Finite Group Databasebeta

← #26232459

Subgroups — #26232459

Order 12032.

1132 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689819C211yesmaximal, characteristic
2D4×#10625329C211yesmaximal, characteristic, complemented
3#20244381C211yesmaximal, characteristic, complemented
4#20244380C211yesmaximal, characteristic, complemented
5#20243851C211yesmaximal, characteristic, complemented
6#20243851C211yesmaximal, characteristic, complemented
7#20243849C211yesmaximal, characteristic, complemented
8#20243849C211yesmaximal, characteristic, complemented
9#20243469C211yesmaximal, characteristic, complemented
10#20243466C211yesmaximal, characteristic, complemented
11#20243377C211yesmaximal, characteristic, complemented
12C4×#13093940C211yesmaximal, characteristic, complemented
13#20243126C211yesmaximal, characteristic, complemented
14C2×#15688891C211yesmaximal, characteristic, complemented
15D4×M16×C47C211yesmaximal, characteristic, complemented
16C22×#10625329C2211yescharacteristic
17C22×#10625329C2211yescharacteristic
18#15689819—21no—
19#15689819—21no—
20#15689819—21no—
21#15689819—21no—
22#15689819—21no—
23#15689819—21no—
24#15689819—21no—
25#15689819—21no—
26C2×#13094019C412yes—
27C2×#13094016C2211yescharacteristic
28C2×#13094006C412yes—
29C2×#13093998C2211yescharacteristic
30C2×#13093998C2211yescharacteristic
31C2×#13093996C412yes—
32C2×C4×D188C2211yescharacteristic
33C2×(C22⋊D47)⋊C4C412yes—
34C2×#13093983C2211yescharacteristic
35C22×C4⋊Dic47C2211yescharacteristic
36#15689201—21no—
37#15689195—21no—
38#15689195—21no—
39D4×C47⋊C8—21no—
40#15689147C2211yescharacteristic
41C2×#13093940C2211yescharacteristic
42C2×#13093940C2211yescharacteristic
43C2×#13093940C2211yescharacteristic
44C2×#13093940C2211yescharacteristic
45#15689087C2211yescharacteristic
46#15689087C2211yescharacteristic
47C4×#10625329C2211yescharacteristic
48#15688891C2211yescharacteristic
49#15688891C2211yescharacteristic
50#15688891C2211yescharacteristic
51#15688891C2211yescharacteristic
52#15688891C2211yescharacteristic
53#15688891C2211yescharacteristic
54#15688891C2211yescharacteristic
55#15688891C2211yescharacteristic
56#15688891C2211yescharacteristic
57#15688891C2211yescharacteristic
58#15688891C2211yescharacteristic
59#15688891C2211yescharacteristic
60C22×M16×C47C2211yescharacteristic
61C22×M16×C47C2211yescharacteristic
62C2×C4×D4×C47C2211yescharacteristic
63C47×#436—21no—
64C47×#435—21no—
65C47×#435—21no—
66C8×D4×C47—21no—
67C47×#423C2211yescharacteristic
68C47×#407C2211yescharacteristic
69C47×#407C2211yescharacteristic
70C4×M16×C47C2211yescharacteristic
