Finite Group Databasebeta

← #26238417

Subgroups — #26238417

Order 12032.

1050 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689198C211yesmaximal, characteristic, complemented
2C2×#15689197C211yesmaximal, characteristic, complemented
3C2×#15689196C211yesmaximal, characteristic, complemented
4C2×#15689147C211yesmaximal, characteristic, complemented
5C4×#13093998C211yesmaximal, characteristic
6#20244186C211yesmaximal, characteristic, complemented
7#20244111C211yesmaximal, characteristic, complemented
8#20244002C211yesmaximal, characteristic, complemented
9#20243995C211yesmaximal, characteristic, complemented
10#20243683C211yesmaximal, characteristic, complemented
11#20243683C211yesmaximal, characteristic, complemented
12#20243572C211yesmaximal, characteristic, complemented
13#20243567C211yesmaximal, characteristic, complemented
14#20243260C211yesmaximal, characteristic, complemented
15C47×#1749C211yesmaximal, characteristic, complemented
16C22×#10625329C2211yescharacteristic
17C22×#10625329C2211yescharacteristic
18C22×#10625324C2211yescharacteristic
19C22×C8×D47C2211yescharacteristic
20C2×#13093998C411yescharacteristic
21C2×C4×D188C2211yescharacteristic
22C2×C4×C22⋊D47C2211yescharacteristic
23C2×C4×C22⋊D47C2211yescharacteristic
24#15689198—24no—
25#15689197—24no—
26#15689196—24no—
27#15689147—24no—
28C2×C4⋊(C47⋊C8)C2211yescharacteristic
29C2×C4⋊(C47⋊C8)C2211yescharacteristic
30C2×C4⋊(C47⋊C8)C2211yescharacteristic
31C2×C4⋊(C47⋊C8)C2211yescharacteristic
32C2×Dic47⋊C8C2211yescharacteristic
33C2×Dic47⋊C8C2211yescharacteristic
34C2×(C2×D47)⋊C8C2211yescharacteristic
35C2×(C2×D47)⋊C8C2211yescharacteristic
36C2×(C2×D47)⋊C8C2211yescharacteristic
37C2×(C2×D47)⋊C8C2211yescharacteristic
38C2×(C2×D47)⋊C8C2211yescharacteristic
39C2×(C2×D47)⋊C8C2211yescharacteristic
40C2×#13093934C2211yescharacteristic
41C2×C8×Dic47C2211yescharacteristic
42#15689025C411yescharacteristic
43#15689021C411yescharacteristic
44#15689014C411yescharacteristic
45#15689014C411yescharacteristic
46#15689002C411yescharacteristic
47#15689002C411yescharacteristic
48#15688983C411yescharacteristic
49C4×C4⋊Dic47C2211yescharacteristic
50C4×(C2×D47)⋊C4C2211yescharacteristic
51C4×(C2×D47)⋊C4C2211yescharacteristic
52#15688877C2211yescharacteristic
53#15688877C2211yescharacteristic
54#15688877C2211yescharacteristic
55#15688877C2211yescharacteristic
56C22×C42×C47C2211yescharacteristic
57C2×C22⋊C8×C47C2211yescharacteristic
58C2×C22⋊C8×C47C2211yescharacteristic
59C2×#97×C47C2211yescharacteristic
60C2×#97×C47C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C47×#336C2211yescharacteristic
63C22×D188C2×C411yescharacteristic
64C22×C22⋊D47C2×C411yescharacteristic
65C22×C22⋊D47C2×C411yescharacteristic
66C22×C4×D47C2311yescharacteristic
67C22×C4×D47C2311yescharacteristic
68C2×#10625329—22no—
69C2×#10625329—22no—
70C2×#10625329—22no—
71C2×#10625329—22no—
72C2×#10625329—41no—
