Finite Group Databasebeta

← #26137853

Subgroups — #26137853

Order 12032.

1778 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689018C212yesmaximal
2C2×C4×Dic47⋊C4C212yesmaximal
3C2×C4×Dic47⋊C4C211yesmaximal, characteristic
4C2×#15688974C211yesmaximal, characteristic
5#20241621C212yesmaximal
6#20241620C212yesmaximal
7Dic47⋊#95C211yesmaximal, characteristic
8#20241615C211yesmaximal, characteristic
9#20241612C211yesmaximal, characteristic
10#95×Dic47C211yesmaximal, characteristic
11C2×C4×C4⋊C4×C47C211yesmaximal, characteristic
12C22×Dic47⋊C4C2212yes—
13C22×Dic47⋊C4C2212yes—
14C22×Dic47⋊C4C2211yescharacteristic
15C22×Dic47⋊C4C2211yescharacteristic
16C22×C4×Dic47C2212yes—
17C22×C4×Dic47C2212yes—
18C22×C4×Dic47C2211yescharacteristic
19C22×C4×Dic47C2211yescharacteristic
20#15689018C4116yescomplemented
21C4×Dic47⋊C4—28no—
22C4×Dic47⋊C4C418yescomplemented
23#15688974—24no—
24C2×C47⋊#95C2211yescharacteristic
25C2×C47⋊#95C2212yes—
26C2×C47⋊#95C2212yes—
27C2×C47⋊#95C2211yescharacteristic
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2211yescharacteristic
33C2×C47⋊#95C2211yescharacteristic
34C22×C4⋊C4×C47C2212yes—
35C22×C42×C47C2212yes—
36C22×C42×C47C2211yescharacteristic
37C4×C4⋊C4×C47—24no—
38C2×#95×C47C2211yescharacteristic
39C2×#95×C47C2211yescharacteristic
40C23×Dic47C2312yes—
41C23×Dic47C2311yescharacteristic
42C23×Dic47C2312yes—
43C23×Dic47C2311yescharacteristic
44C23×Dic47C2311yescharacteristic
45C23×Dic47C2311yescharacteristic
46C2×Dic47⋊C4—24no—
47C2×Dic47⋊C4—24no—
48C2×Dic47⋊C4—24no—
49C2×Dic47⋊C4—24no—
50C2×Dic47⋊C4C2×C418yes—
51C2×Dic47⋊C4C2×C418yes—
52C2×Dic47⋊C4C2×C414yes—
53C2×Dic47⋊C4C2×C418yes—
54C2×Dic47⋊C4C2×C414yes—
55C2×Dic47⋊C4D414yes—
56C2×Dic47⋊C4Q814yes—
57C2×C4×Dic47—22no—
58C2×C4×Dic47—22no—
59C2×C4×Dic47—24no—
60C2×C4×Dic47—24no—
61C2×C4×Dic47—24no—
62C2×C4×Dic47—24no—
63C2×C4×Dic47—24no—
64C2×C4×Dic47—42no—
65C2×C4×Dic47C2×C414yes—
66C2×C4×Dic47C2×C414yes—
67C2×C4×Dic47C2×C418yes—
68C47⋊#95—22no—
69C47⋊#95—24no—
70C47⋊#95—22no—
71C47⋊#95—24no—
72C47⋊#95—24no—
73C47⋊#95—42no—
74C47⋊#95C2×C414yes—
75C47⋊#95C2×C414yes—
76C47⋊#95C2×C418yes—
77C47⋊#95C2×C418yes—
78C23×C4×C47C2312yes—
79C23×C4×C47C2311yescharacteristic
80C23×C4×C47C2311yescharacteristic
81C23×C4×C47C2311yescharacteristic
82C23×C4×C47C2312yes—
83C2×C4⋊C4×C47—24no—
84C2×C4⋊C4×C47—24no—
85C2×C4⋊C4×C47C2×C418yes—
86C2×C42×C47—22no—
87C2×C42×C47—22no—
88C2×C42×C47—24no—
89C2×C42×C47—24no—
90C2×C42×C47—42no—
91C2×C42×C47C2×C414yes—
92#95×C47—22no—
93#95×C47D414yes—
94C24×C47C2411yescharacteristic
95C22×C4×C47—21no—
96C22×C4×C47—21no—
97C22×C4×C47—22no—
98C22×C4×C47—21no—
