Finite Group Databasebeta

← #26218629

Subgroups — #26218629

Order 12032.

1226 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689148C211yesmaximal, characteristic, complemented
2C2×#15689085C211yesmaximal, characteristic
3C2×C22⋊C8×D47C211yesmaximal, characteristic
4C2×#15689080C211yesmaximal, characteristic, complemented
5#20245769C211yesmaximal, characteristic
6#20244004C211yesmaximal, characteristic, complemented
7#20244001C211yesmaximal, characteristic, complemented
8#20244000C211yesmaximal, characteristic, complemented
9#20243996C211yesmaximal, characteristic, complemented
10#20243995C211yesmaximal, characteristic, complemented
11#20243992C211yesmaximal, characteristic, complemented
12#20243991C211yesmaximal, characteristic, complemented
13#20243083C211yesmaximal, characteristic, complemented
14#20243083C211yesmaximal, characteristic, complemented
15C47×#1924C211yesmaximal, characteristic, complemented
16C23×C4×D47C2211yescharacteristic
17C22×#10625324C2211yescharacteristic
18C22×#10625324C2211yescharacteristic
19C22×C8×D47C2211yescharacteristic
20C22×C8×D47C2211yescharacteristic
21C2×#13093981C2211yescharacteristic
22C2×#13093981C2211yescharacteristic
23#15689148—24no—
24C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
25C2×Dic47⋊C8C2211yescharacteristic, complemented
26C2×Dic47⋊C8C2211yescharacteristic, complemented
27#15689085—24no—
28C2×C22⋊(C47⋊C8)C2211yescharacteristic
29C2×C22⋊(C47⋊C8)C2211yescharacteristic
30C2×(C2×D47)⋊C8C2211yescharacteristic
31C2×(C2×D47)⋊C8C2211yescharacteristic
32C2×(C2×D47)⋊C8C2211yescharacteristic
33C2×(C2×D47)⋊C8C2211yescharacteristic
34C22⋊C8×D47—24no—
35#15689080—24no—
36C2×#13093934C2211yescharacteristic, complemented
37C2×C4×C47⋊C8C2211yescharacteristic, complemented
38C2×C8×Dic47C2211yescharacteristic, complemented
39#15688985C411yescharacteristic
40#15688985C411yescharacteristic
41#15688982C411yescharacteristic
42#15688982C411yescharacteristic
43#15688981C411yescharacteristic
44#15688981C411yescharacteristic
45#15688978C411yescharacteristic
46#15688978C411yescharacteristic
47C4×(C2×D47)⋊C4C2211yescharacteristic
48C4×(C2×D47)⋊C4C2211yescharacteristic
49C4×C22⋊Dic47C2211yescharacteristic
50#15688878C2211yescharacteristic, complemented
51#15688878C2211yescharacteristic, complemented
52#15688877C2211yescharacteristic, complemented
53#15688877C2211yescharacteristic, complemented
54#15688877C2211yescharacteristic, complemented
55#15688877C2211yescharacteristic, complemented
56C2×C4⋊C8×C47C2211yescharacteristic, complemented
57C2×C22⋊C8×C47C2211yescharacteristic
58C2×C22⋊C8×C47C2211yescharacteristic
59C2×#97×C47C2211yescharacteristic, complemented
