Finite Group Databasebeta

← #27080936

Subgroups — #27080936

Order 12032.

1920 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256952C211yesmaximal, characteristic
2#20252397C212yesmaximal, complemented
3#20252390C212yesmaximal, complemented
4#20252380C212yesmaximal, complemented
5#20252377C212yesmaximal, complemented
6#20252371C212yesmaximal, complemented
7#20252368C212yesmaximal, complemented
8#20252361C212yesmaximal, complemented
9#20252352C212yesmaximal, complemented
10#20252331C211yesmaximal, characteristic, complemented
11#20252325C211yesmaximal, characteristic, complemented
12#20252123C211yesmaximal, characteristic, complemented
13#20252118C211yesmaximal, characteristic, complemented
14#20252118C211yesmaximal, characteristic, complemented
15#20252094C211yesmaximal, characteristic, complemented
16#20252085C211yesmaximal, characteristic, complemented
17C2×#15689193C211yesmaximal, characteristic, complemented
18#20252043C211yesmaximal, characteristic, complemented
19#20252043C211yesmaximal, characteristic, complemented
20#20251816C211yesmaximal, characteristic, complemented
21#20251804C211yesmaximal, characteristic, complemented
22#405×D47C211yesmaximal, characteristic, complemented
23C47×#2925C211yesmaximal, characteristic, complemented
24C2×#13094031C2211yescharacteristic
25C2×#13094031C2211yescharacteristic
26C22×#10625324C2211yescharacteristic
27C2×M16×D47C2211yescharacteristic
28C2×M16×D47C2211yescharacteristic
29C22×C8×D47C2211yescharacteristic
30#15689846C411yescharacteristic
31#15689838C411yescharacteristic
32#15689833C411yescharacteristic
33#15689823C411yescharacteristic
34#15689823C411yescharacteristic
35#15689814C411yescharacteristic
36#15689814C411yescharacteristic
37#15689813C412yes—
38#15689802C412yes—
39#15689802C412yes—
40#15689778C411yescharacteristic
41#15689769C412yes—
42#15689680C2211yescharacteristic
43#15689657C2212yes—
44#15689651C2212yes—
45#15689651C2212yes—
46#15689630C2211yescharacteristic
47#15689630C2211yescharacteristic
48C4×#10625350C2212yes—
49C2×C4×D188C2211yescharacteristic
50#117×D47C2211yescharacteristic
51#117×D47C2211yescharacteristic
52#15689252C2212yescomplemented
53#15689252C2212yescomplemented
54#15689252C2212yescomplemented
55#15689252C2212yescomplemented
56#15689252C2212yescomplemented
57#15689252C2212yescomplemented
58#15689250C2212yescomplemented
59#15689247C2212yescomplemented
60#15689200C2212yes—
61#15689198C2212yescomplemented
62#15689198C2212yescomplemented
63#15689198C2212yescomplemented
64#15689198C2212yescomplemented
65#15689197C2212yescomplemented
66#15689197C2212yescomplemented
67#15689197C2212yescomplemented
68#15689197C2212yescomplemented
69#15689193C2211yescharacteristic
70#15689193C2211yescharacteristic
71#15689193C2211yescharacteristic
72#15689193C2211yescharacteristic
73#15689193C2211yescharacteristic
74#15689193C2211yescharacteristic
75#15689193C2211yescharacteristic
76#15689193C2211yescharacteristic
77#15689193C2212yes—
78#15689193C2212yes—
79#15689191C2212yescomplemented
80#15689191C2212yescomplemented
81#15689191C2212yescomplemented
82#15689191C2212yescomplemented
83#15689188C2212yes—
84(C22⋊D47)⋊C8C2212yescomplemented
85(C22⋊D47)⋊C8C2212yescomplemented
86(C22⋊D47)⋊C8C2212yescomplemented
87(C22⋊D47)⋊C8C2212yescomplemented
88#15689185C2212yescomplemented
89#15689185C2212yescomplemented
90#15689182C2212yescomplemented
91#15689182C2212yescomplemented
92#15689178C2212yescomplemented
93#15689178C2212yescomplemented
94#15689174C2212yescomplemented
95#15689174C2212yescomplemented
96#15689151C2211yescharacteristic
97#15689151C2211yescharacteristic
98#15689149C2211yescharacteristic
99#15689149C2211yescharacteristic
100#15689086C2211yescharacteristic
101#15689086C2211yescharacteristic
102C2×(C2×D47)⋊C8C2211yescharacteristic
