Finite Group Databasebeta

← #25269515

Subgroups — #25269515

Order 11008.

2642 conjugacy classes of subgroups.

The subgroup lattice has 1208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583484C212yesmaximal, complemented
2#19142945C211yesmaximal, characteristic, complemented
3#19142938C211yesmaximal, characteristic, complemented
4#19142877C211yesmaximal, characteristic, complemented
5#19140525C212yesmaximal, complemented
6#19140333C212yesmaximal, complemented
7#19139723C212yesmaximal, complemented
8#19139721C212yesmaximal, complemented
9#19139693C212yesmaximal, complemented
10#19139691C212yesmaximal, complemented
11#19139019C211yesmaximal, characteristic, complemented
12#19139013C211yesmaximal, characteristic, complemented
13#19138960C211yesmaximal, characteristic, complemented
14#19138954C211yesmaximal, characteristic, complemented
15#19138185C211yesmaximal, characteristic, complemented
16#19138179C211yesmaximal, characteristic, complemented
17#19138111C211yesmaximal, characteristic, complemented
18#19138105C211yesmaximal, characteristic, complemented
19#19137296C212yesmaximal, complemented
20#121×Dic43C211yesmaximal, characteristic, complemented
21#19137101C211yesmaximal, characteristic, complemented
22C2×C4×C22⋊Dic43C211yesmaximal, characteristic, complemented
23C43×#2847C211yesmaximal, characteristic, complemented
24#14583484—216no—
25C2×#13063324C2211yescharacteristic, complemented
26C2×#13063321C2211yescharacteristic, complemented
27C2×#13063318C2212yes—
28C2×#13063318C2212yes—
29C2×#13063312C2212yes—
30C2×#13063311C2212yes—
31C2×#13063307C2212yes—
32C2×#13063306C2212yes—
33C2×#13063302C2212yes—
34C2×#13063299C2211yescharacteristic
35C2×#13063299C2211yescharacteristic
36C2×#13063299C2211yescharacteristic
37C2×#13063297C2212yes—
38C2×#13063297C2212yes—
39C2×#13063297C2212yes—
40C2×#13063296C2212yes—
41C2×#13063294C2212yes—
42C2×D4×Dic43C2212yes—
43C2×D4×Dic43C2211yescharacteristic, complemented
44C2×#13063287C2211yescharacteristic, complemented
45C2×(C22⋊D43)⋊C4C2212yes—
46C22×C22⋊Dic43C2211yescharacteristic
47C22×C22⋊Dic43C2211yescharacteristic
48C22×C4×Dic43C2211yescharacteristic
49C22×C4×Dic43C2211yescharacteristic
50#14582841C2212yescomplemented
51#14582840C2212yescomplemented
52#14582828C2212yescomplemented
53#14582827C2212yes—
54#14582827C2212yes—
55#14582827C2212yescomplemented
56#14582815C2212yescomplemented
57#14582814C2212yes—
58#14582814C2212yes—
59#14582814C2212yescomplemented
60#14582813C2212yes—
61#14582813C2212yes—
62#14582812C2212yescomplemented
63#14582811C2212yescomplemented
64#14582807C2212yes—
65#14582807C2212yes—
66#14582803C2212yescomplemented
67#14582802C2211yescharacteristic, complemented
68#14582802C2211yescharacteristic, complemented
69#14582800C2211yescharacteristic, complemented
70#14582800C2211yescharacteristic, complemented
71#14582799C2212yescomplemented
72#14582799C2212yescomplemented
73#14582798C2211yescharacteristic, complemented
74#14582798C2211yescharacteristic, complemented
75#14582796C2212yescomplemented
76#14582795C2211yescharacteristic, complemented
77#14582795C2211yescharacteristic, complemented
78#14582793C2212yescomplemented
79#14582792C2212yescomplemented
80#14582788C2212yescomplemented
81#14582788C2212yescomplemented
82#14582786C2212yescomplemented
83#14582781C2212yescomplemented
84#14582779C2212yes—
85#14582778C2212yes—
86#14582778C2212yes—
87#14582778C2212yes—
88#14582776C2212yes—
89#14582776C2212yescomplemented
90#14582775C2212yescomplemented
91#14582773C2212yescomplemented
92#14582771C2212yescomplemented
