Finite Group Databasebeta

← #26238508

Subgroups — #26238508

Order 12032.

992 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689199C211yesmaximal, characteristic, complemented
2C2×#15689191C211yesmaximal, characteristic, complemented
3C2×#15689151C211yesmaximal, characteristic, complemented
4#20246630C211yesmaximal, characteristic
5#20244184C211yesmaximal, characteristic, complemented
6#20244103C211yesmaximal, characteristic, complemented
7#20243998C211yesmaximal, characteristic, complemented
8#20243994C211yesmaximal, characteristic, complemented
9#20243685C211yesmaximal, characteristic, complemented
10#20243681C211yesmaximal, characteristic, complemented
11#20243571C211yesmaximal, characteristic, complemented
12#20243569C211yesmaximal, characteristic, complemented
13#20243262C211yesmaximal, characteristic, complemented
14#20243156C211yesmaximal, characteristic, complemented
15C2×C47×#436C211yesmaximal, characteristic, complemented
16C22×#10625324C2211yescharacteristic
17C23×C47⋊C8C2211yescharacteristic
18C2×C4×C22⋊D47C2211yescharacteristic
19C2×C4×C22⋊D47C2211yescharacteristic
20C2×#13093983C2211yescharacteristic
21#15689199—24no—
22#15689191—24no—
23#15689151—24no—
24C2×Dic47⋊C8C2211yescharacteristic
25C2×Dic47⋊C8C2211yescharacteristic
26C2×Dic47⋊C8C2211yescharacteristic
27C2×Dic47⋊C8C2211yescharacteristic
28C2×Dic47⋊C8C2211yescharacteristic
29C2×C22⋊(C47⋊C8)C2211yescharacteristic
30C2×C22⋊(C47⋊C8)C2211yescharacteristic
31C2×C22⋊(C47⋊C8)C2211yescharacteristic
32C2×(C2×D47)⋊C8C2211yescharacteristic
33C2×(C2×D47)⋊C8C2211yescharacteristic
34C2×(C2×D47)⋊C8C2211yescharacteristic
35C2×#13093934C2211yescharacteristic
36C2×#13093934C2211yescharacteristic
37C2×C8×Dic47C2211yescharacteristic
38#15689056C411yescharacteristic
39#15689051C411yescharacteristic
40#15689046C411yescharacteristic
41#15689045C411yescharacteristic
42#15689039C411yescharacteristic
43#15689038C411yescharacteristic
44#15689037C411yescharacteristic
45#15689031C411yescharacteristic
46C4×Dic47⋊C4C2211yescharacteristic
47C4×(C2×D47)⋊C4C2211yescharacteristic
48C4×C22⋊Dic47C2211yescharacteristic
49#15688878C2211yescharacteristic
50#15688878C2211yescharacteristic
51#15688877C2211yescharacteristic
52#15688877C2211yescharacteristic
53#15688877C2211yescharacteristic
54#15688877C2211yescharacteristic
55C22×M16×C47C2211yescharacteristic
56C22×M16×C47C2211yescharacteristic
57C2×C4×D4×C47C2211yescharacteristic
58C47×#436—24no—
59C2×C4⋊C8×C47C2211yescharacteristic
60C2×C22⋊C8×C47C2211yescharacteristic
61C2×C22⋊C8×C47C2211yescharacteristic
62C2×C4×C8×C47C2211yescharacteristic
63C22×C22⋊D47C2×C411yescharacteristic
64C22×C22⋊D47C2×C411yescharacteristic
65C22×C4×D47C2311yescharacteristic
66C2×#10625324—22no—
67C2×#10625324—22no—
68C2×#10625324—41no—
69C22×C47⋊C8—22no—
70C22×C47⋊C8—22no—
71C22×C47⋊C8—41no—
72C22×C47⋊C8C2311yescharacteristic
73C22×C47⋊C8C2311yescharacteristic