60C4×C22⋊C4×C47C2211yescharacteristic
61C47×#336C2211yescharacteristic, complemented
62C47×#336C2211yescharacteristic, complemented
63C24×D47C2×C411yescharacteristic
64C23×Dic47C2×C411yescharacteristic
65C22×C4×D47—22no—
66C22×C4×D47—22no—
67C22×C4×D47—22no—
68C22×C4×D47—22no—
69C22×C4×D47—22no—
70C22×C4×D47—22no—
71C22×C4×D47C2×C411yescharacteristic
72C22×C4×D47C2×C411yescharacteristic
73C22×C4×D47C2311yescharacteristic
74C22×C4×D47C2311yescharacteristic
75C2×#10625324—22no—
76C2×#10625324—22no—
77C2×#10625324—22no—
78C2×#10625324—22no—
79C2×#10625324—22no—
80C2×#10625324D414yes—
81C22×C47⋊C8C2311yescharacteristic
82C22×C47⋊C8C2311yescharacteristic
83C22×C47⋊C8C2311yescharacteristic
84C22×C47⋊C8C2311yescharacteristic
85C2×C8×D47—22no—
86C2×C8×D47—22no—
87C2×C8×D47—22no—
88C2×C8×D47—22no—
89C2×C8×D47—22no—
90C2×C8×D47D414yes—
91#13093981—22no—
92#13093981—22no—
93#13093981—22no—
94#13093981—22no—
95C2×Dic47⋊C4C2×C411yescharacteristic
96C2×Dic47⋊C4C2×C411yescharacteristic
97C2×Dic47⋊C4C2×C411yescharacteristic
98C2×Dic47⋊C4C2×C411yescharacteristic
99C2×C22⋊Dic47C2×C411yescharacteristic
100C2×C22⋊Dic47C2×C411yescharacteristic
101C2×(C2×D47)⋊C4C2×C411yescharacteristic
102C2×(C2×D47)⋊C4C2×C411yescharacteristic
103C2×(C2×D47)⋊C4C2×C411yescharacteristic
104C2×(C2×D47)⋊C4C2×C411yescharacteristic
105C2×(C2×D47)⋊C4C2×C411yescharacteristic
106C2×(C2×D47)⋊C4C2×C411yescharacteristic
107C2×(C2×D47)⋊C4C2×C411yescharacteristic
108C2×(C2×D47)⋊C4C2×C411yescharacteristic
109C2×C4×Dic47C2311yescharacteristic
110C2×C4×Dic47C2311yescharacteristic
111C4⋊(C47⋊C8)—22no—
112Dic47⋊C8—22no—
113Dic47⋊C8—22no—
114C22⋊(C47⋊C8)—22no—
115C22⋊(C47⋊C8)—22no—
116(C2×D47)⋊C8—22no—
117(C2×D47)⋊C8—22no—
118(C2×D47)⋊C8—22no—
119(C2×D47)⋊C8—22no—
120#13093934—22no—
121C4×C47⋊C8—22no—
122C8×Dic47—22no—
123C47⋊#95C2×C411yescharacteristic
124C47⋊#95C2×C411yescharacteristic
125C47⋊#95C2×C411yescharacteristic
126C47⋊#95C2×C411yescharacteristic
127C47⋊#95C2×C411yescharacteristic
128C47⋊#95C2×C411yescharacteristic
129C23×C4×C47C2311yescharacteristic
130C22×C8×C47C2311yescharacteristic
131C22×C8×C47C2311yescharacteristic
132C22×C8×C47C2311yescharacteristic
133C22×C8×C47C2311yescharacteristic
134C2×C22⋊C4×C47C2×C411yescharacteristic
135C2×C22⋊C4×C47C2×C411yescharacteristic
136C2×C42×C47C2311yescharacteristic
137C2×C42×C47C2311yescharacteristic
138C4⋊C8×C47—22no—
139C22⋊C8×C47—22no—
140C22⋊C8×C47—22no—
141#97×C47—22no—
142#95×C47C2×C411yescharacteristic
143#95×C47C2×C411yescharacteristic
144C24×C47C22×C411yescharacteristic
145C23×D47—22no—
146C23×D47—22no—
147C23×D47—22no—
148C23×D47—22no—
149C23×D47—22no—
150C23×D47—41no—
151C23×D47—41no—
