Finite Group Databasebeta

← #26238421

Subgroups — #26238421

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×#15689199C211yesmaximal, characteristic, complemented
2C2×#15689193C211yesmaximal, characteristic, complemented
3C2×#15689192C211yesmaximal, characteristic, complemented
4C4×#13093998C211yesmaximal, characteristic
5#20244185C211yesmaximal, characteristic, complemented
6#20244109C211yesmaximal, characteristic, complemented
7#20244000C211yesmaximal, characteristic, complemented
8#20243993C211yesmaximal, characteristic, complemented
9#20243685C211yesmaximal, characteristic, complemented
10#20243685C211yesmaximal, characteristic, complemented
11#20243569C211yesmaximal, characteristic, complemented
12#20243564C211yesmaximal, characteristic, complemented
13#20243265C211yesmaximal, characteristic, complemented
14#20243150C211yesmaximal, characteristic, complemented
15C2×C47×#423C211yesmaximal, characteristic, complemented
16C22×#10625324C2211yescharacteristic
17C22×C8×D47C2211yescharacteristic
18C2×#13093998C411yescharacteristic
19C2×C4×D188C2211yescharacteristic
20C2×C4×C22⋊D47C2211yescharacteristic
21C2×C4×C22⋊D47C2211yescharacteristic
22#15689199—24no—
23#15689193—24no—
24#15689192—24no—
25C2×Dic47⋊C8C2211yescharacteristic
26C2×Dic47⋊C8C2211yescharacteristic
27C2×C22⋊(C47⋊C8)C2211yescharacteristic
28C2×C22⋊(C47⋊C8)C2211yescharacteristic
29C2×(C2×D47)⋊C8C2211yescharacteristic
30C2×(C2×D47)⋊C8C2211yescharacteristic
31C2×(C2×D47)⋊C8C2211yescharacteristic
32C2×(C2×D47)⋊C8C2211yescharacteristic
33C2×(C2×D47)⋊C8C2211yescharacteristic
34C2×(C2×D47)⋊C8C2211yescharacteristic
35C2×#13093935C2211yescharacteristic
36C2×#13093935C2211yescharacteristic
37C2×#13093934C2211yescharacteristic
38C2×C8×Dic47C2211yescharacteristic
39#15689025C411yescharacteristic
40#15689021C411yescharacteristic
41#15689014C411yescharacteristic
42#15689014C411yescharacteristic
43#15689002C411yescharacteristic
44#15689002C411yescharacteristic
45#15688983C411yescharacteristic
46C4×C4⋊Dic47C2211yescharacteristic
47C4×(C2×D47)⋊C4C2211yescharacteristic
48C4×(C2×D47)⋊C4C2211yescharacteristic
49#15688878C2211yescharacteristic
50#15688878C2211yescharacteristic
51#15688877C2211yescharacteristic
52#15688877C2211yescharacteristic
53#15688877C2211yescharacteristic
54#15688877C2211yescharacteristic
55C22×M16×C47C2211yescharacteristic
56C22×M16×C47C2211yescharacteristic
57C22×C42×C47C2211yescharacteristic
58C47×#423—24no—
59C2×C4⋊C8×C47C2211yescharacteristic
60C2×C4⋊C8×C47C2211yescharacteristic
61C2×C4⋊C8×C47C2211yescharacteristic
62C2×C4⋊C8×C47C2211yescharacteristic
63C22×D188C2×C411yescharacteristic
64C22×C22⋊D47C2×C411yescharacteristic
65C22×C22⋊D47C2×C411yescharacteristic
66C22×C4×D47C2311yescharacteristic
67C22×C4×D47C2311yescharacteristic
68C2×#10625324—22no—
69C2×#10625324—22no—
70C2×#10625324—41no—
71C22×C47⋊C8C2311yescharacteristic
72C22×C47⋊C8C2311yescharacteristic
73C22×C47⋊C8C2311yescharacteristic
74C22×C47⋊C8C2311yescharacteristic
75C2×C8×D47—22no—
76C2×C8×D47—22no—
77C2×C8×D47—41no—
78#13093998—24no—
