Finite Group Databasebeta

← C2×#20246528 #26378856

Subgroups — C2×#20246528 #26378856

Order 12032.

4246 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093994C211yesmaximal, characteristic
2#20246528C2116yesmaximal, direct product factor
3C2×#15689025C211yesmaximal, characteristic, complemented
4C2×#15689024C211yesmaximal, characteristic, complemented
5C2×#15689023C211yesmaximal, characteristic, complemented
6C2×#15689016C211yesmaximal, characteristic, complemented
7C2×#15689015C211yesmaximal, characteristic, complemented
8C2×#15689014C211yesmaximal, characteristic, complemented
9C2×#15689013C211yesmaximal, characteristic, complemented
10C2×#15689012C211yesmaximal, characteristic, complemented
11C2×#15689001C211yesmaximal, characteristic, complemented
12C2×#15689001C211yesmaximal, characteristic, complemented
13C2×#15688999C211yesmaximal, characteristic, complemented
14C2×#15688978C211yesmaximal, characteristic, complemented
15C2×#15688978C211yesmaximal, characteristic, complemented
16C2×C47×#388C211yesmaximal, characteristic, complemented
17C25×D47C2211yescharacteristic
18C23×D188C2211yescharacteristic
19C23×D188C2211yescharacteristic
20C23×C22⋊D47C2211yescharacteristic
21C23×C4×D47C2211yescharacteristic, complemented
22C2×#13093994C4116yescomplemented
23C2×#13093994C2218yes—
24C22×C4⋊Dic47C2211yescharacteristic, complemented
25C22×Dic47⋊C4C2211yescharacteristic, complemented
26C22×C22⋊Dic47C2211yescharacteristic
27C22×C22⋊Dic47C2211yescharacteristic
28C22×(C2×D47)⋊C4C2211yescharacteristic
29C22×(C2×D47)⋊C4C2211yescharacteristic
30C22×(C2×D47)⋊C4C2211yescharacteristic
31C22×(C2×D47)⋊C4C2211yescharacteristic
32C22×(C2×D47)⋊C4C2211yescharacteristic
33C22×(C2×D47)⋊C4C2211yescharacteristic
34C22×(C2×D47)⋊C4C2211yescharacteristic
35C22×(C2×D47)⋊C4C2211yescharacteristic
36C22×(C2×D47)⋊C4C2211yescharacteristic
37C22×(C2×D47)⋊C4C2211yescharacteristic
38C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
39C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
40C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
41C22×C4×Dic47C2211yescharacteristic, complemented
42C22×C4×Dic47C2211yescharacteristic, complemented
43#15689025C2218yescomplemented
44#15689024C2218yescomplemented
45#15689023C2218yescomplemented
46#15689016C2218yescomplemented
47#15689015C2218yescomplemented
48#15689014C2218yescomplemented
49#15689013C2218yescomplemented
50#15689012C2218yescomplemented
51#15689001C2218yescomplemented
52#15689001C2218yescomplemented
53#15688999C2218yescomplemented
54#15688978C2218yescomplemented
55#15688978C2218yescomplemented
56C2×C47⋊#95C2211yescharacteristic, complemented
57C2×C47⋊#95C2211yescharacteristic, complemented
58C2×C47⋊#95C2211yescharacteristic, complemented
59C2×C47⋊#95C2211yescharacteristic, complemented
60C22×C4⋊C4×C47C2211yescharacteristic, complemented
61C22×C22⋊C4×C47C2211yescharacteristic
62C22×C22⋊C4×C47C2211yescharacteristic
63C22×C22⋊C4×C47C2211yescharacteristic
64C22×C42×C47C2211yescharacteristic, complemented
