Finite Group Databasebeta

← #26236531

Subgroups — #26236531

Order 12032.

1302 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689274C211yesmaximal, characteristic
2C2×#15689223C211yesmaximal, characteristic, complemented
3C22×#13093945C211yesmaximal, characteristic
4#20246391C211yesmaximal, characteristic, complemented
5#20244268C211yesmaximal, characteristic, complemented
6#20244088C211yesmaximal, characteristic, complemented
7#20244005C211yesmaximal, characteristic, complemented
8#20243809C211yesmaximal, characteristic, complemented
9#20243746C211yesmaximal, characteristic, complemented
10#20243722C211yesmaximal, characteristic, complemented
11#20243635C211yesmaximal, characteristic, complemented
12#20243575C211yesmaximal, characteristic, complemented
13#20243213C211yesmaximal, characteristic, complemented
14#20243166C211yesmaximal, characteristic, complemented
15D4×C22⋊C4×C47C211yesmaximal, characteristic
16C22×#10625335C2211yescharacteristic
17C22×#10625335C2211yescharacteristic
18C23×C47⋊C8C2211yescharacteristic
19C2×#13094003C2211yescharacteristic
20C2×C4×Dic94C2211yescharacteristic, complemented
21C22×C4⋊Dic47C2211yescharacteristic
22#15689274C418yescomplemented
23#15689223—24no—
24C2×#13093957C2211yescharacteristic, complemented
25C2×#13093957C2211yescharacteristic, complemented
26C2×#13093947C2211yescharacteristic, complemented
27C2×#13093947C2211yescharacteristic, complemented
28C2×#13093945—24no—
29C2×#13093945C2211yescharacteristic
30C2×#13093945C2211yescharacteristic
31C2×#13093945C2211yescharacteristic
32C2×#13093945C2211yescharacteristic
33C2×#13093945C2211yescharacteristic
34C2×#13093945C2211yescharacteristic
35C2×C22⋊(C47⋊C8)C2211yescharacteristic
36C2×#13093935C2211yescharacteristic, complemented
37C2×#13093935C2211yescharacteristic, complemented
38#15689029C2211yescharacteristic, complemented
39#15689021C2211yescharacteristic, complemented
40#15689020—21no—
41#15689010—21no—
42#15688995—21no—
43C4×C4⋊Dic47C2211yescharacteristic, complemented
44C22⋊C4×Dic47—21no—
45#15688885C2211yescharacteristic, complemented
46#15688885C2211yescharacteristic, complemented
47#15688885C2211yescharacteristic, complemented
48#15688885C2211yescharacteristic, complemented
49#15688878C2211yescharacteristic, complemented
50#15688878C2211yescharacteristic, complemented
51C23×D4×C47C2211yescharacteristic
52C2×C4×D4×C47C2211yescharacteristic
53C2×C4×D4×C47C2211yescharacteristic
54C22×C22⋊C4×C47—21no—
55C47×#390C2211yescharacteristic
56C47×#390C2211yescharacteristic
57C47×#386—21no—
58C47×#386—21no—
59C47×#380C2211yescharacteristic
60C47×#379—21no—
61C4×C22⋊C4×C47C2211yescharacteristic
62C22×Dic94C2311yescharacteristic
63C23×Dic47—21no—
64C2×#10625335—22no—
65C2×#10625335—22no—
66C2×#10625335—41no—
67C2×#10625335—41no—
68C2×#10625335C2×C414yescomplemented
69C2×#10625335C2×C414yescomplemented
70C22×C47⋊C8—22no—
71C22×C47⋊C8—22no—
72C22×C47⋊C8—41no—
73C22×C47⋊C8C2311yescharacteristic