93#14582768C2211yescharacteristic, complemented
94#14582768C2211yescharacteristic, complemented
95#14582759C2211yescharacteristic
96#14582759C2211yescharacteristic
97#14582759C2211yescharacteristic
98#14582757C2212yes—
99C4⋊C4×Dic43C2211yescharacteristic, complemented
100C4⋊C4×Dic43C2211yescharacteristic, complemented
101C22⋊C4×Dic43C2212yescomplemented
102C4×C22⋊Dic43C2211yescharacteristic
103C4×C22⋊Dic43C2211yescharacteristic
104C4×C22⋊Dic43C2211yescharacteristic
105C4×C22⋊Dic43C2211yescharacteristic
106C4×C22⋊Dic43C2211yescharacteristic
107C4×C22⋊Dic43C2211yescharacteristic
108C4×C22⋊Dic43C2211yescharacteristic
109C4×C22⋊Dic43C2211yescharacteristic
110#14582746C2212yescomplemented
111C2×C43⋊#95C2211yescharacteristic
112C2×C43⋊#95C2211yescharacteristic
113C24×C4×C43C2211yescharacteristic
114C2×#121×C43C2211yescharacteristic
115C2×#121×C43C2211yescharacteristic
116C2×#121×C43C2211yescharacteristic
117C2×#120×C43C2212yes—
118C43×#386C2212yes—
119C43×#386C2212yes—
120C43×#386C2212yes—
121C43×#380C2211yescharacteristic
122C43×#380C2211yescharacteristic
123C43×#380C2211yescharacteristic
124C22×Dic86C2312yes—
125C22×D172C2311yescharacteristic
126C22×C22⋊D43C2312yes—
127C22×C22⋊D43C2312yes—
128C22×C22⋊D43C2312yes—
129C22×C22⋊D43C2312yes—
130C22×C22⋊D43C2312yes—
131C23×Dic43C2311yescharacteristic
132C23×Dic43C2312yes—
133C23×Dic43C2311yescharacteristic
134C23×Dic43C2311yescharacteristic
135C23×Dic43C2311yescharacteristic
136C22×C4×D43C2312yes—
137#13063324—42no—
138#13063321—42no—
139#13063318—28no—
140#13063318—28no—
141#13063312—28no—
142#13063311—28no—
143#13063307—28no—
144#13063306—28no—
145#13063302—28no—
146#13063299—24no—
147#13063299—42no—
148#13063299—42no—
149#13063297—28no—
150#13063297—28no—
151#13063297—28no—
152#13063296—28no—
153#13063294—28no—
154D4×Dic43—28no—
155D4×Dic43—42no—
156#13063287—42no—
157(C22⋊D43)⋊C4—28no—
158C2×C4⋊Dic43C2312yes—
159C2×C4⋊Dic43C2311yescharacteristic
160C2×C4⋊Dic43C2311yescharacteristic
161C2×C4⋊Dic43C2312yes—
162C2×C4⋊Dic43C2311yescharacteristic
163C2×Dic43⋊C4C2312yes—
164C2×Dic43⋊C4C2312yes—
165C2×Dic43⋊C4C2312yes—
166C2×Dic43⋊C4C2312yes—
167C2×Dic43⋊C4C2312yes—
168C2×Dic43⋊C4C2312yes—
169C2×Dic43⋊C4C2312yes—
170C2×C22⋊Dic43—24no—
171C2×C22⋊Dic43D418yescomplemented
172C2×C22⋊Dic43C2312yes—
173C2×C22⋊Dic43C2312yes—
174C2×C22⋊Dic43C2312yes—
175C2×C22⋊Dic43C2311yescharacteristic
176C2×C22⋊Dic43C2311yescharacteristic
177C2×C22⋊Dic43C2311yescharacteristic
178C2×C22⋊Dic43C2311yescharacteristic
179C2×C22⋊Dic43C2312yes—
180C2×C22⋊Dic43C2312yes—
181C2×C22⋊Dic43C2312yes—
182C2×C22⋊Dic43C2312yes—
183C2×C22⋊Dic43C2312yes—
184C2×C22⋊Dic43C2311yescharacteristic
185C2×C22⋊Dic43C2311yescharacteristic
186C2×C22⋊Dic43C2311yescharacteristic
187C2×C22⋊Dic43C2311yescharacteristic
188C2×(C2×D43)⋊C4C2312yes—
189C2×(C2×D43)⋊C4C2312yes—
190C2×(C2×D43)⋊C4C2312yes—
191C2×(C2×D43)⋊C4C2312yes—
192C2×(C2×D43)⋊C4C2312yes—
193C2×(C2×D43)⋊C4C2312yes—
194C2×(C2×D43)⋊C4C2312yes—
195C2×(C2×D43)⋊C4C2312yes—
196C2×C4×Dic43—42no—
197C2×C4×Dic43—42no—
198C2×C4×Dic43C2312yes—
199C2×C4×Dic43C2312yes—
200C2×C4×Dic43C2311yescharacteristic
201C2×C4×Dic43C2311yescharacteristic
202C2×C4×Dic43C2311yescharacteristic
203C2×C4×Dic43C2311yescharacteristic
204C2×C4×Dic43C2311yescharacteristic
205C2×C4×Dic43C2311yescharacteristic
206C2×C4×Dic43C2311yescharacteristic
207C2×C4×Dic43C2311yescharacteristic
208C43⋊#95C2311yescharacteristic
209C43⋊#95C2312yes—
210C43⋊#95C2312yes—
211C43⋊#95C2311yescharacteristic
212C43⋊#95C2312yes—
213C43⋊#95C2312yes—
214C43⋊#95C2312yes—
