Finite Group Databasebeta

← #25269540

Subgroups — #25269540

Order 11008.

2756 conjugacy classes of subgroups.

The subgroup lattice has 1222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583484C212yesmaximal, complemented
2#19142959C211yesmaximal, characteristic, complemented
3#19142949C211yesmaximal, characteristic, complemented
4#19142938C211yesmaximal, characteristic, complemented
5#19142921C211yesmaximal, characteristic, complemented
6#19140731C212yesmaximal, complemented
7#19140720C212yesmaximal, complemented
8#19139665C212yesmaximal, complemented
9#19139650C212yesmaximal, complemented
10#19139179C211yesmaximal, characteristic, complemented
11#19138960C211yesmaximal, characteristic, complemented
12#19138718C212yesmaximal, complemented
13#19138363C211yesmaximal, characteristic, complemented
14#19138298C211yesmaximal, characteristic, complemented
15#19138228C211yesmaximal, characteristic, complemented
16#19138179C211yesmaximal, characteristic, complemented
17#19138135C212yesmaximal, complemented
18#19138035C211yesmaximal, characteristic, complemented
19#19137250C212yesmaximal, complemented
20#19137101C211yesmaximal, characteristic, complemented
21C2×#14582802C211yesmaximal, characteristic, complemented
22C4×D4×Dic43C211yesmaximal, characteristic, complemented
23C43×#2408C211yesmaximal, characteristic, complemented
24#14583484—216no—
25C2×#13063324C2211yescharacteristic, complemented
26C2×#13063321C2211yescharacteristic
27C2×#13063321C2211yescharacteristic
28C2×#13063318C2212yescomplemented
29C2×#13063318C2212yescomplemented
30C2×#13063312C2212yescomplemented
31C2×#13063311C2212yescomplemented
32C2×#13063311C2212yescomplemented
33C2×#13063307C2212yescomplemented
34C2×#13063306C2212yescomplemented
35C2×#13063302C2212yes—
36C2×#13063299C2211yescharacteristic
37C2×#13063299C2211yescharacteristic, complemented
38C2×#13063297C2212yes—
39C2×#13063297C2212yescomplemented
40C2×#13063297C2212yescomplemented
41C2×#13063296C2212yescomplemented
42C2×#13063294C2212yes—
43C2×#13063294C2212yes—
44C2×D4×Dic43C2211yescharacteristic
45C2×D4×Dic43C2211yescharacteristic
46C2×#13063287C2211yescharacteristic, complemented
47C2×(C22⋊D43)⋊C4C2212yes—
48C22×C4⋊Dic43C2211yescharacteristic
49C22×C22⋊Dic43C2212yes—
50C22×C22⋊Dic43C2212yes—
51C22×C4×Dic43C2211yescharacteristic
52C22×C4×Dic43C2211yescharacteristic, complemented
53#14582833C2212yescomplemented
54#14582827C2212yescomplemented
55#14582822C2212yescomplemented
56#14582821C2212yescomplemented
57#14582820C2212yescomplemented
58#14582815C2212yescomplemented
59#14582815C2212yescomplemented
60#14582815C2212yescomplemented
61#14582814C2212yescomplemented
62#14582813C2212yescomplemented
63#14582811C2212yescomplemented
64#14582807C2212yes—
65#14582807C2212yes—
66#14582807C2212yescomplemented
67#14582802C2211yescharacteristic
68#14582802C2211yescharacteristic
69#14582802C2211yescharacteristic
70#14582802C2211yescharacteristic
71#14582802C2212yes—
72#14582802C2211yescharacteristic
73#14582802C2212yes—
74#14582802C2211yescharacteristic
75#14582801C2211yescharacteristic, complemented
76#14582800C2211yescharacteristic, complemented
77#14582799C2212yescomplemented
78#14582799C2212yescomplemented
79#14582799C2212yescomplemented
80#14582799C2212yescomplemented
81#14582798C2211yescharacteristic, complemented
82#14582797C2211yescharacteristic, complemented
83#14582795C2211yescharacteristic, complemented
84#14582795C2211yescharacteristic, complemented
85#14582793C2212yescomplemented
86#14582793C2212yescomplemented
87#14582793C2212yescomplemented
88#14582792C2212yescomplemented
89#14582788C2212yescomplemented