71C22×D188C2311yescharacteristic
72C22×C22⋊D47C2×C412yes—
73C22×C22⋊D47C2×C412yes—
74C23×Dic47C2×C412yes—
75C22×C4×D47C2×C412yes—
76C2×#10625329—21no—
77C2×#10625329—21no—
78C2×#10625329—22no—
79C2×#10625329—22no—
80C2×#10625329—41no—
81C2×#10625329—41no—
82C2×#10625329C2311yescharacteristic
83C2×#10625329C2311yescharacteristic
84C2×#10625329C2311yescharacteristic
85C2×#10625329C2311yescharacteristic
86C22×C47⋊C8—21no—
87C22×C47⋊C8—21no—
88#13094019—22no—
89#13094019—22no—
90#13094019—22no—
91#13094019—22no—
92#13094016—21no—
93#13094016—21no—
94#13094016—21no—
95#13094016—21no—
96#13094006—22no—
97#13094006—22no—
98#13094006—22no—
99#13094006—22no—
100#13093998—21no—
101#13093998—21no—
102#13093998—21no—
103#13093998—21no—
104#13093998—21no—
105#13093998—21no—
106#13093998—21no—
107#13093998—21no—
108#13093996—22no—
109#13093996—22no—
110#13093996—22no—
111#13093996—22no—
112C4×D188—21no—
113C4×D188—21no—
114C4×D188—21no—
115C4×D188—21no—
116(C22⋊D47)⋊C4—22no—
117(C22⋊D47)⋊C4—22no—
118(C22⋊D47)⋊C4—22no—
119(C22⋊D47)⋊C4—22no—
120#13093983—21no—
121#13093983—21no—
122#13093983—21no—
123#13093983—21no—
124C2×C4⋊Dic47—21no—
125C2×C4⋊Dic47—21no—
126C2×C4⋊Dic47—21no—
127C2×C4⋊Dic47—21no—
128C2×C4⋊Dic47C2×C412yes—
129C2×C4⋊Dic47C2311yescharacteristic
130C2×C4⋊Dic47C2311yescharacteristic
131C2×C4⋊Dic47C2311yescharacteristic
132C2×Dic47⋊C4C2×C412yes—
133C2×Dic47⋊C4C2×C412yes—
134C2×C22⋊Dic47C2×C412yes—
135C2×(C2×D47)⋊C4C2×C412yes—
136C2×(C2×D47)⋊C4C2×C412yes—
137C2×(C2×D47)⋊C4C2×C412yes—
138C2×C4×Dic47C2×C412yes—
139C4⋊(C47⋊C8)—21no—
140C4⋊(C47⋊C8)—21no—
141#13093940—22no—
142#13093940—22no—
143#13093940—41no—
144#13093940—41no—
145C22⋊(C47⋊C8)—21no—
146C22⋊(C47⋊C8)—21no—
147C22⋊(C47⋊C8)—21no—
148C22⋊(C47⋊C8)—21no—
149#13093935—21no—
150C4×C47⋊C8—21no—
151C22×D4×C47C2×C411yescharacteristic
152C23×C4×C47C2311yescharacteristic
153C23×C4×C47C2311yescharacteristic
154C2×M16×C47—21no—
155C2×M16×C47—21no—
156C2×M16×C47—22no—
157C2×M16×C47—22no—
158C2×M16×C47—41no—
159C2×M16×C47—41no—
160C2×M16×C47C2311yescharacteristic
161C2×M16×C47C2311yescharacteristic
162C2×M16×C47C2311yescharacteristic
163C2×M16×C47C2311yescharacteristic
164C22×C8×C47—21no—
165C22×C8×C47—21no—
166C4×D4×C47D411yescharacteristic
167C4×D4×C47D411yescharacteristic
168C4×D4×C47D411yescharacteristic
169C4×D4×C47D411yescharacteristic
170C4×D4×C47D411yescharacteristic
171C4×D4×C47D411yescharacteristic
172C4×D4×C47D411yescharacteristic
173C4×D4×C47D411yescharacteristic
174C2×C4⋊C4×C47C2×C411yescharacteristic
175C2×C22⋊C4×C47C2×C411yescharacteristic