215C43⋊#95C2311yescharacteristic
216C43⋊#95C2312yes—
217C43⋊#95C2312yes—
218C43⋊#95C2312yes—
219C43⋊#95C2312yes—
220C43⋊#95C2311yescharacteristic
221C43⋊#95C2311yescharacteristic
222C43⋊#95C2311yescharacteristic
223C43⋊#95C2311yescharacteristic
224C43⋊#95C2311yescharacteristic
225C25×C43C2311yescharacteristic
226C22×D4×C43C2311yescharacteristic
227C22×D4×C43C2312yes—
228C22×D4×C43C2312yes—
229C22×D4×C43C2312yes—
230C23×C4×C43—24no—
231C23×C4×C43—42no—
232C23×C4×C43—42no—
233C23×C4×C43C2311yescharacteristic
234C23×C4×C43C2311yescharacteristic
235C23×C4×C43C2311yescharacteristic
236C23×C4×C43C2311yescharacteristic
237C23×C4×C43C2311yescharacteristic
238C23×C4×C43C2311yescharacteristic
239#121×C43—24no—
240#121×C43—42no—
241#121×C43—42no—
242#120×C43—28no—
243C2×C4⋊C4×C43C2311yescharacteristic
244C2×C4⋊C4×C43C2311yescharacteristic
245C2×C4⋊C4×C43C2311yescharacteristic
246C2×C22⋊C4×C43C2312yes—
247C2×C22⋊C4×C43C2312yes—
248C2×C22⋊C4×C43C2312yes—
249C2×C22⋊C4×C43C2312yes—
250C2×C22⋊C4×C43C2312yes—
251C2×C22⋊C4×C43C2312yes—
252#95×C43C2312yes—
253#95×C43C2312yes—
254#95×C43C2312yes—
255C24×C43—22no—
256C24×C43—22no—
257C24×C43—41no—
258C24×C43—41no—
259C24×C43—41no—
260C24×C43—41no—
261C24×C43C2×D414yes—
262C24×C43C2412yes—
263C24×C43C2411yescharacteristic
264C24×C43C2411yescharacteristic
265C24×C43C2411yescharacteristic
266C23×D43C2412yes—
267C2×D4×C43—22no—
268C2×D4×C43—22no—
269C2×D4×C43—22no—
270C2×D4×C43—24no—
271C2×D4×C43—24no—
272C2×D4×C43—24no—
273C2×D4×C43—24no—
274C2×D4×C43—24no—
275C2×D4×C43—42no—
276C2×D4×C43—42no—
277C2×D4×C43—42no—
278C2×D4×C43—42no—
279C22×C4×C43—22no—
280C22×C4×C43—22no—
281C22×C4×C43—22no—
282C22×C4×C43—22no—
283C22×C4×C43—22no—
284C22×C4×C43—22no—
285C22×C4×C43—22no—
286C22×C4×C43—22no—
287C22×C4×C43—22no—
288C22×C4×C43—22no—
289C22×C4×C43—22no—
290C22×C4×C43—41no—
291C22×C4×C43—41no—
292C22×C4×C43—41no—
293C22×C4×C43—41no—
294C22×C4×C43—41no—
295C22×C4×C43—41no—
296C22×C4×C43—416no—
297C22×C4×C43#4114yes—
298C22×C4×C43C2412yes—
299C22×C4×C43C2412yes—
300C22×C4×C43C2412yes—
301C22×C4×C43C2411yescharacteristic
302C22×C4×C43C2411yescharacteristic
303C22×C4×C43C2411yescharacteristic
304C22×C4×C43C2411yescharacteristic
305C2×C22⋊D43—24no—
306C2×C22⋊D43—24no—
307C2×C22⋊D43—24no—
308C2×C22⋊D43—24no—
309C2×C22⋊D43—24no—
310C2×C22⋊D43—24no—
311C2×C22⋊D43—24no—
312C2×C22⋊D43—42no—
313C2×C22⋊D43—42no—
314C2×C22⋊D43—42no—
315C2×C22⋊D43—42no—
316C2×C22⋊D43—42no—
317C2×C22⋊D43—42no—
318C2×C22⋊D43—42no—
319C2×C22⋊D43—42no—
320C22×Dic43—24no—
321C22×Dic43—22no—
322C22×Dic43—41no—
323C22×Dic43—41no—
324C22×Dic43—41no—
325C22×Dic43—41no—
326C22×Dic43—41no—
327C22×Dic43—41no—
328C22×Dic43—41no—
329C22×Dic43—41no—
330C22×Dic43—42no—
331C22×Dic43—42no—
332C22×Dic43C2×D414yes—
333C22×Dic43C2×D414yes—
334C22×Dic43#4114yes—
335C22×Dic43C2411yescharacteristic
336C22×Dic43C2411yescharacteristic
337C22×Dic43C2412yes—
338C22×Dic43C2412yes—
339C22×Dic43C2412yes—
340C22×Dic43C2411yescharacteristic
341C22×Dic43C2411yescharacteristic
342C22×Dic43C2411yescharacteristic
343C22×Dic43C2411yescharacteristic
344C22×Dic43C2411yescharacteristic
345C22×Dic43C2411yescharacteristic
346C2×D172—22no—
347C2×D172—22no—
348C2×D172—22no—
349C2×C4×D43—24no—
350C2×C4×D43—42no—
351C2×C4×D43—42no—
352C2×Dic86—24no—
353C2×Dic86—42no—
354C2×Dic86—42no—
355C4⋊C4×C43—22no—
356C4⋊C4×C43—22no—
357C4⋊C4×C43—22no—
358C22⋊C4×C43—24no—
359C22⋊C4×C43—24no—
360C22⋊C4×C43—24no—
361C22⋊C4×C43—24no—
362C22⋊C4×C43—42no—
363C22⋊C4×C43—42no—
364C22⋊Dic43—24no—
365C22⋊Dic43—24no—