90#14582787C2212yescomplemented
91#14582787C2212yescomplemented
92#14582787C2212yescomplemented
93#14582779C2212yescomplemented
94#14582776C2212yes—
95#14582776C2212yes—
96#14582775C2212yescomplemented
97#14582775C2212yescomplemented
98#14582771C2212yes—
99#14582768C2211yescharacteristic, complemented
100#14582759C2211yescharacteristic, complemented
101C4⋊C4×Dic43C2211yescharacteristic, complemented
102C4⋊C4×Dic43C2211yescharacteristic, complemented
103C4⋊C4×Dic43C2211yescharacteristic, complemented
104C4×C4⋊Dic43C2211yescharacteristic, complemented
105C22⋊C4×Dic43C2211yescharacteristic
106C22⋊C4×Dic43C2211yescharacteristic
107C22⋊C4×Dic43C2211yescharacteristic, complemented
108C22⋊C4×Dic43C2211yescharacteristic, complemented
109C4×C22⋊Dic43C2211yescharacteristic
110C4×C22⋊Dic43C2211yescharacteristic, complemented
111#14582746C2212yescomplemented
112C42×Dic43C2211yescharacteristic, complemented
113C23×D4×C43C2211yescharacteristic
114C2×#121×C43C2211yescharacteristic
115C2×#121×C43C2211yescharacteristic
116C2×#120×C43C2212yes—
117C2×C4×D4×C43C2211yescharacteristic
118C43×#394C2212yes—
119C43×#392C2212yes—
120C43×#390C2211yescharacteristic
121C43×#390C2211yescharacteristic
122C43×#380C2211yescharacteristic
123C43×#379C2212yes—
124C22×Dic86C2312yes—
125C22×D172C2311yescharacteristic
126C22×C22⋊D43C2312yes—
127C22×C22⋊D43C2312yes—
128C22×C22⋊D43C2312yes—
129C22×C22⋊D43C2312yes—
130C22×C22⋊D43C2312yes—
131C22×C22⋊D43C2312yes—
132C23×Dic43C2311yescharacteristic
133C23×Dic43C2311yescharacteristic
134C23×Dic43C2312yes—
135C23×Dic43C2311yescharacteristic
136C23×Dic43C2311yescharacteristic
137C22×C4×D43C2312yes—
138#13063324—42no—
139#13063321—42no—
140#13063321—42no—
141#13063318—28no—
142#13063318—28no—
143#13063312—28no—
144#13063311—28no—
145#13063311—44no—
146#13063307—28no—
147#13063306—28no—
148#13063302—28no—
149#13063299—24no—
150#13063299—42no—
151#13063297—28no—
152#13063297—28no—
153#13063297—44no—
154#13063296—28no—
155#13063294—28no—
156#13063294—28no—
157D4×Dic43—24no—
158D4×Dic43D418yescomplemented
159#13063287—42no—
160(C22⋊D43)⋊C4—28no—
161C2×C4⋊Dic43—42no—
162C2×C4⋊Dic43C2312yes—
163C2×C4⋊Dic43C2311yescharacteristic
164C2×C4⋊Dic43C2311yescharacteristic
165C2×C4⋊Dic43C2311yescharacteristic
166C2×C4⋊Dic43C2311yescharacteristic
167C2×C4⋊Dic43C2312yes—
168C2×C4⋊Dic43C2311yescharacteristic
169C2×Dic43⋊C4C2312yes—
170C2×Dic43⋊C4C2312yes—
171C2×Dic43⋊C4C2312yes—
172C2×Dic43⋊C4C2312yes—
173C2×Dic43⋊C4C2312yes—
174C2×Dic43⋊C4C2312yes—
175C2×C22⋊Dic43—28no—
176C2×C22⋊Dic43—44no—
177C2×C22⋊Dic43C2312yes—
178C2×C22⋊Dic43C2312yes—
179C2×C22⋊Dic43C2312yes—
180C2×C22⋊Dic43C2312yes—
181C2×C22⋊Dic43C2312yes—
182C2×C22⋊Dic43C2312yes—
183C2×C22⋊Dic43C2312yes—
184C2×C22⋊Dic43C2312yes—
185C2×C22⋊Dic43C2312yes—
186C2×C22⋊Dic43C2312yes—
187C2×C22⋊Dic43C2311yescharacteristic
188C2×C22⋊Dic43C2312yes—
189C2×C22⋊Dic43C2312yes—
190C2×C22⋊Dic43C2312yes—
191C2×C22⋊Dic43C2311yescharacteristic
192C2×C22⋊Dic43C2311yescharacteristic
193C2×C22⋊Dic43C2311yescharacteristic
194C2×(C2×D43)⋊C4C2312yes—
195C2×(C2×D43)⋊C4C2312yes—
196C2×(C2×D43)⋊C4C2312yes—
197C2×(C2×D43)⋊C4C2312yes—
198C2×(C2×D43)⋊C4C2312yes—
199C2×(C2×D43)⋊C4C2312yes—
200C2×(C2×D43)⋊C4C2312yes—
201C2×C4×Dic43—42no—
202C2×C4×Dic43—42no—
203C2×C4×Dic43C2311yescharacteristic
204C2×C4×Dic43C2311yescharacteristic
205C2×C4×Dic43C2312yes—
206C2×C4×Dic43C2311yescharacteristic
207C2×C4×Dic43C2311yescharacteristic
208C2×C4×Dic43C2311yescharacteristic
209C2×C4×Dic43C2311yescharacteristic
210C2×C4×Dic43C2311yescharacteristic
211C2×C4×Dic43C2311yescharacteristic
212C2×C4×Dic43C2311yescharacteristic