74C22×C47⋊C8C2311yescharacteristic
75C22×C47⋊C8C2311yescharacteristic
76C22×C47⋊C8C2311yescharacteristic
77#13094003—22no—
78#13094003C2×C414yescomplemented
79C4×Dic94—22no—
80C4×Dic94—41no—
81C2×C4⋊Dic47—22no—
82C2×C4⋊Dic47—21no—
83C2×C4⋊Dic47—41no—
84C2×C4⋊Dic47C2311yescharacteristic
85C2×C4⋊Dic47C2311yescharacteristic
86C2×C4⋊Dic47C2311yescharacteristic
87C2×Dic47⋊C4—21no—
88C2×Dic47⋊C4—21no—
89C2×Dic47⋊C4—21no—
90C2×C22⋊Dic47—21no—
91C2×C4×Dic47—21no—
92C2×C4×Dic47—21no—
93#13093957—22no—
94#13093957—41no—
95#13093947—22no—
96#13093947—41no—
97#13093945—22no—
98#13093945—22no—
99#13093945—22no—
100#13093945C2×C414yescomplemented
101#13093945C2×C414yescomplemented
102#13093945D414yes—
103C22⋊(C47⋊C8)C2×C414yescomplemented
104#13093935—22no—
105#13093935—41no—
106C47⋊#95—21no—
107C47⋊#95—21no—
108C47⋊#95—21no—
109C47⋊#95—21no—
110C25×C47—21no—
111C22×D4×C47—22no—
112C22×D4×C47—22no—
113C22×D4×C47—21no—
114C22×D4×C47—22no—
115C22×D4×C47—41no—
116C22×D4×C47—41no—
117C22×D4×C47C2×C414yes—
118C22×D4×C47C2311yescharacteristic
119C22×D4×C47C2311yescharacteristic
120C23×C4×C47—21no—
121C23×C4×C47—21no—
122C23×C4×C47C2311yescharacteristic
123C4×D4×C47—22no—
124C4×D4×C47—22no—
125C4×D4×C47—41no—
126C4×D4×C47—41no—
127C2×C4⋊C4×C47C2311yescharacteristic
128C2×C4⋊C4×C47C2311yescharacteristic
129C2×C22⋊C4×C47—21no—
130C2×C22⋊C4×C47—21no—
131C2×C22⋊C4×C47—21no—
132C2×C22⋊C4×C47—21no—
133C2×C22⋊C4×C47—21no—
134C2×C22⋊C4×C47—21no—
135C2×C22⋊C4×C47—21no—
136C2×C22⋊C4×C47—44no—
137C2×C22⋊C4×C47D411yescharacteristic
138C2×C22⋊C4×C47D411yescharacteristic
139C2×C42×C47C2311yescharacteristic
140C2×C42×C47C2311yescharacteristic
141#95×C47—21no—
142#95×C47D411yescharacteristic
143#95×C47D411yescharacteristic
144C24×C47—21no—
145C24×C47—21no—
146C24×C47—24no—
147C24×C47—42no—
148C24×C47—42no—
149C24×C47—42no—
150C24×C47—42no—
151C24×C47—81no—
152C24×C47—81no—
153C24×C47C2×D411yescharacteristic
154C2×D4×C47—28no—
155C2×D4×C47—24no—
156C2×D4×C47—21no—
157C2×D4×C47—21no—
158C2×D4×C47—21no—
159C2×D4×C47—21no—
160C2×D4×C47—21no—
161C2×D4×C47—21no—
162C2×D4×C47—21no—
163C2×D4×C47—21no—
164C2×D4×C47—44no—
165C2×D4×C47—44no—
166C2×D4×C47—44no—
167C2×D4×C47—42no—
168C2×D4×C47—42no—
169C2×D4×C47C22×C412yes—
170C2×D4×C47C22×C412yes—
171C2×D4×C47C2×D412yes—
172C2×D4×C47#4112yes—
173C22×C4×C47—21no—
174C22×C4×C47—21no—
175C22×C4×C47—21no—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47—21no—
179C22×C4×C47—42no—
180C22×C4×C47—42no—
181C22×C4×C47—42no—
182C22×C4×C47—42no—
183C22×C4×C47—81no—
184C22×C4×C47—81no—
185C22×C4×C47C22×C412yes—
186C22×C4×C47C2×D411yescharacteristic
187C22×C4×C47C2×D411yescharacteristic
188C22×C4×C47C2×D411yescharacteristic
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47#4112yes—
192C22×C4×C47C2411yescharacteristic
193C22×Dic47—21no—
194C22×Dic47—21no—
195C22×Dic47—21no—
196C22×Dic47—21no—
197C22×Dic47—42no—
198C22×Dic47—42no—
199C22×Dic47—81no—
200C2×Dic94—21no—
201C2×Dic94—21no—
202C2×Dic94—21no—