152C23×D47C22×C411yescharacteristic
153C23×D47C22×C411yescharacteristic
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×C47C22×C411yescharacteristic
165C22×C4×C47C2411yescharacteristic
166C22×Dic47—22no—
167C22×Dic47—22no—
168C22×Dic47—22no—
169C22×Dic47C22×C411yescharacteristic
170C22×Dic47C22×C411yescharacteristic
171C22×Dic47C22×C411yescharacteristic
172C22×Dic47C22×C411yescharacteristic
173C22×Dic47C22×C411yescharacteristic
174C22×Dic47C22×C411yescharacteristic
175C2×C4×D47—22no—
176C2×C4×D47—22no—
177C2×C4×D47—22no—
178C2×C4×D47—21no—
179C2×C4×D47—21no—
180C2×C4×D47—21no—
181C2×C4×D47—21no—
182C2×C4×D47—21no—
183C2×C4×D47—21no—
184C2×C4×D47—22no—
185C2×C4×D47—22no—
186C2×C4×D47—22no—
187C2×C4×D47—44no—
188C2×C4×D47—44no—
189C2×C4×D47—44no—
190C2×C4×D47—44no—
191C2×C4×D47C2×D412yes—
192C2×C4×D47C2×D412yes—
193C2×C4×D47#4112yes—
194C2×C4×D47#4112yes—
195C2×C4×D47#4112yes—
196C2×C4×D47#4112yes—
197C2×C8×C47—21no—
198C2×C8×C47—21no—
199C2×C8×C47—21no—
200C2×C8×C47—21no—
201C2×C8×C47—21no—
202C2×C8×C47—21no—
203C2×C8×C47—21no—
204C2×C8×C47—21no—
205C2×C8×C47—21no—
206C2×C8×C47—21no—
207C2×C8×C47C2×D412yes—
208C2×C8×C47C2×D412yes—
209C22⋊C4×C47—22no—
210C22⋊C4×C47—41no—
211C42×C47—21no—
212C42×C47—21no—
213C42×C47—21no—
214C42×C47—21no—
215C22⋊Dic47—22no—
216C22⋊Dic47—41no—
217(C2×D47)⋊C4—22no—
218(C2×D47)⋊C4—22no—
219(C2×D47)⋊C4—22no—
220(C2×D47)⋊C4—22no—
221(C2×D47)⋊C4—22no—
222(C2×D47)⋊C4—22no—
223(C2×D47)⋊C4—41no—
224(C2×D47)⋊C4—41no—
225Dic47⋊C4—22no—
226Dic47⋊C4—22no—
227Dic47⋊C4—22no—
228Dic47⋊C4—22no—
229C4×Dic47—21no—
230C4×Dic47—21no—
231C4×Dic47—21no—
232C4×Dic47—21no—
233C2×C47⋊C8—21no—
234C2×C47⋊C8—21no—
235C2×C47⋊C8—21no—
236C2×C47⋊C8—21no—
237C2×C47⋊C8—21no—
238C2×C47⋊C8—21no—
239C2×C47⋊C8—21no—
240C2×C47⋊C8—21no—
241C2×C47⋊C8—21no—
242C2×C47⋊C8—21no—
243C2×C47⋊C8C2×D412yes—
244C2×C47⋊C8C2×D412yes—
245#10625324—28no—
246#10625324—44no—
247C8×D47—28no—
248C8×D47—44no—
249C23×C47—21no—
250C23×C47—21no—
251C23×C47—21no—
252C23×C47—21no—
253C23×C47—21no—
254C23×C47—21no—
255C23×C47#13112yes—
256C23×C47C23×C411yescharacteristic
257C22×D47—21no—
258C22×D47—21no—
259C22×D47—21no—
260C22×D47—21no—
261C22×D47—28no—
262C22×D47—21no—
263C22×D47—21no—
264C22×D47—21no—
265C22×D47—21no—
266C22×D47—21no—
267C22×D47—21no—
268C22×D47—44no—
269C22×D47—44no—
270C22×D47—44no—
271C22×D47—44no—
272C22×D47—44no—
273C22×D47—44no—
274C22×D47#11712yes—
275C22×D47C4×D412yes—
276C22×D47C4×D412yes—
277C22×D47#13112yes—
278C2×C4×C47—21no—
279C2×C4×C47—21no—
280C2×C4×C47—21no—
281C2×C4×C47—21no—
282C2×C4×C47—21no—
283C2×C4×C47—21no—
284C2×C4×C47—21no—
285C2×C4×C47—21no—
286C2×C4×C47—21no—
287C2×C4×C47—21no—