176C2×C22⋊C4×C47C2×C411yescharacteristic
177C2×C42×C47C2311yescharacteristic
178C4⋊C8×C47—21no—
179C4⋊C8×C47—21no—
180C22⋊C8×C47—21no—
181C22⋊C8×C47—21no—
182C22⋊C8×C47—21no—
183C22⋊C8×C47—21no—
184#97×C47—21no—
185C4×C8×C47—21no—
186C24×C47C22×C411yescharacteristic
187C24×C47C22×C411yescharacteristic
188C23×D47C22×C412yes—
189C2×D4×C47—42no—
190C2×D4×C47C22⋊C411yescharacteristic
191C2×D4×C47C22⋊C411yescharacteristic
192C2×D4×C47C22⋊C411yescharacteristic
193C2×D4×C47C22⋊C411yescharacteristic
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47C22×C411yescharacteristic
203C22×C4×C47C22×C411yescharacteristic
204C22×C4×C47C22×C411yescharacteristic
205C22×C4×C47C22×C411yescharacteristic
206C22×C4×C47C2×D411yescharacteristic
207C22×C4×C47C2×D411yescharacteristic
208C22×C4×C47C2×D411yescharacteristic
209C22×C4×C47C2×D411yescharacteristic
210C22×C4×C47C2×D411yescharacteristic
211C22×C4×C47C2×D411yescharacteristic
212C22×C4×C47C2×D411yescharacteristic
213C22×C4×C47C2×D411yescharacteristic
214C22×C4×C47C2411yescharacteristic
215C2×C22⋊D47—22no—
216C2×C22⋊D47—22no—
217C2×C22⋊D47—22no—
218C2×C22⋊D47—22no—
219C2×C22⋊D47—44no—
220C2×C22⋊D47—82no—
221C22×Dic47—22no—
222C22×Dic47—22no—
223C22×Dic47—82no—
224C22×Dic47C22×C412yes—
225C22×Dic47C22×C412yes—
226C22×Dic47C22×C412yes—
227C2×D188—21no—
228C2×D188—21no—
229C2×D188—21no—
230C2×D188—21no—
231C2×D188—21no—
232C2×D188—21no—
233C2×C4×D47—22no—
234C2×C4×D47—22no—
235C2×C4×D47—82no—
236M16×C47—21no—
237M16×C47—21no—
238M16×C47—21no—
239M16×C47—21no—
240M16×C47—21no—
241M16×C47—21no—
242M16×C47—21no—
243M16×C47—42no—
244M16×C47—42no—
245M16×C47#4112yes—
246C2×C8×C47—21no—
247C2×C8×C47—21no—
248C2×C8×C47—21no—
249C2×C8×C47—21no—
250C2×C8×C47—42no—
251C2×C8×C47—42no—
252C4⋊C4×C47C22⋊C411yescharacteristic
253C4⋊C4×C47C22⋊C411yescharacteristic
254C4⋊C4×C47C22⋊C411yescharacteristic
255C4⋊C4×C47C22⋊C411yescharacteristic
256C22⋊C4×C47C22⋊C411yescharacteristic
257C22⋊C4×C47C22⋊C411yescharacteristic
258C22⋊C4×C47C22⋊C411yescharacteristic
259C22⋊C4×C47C22⋊C411yescharacteristic
260C22⋊C4×C47C22⋊C411yescharacteristic
261C22⋊C4×C47C22⋊C411yescharacteristic
262C22⋊C4×C47C22⋊C411yescharacteristic
263C22⋊C4×C47C22⋊C411yescharacteristic
264C42×C47C2×D411yescharacteristic
265C42×C47C2×D411yescharacteristic
266C42×C47C2×D411yescharacteristic
267C42×C47C2×D411yescharacteristic
268C22⋊Dic47—22no—
269C22⋊Dic47—22no—
270(C2×D47)⋊C4—22no—
271(C2×D47)⋊C4—22no—
272(C2×D47)⋊C4—22no—
273(C2×D47)⋊C4—22no—
274(C2×D47)⋊C4—22no—
275(C2×D47)⋊C4—22no—
276C4⋊Dic47—22no—
277C4⋊Dic47—22no—
278C4⋊Dic47—21no—