203C2×Dic94—21no—
204C2×Dic94—21no—
205C2×Dic94C22×C412yes—
206C4⋊C4×C47—21no—
207C4⋊C4×C47—21no—
208C4⋊C4×C47—21no—
209C4⋊C4×C47—21no—
210C22⋊C4×C47—22no—
211C22⋊C4×C47—22no—
212C22⋊C4×C47—42no—
213C22⋊C4×C47—42no—
214C22⋊C4×C47—42no—
215C22⋊C4×C47—42no—
216C22⋊C4×C47—42no—
217C22⋊C4×C47—81no—
218C22⋊C4×C47—81no—
219C42×C47—21no—
220C42×C47—21no—
221C42×C47—21no—
222C42×C47—21no—
223C22⋊Dic47—24no—
224#10625335—28no—
225#10625335—44no—
226C4⋊Dic47—21no—
227C4⋊Dic47—21no—
228C4⋊Dic47—21no—
229C4⋊Dic47—21no—
230C4⋊Dic47—42no—
231C4⋊Dic47C22×C412yes—
232C4⋊Dic47C2×D412yes—
233Dic47⋊C4—24no—
234Dic47⋊C4—42no—
235Dic47⋊C4—81no—
236C4×Dic47—42no—
237C4×Dic47—81no—
238C2×C47⋊C8—21no—
239C2×C47⋊C8—21no—
240C2×C47⋊C8—21no—
241C2×C47⋊C8—21no—
242C2×C47⋊C8—21no—
243C2×C47⋊C8—21no—
244C2×C47⋊C8—21no—
245C2×C47⋊C8—21no—
246C2×C47⋊C8—21no—
247C2×C47⋊C8—44no—
248C2×C47⋊C8C22×C412yes—
249C2×C47⋊C8C22×C412yes—
250C2×C47⋊C8C2×D412yes—
251C23×C47—21no—
252C23×C47—21no—
253C23×C47—21no—
254C23×C47—21no—
255C23×C47—22no—
256C23×C47—22no—
257C23×C47—22no—
258C23×C47—22no—
259C23×C47—48no—
260C23×C47—41no—
261C23×C47—41no—
262C23×C47—41no—
263C23×C47—41no—
264C23×C47—41no—
265C23×C47—41no—
266C23×C47—41no—
267C23×C47—41no—
268C23×C47—41no—
269C23×C47—41no—
270C23×C47—48no—
271C23×C47—84no—
272C23×C47—84no—
273C23×C47—84no—
274C23×C47—84no—
275C23×C47—84no—
276C23×C47C4×D412yes—
277C23×C47AGL(1,ℤ/8)12yes—
278C23×C47#13712yes—
279C23×C47C22×D411yescharacteristic
280D4×C47—22no—
281D4×C47—22no—
282D4×C47—22no—
283D4×C47—22no—
284D4×C47—22no—
285D4×C47—48no—
286D4×C47—41no—
287D4×C47—41no—
288D4×C47C4×D414yes—
289C2×C4×C47—21no—
290C2×C4×C47—21no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—21no—
296C2×C4×C47—21no—
297C2×C4×C47—21no—
298C2×C4×C47—21no—
299C2×C4×C47—21no—
300C2×C4×C47—21no—
301C2×C4×C47—21no—
302C2×C4×C47—21no—
303C2×C4×C47—21no—
304C2×C4×C47—21no—
305C2×C4×C47—21no—
306C2×C4×C47—21no—
307C2×C4×C47—41no—
308C2×C4×C47—41no—
309C2×C4×C47—41no—
310C2×C4×C47—41no—
311C2×C4×C47—41no—
312C2×C4×C47—41no—
313C2×C4×C47—84no—
314C2×C4×C47—84no—
315C2×C4×C47C4×D412yes—
316C2×C4×C47C23×C411yescharacteristic
317C2×C4×C47C22×D411yescharacteristic
318C2×C4×C47C2×#4111yescharacteristic
319C2×C4×C47C2×#4111yescharacteristic
320C2×C4×C47H(5,𝔽2)11yescharacteristic
321C2×C4×C47H(5,𝔽2)11yescharacteristic
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—22no—
325C2×Dic47—41no—
326C2×Dic47—41no—
327C2×Dic47—41no—
328C2×Dic47—41no—
329C2×Dic47—41no—
330C2×Dic47—41no—
331C2×Dic47—41no—
332C2×Dic47—41no—
333C2×Dic47—41no—
334C2×Dic47—84no—
335Dic94—22no—
336Dic94—22no—
337Dic94—41no—
338Dic94—41no—
339C47⋊C8—22no—
340C47⋊C8—22no—
341C47⋊C8—22no—
342C47⋊C8—41no—
343#22854—471nomaximal, Sylow
344C22×C47—22no—
345C22×C47—22no—
346C22×C47—22no—
347C22×C47—22no—
348C22×C47—22no—
349C22×C47—22no—
350C22×C47—24no—
351C22×C47—42no—
352C22×C47—42no—
353C22×C47—42no—
354C22×C47—42no—
355C22×C47—42no—
356C22×C47—42no—