213C2×C4×Dic43C2311yescharacteristic
214C2×C4×Dic43C2311yescharacteristic
215C2×C4×Dic43C2311yescharacteristic
216C43⋊#95C2312yes—
217C43⋊#95C2312yes—
218C43⋊#95C2312yes—
219C43⋊#95C2312yes—
220C43⋊#95C2312yes—
221C43⋊#95C2312yes—
222C43⋊#95C2311yescharacteristic
223C43⋊#95C2311yescharacteristic
224C43⋊#95C2311yescharacteristic
225C43⋊#95C2311yescharacteristic
226C43⋊#95C2311yescharacteristic
227C43⋊#95C2311yescharacteristic
228C25×C43C2312yes—
229C22×D4×C43—24no—
230C22×D4×C43—42no—
231C22×D4×C43—42no—
232C22×D4×C43C2311yescharacteristic
233C22×D4×C43C2311yescharacteristic
234C22×D4×C43C2311yescharacteristic
235C22×D4×C43C2312yes—
236C22×D4×C43C2312yes—
237C22×D4×C43C2312yes—
238C23×C4×C43C2311yescharacteristic
239C23×C4×C43C2311yescharacteristic
240#121×C43—42no—
241#121×C43—42no—
242#120×C43—28no—
243C4×D4×C43—24no—
244C2×C4⋊C4×C43C2311yescharacteristic
245C2×C4⋊C4×C43C2311yescharacteristic
246C2×C4⋊C4×C43C2311yescharacteristic
247C2×C22⋊C4×C43C2312yes—
248C2×C22⋊C4×C43C2312yes—
249C2×C22⋊C4×C43C2311yescharacteristic
250C2×C22⋊C4×C43C2311yescharacteristic
251C2×C22⋊C4×C43C2312yes—
252C2×C22⋊C4×C43C2312yes—
253C2×C22⋊C4×C43C2312yes—
254C2×C22⋊C4×C43C2312yes—
255C2×C22⋊C4×C43C2312yes—
256C2×C42×C43C2311yescharacteristic
257#95×C43C2312yes—
258C24×C43—24no—
259C24×C43—24no—
260C24×C43—24no—
261C24×C43—42no—
262C24×C43—42no—
263C24×C43—42no—
264C24×C43—42no—
265C24×C43C2412yes—
266C24×C43C2412yes—
267C24×C43C2411yescharacteristic
268C24×C43C2411yescharacteristic
269C23×D43C2412yes—
270C2×D4×C43—24no—
271C2×D4×C43—22no—
272C2×D4×C43—22no—
273C2×D4×C43—22no—
274C2×D4×C43—22no—
275C2×D4×C43—22no—
276C2×D4×C43—22no—
277C2×D4×C43—24no—
278C2×D4×C43—24no—
279C2×D4×C43—22no—
280C2×D4×C43—22no—
281C2×D4×C43—42no—
282C2×D4×C43—42no—
283C2×D4×C43—42no—
284C2×D4×C43—42no—
285C2×D4×C43—42no—
286C2×D4×C43—42no—
287C2×D4×C43—416no—
288C2×D4×C43C2×D414yes—
289C22×C4×C43—22no—
290C22×C4×C43—22no—
291C22×C4×C43—22no—
292C22×C4×C43—22no—
293C22×C4×C43—22no—
294C22×C4×C43#4114yes—
295C22×C4×C43C2412yes—
296C22×C4×C43C2412yes—
297C22×C4×C43C2411yescharacteristic
298C22×C4×C43C2411yescharacteristic
299C22×C4×C43C2411yescharacteristic
300C22×C4×C43C2411yescharacteristic
301C22×C4×C43C2411yescharacteristic
302C2×C22⋊D43—24no—
303C2×C22⋊D43—24no—
304C2×C22⋊D43—24no—
305C2×C22⋊D43—24no—
306C2×C22⋊D43—24no—
307C2×C22⋊D43—24no—
308C2×C22⋊D43—24no—
309C2×C22⋊D43—24no—
310C2×C22⋊D43—42no—
311C2×C22⋊D43—42no—
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—22no—
321C22×Dic43—22no—
322C22×Dic43—22no—
323C22×Dic43—24no—
324C22×Dic43—22no—
325C22×Dic43—41no—
326C22×Dic43—41no—
327C22×Dic43—41no—
328C22×Dic43—41no—
329C22×Dic43—41no—
330C22×Dic43—41no—
331C22×Dic43—42no—
332C22×Dic43—42no—
333C22×Dic43C2×D414yes—
334C22×Dic43C2×D414yescomplemented
335C22×Dic43C2411yescharacteristic
336C22×Dic43C2412yes—
337C22×Dic43C2412yes—
338C22×Dic43C2412yes—
339C22×Dic43C2411yescharacteristic
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—22no—
361C22⋊C4×C43—24no—
362C22⋊C4×C43—22no—
363C22⋊C4×C43—42no—
364C22⋊C4×C43—42no—
365C22⋊C4×C43—42no—
366C22⋊C4×C43—42no—
367C42×C43—22no—
368C22⋊Dic43—24no—
369C22⋊Dic43—24no—
370C22⋊Dic43—24no—
371C22⋊Dic43—24no—
372C22⋊Dic43—24no—
373C22⋊Dic43—24no—
374C22⋊Dic43—22no—
375C22⋊Dic43—24no—
376C22⋊Dic43—24no—
377C22⋊Dic43—24no—
378C22⋊Dic43—24no—
379C22⋊Dic43—24no—
380C22⋊Dic43—42no—
381C22⋊Dic43—42no—
382C22⋊Dic43C2×D414yes—
383C22⋊Dic43C2×D414yescomplemented
384C22⋊Dic43#4114yes—
385(C2×D43)⋊C4—24no—
386(C2×D43)⋊C4—24no—
387(C2×D43)⋊C4—24no—
388(C2×D43)⋊C4—24no—
389(C2×D43)⋊C4—42no—
390(C2×D43)⋊C4—42no—