279C4⋊Dic47—21no—
280C4⋊Dic47—21no—
281C4⋊Dic47—21no—
282C4⋊Dic47—21no—
283C4⋊Dic47—21no—
284Dic47⋊C4—22no—
285Dic47⋊C4—22no—
286Dic47⋊C4—22no—
287Dic47⋊C4—22no—
288C4×Dic47—22no—
289C4×Dic47—22no—
290#10625329—21no—
291#10625329—21no—
292#10625329—21no—
293#10625329—21no—
294#10625329—21no—
295#10625329—21no—
296#10625329—21no—
297#10625329—42no—
298#10625329—42no—
299#10625329#4112yes—
300C2×C47⋊C8—21no—
301C2×C47⋊C8—21no—
302C2×C47⋊C8—21no—
303C2×C47⋊C8—21no—
304C2×C47⋊C8—42no—
305C2×C47⋊C8—42no—
306C23×C47—21no—
307C23×C47—21no—
308C23×C47—22no—
309C23×C47—21no—
310C23×C47—21no—
311C23×C47—41no—
312C23×C47—41no—
313C23×C47—41no—
314C23×C47C2×C22⋊C411yescharacteristic
315C23×C47C2×C22⋊C411yescharacteristic
316C23×C47C2×C22⋊C411yescharacteristic
317C23×C47C2×C22⋊C411yescharacteristic
318C23×C47C23×C411yescharacteristic
319C22×D47—22no—
320C22×D47—22no—
321C22×D47—22no—
322C22×D47—42no—
323C22×D47—42no—
324D4×C47—22no—
325D4×C47—22no—
326D4×C47—41no—
327D4×C47—41no—
328C2×C4×C47—21no—
329C2×C4×C47—21no—
330C2×C4×C47—21no—
331C2×C4×C47—21no—
332C2×C4×C47—21no—
333C2×C4×C47—21no—
334C2×C4×C47—21no—
335C2×C4×C47—21no—
336C2×C4×C47—21no—
337C2×C4×C47—21no—
338C2×C4×C47—21no—
339C2×C4×C47—21no—
340C2×C4×C47—21no—
341C2×C4×C47—21no—
342C2×C4×C47—21no—
343C2×C4×C47—21no—
344C2×C4×C47—21no—
345C2×C4×C47—21no—
346C2×C4×C47—21no—
347C2×C4×C47—21no—
348C2×C4×C47—41no—
349C2×C4×C47—41no—
350C2×C4×C47C2×C22⋊C411yescharacteristic
351C2×C4×C47C2×C22⋊C411yescharacteristic
352C2×C4×C47C2×C22⋊C411yescharacteristic
353C2×C4×C47C2×C22⋊C411yescharacteristic
354C2×C4×C47C2×C22⋊C411yescharacteristic
355C2×C4×C47C2×C22⋊C411yescharacteristic
356C2×C4×C47C2×C22⋊C411yescharacteristic
357C2×C4×C47C2×C22⋊C411yescharacteristic
358C2×C4×C47C22×D411yescharacteristic
359C2×C4×C47C22×D411yescharacteristic
360C2×C4×C47C2×#4111yescharacteristic
361C2×C4×C47C2×#4111yescharacteristic
362C2×C4×C47H(5,𝔽2)11yescharacteristic
363C2×C4×C472−1+411yescharacteristic
364C22⋊D47—44no—
365C22⋊D47—44no—
366C22⋊D47—82no—
367C22⋊D47—82no—
368C2×Dic47—22no—
369C2×Dic47—22no—
370C2×Dic47—22no—
371C2×Dic47—42no—
372C2×Dic47—42no—
373C2×Dic47—42no—
374C2×Dic47—82no—
375C2×Dic47—82no—
376D188—41no—
377D188—41no—
378D188—41no—
379D188—41no—
380C4×D47—82no—
381C4×D47—82no—
382C8×C47—22no—
383C8×C47—41no—
384C8×C47—41no—
385C8×C47—41no—
386C47⋊C8—22no—
387C47⋊C8—41no—
388C47⋊C8—41no—
389C47⋊C8—41no—
390#22482—471nomaximal, Sylow
391C22×C47—21no—
392C22×C47—21no—
393C22×C47—21no—
394C22×C47—21no—
395C22×C47—21no—
396C22×C47—21no—
397C22×C47—21no—
398C22×C47—21no—