103C2×(C2×D47)⋊C8C2211yescharacteristic
104#15689081C2211yescharacteristic
105#15689081C2211yescharacteristic
106#15689080C2212yescomplemented
107#15689080C2212yescomplemented
108#15689079C2211yescharacteristic
109#15689079C2211yescharacteristic
110#15689079C2212yescomplemented
111#15689079C2212yescomplemented
112#15689078C2211yescharacteristic
113#15689078C2211yescharacteristic
114#15689077C2212yescomplemented
115#15689077C2212yescomplemented
116C4×#10625329C2211yescharacteristic
117C4×#10625329C2212yescomplemented
118#15689075C2212yescomplemented
119C4×#10625324C2212yescomplemented
120C2×#13093935C2211yescharacteristic
121C2×#13093935C2212yescomplemented
122#97×D47C2212yescomplemented
123C4×C8×D47C2212yescomplemented
124C4×#41×C47C2211yescharacteristic
125C47×#433C2212yescomplemented
126C47×#433C2212yescomplemented
127C47×#432C2212yescomplemented
128C47×#431C2212yescomplemented
129C47×#423C2211yescharacteristic
130C2×C4⋊C8×C47C2211yescharacteristic
131C47×#408C2211yescharacteristic
132C47×#408C2211yescharacteristic
133C47×#405C2211yescharacteristic
134C47×#405C2211yescharacteristic
135C2×#10625350C2×C412yes—
136C22×D188C2×C411yescharacteristic
137C22×C4×D47C2311yescharacteristic
138C22×C4×D47C2311yescharacteristic
139#13094031—24no—
140#13094031—24no—
141C2×#10625329C2311yescharacteristic
142C2×#10625329C2312yes—
143C2×#10625329C2312yes—
144C2×#10625329C2311yescharacteristic
145C2×#10625324—24no—
146C2×#10625324C2311yescharacteristic
147C2×#10625324C2312yes—
148C2×#10625324C2311yescharacteristic
149C2×#10625324C2311yescharacteristic
150C2×#10625324C2312yes—
151C2×#10625324C2311yescharacteristic
152M16×D47—24no—
153M16×D47—24no—
154C22×C47⋊C8C2311yescharacteristic
155C22×C47⋊C8C2312yes—
156C22×C47⋊C8C2312yes—
157C22×C47⋊C8C2311yescharacteristic
158C2×C8×D47—24no—
159C2×C8×D47C2311yescharacteristic
160C2×C8×D47C2312yes—
161C2×C8×D47C2311yescharacteristic
162C2×C8×D47C2311yescharacteristic
163C2×C8×D47C2312yes—
164C2×C8×D47C2311yescharacteristic
165#13094024C2×C411yescharacteristic
166#13094024C2×C411yescharacteristic
167#13094019C2×C412yes—
168#13094019C2×C412yes—
169#13094018C2×C412yes—
170#13094018C2×C412yes—
171#13094017C2×C412yes—
172#13094017C2×C412yes—
173#13094016C2×C412yes—
174#13094016C2×C411yescharacteristic
175#13094016C2×C411yescharacteristic
176#13094014C2×C412yes—
177#13094014C2×C412yes—
178#13094012C2×C412yes—
179#13094010C2×C412yes—
180#13094010C2×C412yes—
181#13094009C2×C412yes—
182#13094009C2×C412yes—
183#13094007C2×C412yes—
184#13094007C2×C412yes—
185#13094006C2×C412yes—
186#13094006C2×C412yes—
187#13094005C2×C412yes—
188#13094005C2×C412yes—
189#13094003C2×C412yes—
190#13094003C2×C412yes—
191#13094003C2×C412yes—
192#13094002C2×C412yes—
193#13094002C2×C412yes—
194#13094000C2×C411yescharacteristic
195#13094000C2×C411yescharacteristic
196#13094000C2×C411yescharacteristic
197#13094000C2×C411yescharacteristic
198#13093998C2×C412yes—
199#13093997C2×C412yes—
200#13093997C2×C412yes—
201#13093995C2×C411yescharacteristic
202#13093995C2×C411yescharacteristic
203#13093995C2×C411yescharacteristic
204#13093995C2×C411yescharacteristic
205#13093992C2×C412yes—
206#13093992C2×C412yes—
207C4×Dic94C2×C412yes—
208C4×Dic94C2312yes—
209C4×Dic94C2312yes—
210C4×D188C2×C412yes—
211C4×D188C2×C411yescharacteristic
212C4×D188C2×C411yescharacteristic
213C4×D188C2×C411yescharacteristic
214C4×D188C2×C411yescharacteristic
215C4×D188C2311yescharacteristic
216C4×D188C2311yescharacteristic
217C4×D188C2311yescharacteristic
218C4×D188C2311yescharacteristic
219C4×C22⋊D47C2×C412yes—
220C4×C22⋊D47C2×C412yes—
221C4×C22⋊D47C2312yes—
222C4×C22⋊D47C2312yes—
223C4×C22⋊D47C2312yes—
224C4×C22⋊D47C2312yes—
225#13093983C2×C412yes—
226#13093983C2311yescharacteristic
227#13093983C2311yescharacteristic