73C2×#10625329—41no—
74C2×#10625324—22no—
75C2×#10625324—22no—
76C2×#10625324—41no—
77C22×C47⋊C8C2311yescharacteristic
78C22×C47⋊C8C2311yescharacteristic
79C22×C47⋊C8C2311yescharacteristic
80C22×C47⋊C8C2311yescharacteristic
81C2×C8×D47—22no—
82C2×C8×D47—22no—
83C2×C8×D47—41no—
84#13093998—24no—
85C4×D188—22no—
86C4×D188—22no—
87C4×C22⋊D47—22no—
88C4×C22⋊D47—22no—
89C4×C22⋊D47—22no—
90C4×C22⋊D47—22no—
91C2×C4⋊Dic47C2×C411yescharacteristic
92C2×C4⋊Dic47C2×C411yescharacteristic
93C2×C4⋊Dic47C2×C411yescharacteristic
94C2×Dic47⋊C4C2×C411yescharacteristic
95C2×Dic47⋊C4C2×C411yescharacteristic
96C2×C22⋊Dic47C2×C411yescharacteristic
97C2×C22⋊Dic47C2×C411yescharacteristic
98C2×(C2×D47)⋊C4C2×C411yescharacteristic
99C2×(C2×D47)⋊C4C2×C411yescharacteristic
100C2×(C2×D47)⋊C4C2×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×C4×Dic47C2311yescharacteristic
107C2×C4×Dic47C2311yescharacteristic
108C4⋊(C47⋊C8)—22no—
109C4⋊(C47⋊C8)—22no—
110C4⋊(C47⋊C8)—22no—
111C4⋊(C47⋊C8)D414yescomplemented
112Dic47⋊C8—22no—
113Dic47⋊C8—22no—
114(C2×D47)⋊C8—22no—
115(C2×D47)⋊C8—22no—
116(C2×D47)⋊C8—22no—
117(C2×D47)⋊C8—22no—
118(C2×D47)⋊C8—41no—
119(C2×D47)⋊C8—41no—
120#13093934—22no—
121C8×Dic47—22no—
122C47⋊#95C2×C411yescharacteristic
123C47⋊#95C2×C411yescharacteristic
124C47⋊#95C2×C411yescharacteristic
125C47⋊#95C2×C411yescharacteristic
126C47⋊#95C2×C411yescharacteristic
127C47⋊#95C2×C411yescharacteristic
128C23×C4×C47C2×C411yescharacteristic
129C23×C4×C47C2×C411yescharacteristic
130C23×C4×C47C2311yescharacteristic
131C22×C8×C47C2311yescharacteristic
132C22×C8×C47C2311yescharacteristic
133C22×C8×C47C2311yescharacteristic
134C22×C8×C47C2311yescharacteristic
135C2×C42×C47—22no—
136C2×C42×C47—22no—
137C2×C42×C47C2×C411yescharacteristic
138C2×C42×C47C2×C411yescharacteristic
139C2×C42×C47C2311yescharacteristic
140C2×C42×C47C2311yescharacteristic
141C22⋊C8×C47—22no—
142C22⋊C8×C47D414yescomplemented
143#97×C47—22no—
144#97×C47—22no—
145C24×C47C22×C411yescharacteristic
146C23×D47C22×C411yescharacteristic
147C23×D47C22×C411yescharacteristic
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47—22no—
153C22×C4×C47—22no—
154C22×C4×C47—22no—
155C22×C4×C47—41no—
156C22×C4×C47—41no—
157C22×C4×C47—41no—
158C22×C4×C47C22×C411yescharacteristic
159C22×C4×C47C22×C411yescharacteristic
160C22×C4×C47C22×C411yescharacteristic
161C22×C4×C47C22×C411yescharacteristic
162C22×C4×C47C22×C411yescharacteristic
163C22×C4×C47C2×D412yes—
164C22×C4×C47#4112yes—
165C22×C4×C47C2411yescharacteristic
166C2×C22⋊D47—22no—
167C2×C22⋊D47—22no—
168C2×C22⋊D47—22no—
169C2×C22⋊D47—22no—
170C2×C22⋊D47—41no—
171C2×C22⋊D47—41no—
172C22×Dic47C22×C411yescharacteristic
173C22×Dic47C22×C411yescharacteristic
174C22×Dic47C22×C411yescharacteristic
175C22×Dic47C22×C411yescharacteristic
176C22×Dic47C22×C411yescharacteristic
177C22×Dic47C22×C411yescharacteristic
178C2×D188—22no—
179C2×D188—22no—
180C2×D188—41no—
