Finite Group Databasebeta

← #26182270

Subgroups — #26182270

Order 12032.

1446 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689634C211yesmaximal, characteristic
2C22×C22⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
3#20241753C212yesmaximal, complemented
4#20241749C212yesmaximal, complemented
5#20241737C214yesmaximal, complemented
6#20241704C214yesmaximal, complemented
7C2×C47×#407C211yesmaximal, characteristic, complemented
8C22×#10625350C411yescharacteristic
9C23×C47⋊C8—21no—
10#15689634—21no—
11#15689634—21no—
12#15689634—21no—
13#15689634—21no—
14#15689634—21no—
15#15689634—21no—
16#15689634—21no—
17#15689634—21no—
18C2×#13094007C2212yes—
19C2×#13094003C411yescharacteristic
20C2×#13094003C2211yescharacteristic
21C2×#13093998C411yescharacteristic
22C2×#13093998C2211yescharacteristic
23C2×#13093993C412yes—
24C2×C4×C22⋊D47C412yes—
25C2×C4×C22⋊D47C2212yes—
26C2×#13093983C411yescharacteristic
27C2×C22⋊(C47⋊C8)—21no—
28C2×C22⋊(C47⋊C8)—21no—
29C2×C22⋊(C47⋊C8)—21no—
30C2×C22⋊(C47⋊C8)C2212yes—
31C2×C22⋊(C47⋊C8)C2212yes—
32C2×C22⋊(C47⋊C8)C2212yes—
33#15688848C2218yescomplemented
34#15688846C2218yescomplemented
35C24×C4×C47C2211yescharacteristic
36C22×M16×C47—21no—
37C47×#407—21no—
38C47×#407—21no—
39C47×#407C2212yes—
40C47×#407C2212yes—
41C2×C22⋊C8×C47—21no—
42C2×C22⋊C8×C47C2212yes—
43C2×#10625350—21no—
44C2×#10625350—21no—
45C2×#10625350—21no—
46C2×#10625350—21no—
47C2×#10625350—44no—
48C22×Dic94C2×C411yescharacteristic
49C22×D188C2×C411yescharacteristic
50C22×C22⋊D47C2×C412yes—
51C22×C22⋊D47C2×C412yes—
52C22×C22⋊D47C2×C412yes—
53C22×C4×D47C2×C412yes—
54C22×C47⋊C8—22no—
55C22×C47⋊C8—22no—
56C22×C47⋊C8—22no—
57C22×C47⋊C8—44no—
58#13094007—22no—
59#13094007—22no—
60#13094007—22no—
61#13094007—22no—
62#13094003—21no—
63#13094003—21no—
64#13094003—21no—
65#13094003—21no—
66#13094003—21no—
67#13094003—21no—
68#13094003—21no—
69#13094003—21no—
70#13093998—21no—
71#13093998—21no—
72#13093998—21no—
73#13093998—21no—
74#13093998—21no—
75#13093998—21no—
76#13093998—21no—
77#13093998—21no—
78#13093993—22no—
79#13093993—22no—
80#13093993—22no—
81#13093993—22no—
82C4×C22⋊D47—22no—
83C4×C22⋊D47—22no—
84C4×C22⋊D47—22no—
85C4×C22⋊D47—22no—
86C4×C22⋊D47—22no—
87C4×C22⋊D47—22no—
88C4×C22⋊D47—22no—
89C4×C22⋊D47—22no—
90#13093983—21no—
91#13093983—21no—
92#13093983—21no—
93#13093983—21no—
94C2×C4⋊Dic47C2×C411yescharacteristic
95C2×C4⋊Dic47C2×C411yescharacteristic
96C2×Dic47⋊C4C2×C412yes—
97C2×Dic47⋊C4C2312yes—
98C2×C22⋊Dic47C2×C412yes—
99C2×C22⋊Dic47C2×C412yes—
100C2×C22⋊Dic47C2×C412yes—
101C2×(C2×D47)⋊C4C2×C412yes—
102C2×(C2×D47)⋊C4C2312yes—
103C2×C4×Dic47C2×C412yes—
104C22⋊(C47⋊C8)—22no—
105C22⋊(C47⋊C8)—22no—
106C22⋊(C47⋊C8)—22no—
107C22⋊(C47⋊C8)C2314yes—