399C22×C47—21no—
400C22×C47—21no—
401C22×C47—21no—
402C22×C47—21no—
403C22×C47—21no—
404C22×C47—42no—
405C22×C47—42no—
406C22×C47—81no—
407C22×C47—81no—
408C22×C47#41312yes—
409C22×C47C22×C22⋊C411yescharacteristic
410C22×C47C4×#4111yescharacteristic
411C22×C47#52011yescharacteristic
412C2×D47—42no—
413C2×D47—42no—
414C2×D47—42no—
415C2×D47—82no—
416C2×D47—82no—
417C4×C47—21no—
418C4×C47—21no—
419C4×C47—21no—
420C4×C47—21no—
421C4×C47—21no—
422C4×C47—21no—
423C4×C47—21no—
424C4×C47—21no—
425C4×C47#54611yescharacteristic
426C4×C47#54611yescharacteristic
427C4×C47#54711yescharacteristic
428C4×C47#54711yescharacteristic
429Dic47—42no—
430Dic47—42no—
431Dic47—42no—
432C2×#553—471no—
433D4×M16—471no—
434D4×M16D4711yescharacteristic, complemented
435#1998—471no—
436#1998—471no—
437#1900—471no—
438#1900—471no—
439#1900—471no—
440#1900—471no—
441#1822—471no—
442#1821—471no—
443#1800—471no—
444C4×#100—471no—
445#1742—471no—
446C2×#343—471no—
447C2×C47—21no—
448C2×C47—21no—
449C2×C47—22no—
450C2×C47—41no—
451C2×C47—41no—
452C2×C47—41no—
453C2×C47#233911yescharacteristic
454C2×C47C2×#41311yescharacteristic
455C2×C47#288811yescharacteristic
456D47—82no—
457C22×M16—471no—
458C22×M16—471no—
459C22×M16C2×D4711yescharacteristic
460C22×M16C2×D4711yescharacteristic
461#553—941no—
462#553—941no—
463#553—941no—
464#553—941no—
465#553—941no—
466#553—941no—
467#553—941no—
468#553—941no—
469C2×#126—472no—
470C2×#125—471no—
471C2×#123—472no—
472C2×#121—472no—
473C2×#121—471no—
474C2×#121—471no—
475C2×C4×D4—472no—
476C2×C4×D4—471no—
477C2×C4×D4C2×D4711yescharacteristic
478C2×#117—471no—
479C22×C4⋊C4—471no—
480#436—21no—
481#436—941no—
482#435—21no—
483#435—21no—
484#435—941no—
485#435—941no—
486C8×D4—21no—
487C8×D4—941no—
488#423—471no—
489#423C2×D4711yescharacteristic
490C2×#100—471no—
491C2×#100—471no—
492C2×#100—471no—
493C2×#100—471no—
494#407—471no—
495#407—471no—
496#407C2×D4711yescharacteristic
497#407C2×D4711yescharacteristic
498C4×M16—471no—
499C4×M16C2×D4711yescharacteristic
500#343—471no—
501#343—471no—
502#343—471no—
503#343—471no—
504#343—471no—
505#343—471no—
506#343—471no—
507#343—471no—
508#343—471no—
509#343—471no—
510#343—471no—
511#343—471no—
512C47#2248211yescharacteristic, complemented, Sylow
513C22×D4—472no—
514C22×D4—472no—
515C22×D4—471no—
516C22×D4C4×D4711yescharacteristic
517C23×C4—472no—
518C23×C4—472no—
519C23×C4C22×D4711yescharacteristic
520C23×C4C22×D4711yescharacteristic
521C2×M16—21no—
522C2×M16—21no—
523C2×M16—22no—
524C2×M16—22no—
525C2×M16—41no—
526C2×M16—41no—
527C2×M16—471no—
528C2×M16—471no—
529C2×M16—471no—