74C22×C47⋊C8C2311yescharacteristic
75C22×C47⋊C8C2311yescharacteristic
76C4×C22⋊D47—22no—
77C4×C22⋊D47—22no—
78C4×C22⋊D47—22no—
79C4×C22⋊D47—22no—
80#13093983—22no—
81#13093983—22no—
82C2×C4⋊Dic47C2×C411yescharacteristic
83C2×C4⋊Dic47C2×C411yescharacteristic
84C2×Dic47⋊C4C2×C411yescharacteristic
85C2×Dic47⋊C4C2×C411yescharacteristic
86C2×Dic47⋊C4C2×C411yescharacteristic
87C2×Dic47⋊C4C2×C411yescharacteristic
88C2×C22⋊Dic47C2×C411yescharacteristic
89C2×C22⋊Dic47C2×C411yescharacteristic
90C2×C22⋊Dic47C2×C411yescharacteristic
91C2×C22⋊Dic47C2×C411yescharacteristic
92C2×C22⋊Dic47C2×C411yescharacteristic
93C2×C22⋊Dic47C2×C411yescharacteristic
94C2×(C2×D47)⋊C4C2×C411yescharacteristic
95C2×(C2×D47)⋊C4C2×C411yescharacteristic
96C2×(C2×D47)⋊C4C2×C411yescharacteristic
97C2×(C2×D47)⋊C4C2×C411yescharacteristic
98C2×C4×Dic47C2311yescharacteristic
99C2×C4×Dic47C2311yescharacteristic
100C2×C4×Dic47C2311yescharacteristic
101Dic47⋊C8—22no—
102Dic47⋊C8—22no—
103Dic47⋊C8—22no—
104Dic47⋊C8—22no—
105Dic47⋊C8D414yescomplemented
106C22⋊(C47⋊C8)—22no—
107C22⋊(C47⋊C8)—22no—
108C22⋊(C47⋊C8)—41no—
109(C2×D47)⋊C8—22no—
110(C2×D47)⋊C8—22no—
111(C2×D47)⋊C8—41no—
112#13093934—22no—
113#13093934—22no—
114C8×Dic47—22no—
115C47⋊#95C2×C411yescharacteristic
116C47⋊#95C2×C411yescharacteristic
117C47⋊#95C2×C411yescharacteristic
118C47⋊#95C2×C411yescharacteristic
119C47⋊#95C2×C411yescharacteristic
120C47⋊#95C2×C411yescharacteristic
121C22×D4×C47C2×C411yescharacteristic
122C23×C4×C47C2311yescharacteristic
123C23×C4×C47C2311yescharacteristic
124C2×M16×C47—22no—
125C2×M16×C47—22no—
126C2×M16×C47—22no—
127C2×M16×C47—22no—
128C2×M16×C47—41no—
129C2×M16×C47—41no—
130C22×C8×C47C2311yescharacteristic
131C22×C8×C47C2311yescharacteristic
132C22×C8×C47C2311yescharacteristic
133C22×C8×C47C2311yescharacteristic
134C4×D4×C47—22no—
135C4×D4×C47—22no—
136C2×C4⋊C4×C47C2×C411yescharacteristic
137C2×C22⋊C4×C47C2×C411yescharacteristic
138C2×C22⋊C4×C47C2×C411yescharacteristic
139C2×C42×C47C2311yescharacteristic
140C4⋊C8×C47—22no—
141C22⋊C8×C47—22no—
142C22⋊C8×C47D414yescomplemented
143C4×C8×C47—22no—
144C24×C47C22×C411yescharacteristic
145C24×C47C22×C411yescharacteristic
146C23×D47C22×C411yescharacteristic
147C2×D4×C47—22no—
148C2×D4×C47—22no—
149C2×D4×C47—41no—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47—21no—
157C22×C4×C47—21no—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47C22×C411yescharacteristic
161C22×C4×C47C22×C411yescharacteristic
162C22×C4×C47C22×C411yescharacteristic
163C22×C4×C47C22×C411yescharacteristic
164C22×C4×C47C2×D412yes—
165C22×C4×C47#4112yes—
166C22×C4×C47C2411yescharacteristic
167C2×C22⋊D47—22no—
168C2×C22⋊D47—22no—
169C2×C22⋊D47—41no—
170C2×C22⋊D47—41no—
171C2×C22⋊D47—41no—
172C2×C22⋊D47—41no—
173C22×Dic47C22×C411yescharacteristic
174C22×Dic47C22×C411yescharacteristic
175C22×Dic47C22×C411yescharacteristic
176C22×Dic47C22×C411yescharacteristic