391(C2×D43)⋊C4—42no—
392C4⋊Dic43—22no—
393C4⋊Dic43—22no—
394C4⋊Dic43—22no—
395C4⋊Dic43—24no—
396C4⋊Dic43—22no—
397C4⋊Dic43—42no—
398C4⋊Dic43C2×D414yescomplemented
399Dic43⋊C4—24no—
400Dic43⋊C4—24no—
401Dic43⋊C4—24no—
402Dic43⋊C4—24no—
403Dic43⋊C4—42no—
404Dic43⋊C4—42no—
405C4×Dic43—22no—
406C4×Dic43—22no—
407C4×Dic43—22no—
408C4×Dic43—22no—
409C4×Dic43—24no—
410C4×Dic43—22no—
411C4×Dic43—22no—
412C4×Dic43—41no—
413C4×Dic43—41no—
414C4×Dic43—41no—
415C4×Dic43—41no—
416C4×Dic43—41no—
417C4×Dic43C2×D414yescomplemented
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—21no—
428C23×C43—22no—
429C23×C43—22no—
430C23×C43—22no—
431C23×C43—22no—
432C23×C43—22no—
433C23×C43—22no—
434C23×C43—22no—
435C23×C43—22no—
436C23×C43—22no—
437C23×C43—22no—
438C23×C43—22no—
439C23×C43—22no—
440C23×C43—22no—
441C23×C43—22no—
442C23×C43—48no—
443C23×C43—48no—
444C23×C43—48no—
445C23×C43—84no—
446C23×C43—84no—
447C23×C43—84no—
448C23×C43—84no—
449C23×C43C22×D412yes—
450C23×C43C22×D412yes—
451C23×C43C2×#4112yes—
452C23×C43C2×#4112yes—
453C23×C43C2511yescharacteristic
454C22×D43—22no—
455C22×D43—22no—
456C22×D43—22no—
457C22×D43—22no—
458C22×D43—22no—
459C22×D43—22no—
460C22×D43—22no—
461D4×C43—28no—
462D4×C43—48no—
463D4×C43—44no—
464D4×C43—44no—
465D4×C43—84no—
466D4×C43—84no—
467C2×C4×C43—21no—
468C2×C4×C43—21no—
469C2×C4×C43—21no—
470C2×C4×C43—21no—
471C2×C4×C43—28no—
472C2×C4×C43—22no—
473C2×C4×C43—22no—
474C2×C4×C43—21no—
475C2×C4×C43—21no—
476C2×C4×C43—21no—
477C2×C4×C43—21no—
478C2×C4×C43—22no—
479C2×C4×C43—22no—
480C2×C4×C43—21no—
481C2×C4×C43—22no—
482C2×C4×C43—21no—
483C2×C4×C43—22no—
484C2×C4×C43—44no—
485C2×C4×C43C22×D412yes—
486C2×C4×C43C2×#4112yes—
487C2×C4×C43C2×#4112yes—
488C2×C4×C43H(5,𝔽2)12yes—
489C2×C4×C43H(5,𝔽2)12yes—
490C22⋊D43—48no—
491C22⋊D43—84no—
492C22⋊D43—84no—
493C22⋊D43—84no—
494C22⋊D43—84no—
495C22⋊D43—84no—
496C2×Dic43—21no—
497C2×Dic43—21no—
498C2×Dic43—21no—
499C2×Dic43—21no—
500C2×Dic43—21no—
501C2×Dic43—21no—
502C2×Dic43—21no—
503C2×Dic43—21no—
504C2×Dic43—21no—
505C2×Dic43—21no—
506C2×Dic43—21no—
507C2×Dic43—21no—
508C2×Dic43—21no—
509C2×Dic43—21no—
510C2×Dic43—22no—
511C2×Dic43—22no—
512C2×Dic43—22no—
513C2×Dic43—22no—
514C2×Dic43—21no—
515C2×Dic43—22no—
516C2×Dic43—21no—
517C2×Dic43—22no—
518C2×Dic43—22no—
519C2×Dic43—22no—
520C2×Dic43—22no—
521C2×Dic43—21no—
522C2×Dic43—44no—
523C2×Dic43—44no—
524C2×Dic43—44no—
525C2×Dic43—44no—
526C2×Dic43—84no—
527C2×Dic43C22×D412yes—
528C2×Dic43C22×D412yes—
529C2×Dic43C22×D412yes—
530C2×Dic43C22×D412yes—
531C2×Dic43C2×#4112yes—
532C2×Dic43C2×#4112yes—
533C2×Dic43H(5,𝔽2)12yes—
534D172—44no—
535C4×D43—84no—
536Dic86—84no—
537#35007—431nomaximal, Sylow
538C22×C43—22no—
539C22×C43—22no—
540C22×C43—22no—
541C22×C43—22no—
542C22×C43—22no—
543C22×C43—22no—
544C22×C43—22no—
545C22×C43—22no—
546C22×C43—22no—
547C22×C43—41no—
548C22×C43—41no—
549C22×C43—41no—
550C22×C43—41no—
551C22×C43—42no—
552C22×C43—42no—
553C22×C43—42no—
554C22×C43—42no—
555C22×C43—42no—
556C22×C43—42no—
557C22×C43—42no—
558C22×C43—42no—
559C22×C43—42no—
560C22×C43—42no—
561C22×C43—42no—
562C22×C43—42no—
563C22×C43—42no—
564C22×C43—42no—
565C22×C43—816no—
566C22×C43#53214yes—
567C22×C43C23×D411yescharacteristic
568C22×C43C22×#4111yescharacteristic
569C22×C43C22×#4111yescharacteristic
570C22×C43C2×H(5,𝔽2)11yescharacteristic
571C22×C43C2×H(5,𝔽2)11yescharacteristic
572C22×C43C2×H(5,𝔽2)11yescharacteristic
573C22×C43#58511yescharacteristic
574C2×D43—42no—
575C2×D43—42no—
576C2×D43—42no—
577C2×D43—42no—
578C2×D43—42no—
579C2×D43—42no—
580C2×D43—42no—
581C4×C43—22no—
582C4×C43—22no—
583C4×C43—41no—