357C22×C47—42no—
358C22×C47—42no—
359C22×C47—42no—
360C22×C47—816no—
361C22×C47—81no—
362C22×C47—81no—
363C22×C47—81no—
364C22×C47—81no—
365C22×C47#44014yescomplemented
366C22×C47C2×C4×D411yescharacteristic
367C22×C47D4211yescharacteristic
368C22×C47#54611yescharacteristic
369C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
370C22×C47C2×#13711yescharacteristic
371C22×C47#57611yescharacteristic
372C22×C47#57711yescharacteristic
373C4×C47—22no—
374C4×C47—41no—
375C4×C47—41no—
376C4×C47—41no—
377C4×C47—41no—
378C4×C47—81no—
379C4×C47—81no—
380C4×C47C2×C4×D411yescharacteristic
381C4×C47#51811yescharacteristic
382C4×C47#54611yescharacteristic
383C4×C47#55111yescharacteristic
384Dic47—42no—
385Dic47—42no—
386Dic47—42no—
387Dic47—81no—
388C2×#450—471no—
389C2×#440—471no—
390C22×#102—471no—
391#2360—471no—
392D4×C22⋊C4D4711yescharacteristic
393#1973—471no—
394#1936—471no—
395#1925—471no—
396#1892—471no—
397#1880—471no—
398#1877—471no—
399#1862—471no—
400#1852—471no—
401#1762—471no—
402#1752—471no—
403C2×C47—24no—
404C2×C47—44no—
405C2×C47—82no—
406C2×C47#235811yescharacteristic
407C2×C47C2×#44011yescharacteristic
408C2×C47#294611yescharacteristic
409C2×C47#326411yescharacteristic
410C2×C47#326611yescharacteristic
411C2×C47#331011yescharacteristic
412C2×C47#331411yescharacteristic
413C23×D4C2×D4711yescharacteristic
414C22×SD16—471no—
415C22×SD16—471no—
416C23×C8—471no—
417C2×C22⋊Q8—471no—
418C2×C4×Q8—471no—
419C2×C4×D4C2×D4711yescharacteristic
420C2×C4×D4C2×D4711yescharacteristic
421C22×C4⋊C4—471no—
422C22×C22⋊C4—21no—
423#450—478no—
424#440—944no—
425C2×#107—471no—
426C2×#107—471no—
427C2×#103—471no—
428C2×#103—471no—
429C2×#102—471no—
430C2×#102—471no—
431C2×#102—471no—
432C2×#102—471no—
433C2×#102—471no—
434C2×#102—471no—
435C2×#102—944no—
436C2×C22⋊C8—471no—
437C2×#97—471no—
438C2×#97—471no—
439#391—471no—
440#390C2×D4711yescharacteristic
441#390C2×D4711yescharacteristic
442#389—471no—
443#389—941no—
444#387—941no—
445#386—21no—
446#386—21no—
447#385—941no—
448#380C2×D4711yescharacteristic
449#379—21no—
450C4×C4⋊C4—471no—
451C4×C22⋊C4—941no—
452C4×C22⋊C4C2×D4711yescharacteristic
453#340—471no—
454#340—471no—
455#340—471no—
456#340—471no—
457#336—471no—
458#336—471no—
459C47#2285411yescharacteristic, complemented, Sylow
460C25—21no—
461C22×Q8—471no—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—22no—
465C22×D4—21no—
466C22×D4—41no—
467C22×D4—41no—
468C22×D4C4×D4714yes—
469C22×D4C22×D4711yescharacteristic
470C22×D4C22×D4711yescharacteristic
471C23×C4—21no—
472C23×C4—21no—
473C23×C4—941no—
474C23×C4C22×D4711yescharacteristic
475C2×SD16—474no—
476C2×SD16—474no—
477C2×SD16—942no—
478C2×SD16—942no—
479C2×SD16—1881no—
480C2×SD16—1881no—
481C22×C8—471no—
482C22×C8—471no—
483C22×C8—471no—
484C22×C8—471no—
485C22×C8—942no—
486C22×C8—942no—
487C22×C8—1881no—
488C22⋊Q8—474no—
489C22⋊Q8—942no—
490C4×Q8—942no—
491C4×Q8—1881no—
492C4×D4—22no—
493C4×D4—22no—
494C4×D4—41no—
495C4×D4—41no—
496C2×C4⋊C4—471no—
