yesmaximal, characteristic
5C2×#14582774C211yesmaximal, characteristic, complemented
6C2×#14582773C211yesmaximal, characteristic, complemented
7C2×#14582771C211yesmaximal, characteristic, complemented
8#19132859C211yesmaximal, characteristic, complemented
9#19132858C211yesmaximal, characteristic, complemented
10#19132838C211yesmaximal, characteristic, complemented
11#19132829C211yesmaximal, characteristic, complemented
12#19132826C211yesmaximal, characteristic, complemented
13(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
15C43×#1439C211yesmaximal, characteristic, complemented
16C23×C22⋊D43C2211yescharacteristic
17C24×Dic43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21C2×(C22⋊D43)⋊C4—24no—
22C2×(C22⋊D43)⋊C4—24no—
23C2×(C22⋊D43)⋊C4—24no—
24C22×C4⋊Dic43C2211yescharacteristic
25C22×C4⋊Dic43C2211yescharacteristic
26C22×Dic43⋊C4C2211yescharacteristic
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×C22⋊Dic43C2211yescharacteristic
34C22×C22⋊Dic43C2211yescharacteristic
35C22×(C2×D43)⋊C4C2211yescharacteristic
36C22×(C2×D43)⋊C4C2211yescharacteristic
37C22×(C2×D43)⋊C4C2211yescharacteristic
38C22×C4×Dic43C2211yescharacteristic
39#14582775—24no—
40#14582775C418yescomplemented
41#14582774—24no—
42#14582773—24no—
43#14582771—24no—
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
53C2×C43⋊#95C2211yescharacteristic
54C2×C43⋊#95C2211yescharacteristic
55C22×C4⋊C4×C43C2211yescharacteristic
56C22×C22⋊C4×C43C2211yescharacteristic
57C22×C22⋊C4×C43C2211yescharacteristic
58C22×C22⋊C4×C43C2211yescharacteristic
59C2×#95×C43C2211yescharacteristic
60C2×#95×C43C2211yescharacteristic
61C2×#95×C43C2211yescharacteristic
62C24×D43C2311yescharacteristic
63C22×C22⋊D43—22no—
64C22×C22⋊D43—22no—
65C22×C22⋊D43—22no—
66C22×C22⋊D43—22no—
67C22×C22⋊D43C2×C414yes—
68C22×C22⋊D43D414yes—
69C22×C22⋊D43Q814yes—
70C23×Dic43—22no—
71C23×Dic43—22no—
72C23×Dic43—22no—
73C23×Dic43—22no—
74C23×Dic43—22no—
75C23×Dic43—41no—
76C23×Dic43—41no—
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81C23×Dic43C2311yescharacteristic
82C23×Dic43C2311yescharacteristic
83C23×Dic43C2311yescharacteristic
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—22no—
98C22×C4×D43—22no—
99C22×C4×D43—41no—
100C22×C4×D43—41no—
101C22×C4×D43—41no—
102C22×C4×D43—41no—
103C22×C4×D43C2×C414yescomplemented
104C22×C4×D43D414yes—
105(C22⋊D43)⋊C4—232no—
106C2×C4⋊Dic43—22no—
107C2×C4⋊Dic43—22no—
108C2×C4⋊Dic43—22no—
109C2×C4⋊Dic43—22no—
110C2×C4⋊Dic43—41no—
111C2×C4⋊Dic43D414yescomplemented
112C2×Dic43⋊C4—22no—
113C2×Dic43⋊C4—22no—
114C2×Dic43⋊C4—22no—
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×C22⋊Dic43—22no—
126C2×C22⋊Dic43—22no—
127C2×C22⋊Dic43—22no—
128C2×C22⋊Dic43—22no—
129C2×C22⋊Dic43—41no—
130C2×C22⋊Dic43C2×C414yescomplemented
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)⋊C4C2×C414yescomplemented
139C2×(C2×D43)⋊C4D414yes—
140C2×C4×Dic43—22no—
141C2×C4×Dic43—22no—
142C2×C4×Dic43—22no—
143C43⋊#95—22no—
144C43⋊#95—22no—
145C43⋊#95—22no—
146C43⋊#95—22no—
147C43⋊#95—22no—
148C43⋊#95—22no—
149C43⋊#95—22no—
150C43⋊#95—22no—
151C43⋊#95—41no—
152C43⋊#95C2×C414yescomplemented
153C43⋊#95C2×C414yescomplemented
154C25×C43C2311yescharacteristic
155C23×C4×C43C2311yescharacteristic