181C2×C4×D47—21no—
182C2×C4×D47—21no—
183C2×C4×D47—21no—
184C2×C4×D47—21no—
185C2×C4×D47—21no—
186C2×C4×D47—21no—
187C2×C4×D47—21no—
188C2×C4×D47—21no—
189C2×C4×D47—21no—
190C2×C4×D47—21no—
191C2×C4×D47—21no—
192C2×C4×D47—21no—
193C2×C8×C47—21no—
194C2×C8×C47—21no—
195C2×C8×C47—21no—
196C2×C8×C47—21no—
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×C47C2×D412yes—
204C2×C8×C47C2×D412yes—
205C42×C47—22no—
206C42×C47—22no—
207C42×C47—21no—
208C42×C47—21no—
209C42×C47C2×D412yes—
210C42×C47#4112yes—
211C22⋊Dic47—22no—
212C22⋊Dic47—22no—
213(C2×D47)⋊C4—22no—
214(C2×D47)⋊C4—22no—
215(C2×D47)⋊C4—22no—
216(C2×D47)⋊C4—22no—
217(C2×D47)⋊C4—22no—
218(C2×D47)⋊C4—41no—
219(C2×D47)⋊C4—41no—
220(C2×D47)⋊C4M1614yescomplemented
221C4⋊Dic47—22no—
222C4⋊Dic47—22no—
223C4⋊Dic47—41no—
224Dic47⋊C4—22no—
225Dic47⋊C4—22no—
226C4×Dic47—21no—
227C4×Dic47—21no—
228C4×Dic47—21no—
229C4×Dic47—21no—
230#10625329—44no—
231#10625329—44no—
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—21no—
239C2×C47⋊C8—21no—
240C2×C47⋊C8—21no—
241C2×C47⋊C8—21no—
242C2×C47⋊C8C2×D412yes—
243C2×C47⋊C8C2×D412yes—
244#10625324—44no—
245C8×D47—44no—
246C23×C47—21no—
247C23×C47—21no—
248C23×C47—21no—
249C23×C47—21no—
250C23×C47—21no—
251C23×C47—21no—
252C23×C47C4×D412yes—
253C23×C47C23×C411yescharacteristic
254C22×D47—21no—
255C22×D47—21no—
256C22×D47—21no—
257C22×D47—21no—
258C22×D47—21no—
259C22×D47—21no—
260C22×D47—21no—
261C22×D47—21no—
262C22×D47—21no—
263C22×D47—21no—
264C22×D47—21no—
265C22×D47—21no—
266C22×D47—21no—
267C22×D47C2×M1612yes—
268C2×C4×C47—21no—
269C2×C4×C47—21no—
270C2×C4×C47—21no—
271C2×C4×C47—21no—
272C2×C4×C47—21no—
273C2×C4×C47—21no—
274C2×C4×C47—21no—
275C2×C4×C47—21no—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—21no—
281C2×C4×C47—21no—
282C2×C4×C47—21no—
283C2×C4×C47—44no—
284C2×C4×C47—44no—
285C2×C4×C47C4×D412yes—
286C2×C4×C47C4×D412yes—
287C2×C4×C47C4×D412yes—
288C2×C4×C47C2×M1612yes—
289C2×C4×C47C22×D411yescharacteristic
290C2×C4×C47C22×D411yescharacteristic
291C2×C4×C47C2×#4111yescharacteristic
292C2×C4×C47C2×#4111yescharacteristic
293C2×C4×C47H(5,𝔽2)11yescharacteristic
294C2×C4×C472−1+411yescharacteristic
295C22⋊D47—44no—
296C22⋊D47—44no—
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×Dic47—21no—
312C2×Dic47—21no—
313C2×Dic47—21no—
314C2×Dic47C2×M1612yes—
315D188—44no—
316C4×D47—41no—
317C4×D47—41no—
318C4×D47—41no—
319C4×D47—41no—
320C4×D47—41no—
321C4×D47—41no—
322C4×D47—41no—
323C4×D47—41no—
324C8×C47—22no—
325C8×C47—22no—
326C8×C47—41no—
327C8×C47—41no—
328C47⋊C8—22no—
329C47⋊C8—22no—
330C47⋊C8—41no—
331C47⋊C8—41no—
332#22988—471nomaximal, Sylow
333C22×C47—22no—
334C22×C47—22no—
335C22×C47—22no—
336C22×C47—41no—
337C22×C47—41no—
338C22×C47—41no—
339C22×C47—41no—
340C22×C47C2×C4×D411yescharacteristic
341C22×C47C2×C4×D411yescharacteristic
342C22×C47#52011yescharacteristic
343C22×C47C22×M1611yescharacteristic