366C22⋊Dic43—22no—
367C22⋊Dic43—22no—
368C22⋊Dic43—22no—
369C22⋊Dic43—22no—
370C22⋊Dic43—24no—
371C22⋊Dic43—24no—
372C22⋊Dic43—24no—
373C22⋊Dic43—24no—
374C22⋊Dic43—42no—
375C22⋊Dic43—42no—
376C22⋊Dic43C2×D414yes—
377C22⋊Dic43C2×D414yes—
378C22⋊Dic43C2×D414yes—
379C22⋊Dic43C2×D414yes—
380(C2×D43)⋊C4—24no—
381(C2×D43)⋊C4—24no—
382(C2×D43)⋊C4—24no—
383(C2×D43)⋊C4—24no—
384(C2×D43)⋊C4—42no—
385(C2×D43)⋊C4—42no—
386(C2×D43)⋊C4—42no—
387(C2×D43)⋊C4—42no—
388C4⋊Dic43—22no—
389C4⋊Dic43—22no—
390C4⋊Dic43—22no—
391C4⋊Dic43—24no—
392C4⋊Dic43—24no—
393Dic43⋊C4—24no—
394Dic43⋊C4—24no—
395Dic43⋊C4—24no—
396Dic43⋊C4—24no—
397Dic43⋊C4—24no—
398Dic43⋊C4—42no—
399Dic43⋊C4—42no—
400C4×Dic43—22no—
401C4×Dic43—22no—
402C4×Dic43—22no—
403C4×Dic43—22no—
404C4×Dic43—24no—
405C4×Dic43—24no—
406C4×Dic43—41no—
407C4×Dic43—41no—
408C4×Dic43—41no—
409C4×Dic43—41no—
410C23×C43—21no—
411C23×C43—21no—
412C23×C43—21no—
413C23×C43—21no—
414C23×C43—28no—
415C23×C43—21no—
416C23×C43—21no—
417C23×C43—21no—
418C23×C43—21no—
419C23×C43—21no—
420C23×C43—21no—
421C23×C43—21no—
422C23×C43—21no—
423C23×C43—21no—
424C23×C43—21no—
425C23×C43—21no—
426C23×C43—21no—
427C23×C43—22no—
428C23×C43—22no—
429C23×C43—22no—
430C23×C43—22no—
431C23×C43—22no—
432C23×C43—22no—
433C23×C43—22no—
434C23×C43—44no—
435C23×C43—44no—
436C23×C43—44no—
437C23×C43—44no—
438C23×C43—44no—
439C23×C43—44no—
440C23×C43C22×D412yes—
441C23×C43C22×D412yes—
442C23×C43C22×D412yes—
443C23×C43C2×#4112yes—
444C23×C43C2×#4112yes—
445C23×C43C2511yescharacteristic
446C22×D43—22no—
447C22×D43—22no—
448C22×D43—22no—
449C22×D43—22no—
450C22×D43—22no—
451C22×D43—22no—
452C22×D43—22no—
453D4×C43—48no—
454D4×C43—44no—
455D4×C43—84no—
456D4×C43—84no—
457C2×C4×C43—21no—
458C2×C4×C43—21no—
459C2×C4×C43—28no—
460C2×C4×C43—22no—
461C2×C4×C43—22no—
462C2×C4×C43—22no—
463C2×C4×C43—22no—
464C2×C4×C43—22no—
465C2×C4×C43—21no—
466C2×C4×C43—21no—
467C2×C4×C43—22no—
468C2×C4×C43—21no—
469C2×C4×C43—21no—
470C2×C4×C43—22no—
471C2×C4×C43—21no—
472C2×C4×C43—21no—
473C2×C4×C43—22no—
474C2×C4×C43—22no—
475C2×C4×C43—44no—
476C2×C4×C43—44no—
477C2×C4×C43—44no—
478C2×C4×C43—44no—
479C2×C4×C43—44no—
480C2×C4×C43C2×#4112yes—
481C2×C4×C43C2×#4112yes—
482C2×C4×C43H(5,𝔽2)12yes—
483C2×C4×C43H(5,𝔽2)12yes—
484C22⋊D43—48no—
485C22⋊D43—84no—
486C22⋊D43—84no—
487C22⋊D43—84no—
488C22⋊D43—84no—
489C2×Dic43—21no—
490C2×Dic43—21no—
491C2×Dic43—21no—
492C2×Dic43—21no—
493C2×Dic43—21no—
494C2×Dic43—21no—
495C2×Dic43—21no—
496C2×Dic43—21no—
497C2×Dic43—21no—
498C2×Dic43—21no—
499C2×Dic43—21no—
500C2×Dic43—21no—
501C2×Dic43—22no—
502C2×Dic43—22no—
503C2×Dic43—22no—
504C2×Dic43—22no—
505C2×Dic43—22no—
506C2×Dic43—21no—
507C2×Dic43—21no—
508C2×Dic43—21no—
509C2×Dic43—21no—
510C2×Dic43—22no—
511C2×Dic43—22no—
512C2×Dic43—22no—
513C2×Dic43—21no—
514C2×Dic43—21no—
515C2×Dic43—22no—
516C2×Dic43—44no—
517C2×Dic43—44no—
518C2×Dic43—44no—
519C2×Dic43—44no—
520C2×Dic43—84no—
521C2×Dic43C22×D412yes—
522C2×Dic43C22×D412yes—
523C2×Dic43C22×D412yes—
524C2×Dic43C22×D412yes—
525C2×Dic43C2×#4112yes—
526C2×Dic43C2×#4112yes—
527D172—44no—
528C4×D43—84no—
529Dic86—84no—
530#35005—431nomaximal, Sylow
531C22×C43—22no—
532C22×C43—22no—
533C22×C43—22no—
534C22×C43—22no—
535C22×C43—22no—
536C22×C43—22no—
537C22×C43—22no—
538C22×C43—22no—
539C22×C43—22no—
540C22×C43—22no—
541C22×C43—22no—
542C22×C43—22no—
543C22×C43—416no—
544C22×C43—41no—
545C22×C43—41no—
546C22×C43—41no—
547C22×C43—41no—
548C22×C43—41no—
549C22×C43—41no—
550C22×C43—41no—
551C22×C43—41no—
552C22×C43—42no—
553C22×C43—42no—
554C22×C43—42no—
555C22×C43—42no—