530C2×M16—471no—
531C2×M16—941no—
532C2×M16—941no—
533C2×M16—942no—
534C2×M16—942no—
535C2×M16—1881no—
536C2×M16—1881no—
537C2×M16C22×D4711yescharacteristic
538C2×M16C22×D4711yescharacteristic
539C2×M16C22×D4711yescharacteristic
540C2×M16C22×D4711yescharacteristic
541C22×C8—21no—
542C22×C8—21no—
543C22×C8—941no—
544C22×C8—941no—
545#126—942no—
546#126—942no—
547#126—942no—
548#126—942no—
549#125—941no—
550#125—941no—
551#125—941no—
552#125—941no—
553#123—942no—
554#123—942no—
555#123—942no—
556#123—942no—
557#121—942no—
558#121—942no—
559#121—942no—
560#121—942no—
561#121—941no—
562#121—941no—
563#121—941no—
564#121—941no—
565#121—941no—
566#121—941no—
567#121—941no—
568#121—941no—
569C4×D4—942no—
570C4×D4—942no—
571C4×D4—942no—
572C4×D4—942no—
573C4×D4—941no—
574C4×D4—941no—
575C4×D4—941no—
576C4×D4—941no—
577C4×D4D18811yescharacteristic
578C4×D4D18811yescharacteristic
579C4×D4D18811yescharacteristic
580C4×D4D18811yescharacteristic
581C4×D4C22⋊D4711yescharacteristic
582C4×D4C22⋊D4711yescharacteristic
583C4×D4C22⋊D4711yescharacteristic
584C4×D4C22⋊D4711yescharacteristic
585#117—941no—
586#117—941no—
587#117—941no—
588#117—941no—
589C2×C4⋊C4—472no—
590C2×C4⋊C4—472no—
591C2×C4⋊C4—472no—
592C2×C4⋊C4—471no—
593C2×C4⋊C4—471no—
594C2×C4⋊C4—471no—
595C2×C4⋊C4—941no—
596C2×C4⋊C4—941no—
597C2×C4⋊C4—941no—
598C2×C4⋊C4—941no—
599C2×C4⋊C4C4×D4711yescharacteristic
600C2×C22⋊C4—472no—
601C2×C22⋊C4—472no—
602C2×C22⋊C4—472no—
603C2×C22⋊C4—472no—
604C2×C22⋊C4C4×D4711yescharacteristic
605C2×C22⋊C4C4×D4711yescharacteristic
606C2×C42—472no—
607C2×C42C22×D4711yescharacteristic
608C4⋊C8—21no—
609C4⋊C8—21no—
610C4⋊C8—941no—
611C4⋊C8—941no—
612#100—942no—
613#100—942no—
614#100—1881no—
615#100—1881no—
616C22⋊C8—21no—
617C22⋊C8—21no—
618C22⋊C8—21no—
619C22⋊C8—21no—
620C22⋊C8—941no—
621C22⋊C8—941no—
622C22⋊C8—941no—
623C22⋊C8—941no—
624#97—21no—
625#97—941no—
626C4×C8—21no—
627C4×C8—941no—
628C24—472no—
629C24C2×C4×D4711yescharacteristic
630C24C2×C4×D4711yescharacteristic
631C2×D4—42no—
632C2×D4—942no—
633C2×D4—942no—
634C2×D4—942no—
635C2×D4—942no—
636C2×D4—941no—
637C2×D4—941no—
638C2×D4—941no—
639C2×D4—941no—
640C2×D4—941no—
641C2×D4—941no—
642C2×D4—3762no—
643C2×D4—1884no—
644C2×D4(C2×D47)⋊C411yescharacteristic
645C2×D4(C2×D47)⋊C411yescharacteristic
646C2×D4(C2×D47)⋊C411yescharacteristic
647C2×D4(C2×D47)⋊C411yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—472no—
657C22×C4—472no—
658C22×C4—472no—
659C22×C4—942no—
660C22×C4—942no—
661C22×C4—942no—
662C22×C4—942no—
663C22×C4—3762no—
664C22×C4—3762no—
665C22×C4C2×C4×D4711yescharacteristic