156C23×C4×C43C2311yescharacteristic
157C23×C4×C43C2311yescharacteristic
158C23×C4×C43C2311yescharacteristic
159C23×C4×C43C2311yescharacteristic
160C23×C4×C43C2311yescharacteristic
161C2×C4⋊C4×C43—22no—
162C2×C4⋊C4×C43—22no—
163C2×C4⋊C4×C43—22no—
164C2×C22⋊C4×C43—22no—
165C2×C22⋊C4×C43—22no—
166C2×C22⋊C4×C43—22no—
167C2×C22⋊C4×C43—22no—
168C2×C22⋊C4×C43—22no—
169C2×C22⋊C4×C43—22no—
170C2×C22⋊C4×C43—22no—
171C2×C22⋊C4×C43—41no—
172C2×C22⋊C4×C43C2×C414yescomplemented
173#95×C43—22no—
174#95×C43—22no—
175#95×C43—41no—
176C24×C43—21no—
177C24×C43—21no—
178C24×C43—21no—
179C24×C43—21no—
180C24×C43—21no—
181C24×C43—21no—
182C24×C43—21no—
183C24×C43—21no—
184C24×C43—21no—
185C24×C43—21no—
186C24×C43—21no—
187C24×C43—21no—
188C24×C43C22×C412yes—
189C24×C43C2×D412yes—
190C24×C43C2×Q812yes—
191C24×C43C2411yescharacteristic
192C23×D43—21no—
193C23×D43—21no—
194C23×D43—21no—
195C23×D43—21no—
196C23×D43—21no—
197C23×D43—21no—
198C23×D43—21no—
199C23×D43—21no—
200C23×D43C22×C412yes—
201C23×D43C2×D412yes—
202C23×D43C2×D412yes—
203C23×D43C2×D412yes—
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×C43C22×C412yes—
243C22×C4×C43C22×C412yes—
244C22×C4×C43C2×D412yes—
245C22×C4×C43C2×D412yes—
246C22×C4×C43C2×D412yes—
247C22×C4×C43C2×D412yes—
248C22×C4×C43#4112yes—
249C2×C22⋊D43—28no—
250C2×C22⋊D43—28no—
251C2×C22⋊D43—28no—
252C2×C22⋊D43—28no—
253C2×C22⋊D43—28no—
254C2×C22⋊D43—28no—
255C2×C22⋊D43C4⋊C4116yescomplemented
256C22×Dic43—28no—
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×Dic43—21no—
292C22×Dic43—21no—
293C22×Dic43—21no—
294C22×Dic43—44no—
295C22×Dic43—44no—
296C22×Dic43—44no—
297C22×Dic43—44no—
298C22×Dic43—44no—
299C22×Dic43—44no—
300C22×Dic43C22×C412yes—
301C22×Dic43C22×C412yes—
302C22×Dic43C22×C412yes—
303C22×Dic43C2×D412yes—
304C22×Dic43C2×D412yes—
305C22×Dic43C2×D412yes—
306C22×Dic43C2×D412yes—
307C22×Dic43C2×D412yes—
308C22×Dic43C2×D412yes—
309C22×Dic43C2×D412yes—
310C22×Dic43C2×Q812yes—
311C22×Dic43#4112yes—
312C2×C4×D43—28no—
313C2×C4×D43—28no—
314C2×C4×D43—28no—
315C2×C4×D43—28no—
316C2×C4×D43—28no—
317C2×C4×D43—28no—
318C2×C4×D43—28no—
319C2×C4×D43—28no—
320C2×C4×D43—28no—
321C2×C4×D43—28no—
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—
334C22⋊C4×C43—28no—
335C22⋊C4×C43—28no—
336C22⋊C4×C43—44no—
337C22⋊Dic43—28no—
338C22⋊Dic43—44no—
339(C2×D43)⋊C4—28no—
340(C2×D43)⋊C4—28no—
341(C2×D43)⋊C4—44no—
342C4⋊Dic43—28no—
343C4⋊Dic43—44no—
344Dic43⋊C4—28no—
345Dic43⋊C4—28no—
346Dic43⋊C4—28no—
347Dic43⋊C4—44no—
348C4×Dic43—28no—
349C23×C43—22no—
350C23×C43—22no—
351C23×C43—22no—
352C23×C43—22no—
353C23×C43—22no—
354C23×C43—22no—
355C23×C43—22no—
356C23×C43—22no—
357C23×C43—22no—
358C23×C43—22no—
359C23×C43—22no—
360C23×C43—22no—
361C23×C43—22no—
362C23×C43—22no—
363C23×C43—22no—
364C23×C43—22no—
365C23×C43—22no—
366C23×C43—22no—
367C23×C43—41no—
368C23×C43—41no—
369C23×C43—41no—
370C23×C43—41no—
371C23×C43—41no—
372C23×C43—41no—
373C23×C43—41no—
374C23×C43—41no—
375C23×C43—41no—
376C23×C43—41no—
377C23×C43—41no—
378C23×C43—41no—
379C23×C43—41no—
380C23×C43—41no—
381C23×C43—41no—
382C23×C43—41no—
383C23×C43C2×C4⋊C414yescomplemented
384C23×C43C23×C411yescharacteristic
385C23×C43C22×D411yescharacteristic
386C23×C43C22×D411yescharacteristic