556C22×C43—42no—
557C22×C43—42no—
558C22×C43—42no—
559C22×C43#53214yes—
560C22×C43C23×D411yescharacteristic
561C22×C43C22×#4111yescharacteristic
562C22×C43C22×#4111yescharacteristic
563C22×C43C2×H(5,𝔽2)11yescharacteristic
564C22×C43C2×H(5,𝔽2)11yescharacteristic
565C22×C43#58511yescharacteristic
566C22×C43#58511yescharacteristic
567C2×D43—42no—
568C2×D43—42no—
569C2×D43—42no—
570C2×D43—42no—
571C2×D43—42no—
572C2×D43—42no—
573C2×D43—42no—
574C4×C43—22no—
575C4×C43—42no—
576C4×C43—41no—
577C4×C43—41no—
578C4×C43—42no—
579C4×C43—42no—
580C4×C43#53814yescomplemented
581Dic43—22no—
582Dic43—22no—
583Dic43—22no—
584Dic43—22no—
585Dic43—22no—
586Dic43—22no—
587Dic43—42no—
588Dic43—42no—
589Dic43—42no—
590Dic43—41no—
591Dic43—41no—
592C2×#538—432no—
593#2857—431no—
594#2856—431no—
595#2847—431no—
596#2847D4311yescharacteristic, complemented
597#2639—432no—
598#2617—432no—
599#2559—432no—
600#2559—432no—
601#2557—432no—
602#2557—432no—
603#2496—431no—
604#2496—431no—
605#2491—431no—
606#2491—431no—
607#2428—431no—
608#2428—431no—
609#2422—431no—
610#2422—431no—
611#2325—432no—
612C4×#121—431no—
613C4×#121—431no—
614C2×C4×C22⋊C4—431no—
615C2×C43—24no—
616C2×C43—42no—
617C2×C43—42no—
618C2×C43—82no—
619C2×C43C2×#53211yescharacteristic
620C2×C43C2×#53811yescharacteristic
621C2×C43#345511yescharacteristic
622C2×C43#349611yescharacteristic
623C2×C43#349611yescharacteristic
624C2×C43#350511yescharacteristic
625C2×C43#350611yescharacteristic
626D43—82no—
627C24×C4C2×D4311yescharacteristic
628#538—8616no—
629C2×C4⋊Q8—431no—
630C2×#127—431no—
631C2×#126—432no—
632C2×#126—432no—
633C2×#124—432no—
634C2×#124—432no—
635C2×#123—432no—
636C2×#123—432no—
637C2×C22⋊Q8—432no—
638C2×#121—432no—
639C2×#121—432no—
640C2×#121—432no—
641C2×#121—432no—
642C2×#121—431no—
643C2×#121—431no—
644C2×#121—431no—
645C2×#121C2×D4311yescharacteristic
646C2×#121C2×D4311yescharacteristic
647C2×#121C2×D4311yescharacteristic
648C2×#120—432no—
649C2×#120C2×D4312yes—
650C2×C4×D4—432no—
651C2×C4×D4—431no—
652C2×C4×D4—431no—
653C2×C4×D4—432no—
654C22×C22⋊C4—431no—
655C22×C22⋊C4—431no—
656C22×C42—431no—
657C22×C42—431no—
658#400—432no—
659#400—432no—
660#397—432no—
661#397—432no—
662#397—432no—
663#397—432no—
664#394—432no—
665#394—432no—
666#394—432no—
667#394—432no—
668#394—432no—
669#394—432no—
670#393—432no—
671#393—432no—
672#392—432no—
673#392—432no—
674#391—432no—
675#390—431no—
676#390—431no—
677#390—431no—
678#390—431no—
679#390—432no—
680#390—432no—
681#389—431no—
682#389—431no—
683#389—431no—
684#389—431no—
685#389—432no—
686#388—432no—
687#388—432no—
688#388—432no—
689#388—432no—
690#387—432no—
691#387—432no—
692#386—432no—
693#386—432no—
694#386—432no—
695#386—432no—
696#386—432no—
697#386—432no—
698#386—432no—
699#386C2×D4312yes—
700#386C2×D4312yes—
701#386C2×D4312yes—
702#385—432no—
703#385—432no—
704#384—431no—
705#384—431no—
706#380—431no—
707#380—431no—
708#380—431no—
709#380—432no—
710#380C2×D4311yescharacteristic
711#380C2×D4311yescharacteristic
712#380C2×D4311yescharacteristic
713C4×C4⋊C4—431no—
714C4×C4⋊C4—431no—
715C4×C22⋊C4—431no—
716C4×C22⋊C4—431no—
717C4×C22⋊C4—431no—
718C4×C22⋊C4—431no—
719C4×C22⋊C4—431no—
720C4×C22⋊C4—431no—
721C4×C22⋊C4—431no—
722C4×C22⋊C4—431no—
723C4×C22⋊C4—432no—
724C4×C22⋊C4—432no—
725C2×#95—431no—
726C2×#95—431no—
727C43#3500511yescharacteristic, complemented, Sylow
728C25C22×D4311yescharacteristic
729C22×Q8—432no—
730C22×D4—432no—
731C22×D4—432no—
732C22×D4—432no—
733C22×D4—432no—
734C22×D4—432no—
735C22×D4—431no—
736C22×D4C22×D4312yes—