584C4×C43—41no—
585C4×C43—42no—
586C4×C43—42no—
587C4×C43#53814yescomplemented
588Dic43—22no—
589Dic43—22no—
590Dic43—22no—
591Dic43—22no—
592Dic43—22no—
593Dic43—22no—
594Dic43—22no—
595Dic43—42no—
596Dic43—42no—
597Dic43—42no—
598Dic43—41no—
599C2×#538—432no—
600#2860—431no—
601#2858—431no—
602#2856—431no—
603#2854—431no—
604#2662—432no—
605#2661—432no—
606#2555—432no—
607#2554—432no—
608#2512—431no—
609#2491—431no—
610#2472—432no—
611#2445—431no—
612#2440—431no—
613#2433—431no—
614#2428—431no—
615#2424—432no—
616#2416—431no—
617#2408D4311yescharacteristic, complemented
618#2321—432no—
619C4×#121—431no—
620C2×#390—431no—
621C42×D4—431no—
622C2×C43—24no—
623C2×C43—42no—
624C2×C43—82no—
625C2×C43—82no—
626C2×C43C2×#53211yescharacteristic
627C2×C43C2×#53811yescharacteristic
628C2×C43#346011yescharacteristic
629C2×C43#349611yescharacteristic
630C2×C43#349811yescharacteristic
631C2×C43#351411yescharacteristic
632C2×C43#351911yescharacteristic
633D43—82no—
634C23×D4C2×D4311yescharacteristic
635#538—8616no—
636C2×C4⋊Q8—431no—
637C2×#127—431no—
638C2×#127—431no—
639C2×#126—432no—
640C2×#126—432no—
641C2×#124—432no—
642C2×#124—432no—
643C2×#124—432no—
644C2×#123—432no—
645C2×#123—432no—
646C2×C22⋊Q8—432no—
647C2×#121—432no—
648C2×#121—432no—
649C2×#121—432no—
650C2×#121—431no—
651C2×#121—432no—
652C2×#121—431no—
653C2×#121C2×D4311yescharacteristic
654C2×#121C2×D4311yescharacteristic
655C2×#120—432no—
656C2×#120—432no—
657C2×#120C2×D4312yes—
658C2×C4×D4—431no—
659C2×C4×D4—431no—
660C2×C4×D4—431no—
661C2×C4×D4—432no—
662C2×C4×D4C2×D4311yescharacteristic
663C22×C4⋊C4—431no—
664C22×C22⋊C4—432no—
665C22×C22⋊C4—432no—
666C22×C42—431no—
667C22×C42—431no—
668#398—432no—
669#397—432no—
670#396—432no—
671#396—432no—
672#395—432no—
673#394—432no—
674#394—432no—
675#394—432no—
676#394—432no—
677#394—432no—
678#394C2×D4312yes—
679#393—432no—
680#392—432no—
681#392—432no—
682#392—432no—
683#392C2×D4312yes—
684#390—431no—
685#390—431no—
686#390—431no—
687#390—431no—
688#390—432no—
689#390—431no—
690#390—431no—
691#390—432no—
692#390—431no—
693#390—432no—
694#390—432no—
695#390—432no—
696#390—432no—
697#390—431no—
698#390C2×D4311yescharacteristic
699#390C2×D4311yescharacteristic
700#389—431no—
701#389—431no—
702#389—431no—
703#389—431no—
704#388—432no—
705#388—432no—
706#388—432no—
707#388—432no—
708#388—432no—
709#388—432no—
710#388—432no—
711#388—432no—
712#386—432no—
713#386—432no—
714#386—432no—
715#386—432no—
716#386—432no—
717#385—432no—
718#384—431no—
719#380—431no—
720#380C2×D4311yescharacteristic
721#379C2×D4312yes—
722C4×C4⋊C4—431no—
723C4×C4⋊C4—431no—
724C4×C4⋊C4—431no—
725C4×C4⋊C4—431no—
726C4×C22⋊C4—431no—
727C4×C22⋊C4—431no—
728C4×C22⋊C4—431no—
729C4×C22⋊C4—431no—
730C4×C22⋊C4—431no—
731C4×C22⋊C4—431no—
732C4×C22⋊C4—432no—
733C43—431no—
734C43#3500711yescharacteristic, complemented, Sylow
735C25C22×D4312yes—
736C22×Q8—432no—
737C22×D4—24no—
738C22×D4—42no—
739C22×D4—42no—
740C22×D4—432no—
741C22×D4—432no—
742C22×D4—432no—
743C22×D4—432no—
744C22×D4—432no—
745C22×D4—432no—
746C22×D4—431no—
747C22×D4C22×D4311yescharacteristic
748C22×D4C22×D4311yescharacteristic
749C22×D4C22×D4311yescharacteristic
750C22×D4C22×D4312yes—
751C22×D4C22×D4312yes—
752C22×D4C22×D4312yes—
753C23×C4—431no—
754C23×C4—431no—
755C23×C4—431no—
756C23×C4—431no—
757C23×C4—432no—
758C23×C4—432no—
759C23×C4C22×D4311yescharacteristic
760C23×C4C22×D4311yescharacteristic
761C4⋊Q8—1722no—
762#127—1722no—
763#127—1722no—
764#126—868no—
765#126—868no—
766#124—868no—
767#124—868no—
768#124—1724no—
769#123—868no—
770#123—868no—
771C22⋊Q8—868no—
772#121—42no—
773#121—42no—