65C47×#388C2218yescomplemented
66C2×#95×C47C2211yescharacteristic, complemented
67C2×#95×C47C2211yescharacteristic, complemented
68C24×D47—42no—
69C24×D47—42no—
70C24×D47—42no—
71C24×D47—42no—
72C24×D47—42no—
73C24×D47—42no—
74C24×D47C2×C418yescomplemented
75C24×D47C2311yescharacteristic
76C24×D47C2311yescharacteristic
77C24×D47C2311yescharacteristic
78C24×D47C2314yes—
79C22×D188—42no—
80C22×D188—42no—
81C22×D188—42no—
82C22×D188—42no—
83C22×D188C2×C418yes—
84C22×D188C2×C418yes—
85C22×D188C2314yes—
86C22×D188C2314yes—
87C22×C22⋊D47—42no—
88C22×C22⋊D47—42no—
89C22×C22⋊D47C2×C418yes—
90C22×C22⋊D47C2314yes—
91C23×Dic47C2311yescharacteristic
92C23×Dic47C2311yescharacteristic
93C23×Dic47C2311yescharacteristic
94C23×Dic47C2311yescharacteristic
95C23×Dic47C2311yescharacteristic
96C22×C4×D47—42no—
97C22×C4×D47—42no—
98C22×C4×D47—42no—
99C22×C4×D47C2314yescomplemented
100#13093994C2×C4164yescomplemented
101C2×C4⋊Dic47—42no—
102C2×C4⋊Dic47C2314yescomplemented
103C2×Dic47⋊C4—42no—
104C2×Dic47⋊C4C2314yescomplemented
105C2×C22⋊Dic47—42no—
106C2×C22⋊Dic47—42no—
107C2×C22⋊Dic47C2314yes—
108C2×C22⋊Dic47C2314yes—
109C2×(C2×D47)⋊C4—42no—
110C2×(C2×D47)⋊C4—42no—
111C2×(C2×D47)⋊C4—42no—
112C2×(C2×D47)⋊C4—42no—
113C2×(C2×D47)⋊C4—42no—
114C2×(C2×D47)⋊C4—42no—
115C2×(C2×D47)⋊C4—42no—
116C2×(C2×D47)⋊C4—42no—
117C2×(C2×D47)⋊C4—42no—
118C2×(C2×D47)⋊C4—42no—
119C2×(C2×D47)⋊C4—42no—
120C2×(C2×D47)⋊C4C2×C418yescomplemented
121C2×(C2×D47)⋊C4C2×C418yescomplemented
122C2×(C2×D47)⋊C4C2314yes—
123C2×(C2×D47)⋊C4C2314yes—
124C2×(C2×D47)⋊C4C2314yes—
125C2×(C2×D47)⋊C4C2314yes—
126C2×(C2×D47)⋊C4C2314yes—
127C2×(C2×D47)⋊C4C2314yes—
128C2×(C2×D47)⋊C4C2314yes—
129C2×(C2×D47)⋊C4C2314yes—
130C2×(C2×D47)⋊C4C2314yes—
131C2×(C2×D47)⋊C4C2314yes—
132C2×(C2×D47)⋊C4C2314yescomplemented
133C2×(C2×D47)⋊C4C2314yescomplemented
134C2×(C2×D47)⋊C4C2314yescomplemented
135C2×C4×Dic47—42no—
136C2×C4×Dic47—42no—
137C2×C4×Dic47C2314yescomplemented
138C2×C4×Dic47C2314yescomplemented
139C47⋊#95C2314yescomplemented
140C47⋊#95C2314yescomplemented
141C47⋊#95C2314yescomplemented
142C47⋊#95C2314yescomplemented
143C25×C47C2311yescharacteristic
144C23×C4×C47C2311yescharacteristic
145C23×C4×C47C2311yescharacteristic
146C23×C4×C47C2311yescharacteristic
147C23×C4×C47C2311yescharacteristic
148C23×C4×C47C2311yescharacteristic
149C23×C4×C47C2311yescharacteristic
150C2×C4⋊C4×C47—42no—
151C2×C4⋊C4×C47C2314yescomplemented
152C2×C22⋊C4×C47—42no—
153C2×C22⋊C4×C47—42no—
154C2×C22⋊C4×C47C2×C418yescomplemented
155C2×C22⋊C4×C47C2314yes—
156C2×C22⋊C4×C47C2314yes—
157C2×C22⋊C4×C47C2314yes—
158C2×C42×C47—42no—
159C2×C42×C47C2314yescomplemented
160#95×C47C2314yescomplemented
161#95×C47C2314yescomplemented
162C24×C47—22no—
163C24×C47—22no—
164C24×C47—22no—
165C24×C47—22no—
166C24×C47—22no—
167C24×C47—22no—
168C24×C47C22×C414yes—
169C24×C47C2412yes—
170C24×C47C2411yescharacteristic
171C23×D47—22no—
172C23×D47—22no—
173C23×D47—22no—
174C23×D47—22no—
175C23×D47—22no—
176C23×D47—22no—
177C23×D47—22no—
178C23×D47—22no—
179C23×D47—22no—