387C23×C43C22×D411yescharacteristic
388C23×C43C22×D411yescharacteristic
389C23×C43C22×D411yescharacteristic
390C23×C43C22×Q811yescharacteristic
391C23×C43C2×#4111yescharacteristic
392C23×C43C2×#4111yescharacteristic
393C23×C43C2×#4111yescharacteristic
394C23×C43C2×#4111yescharacteristic
395C23×C43H(5,𝔽2)11yescharacteristic
396C23×C43H(5,𝔽2)11yescharacteristic
397C23×C432−1+411yescharacteristic
398C23×C432−1+411yescharacteristic
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—22no—
411C22×D43—22no—
412C22×D43—22no—
413C22×D43—22no—
414C22×D43—22no—
415C22×D43—22no—
416C22×D43—22no—
417C22×D43—22no—
418C22×D43—22no—
419C22×D43—22no—
420C22×D43—22no—
421C22×D43—22no—
422C22×D43—22no—
423C22×D43—22no—
424C22×D43—22no—
425C22×D43—22no—
426C22×D43—22no—
427C22×D43C2×C4⋊C414yes—
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—41no—
453C2×C4×C43—41no—
454C2×C4×C43—41no—
455C2×C4×C43—41no—
456C2×C4×C43—41no—
457C2×C4×C43—41no—
458C2×C4×C43—41no—
459C2×C4×C43—41no—
460C2×C4×C43—41no—
461C2×C4×C43—41no—
462C2×C4×C43—41no—
463C2×C4×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×C43C4×D414yescomplemented
476C22⋊D43—232no—
477C2×Dic43—22no—
478C2×Dic43—22no—
479C2×Dic43—22no—
480C2×Dic43—22no—
481C2×Dic43—22no—
482C2×Dic43—22no—
483C2×Dic43—22no—
484C2×Dic43—22no—
485C2×Dic43—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—22no—
502C2×Dic43—22no—
503C2×Dic43—22no—
504C2×Dic43—416no—
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×Dic43C2×C4⋊C414yescomplemented
525C2×Dic43C4×D414yescomplemented
526C2×Dic43#12014yes—
527C4×D43—232no—
528C4×D43—416no—
529C4×D43—416no—
530#14015—431nomaximal, Sylow
531C22×C43—24no—
532C22×C43—24no—
533C22×C43—24no—
534C22×C43—42no—
535C22×C43—42no—
536C22×C43—42no—
537C22×C43—42no—
538C22×C43—42no—
539C22×C43—42no—
540C22×C43—42no—
541C22×C43—42no—
542C22×C43—42no—
543C22×C43—42no—
544C22×C43—42no—
545C22×C43—42no—
546C22×C43C22×C4⋊C411yescharacteristic
547C22×C43C2×C4×D411yescharacteristic
548C22×C43C2×C4×D411yescharacteristic
549C22×C43C2×C4×D411yescharacteristic
550C22×C43C2×C4×D411yescharacteristic
551C22×C43#52011yescharacteristic
552C22×C43#52011yescharacteristic
553C22×C43C2×#12011yescharacteristic
554C22×C43C2×#12011yescharacteristic
555C22×C43C2×C22⋊Q811yescharacteristic
556C22×C43C2×C22⋊Q811yescharacteristic
557C22×C43C2×#12311yescharacteristic
558C22×C43#52511yescharacteristic
559C22×C43#52511yescharacteristic
560C22×C43#52511yescharacteristic
561C22×C43#53411yescharacteristic
562C22×C43#53611yescharacteristic
563C22×C43#53911yescharacteristic
564C22×C43#53911yescharacteristic
565C22×C43D4211yescharacteristic
566C22×C43D4211yescharacteristic
567C22×C43D4211yescharacteristic
568C22×C43D4211yescharacteristic
569C22×C43#54711yescharacteristic
570C22×C43#54711yescharacteristic
571C22×C43#54711yescharacteristic
572C22×C43#54711yescharacteristic
573C22×C43#54811yescharacteristic
574C22×C43#54811yescharacteristic
575C22×C43D4×Q811yescharacteristic
576C22×C43D4×Q811yescharacteristic
577C22×C43#55311yescharacteristic
578C22×C43#55311yescharacteristic
579C22×C43#55411yescharacteristic
580C22×C43#55411yescharacteristic
581C2×D43—24no—
582C2×D43—24no—
583C2×D43—24no—
584C2×D43—24no—
585C2×D43—24no—