344C22×C47#56811yescharacteristic
345C22×C47#56811yescharacteristic
346C22×C47#56811yescharacteristic
347C2×D47—22no—
348C2×D47—22no—
349C2×D47—22no—
350C2×D47—41no—
351C2×D47—41no—
352C2×D47—41no—
353C2×D47—41no—
354C2×D47—41no—
355C2×D47—41no—
356C2×D47—41no—
357C2×D47—41no—
358C2×D47—41no—
359C2×D47—41no—
360C2×D47—41no—
361C4×C47—22no—
362C4×C47—22no—
363C4×C47—22no—
364C4×C47—22no—
365C4×C47—41no—
366C4×C47D4211yescharacteristic
367C4×C47#54711yescharacteristic
368C4×C47#54811yescharacteristic
369C4×C47#55311yescharacteristic
370Dic47—22no—
371Dic47—41no—
372Dic47—41no—
373Dic47—41no—
374Dic47—41no—
375Dic47—41no—
376C2×#436—471no—
377C2×#435—471no—
378C2×#435—471no—
379C2×#423—471no—
380C4×#121—471no—
381#1955—471no—
382#1940—471no—
383#1924—471no—
384#1923—471no—
385#1870—471no—
386#1870—471no—
387#1851—471no—
388#1850—471no—
389#1771—471no—
390#1749D4711yescharacteristic, complemented
391C2×C47—42no—
392C2×C47#236111yescharacteristic
393C2×C47#293011yescharacteristic
394C2×C47#293211yescharacteristic
395C2×C47D4×M1611yescharacteristic
396C2×C47D4×M1611yescharacteristic
397C2×C47#298911yescharacteristic
398C2×C47#299511yescharacteristic
399D47—42no—
400D47—81no—
401C22×M16—471no—
402C22×M16—471no—
403C22×M16—471no—
404C23×C8—471no—
405C2×#121—471no—
406C2×C4×D4—471no—
407C2×C4×D4—471no—
408C2×C4×D4—471no—
409C22×C42C2×D4711yescharacteristic
410#436—944no—
411#435—944no—
412#435—944no—
413#423—944no—
414C2×C4⋊C8—471no—
415C2×C4⋊C8—471no—
416C2×C4⋊C8—471no—
417C2×C4⋊C8—471no—
418C2×C4⋊C8—471no—
419C2×C4⋊C8—471no—
420C2×C22⋊C8—471no—
421C2×C22⋊C8—471no—
422C2×C22⋊C8—471no—
423C2×C22⋊C8—471no—
424C2×C22⋊C8—471no—
425C2×C22⋊C8—471no—
426C2×C22⋊C8C2×D4711yescharacteristic
427C2×C22⋊C8C2×D4711yescharacteristic
428C2×#97—471no—
429C2×#97C2×D4711yescharacteristic
430C2×#97C2×D4711yescharacteristic
431C2×C4×C8—471no—
432#390—471no—
433#389—471no—
434#388—471no—
435#388—471no—
436#386—471no—
437#386—471no—
438#380—471no—
439C4×C4⋊C4—471no—
440C4×C22⋊C4—471no—
441C4×C22⋊C4—471no—
442#336—471no—
443#336—471no—
444#336—471no—
445#336—471no—
446#336C2×D4711yescharacteristic
447#336C2×D4711yescharacteristic
448C47#2298811yescharacteristic, complemented, Sylow
449C22×D4—471no—
450C22×D4—471no—
451C22×D4—471no—
452C23×C4—471no—
453C23×C4—471no—
454C23×C4C4×D4711yescharacteristic
455C23×C4C4×D4711yescharacteristic
456C23×C4C22×D4711yescharacteristic
457C2×M16—942no—
458C2×M16—942no—
459C2×M16—942no—
460C2×M16—942no—
461C2×M16—942no—
462C2×M16—942no—
463C2×M16—1881no—
464C2×M16—1881no—
465C2×M16—1881no—
466C22×C8—471no—
467C22×C8—471no—
468C22×C8—471no—
469C22×C8—471no—
470C22×C8—942no—
471C22×C8—942no—
472C22×C8—1881no—
473C22×C8C22×D4711yescharacteristic
474C22×C8C22×D4711yescharacteristic
475C22×C8C22×D4711yescharacteristic
476C22×C8C22×D4711yescharacteristic
477#121—944no—
478C4×D4—942no—
479C4×D4—942no—
480C4×D4—942no—
481C4×D4—942no—
482C4×D4—942no—