99C22×C4×C47—21no—
100C22×C4×C47—22no—
101C22×C4×C47—22no—
102C22×C4×C47—22no—
103C22×C4×C47—21no—
104C22×C4×C47—22no—
105C22×C4×C47—22no—
106C22×C4×C47—22no—
107C22×C4×C47—21no—
108C22×C4×C47—22no—
109C22×C4×C47—22no—
110C22×C4×C47—22no—
111C22×C4×C47—22no—
112C22×C4×C47—22no—
113C22×C4×C47—22no—
114C22×C4×C47C22×C414yes—
115C22×C4×C47C22×C412yes—
116C22×C4×C47C22×C414yes—
117C22×C4×C47C22×C412yes—
118C22×C4×C47C22×C412yes—
119C22×C4×C47C22×C414yes—
120C22×C4×C47C2×D412yes—
121C22×C4×C47C2×D414yes—
122C22×C4×C47C2×D412yes—
123C22×C4×C47C2×Q812yes—
124C22×C4×C47#4112yes—
125C22×C4×C47#4114yes—
126C22×Dic47—21no—
127C22×Dic47—21no—
128C22×Dic47—21no—
129C22×Dic47—21no—
130C22×Dic47—22no—
131C22×Dic47—21no—
132C22×Dic47—21no—
133C22×Dic47—22no—
134C22×Dic47—22no—
135C22×Dic47—22no—
136C22×Dic47—22no—
137C22×Dic47—22no—
138C22×Dic47—22no—
139C22×Dic47—22no—
140C22×Dic47—22no—
141C22×Dic47—22no—
142C22×Dic47—22no—
143C22×Dic47—21no—
144C22×Dic47—22no—
145C22×Dic47—22no—
146C22×Dic47—22no—
147C22×Dic47—22no—
148C22×Dic47—21no—
149C22×Dic47C22×C412yes—
150C22×Dic47C22×C414yes—
151C22×Dic47C22×C414yes—
152C22×Dic47C22×C412yes—
153C22×Dic47C22×C414yes—
154C22×Dic47C22×C412yes—
155C22×Dic47C22×C412yes—
156C22×Dic47C22×C414yes—
157C22×Dic47C2×D412yes—
158C22×Dic47C2×D412yes—
159C22×Dic47C2×Q812yes—
160C22×Dic47C2×Q812yes—
161C22×Dic47#4114yes—
162C4⋊C4×C47—216no—
163C42×C47—28no—
164C42×C47—48no—
165Dic47⋊C4—216no—
166Dic47⋊C4—216no—
167Dic47⋊C4C42116yescomplemented
168Dic47⋊C4C4⋊C4116yescomplemented
169C4×Dic47—28no—
170C4×Dic47—28no—
171C4×Dic47—216no—
172C4×Dic47—48no—
173C23×C47C23×C411yescharacteristic
174C23×C47C23×C412yes—
175C23×C47C22×D411yescharacteristic
176C23×C47C22×D411yescharacteristic
177C23×C47C22×Q811yescharacteristic
178C23×C47C2×#4112yes—
179C23×C47C2×#4111yescharacteristic
180C23×C47C2×#4112yes—
181C23×C47H(5,𝔽2)11yescharacteristic
182C23×C472−1+412yes—
183C23×C472−1+411yescharacteristic
184C2×C4×C47—22no—
185C2×C4×C47—24no—
186C2×C4×C47—22no—
187C2×C4×C47—22no—
188C2×C4×C47—24no—
189C2×C4×C47—22no—
190C2×C4×C47—24no—
191C2×C4×C47—22no—
192C2×C4×C47—24no—
193C2×C4×C47—22no—
194C2×C4×C47—24no—
195C2×C4×C47—22no—
196C2×C4×C47—24no—
197C2×C4×C47—24no—
198C2×C4×C47—22no—
199C2×C4×C47—24no—
200C2×C4×C47—22no—
201C2×C4×C47—24no—
202C2×C4×C47—24no—
203C2×C4×C47—22no—
204C2×C4×C47—24no—
205C2×C4×C47—24no—
206C2×C4×C47—24no—
207C2×C4×C47—42no—
208C2×C4×C47—42no—
209C2×C4×C47—42no—
210C2×C4×C47—42no—
211C2×C4×C47C2×C4214yes—
212C2×C4×C47C2×C4⋊C414yes—
213C2×C4×C47C4×D414yes—
214C2×C4×C47C4×D418yes—
215C2×Dic47—22no—
216C2×Dic47—22no—
217C2×Dic47—24no—
218C2×Dic47—22no—
