Finite Group Databasebeta

← #26138612

Subgroups — #26138612

Order 12032.

2314 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093986C211yesmaximal, characteristic
2C2×#15689025C211yesmaximal, characteristic
3C2×#15689024C211yesmaximal, characteristic
4C2×#15688985C212yesmaximal, complemented
5#20241636C212yesmaximal, complemented
6#20241636C212yesmaximal, complemented
7#20241617C211yesmaximal, characteristic, complemented
8#20241617C211yesmaximal, characteristic, complemented
9(C2×D47)⋊#95C212yesmaximal, complemented
10C4×C47⋊#95C211yesmaximal, characteristic, complemented
11C47×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×D188C2211yescharacteristic
13C23×C4×D47C2212yes—
14C2×#13093986—24no—
15C2×#13093986—24no—
16C2×#13093986C418yescomplemented
17C22×C4⋊Dic47C2211yescharacteristic
18C22×(C2×D47)⋊C4C2212yes—
19C22×(C2×D47)⋊C4C2212yes—
20C22×(C2×D47)⋊C4C2212yes—
21C22×(C2×D47)⋊C4C2212yes—
22C22×(C2×D47)⋊C4C2212yes—
23C22×C4×Dic47C2211yescharacteristic
24C22×C4×Dic47C2211yescharacteristic
25#15689025—24no—
26#15689024—24no—
27#15688985—28no—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2211yescharacteristic
31C2×C47⋊#95C2211yescharacteristic
32C2×C47⋊#95C2211yescharacteristic
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35C2×C47⋊#95C2211yescharacteristic
36C22×C4⋊C4×C47C2211yescharacteristic
37C22×C4⋊C4×C47C2211yescharacteristic
38C22×C42×C47C2211yescharacteristic
39C2×#95×C47C2212yes—
40C2×#95×C47C2212yes—
41C24×D47C2312yes—
42C22×D188—22no—
43C22×D188—22no—
44C22×D188—22no—
45C22×D188—22no—
46C22×D188C2×C414yes—
47C22×D188D414yes—
48C22×D188D414yes—
49C23×Dic47C2312yes—
50C23×Dic47C2311yescharacteristic
51C23×Dic47C2311yescharacteristic
52C23×Dic47C2311yescharacteristic
53C23×Dic47C2311yescharacteristic
54C22×C4×D47—24no—
55C22×C4×D47—24no—
56C22×C4×D47—24no—
57C22×C4×D47—24no—
58C22×C4×D47—42no—
59C22×C4×D47—42no—
60C22×C4×D47C2×C418yes—
61#13093986—232no—
62C2×C4⋊Dic47—22no—
63C2×C4⋊Dic47—22no—
64C2×C4⋊Dic47—22no—
65C2×(C2×D47)⋊C4—24no—
66C2×(C2×D47)⋊C4—24no—
67C2×(C2×D47)⋊C4—24no—
68C2×(C2×D47)⋊C4—24no—
69C2×(C2×D47)⋊C4—24no—
70C2×(C2×D47)⋊C4—24no—
71C2×(C2×D47)⋊C4—24no—
72C2×(C2×D47)⋊C4—24no—
73C2×(C2×D47)⋊C4—24no—
74C2×(C2×D47)⋊C4—24no—
75C2×(C2×D47)⋊C4—42no—
76C2×(C2×D47)⋊C4—42no—
77C2×(C2×D47)⋊C4—42no—
78C2×(C2×D47)⋊C4—42no—
79C2×(C2×D47)⋊C4C2×C418yes—
80C2×C4×Dic47—22no—
81C2×C4×Dic47—22no—
82C2×C4×Dic47—22no—
83C2×C4×Dic47—22no—
84C2×C4×Dic47—22no—
85C2×C4×Dic47C2×C414yes—
86C47⋊#95—22no—
87C47⋊#95—24no—
88C47⋊#95—24no—
89C47⋊#95—22no—
90C47⋊#95—22no—
91C47⋊#95—42no—
92C47⋊#95—42no—
93C47⋊#95D414yescomplemented
94C23×C4×C47C2312yes—
95C23×C4×C47C2312yes—
96C23×C4×C47C2311yescharacteristic
97C23×C4×C47C2311yescharacteristic
98C23×C4×C47C2311yescharacteristic
99C2×C4⋊C4×C47—22no—
100C2×C4⋊C4×C47—22no—
101C2×C4⋊C4×C47—22no—
102C2×C4⋊C4×C47—22no—
103C2×C4⋊C4×C47—22no—
104C2×C4⋊C4×C47C2×C414yes—
105C2×C42×C47—22no—
106C2×C42×C47—22no—
107C2×C42×C47—22no—
108#95×C47—24no—
109#95×C47—42no—