483C4×D4—942no—
484C2×C4⋊C4—471no—
485C2×C4⋊C4—471no—
486C2×C4⋊C4—471no—
487C2×C4⋊C4—471no—
488C2×C4⋊C4—471no—
489C2×C22⋊C4—471no—
490C2×C22⋊C4—471no—
491C2×C22⋊C4—471no—
492C2×C22⋊C4—471no—
493C2×C22⋊C4—471no—
494C2×C22⋊C4—471no—
495C2×C22⋊C4—471no—
496C2×C22⋊C4—471no—
497C2×C22⋊C4—471no—
498C2×C22⋊C4—471no—
499C2×C42—22no—
500C2×C42—22no—
501C2×C42—471no—
502C2×C42—471no—
503C2×C42C4×D4711yescharacteristic
504C2×C42C4×D4711yescharacteristic
505C2×C42C22×D4711yescharacteristic
506C2×C42C22×D4711yescharacteristic
507C4⋊C8—474no—
508C4⋊C8—942no—
509C4⋊C8—942no—
510C4⋊C8—942no—
511C4⋊C8—942no—
512C4⋊C8—942no—
513C22⋊C8—22no—
514C22⋊C8—942no—
515C22⋊C8—942no—
516C22⋊C8—942no—
517C22⋊C8—942no—
518C22⋊C8—1881no—
519C22⋊C8—1881no—
520C22⋊C8D18814yescomplemented
521#97—22no—
522#97—22no—
523#97—942no—
524C4×C8—942no—
525#95—471no—
526#95—471no—
527#95—471no—
528#95—471no—
529#95—471no—
530#95—471no—
531C24—471no—
532C24—471no—
533C24C2×C4×D4711yescharacteristic
534C2×D4—942no—
535C2×D4—942no—
536C2×D4—942no—
537C2×D4—942no—
538C2×D4—942no—
539C2×D4—942no—
540C2×D4—1881no—
541C2×D4—1881no—
542C2×D4—1881no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—471no—
554C22×C4—471no—
555C22×C4—471no—
556C22×C4—471no—
557C22×C4—471no—
558C22×C4—471no—
559C22×C4—941no—
560C22×C4—941no—
561C22×C4—941no—
562C22×C4—941no—
563C22×C4—941no—
564C22×C4—941no—
565C22×C4—941no—
566C22×C4—941no—
567C22×C4—941no—
568C22×C4—941no—
569C22×C4—941no—
570C22×C4—941no—
571C22×C4C2×C4×D4711yescharacteristic
572C22×C4C2×C4×D4711yescharacteristic
573C22×C4C2×C4×D4711yescharacteristic
574C22×C4C2×C4×D4711yescharacteristic
575C22×C4C2×C4×D4711yescharacteristic
576C22×C4C2×D18812yes—
577C22×C4#1062535012yes—
578C22×C4C23×D4711yescharacteristic
579M16—1884no—
580M16—1884no—
581M16—1884no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—472no—
593C2×C8—472no—
594C2×C8—941no—
595C2×C8—941no—
596C2×C8—941no—
597C2×C8—941no—
598C2×C8—941no—
599C2×C8—941no—
600C2×C8—941no—
601C2×C8—941no—
602C2×C8—941no—
603C2×C8—941no—
604C2×C8—1884no—
605C2×C8C2×D18812yes—
606C2×C8C2×D18812yes—
607C4⋊C4—942no—
608C4⋊C4—942no—
609C4⋊C4—942no—
610C4⋊C4—942no—
611C4⋊C4—1881no—
612C22⋊C4—474no—
613C22⋊C4—942no—
614C22⋊C4—942no—
615C22⋊C4—942no—
616C22⋊C4—942no—
617C22⋊C4—942no—
618C22⋊C4—942no—
619C22⋊C4—942no—
620C22⋊C4—1881no—
621C22⋊C4—1881no—
622C42—22no—
623C42—22no—
624C42—21no—
625C42—21no—
626C42—941no—
627C42—941no—
628C42—941no—
629C42—941no—
630C42D4×D4712yes—
631C42#1062535212yes—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—472no—
639C23—941no—
640C23—941no—
641C23—941no—
642C23—941no—
643C23—941no—
644C23—941no—
645C23—941no—
646C23—941no—
647C23—941no—
648C23—941no—
649C23—941no—
650C23—941no—
651C23—941no—
652C23C4×D18812yes—
653C23C22×C4×D4711yescharacteristic
654D4—1884no—
655D4—1884no—
656D4—1884no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—44no—