586C2×D43—24no—
587C2×D43—24no—
588C2×D43—24no—
589C2×D43—24no—
590C2×D43—24no—
591C2×D43—24no—
592C2×D43—24no—
593C2×D43—24no—
594C2×D43—24no—
595C2×D43#38518yescomplemented
596C4×C43—24no—
597C4×C43—42no—
598C4×C43—42no—
599C4×C43—42no—
600C4×C43—42no—
601C4×C43—81no—
602Dic43—24no—
603Dic43—24no—
604Dic43—24no—
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#1439D4311yescharacteristic, complemented
620#1436—431no—
621#1436—431no—
622C22⋊#95—431no—
623C22⋊#95—431no—
624C2×C43—44no—
625C2×C43C2×#38511yescharacteristic
626C2×C43C4×#12011yescharacteristic
627C2×C43#232211yescharacteristic
628C2×C43D4×C4⋊C411yescharacteristic
629C2×C43D4×C4⋊C411yescharacteristic
630C2×C43#236111yescharacteristic
631C2×C43#236111yescharacteristic
632C2×C43#240311yescharacteristic
633C2×C43#240611yescharacteristic
634C2×C43#240911yescharacteristic
635C2×C43#244311yescharacteristic
636C2×C43#244311yescharacteristic
637C2×C43#244911yescharacteristic
638C2×C43#244911yescharacteristic
639C2×C43#257911yescharacteristic
640D43—28no—
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⋊C4C2×D4311yescharacteristic
665C22×C22⋊C4C2×D4311yescharacteristic
666C22×C22⋊C4C2×D4311yescharacteristic
667C22×C42—431no—
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×#95—431no—
683C2×#95—431no—
684C2×#95C2×D4311yescharacteristic
685C2×#95C2×D4311yescharacteristic
686C2×#95C2×D4311yescharacteristic
687C43#1401511yescharacteristic, complemented, Sylow
688C25—431no—
689C25C22×D4311yescharacteristic
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—431no—
703C23×C4—434no—
704C23×C4—434no—
705C23×C4—431no—
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—862no—
726C23×C4—1721no—
727C23×C4—1721no—
728C23×C4—1721no—
729C23×C4—1721no—
730C23×C4—1721no—
731C23×C4—1721no—
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—22no—
742C2×C4⋊C4—434no—
743C2×C4⋊C4—434no—
744C2×C4⋊C4—8632no—
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—862no—
759C2×C4⋊C4—1721no—
760C2×C4⋊C4—1721no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4—22no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—22no—
768C2×C22⋊C4—41no—
769C2×C22⋊C4—434no—
770C2×C22⋊C4—434no—
771C2×C22⋊C4—434no—
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⋊C4C4×D4314yescomplemented
785C2×C42—862no—
786C2×C42—862no—
787C2×C42—862no—
788#95—22no—
789#95—22no—
790#95—41no—
791#95—434no—
792#95—434no—
793#95—862no—
794#95—862no—
795#95—862no—
796#95—862no—
797#95—862no—
798#95—862no—
799#95—862no—
800#95—862no—
801#95—1721no—
802C24—21no—
803C24—21no—
804C24—21no—
805C24—21no—
806C24—21no—
807C24—21no—
808C24—21no—
809C24—21no—
810C24—21no—
811C24—21no—
812C24—21no—
813C24—21no—
814C24—432no—
815C24—432no—
816C24—432no—
817C24—432no—
818C24—432no—
819C24—432no—
820C24—432no—
821C24—861no—
822C24—861no—
823C24—861no—
824C24—861no—
825C24—861no—
826C24—861no—
827C24—861no—
828C24—861no—
829C24C2×C4×D4312yes—
830C24D4×D4312yes—
831C24Q8×D4312yes—
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—432no—
876C22×C4—432no—
877C22×C4—432no—
878C22×C4—432no—
879C22×C4—432no—
880C22×C4—432no—
881C22×C4—432no—
882C22×C4—432no—
883C22×C4—432no—
884C22×C4—432no—
885C22×C4—432no—
886C22×C4—432no—
887C22×C4—868no—