79C4×D188—22no—
80C4×D188—22no—
81C4×C22⋊D47—22no—
82C4×C22⋊D47—22no—
83C4×C22⋊D47—22no—
84C4×C22⋊D47—22no—
85C2×C4⋊Dic47C2×C411yescharacteristic
86C2×C4⋊Dic47C2×C411yescharacteristic
87C2×C4⋊Dic47C2×C411yescharacteristic
88C2×Dic47⋊C4C2×C411yescharacteristic
89C2×Dic47⋊C4C2×C411yescharacteristic
90C2×C22⋊Dic47C2×C411yescharacteristic
91C2×C22⋊Dic47C2×C411yescharacteristic
92C2×(C2×D47)⋊C4C2×C411yescharacteristic
93C2×(C2×D47)⋊C4C2×C411yescharacteristic
94C2×(C2×D47)⋊C4C2×C411yescharacteristic
95C2×(C2×D47)⋊C4C2×C411yescharacteristic
96C2×(C2×D47)⋊C4C2×C411yescharacteristic
97C2×(C2×D47)⋊C4C2×C411yescharacteristic
98C2×(C2×D47)⋊C4C2×C411yescharacteristic
99C2×(C2×D47)⋊C4C2×C411yescharacteristic
100C2×C4×Dic47C2311yescharacteristic
101C2×C4×Dic47C2311yescharacteristic
102Dic47⋊C8—22no—
103Dic47⋊C8—22no—
104C22⋊(C47⋊C8)—22no—
105C22⋊(C47⋊C8)D414yescomplemented
106(C2×D47)⋊C8—22no—
107(C2×D47)⋊C8—22no—
108(C2×D47)⋊C8—22no—
109(C2×D47)⋊C8—22no—
110(C2×D47)⋊C8—41no—
111(C2×D47)⋊C8—41no—
112#13093935—22no—
113#13093935—22no—
114#13093934—22no—
115C8×Dic47—22no—
116C47⋊#95C2×C411yescharacteristic
117C47⋊#95C2×C411yescharacteristic
118C47⋊#95C2×C411yescharacteristic
119C47⋊#95C2×C411yescharacteristic
120C47⋊#95C2×C411yescharacteristic
121C47⋊#95C2×C411yescharacteristic
122C23×C4×C47C2×C411yescharacteristic
123C23×C4×C47C2×C411yescharacteristic
124C23×C4×C47C2311yescharacteristic
125C2×M16×C47—22no—
126C2×M16×C47—22no—
127C2×M16×C47—22no—
128C2×M16×C47—22no—
129C2×M16×C47—41no—
130C2×M16×C47—41no—
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
141C4⋊C8×C47—22no—
142C4⋊C8×C47—22no—
143C4⋊C8×C47—22no—
144C4⋊C8×C47D414yescomplemented
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—
193M16×C47—44no—
194M16×C47—44no—
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×C47—21no—
204C2×C8×C47—21no—
205C2×C8×C47C2×D412yes—
206C2×C8×C47C2×D412yes—
207C42×C47—22no—
208C42×C47—22no—
209C42×C47—21no—
210C42×C47—21no—
211C42×C47C2×D412yes—
212C42×C47#4112yes—
213C22⋊Dic47—22no—
214C22⋊Dic47—22no—
215(C2×D47)⋊C4—22no—
216(C2×D47)⋊C4—22no—
217(C2×D47)⋊C4—22no—
218(C2×D47)⋊C4—22no—
219(C2×D47)⋊C4—22no—
220(C2×D47)⋊C4—41no—
221(C2×D47)⋊C4—41no—
222(C2×D47)⋊C4M1614yescomplemented
223C4⋊Dic47—22no—
224C4⋊Dic47—22no—
225C4⋊Dic47—41no—
226Dic47⋊C4—22no—
227Dic47⋊C4—22no—
228C4×Dic47—21no—
229C4×Dic47—21no—
230C4×Dic47—21no—
231C4×Dic47—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—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×#423D4711yescharacteristic, complemented
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#1749—471no—
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×M16C2×D4711yescharacteristic
403C22×M16C2×D4711yescharacteristic
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—24no—
414C2×C4⋊C8—471no—
415C2×C4⋊C8—471no—
416C2×C4⋊C8C2×D4711yescharacteristic
417C2×C4⋊C8C2×D4711yescharacteristic
418C2×C4⋊C8C2×D4711yescharacteristic
419C2×C4⋊C8C2×D4711yescharacteristic
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⋊C8—471no—
427C2×C22⋊C8—471no—
428C2×#97—471no—