288C2×C4×C47—21no—
289C2×C4×C47—21no—
290C2×C4×C47—21no—
291C2×C4×C47—21no—
292C2×C4×C47—21no—
293C2×C4×C47—41no—
294C2×C4×C47—41no—
295C2×C4×C47—41no—
296C2×C4×C47—41no—
297C2×C4×C47C22×D411yescharacteristic
298C2×C4×C47C22×D411yescharacteristic
299C2×C4×C47C2×#4111yescharacteristic
300C2×C4×C47C2×#4111yescharacteristic
301C2×C4×C47C2×#4111yescharacteristic
302C2×C4×C47C2×#4111yescharacteristic
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×Dic47—21no—
312C2×Dic47—21no—
313C2×Dic47—21no—
314C2×Dic47—21no—
315C2×Dic47—21no—
316C2×Dic47—21no—
317C2×Dic47—21no—
318C2×Dic47—44no—
319C2×Dic47#11712yes—
320C2×Dic47C4×D412yes—
321C2×Dic47C4×D412yes—
322C4×D47—44no—
323C4×D47—41no—
324C4×D47—41no—
325C4×D47—41no—
326C4×D47—41no—
327C4×D47—44no—
328C4×D47#12114yes—
329C4×D47#12314yes—
330C4×D47#12414yes—
331C4×D47#12614yes—
332C8×C47—22no—
333C8×C47—22no—
334C8×C47—41no—
335C8×C47—41no—
336C47⋊C8—22no—
337C47⋊C8—22no—
338C47⋊C8—41no—
339C47⋊C8—41no—
340#21053—471nomaximal, Sylow
341C22×C47—22no—
342C22×C47—22no—
343C22×C47—22no—
344C22×C47—41no—
345C22×C47—41no—
346C22×C47—41no—
347C22×C47—41no—
348C22×C47C2×#11711yescharacteristic
349C22×C47C2×C4×D411yescharacteristic
350C22×C47C2×C4×D411yescharacteristic
351C22×C47C2×#13111yescharacteristic
352C22×C47C2×#13111yescharacteristic
353C22×C47#56811yescharacteristic
354C22×C47#56811yescharacteristic
355C2×D47—22no—
356C2×D47—22no—
357C2×D47—22no—
358C2×D47—22no—
359C2×D47—22no—
360C2×D47—22no—
361C2×D47—22no—
362C2×D47—22no—
363C2×D47—22no—
364C2×D47—416no—
365C2×D47—41no—
366C2×D47—41no—
367C2×D47—41no—
368C2×D47—41no—
369C2×D47#38814yes—
370C4×C47—41no—
371C4×C47—41no—
372C4×C47—41no—
373C4×C47—41no—
374C4×C47—41no—
375C4×C47C2×#12111yescharacteristic
376C4×C47C2×#12311yescharacteristic
377C4×C47C2×#12411yescharacteristic
378C4×C47C2×#12611yescharacteristic
379Dic47—41no—
380Dic47—41no—
381Dic47—41no—
382Dic47—41no—
383Dic47—41no—
384Dic47#38814yes—
385C2×#424—471no—
386C2×#407—471no—
387C22×C22⋊C8—471no—
388C2×#405—471no—
389#2280—471no—
390#1924—471no—
391#1924—471no—
392#1924—471no—
393#1924D4711yescharacteristic, complemented
394#1923—471no—
395#1923—471no—
396#1923—471no—
397#1923—471no—
398#1729—471no—
399#1729—471no—
400C2×C47—42no—
401C2×C47C2×#38811yescharacteristic
402C2×C47#292411yescharacteristic
403C2×C47#292411yescharacteristic
404C2×C47#292911yescharacteristic
405C2×C47#293011yescharacteristic
406C2×C47#293311yescharacteristic
407C2×C47#293311yescharacteristic
408D47—24no—
409D47—42no—
410C24×C4—471no—
411C22×M16—471no—
412C22×M16—471no—
413C23×C8—471no—
414C23×C8—471no—
415C2×#117—471no—
416C2×#117—471no—
417#424—944no—