497C2×C4⋊C4—471no—
498C2×C4⋊C4—471no—
499C2×C4⋊C4—942no—
500C2×C4⋊C4—941no—
501C2×C4⋊C4—941no—
502C2×C4⋊C4—941no—
503C2×C4⋊C4—941no—
504C2×C4⋊C4—1881no—
505C2×C4⋊C4C22×D4711yescharacteristic
506C2×C4⋊C4C22×D4711yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—44no—
515C2×C22⋊C4—941no—
516C2×C22⋊C4C22⋊D4711yescharacteristic
517C2×C22⋊C4C22⋊D4711yescharacteristic
518C2×C42—941no—
519C2×C42—941no—
520C2×C42C22×D4711yescharacteristic
521C2×C42C22×D4711yescharacteristic
522#107—942no—
523#107—1881no—
524#103—942no—
525#103—1881no—
526#102—474no—
527#102—474no—
528#102—474no—
529#102—942no—
530#102—942no—
531#102—942no—
532C22⋊C8—474no—
533#97—942no—
534#97—1881no—
535#95—21no—
536#95—941no—
537#95—941no—
538#95—941no—
539#95—941no—
540#95C22⋊D4711yescharacteristic
541#95C22⋊D4711yescharacteristic
542C24—21no—
543C24—21no—
544C24—24no—
545C24—42no—
546C24—42no—
547C24—42no—
548C24—42no—
549C24—81no—
550C24—81no—
551C24C2×C22⋊D4711yescharacteristic
552C2×Q8—472no—
553C2×Q8—941no—
554C2×Q8—941no—
555C2×Q8—941no—
556C2×Q8—941no—
557C2×Q8—941no—
558C2×D4—28no—
559C2×D4—24no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4C2×C4×D4712yes—
574C2×D4C2×C4×D4712yes—
575C2×D4D4×D4712yes—
576C2×D4#1062535212yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—81no—
588C22×C4—81no—
589C22×C4—941no—
590C22×C4—941no—
591C22×C4—941no—
592C22×C4—941no—
593C22×C4—3761no—
594C22×C4—1882no—
595C22×C4—1882no—
596C22×C4C2×C4×D4712yes—
597C22×C4#1062535012yes—
598C22×C4C2×C22⋊D4711yescharacteristic
599C22×C4C2×C22⋊D4711yescharacteristic
600C22×C4C2×C22⋊D4711yescharacteristic
601C22×C4C2×C22⋊D4711yescharacteristic
602C22×C4C2×C22⋊D4711yescharacteristic
603C22×C4C23×D4711yescharacteristic
604SD16—948no—
605SD16—1884no—
606C2×C8—472no—
607C2×C8—472no—
608C2×C8—472no—
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—941no—
618C2×C8—1884no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—472no—
624C4⋊C4—472no—
625C4⋊C4—944no—
626C4⋊C4—941no—
627C4⋊C4—941no—
628C4⋊C4—941no—
629C4⋊C4—941no—
630C4⋊C4—3761no—
631C4⋊C4—1882no—
632C4⋊C4—1882no—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—81no—
641C22⋊C4—81no—
642C22⋊C4—944no—
643C42—21no—
644C42—21no—
645C42—21no—
646C42—21no—
647C42—3761no—
648C42—1882no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—48no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—48no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—84no—
670C23—84no—
671C23—84no—
672C23—84no—
673C23—84no—
674C23C4×C22⋊D4712yes—
675C23#1309405012yes—
676C23#1309405412yes—
677C23C22×C22⋊D4711yescharacteristic
678Q8—942no—
679Q8—942no—
680Q8—1881no—
681Q8—1881no—
682D4—22no—
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—48no—
688D4—41no—
689D4—41no—
690D4(C22⋊D47)⋊C414yes—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—84no—
716C2×C4—84no—
717C2×C4—942no—
718C2×C4—942no—
719C2×C4—942no—
720C2×C4—3764no—
721C2×C4—1881no—
722C2×C4—1881no—
723C2×C4—1881no—
724C2×C4—1881no—