666C22×C4C2×C4×D4711yescharacteristic
667C22×C4C2×C4×D4711yescharacteristic
668C22×C4C2×C4×D4711yescharacteristic
669C22×C4C2×D18811yescharacteristic
670C22×C4C2×D18811yescharacteristic
671C22×C4C2×D18811yescharacteristic
672C22×C4C2×D18811yescharacteristic
673C22×C4C2×C22⋊D4711yescharacteristic
674C22×C4C2×C22⋊D4711yescharacteristic
675C22×C4C2×C22⋊D4711yescharacteristic
676C22×C4C2×C22⋊D4711yescharacteristic
677C22×C4C23×D4711yescharacteristic
678M16—21no—
679M16—21no—
680M16—21no—
681M16—21no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—42no—
686M16—42no—
687M16—472no—
688M16—941no—
689M16—941no—
690M16—941no—
691M16—941no—
692M16—941no—
693M16—941no—
694M16—941no—
695M16—1882no—
696M16—1882no—
697M16#1062535212yes—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—42no—
703C2×C8—42no—
704C2×C8—941no—
705C2×C8—941no—
706C2×C8—941no—
707C2×C8—941no—
708C2×C8—1882no—
709C2×C8—1882no—
710C4⋊C4—942no—
711C4⋊C4—942no—
712C4⋊C4—942no—
713C4⋊C4—942no—
714C4⋊C4—942no—
715C4⋊C4—942no—
716C4⋊C4—941no—
717C4⋊C4—941no—
718C4⋊C4—941no—
719C4⋊C4—941no—
720C4⋊C4—941no—
721C4⋊C4—941no—
722C4⋊C4(C2×D47)⋊C411yescharacteristic
723C4⋊C4(C2×D47)⋊C411yescharacteristic
724C4⋊C4(C2×D47)⋊C411yescharacteristic
725C4⋊C4(C2×D47)⋊C411yescharacteristic
726C22⋊C4—942no—
727C22⋊C4—942no—
728C22⋊C4—942no—
729C22⋊C4—942no—
730C22⋊C4—942no—
731C22⋊C4—942no—
732C22⋊C4—942no—
733C22⋊C4—942no—
734C22⋊C4(C2×D47)⋊C411yescharacteristic
735C22⋊C4(C2×D47)⋊C411yescharacteristic
736C22⋊C4(C2×D47)⋊C411yescharacteristic
737C22⋊C4(C2×D47)⋊C411yescharacteristic
738C22⋊C4(C2×D47)⋊C411yescharacteristic
739C22⋊C4(C2×D47)⋊C411yescharacteristic
740C22⋊C4(C2×D47)⋊C411yescharacteristic
741C22⋊C4(C2×D47)⋊C411yescharacteristic
742C42—942no—
743C42—942no—
744C42C2×D18811yescharacteristic
745C42C2×D18811yescharacteristic
746C42C2×C22⋊D4711yescharacteristic
747C42C2×C22⋊D4711yescharacteristic
748C23—21no—
749C23—21no—
750C23—22no—
751C23—21no—
752C23—21no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—942no—
757C23—942no—
758C23—942no—
759C23—1882no—
760C23—1882no—
761C23C2×(C2×D47)⋊C411yescharacteristic
762C23C2×(C2×D47)⋊C411yescharacteristic
763C23C2×(C2×D47)⋊C411yescharacteristic
764C23C2×(C2×D47)⋊C411yescharacteristic
765C23C22×C4×D4711yescharacteristic
766D4—22no—
767D4—22no—
768D4—41no—
769D4—41no—
770D4—3762no—
771D4—3762no—
772D4—1884no—
773D4—1884no—
774D4—1881no—
775D4—1881no—
776D4—1881no—
777D4—1881no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—942no—
801C2×C4—942no—
802C2×C4—942no—
803C2×C4—3762no—
804C2×C4—3762no—