219C2×Dic47—24no—
220C2×Dic47—22no—
221C2×Dic47—22no—
222C2×Dic47—22no—
223C2×Dic47—22no—
224C2×Dic47—22no—
225C2×Dic47—22no—
226C2×Dic47—24no—
227C2×Dic47—24no—
228C2×Dic47—24no—
229C2×Dic47—22no—
230C2×Dic47—24no—
231C2×Dic47—24no—
232C2×Dic47—24no—
233C2×Dic47—22no—
234C2×Dic47—42no—
235C2×Dic47—42no—
236C2×Dic47—42no—
237C2×Dic47—42no—
238C2×Dic47—42no—
239C2×Dic47—42no—
240C2×Dic47—42no—
241C2×Dic47—42no—
242C2×Dic47—42no—
243C2×Dic47—42no—
244C2×Dic47C2×C4214yes—
245C2×Dic47C2×C4214yes—
246C2×Dic47C2×C4⋊C414yes—
247C2×Dic47C2×C4⋊C414yes—
248C2×Dic47#11714yes—
249C2×Dic47C4×D418yes—
250C2×Dic47C4×Q818yes—
251#13821—471nomaximal, Sylow
252C22×C47C22×C4211yescharacteristic
253C22×C47C22×C4⋊C411yescharacteristic
254C22×C47C2×#11711yescharacteristic
255C22×C47C2×C4×D412yes—
256C22×C47C2×C4×D411yescharacteristic
257C22×C47C2×C4×D412yes—
258C22×C47C2×C4×Q812yes—
259C22×C47C4×#4111yescharacteristic
260C22×C47C4×#4112yes—
261C22×C47#51912yes—
262C22×C47#51911yescharacteristic
263C22×C47#52012yes—
264C22×C47#52011yescharacteristic
265C22×C47D4211yescharacteristic
266C22×C47#54712yes—
267C22×C47#54711yescharacteristic
268C22×C47#54812yes—
269C22×C47D4×Q811yescharacteristic
270C22×C47#55212yes—
271C22×C47#55312yes—
272C22×C47#55411yescharacteristic
273C22×C47#55612yes—
274C22×C47#55712yes—
275C4×C47—24no—
276C4×C47—24no—
277C4×C47—28no—
278C4×C47—24no—
279C4×C47—44no—
280Dic47—24no—
281Dic47—24no—
282Dic47—42no—
283Dic47—44no—
284Dic47—44no—
285Dic47C4×C4⋊C418yescomplemented
286C2×#389—472no—
287C2×C4×C4⋊C4—471no—
288C2×C4×C4⋊C4—472no—
289C2×C4×C4⋊C4—471no—
290C2×C4×C4⋊C4D4711yescharacteristic
291#1436—472no—
292#1436—472no—
293C4⋊#95—471no—
294#1434—471no—
295#1434—471no—
296C4×#95—471no—
297C2×C47C2×C4×C4⋊C411yescharacteristic
298C2×C47C42×D411yescharacteristic
299C2×C47#227611yescharacteristic
300C2×C47#234411yescharacteristic
301C2×C47#234711yescharacteristic
302C2×C47D4×C4⋊C411yescharacteristic
303C2×C47#235111yescharacteristic
304C2×C47#236112yes—
305C2×C47#236212yes—
306C2×C47#236512yes—
307C2×C47#237012yes—
308C22×C4⋊C4—471no—
309C22×C4⋊C4—471no—
310C22×C4⋊C4—472no—
311C22×C4⋊C4—472no—
312C22×C4⋊C4C2×D4712yes—
313C22×C42—471no—
314C22×C42—472no—
315C22×C42—471no—
316C22×C42—472no—
317C22×C42C2×D4712yes—
318C22×C42C2×D4711yescharacteristic
319#389—4716no—
320C4×C4⋊C4—24no—
321C4×C4⋊C4—478no—
322C4×C4⋊C4—948no—
323C4×C4⋊C4—944no—
324C2×#95—472no—
325C2×#95—472no—
326C2×#95—471no—
327C2×#95—471no—
328C2×#95—471no—
329C2×#95—472no—
330C2×#95—471no—
331C2×#95—472no—
332C2×#95—472no—
333C2×#95—472no—
334C2×#95C2×D4711yescharacteristic
335C2×#95C2×D4711yescharacteristic