108C25×C47C2×C411yescharacteristic
109C23×C4×C47—44no—
110C23×C4×C47C2×C411yescharacteristic
111C23×C4×C47C2×C411yescharacteristic
112C23×C4×C47C2×C411yescharacteristic
113C23×C4×C47D411yescharacteristic
114C23×C4×C47D411yescharacteristic
115C23×C4×C47D411yescharacteristic
116C23×C4×C47D411yescharacteristic
117C23×C4×C47D411yescharacteristic
118C23×C4×C47D411yescharacteristic
119C23×C4×C47D411yescharacteristic
120C23×C4×C47D411yescharacteristic
121C23×C4×C47C2311yescharacteristic
122C23×C4×C47C2311yescharacteristic
123C23×C4×C47C2311yescharacteristic
124C2×M16×C47—22no—
125C2×M16×C47—22no—
126C2×M16×C47—44no—
127C22×C8×C47—22no—
128C22⋊C8×C47—22no—
129C22⋊C8×C47—22no—
130C22⋊C8×C47—22no—
131C22⋊C8×C47C2314yes—
132C24×C47—24no—
133C24×C47—42no—
134C24×C47—42no—
135C24×C47C22⋊C411yescharacteristic
136C24×C47C22⋊C411yescharacteristic
137C24×C47C22⋊C411yescharacteristic
138C24×C47C22⋊C411yescharacteristic
139C24×C47C22×C411yescharacteristic
140C24×C47C22×C411yescharacteristic
141C24×C47C22×C411yescharacteristic
142C23×D47C22×C412yes—
143C22×C4×C47—24no—
144C22×C4×C47—24no—
145C22×C4×C47—24no—
146C22×C4×C47—42no—
147C22×C4×C47—42no—
148C22×C4×C47—42no—
149C22×C4×C47—42no—
150C22×C4×C47—42no—
151C22×C4×C47—42no—
152C22×C4×C47—42no—
153C22×C4×C47—42no—
154C22×C4×C47—42no—
155C22×C4×C47—42no—
156C22×C4×C47—42no—
157C22×C4×C47C22⋊C411yescharacteristic
158C22×C4×C47C22⋊C411yescharacteristic
159C22×C4×C47C22⋊C411yescharacteristic
160C22×C4×C47C22⋊C411yescharacteristic
161C22×C4×C47C22⋊C411yescharacteristic
162C22×C4×C47C22⋊C411yescharacteristic
163C22×C4×C47C22⋊C411yescharacteristic
164C22×C4×C47C22⋊C411yescharacteristic
165C22×C4×C47C22⋊C411yescharacteristic
166C22×C4×C47C22⋊C411yescharacteristic
167C22×C4×C47C22⋊C411yescharacteristic
168C22×C4×C47C22⋊C411yescharacteristic
169C22×C4×C47C22×C411yescharacteristic
170C22×C4×C47C22×C411yescharacteristic
171C22×C4×C47C22×C411yescharacteristic
172C22×C4×C47C2×D411yescharacteristic
173C22×C4×C47C2×D411yescharacteristic
174C22×C4×C47C2×D411yescharacteristic
175C22×C4×C47C2×D411yescharacteristic
176C22×C4×C47C2×D411yescharacteristic
177C22×C4×C47C2×D411yescharacteristic
178C22×C4×C47C2×D411yescharacteristic
179C22×C4×C47C2×D411yescharacteristic
180C22×C4×C47C2×D411yescharacteristic
181C22×C4×C47C2×D411yescharacteristic
182C22×C4×C47C2×D411yescharacteristic
183C22×C4×C47C2×D411yescharacteristic
184C22×C4×C47C2411yescharacteristic
185C2×C22⋊D47—22no—
186C2×C22⋊D47—22no—
187C2×C22⋊D47—22no—
188C2×C22⋊D47—22no—
189C2×C22⋊D47—22no—
190C2×C22⋊D47—22no—
191C2×C22⋊D47—28no—
192C2×C22⋊D47—44no—
193C2×C22⋊D47—44no—
194C22×Dic47C22×C412yes—
195C22×Dic47C22×C412yes—
196C22×Dic47C22×C412yes—
197#10625350—44no—
198#10625350—44no—
199#10625350—44no—
200#10625350—44no—