418C2×C4⋊C8—471no—
419C2×C4⋊C8—471no—
420C2×C4⋊C8—471no—
421C2×C4⋊C8C2×D4711yescharacteristic, complemented
422#407—944no—
423C2×C22⋊C8—471no—
424C2×C22⋊C8—471no—
425C2×C22⋊C8—471no—
426C2×C22⋊C8—471no—
427C2×C22⋊C8—471no—
428C2×C22⋊C8—471no—
429C2×C22⋊C8—944no—
430C2×C22⋊C8C2×D4711yescharacteristic
431C2×C22⋊C8C2×D4711yescharacteristic
432#405—944no—
433C2×#97—471no—
434C2×#97C2×D4711yescharacteristic, complemented
435C2×C4×C8—471no—
436C2×C4×C8—471no—
437#381—471no—
438#381—471no—
439#380—471no—
440#380—471no—
441#380—471no—
442#380—471no—
443#379—471no—
444#379—471no—
445C4×C22⋊C4—471no—
446C4×C22⋊C4—471no—
447C4×C22⋊C4—471no—
448C4×C22⋊C4C2×D4711yescharacteristic
449#336—471no—
450#336—471no—
451#336—471no—
452#336—471no—
453#336—471no—
454#336—471no—
455#336C2×D4711yescharacteristic, complemented
456#336C2×D4711yescharacteristic, complemented
457C47#2105311yescharacteristic, complemented, Sylow
458C25—471no—
459C23×C4—471no—
460C23×C4—471no—
461C23×C4—471no—
462C23×C4—471no—
463C23×C4—471no—
464C23×C4—942no—
465C23×C4—942no—
466C23×C4—942no—
467C23×C4—942no—
468C23×C4—942no—
469C23×C4—942no—
470C23×C4C22×D4711yescharacteristic
471C2×M16—474no—
472C2×M16—942no—
473C2×M16—942no—
474C2×M16—942no—
475C2×M16—942no—
476C2×M16—942no—
477C22×C8—471no—
478C22×C8—471no—
479C22×C8—474no—
480C22×C8—471no—
481C22×C8—471no—
482C22×C8—942no—
483C22×C8—942no—
484C22×C8—942no—
485C22×C8—942no—
486C22×C8—942no—
487C22×C8C22×D4711yescharacteristic
488C22×C8C22×D4711yescharacteristic
489C22×C8C22×D4711yescharacteristic
490C22×C8C22×D4711yescharacteristic
491#117—942no—
492#117—942no—
493#117—942no—
494#117—942no—
495C2×C4⋊C4—471no—
496C2×C4⋊C4—471no—
497C2×C4⋊C4—471no—
498C2×C4⋊C4—471no—
499C2×C22⋊C4—471no—
500C2×C22⋊C4—471no—
501C2×C22⋊C4—471no—
502C2×C22⋊C4—471no—
503C2×C22⋊C4—471no—
504C2×C22⋊C4—471no—
505C2×C22⋊C4—471no—
506C2×C22⋊C4—471no—
507C2×C22⋊C4—471no—
508C2×C22⋊C4—471no—
509C2×C22⋊C4C4×D4711yescharacteristic
510C2×C22⋊C4C4×D4711yescharacteristic
511C2×C42—471no—
512C2×C42—471no—
513C2×C42C22×D4711yescharacteristic
514C2×C42C22×D4711yescharacteristic
515C4⋊C8—22no—
516C4⋊C8—942no—
517C4⋊C8—942no—
518C4⋊C8—942no—
519C22⋊C8—22no—
520C22⋊C8—22no—
521C22⋊C8—942no—
522C22⋊C8—942no—
523C22⋊C8—942no—
524C22⋊C8—942no—
525C22⋊C8—942no—
526C22⋊C8—942no—
527#97—22no—
528#97—942no—
529C4×C8—942no—
530C4×C8—942no—
531#95—471no—
532#95—471no—
533#95—471no—
534#95—471no—
535#95—471no—
536#95—471no—
537#95C4×D4711yescharacteristic
538#95C4×D4711yescharacteristic
539C24—471no—
540C24—471no—
541C24—942no—
542C24—942no—
543C24—942no—
544C24—942no—
545C24—942no—
546C24—1881no—
547C24—1881no—
548C24C2×C4×D4711yescharacteristic