805C2×C4—3762no—
806C2×C4—3762no—
807C2×C4—1882no—
808C2×C4—1882no—
809C2×C4—1882no—
810C2×C4C2×(C2×D47)⋊C411yescharacteristic
811C2×C4C2×(C2×D47)⋊C411yescharacteristic
812C2×C4C2×(C2×D47)⋊C411yescharacteristic
813C2×C4C2×(C2×D47)⋊C411yescharacteristic
814C2×C4C2×(C2×D47)⋊C411yescharacteristic
815C2×C4C2×(C2×D47)⋊C411yescharacteristic
816C2×C4C2×(C2×D47)⋊C411yescharacteristic
817C2×C4C2×(C2×D47)⋊C411yescharacteristic
818C2×C4C22×C22⋊D4711yescharacteristic
819C2×C4C22×D18811yescharacteristic
820C2×C4#41×D4711yescharacteristic
821C2×C4C2×#1062535211yescharacteristic
822C2×C4#1309406911yescharacteristic
823C2×C4#1309407111yescharacteristic
824C8—22no—
825C8—41no—
826C8—41no—
827C8—41no—
828C8—942no—
829C8—1881no—
830C8—1881no—
831C8—1881no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—21no—
845C22—42no—
846C22—42no—
847C22—81no—
848C22—81no—
849C22—3762no—
850C22—3762no—
851C22—1882no—
852C22—1882no—
853C22—1882no—
854C22#1568910512yes—
855C22C22×(C2×D47)⋊C411yescharacteristic
856C22C4×#1062535211yescharacteristic
857C22#1568960211yescharacteristic
858C4—21no—
859C4—21no—
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—21no—
865C4—21no—
866C4—1882no—
867C4—1882no—
868C4—1882no—
869C4#1568976711yescharacteristic
870C4#1568976811yescharacteristic
871C4#1568977211yescharacteristic
872C4#1568977711yescharacteristic
873C2—21no—
874C2—21no—
875C2—22no—
876C2—41no—
877C2—41no—
878C2—41no—
879C2—3762no—
880C2#2024621311yescharacteristic
881C2C2×#1568910511yescharacteristic
882C2#2025186611yescharacteristic
subgroupG/H
centerC22C22×(C2×D47)⋊C4
commutatorC23×C47C23×C4
FrattiniC22×C4C23×D47
FittingD4×M16×C47C2
socleC22×C47C22×C22⋊C4
prime radicalC2×#15689819C2
cosocleC22×C4×C47C24
hypercenterD4×M16D47
hypocenterC47#22482
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ D4×M16

Complements

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

NH ≅ G/Ntype
2. D4×#10625329C2semidirect
3. #20244381C2semidirect
4. #20244380C2semidirect
5. #20243851C2semidirect
6. #20243851C2semidirect
7. #20243849C2semidirect
8. #20243849C2semidirect
9. #20243469C2semidirect
10. #20243466C2semidirect
11. #20243377C2semidirect
12. C4×#13093940C2semidirect
13. #20243126C2semidirect
14. C2×#15688891C2semidirect
15. D4×M16×C47C2semidirect
434. D4×M16D47semidirect
512. C47#22482semidirect

Maximal subgroups

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

subgroupindex
C2×#156898192
D4×#106253292
#202443812
#202443802
#202438512
#202438492
#202434692
#202434662
#202433772
C4×#130939402
#202431262
C2×#156888912
D4×M16×C472
#2248247