201C2×D188—21no—
202C2×D188—21no—
203C2×D188—42no—
204C2×C4×D47—22no—
205C2×C4×D47—22no—
206C2×C4×D47—44no—
207C2×Dic94—21no—
208C2×Dic94—21no—
209C2×Dic94—42no—
210M16×C47—44no—
211M16×C47—44no—
212C2×C8×C47—24no—
213C2×C8×C47—44no—
214C22⋊Dic47—22no—
215C22⋊Dic47—22no—
216C22⋊Dic47—22no—
217C22⋊Dic47—22no—
218C22⋊Dic47—22no—
219C22⋊Dic47—22no—
220(C2×D47)⋊C4—22no—
221(C2×D47)⋊C4—22no—
222(C2×D47)⋊C4—22no—
223(C2×D47)⋊C4—22no—
224C4⋊Dic47—21no—
225C4⋊Dic47—21no—
226C4⋊Dic47—21no—
227C4⋊Dic47—21no—
228Dic47⋊C4—22no—
229Dic47⋊C4—22no—
230Dic47⋊C4—22no—
231Dic47⋊C4—22no—
232C4×Dic47—22no—
233C4×Dic47—22no—
234C2×C47⋊C8—24no—
235C2×C47⋊C8—44no—
236C2×C47⋊C8—44no—
237C2×C47⋊C8—44no—
238C23×C47—22no—
239C23×C47—22no—
240C23×C47—22no—
241C23×C47—22no—
242C23×C47—22no—
243C23×C47—22no—
244C23×C47—22no—
245C23×C47—22no—
246C23×C47—22no—
247C23×C47—22no—
248C23×C47—22no—
249C23×C47—22no—
250C23×C47—41no—
251C23×C47—41no—
252C23×C47—41no—
253C23×C47—41no—
254C23×C47—41no—
255C23×C47—41no—
256C23×C47—41no—
257C23×C47—41no—
258C23×C47—416no—
259C23×C47C2×C22⋊C411yescharacteristic
260C23×C47C2×C22⋊C411yescharacteristic
261C23×C47C2×C22⋊C411yescharacteristic
262C23×C47C2×C22⋊C411yescharacteristic
263C23×C47C2×C22⋊C411yescharacteristic
264C23×C47C2×C22⋊C411yescharacteristic
265C23×C47#13114yes—
266C23×C47C23×C411yescharacteristic
267C22×D47—22no—
268C22×D47—24no—
269C22×D47—42no—
270C22×D47—42no—
271C2×C4×C47—22no—
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—41no—
287C2×C4×C47—41no—
288C2×C4×C47—41no—
289C2×C4×C47—41no—
290C2×C4×C47—41no—
291C2×C4×C47—41no—
292C2×C4×C47—41no—
293C2×C4×C47—41no—
294C2×C4×C47—41no—
295C2×C4×C47—41no—
296C2×C4×C47—41no—
297C2×C4×C47—41no—
298C2×C4×C47#9914yes—
299C2×C4×C47C2×C22⋊C411yescharacteristic
300C2×C4×C47C2×C22⋊C411yescharacteristic
301C2×C4×C47C2×C22⋊C411yescharacteristic
302C2×C4×C47C2×C22⋊C411yescharacteristic
303C2×C4×C47C2×C22⋊C411yescharacteristic
304C2×C4×C47C2×C22⋊C411yescharacteristic
305C2×C4×C47C22×D411yescharacteristic
306C2×C4×C47C22×D411yescharacteristic
307C22⋊D47—44no—
308C22⋊D47—44no—
309C22⋊D47—44no—
310C22⋊D47—44no—
311C22⋊D47—44no—
312C22⋊D47—44no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—24no—
317C2×Dic47—42no—
318C2×Dic47—42no—
319D188—42no—
320D188—42no—
321C4×D47—44no—
322C4×D47—44no—
323Dic94—42no—
324Dic94—42no—
325C8×C47—44no—
326C47⋊C8—44no—
327#17381—471nomaximal, Sylow
328C22×C47—28no—
329C22×C47—21no—
330C22×C47—21no—
331C22×C47—21no—
332C22×C47—21no—
333C22×C47—21no—
334C22×C47—21no—
335C22×C47—21no—
336C22×C47—21no—
337C22×C47—21no—
338C22×C47—21no—
339C22×C47—21no—
340C22×C47—21no—
341C22×C47—21no—
342C22×C47—21no—
343C22×C47—21no—
344C22×C47—21no—
345C22×C47—44no—
346C22×C47—44no—