429C2×#97—471no—
430C2×#97—471no—
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#336—471no—
447#336—471no—
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—22no—
458C2×M16—22no—
459C2×M16—22no—
460C2×M16—22no—
461C2×M16—41no—
462C2×M16—41no—
463C2×M16—942no—
464C2×M16—942no—
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—22no—
508C4⋊C8—22no—
509C4⋊C8—22no—
510C4⋊C8—942no—
511C4⋊C8—942no—
512C4⋊C8C22⋊D4714yescomplemented
513C22⋊C8—474no—
514C22⋊C8—942no—
515C22⋊C8—942no—
516C22⋊C8—942no—
517C22⋊C8—942no—
518C22⋊C8—942no—
519C22⋊C8—1881no—
520C22⋊C8—1881no—
521#97—942no—
522#97—942no—
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×C4D4×D4712yes—
577C22×C4#1062535412yes—
578C22×C4C23×D4711yescharacteristic
579M16—44no—
580M16—44no—
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×C22⋊D4712yes—
606C2×C8C2×C22⋊D4712yes—
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—
630C42#1062535012yes—
631C42C2×C22⋊D4712yes—
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—
652C23#1309398612yes—
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×C4C4×C22⋊D4712yes—
701C2×C4C4×C22⋊D4712yes—
702C2×C4#1309398612yes—
703C2×C4M16×D4712yes—
704C2×C4C2×D4×D4711yescharacteristic
705C2×C4C22×C22⋊D4711yescharacteristic
706C2×C4C2×#1062535011yescharacteristic
707C2×C4C2×#1062535411yescharacteristic
708C2×C4#1309406911yescharacteristic
709C2×C4#1309407211yescharacteristic
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×C4×C22⋊D4711yescharacteristic
740C22C2×#1309398611yescharacteristic
741C22#1568960411yescharacteristic
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×C22⋊D4711yescharacteristic
758C4#1568977411yescharacteristic
759C4#1568978411yescharacteristic
760C4#1568982111yescharacteristic
761C2—42no—
762C2—3761no—
763C2—1882no—
764C2#2024640411yescharacteristic
765C2#2025209111yescharacteristic
766C2#2025210511yescharacteristic
767C2M16×C22⋊D4711yescharacteristic
768C2#2025212311yescharacteristic
769C2#2025250211yescharacteristic
770C2#2025255511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC2×C47×#423C2
prime radicalC2×#13093998C4
cosocleC22×C4×C47C24
hypercenterC2×#423D47
hypocenterC47#22988
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×#423

Complements

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

NH ≅ G/Ntype
1. C2×#15689199C2semidirect
2. C2×#15689193C2semidirect
3. C2×#15689192C2semidirect
5. #20244185C2semidirect
6. #20244109C2semidirect
7. #20244000C2semidirect
8. #20243993C2semidirect
9. #20243685C2semidirect
10. #20243685C2semidirect
11. #20243569C2semidirect
12. #20243564C2semidirect
13. #20243265C2semidirect
14. #20243150C2semidirect
15. C2×C47×#423C2semidirect
105. C22⋊(C47⋊C8)D4semidirect
144. C4⋊C8×C47D4semidirect
222. (C2×D47)⋊C4M16semidirect
379. C2×#423D47semidirect
448. C47#22988semidirect
512. C4⋊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×#156891932
C2×#156891922
C4×#130939982
#202441852
#202441092
#202440002
#202439932
#202436852
#202435692
#202435642
#202432652
#202431502
C2×C47×#4232
#2298847