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—471no—
556C22×C4—472no—
557C22×C4—472no—
558C22×C4—472no—
559C22×C4—472no—
560C22×C4—472no—
561C22×C4—472no—
562C22×C4—471no—
563C22×C4—471no—
564C22×C4—471no—
565C22×C4—471no—
566C22×C4—471no—
567C22×C4—942no—
568C22×C4—942no—
569C22×C4—942no—
570C22×C4—942no—
571C22×C4—942no—
572C22×C4—942no—
573C22×C4—942no—
574C22×C4—942no—
575C22×C4—942no—
576C22×C4—941no—
577C22×C4—941no—
578C22×C4—941no—
579C22×C4—941no—
580C22×C4—941no—
581C22×C4—941no—
582C22×C4—1884no—
583C22×C4—1884no—
584C22×C4—1884no—
585C22×C4—1884no—
586C22×C4C2×C4×D4711yescharacteristic
587C22×C4C2×C4×D4711yescharacteristic
588C22×C4C2×C4×D4711yescharacteristic
589C22×C4C2×C4×D4711yescharacteristic
590C22×C4C2×C4×D4711yescharacteristic
591C22×C4C23×D4711yescharacteristic
592M16—948no—
593M16—1884no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—472no—
605C2×C8—472no—
606C2×C8—948no—
607C2×C8—941no—
608C2×C8—941no—
609C2×C8—941no—
610C2×C8—941no—
611C2×C8—941no—
612C2×C8—941no—
613C2×C8—941no—
614C2×C8—941no—
615C2×C8—941no—
616C2×C8—941no—
617C2×C8—1884no—
618C2×C8D4×D4712yes—
619C2×C8D4×D4712yes—
620C4⋊C4—942no—
621C4⋊C4—942no—
622C4⋊C4—942no—
623C4⋊C4—942no—
624C22⋊C4—22no—
625C22⋊C4—41no—
626C22⋊C4—942no—
627C22⋊C4—942no—
628C22⋊C4—942no—
629C22⋊C4—942no—
630C22⋊C4—942no—
631C22⋊C4—942no—
632C22⋊C4—942no—
633C22⋊C4—1881no—
634C22⋊C4—1881no—
635C22⋊C4—1881no—
636C42—21no—
637C42—21no—
638C42—21no—
639C42—21no—
640C42—941no—
641C42—941no—
642C42—941no—
643C42—941no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—472no—
651C23—472no—
652C23—472no—
653C23—472no—
654C23—948no—
655C23—941no—
656C23—941no—
657C23—941no—
658C23—941no—
659C23—941no—
660C23—941no—
661C23—941no—
662C23—941no—
663C23—941no—
664C23—941no—
665C23—1884no—
666C23—1884no—
667C23—1884no—
668C23—1884no—
669C23—1884no—
670C23—1884no—
671C23#1309403212yes—
672C23C22×C4×D4711yescharacteristic
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—472no—
693C2×C4—472no—
694C2×C4—472no—
695C2×C4—474no—
696C2×C4—474no—
697C2×C4—474no—
698C2×C4—474no—
699C2×C4—941no—
700C2×C4—941no—
701C2×C4—941no—
702C2×C4—941no—
703C2×C4—941no—
704C2×C4—941no—
705C2×C4—941no—
706C2×C4—941no—
707C2×C4—941no—
708C2×C4—941no—
709C2×C4—941no—
710C2×C4—941no—
711C2×C4—941no—
712C2×C4—941no—
713C2×C4—941no—
714C2×C4—1884no—
715C2×C4—1884no—
716C2×C4—1884no—
717C2×C4—1881no—
718C2×C4—1881no—
719C2×C4—1881no—
720C2×C4—1881no—
721C2×C4C2×D4×D4711yescharacteristic
722C2×C4C2×D4×D4711yescharacteristic
723C2×C4#41×D4711yescharacteristic
724C2×C4#41×D4711yescharacteristic
725C2×C4#41×D4711yescharacteristic