228#13093982C2×C411yescharacteristic
229#13093982C2×C411yescharacteristic
230#13093982C2×C411yescharacteristic
231#13093982C2×C411yescharacteristic
232#13093981C2×C412yes—
233#13093981C2×C412yes—
234#13093981C2312yes—
235#13093981C2312yes—
236#13093980C2×C412yes—
237#13093980C2×C412yes—
238C2×C4⋊Dic47C2×C411yescharacteristic
239C4⋊C4×D47C2×C411yescharacteristic
240C4⋊C4×D47C2×C411yescharacteristic
241C4⋊C4×D47C2×C411yescharacteristic
242C4⋊C4×D47C2×C411yescharacteristic
243C2×(C2×D47)⋊C4C2×C411yescharacteristic
244C2×(C2×D47)⋊C4C2×C411yescharacteristic
245C22⋊C4×D47C2×C412yes—
246C22⋊C4×D47C2×C412yes—
247C42×D47C2312yes—
248C42×D47C2312yes—
249Dic47⋊C8C2312yes—
250Dic47⋊C8C2312yes—
251Dic47⋊C8C2312yes—
252Dic47⋊C8C2312yes—
253Dic47⋊C8C2312yes—
254Dic47⋊C8C2312yes—
255Dic47⋊C8C2312yes—
256Dic47⋊C8C2312yes—
257(C2×D47)⋊C8C2311yescharacteristic
258(C2×D47)⋊C8C2311yescharacteristic
259(C2×D47)⋊C8C2311yescharacteristic
260(C2×D47)⋊C8C2311yescharacteristic
261(C2×D47)⋊C8C2311yescharacteristic
262(C2×D47)⋊C8C2311yescharacteristic
263(C2×D47)⋊C8C2311yescharacteristic
264(C2×D47)⋊C8C2311yescharacteristic
265(C2×D47)⋊C8C2312yes—
266(C2×D47)⋊C8C2312yes—
267(C2×D47)⋊C8C2312yes—
268(C2×D47)⋊C8C2312yes—
269#13093935C2311yescharacteristic
270#13093935C2311yescharacteristic
271#13093935C2311yescharacteristic
272#13093935C2311yescharacteristic
273#13093935C2312yes—
274#13093935C2312yes—
275#13093935C2312yes—
276#13093934C2312yes—
277#13093934C2312yes—
278#13093934C2312yes—
279#13093934C2312yes—
280C4×C47⋊C8C2312yes—
281C4×C47⋊C8C2312yes—
282C4×C47⋊C8C2312yes—
283C8×Dic47C2312yes—
284C8×Dic47C2312yes—
285C8×Dic47C2312yes—
286C8×Dic47C2312yes—
287C2×#41×C47C2311yescharacteristic
288C2×M16×C47C2311yescharacteristic
289C2×M16×C47C2311yescharacteristic
290C22×C8×C47C2311yescharacteristic
291C22×C8×C47C2311yescharacteristic
292C4×Q8×C47C2×C411yescharacteristic
293C4×Q8×C47C2×C411yescharacteristic
294C4×D4×C47C2×C412yes—
295C4×D4×C47C2×C411yescharacteristic
296C4×D4×C47C2×C412yes—
297C4×D4×C47C2×C411yescharacteristic
298#117×C47C2311yescharacteristic
299#117×C47C2312yes—
300C2×C42×C47C2311yescharacteristic
301C2×C42×C47C2312yes—
302C4⋊C8×C47C2311yescharacteristic
303C4⋊C8×C47C2311yescharacteristic
304C4⋊C8×C47C2312yes—
305C4⋊C8×C47C2311yescharacteristic
306C4⋊C8×C47C2311yescharacteristic
307C4⋊C8×C47C2312yes—
308C22⋊C8×C47C2312yes—
309C22⋊C8×C47C2312yes—
310C22⋊C8×C47C2312yes—
311C22⋊C8×C47C2312yes—
312#97×C47C2312yes—
313#97×C47C2312yes—
314C4×C8×C47C2312yes—
315C4×C8×C47C2312yes—
316C23×D47C22×C411yescharacteristic
317C23×D47C22×C411yescharacteristic
318#41×C47—22no—
319#41×C47—22no—
320C2×Q8×C47C22×C411yescharacteristic
321C2×D4×C47C22×C412yes—
322C2×D4×C47C22×C411yescharacteristic
323C22×C4×C47C22×C411yescharacteristic
324C22×C4×C47C22×C411yescharacteristic
325C22×C4×C47C22×C412yes—
326C22×C4×C47C22×C412yes—
327C22×C4×C47C2412yes—
328C22×C4×C47C2411yescharacteristic
329C2×C22⋊D47C22×C412yes—
330C2×C22⋊D47C22×C412yes—
331C2×C22⋊D47C22×C412yes—
332C2×C22⋊D47C22×C412yes—
333C22×Dic47C22×C411yescharacteristic
334C22×Dic47C22×C411yescharacteristic
335#10625350—44no—
336C2×D188—42no—
337C2×D188C22×C411yescharacteristic
338C2×D188C22×C411yescharacteristic
339C2×D188C22×C411yescharacteristic
340C2×D188C22×C411yescharacteristic
341C2×C4×D47—22no—
342C2×C4×D47—22no—
343C2×C4×D47—22no—
344C2×C4×D47—22no—
345C2×C4×D47C22×C412yes—
346C2×C4×D47C22×C411yescharacteristic
347C2×C4×D47C22×C411yescharacteristic
348C2×C4×D47C22×C411yescharacteristic
349C2×C4×D47C22×C411yescharacteristic
350C2×C4×D47C22×C412yes—
351C2×C4×D47C22×C412yes—
352C2×C4×D47C22×C412yes—
353C2×C4×D47C2411yescharacteristic
354C2×C4×D47C2411yescharacteristic
355C2×C4×D47C2411yescharacteristic
356C2×C4×D47C2411yescharacteristic
357C2×Dic94C22×C412yes—
358C2×Dic94C22×C412yes—