110C24×C47C2411yescharacteristic
111C23×D47—22no—
112C23×D47—22no—
113C23×D47—22no—
114C23×D47—22no—
115C23×D47—22no—
116C23×D47—22no—
117C23×D47—22no—
118C23×D47—22no—
119C23×D47—22no—
120C23×D47—22no—
121C23×D47—22no—
122C23×D47—22no—
123C23×D47C22×C414yes—
124C23×D47C2×D414yes—
125C23×D47C2×D414yes—
126C22×C4×C47—21no—
127C22×C4×C47—21no—
128C22×C4×C47—22no—
129C22×C4×C47—22no—
130C22×C4×C47—22no—
131C22×C4×C47—21no—
132C22×C4×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
137C22×C4×C47—22no—
138C22×C4×C47—22no—
139C22×C4×C47—21no—
140C22×C4×C47—21no—
141C22×C4×C47—22no—
142C22×C4×C47—21no—
143C22×C4×C47—21no—
144C22×C4×C47—22no—
145C22×C4×C47—22no—
146C22×C4×C47—22no—
147C22×C4×C47—22no—
148C22×C4×C47—22no—
149C22×C4×C47—22no—
150C22×C4×C47—22no—
151C22×C4×C47C22×C414yes—
152C22×C4×C47C22×C412yes—
153C22×C4×C47C2×D412yes—
154C22×C4×C47C2×D412yes—
155C22×C4×C47C2×D412yes—
156C22×C4×C47#4112yes—
157C22×C4×C47#4112yes—
158C22×C4×C47#4112yes—
159C22×C4×C47#4112yes—
160C22×C4×C47#4112yes—
161C22×Dic47—21no—
162C22×Dic47—21no—
163C22×Dic47—21no—
164C22×Dic47—21no—
165C22×Dic47—21no—
166C22×Dic47—21no—
167C22×Dic47—21no—
168C22×Dic47—21no—
169C22×Dic47—21no—
170C22×Dic47—21no—
171C22×Dic47—21no—
172C22×Dic47—21no—
173C22×Dic47—21no—
174C22×Dic47—21no—
175C22×Dic47—21no—
176C22×Dic47—21no—
177C22×Dic47—21no—
178C22×Dic47—21no—
179C22×Dic47—21no—
180C22×Dic47—21no—
181C22×Dic47—21no—
182C22×Dic47—21no—
183C22×Dic47—22no—
184C22×Dic47—22no—
185C22×Dic47—22no—
186C22×Dic47—22no—
187C22×Dic47—22no—
188C22×Dic47—22no—
189C22×Dic47—22no—
190C22×Dic47C22×C412yes—
191C22×Dic47C22×C412yes—
192C22×Dic47C2×D412yes—
193C22×Dic47C2×D412yes—
194C22×Dic47#4112yes—
195C22×Dic47#4112yes—
196C2×D188—28no—
197C2×D188—28no—
198C2×D188—28no—
199C2×D188—28no—
200C2×D188—28no—
201C2×D188—28no—
202C2×D188C22⋊C4116yes—
203C2×C4×D47—216no—
204C2×C4×D47—216no—
205C2×C4×D47—48no—
206C2×C4×D47—48no—
207C2×C4×D47—48no—
208C2×C4×D47—48no—
209C2×C4×D47—48no—
210C4⋊C4×C47—28no—
211C4⋊C4×C47—44no—
212C42×C47—44no—
213(C2×D47)⋊C4—216no—
214(C2×D47)⋊C4—48no—
215(C2×D47)⋊C4—48no—
216(C2×D47)⋊C4—48no—
217(C2×D47)⋊C4—48no—
218C4⋊Dic47—44no—
219C4×Dic47—28no—
220C4×Dic47—44no—
221C23×C47C23×C411yescharacteristic
222C23×C47C22×D411yescharacteristic
223C23×C47C22×D411yescharacteristic
224C23×C47C22×D411yescharacteristic
225C23×C47C2×#4111yescharacteristic
226C23×C47C2×#4111yescharacteristic
227C23×C47C2×#4111yescharacteristic
228C23×C47C2×#4111yescharacteristic
229C23×C47C2×#4111yescharacteristic
230C23×C47C2×#4111yescharacteristic
231C23×C47C2×#4111yescharacteristic
232C23×C47H(5,𝔽2)11yescharacteristic
233C23×C47H(5,𝔽2)11yescharacteristic
234C23×C47H(5,𝔽2)11yescharacteristic
235C23×C472−1+411yescharacteristic
236C22×D47—24no—
237C22×D47—24no—
238C22×D47—24no—
239C22×D47—24no—
240C22×D47—24no—
241C22×D47—24no—
242C22×D47—24no—
243C22×D47—24no—
244C22×D47—24no—
245C22×D47—24no—
246C22×D47—24no—
247C22×D47—24no—
248C22×D47—24no—
249C22×D47—24no—
250C22×D47—24no—
251C22×D47—24no—