774#121—868no—
775#121—868no—
776#121—868no—
777#121—864no—
778#121—1724no—
779#121—1722no—
780#120—28no—
781#120—868no—
782#120—868no—
783C4×D4—24no—
784C4×D4—438no—
785C4×D4—868no—
786C4×D4—864no—
787C4×D4—1722no—
788C2×C4⋊C4—431no—
789C2×C4⋊C4—431no—
790C2×C4⋊C4—431no—
791C2×C4⋊C4—432no—
792C2×C4⋊C4—431no—
793C2×C4⋊C4—432no—
794C2×C4⋊C4—432no—
795C2×C4⋊C4—432no—
796C2×C4⋊C4—431no—
797C2×C4⋊C4—432no—
798C2×C4⋊C4—432no—
799C2×C4⋊C4—432no—
800C2×C4⋊C4—432no—
801C2×C4⋊C4—1722no—
802C2×C4⋊C4C22×D4311yescharacteristic
803C2×C4⋊C4C22×D4311yescharacteristic
804C2×C4⋊C4C22×D4311yescharacteristic
805C2×C22⋊C4—431no—
806C2×C22⋊C4—431no—
807C2×C22⋊C4—431no—
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—431no—
815C2×C22⋊C4—432no—
816C2×C22⋊C4—432no—
817C2×C22⋊C4—432no—
818C2×C22⋊C4—432no—
819C2×C22⋊C4—432no—
820C2×C22⋊C4—432no—
821C2×C22⋊C4—432no—
822C2×C22⋊C4—432no—
823C2×C22⋊C4—432no—
824C2×C22⋊C4—432no—
825C2×C22⋊C4—432no—
826C2×C22⋊C4—432no—
827C2×C22⋊C4—432no—
828C2×C22⋊C4—432no—
829C2×C22⋊C4—868no—
830C2×C22⋊C4—1724no—
831C2×C22⋊C4C22×D4312yes—
832C2×C22⋊C4C22×D4311yescharacteristic
833C2×C22⋊C4C22×D4311yescharacteristic
834C2×C22⋊C4C22×D4312yes—
835C2×C22⋊C4C22×D4312yes—
836C2×C22⋊C4C22×D4312yes—
837C2×C22⋊C4C22×D4312yes—
838C2×C22⋊C4C22×D4312yes—
839C2×C22⋊C4C22×D4312yes—
840C2×C42—431no—
841C2×C42—432no—
842C2×C42—431no—
843C2×C42—431no—
844C2×C42—431no—
845C2×C42—431no—
846C2×C42—431no—
847C2×C42—431no—
848C2×C42—431no—
849C2×C42—431no—
850C2×C42—431no—
851C2×C42—431no—
852C2×C42—431no—
853C2×C42—1722no—
854C2×C42—1722no—
855C2×C42C22×D4311yescharacteristic
856#95—431no—
857#95—431no—
858#95—431no—
859#95—431no—
860#95—431no—
861#95—431no—
862#95—432no—
863#95—432no—
864#95—432no—
865#95—432no—
866#95—432no—
867#95—432no—
868#95C22×D4312yes—
869C24—24no—
870C24—24no—
871C24—24no—
872C24—42no—
873C24—42no—
874C24—42no—
875C24—42no—
876C24—432no—
877C24C23×D4312yes—
878C24C23×D4312yes—
879C24C23×D4311yescharacteristic
880C24C23×D4311yescharacteristic
881C2×Q8—864no—
882C2×Q8—1722no—
883C2×Q8—1722no—
884C2×D4—22no—
885C2×D4—22no—
886C2×D4—24no—
887C2×D4—24no—
888C2×D4—24no—
889C2×D4—22no—
890C2×D4—22no—
891C2×D4—22no—
892C2×D4—22no—
893C2×D4—22no—
894C2×D4—22no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—416no—
898C2×D4—42no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—864no—
903C2×D4—864no—
904C2×D4—864no—
905C2×D4—864no—
906C2×D4—864no—
907C2×D4—864no—
908C2×D4—864no—
909C2×D4—864no—
910C2×D4—862no—
911C2×D4—862no—
912C2×D4—862no—
913C2×D4—1722no—
914C2×D4—1722no—
915C2×D4—1722no—
916C2×D4—1722no—
917C2×D4—1722no—
918C2×D4—1722no—
919C2×D4—1722no—
920C2×D4—1722no—
921C2×D4—1722no—
922C2×D4—1722no—
923C2×D4D4×D4314yes—
924C22×C4—22no—
925C22×C4—22no—
926C22×C4—22no—
927C22×C4—22no—
928C22×C4—22no—
929C22×C4—431no—
930C22×C4—431no—
931C22×C4—431no—
932C22×C4—431no—
933C22×C4—431no—
934C22×C4—431no—
935C22×C4—431no—
936C22×C4—434no—
937C22×C4—434no—
938C22×C4—431no—
939C22×C4—432no—
940C22×C4—432no—
941C22×C4—432no—
942C22×C4—864no—
943C22×C4—862no—
944C22×C4—862no—
945C22×C4—862no—
946C22×C4—864no—
947C22×C4—862no—
948C22×C4—1722no—
949C22×C4—1722no—
950C22×C4—1722no—
951C22×C4—1722no—
952C22×C4—1721no—
953C22×C4—1721no—
954C22×C4—1721no—
955C22×C4—1721no—
956C22×C4—1721no—
957C22×C4—1721no—
958C22×C4#1062190014yes—
959C22×C4C23×D4311yescharacteristic
960C22×C4C23×D4311yescharacteristic
961C22×C4C23×D4312yes—
962C22×C4C23×D4312yes—
963C22×C4C23×D4311yescharacteristic
964C22×C4C23×D4311yescharacteristic
965C22×C4C23×D4311yescharacteristic
966C4⋊C4—22no—
967C4⋊C4—22no—
968C4⋊C4—22no—
969C4⋊C4—434no—