177C22×Dic47C22×C411yescharacteristic
178C22×Dic47C22×C411yescharacteristic
179C22×Dic47C22×C411yescharacteristic
180C2×C4×D47—21no—
181C2×C4×D47—21no—
182C2×C4×D47—21no—
183C2×C4×D47—21no—
184C2×C4×D47—21no—
185C2×C4×D47—21no—
186M16×C47—44no—
187M16×C47—44no—
188C2×C8×C47—21no—
189C2×C8×C47—21no—
190C2×C8×C47—21no—
191C2×C8×C47—21no—
192C2×C8×C47—21no—
193C2×C8×C47—21no—
194C2×C8×C47—21no—
195C2×C8×C47—21no—
196C2×C8×C47—21no—
197C2×C8×C47C2×D412yes—
198C2×C8×C47C2×D412yes—
199C2×C8×C47C2×D412yes—
200C4⋊C4×C47—22no—
201C22⋊C4×C47—22no—
202C22⋊C4×C47—22no—
203C42×C47—21no—
204C42×C47—21no—
205C22⋊Dic47—22no—
206C22⋊Dic47—22no—
207C22⋊Dic47—22no—
208C22⋊Dic47—22no—
209C22⋊Dic47—41no—
210C22⋊Dic47—41no—
211(C2×D47)⋊C4—22no—
212(C2×D47)⋊C4—22no—
213(C2×D47)⋊C4—22no—
214(C2×D47)⋊C4—41no—
215C4⋊Dic47—22no—
216C4⋊Dic47—22no—
217Dic47⋊C4—22no—
218Dic47⋊C4—22no—
219Dic47⋊C4—22no—
220Dic47⋊C4—41no—
221C4×Dic47—21no—
222C4×Dic47—21no—
223C4×Dic47—21no—
224C4×Dic47—21no—
225C4×Dic47C2×D412yes—
226C4×Dic47#4112yes—
227C2×C47⋊C8—21no—
228C2×C47⋊C8—21no—
229C2×C47⋊C8—21no—
230C2×C47⋊C8—21no—
231C2×C47⋊C8—21no—
232C2×C47⋊C8—21no—
233C2×C47⋊C8—21no—
234C2×C47⋊C8—21no—
235C2×C47⋊C8—21no—
236C2×C47⋊C8—21no—
237C2×C47⋊C8—21no—
238C2×C47⋊C8—44no—
239C2×C47⋊C8C2×D412yes—
240#10625324—44no—
241C23×C47—21no—
242C23×C47—21no—
243C23×C47—21no—
244C23×C47—21no—
245C23×C47—21no—
246C23×C47—21no—
247C23×C47—21no—
248C23×C47—21no—
249C23×C47—21no—
250C23×C47—21no—
251C23×C47—21no—
252C23×C47—21no—
253C23×C47—21no—
254C23×C47C4×D412yes—
255C23×C47C23×C411yescharacteristic
256C22×D47—21no—
257C22×D47—21no—
258C22×D47—21no—
259C22×D47—21no—
260C22×D47—21no—
261C22×D47—21no—
262C22×D47—21no—
263D4×C47—44no—
264C2×C4×C47—21no—
265C2×C4×C47—21no—
266C2×C4×C47—21no—
267C2×C4×C47—21no—
268C2×C4×C47—22no—
269C2×C4×C47—22no—
270C2×C4×C47—22no—
271C2×C4×C47—22no—
272C2×C4×C47—21no—
273C2×C4×C47—21no—
274C2×C4×C47—21no—
275C2×C4×C47—21no—
276C2×C4×C47—21no—
277C2×C4×C47—21no—
278C2×C4×C47—41no—
279C2×C4×C47—41no—
280C2×C4×C47—41no—
281C2×C4×C47—41no—
282C2×C4×C47C4×D412yes—
283C2×C4×C47#13112yes—
284C2×C4×C47C22×D411yescharacteristic
285C2×C4×C47C22×D411yescharacteristic
286C2×C4×C47C2×#4111yescharacteristic
287C2×C4×C47C2×#4111yescharacteristic
288C2×C4×C47H(5,𝔽2)11yescharacteristic
289C2×C4×C472−1+411yescharacteristic
290C22⋊D47—44no—
291C22⋊D47—44no—
292C2×Dic47—21no—
293C2×Dic47—21no—
294C2×Dic47—21no—
295C2×Dic47—21no—
296C2×Dic47—21no—
297C2×Dic47—21no—
298C2×Dic47—21no—
299C2×Dic47—21no—
300C2×Dic47—21no—
301C2×Dic47—21no—
302C2×Dic47—21no—
303C2×Dic47—21no—
304C2×Dic47—21no—
305C2×Dic47—21no—
306C2×Dic47—21no—
307C2×Dic47—21no—
308C2×Dic47—21no—
309C2×Dic47—21no—
310C2×Dic47—21no—
311C2×Dic47C4×D412yes—
312C2×Dic47C4×D412yes—
313C4×D47—41no—
314C4×D47—41no—
315C4×D47—41no—
316C4×D47—41no—
317C8×C47—22no—
318C8×C47—22no—
319C8×C47—22no—
320C8×C47—41no—