726C2×C4#41×D4711yescharacteristic
727C8—22no—
728C8—22no—
729C8—41no—
730C8—41no—
731C8—942no—
732C8—942no—
733C8—1881no—
734C8—1881no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—474no—
743C22—942no—
744C22—942no—
745C22—942no—
746C22—942no—
747C22—942no—
748C22—942no—
749C22—942no—
750C22—942no—
751C22—942no—
752C22—18816no—
753C22—1881no—
754C22—1881no—
755C22—1881no—
756C22—1881no—
757C22#117×D4711yescharacteristic
758C22C4×D4×D4711yescharacteristic
759C22C4×D4×D4711yescharacteristic
760C22#131×D4711yescharacteristic
761C22C2×#1309403211yescharacteristic
762C22#1568988811yescharacteristic
763C22#1568988911yescharacteristic
764C4—41no—
765C4—41no—
766C4—41no—
767C4—41no—
768C4—41no—
769C4—474no—
770C4—1881no—
771C4—1881no—
772C4—1881no—
773C4—1881no—
774C4—1881no—
775C4#121×D4711yescharacteristic
776C4#123×D4711yescharacteristic
777C4#124×D4711yescharacteristic
778C4#126×D4711yescharacteristic
779C2—42no—
780C2—944no—
781C2—1882no—
782C2#388×D4711yescharacteristic
783C2#2025204411yescharacteristic
784C2#2025204711yescharacteristic
785C2#2025207911yescharacteristic
786C2#2025208611yescharacteristic
787C2#2025211411yescharacteristic
788C2#2025211711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC47×#1924C2
prime radicalC24×D47C2×C4
cosocleC22×C4×C47C24
hypercenter#1924D47
hypocenterC47#21053
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1924

Complements

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

NH ≅ G/Ntype
1. C2×#15689148C2semidirect
4. C2×#15689080C2semidirect
6. #20244004C2semidirect
7. #20244001C2semidirect
8. #20244000C2semidirect
9. #20243996C2semidirect
10. #20243995C2semidirect
11. #20243992C2semidirect
12. #20243991C2semidirect
13. #20243083C2semidirect
14. #20243083C2semidirect
15. C47×#1924C2semidirect
24. C2×C4⋊(C47⋊C8)C22semidirect
25. C2×Dic47⋊C8C22semidirect
26. C2×Dic47⋊C8C22semidirect
36. C2×#13093934C22semidirect
37. C2×C4×C47⋊C8C22semidirect
38. C2×C8×Dic47C22semidirect
50. #15688878C22semidirect
51. #15688878C22semidirect
52. #15688877C22semidirect
53. #15688877C22semidirect
54. #15688877C22semidirect
55. #15688877C22semidirect
56. C2×C4⋊C8×C47C22semidirect
59. C2×#97×C47C22semidirect
61. C47×#336C22semidirect
62. C47×#336C22semidirect
393. #1924D47semidirect
421. C2×C4⋊C8C2×D47semidirect
434. C2×#97C2×D47semidirect
455. #336C2×D47semidirect
456. #336C2×D47semidirect
457. C47#21053semidirect

Maximal subgroups

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

subgroupindex
C2×#156891482
C2×#156890852
C2×C22⋊C8×D472
C2×#156890802
#202457692
#202440042
#202440012
#202440002
#202439962
#202439952
#202439922
#202439912
#202430832
C47×#19242
#2105347