970C4⋊C4—864no—
971C4⋊C4—862no—
972C4⋊C4—864no—
973C4⋊C4—864no—
974C4⋊C4—864no—
975C4⋊C4—864no—
976C4⋊C4—862no—
977C4⋊C4—862no—
978C4⋊C4—862no—
979C4⋊C4—1722no—
980C4⋊C4—1722no—
981C4⋊C4—1722no—
982C22⋊C4—24no—
983C22⋊C4—22no—
984C22⋊C4—24no—
985C22⋊C4—24no—
986C22⋊C4—22no—
987C22⋊C4—42no—
988C22⋊C4—42no—
989C22⋊C4—42no—
990C22⋊C4—42no—
991C22⋊C4—434no—
992C22⋊C4—434no—
993C22⋊C4—434no—
994C22⋊C4—864no—
995C22⋊C4—864no—
996C22⋊C4—864no—
997C22⋊C4—864no—
998C22⋊C4—864no—
999C22⋊C4—864no—
1000C22⋊C4—864no—
1001C22⋊C4—864no—
1002C22⋊C4—862no—
1003C22⋊C4—864no—
1004C22⋊C4—864no—
1005C22⋊C4—864no—
1006C22⋊C4—864no—
1007C22⋊C4—864no—
1008C22⋊C4—864no—
1009C22⋊C4—864no—
1010C22⋊C4—1722no—
1011C22⋊C4—1722no—
1012C22⋊C4—1722no—
1013C22⋊C4—1722no—
1014C22⋊C4—1722no—
1015C42—22no—
1016C42—434no—
1017C42—864no—
1018C42—862no—
1019C42—862no—
1020C42—862no—
1021C42—862no—
1022C42—862no—
1023C42—862no—
1024C42—1721no—
1025C42—1721no—
1026C42—1721no—
1027C42—1721no—
1028C42—1721no—
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
1034C23—21no—
1035C23—21no—
1036C23—21no—
1037C23—21no—
1038C23—21no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—48no—
1054C23—48no—
1055C23—48no—
1056C23—84no—
1057C23—84no—
1058C23—84no—
1059C23—84no—
1060C23—862no—
1061C23—862no—
1062C23—862no—
1063C23—862no—
1064C23—862no—
1065C23—862no—
1066C23—862no—
1067C23C2×D4×D4312yes—
1068C23C2×D4×D4312yes—
1069C23#41×D4312yes—
1070C23C2×#1062190012yes—
1071C23C24×D4311yescharacteristic
1072Q8—3444no—
1073D4—28no—
1074D4—48no—
1075D4—44no—
1076D4—44no—
1077D4—84no—
1078D4—84no—
1079D4—3444no—
1080D4—3444no—
1081D4—3444no—
1082D4—3444no—
1083D4—3444no—
1084D4—1728no—
1085D4—1724no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—28no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—22no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—21no—
1102C2×C4—22no—
1103C2×C4—44no—
1104C2×C4—432no—
1105C2×C4—432no—
1106C2×C4—432no—
1107C2×C4—432no—
1108C2×C4—432no—
1109C2×C4—432no—
1110C2×C4—432no—
1111C2×C4—861no—
1112C2×C4—861no—
1113C2×C4—861no—
1114C2×C4—861no—
1115C2×C4—861no—
1116C2×C4—861no—
1117C2×C4—861no—
1118C2×C4—861no—
1119C2×C4—861no—
1120C2×C4—861no—
1121C2×C4—861no—
1122C2×C4—861no—
1123C2×C4—861no—
1124C2×C4—861no—
1125C2×C4—862no—
1126C2×C4—862no—
1127C2×C4—862no—
1128C2×C4—862no—
1129C2×C4—861no—
1130C2×C4—862no—
1131C2×C4—862no—
1132C2×C4—862no—
1133C2×C4—861no—
1134C2×C4—861no—
1135C2×C4—862no—
1136C2×C4—862no—
1137C2×C4—3444no—
1138C2×C4—3444no—
1139C2×C4—1724no—
1140C2×C4—1724no—
1141C2×C4—1724no—
1142C2×C4—1724no—
1143C2×C4C2×D4×D4312yes—
1144C2×C4C2×#1062190012yes—
1145C2×C4C2×#1062190012yes—
1146C2×C4#1306337012yes—
1147C2×C4#1306337012yes—
1148C22—22no—
1149C22—22no—
1150C22—22no—
1151C22—22no—
1152C22—22no—
1153C22—22no—
1154C22—22no—
1155C22—22no—
1156C22—22no—
1157C22—41no—
1158C22—41no—
1159C22—41no—
1160C22—41no—
1161C22—42no—
1162C22—42no—
1163C22—42no—
1164C22—42no—
1165C22—42no—
1166C22—42no—
1167C22—42no—
1168C22—42no—
1169C22—42no—
1170C22—42no—
1171C22—42no—
1172C22—42no—
1173C22—42no—
1174C22—42no—
1175C22—816no—
1176C22—1722no—
1177C22—1722no—
1178C22—1722no—
1179C22—1722no—
1180C22—1722no—
1181C22—1722no—
1182C22—1722no—
1183C22#1458344414yes—
1184C22C22×D4×D4311yescharacteristic
1185C22C2×#41×D4311yescharacteristic
1186C22C22×#1062190011yescharacteristic
1187C22H(5,𝔽2)×D4311yescharacteristic
1188C22C2×#1306337011yescharacteristic
1189C22C2×#1306337011yescharacteristic
1190C22#1458373411yescharacteristic
1191C4—22no—
1192C4—22no—
1193C4—42no—
1194C4—42no—
1195C4—41no—
1196C4—41no—
1197C4—862no—
1198C4—862no—
1199C4—862no—