673C2×C4—44no—
674C2×C4—472no—
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—941no—
685C2×C4—941no—
686C2×C4—941no—
687C2×C4—941no—
688C2×C4—941no—
689C2×C4—941no—
690C2×C4—941no—
691C2×C4—941no—
692C2×C4—1881no—
693C2×C4—1881no—
694C2×C4—1881no—
695C2×C4—1881no—
696C2×C4—1881no—
697C2×C4—1881no—
698C2×C4—1881no—
699C2×C4—1881no—
700C2×C4(C22⋊D47)⋊C412yes—
701C2×C4(C22⋊D47)⋊C412yes—
702C2×C4C4×D18812yes—
703C2×C4M16×D4712yes—
704C2×C4C2×D4×D4711yescharacteristic
705C2×C4C22×D18811yescharacteristic
706C2×C4C2×#1062535211yescharacteristic
707C2×C4C2×#1062535011yescharacteristic
708C2×C4#1309407011yescharacteristic
709C2×C4#1309407111yescharacteristic
710C8—22no—
711C8—22no—
712C8—41no—
713C8—41no—
714C8—942no—
715C8—942no—
716C8—1881no—
717C8—1881no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—942no—
726C22—942no—
727C22—942no—
728C22—1881no—
729C22—1881no—
730C22—1881no—
731C22—1881no—
732C22—1881no—
733C22—1881no—
734C22—1881no—
735C22—1881no—
736C22—1881no—
737C22—1881no—
738C22—1881no—
739C22C2×(C22⋊D47)⋊C411yescharacteristic
740C22C2×C4×D18811yescharacteristic
741C22#1568960311yescharacteristic
742C22C2×M16×D4711yescharacteristic
743C22#1568988911yescharacteristic
744C22#1568988911yescharacteristic
745C22#1568988911yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—41no—
751C4—942no—
752C4—1881no—
753C4—1881no—
754C4—1881no—
755C4—1881no—
756C4—1881no—
757C4D4×D18811yescharacteristic
758C4#1568977711yescharacteristic
759C4#1568978211yescharacteristic
760C4#1568981911yescharacteristic
761C2—42no—
762C2—3761no—
763C2—1882no—
764C2#2024640211yescharacteristic
765C2#2025208711yescharacteristic
766C2#2025210711yescharacteristic
767C2#2025212011yescharacteristic
768C2M16×D18811yescharacteristic
769C2#2025250711yescharacteristic
770C2#2025256011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC47×#1749C2
prime radicalC2×#13093998C4
cosocleC22×C4×C47C24
hypercenter#1749D47
hypocenterC47#22988
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1749

Complements

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

NH ≅ G/Ntype
1. C2×#15689198C2semidirect
2. C2×#15689197C2semidirect
3. C2×#15689196C2semidirect
4. C2×#15689147C2semidirect
6. #20244186C2semidirect
7. #20244111C2semidirect
8. #20244002C2semidirect
9. #20243995C2semidirect
10. #20243683C2semidirect
11. #20243683C2semidirect
12. #20243572C2semidirect
13. #20243567C2semidirect
14. #20243260C2semidirect
15. C47×#1749C2semidirect
111. C4⋊(C47⋊C8)D4semidirect
142. C22⋊C8×C47D4semidirect
220. (C2×D47)⋊C4M16semidirect
390. #1749D47semidirect
448. C47#22988semidirect
520. C22⋊C8D188semidirect

Maximal subgroups

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

subgroupindex
C2×#156891982
C2×#156891972
C2×#156891962
C2×#156891472
C4×#130939982
#202441862
#202441112
#202440022
#202439952
#202436832
#202435722
#202435672
#202432602
C47×#17492
#2298847