359M16×C47—22no—
360M16×C47—22no—
361C2×C8×C47—22no—
362C2×C8×C47—22no—
363C2×C8×C47C2411yescharacteristic
364C2×C8×C47C2411yescharacteristic
365C2×C8×C47C2411yescharacteristic
366C2×C8×C47C2411yescharacteristic
367C2×C8×C47C2412yes—
368C2×C8×C47C2412yes—
369C4⋊C4×C47C22×C411yescharacteristic
370C4⋊C4×C47C22×C411yescharacteristic
371C4⋊C4×C47C22×C412yes—
372C4⋊C4×C47C22×C412yes—
373C22⋊C4×C47C22×C412yes—
374C22⋊C4×C47C22×C412yes—
375C22⋊C4×C47C22×C412yes—
376C42×C47C22×C412yes—
377C42×C47C22×C411yescharacteristic
378C42×C47C22×C411yescharacteristic
379C42×C47C22×C412yes—
380C42×C47C2411yescharacteristic
381C42×C47C2411yescharacteristic
382C42×C47C2412yes—
383C22⋊Dic47C22×C412yes—
384C22⋊Dic47C22×C412yes—
385C22⋊Dic47C22×C412yes—
386C22⋊Dic47C22×C412yes—
387C22⋊Dic47C22×C412yes—
388C22⋊Dic47C22×C412yes—
389(C2×D47)⋊C4C22×C412yes—
390(C2×D47)⋊C4C22×C412yes—
391(C2×D47)⋊C4C22×C412yes—
392(C2×D47)⋊C4C22×C412yes—
393(C2×D47)⋊C4C22×C411yescharacteristic
394(C2×D47)⋊C4C22×C411yescharacteristic
395(C2×D47)⋊C4C22×C411yescharacteristic
396(C2×D47)⋊C4C22×C411yescharacteristic
397(C2×D47)⋊C4C22×C411yescharacteristic
398(C2×D47)⋊C4C22×C411yescharacteristic
399(C2×D47)⋊C4C22×C411yescharacteristic
400(C2×D47)⋊C4C22×C411yescharacteristic
401(C2×D47)⋊C4C22×C412yes—
402(C2×D47)⋊C4C22×C412yes—
403(C2×D47)⋊C4C22×C412yes—
404(C2×D47)⋊C4C22×C412yes—
405C4⋊Dic47C22×C411yescharacteristic
406C4⋊Dic47C22×C411yescharacteristic
407C4⋊Dic47C22×C411yescharacteristic
408C4⋊Dic47C22×C411yescharacteristic
409C4⋊Dic47C22×C411yescharacteristic
410C4⋊Dic47C22×C411yescharacteristic
411C4⋊Dic47C22×C411yescharacteristic
412C4⋊Dic47C22×C411yescharacteristic
413C4⋊Dic47C22×C412yes—
414C4⋊Dic47C22×C412yes—
415Dic47⋊C4C22×C412yes—
416Dic47⋊C4C22×C412yes—
417Dic47⋊C4C22×C412yes—
418Dic47⋊C4C22×C412yes—
419Dic47⋊C4C22×C412yes—
420Dic47⋊C4C22×C412yes—
421Dic47⋊C4C22×C412yes—
422Dic47⋊C4C22×C412yes—
423Dic47⋊C4C22×C412yes—
424Dic47⋊C4C22×C412yes—
425Dic47⋊C4C22×C412yes—
426Dic47⋊C4C22×C412yes—
427C4×Dic47C22×C412yes—
428C4×Dic47C22×C412yes—
429C4×Dic47C22×C412yes—
430C4×Dic47C22×C412yes—
431C4×Dic47C2412yes—
432C4×Dic47C2412yes—
433#10625329—22no—
434#10625329—24no—
435#10625329—24no—
436#10625329#4114yescomplemented
437C2×C47⋊C8—22no—
438C2×C47⋊C8—24no—
439C2×C47⋊C8—24no—
440C2×C47⋊C8#4114yescomplemented
441C2×C47⋊C8C2412yes—
442C2×C47⋊C8C2411yescharacteristic
443C2×C47⋊C8C2411yescharacteristic
444C2×C47⋊C8C2412yes—
445C2×C47⋊C8C2411yescharacteristic
446C2×C47⋊C8C2411yescharacteristic
447#10625324—24no—
448#10625324—24no—
449#10625324—22no—
450#10625324—22no—
451#10625324—22no—
452#10625324—22no—
453C8×D47—22no—
454C8×D47—22no—
455C8×D47—22no—
456C8×D47—22no—
457C8×D47—24no—
458C8×D47—24no—
459C23×C47C23×C412yes—
460C23×C47C23×C411yescharacteristic
461C22×D47—22no—
462C22×D47—22no—
463C22×D47—22no—
464C22×D47—41no—
465C22×D47—41no—
466C22×D47—41no—
467C22×D47C23×C411yescharacteristic
468C22×D47C23×C411yescharacteristic
469C22×D47C23×C411yescharacteristic
470C22×D47C23×C411yescharacteristic
471Q8×C47—22no—
472D4×C47—24no—
473D4×C47—22no—
474C2×C4×C47—22no—
475C2×C4×C47—22no—
476C2×C4×C47—41no—
477C2×C4×C47—42no—
478C2×C4×C47—41no—
479C2×C4×C47—42no—
480C2×C4×C47C23×C412yes—
481C2×C4×C47C23×C412yes—
482C2×C4×C47C23×C411yescharacteristic
483C2×C4×C47C23×C411yescharacteristic
484C2×C4×C47C23×C412yes—
485C2×C4×C47C23×C411yescharacteristic
486C2×C4×C47C23×C411yescharacteristic
487C2×C4×C47C23×C411yescharacteristic
488C2×C4×C47C2×#4112yes—
489C2×C4×C47C2×#4112yes—
490C2×C4×C47C2511yescharacteristic
491C22⋊D47—24no—
492C22⋊D47—42no—
493C22⋊D47—42no—
494C22⋊D47—42no—
495C2×Dic47—22no—
496C2×Dic47—22no—
497C2×Dic47C23×C411yescharacteristic
498C2×Dic47C23×C411yescharacteristic
499C2×Dic47C23×C412yes—
500C2×Dic47C23×C412yes—