1200C4—862no—
1201C4—862no—
1202C4—862no—
1203C4—862no—
1204C4—1722no—
1205C4—1722no—
1206C4—1721no—
1207C4—1722no—
1208C4#1458348414yescomplemented
1209C2—24no—
1210C2—42no—
1211C2—82no—
1212C2—82no—
1213C2—3442no—
1214C2C2×#1458344411yescharacteristic
1215C2C2×#1458348411yescharacteristic
1216C2#1914800811yescharacteristic
1217C2#1914835111yescharacteristic
1218C2#1914836711yescharacteristic
1219C2#1914855311yescharacteristic
1220C2#1914862411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D43
commutator, socle, cosocleC23×C43C25
FittingC43×#2408C2
hypercenter#2408D43
hypocenterC43#35007
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2408

Complements

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

NH ≅ G/Ntype
1. C2×#14583484C2semidirect
2. #19142959C2semidirect
3. #19142949C2semidirect
4. #19142938C2semidirect
5. #19142921C2semidirect
6. #19140731C2semidirect
7. #19140720C2semidirect
8. #19139665C2semidirect
9. #19139650C2semidirect
10. #19139179C2semidirect
11. #19138960C2semidirect
12. #19138718C2semidirect
13. #19138363C2semidirect
14. #19138298C2semidirect
15. #19138228C2semidirect
16. #19138179C2semidirect
17. #19138135C2semidirect
18. #19138035C2semidirect
19. #19137250C2semidirect
20. #19137101C2semidirect
21. C2×#14582802C2semidirect
22. C4×D4×Dic43C2semidirect
23. C43×#2408C2semidirect
25. C2×#13063324C22semidirect
28. C2×#13063318C22semidirect
29. C2×#13063318C22semidirect
30. C2×#13063312C22semidirect
31. C2×#13063311C22semidirect
32. C2×#13063311C22semidirect
33. C2×#13063307C22semidirect
34. C2×#13063306C22semidirect
37. C2×#13063299C22semidirect
39. C2×#13063297C22semidirect
40. C2×#13063297C22semidirect
41. C2×#13063296C22semidirect
46. C2×#13063287C22semidirect
52. C22×C4×Dic43C22semidirect
53. #14582833C22semidirect
54. #14582827C22semidirect
55. #14582822C22semidirect
56. #14582821C22semidirect
57. #14582820C22semidirect
58. #14582815C22semidirect
59. #14582815C22semidirect
60. #14582815C22semidirect
61. #14582814C22semidirect
62. #14582813C22semidirect
63. #14582811C22semidirect
66. #14582807C22semidirect
75. #14582801C22semidirect
76. #14582800C22semidirect
77. #14582799C22semidirect
78. #14582799C22semidirect
79. #14582799C22semidirect
80. #14582799C22semidirect
81. #14582798C22semidirect
82. #14582797C22semidirect
83. #14582795C22semidirect
84. #14582795C22semidirect
85. #14582793C22semidirect
86. #14582793C22semidirect
87. #14582793C22semidirect
88. #14582792C22semidirect
89. #14582788C22semidirect
90. #14582787C22semidirect
91. #14582787C22semidirect
92. #14582787C22semidirect
93. #14582779C22semidirect
96. #14582775C22semidirect
97. #14582775C22semidirect
99. #14582768C22semidirect
100. #14582759C22semidirect
101. C4⋊C4×Dic43C22semidirect
102. C4⋊C4×Dic43C22semidirect
103. C4⋊C4×Dic43C22semidirect
104. C4×C4⋊Dic43C22semidirect
107. C22⋊C4×Dic43C22semidirect
108. C22⋊C4×Dic43C22semidirect
110. C4×C22⋊Dic43C22semidirect
111. #14582746C22semidirect
112. C42×Dic43C22semidirect
158. D4×Dic43D4semidirect
334. C22×Dic43C2×D4semidirect
383. C22⋊Dic43C2×D4semidirect
398. C4⋊Dic43C2×D4semidirect
417. C4×Dic43C2×D4semidirect
587. C4×C43#538semidirect
617. #2408D43semidirect
734. C43#35007semidirect
1208. C4#14583484semidirect

Maximal subgroups

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

subgroupindex
C2×#145834842
#191429592
#191429492
#191429382
#191429212
#191407312
#191407202
#191396652
#191396502
#191391792
#191389602
#191387182
#191383632
#191382982
#191382282
#191381792
#191381352
#191380352
#191372502
#191371012
C2×#145828022
C4×D4×Dic432
C43×#24082
#3500743