737C22×D4C22×D4311yescharacteristic
738C22×D4C22×D4312yes—
739C22×D4C22×D4312yes—
740C23×C4—24no—
741C23×C4—42no—
742C23×C4—42no—
743C23×C4—431no—
744C23×C4—431no—
745C23×C4—431no—
746C23×C4—431no—
747C23×C4—432no—
748C23×C4—432no—
749C23×C4C22×D4311yescharacteristic
750C23×C4C22×D4311yescharacteristic
751C23×C4C22×D4311yescharacteristic
752C23×C4C22×D4311yescharacteristic
753C23×C4C22×D4311yescharacteristic
754C23×C4C22×D4311yescharacteristic
755C4⋊Q8—1722no—
756#127—1722no—
757#126—868no—
758#126—868no—
759#124—868no—
760#124—868no—
761#123—868no—
762#123—868no—
763C22⋊Q8—868no—
764#121—24no—
765#121—42no—
766#121—42no—
767#121—868no—
768#121—868no—
769#121—868no—
770#121—868no—
771#121—864no—
772#121—1722no—
773#121—1722no—
774#120—28no—
775#120—868no—
776C4×D4—868no—
777C4×D4—868no—
778C4×D4—1722no—
779C4×D4—1722no—
780C2×C4⋊C4—431no—
781C2×C4⋊C4—432no—
782C2×C4⋊C4—432no—
783C2×C4⋊C4—432no—
784C2×C4⋊C4—432no—
785C2×C4⋊C4—432no—
786C2×C4⋊C4—431no—
787C2×C4⋊C4—432no—
788C2×C4⋊C4—431no—
789C2×C4⋊C4—432no—
790C2×C4⋊C4—432no—
791C2×C4⋊C4—432no—
792C2×C4⋊C4C22×D4311yescharacteristic
793C2×C4⋊C4C22×D4311yescharacteristic
794C2×C4⋊C4C22×D4311yescharacteristic
795C2×C22⋊C4—438no—
796C2×C22⋊C4—431no—
797C2×C22⋊C4—431no—
798C2×C22⋊C4—431no—
799C2×C22⋊C4—431no—
800C2×C22⋊C4—431no—
801C2×C22⋊C4—431no—
802C2×C22⋊C4—431no—
803C2×C22⋊C4—431no—
804C2×C22⋊C4—432no—
805C2×C22⋊C4—432no—
806C2×C22⋊C4—432no—
807C2×C22⋊C4—432no—
808C2×C22⋊C4—432no—
809C2×C22⋊C4—432no—
810C2×C22⋊C4—432no—
811C2×C22⋊C4—432no—
812C2×C22⋊C4—432no—
813C2×C22⋊C4—432no—
814C2×C22⋊C4—432no—
815C2×C22⋊C4—432no—
816C2×C22⋊C4—432no—
817C2×C22⋊C4—432no—
818C2×C22⋊C4—432no—
819C2×C22⋊C4—432no—
820C2×C22⋊C4—864no—
821C2×C22⋊C4C22×D4312yes—
822C2×C22⋊C4C22×D4312yes—
823C2×C22⋊C4C22×D4312yes—
824C2×C22⋊C4C22×D4312yes—
825C2×C22⋊C4C22×D4312yes—
826C2×C22⋊C4C22×D4312yes—
827C2×C42—432no—
828C2×C42—432no—
829C2×C42—431no—
830C2×C42—431no—
831C2×C42—431no—
832C2×C42—431no—
833C2×C42—431no—
834C2×C42—431no—
835C2×C42—431no—
836C2×C42—431no—
837C2×C42—1722no—
838C2×C42—1722no—
839#95—431no—
840#95—431no—
841#95—431no—
842#95—431no—
843#95—431no—
844#95—431no—
845#95—431no—
846#95—431no—
847#95—432no—
848#95—432no—
849#95—432no—
850#95—432no—
851#95—432no—
852#95—432no—
853#95—432no—
854#95—432no—
855#95—432no—
856#95C22×D4312yes—
857#95C22×D4312yes—
858#95C22×D4312yes—
859C24—22no—
860C24—22no—
861C24—41no—
862C24—41no—
863C24—41no—
864C24—41no—
865C24—432no—
866C24D4×D4314yes—
867C24C23×D4312yes—
868C24C23×D4311yescharacteristic
869C24C23×D4311yescharacteristic
870C24C23×D4311yescharacteristic
871C2×Q8—864no—
872C2×Q8—1722no—
873C2×Q8—1722no—
874C2×D4—24no—
875C2×D4—24no—
876C2×D4—24no—
877C2×D4—24no—
878C2×D4—24no—
879C2×D4—22no—
880C2×D4—22no—
881C2×D4—22no—
882C2×D4—42no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—864no—
887C2×D4—864no—
888C2×D4—864no—
889C2×D4—864no—
890C2×D4—864no—
891C2×D4—864no—
892C2×D4—864no—
893C2×D4—862no—
894C2×D4—862no—
895C2×D4—862no—
896C2×D4—1722no—
897C2×D4—1722no—
898C2×D4—1722no—
899C2×D4—1722no—
900C2×D4—1722no—
901C2×D4—1722no—
902C2×D4—1722no—
903C2×D4—1722no—
904C22×C4—22no—
905C22×C4—22no—
906C22×C4—22no—
907C22×C4—22no—
908C22×C4—22no—
909C22×C4—22no—
910C22×C4—22no—
911C22×C4—22no—
912C22×C4—22no—
913C22×C4—22no—
914C22×C4—22no—
915C22×C4—41no—
916C22×C4—41no—
917C22×C4—41no—
918C22×C4—41no—
919C22×C4—41no—
920C22×C4—41no—
921C22×C4—416no—
922C22×C4—431no—
923C22×C4—431no—
924C22×C4—431no—
925C22×C4—431no—
926C22×C4—431no—
927C22×C4—431no—
928C22×C4—434no—
929C22×C4—434no—