501C2×Dic47C23×C412yes—
502C2×Dic47C23×C412yes—
503C2×Dic47C23×C411yescharacteristic
504C2×Dic47C23×C411yescharacteristic
505D188—22no—
506D188—22no—
507D188—41no—
508D188—41no—
509C4×D47—24no—
510C4×D47—22no—
511C4×D47—22no—
512C4×D47—22no—
513C4×D47—22no—
514C4×D47—21no—
515C4×D47—21no—
516C4×D47—21no—
517C4×D47—21no—
518C4×D47—21no—
519C4×D47—21no—
520C4×D47—21no—
521C4×D47—21no—
522C4×D47—42no—
523C4×D47—42no—
524C4×D47—42no—
525Dic94—42no—
526Dic94—42no—
527C8×C47—21no—
528C8×C47—21no—
529C8×C47—22no—
530C8×C47—22no—
531C8×C47—21no—
532C8×C47—21no—
533C47⋊C8—21no—
534C47⋊C8—21no—
535C47⋊C8—22no—
536C47⋊C8C2×#4112yes—
537C47⋊C8C2×#4114yes—
538C47⋊C8C2×#4112yes—
539#60216—471nomaximal, Sylow
540C22×C47—21no—
541C22×C47—21no—
542C22×C47—22no—
543C22×C47—22no—
544C22×C47—22no—
545C22×C47C4×#4112yes—
546C22×C47C24×C411yescharacteristic
547C2×D47—21no—
548C2×D47—21no—
549C2×D47—21no—
550C2×D47—21no—
551C2×D47—21no—
552C2×D47—21no—
553C2×D47—21no—
554C2×D47—21no—
555C2×D47—21no—
556C2×D47—21no—
557C2×D47—21no—
558C2×D47—44no—
559C2×D47—82no—
560C2×D47#56812yes—
561C4×C47—22no—
562C4×C47—21no—
563C4×C47—22no—
564C4×C47—21no—
565C4×C47—21no—
566C4×C47—22no—
567C4×C47—21no—
568C4×C47C4×#4112yes—
569C4×C47C22×#4111yescharacteristic
570C4×C47C22×#4111yescharacteristic
571Dic47—21no—
572Dic47—21no—
573Dic47—21no—
574Dic47—21no—
575Dic47—22no—
576Dic47—22no—
577Dic47—22no—
578Dic47—22no—
579#3475—471no—
580#2970—472no—
581#2969—472no—
582#2968—472no—
583#2968—472no—
584#2967—472no—
585#2967—472no—
586#2966—472no—
587#2965—472no—
588#2962—471no—
589#2961—471no—
590D4×M16—471no—
591#2933—471no—
592#2933—471no—
593#2930—471no—
594#2929—471no—
595C2×#435—471no—
596#2925D4711yescharacteristic, complemented
597#2924—471no—
598#2924—471no—
599#2875—471no—
600#2873—471no—
601C2×#405—471no—
602C2×C47—22no—
603C2×C47—42no—
604C2×C47C2×C4×#4111yescharacteristic
605C2×C47C2×#56811yescharacteristic
606C2×C47#357311yescharacteristic
607D47—22no—
608D47—41no—
609D47—41no—
610D47—41no—
611C2×#131—471no—
612C2×#131—471no—
613C22×M16—471no—
614C22×M16—471no—
615C22×M16—471no—
616C23×C8—471no—
617#556—471no—
618#555—471no—
619#554—471no—
620#553—471no—
621#553—471no—
622#552—471no—
623#552—471no—
624#552—472no—
625#551—472no—
626#551—472no—
627#547—471no—
628#546—472no—
629#533—471no—
630#529—472no—
631#529—472no—
632#529—472no—
633#525—471no—
634#525—471no—
635C4×#41—472no—
636C4×#41C2×D4711yescharacteristic
637C2×C4×D4—471no—
638C2×#117—471no—
639C2×#117—471no—
640#446—472no—
641#446—472no—
642#446—472no—
643#446—472no—
644#446—472no—
645#446—472no—
646#446—472no—
647C8×Q8—472no—
648#436—472no—
649#436—472no—
650#436—472no—
651#436—472no—
652#436—472no—
653#435—471no—
654#435—471no—
655#435—471no—
656#435—471no—
657#435—471no—
658#435—471no—
659#435—471no—
660#435—471no—
661#435—472no—
662#435—472no—
663#435—472no—
664#435—472no—
665#435—472no—
666#435—472no—
667#435—472no—
668#435—472no—
669#435—472no—
670#435—472no—
671C8×D4—472no—
672C8×D4—472no—
673C8×D4—472no—
674C8×D4—472no—
675C8×D4—472no—
676#433—472no—
677#433—472no—
678#433—472no—
679#433—472no—
680#433C2×D4712yescomplemented
681#433C2×D4712yescomplemented
682#432—472no—
683#432—472no—
684#432C2×D4712yescomplemented
685#431—472no—
686#431—472no—
687#431C2×D4712yescomplemented
688#424—471no—
689#424—471no—
690#424—471no—
691#424—471no—
692#423C2×D4711yescharacteristic
693C2×C4⋊C8C2×D4711yescharacteristic
694#408C2×D4711yescharacteristic
695#408C2×D4711yescharacteristic
696#407—471no—
697#407—471no—
698C2×C22⋊C8—471no—
699C2×C22⋊C8—471no—
700#405—471no—
701#405—471no—
702#405—471no—
703#405—471no—
704#405—471no—
705#405—471no—
706#405—472no—
707#405—472no—
708#405—472no—
709#405—472no—
710#405—472no—
711#405—472no—
712#405C2×D4711yescharacteristic
713#405C2×D4711yescharacteristic