888C22×C4—868no—
889C22×C4—868no—
890C22×C4—868no—
891C22×C4—868no—
892C22×C4—868no—
893C22×C4—868no—
894C22×C4—868no—
895C22×C4—868no—
896C22×C4—861no—
897C22×C4—861no—
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—868no—
909C22×C4—868no—
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—861no—
923C22×C4—861no—
924C22×C4—861no—
925C22×C4—861no—
926C22×C4—861no—
927C22×C4—861no—
928C22×C4—861no—
929C22×C4—861no—
930C22×C4—861no—
931C22×C4—861no—
932C22×C4—861no—
933C22×C4—861no—
934C22×C4—861no—
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×C4—1724no—
948C22×C4—1724no—
949C22×C4—1724no—
950C22×C4—1724no—
951C22×C4—1724no—
952C22×C4C2×C4×D4312yes—
953C22×C4C2×C4×D4312yes—
954C22×C4D4×D4312yes—
955C22×C4D4×D4312yes—
956C22×C4D4×D4312yes—
957C22×C4D4×D4312yes—
958C22×C4#1062190012yes—
959C4⋊C4—28no—
960C4⋊C4—868no—
961C4⋊C4—868no—
962C4⋊C4—868no—
963C4⋊C4—868no—
964C4⋊C4—1724no—
965C4⋊C4—1724no—
966C22⋊C4—28no—
967C22⋊C4—28no—
968C22⋊C4—44no—
969C22⋊C4—868no—
970C22⋊C4—868no—
971C22⋊C4—868no—
972C22⋊C4—1724no—
973C22⋊C4—1724no—
974C42—868no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—434no—
1010C23—434no—
1011C23—434no—
1012C23—434no—
1013C23—434no—
1014C23—434no—
1015C23—434no—
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—862no—
1030C23—862no—
1031C23—862no—
1032C23—862no—
1033C23—862no—
1034C23—862no—
1035C23—862no—
1036C23—862no—
1037C23—862no—
1038C23—862no—
1039C23—862no—
1040C23—862no—
1041C23—862no—
1042C23—862no—
1043C23—862no—
1044C23C4⋊C4×D4314yescomplemented
1045C23C22×C4×D4311yescharacteristic
1046C23C2×D4×D4311yescharacteristic
1047C23C2×D4×D4311yescharacteristic
1048C23C2×D4×D4311yescharacteristic
1049C23C2×D4×D4311yescharacteristic
1050C23C2×D4×D4311yescharacteristic
1051C23C2×Q8×D4311yescharacteristic
1052C23#41×D4311yescharacteristic
1053C23#41×D4311yescharacteristic
1054C23#41×D4311yescharacteristic
1055C23C2×#1062190011yescharacteristic
1056C23#1306337011yescharacteristic
1057C23#1306337111yescharacteristic
1058C23#1306337211yescharacteristic
1059C23#1306337211yescharacteristic
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—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
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—434no—
1103C2×C4—434no—
1104C2×C4—434no—
1105C2×C4—8632no—
1106C2×C4—862no—
1107C2×C4—862no—
1108C2×C4—862no—
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—862no—
1128C2×C4—862no—
1129C2×C4—862no—
1130C2×C4—862no—
1131C2×C4—862no—
1132C2×C4—862no—
1133C2×C4—17216no—
1134C2×C4—17216no—
1135C2×C4—17216no—
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×C4—1721no—
1154C2×C4—1721no—
1155C2×C4(C22⋊D43)⋊C414yescomplemented
1156C22—24no—
1157C22—24no—
1158C22—24no—
1159C22—42no—
1160C22—42no—
1161C22—42no—
1162C22—42no—
1163C22—42no—
1164C22—42no—
1165C22—42no—
1166C22—42no—
1167C22—42no—
1168C22—42no—
1169C22—42no—
1170C22—42no—
1171C22—438no—
1172C22—864no—
1173C22—864no—
1174C22—864no—
1175C22—864no—
1176C22—864no—
1177C22—864no—
1178C22—864no—
1179C22—864no—
1180C22—864no—
1181C22—864no—
1182C22—864no—
1183C22—864no—
1184C22—864no—
1185C22—864no—
1186C22C2×C4⋊C4×D4311yescharacteristic
1187C22C4×D4×D4311yescharacteristic
1188C22C4×D4×D4311yescharacteristic