252C22×D47—24no—
253C22×D47—24no—
254C22×D47—42no—
255C22×D47—42no—
256C22×D47—42no—
257C22×D47—42no—
258C22×D47—42no—
259C22×D47—42no—
260C22×D47—42no—
261C22×D47—42no—
262C22×D47—42no—
263C22×D47—42no—
264C22×D47—42no—
265C22×D47—42no—
266C22×D47—42no—
267C22×D47—42no—
268C22×D47—42no—
269C22×D47—42no—
270C22×D47C2×C22⋊C418yes—
271C2×C4×C47—24no—
272C2×C4×C47—24no—
273C2×C4×C47—24no—
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—41no—
281C2×C4×C47—41no—
282C2×C4×C47—41no—
283C2×C4×C47—41no—
284C2×C4×C47—42no—
285C2×C4×C47—42no—
286C2×C4×C47—42no—
287C2×C4×C47—42no—
288C2×C4×C47—41no—
289C2×C4×C47—41no—
290C2×C4×C47—41no—
291C2×C4×C47—41no—
292C2×C4×C47—42no—
293C2×C4×C47—42no—
294C2×C4×C47—42no—
295C2×C4×C47—42no—
296C2×C4×C47—42no—
297C2×C4×C47—42no—
298C2×C4×C47—42no—
299C2×C4×C47C2×C22⋊C414yes—
300C2×C4×C47#11714yes—
301C2×C4×C47#11714yes—
302C2×C4×C47#12314yes—
303C2×C4×C47#12314yes—
304C2×C4×C47#12314yes—
305C2×C4×C47#12314yes—
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—41no—
322C2×Dic47—41no—
323C2×Dic47—41no—
324C2×Dic47—41no—
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—42no—
334C2×Dic47—42no—
335C2×Dic47—42no—
336C2×Dic47—42no—
337C2×Dic47—42no—
338C2×Dic47—42no—
339C2×Dic47—42no—
340C2×Dic47C4×D414yes—
341D188—232no—
342C4×D47—432no—
343#13916—471nomaximal, Sylow
344C22×C47C22×C22⋊C411yescharacteristic
345C22×C47C2×#11711yescharacteristic
346C22×C47C2×#11711yescharacteristic
347C22×C47C2×C4×D411yescharacteristic
348C22×C47C4×#4111yescharacteristic
349C22×C47#51811yescharacteristic
350C22×C47#52011yescharacteristic
351C22×C47C2×#12311yescharacteristic
352C22×C47C2×#12311yescharacteristic
353C22×C47C2×#12311yescharacteristic
354C22×C47C2×#12311yescharacteristic
355C22×C47#52911yescharacteristic
356C22×C47#52911yescharacteristic
357C22×C47#53211yescharacteristic
358C22×C47#53211yescharacteristic
359C22×C47#54011yescharacteristic
360C22×C47#54011yescharacteristic
361C22×C47#54211yescharacteristic
362C22×C47#54211yescharacteristic
363C22×C47D4211yescharacteristic
364C22×C47D4211yescharacteristic
365C22×C47#54611yescharacteristic
366C22×C47#54611yescharacteristic
367C22×C47#54611yescharacteristic
368C22×C47#54611yescharacteristic
369C22×C47#54711yescharacteristic
370C22×C47#54711yescharacteristic
371C22×C47#54711yescharacteristic
372C22×C47#55011yescharacteristic
373C22×C47#55311yescharacteristic
374C22×C47#55311yescharacteristic
375C22×C47#55511yescharacteristic
376C22×C47#55611yescharacteristic
377C22×C47#55911yescharacteristic
378C22×C47#55911yescharacteristic
379C2×D47—28no—
380C2×D47—28no—
381C2×D47—28no—
382C2×D47—44no—
383C2×D47—44no—
384C2×D47—44no—
385C2×D47—44no—
386C2×D47—44no—
387C2×D47—44no—
388C2×D47—44no—
389C2×D47—44no—
390C2×D47—44no—
391C2×D47—44no—
392C2×D47—44no—
393C2×D47—44no—
394C4×C47—44no—
395C4×C47—42no—
396C4×C47—42no—
397C4×C47—82no—
398C4×C47#38118yescomplemented
399Dic47—24no—
400Dic47—42no—
401Dic47—42no—
402Dic47—42no—
403Dic47—82no—
404C22×C4×D4—471no—
405C2×#390—471no—