714C4×M16—471no—
715C4×M16—472no—
716C4×M16—472no—
717C4×M16—472no—
718C2×#97—471no—
719C2×#97—472no—
720C2×#97—472no—
721C2×C4×C8—472no—
722C47#6021611yescharacteristic, complemented, Sylow
723C2×#41—472no—
724C2×#41C22×D4711yescharacteristic
725C22×D4—471no—
726C23×C4—471no—
727C23×C4—471no—
728#131—944no—
729#131—944no—
730C2×M16—471no—
731C2×M16—471no—
732C2×M16—472no—
733C2×M16—472no—
734C2×M16—471no—
735C2×M16—472no—
736C2×M16—471no—
737C2×M16—471no—
738C2×M16—471no—
739C2×M16—472no—
740C2×M16—944no—
741C2×M16—944no—
742C2×M16—944no—
743C2×M16C22×D4711yescharacteristic
744C2×M16C22×D4711yescharacteristic
745C22×C8—471no—
746C22×C8—471no—
747C22×C8—472no—
748C22×C8—472no—
749C22×C8—471no—
750C22×C8—471no—
751C22×C8—471no—
752C22×C8—471no—
753C22×C8—472no—
754C22×C8—472no—
755C22×C8—944no—
756C22×C8C22×D4711yescharacteristic
757C22×C8C22×D4711yescharacteristic
758C4⋊Q8—471no—
759C4⋊Q8—471no—
760#126—472no—
761#126—472no—
762#126—472no—
763#126—472no—
764#126—472no—
765#126—472no—
766#125—472no—
767#125—472no—
768#125—472no—
769#125—471no—
770#125—471no—
771#124—472no—
772#124—472no—
773#124—472no—
774#123—472no—
775#123—472no—
776#123—472no—
777#123—472no—
778#123—472no—
779#123—472no—
780#123—472no—
781#123—472no—
782C22⋊Q8—471no—
783C22⋊Q8—471no—
784C22⋊Q8—471no—
785C22⋊Q8—471no—
786C22⋊Q8—472no—
787C22⋊Q8—472no—
788C22⋊Q8—472no—
789C22⋊Q8—472no—
790C22⋊Q8—472no—
791#121—471no—
792#121—471no—
793#121—471no—
794#121—471no—
795#121—472no—
796#121—472no—
797#121—472no—
798#120—472no—
799#120—472no—
800C4×Q8—472no—
801C4×Q8—472no—
802C4×Q8—472no—
803C4×Q8C4×D4711yescharacteristic
804C4×Q8C4×D4711yescharacteristic
805C4×D4—472no—
806C4×D4—472no—
807C4×D4—472no—
808C4×D4—472no—
809C4×D4—472no—
810C4×D4—472no—
811C4×D4—471no—
812C4×D4—471no—
813C4×D4—471no—
814C4×D4—471no—
815C4×D4—472no—
816C4×D4—471no—
817C4×D4—471no—
818C4×D4—471no—
819C4×D4—471no—
820C4×D4C4×D4712yes—
821C4×D4C4×D4711yescharacteristic
822C4×D4C4×D4712yes—
823C4×D4C4×D4711yescharacteristic
824#117—472no—
825#117—471no—
826#117—471no—
827#117—471no—
828#117—471no—
829#117—471no—
830#117—471no—
831#117—472no—
832#117—472no—
833#117—472no—
834#117—472no—
835#117—472no—
836#117—472no—
837#117C22×D4711yescharacteristic
838#117C22×D4712yes—
839C2×C4⋊C4—471no—
840C2×C4⋊C4—471no—
841C2×C4⋊C4—471no—
842C2×C4⋊C4—471no—
843C2×C4⋊C4—471no—
844C2×C22⋊C4—471no—
845C2×C22⋊C4—471no—
846C2×C22⋊C4—472no—
847C2×C22⋊C4—472no—
848C2×C42—472no—
849C2×C42—472no—
850C2×C42C22×D4711yescharacteristic
851C2×C42C22×D4712yes—
852C4⋊C8—472no—
853C4⋊C8—472no—
854C4⋊C8—472no—
855C4⋊C8—472no—
856C4⋊C8—472no—
857C4⋊C8—472no—
858C4⋊C8—472no—
859C4⋊C8—472no—
860C4⋊C8C22×D4711yescharacteristic
861C4⋊C8C22×D4711yescharacteristic
862C4⋊C8C22×D4711yescharacteristic
863C4⋊C8C22×D4711yescharacteristic
864C4⋊C8C22×D4712yes—
865C4⋊C8C22×D4712yes—
866C22⋊C8—471no—
867C22⋊C8—471no—
868C22⋊C8—471no—
869C22⋊C8—471no—
870C22⋊C8—471no—
871C22⋊C8—471no—
872C22⋊C8—471no—
873C22⋊C8—471no—
874C22⋊C8—472no—
875C22⋊C8—472no—
876C22⋊C8—472no—
877C22⋊C8—472no—
878C22⋊C8C22×D4712yes—
879C22⋊C8C22×D4712yes—
880C22⋊C8C22×D4712yes—
881C22⋊C8C22×D4712yes—
882#97—472no—
883#97—472no—
884#97—472no—
885#97—472no—
886#97—471no—
887#97—472no—
888#97—471no—
889#97—472no—
890#97—472no—
891#97—471no—
892#97—471no—
893#97C22×D4712yes—
894#97C22×D4712yes—
895C4×C8—472no—
896C4×C8—472no—
897C4×C8—472no—
898C4×C8—472no—
899C4×C8—472no—
900C4×C8—472no—
901C4×C8—472no—
902C4×C8C22×D4712yes—
903C4×C8C22×D4712yes—
904C24—471no—
905C24—471no—
906#41—22no—
907#41—22no—
908#41—1884no—
909C2×Q8—472no—
910C2×Q8—472no—
911C2×Q8C2×C4×D4711yescharacteristic
912C2×D4—472no—
913C2×D4—472no—
914C2×D4—472no—
915C2×D4—472no—
916C2×D4—471no—
917C2×D4—471no—
918C2×D4—471no—
919C2×D4—471no—