347C22×C47—44no—
348C22×C47—44no—
349C22×C47—44no—
350C22×C47—44no—
351C22×C47#40812yes—
352C22×C47#40812yes—
353C22×C47C2×#9912yes—
354C22×C47#41312yes—
355C22×C47C22×C22⋊C411yescharacteristic
356C22×C47C2×#13112yes—
357C2×D47—42no—
358C2×D47—42no—
359C2×D47—42no—
360C2×D47—84no—
361C4×C47—21no—
362C4×C47—21no—
363C4×C47—21no—
364C4×C47—21no—
365C4×C47—21no—
366C4×C47—21no—
367C4×C47C2×#9912yes—
368C4×C47C2×#9912yes—
369Dic47—42no—
370Dic47—42no—
371Dic47—42no—
372C2×#525—471no—
373C2×#407D4711yescharacteristic, complemented
374C22×C22⋊C8—471no—
375#1472—472no—
376#1471—472no—
377#1468—474no—
378#1459—474no—
379C2×C47—22no—
380C2×C47—22no—
381C2×C47—22no—
382C2×C47—22no—
383C2×C47—22no—
384C2×C47—41no—
385C2×C47—41no—
386C2×C47C2×#40811yescharacteristic
387C2×C47C22×#9911yescharacteristic
388C2×C47C2×#41311yescharacteristic
389D47—82no—
390C22×#41—471no—
391C24×C4C2×D4711yescharacteristic
392C22×M16—21no—
393C23×C8—941no—
394#525—941no—
395#525—941no—
396#525—941no—
397#525—941no—
398#525—941no—
399#525—941no—
400#525—941no—
401#525—941no—
402C2×#123—472no—
403C2×C22⋊Q8—471no—
404C2×C22⋊Q8—471no—
405C2×#121—471no—
406C2×#121—471no—
407C2×#120—472no—
408C2×C4×D4—472no—
409C2×C4×D4—472no—
410C2×#117—471no—
411#407—21no—
412#407—21no—
413#407C2×D4712yes—
414#407C2×D4712yes—
415C2×C22⋊C8—21no—
416C2×C22⋊C8—472no—
417C2×C22⋊C8—472no—
418C2×C22⋊C8—472no—
419C2×C22⋊C8—941no—
420C2×C22⋊C8—941no—
421C2×C22⋊C8—941no—
422C2×C22⋊C8C2×D4712yes—
423#324—478no—
424#323—478no—
425C47#1738111yescharacteristic, complemented, Sylow
426C25C4×D4711yescharacteristic
427C2×#41—941no—
428C2×#41—941no—
429C2×#41—941no—
430C2×#41—941no—
431C2×#41—1884no—
432C22×Q8—471no—
433C22×D4—472no—
434C22×D4—472no—
435C22×D4—472no—
436C22×D4—471no—
437C23×C4—44no—
438C23×C4—472no—
439C23×C4C4×D4711yescharacteristic
440C23×C4C4×D4711yescharacteristic
441C23×C4C4×D4711yescharacteristic
442C23×C4D18811yescharacteristic
443C23×C4D18811yescharacteristic
444C23×C4D18811yescharacteristic
445C23×C4D18811yescharacteristic
446C23×C4C22⋊D4711yescharacteristic
447C23×C4C22⋊D4711yescharacteristic
448C23×C4C22⋊D4711yescharacteristic
449C23×C4C22⋊D4711yescharacteristic
450C23×C4C22×D4711yescharacteristic
451C23×C4C22×D4711yescharacteristic
452C23×C4C22×D4711yescharacteristic
453C2×M16—22no—
454C2×M16—22no—
455C2×M16—44no—
456C22×C8—22no—
457C22×C8—942no—
458C22×C8—942no—
459C22×C8—942no—
460C22×C8—1884no—
461#123—942no—
462#123—942no—
463#123—942no—
464#123—942no—
465C22⋊Q8—941no—
466C22⋊Q8—941no—
467C22⋊Q8—941no—
468C22⋊Q8—941no—
469C22⋊Q8—941no—
470C22⋊Q8—941no—
471C22⋊Q8—941no—
472C22⋊Q8—941no—
473#121—941no—
474#121—941no—
475#121—941no—
476#121—941no—
477#121—941no—
478#121—941no—
479#121—941no—
480#121—941no—