406C2×#390—471no—
407C2×#381—472no—
408#1440—472no—
409#1440—472no—
410C4⋊#95—471no—
411C4⋊#95—471no—
412C4⋊#95D4711yescharacteristic, complemented
413C22⋊#95—472no—
414C4×#95—471no—
415C2×C47C2×#38111yescharacteristic
416C2×C47#229311yescharacteristic
417C2×C47#231911yescharacteristic
418C2×C47D4×C22⋊C411yescharacteristic
419C2×C47#233911yescharacteristic
420C2×C47#235411yescharacteristic
421C2×C47#235711yescharacteristic
422C2×C47#242011yescharacteristic
423C2×C47#242011yescharacteristic
424C2×C47#242211yescharacteristic
425C2×C47#242211yescharacteristic
426C2×C47#244511yescharacteristic
427C2×C47#244511yescharacteristic
428C2×C47#244711yescharacteristic
429C2×C47#244711yescharacteristic
430D47—48no—
431C23×D4—471no—
432C24×C4—472no—
433C2×C4×D4—478no—
434C2×C4×D4—944no—
435C2×C4×D4—944no—
436C22×C4⋊C4—471no—
437C22×C4⋊C4C2×D4711yescharacteristic
438C22×C4⋊C4C2×D4711yescharacteristic
439C22×C22⋊C4—472no—
440C22×C22⋊C4—472no—
441C22×C22⋊C4—472no—
442C22×C22⋊C4—472no—
443C22×C22⋊C4—472no—
444C22×C42—471no—
445C22×C42—471no—
446C22×C42C2×D4711yescharacteristic
447#390—944no—
448#390—944no—
449#381—948no—
450C2×#95—471no—
451C2×#95—471no—
452C2×#95—471no—
453C2×#95—471no—
454C2×#95—472no—
455C2×#95—472no—
456C2×#95—472no—
457C2×#95—472no—
458C2×#95C2×D4712yes—
459C2×#95C2×D4712yes—
460C47#1391611yescharacteristic, complemented, Sylow
461C25—472no—
462C22×D4—474no—
463C22×D4—474no—
464C22×D4—474no—
465C22×D4—942no—
466C22×D4—942no—
467C22×D4—942no—
468C22×D4—942no—
469C23×C4—471no—
470C23×C4—471no—
471C23×C4—471no—
472C23×C4—471no—
473C23×C4—478no—
474C23×C4—472no—
475C23×C4—944no—
476C23×C4—944no—
477C23×C4—944no—
478C23×C4—944no—
479C23×C4—1882no—
480C23×C4—1882no—
481C23×C4C22×D4712yes—
482C23×C4C22×D4712yes—
483C23×C4C22×D4711yescharacteristic
484C23×C4C22×D4711yescharacteristic
485C23×C4C22×D4711yescharacteristic
486C4×D4—9432no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—22no—
492C2×C4⋊C4—942no—
493C2×C4⋊C4—942no—
494C2×C4⋊C4—942no—
495C2×C4⋊C4C4×D4714yes—
496C2×C22⋊C4—478no—
497C2×C22⋊C4—944no—
498C2×C22⋊C4—944no—
499C2×C22⋊C4—944no—
500C2×C22⋊C4—944no—
501C2×C22⋊C4—944no—
502C2×C22⋊C4—944no—
503C2×C22⋊C4—944no—
504C2×C22⋊C4—944no—
505C2×C22⋊C4—944no—
506C2×C22⋊C4—944no—
507C2×C22⋊C4—1882no—
508C2×C22⋊C4—1882no—
509C2×C22⋊C4—1882no—
510C2×C22⋊C4—1882no—
511C2×C42—22no—
512C2×C42—22no—
513C2×C42—22no—
514C2×C42—474no—
515C2×C42—942no—
516C2×C42—942no—
517C2×C42—942no—
518C2×C42—942no—
519C2×C42—942no—
520#95—24no—
521#95—42no—
522#95—474no—
523#95—942no—
524#95—942no—
525#95—944no—
526#95—944no—
527#95—942no—
528#95—1882no—
529#95—1882no—
530C24—474no—
531C24—474no—
532C24—474no—
533C24—942no—
534C24—942no—
535C24—942no—
536C24—942no—
537C24—942no—
538C24—942no—
539C24—942no—
540C24—942no—
541C24—942no—
542C24—942no—
543C24—942no—
544C24—942no—
545C24C23×D4711yescharacteristic
546C2×D4—4716no—
547C2×D4—948no—
548C2×D4—948no—
549C2×D4—948no—
550C2×D4—948no—
551C2×D4—948no—
552C2×D4—948no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—472no—