321C47⋊C8—22no—
322C47⋊C8—41no—
323C47⋊C8—41no—
324C47⋊C8—41no—
325#22994—471nomaximal, Sylow
326C22×C47—22no—
327C22×C47—22no—
328C22×C47—22no—
329C22×C47—41no—
330C22×C47—41no—
331C22×C47—41no—
332C22×C47—41no—
333C22×C47—41no—
334C22×C47—41no—
335C22×C47—41no—
336C22×C47—41no—
337C22×C47—41no—
338C22×C47—41no—
339C22×C47—41no—
340C22×C47C2×C4×D411yescharacteristic
341C22×C47C2×C4×D411yescharacteristic
342C22×C47#52011yescharacteristic
343C22×C47C2×#13111yescharacteristic
344C22×C47#56811yescharacteristic
345C22×C47#56811yescharacteristic
346C22×C47#56811yescharacteristic
347C2×D47—41no—
348C2×D47—41no—
349C2×D47—41no—
350C2×D47—41no—
351C2×D47—41no—
352C2×D47—41no—
353C2×D47—41no—
354C4×C47—22no—
355C4×C47—22no—
356C4×C47—41no—
357C4×C47—41no—
358C4×C47D4211yescharacteristic
359C4×C47#54711yescharacteristic
360C4×C47#54811yescharacteristic
361C4×C47#55311yescharacteristic
362Dic47—22no—
363Dic47—22no—
364Dic47—41no—
365Dic47—41no—
366Dic47—41no—
367Dic47—41no—
368Dic47—41no—
369C2×#436—471no—
370C2×#436D4711yescharacteristic, complemented
371C2×#435—471no—
372C2×#424—471no—
373#2392—471no—
374#1955—471no—
375#1939—471no—
376#1924—471no—
377#1923—471no—
378#1870—471no—
379#1869—471no—
380#1851—471no—
381#1851—471no—
382#1771—471no—
383#1750—471no—
384C2×C47—42no—
385C2×C47—81no—
386C2×C47#236111yescharacteristic
387C2×C47#293011yescharacteristic
388C2×C47#293011yescharacteristic
389C2×C47#293311yescharacteristic
390C2×C47#293511yescharacteristic
391C2×C47#299311yescharacteristic
392C2×C47#299511yescharacteristic
393D47—81no—
394C22×M16—471no—
395C22×M16C2×D4711yescharacteristic
396C22×M16C2×D4711yescharacteristic
397C23×C8—471no—
398C2×C4×D4—471no—
399C2×C4×D4—471no—
400C2×C4×D4C2×D4711yescharacteristic
401C2×#117—471no—
402#436—24no—
403#436—944no—
404#435—944no—
405#424—944no—
406C2×C4⋊C8—471no—
407C2×C4⋊C8—471no—
408C2×C4⋊C8—471no—
409C2×C4⋊C8—471no—
410C2×C4⋊C8—471no—
411C2×C4⋊C8C2×D4711yescharacteristic
412C2×C22⋊C8—471no—
413C2×C22⋊C8—471no—
414C2×C22⋊C8—471no—
415C2×C22⋊C8—471no—
416C2×C22⋊C8—471no—
417C2×C22⋊C8—471no—
418C2×C22⋊C8C2×D4711yescharacteristic
419C2×C22⋊C8C2×D4711yescharacteristic
420C2×#97—471no—
421C2×#97—471no—
422C2×C4×C8—471no—
423C2×C4×C8C2×D4711yescharacteristic
424#398—471no—
425#397—471no—
426#396—471no—
427#396—471no—
428#394—471no—
429#394—471no—
430#394—471no—
431#392—471no—
432C4×C4⋊C4—471no—
433C4×C22⋊C4—471no—
434C4×C22⋊C4—471no—
435#336—471no—
436#336—471no—
437#336—471no—
438#336—471no—
439#336—471no—
440#336—471no—
441C47#2299411yescharacteristic, complemented, Sylow
442C22×D4—471no—
443C22×D4—471no—
444C22×D4C4×D4711yescharacteristic
445C23×C4—471no—
446C23×C4C22×D4711yescharacteristic
447C23×C4C22×D4711yescharacteristic
448C2×M16—22no—
449C2×M16—22no—
450C2×M16—22no—
451C2×M16—22no—
452C2×M16—41no—
453C2×M16—41no—
454C2×M16—942no—
455C2×M16—942no—
456C2×M16—1881no—
457C22×C8—471no—