1189C22C4×D4×D4311yescharacteristic
1190C22C2×(C22⋊D43)⋊C411yescharacteristic
1191C22#1458337811yescharacteristic
1192C22#1458337911yescharacteristic
1193C22#120×D4311yescharacteristic
1194C22#120×D4311yescharacteristic
1195C22C22⋊Q8×D4311yescharacteristic
1196C22C22⋊Q8×D4311yescharacteristic
1197C22#123×D4311yescharacteristic
1198C22#1458340711yescharacteristic
1199C22#1458340911yescharacteristic
1200C22#1458340911yescharacteristic
1201C22#1458345711yescharacteristic
1202C22#1458346911yescharacteristic
1203C22#1458349011yescharacteristic
1204C22#1458349211yescharacteristic
1205C22#1458353111yescharacteristic
1206C22#1458353311yescharacteristic
1207C22#1458353311yescharacteristic
1208C22#1458353411yescharacteristic
1209C22#1458354711yescharacteristic
1210C22#1458354711yescharacteristic
1211C22#1458354911yescharacteristic
1212C22#1458354911yescharacteristic
1213C22#1458355711yescharacteristic
1214C22#1458355711yescharacteristic
1215C22#1458356211yescharacteristic
1216C22#1458356211yescharacteristic
1217C22#1458359611yescharacteristic
1218C22#1458360011yescharacteristic
1219C22#1458360311yescharacteristic
1220C22#1458360711yescharacteristic
1221C4—24no—
1222C4—42no—
1223C4—42no—
1224C4—42no—
1225C4—42no—
1226C4—81no—
1227C4—864no—
1228C4—864no—
1229C4—864no—
1230C4—3441no—
1231C4—1722no—
1232C4—1722no—
1233C4—1722no—
1234C2—44no—
1235C2—868no—
1236C2#385×D4311yescharacteristic
1237C2#1913710011yescharacteristic
1238C2#1913726511yescharacteristic
1239C2#1913749111yescharacteristic
1240C2#1913749311yescharacteristic
1241C2#1913760811yescharacteristic
1242C2#1913761611yescharacteristic
1243C2#1913790411yescharacteristic
1244C2#1913792511yescharacteristic
1245C2#1913795311yescharacteristic
1246C2#1913832311yescharacteristic
1247C2#1913832511yescharacteristic
1248C2#1913840511yescharacteristic
1249C2#1913840711yescharacteristic
1250C2#1913993711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1439C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenter#1439D43
hypocenterC43#14015
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D43C2semidirect
5. C2×#14582774C2semidirect
6. C2×#14582773C2semidirect
7. C2×#14582771C2semidirect
8. #19132859C2semidirect
9. #19132858C2semidirect
10. #19132838C2semidirect
11. #19132829C2semidirect
12. #19132826C2semidirect
13. (C2×D43)⋊#95C2semidirect
14. (C2×D43)⋊#95C2semidirect
15. C43×#1439C2semidirect
40. #14582775C4semidirect
103. C22×C4×D43C2×C4semidirect
111. C2×C4⋊Dic43D4semidirect
123. C2×Dic43⋊C4D4semidirect
130. C2×C22⋊Dic43C2×C4semidirect
138. C2×(C2×D43)⋊C4C2×C4semidirect
152. C43⋊#95C2×C4semidirect
153. C43⋊#95C2×C4semidirect
172. C2×C22⋊C4×C43C2×C4semidirect
255. C2×C22⋊D43C4⋊C4semidirect
383. C23×C43C2×C4⋊C4semidirect
475. C2×C4×C43C4×D4semidirect
524. C2×Dic43C2×C4⋊C4semidirect
525. C2×Dic43C4×D4semidirect
595. C2×D43#385semidirect
619. #1439D43semidirect
687. C43#14015semidirect
784. C2×C22⋊C4C4×D43semidirect
1044. C23C4⋊C4×D43semidirect
1155. C2×C4(C22⋊D43)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×(C22⋊D43)⋊C42
C22×C4⋊C4×D432
C2×#145827752
C2×#145827742
C2×#145827732
C2×#145827712
#191328592
#191328582
#191328382
#191328292
#191328262
(C2×D43)⋊#952
C43×#14392
#1401543