579C22×C4—472no—
580C22×C4—472no—
581C22×C4—472no—
582C22×C4—472no—
583C22×C4—472no—
584C22×C4—9416no—
585C22×C4—9416no—
586C22×C4—941no—
587C22×C4—941no—
588C22×C4—941no—
589C22×C4—941no—
590C22×C4—941no—
591C22×C4—941no—
592C22×C4—941no—
593C22×C4—941no—
594C22×C4—941no—
595C22×C4—941no—
596C22×C4—941no—
597C22×C4—941no—
598C22×C4—941no—
599C22×C4—941no—
600C22×C4—941no—
601C22×C4—941no—
602C22×C4—941no—
603C22×C4—941no—
604C22×C4—941no—
605C22×C4—941no—
606C22×C4—941no—
607C22×C4—941no—
608C22×C4—942no—
609C22×C4—942no—
610C22×C4—942no—
611C22×C4—942no—
612C22×C4—942no—
613C22×C4—942no—
614C22×C4—942no—
615C22×C4—1888no—
616C22×C4—1888no—
617C22×C4—1888no—
618C22×C4—1888no—
619C22×C4—1888no—
620C22×C4C2×C4×D4714yes—
621C22×C4C2×C4×D4712yes—
622C22×C4#1062535012yes—
623C22×C4#1062535012yes—
624C22×C4D4×D4712yes—
625C22×C4D4×D4712yes—
626C22×C4D4×D4712yes—
627C22×C4#1062535212yes—
628C22×C4#1062535412yes—
629C22×C4#1062535412yes—
630C4⋊C4—28no—
631C4⋊C4—44no—
632C4⋊C4—1884no—
633C22⋊C4—9416no—
634C22⋊C4—1888no—
635C22⋊C4—1888no—
636C22⋊C4—1888no—
637C22⋊C4—1888no—
638C42—44no—
639C42—948no—
640C42—1884no—
641C23—478no—
642C23—944no—
643C23—944no—
644C23—944no—
645C23—944no—
646C23—944no—
647C23—944no—
648C23—944no—
649C23—944no—
650C23—944no—
651C23—944no—
652C23—944no—
653C23—944no—
654C23—944no—
655C23—944no—
656C23—944no—
657C23—944no—
658C23—944no—
659C23—944no—
660C23—1882no—
661C23—1882no—
662C23—1882no—
663C23—1882no—
664C23—1882no—
665C23—1882no—
666C23—1882no—
667C23—1882no—
668C23—1882no—
669C23—1882no—
670C23—1882no—
671C23—1882no—
672C23—1882no—
673C23—1882no—
674C23—1882no—
675C23—1882no—
676C23C22×C4×D4711yescharacteristic
677C23C2×D4×D4711yescharacteristic
678C23C2×D4×D4711yescharacteristic
679C23C2×D4×D4711yescharacteristic
680C23#41×D4711yescharacteristic
681C23#41×D4711yescharacteristic
682C23C2×#1062535211yescharacteristic
683C23C2×#1062535011yescharacteristic
684C23C2×#1062535011yescharacteristic
685C23C2×#1062535411yescharacteristic
686C23C2×#1062535411yescharacteristic
687C23#1309406911yescharacteristic
688C23#1309407011yescharacteristic
689C23#1309407011yescharacteristic
690C23#1309407211yescharacteristic
691D4—9432no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—41no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—474no—
721C2×C4—942no—
722C2×C4—942no—
723C2×C4—942no—
724C2×C4—942no—
725C2×C4—942no—
726C2×C4—942no—
727C2×C4—942no—
728C2×C4—942no—
729C2×C4—942no—
730C2×C4—942no—
731C2×C4—942no—
732C2×C4—942no—
733C2×C4—942no—
734C2×C4—942no—
735C2×C4—942no—
736C2×C4—18832no—
737C2×C4—1882no—
738C2×C4—1882no—
739C2×C4—1882no—
740C2×C4—1882no—
741C2×C4—1882no—
742C2×C4—1882no—
743C2×C4—1882no—
744C2×C4—1881no—
745C2×C4—1881no—
746C2×C4—1881no—
747C2×C4—1881no—
748C2×C4—1881no—
749C2×C4—1881no—
750C2×C4—1881no—
751C2×C4—1881no—
752C2×C4—1881no—
753C2×C4—1881no—
754C2×C4—1881no—
755C2×C4—1881no—
756C2×C4C22⋊C4×D4714yes—
757C2×C4#1309398114yes—
758C2×C4#1309398214yes—
759C2×C4#1309400614yes—