481#120—942no—
482#120—942no—
483#120—942no—
484#120—942no—
485C4×D4—942no—
486C4×D4—942no—
487C4×D4—942no—
488C4×D4—942no—
489C4×D4—942no—
490C4×D4—942no—
491C4×D4—942no—
492C4×D4—942no—
493#117—941no—
494#117—941no—
495#117—941no—
496#117—941no—
497C2×C4⋊C4—471no—
498C2×C4⋊C4—471no—
499C2×C4⋊C4—472no—
500C2×C4⋊C4—472no—
501C2×C22⋊C4—472no—
502C2×C22⋊C4—472no—
503C2×C22⋊C4—472no—
504C2×C22⋊C4—472no—
505C2×C22⋊C4—472no—
506C2×C42—472no—
507C22⋊C8—22no—
508C22⋊C8—22no—
509C22⋊C8—22no—
510C22⋊C8—474no—
511C22⋊C8—942no—
512C22⋊C8—942no—
513C22⋊C8—942no—
514C22⋊C8C22×D4714yes—
515C24—24no—
516C24—42no—
517C24—42no—
518C24—472no—
519C24(C2×D47)⋊C411yescharacteristic
520C24(C2×D47)⋊C411yescharacteristic
521C24(C2×D47)⋊C411yescharacteristic
522C24(C2×D47)⋊C411yescharacteristic
523C24C2×C4×D4711yescharacteristic
524C24C2×C4×D4711yescharacteristic
525C24C2×C4×D4711yescharacteristic
526#41—1884no—
527#41—1884no—
528#41—1884no—
529#41—1884no—
530C2×Q8—941no—
531C2×Q8—941no—
532C2×Q8—1882no—
533C2×D4—942no—
534C2×D4—942no—
535C2×D4—942no—
536C2×D4—942no—
537C2×D4—942no—
538C2×D4—942no—
539C2×D4—948no—
540C2×D4—941no—
541C2×D4—941no—
542C2×D4—1882no—
543C2×D4—1884no—
544C2×D4—1884no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—472no—
560C22×C4—472no—
561C22×C4—472no—
562C22×C4—942no—
563C22×C4—942no—
564C22×C4—1884no—
565C22×C4(C2×D47)⋊C411yescharacteristic
566C22×C4(C2×D47)⋊C411yescharacteristic
567C22×C4(C2×D47)⋊C411yescharacteristic
568C22×C4(C2×D47)⋊C411yescharacteristic
569C22×C4(C2×D47)⋊C411yescharacteristic
570C22×C4(C2×D47)⋊C411yescharacteristic
571C22×C4(C2×D47)⋊C411yescharacteristic
572C22×C4(C2×D47)⋊C411yescharacteristic
573C22×C4(C2×D47)⋊C411yescharacteristic
574C22×C4(C2×D47)⋊C411yescharacteristic
575C22×C4(C2×D47)⋊C411yescharacteristic
576C22×C4(C2×D47)⋊C411yescharacteristic
577C22×C4C2×C4×D4711yescharacteristic
578C22×C4C2×C4×D4711yescharacteristic
579C22×C4C2×C4×D4711yescharacteristic
580C22×C4C2×D18811yescharacteristic
581C22×C4C2×D18811yescharacteristic
582C22×C4C2×D18811yescharacteristic
583C22×C4C2×D18811yescharacteristic
584C22×C4C2×D18811yescharacteristic
585C22×C4C2×D18811yescharacteristic
586C22×C4C2×C22⋊D4711yescharacteristic
587C22×C4C2×C22⋊D4711yescharacteristic
588C22×C4C2×C22⋊D4711yescharacteristic
589C22×C4C2×C22⋊D4711yescharacteristic
590C22×C4C2×C22⋊D4711yescharacteristic
591C22×C4C2×C22⋊D4711yescharacteristic
592C22×C4C23×D4711yescharacteristic
593M16—44no—
594M16—44no—
595C2×C8—24no—
596C2×C8—44no—
597C2×C8—944no—
598C2×C8—1884no—
599C2×C8—1884no—
600C2×C8—1884no—
601C4⋊C4—942no—
602C4⋊C4—942no—
603C4⋊C4—941no—
604C4⋊C4—941no—
605C4⋊C4—941no—
606C4⋊C4—941no—
607C4⋊C4—942no—
608C4⋊C4—942no—
609C22⋊C4—942no—
610C22⋊C4—942no—
611C22⋊C4—942no—