458C22×C8—471no—
459C22×C8—471no—
460C22×C8—471no—
461C22×C8—942no—
462C22×C8—942no—
463C22×C8—1881no—
464C22×C8C22×D4711yescharacteristic
465C22×C8C22×D4711yescharacteristic
466C22×C8C22×D4711yescharacteristic
467C22×C8C22×D4711yescharacteristic
468C4×D4—22no—
469C4×D4—22no—
470C4×D4—942no—
471C4×D4—942no—
472C4×D4—942no—
473C4×D4—942no—
474#117—942no—
475#117—942no—
476C2×C4⋊C4—471no—
477C2×C4⋊C4—471no—
478C2×C4⋊C4—471no—
479C2×C4⋊C4—471no—
480C2×C4⋊C4—471no—
481C2×C4⋊C4—471no—
482C2×C4⋊C4C4×D4711yescharacteristic
483C2×C22⋊C4—471no—
484C2×C22⋊C4—471no—
485C2×C22⋊C4—471no—
486C2×C22⋊C4—471no—
487C2×C22⋊C4—471no—
488C2×C22⋊C4—471no—
489C2×C22⋊C4—471no—
490C2×C22⋊C4—471no—
491C2×C22⋊C4—471no—
492C2×C22⋊C4—471no—
493C2×C22⋊C4C4×D4711yescharacteristic
494C2×C22⋊C4C4×D4711yescharacteristic
495C2×C42—471no—
496C2×C42—471no—
497C2×C42—471no—
498C2×C42C22×D4711yescharacteristic
499C4⋊C8—22no—
500C4⋊C8—474no—
501C4⋊C8—942no—
502C4⋊C8—942no—
503C4⋊C8—942no—
504C4⋊C8—942no—
505C22⋊C8—22no—
506C22⋊C8—942no—
507C22⋊C8—942no—
508C22⋊C8—942no—
509C22⋊C8—942no—
510C22⋊C8—1881no—
511C22⋊C8—1881no—
512C22⋊C8C22⋊D4714yescomplemented
513#97—942no—
514#97—942no—
515C4×C8—22no—
516C4×C8—942no—
517#95—471no—
518#95—471no—
519#95—471no—
520#95—471no—
521#95—471no—
522#95—471no—
523C24—471no—
524C24C2×C4×D4711yescharacteristic
525C24C2×C4×D4711yescharacteristic
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—41no—
529C2×D4—942no—
530C2×D4—942no—
531C2×D4—1881no—
532C2×D4—1881no—
533C2×D4—1881no—
534C2×D4—1881no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—471no—
546C22×C4—471no—
547C22×C4—471no—
548C22×C4—471no—
549C22×C4—471no—
550C22×C4—471no—
551C22×C4—471no—
552C22×C4—941no—
553C22×C4—941no—
554C22×C4—941no—
555C22×C4—941no—
556C22×C4—941no—
557C22×C4—941no—
558C22×C4C2×C4×D4711yescharacteristic
559C22×C4C2×C4×D4711yescharacteristic
560C22×C4C2×C4×D4711yescharacteristic
561C22×C4C2×C4×D4711yescharacteristic
562C22×C4#1062535012yes—
563C22×C4C2×C22⋊D4712yes—
564C22×C4C23×D4711yescharacteristic
565M16—44no—
566M16—44no—
567M16—1884no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—472no—
578C2×C8—941no—
579C2×C8—941no—
580C2×C8—941no—
581C2×C8—941no—
582C2×C8—941no—
583C2×C8—941no—
584C2×C8—941no—
585C2×C8—941no—
586C2×C8—941no—
587C2×C8—941no—
588C2×C8—941no—
589C2×C8—1884no—
590C2×C8D4×D4712yes—
591C2×C8C2×C22⋊D4712yes—
592C2×C8C2×C22⋊D4712yes—
593C4⋊C4—22no—
594C4⋊C4—942no—
595C4⋊C4—942no—
596C4⋊C4—942no—
597C4⋊C4—942no—
598C4⋊C4—942no—
599C4⋊C4—1881no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—942no—
603C22⋊C4—942no—
604C22⋊C4—942no—
605C22⋊C4—942no—
606C22⋊C4—942no—
607C22⋊C4—942no—
608C22⋊C4—942no—
609C22⋊C4—1881no—
610C22⋊C4—1881no—
611C22⋊C4—1881no—
612C42—21no—
613C42—21no—
614C42—472no—
615C42—472no—
616C42—941no—
617C42—941no—
618C42—941no—
619C42—941no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—941no—