760C2×C4#1309400614yes—
761C2×C4#1309400914yes—
762C2×C4#1309400914yes—
763C22—948no—
764C22—948no—
765C22—948no—
766C22—1884no—
767C22—1884no—
768C22—1884no—
769C22—1884no—
770C22—1884no—
771C22—1884no—
772C22—1884no—
773C22—1884no—
774C22—1884no—
775C22—1884no—
776C22—1884no—
777C22—1884no—
778C22C2×C22⋊C4×D4711yescharacteristic
779C22C2×#1309398111yescharacteristic
780C22C2×#1309398211yescharacteristic
781C22C4×D4×D4711yescharacteristic
782C22C4×#1062535411yescharacteristic
783C22#1568959511yescharacteristic
784C22#1568960511yescharacteristic
785C22C2×#1309400611yescharacteristic
786C22C2×#1309400611yescharacteristic
787C22C2×#1309400911yescharacteristic
788C22C2×#1309400911yescharacteristic
789C22#1568965811yescharacteristic
790C22#1568965911yescharacteristic
791C22#1568966811yescharacteristic
792C22#1568967411yescharacteristic
793C22#1568972611yescharacteristic
794C22#1568972911yescharacteristic
795C22#1568974611yescharacteristic
796C22#1568974711yescharacteristic
797C22#1568975711yescharacteristic
798C22#1568975811yescharacteristic
799C22#1568976411yescharacteristic
800C22#1568976611yescharacteristic
801C22#1568976611yescharacteristic
802C22#1568977011yescharacteristic
803C22#1568977411yescharacteristic
804C22#1568977511yescharacteristic
805C22#1568977611yescharacteristic
806C22#1568979411yescharacteristic
807C22#1568981711yescharacteristic
808C22#1568982111yescharacteristic
809C22#1568983611yescharacteristic
810C22#1568984511yescharacteristic
811C22#1568985611yescharacteristic
812C22#1568985811yescharacteristic
813C4—42no—
814C4—42no—
815C4—44no—
816C4—82no—
817C4—944no—
818C4—3762no—
819C4—1882no—
820C4—1882no—
821C4—1882no—
822C4#1568898518yescomplemented
823C2—1888no—
824C2C2×#1568898511yescharacteristic
825C2#2024584611yescharacteristic
826C2#2024602711yescharacteristic
827C2#2024620911yescharacteristic
828C2#2024621711yescharacteristic
829C2#2024633311yescharacteristic
830C2#2024635711yescharacteristic
831C2#2024688211yescharacteristic
832C2#2024688311yescharacteristic
833C2#2024690411yescharacteristic
834C2#2024690511yescharacteristic
835C2#2024715511yescharacteristic
836C2#2024715611yescharacteristic
837C2#2024717711yescharacteristic
838C2#2024717811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC47×C4⋊#95C2
socle, cosocleC24×C47C24
prime radicalC23×D188C22
hypercenterC4⋊#95D47
hypocenterC47#13916
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#15688985C2semidirect
5. #20241636C2semidirect
6. #20241636C2semidirect
7. #20241617C2semidirect
8. #20241617C2semidirect
9. (C2×D47)⋊#95C2semidirect
10. C4×C47⋊#95C2semidirect
11. C47×C4⋊#95C2semidirect
16. C2×#13093986C4semidirect
93. C47⋊#95D4semidirect
398. C4×C47#381semidirect
412. C4⋊#95D47semidirect
460. C47#13916semidirect
822. C4#15688985semidirect

Maximal subgroups

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

subgroupindex
C22×#130939862
C2×#156890252
C2×#156890242
C2×#156889852
#202416362
#202416172
(C2×D47)⋊#952
C4×C47⋊#952
C47×C4⋊#952
#1391647