930C22×C4—434no—
931C22×C4—431no—
932C22×C4—431no—
933C22×C4—432no—
934C22×C4—432no—
935C22×C4—432no—
936C22×C4—864no—
937C22×C4—864no—
938C22×C4—862no—
939C22×C4—1722no—
940C22×C4—1722no—
941C22×C4—1722no—
942C22×C4—1722no—
943C22×C4—1721no—
944C22×C4—1721no—
945C22×C4—1721no—
946C22×C4—1721no—
947C22×C4—1721no—
948C22×C4—1721no—
949C22×C4—1721no—
950C22×C4—1721no—
951C22×C4#1062190014yes—
952C22×C4C23×D4311yescharacteristic
953C22×C4C23×D4311yescharacteristic
954C22×C4C23×D4312yes—
955C22×C4C23×D4312yes—
956C22×C4C23×D4312yes—
957C22×C4C23×D4311yescharacteristic
958C22×C4C23×D4311yescharacteristic
959C4⋊C4—22no—
960C4⋊C4—22no—
961C4⋊C4—22no—
962C4⋊C4—864no—
963C4⋊C4—864no—
964C4⋊C4—864no—
965C4⋊C4—864no—
966C4⋊C4—864no—
967C4⋊C4—864no—
968C4⋊C4—864no—
969C4⋊C4—862no—
970C4⋊C4—862no—
971C4⋊C4—862no—
972C4⋊C4—1722no—
973C4⋊C4—1722no—
974C22⋊C4—24no—
975C22⋊C4—24no—
976C22⋊C4—24no—
977C22⋊C4—24no—
978C22⋊C4—42no—
979C22⋊C4—42no—
980C22⋊C4—434no—
981C22⋊C4—434no—
982C22⋊C4—434no—
983C22⋊C4—434no—
984C22⋊C4—864no—
985C22⋊C4—864no—
986C22⋊C4—864no—
987C22⋊C4—862no—
988C22⋊C4—862no—
989C22⋊C4—862no—
990C22⋊C4—862no—
991C22⋊C4—864no—
992C22⋊C4—864no—
993C22⋊C4—864no—
994C22⋊C4—864no—
995C22⋊C4—864no—
996C22⋊C4—864no—
997C22⋊C4—864no—
998C22⋊C4—1722no—
999C22⋊C4—1722no—
1000C22⋊C4—1722no—
1001C22⋊C4—1722no—
1002C22⋊C4—1722no—
1003C22⋊C4—1722no—
1004C42—864no—
1005C42—864no—
1006C42—862no—
1007C42—862no—
1008C42—862no—
1009C42—862no—
1010C42—1721no—
1011C42—1721no—
1012C42—1721no—
1013C42—1721no—
1014C23—21no—
1015C23—21no—
1016C23—21no—
1017C23—21no—
1018C23—28no—
1019C23—21no—
1020C23—21no—
1021C23—21no—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—21no—
1027C23—21no—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—44no—
1039C23—44no—
1040C23—44no—
1041C23—44no—
1042C23—44no—
1043C23—44no—
1044C23—862no—
1045C23—862no—
1046C23—862no—
1047C23—862no—
1048C23—862no—
1049C23—862no—
1050C23—862no—
1051C23C2×D4×D4312yes—
1052C23C2×D4×D4312yes—
1053C23C2×D4×D4312yes—
1054C23#41×D4312yes—
1055C23C2×#1062190012yes—
1056C23C24×D4311yescharacteristic
1057Q8—3444no—
1058D4—48no—
1059D4—44no—
1060D4—84no—
1061D4—84no—
1062D4—3444no—
1063D4—3444no—
1064D4—3444no—
1065D4—3444no—
1066D4—1728no—
1067D4—1724no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—28no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—44no—
1087C2×C4—44no—
1088C2×C4—44no—
1089C2×C4—44no—
1090C2×C4—44no—
1091C2×C4—432no—
1092C2×C4—432no—
1093C2×C4—432no—
1094C2×C4—432no—
1095C2×C4—432no—
1096C2×C4—432no—
1097C2×C4—861no—
1098C2×C4—861no—
1099C2×C4—861no—
1100C2×C4—861no—
1101C2×C4—861no—
1102C2×C4—861no—
1103C2×C4—861no—
1104C2×C4—861no—
1105C2×C4—861no—
1106C2×C4—861no—
1107C2×C4—861no—
1108C2×C4—861no—
1109C2×C4—862no—
1110C2×C4—862no—
1111C2×C4—862no—
1112C2×C4—861no—
1113C2×C4—861no—
1114C2×C4—862no—
1115C2×C4—862no—
1116C2×C4—861no—
1117C2×C4—861no—
1118C2×C4—862no—
1119C2×C4—862no—
1120C2×C4—861no—
1121C2×C4—861no—
1122C2×C4—862no—
1123C2×C4—862no—
1124C2×C4—3444no—
1125C2×C4—3444no—
1126C2×C4—1724no—
1127C2×C4—1724no—
1128C2×C4—1724no—
1129C2×C4—1724no—
1130C2×C4C2×#1062190012yes—
1131C2×C4C2×#1062190012yes—
1132C2×C4#1306337012yes—
1133C2×C4#1306337012yes—
1134C22—22no—
1135C22—22no—
1136C22—22no—
1137C22—22no—
1138C22—22no—
1139C22—22no—
1140C22—22no—
1141C22—22no—
1142C22—22no—
1143C22—22no—
1144C22—22no—
1145C22—22no—
1146C22—416no—
1147C22—41no—
1148C22—41no—
1149C22—41no—
1150C22—41no—
1151C22—41no—
1152C22—41no—
1153C22—41no—
1154C22—41no—
1155C22—42no—
1156C22—42no—