336C47#1382111yescharacteristic, complemented, Sylow
337C23×C4—471no—
338C23×C4—471no—
339C23×C4—471no—
340C23×C4—472no—
341C23×C4—472no—
342C23×C4—471no—
343C23×C4C22×D4712yes—
344C23×C4C22×D4711yescharacteristic
345C23×C4C22×D4712yes—
346C23×C4C22×D4711yescharacteristic
347C23×C4C22×D4711yescharacteristic
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—474no—
351C2×C4⋊C4—474no—
352C2×C4⋊C4—478no—
353C2×C4⋊C4—474no—
354C2×C4⋊C4—474no—
355C2×C4⋊C4—478no—
356C2×C4⋊C4—478no—
357C2×C4⋊C4—944no—
358C2×C4⋊C4—944no—
359C2×C4⋊C4—944no—
360C2×C4⋊C4—944no—
361C2×C4⋊C4C4×D4718yes—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—24no—
365C2×C42—24no—
366C2×C42—42no—
367C2×C42—474no—
368C2×C42—474no—
369C2×C42—478no—
370C2×C42—944no—
371C2×C42—944no—
372C2×C42—944no—
373C2×C42—942no—
374C2×C42—942no—
375C2×C42—944no—
376C2×C42—944no—
377C2×C42—1882no—
378C2×C42C4×D4714yes—
379#95—22no—
380#95—474no—
381#95—474no—
382#95—478no—
383#95—478no—
384#95—944no—
385#95—942no—
386#95—944no—
387#95—944no—
388#95—942no—
389#95—1882no—
390#95C22⋊D4714yes—
391C24C23×D4711yescharacteristic
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—472no—
412C22×C4—474no—
413C22×C4—472no—
414C22×C4—472no—
415C22×C4—474no—
416C22×C4—472no—
417C22×C4—472no—
418C22×C4—474no—
419C22×C4—472no—
420C22×C4—472no—
421C22×C4—472no—
422C22×C4—474no—
423C22×C4—474no—
424C22×C4—941no—
425C22×C4—941no—
426C22×C4—941no—
427C22×C4—941no—
428C22×C4—942no—
429C22×C4—941no—
430C22×C4—941no—
431C22×C4—942no—
432C22×C4—942no—
433C22×C4—942no—
434C22×C4—942no—
435C22×C4—942no—
436C22×C4—942no—
437C22×C4—942no—
438C22×C4—942no—
439C22×C4—942no—
440C22×C4—942no—
441C22×C4—941no—
442C22×C4—942no—
443C22×C4—942no—
444C22×C4—942no—
445C22×C4—942no—
446C22×C4—941no—
447C22×C4C2×C4×D4714yes—
448C22×C4C2×C4×D4712yes—
449C22×C4C2×C4×D4714yes—
450C22×C4C2×C4×D4712yes—
451C22×C4C2×C4×D4712yes—
452C22×C4C2×C4×D4714yes—
453C22×C4#1062535012yes—
454C22×C4#1062535014yes—
455C22×C4D4×D4712yes—
456C22×C4Q8×D4712yes—
457C22×C4C2×C22⋊D4712yes—
458C22×C4C2×C22⋊D4714yes—
459C4⋊C4—216no—
460C4⋊C4—4716no—
461C4⋊C4—4716no—
462C4⋊C4—9416no—
463C4⋊C4—9416no—
464C42—28no—
465C42—48no—
466C42—948no—
467C42—9416no—
468C42—948no—
469C42—1888no—
470C23C22×C4×D4711yescharacteristic
471C23C22×C4×D4712yes—
472C23C2×D4×D4711yescharacteristic
473C23C22×C22⋊D4711yescharacteristic
474C23C2×Q8×D4711yescharacteristic
475C23#41×D4712yes—
476C23C2×#1062535011yescharacteristic
477C23C2×#1062535012yes—
478C23#1309406911yescharacteristic
479C23#1309407112yes—
480C23#1309407211yescharacteristic