634C23—941no—
635C23—941no—
636C23—941no—
637C23—941no—
638C23—941no—
639C23—941no—
640C23C4×C22⋊D4712yes—
641C23C22×C4×D4711yescharacteristic
642D4—44no—
643D4—1884no—
644D4—1884no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—472no—
664C2×C4—472no—
665C2×C4—941no—
666C2×C4—941no—
667C2×C4—941no—
668C2×C4—941no—
669C2×C4—941no—
670C2×C4—941no—
671C2×C4—941no—
672C2×C4—941no—
673C2×C4—941no—
674C2×C4—941no—
675C2×C4—941no—
676C2×C4—941no—
677C2×C4—941no—
678C2×C4—941no—
679C2×C4—941no—
680C2×C4—941no—
681C2×C4—941no—
682C2×C4—941no—
683C2×C4—941no—
684C2×C4—1881no—
685C2×C4—1881no—
686C2×C4—1881no—
687C2×C4—1881no—
688C2×C4C4×C22⋊D4712yes—
689C2×C4#1309403212yes—
690C2×C4C2×D4×D4711yescharacteristic
691C2×C4C22×C22⋊D4711yescharacteristic
692C2×C4#41×D4711yescharacteristic
693C2×C4C2×#1062535011yescharacteristic
694C2×C4#1309406911yescharacteristic
695C2×C4#1309407111yescharacteristic
696C8—22no—
697C8—22no—
698C8—22no—
699C8—41no—
700C8—942no—
701C8—1881no—
702C8—1881no—
703C8—1881no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—1881no—
719C22—1881no—
720C22—1881no—
721C22—1881no—
722C22—1881no—
723C22—1881no—
724C22—1881no—
725C22C4×D4×D4711yescharacteristic
726C22C2×C4×C22⋊D4711yescharacteristic
727C22#1568960211yescharacteristic
728C22C2×#1309403211yescharacteristic
729C22#1568988811yescharacteristic
730C22#1568988811yescharacteristic
731C22#1568988911yescharacteristic
732C4—22no—
733C4—22no—
734C4—41no—
735C4—41no—
736C4—942no—
737C4—942no—
738C4—1881no—
739C4—1881no—
740C4—1881no—
741C4—1881no—
742C4—1881no—
743C4D4×C22⋊D4711yescharacteristic
744C4#1568977211yescharacteristic
745C4#1568978211yescharacteristic
746C4#1568982211yescharacteristic
747C2—42no—
748C2—81no—
749C2—3761no—
750C2#2024640511yescharacteristic
751C2#2025208811yescharacteristic
752C2#2025208911yescharacteristic
753C2#2025211311yescharacteristic
754C2#2025213311yescharacteristic
755C2#2025253211yescharacteristic
756C2#2025255211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC2×C47×#436C2
prime radical#15689031C4
cosocleC22×C4×C47C24
hypercenterC2×#436D47
hypocenterC47#22994
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
1. C2×#15689199C2semidirect
2. C2×#15689191C2semidirect
3. C2×#15689151C2semidirect
5. #20244184C2semidirect
6. #20244103C2semidirect
7. #20243998C2semidirect
8. #20243994C2semidirect
9. #20243685C2semidirect
10. #20243681C2semidirect
11. #20243571C2semidirect
12. #20243569C2semidirect
13. #20243262C2semidirect
14. #20243156C2semidirect
15. C2×C47×#436C2semidirect
105. Dic47⋊C8D4semidirect
142. C22⋊C8×C47D4semidirect
370. C2×#436D47semidirect
441. C47#22994semidirect
512. C22⋊C8C22⋊D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156891992
C2×#156891912
C2×#156891512
#202466302
#202441842
#202441032
#202439982
#202439942
#202436852
#202436812
#202435712
#202435692
#202432622
#202431562
C2×C47×#4362
#2299447