1157C22—42no—
1158C22—42no—
1159C22—42no—
1160C22—42no—
1161C22—42no—
1162C22—1722no—
1163C22—1722no—
1164C22—1722no—
1165C22—1722no—
1166C22—1722no—
1167C22—1722no—
1168C22—1722no—
1169C22#1458344414yes—
1170C22C22×D4×D4311yescharacteristic
1171C22C2×#41×D4311yescharacteristic
1172C22C22×#1062190011yescharacteristic
1173C22C2×#1306337011yescharacteristic
1174C22C2×#1306337011yescharacteristic
1175C22#1458373511yescharacteristic
1176C22#1458373511yescharacteristic
1177C4—22no—
1178C4—42no—
1179C4—42no—
1180C4—42no—
1181C4—41no—
1182C4—41no—
1183C4—862no—
1184C4—862no—
1185C4—862no—
1186C4—862no—
1187C4—862no—
1188C4—862no—
1189C4—1722no—
1190C4—1722no—
1191C4—1722no—
1192C4—1721no—
1193C4—1721no—
1194C4#1458348414yescomplemented
1195C2—24no—
1196C2—42no—
1197C2—42no—
1198C2—82no—
1199C2—3442no—
1200C2C2×#1458344411yescharacteristic
1201C2C2×#1458348411yescharacteristic
1202C2#1914798311yescharacteristic
1203C2#1914835211yescharacteristic
1204C2#1914835211yescharacteristic
1205C2#1914842311yescharacteristic
1206C2#1914843811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D43
commutator, socle, cosocleC23×C43C25
FittingC43×#2847C2
hypercenter#2847D43
hypocenterC43#35005
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2847

Complements

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

NH ≅ G/Ntype
1. C2×#14583484C2semidirect
2. #19142945C2semidirect
3. #19142938C2semidirect
4. #19142877C2semidirect
5. #19140525C2semidirect
6. #19140333C2semidirect
7. #19139723C2semidirect
8. #19139721C2semidirect
9. #19139693C2semidirect
10. #19139691C2semidirect
11. #19139019C2semidirect
12. #19139013C2semidirect
13. #19138960C2semidirect
14. #19138954C2semidirect
15. #19138185C2semidirect
16. #19138179C2semidirect
17. #19138111C2semidirect
18. #19138105C2semidirect
19. #19137296C2semidirect
20. #121×Dic43C2semidirect
21. #19137101C2semidirect
22. C2×C4×C22⋊Dic43C2semidirect
23. C43×#2847C2semidirect
25. C2×#13063324C22semidirect
26. C2×#13063321C22semidirect
43. C2×D4×Dic43C22semidirect
44. C2×#13063287C22semidirect
50. #14582841C22semidirect
51. #14582840C22semidirect
52. #14582828C22semidirect
55. #14582827C22semidirect
56. #14582815C22semidirect
59. #14582814C22semidirect
62. #14582812C22semidirect
63. #14582811C22semidirect
66. #14582803C22semidirect
67. #14582802C22semidirect
68. #14582802C22semidirect
69. #14582800C22semidirect
70. #14582800C22semidirect
71. #14582799C22semidirect
72. #14582799C22semidirect
73. #14582798C22semidirect
74. #14582798C22semidirect
75. #14582796C22semidirect
76. #14582795C22semidirect
77. #14582795C22semidirect
78. #14582793C22semidirect
79. #14582792C22semidirect
80. #14582788C22semidirect
81. #14582788C22semidirect
82. #14582786C22semidirect
83. #14582781C22semidirect
89. #14582776C22semidirect
90. #14582775C22semidirect
91. #14582773C22semidirect
92. #14582771C22semidirect
93. #14582768C22semidirect
94. #14582768C22semidirect
99. C4⋊C4×Dic43C22semidirect
100. C4⋊C4×Dic43C22semidirect
101. C22⋊C4×Dic43C22semidirect
110. #14582746C22semidirect
171. C2×C22⋊Dic43D4semidirect
580. C4×C43#538semidirect
596. #2847D43semidirect
727. C43#35005semidirect
1194. C4#14583484semidirect

Maximal subgroups

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

subgroupindex
C2×#145834842
#191429452
#191429382
#191428772
#191405252
#191403332
#191397232
#191397212
#191396932
#191396912
#191390192
#191390132
#191389602
#191389542
#191381852
#191381792
#191381112
#191381052
#191372962
#121×Dic432
#191371012
C2×C4×C22⋊Dic432
C43×#28472
#3500543