920C2×D4—1882no—
921C2×D4C2×C4×D4712yes—
922C2×D4C2×C4×D4711yescharacteristic
923C22×C4—471no—
924C22×C4—471no—
925C22×C4—472no—
926C22×C4—471no—
927C22×C4—471no—
928C22×C4—471no—
929C22×C4—471no—
930C22×C4—471no—
931C22×C4—471no—
932C22×C4—471no—
933C22×C4—471no—
934C22×C4—472no—
935C22×C4—472no—
936C22×C4—472no—
937C22×C4—942no—
938C22×C4—942no—
939C22×C4—942no—
940C22×C4—942no—
941C22×C4C2×C4×D4711yescharacteristic
942C22×C4C2×C4×D4711yescharacteristic
943C22×C4C2×C4×D4712yes—
944C22×C4C2×C4×D4712yes—
945C22×C4C23×D4712yes—
946C22×C4C23×D4711yescharacteristic
947M16—22no—
948M16—22no—
949M16—474no—
950M16—942no—
951M16—942no—
952M16—942no—
953M16—942no—
954M16—944no—
955M16—944no—
956M16—944no—
957M16—944no—
958M16—942no—
959C2×C8—22no—
960C2×C8—22no—
961C2×C8—474no—
962C2×C8—471no—
963C2×C8—472no—
964C2×C8—471no—
965C2×C8—471no—
966C2×C8—472no—
967C2×C8—471no—
968C2×C8—942no—
969C2×C8—942no—
970C2×C8—942no—
971C2×C8—942no—
972C2×C8—944no—
973C2×C8—944no—
974C2×C8—944no—
975C2×C8—944no—
976C2×C8—942no—
977C2×C8C23×D4711yescharacteristic
978C2×C8C23×D4711yescharacteristic
979C2×C8C23×D4712yes—
980C2×C8C23×D4712yes—
981C2×C8C23×D4711yescharacteristic
982C2×C8C23×D4711yescharacteristic
983C4⋊C4—472no—
984C4⋊C4—472no—
985C4⋊C4—472no—
986C4⋊C4—472no—
987C4⋊C4—472no—
988C4⋊C4—472no—
989C4⋊C4—472no—
990C4⋊C4—472no—
991C4⋊C4—472no—
992C4⋊C4—472no—
993C4⋊C4—472no—
994C4⋊C4—472no—
995C4⋊C4—471no—
996C4⋊C4—471no—
997C4⋊C4—471no—
998C4⋊C4—471no—
999C4⋊C4—471no—
1000C4⋊C4—471no—
1001C4⋊C4—471no—
1002C4⋊C4—471no—
1003C4⋊C4—472no—
1004C4⋊C4—472no—
1005C4⋊C4C2×C4×D4711yescharacteristic
1006C4⋊C4C2×C4×D4711yescharacteristic
1007C4⋊C4C2×C4×D4712yes—
1008C4⋊C4C2×C4×D4712yes—
1009C22⋊C4—472no—
1010C22⋊C4—472no—
1011C22⋊C4—472no—
1012C22⋊C4—472no—
1013C22⋊C4—472no—
1014C22⋊C4—472no—
1015C22⋊C4—471no—
1016C22⋊C4—471no—
1017C22⋊C4—472no—
1018C22⋊C4—472no—
1019C22⋊C4—472no—
1020C22⋊C4—472no—
1021C22⋊C4—471no—
1022C22⋊C4—471no—
1023C22⋊C4—471no—
1024C22⋊C4—471no—
1025C22⋊C4—471no—
1026C22⋊C4—471no—
1027C22⋊C4—472no—
1028C22⋊C4—472no—
1029C22⋊C4—472no—
1030C22⋊C4—472no—
1031C22⋊C4C2×C4×D4712yes—
1032C22⋊C4C2×C4×D4712yes—
1033C22⋊C4C2×C4×D4712yes—
1034C42—472no—
1035C42—472no—
1036C42—472no—
1037C42—472no—
1038C42—472no—
1039C42—472no—
1040C42C2×C4×D4712yes—
1041C42C2×C4×D4711yescharacteristic
1042C42C2×C4×D4711yescharacteristic
1043C42C2×C4×D4712yes—
1044C42C23×D4712yes—
1045C42C23×D4711yescharacteristic
1046C42C23×D4711yescharacteristic
1047C23—471no—
1048C23—471no—
1049C23—471no—
1050C23—471no—
1051C23—942no—
1052C23—942no—
1053C23—942no—
1054C23—1881no—
1055C23—1881no—
1056C23—1881no—
1057C23C22×C4×D4712yes—
1058C23C22×C4×D4711yescharacteristic
1059Q8—22no—
1060Q8—1882no—
1061Q8—1882no—
1062D4—24no—
1063D4—22no—
1064D4—942no—
1065D4—942no—
1066D4—944no—
1067D4—1881no—
1068D4—1881no—
1069D4—1882no—
1070D4—1882no—
1071D4—1882no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—42no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—42no—
1078C2×C4—471no—
1079C2×C4—471no—
1080C2×C4—472no—
1081C2×C4—472no—
1082C2×C4—472no—
1083C2×C4—472no—
1084C2×C4—471no—
1085C2×C4—471no—
1086C2×C4—944no—
1087C2×C4—942no—
1088C2×C4—942no—
1089C2×C4—942no—
1090C2×C4—942no—
1091C2×C4—942no—
1092C2×C4—942no—
1093C2×C4—941no—
1094C2×C4—941no—
1095C2×C4—941no—
1096C2×C4—941no—
1097C2×C4—941no—
1098C2×C4—941no—
1099C2×C4—941no—
1100C2×C4—941no—
1101C2×C4—1882no—
1102C2×C4—1882no—
1103C2×C4—1882no—
1104C2×C4C22×C4×D4712yes—
1105C2×C4C22×C4×D4712yes—
1106C2×C4C22×C4×D4711yescharacteristic
1107C2×C4C22×C4×D4711yescharacteristic
1108C2×C4C22×C4×D4712yes—
1109C2×C4C22×C4×D4711yescharacteristic
1110C2×C4C22×C4×D4711yescharacteristic
1111C2×C4C22×C4×D4711yescharacteristic
1112C2×C4#41×D4712yes—
1113C2×C4#41×D4712yes—
1114C2×C4C24×D4711yescharacteristic