612C22⋊C4—942no—
613C22⋊C4—942no—
614C22⋊C4—942no—
615C22⋊C4—942no—
616C22⋊C4—942no—
617C22⋊C4—942no—
618C22⋊C4—942no—
619C42—942no—
620C42—942no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—416no—
642C23—944no—
643C23—942no—
644C23—1882no—
645C23—1882no—
646C23C2×(C2×D47)⋊C411yescharacteristic
647C23C2×(C2×D47)⋊C411yescharacteristic
648C23C2×(C2×D47)⋊C411yescharacteristic
649C23C2×(C2×D47)⋊C411yescharacteristic
650C23C2×(C2×D47)⋊C411yescharacteristic
651C23C2×(C2×D47)⋊C411yescharacteristic
652C23#1309403214yes—
653C23C22×C4×D4711yescharacteristic
654Q8—1882no—
655Q8—1882no—
656D4—1882no—
657D4—1884no—
658D4—1884no—
659D4—1884no—
660D4—1884no—
661D4—1884no—
662D4—1884no—
663D4—1882no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—942no—
692C2×C4—942no—
693C2×C4—942no—
694C2×C4—944no—
695C2×C4—1884no—
696C2×C4—1884no—
697C2×C4—1882no—
698C2×C4—1882no—
699C2×C4#1309393814yes—
700C2×C4C2×(C2×D47)⋊C411yescharacteristic
701C2×C4C2×(C2×D47)⋊C411yescharacteristic
702C2×C4C2×(C2×D47)⋊C411yescharacteristic
703C2×C4C2×(C2×D47)⋊C411yescharacteristic
704C2×C4C2×(C2×D47)⋊C411yescharacteristic
705C2×C4C2×(C2×D47)⋊C411yescharacteristic
706C2×C4C22×C22⋊D4711yescharacteristic
707C2×C4C22×D18811yescharacteristic
708C8—44no—
709C8—1884no—
710C22—28no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—44no—
728C22—44no—
729C22—44no—
730C22—44no—
731C22—44no—
732C22—44no—
733C22—3764no—
734C22—1882no—
735C22—1882no—
736C22—1882no—
737C22#1568909112yes—
738C22#1568909112yes—
739C22C2×#1309393812yes—
740C22#1568910512yes—
741C22C22×(C2×D47)⋊C411yescharacteristic
742C22C2×#1309403212yes—
743C4—21no—
744C4—21no—
745C4—21no—
746C4—21no—
747C4—21no—
748C4—21no—
749C4—1882no—
750C4—1882no—
751C4—1882no—
752C4C2×#1309393812yes—
753C4C2×#1309393812yes—
754C2—22no—
755C2—22no—
756C2—22no—
757C2—22no—
758C2—22no—
759C2—41no—
760C2—41no—
761C2—3762no—
762C2C2×#1568909111yescharacteristic
763C2C22×#1309393811yescharacteristic
764C2C2×#1568910511yescharacteristic
subgroupG/H
centerC2×C4C2×(C2×D47)⋊C4
commutatorC23×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#407C2
socleC22×C47C22×C22⋊C4
prime radicalC2×#15689634C2
cosocleC22×C4×C47C24
hypercenterC2×#407D47
hypocenterC47#17381
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C22×C22⋊(C47⋊C8)C2semidirect
3. #20241753C2semidirect
4. #20241749C2semidirect
5. #20241737C2semidirect
6. #20241704C2semidirect
7. C2×C47×#407C2semidirect
33. #15688848C22semidirect
34. #15688846C22semidirect
373. C2×#407D47semidirect
425. C47#17381semidirect

Maximal subgroups

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

subgroupindex
C2×#156896342
C22×C22⋊(C47⋊C8)2
#202417532
#202417492
#202417372
#202417042
C2×C47×#4072
#1738147