725C2×C4—1881no—
726C2×C4—1881no—
727C2×C4—1881no—
728C2×C4—1881no—
729C2×C4—1881no—
730C2×C4C4×C22⋊D4712yes—
731C2×C4C22×C4×D4711yescharacteristic
732C2×C4C2×D4×D4711yescharacteristic
733C2×C4C2×#1062535211yescharacteristic
734C2×C4C2×#1062535011yescharacteristic
735C2×C4#1309406911yescharacteristic
736C2×C4#1309406911yescharacteristic
737C8—942no—
738C8—942no—
739C8—942no—
740C8—1881no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—24no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—816no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22#1568922314yescomplemented
763C22C2×C4×C22⋊D4711yescharacteristic
764C22D4×C22⋊D4711yescharacteristic
765C22#1568976711yescharacteristic
766C22C2×#1309405011yescharacteristic
767C22C2×#1309405411yescharacteristic
768C22#1568992611yescharacteristic
769C22#1568993411yescharacteristic
770C4—22no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—81no—
776C4—81no—
777C4—3761no—
778C4—1882no—
779C4—1882no—
780C4—1882no—
781C4C2×(C22⋊D47)⋊C411yescharacteristic
782C4#1568959611yescharacteristic
783C4#1568976311yescharacteristic
784C4#1568979911yescharacteristic
785C2—24no—
786C2—44no—
787C2—82no—
788C2#2024636711yescharacteristic
789C2C2×#1568922311yescharacteristic
790C2#2025222011yescharacteristic
791C2#2025486411yescharacteristic
792C2#2025489411yescharacteristic
793C2#2025540911yescharacteristic
794C2#2025546911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingD4×C22⋊C4×C47C2
socleC23×C47C22×D4
prime radicalC23×D4×C47C22
cosocleC22×C4×C47C24
hypercenterD4×C22⋊C4D47
hypocenterC47#22854
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#15689223C2semidirect
4. #20246391C2semidirect
5. #20244268C2semidirect
6. #20244088C2semidirect
7. #20244005C2semidirect
8. #20243809C2semidirect
9. #20243746C2semidirect
10. #20243722C2semidirect
11. #20243635C2semidirect
12. #20243575C2semidirect
13. #20243213C2semidirect
14. #20243166C2semidirect
20. C2×C4×Dic94C22semidirect
22. #15689274C4semidirect
24. C2×#13093957C22semidirect
25. C2×#13093957C22semidirect
26. C2×#13093947C22semidirect
27. C2×#13093947C22semidirect
36. C2×#13093935C22semidirect
37. C2×#13093935C22semidirect
38. #15689029C22semidirect
39. #15689021C22semidirect
43. C4×C4⋊Dic47C22semidirect
45. #15688885C22semidirect
46. #15688885C22semidirect
47. #15688885C22semidirect
48. #15688885C22semidirect
49. #15688878C22semidirect
50. #15688878C22semidirect
68. C2×#10625335C2×C4semidirect
69. C2×#10625335C2×C4semidirect
78. #13094003C2×C4semidirect
100. #13093945C2×C4semidirect
101. #13093945C2×C4semidirect
103. C22⋊(C47⋊C8)C2×C4semidirect
365. C22×C47#440semidirect
459. C47#22854semidirect
762. C22#15689223semidirect

Maximal subgroups

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

subgroupindex
C2×#156892742
C2×#156892232
C22×#130939452
#202463912
#202442682
#202440882
#202440052
#202438092
#202437462
#202437222
#202436352
#202435752
#202432132
#202431662
D4×C22⋊C4×C472
#2285447