1115C8—21no—
1116C8—21no—
1117C8—21no—
1118C8—21no—
1119C8—22no—
1120C8—22no—
1121C8—472no—
1122C8—472no—
1123C8—474no—
1124C8—941no—
1125C8—942no—
1126C8—941no—
1127C22—21no—
1128C22—21no—
1129C22—22no—
1130C22—22no—
1131C22—22no—
1132C22—472no—
1133C22—941no—
1134C22—941no—
1135C22—941no—
1136C22—941no—
1137C22—941no—
1138C22—941no—
1139C22—941no—
1140C22—941no—
1141C22—941no—
1142C22—941no—
1143C22—941no—
1144C22—3762no—
1145C22—1884no—
1146C22#1568959112yes—
1147C22C23×C4×D4711yescharacteristic
1148C4—21no—
1149C4—22no—
1150C4—21no—
1151C4—21no—
1152C4—22no—
1153C4—21no—
1154C4—22no—
1155C4—942no—
1156C4—942no—
1157C4—942no—
1158C4—942no—
1159C4—941no—
1160C4—941no—
1161C4—941no—
1162C4—941no—
1163C4#1568959112yes—
1164C4C2×#41×D4711yescharacteristic
1165C4C2×#41×D4711yescharacteristic
1166C2—22no—
1167C2—42no—
1168C2—942no—
1169C2—1881no—
1170C2—1881no—
1171C2—1881no—
1172C2C2×#1568959111yescharacteristic
1173C2#568×D4711yescharacteristic
1174C2#2025809911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D47
commutator, socleC22×C47C24×C4
FittingC47×#2925C2
prime radical#20256952C2
cosocleC2×C4×C47C25
hypercenter#2925D47
hypocenterC47#60216
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #2925

Complements

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

NH ≅ G/Ntype
2. #20252397C2semidirect
3. #20252390C2semidirect
4. #20252380C2semidirect
5. #20252377C2semidirect
6. #20252371C2semidirect
7. #20252368C2semidirect
8. #20252361C2semidirect
9. #20252352C2semidirect
10. #20252331C2semidirect
11. #20252325C2semidirect
12. #20252123C2semidirect
13. #20252118C2semidirect
14. #20252118C2semidirect
15. #20252094C2semidirect
16. #20252085C2semidirect
17. C2×#15689193C2semidirect
18. #20252043C2semidirect
19. #20252043C2semidirect
20. #20251816C2semidirect
21. #20251804C2semidirect
22. #405×D47C2semidirect
23. C47×#2925C2semidirect
52. #15689252C22semidirect
53. #15689252C22semidirect
54. #15689252C22semidirect
55. #15689252C22semidirect
56. #15689252C22semidirect
57. #15689252C22semidirect
58. #15689250C22semidirect
59. #15689247C22semidirect
61. #15689198C22semidirect
62. #15689198C22semidirect
63. #15689198C22semidirect
64. #15689198C22semidirect
65. #15689197C22semidirect
66. #15689197C22semidirect
67. #15689197C22semidirect
68. #15689197C22semidirect
79. #15689191C22semidirect
80. #15689191C22semidirect
81. #15689191C22semidirect
82. #15689191C22semidirect
84. (C22⋊D47)⋊C8C22semidirect
85. (C22⋊D47)⋊C8C22semidirect
86. (C22⋊D47)⋊C8C22semidirect
87. (C22⋊D47)⋊C8C22semidirect
88. #15689185C22semidirect
89. #15689185C22semidirect
90. #15689182C22semidirect
91. #15689182C22semidirect
92. #15689178C22semidirect
93. #15689178C22semidirect
94. #15689174C22semidirect
95. #15689174C22semidirect
106. #15689080C22semidirect
107. #15689080C22semidirect
110. #15689079C22semidirect
111. #15689079C22semidirect
114. #15689077C22semidirect
115. #15689077C22semidirect
117. C4×#10625329C22semidirect
118. #15689075C22semidirect
119. C4×#10625324C22semidirect
121. C2×#13093935C22semidirect
122. #97×D47C22semidirect
123. C4×C8×D47C22semidirect
125. C47×#433C22semidirect
126. C47×#433C22semidirect
127. C47×#432C22semidirect
128. C47×#431C22semidirect
436. #10625329#41semidirect
440. C2×C47⋊C8#41semidirect
596. #2925D47semidirect
680. #433C2×D47semidirect
681. #433C2×D47semidirect
684. #432C2×D47semidirect
687. #431C2×D47semidirect
722. C47#60216semidirect

Maximal subgroups

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

subgroupindex
#202569522
#202523972
#202523902
#202523802
#202523772
#202523712
#202523682
#202523612
#202523522
#202523312
#202523252
#202521232
#202521182
#202520942
#202520852
C2×#156891932
#202520432
#202518162
#202518042
#405×D472
C47×#29252
#6021647