481C2×C4—22no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—24no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—22no—
497C2×C4—24no—
498C2×C4—22no—
499C2×C4—24no—
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—474no—
509C2×C4—474no—
510C2×C4—474no—
511C2×C4—478no—
512C2×C4—478no—
513C2×C4—474no—
514C2×C4—474no—
515C2×C4—942no—
516C2×C4—942no—
517C2×C4—942no—
518C2×C4—942no—
519C2×C4—942no—
520C2×C4—942no—
521C2×C4—944no—
522C2×C4—942no—
523C2×C4—944no—
524C2×C4—942no—
525C2×C4—942no—
526C2×C4—944no—
527C2×C4—944no—
528C2×C4—944no—
529C2×C4—942no—
530C2×C4—944no—
531C2×C4—944no—
532C2×C4—944no—
533C2×C4—942no—
534C2×C4—1882no—
535C2×C4—1882no—
536C2×C4—1882no—
537C2×C4—1882no—
538C2×C4—1882no—
539C2×C4—1882no—
540C2×C4—1882no—
541C2×C4—1882no—
542C2×C4—1882no—
543C2×C4—1882no—
544C2×C4C42×D4714yes—
545C2×C4C4⋊C4×D4714yes—
546C2×C4C4×C22⋊D4714yes—
547C2×C4C4×C22⋊D4718yes—
548C22C2×C42×D4711yescharacteristic
549C22C2×C4⋊C4×D4711yescharacteristic
550C22#117×D4711yescharacteristic
551C22C4×D4×D4712yes—
552C22C2×C4×C22⋊D4711yescharacteristic
553C22C2×C4×C22⋊D4712yes—
554C22C4×Q8×D4712yes—
555C22C4×#1062535011yescharacteristic
556C22C4×#1062535012yes—
557C22#1568959912yes—
558C22#1568960011yescharacteristic
559C22#1568960212yes—
560C22#1568960411yescharacteristic
561C22D4×C22⋊D4711yescharacteristic
562C22#1568977212yes—
563C22#1568977411yescharacteristic
564C22#1568978212yes—
565C22Q8×C22⋊D4711yescharacteristic
566C22#1568980612yes—
567C22#1568982212yes—
568C22#1568982811yescharacteristic
569C22#1568984512yes—
570C22#1568985112yes—
571C4—24no—
572C4—28no—
573C4—24no—
574C4—24no—
575C4—44no—
576C4—478no—
577C4—944no—
578C4—944no—
579C4—1882no—
580C4—1884no—
581C4—1884no—
582C2C4×C4⋊C4×D4711yescharacteristic
583C2C42×C22⋊D4711yescharacteristic
584C2#2024575211yescharacteristic
585C2#2024625811yescharacteristic
586C2#2024628211yescharacteristic
587C2C4⋊C4×C22⋊D4711yescharacteristic
588C2#2024630811yescharacteristic
589C2#2024640512yes—
590C2#2024641612yes—
591C2#2024644212yes—
592C2#2024648512yes—
subgroupG/H
center, FrattiniC24C23×D47
commutatorC22×C47C22×C42
FittingC2×C4×C4⋊C4×C47C2
socle, prime radical, cosocleC24×C47C24
hypercenterC2×C4×C4⋊C4D47
hypocenterC47#13821
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
20. #15689018C4semidirect
22. C4×Dic47⋊C4C4semidirect
167. Dic47⋊C4C42semidirect
168. Dic47⋊C4C4⋊C4semidirect
285. Dic47C4×C4⋊C4semidirect
336. C47#13821semidirect

Maximal subgroups

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

subgroupindex
C2×#156890182
C2×C4×Dic47⋊C42
C2×#156889742
#202416212
#202416202
Dic47⋊#952
#202416152
#202416122
#95×Dic472
C2×C4×C4⋊C4×C472
#1382147