180C23×D47—22no—
181C23×D47—22no—
182C23×D47—22no—
183C23×D47—22no—
184C23×D47—22no—
185C23×D47—22no—
186C23×D47—22no—
187C23×D47—22no—
188C23×D47—22no—
189C23×D47—416no—
190C23×D47—416no—
191C23×D47—416no—
192C23×D47—44no—
193C23×D47—44no—
194C23×D47—44no—
195C23×D47—44no—
196C23×D47—44no—
197C23×D47—44no—
198C23×D47—416no—
199C23×D47—416no—
200C23×D47—416no—
201C23×D47—416no—
202C23×D47C22×C414yes—
203C23×D47C22×C414yes—
204C23×D47C22×C414yes—
205C23×D47C22×C4116yescomplemented
206C23×D47C2412yes—
207C23×D47C2412yes—
208C23×D47C2412yes—
209C22×C4×C47—22no—
210C22×C4×C47—22no—
211C22×C4×C47—22no—
212C22×C4×C47—22no—
213C22×C4×C47—22no—
214C22×C4×C47—22no—
215C22×C4×C47—22no—
216C22×C4×C47—22no—
217C22×C4×C47—22no—
218C22×C4×C47—22no—
219C22×C4×C47—22no—
220C22×C4×C47—22no—
221C22×C4×C47—22no—
222C22×C4×C47—22no—
223C22×C4×C47—22no—
224C22×C4×C47—22no—
225C22×C4×C47C22×C414yes—
226C22×C4×C47C22×C414yes—
227C22×C4×C47C2412yes—
228C22×C4×C47C2412yes—
229C22×C4×C47C2412yes—
230C22×C4×C47C2412yes—
231C22×C4×C47C2412yes—
232C22×C4×C47C2412yes—
233C2×C22⋊D47—416no—
234C2×C22⋊D47—44no—
235C2×C22⋊D47—44no—
236C2×C22⋊D47C22×C4116yes—
237C22×Dic47—22no—
238C22×Dic47—22no—
239C22×Dic47—22no—
240C22×Dic47—22no—
241C22×Dic47—22no—
242C22×Dic47—22no—
243C22×Dic47—22no—
244C22×Dic47—22no—
245C22×Dic47—22no—
246C22×Dic47—22no—
247C22×Dic47—22no—
248C22×Dic47—22no—
249C22×Dic47—22no—
250C22×Dic47—22no—
251C22×Dic47C22×C414yes—
252C22×Dic47C2412yes—
253C22×Dic47C2412yes—
254C22×Dic47C2412yes—
255C22×Dic47C2412yes—
256C22×Dic47C2412yes—
257C2×D188—416no—
258C2×D188—416no—
259C2×D188—44no—
260C2×D188—44no—
261C2×D188—44no—
262C2×D188—44no—
263C2×D188C22×C4116yes—
264C2×D188C22×C4116yes—
265C2×C4×D47—44no—
266C2×C4×D47—44no—
267C2×C4×D47—44no—
268C2×C4×D47—416no—
269C4⋊C4×C47—44no—
270C22⋊C4×C47—44no—
271C22⋊C4×C47—44no—
272C22⋊C4×C47C22×C4116yescomplemented
273C42×C47—44no—
274C22⋊Dic47—44no—
275C22⋊Dic47—44no—
276(C2×D47)⋊C4—44no—
277(C2×D47)⋊C4—44no—
278(C2×D47)⋊C4—44no—
279(C2×D47)⋊C4—44no—
280(C2×D47)⋊C4—44no—
281(C2×D47)⋊C4—44no—
282(C2×D47)⋊C4—44no—
283(C2×D47)⋊C4—44no—
284(C2×D47)⋊C4—44no—
285(C2×D47)⋊C4—44no—
286(C2×D47)⋊C4—44no—
287(C2×D47)⋊C4C22×C4116yescomplemented
288(C2×D47)⋊C4C22×C4116yescomplemented
289C4⋊Dic47—44no—
290Dic47⋊C4—44no—
291C4×Dic47—44no—
292C4×Dic47—44no—
293C23×C47—28no—
294C23×C47—28no—
295C23×C47—28no—
296C23×C47—22no—
297C23×C47—22no—
298C23×C47—22no—
299C23×C47—22no—
300C23×C47—22no—
301C23×C47—22no—
302C23×C47—44no—
303C23×C47—44no—
304C23×C47—44no—
305C23×C47—44no—
306C23×C47C23×C414yes—
307C23×C47C23×C412yes—
308C23×C47H(5,𝔽2)12yes—
309C23×C47H(5,𝔽2)12yes—
310C23×C47H(5,𝔽2)12yes—
311C23×C47H(5,𝔽2)12yes—
312C23×C47H(5,𝔽2)12yes—
313C23×C47H(5,𝔽2)12yes—
314C23×C47C2511yescharacteristic
315C22×D47—28no—
316C22×D47—28no—
317C22×D47—28no—
318C22×D47—28no—
319C22×D47—28no—
320C22×D47—28no—
321C22×D47—28no—
322C22×D47—28no—
323C22×D47—28no—
324C22×D47—22no—
325C22×D47—22no—
326C22×D47—22no—
327C22×D47—22no—
328C22×D47—22no—
329C22×D47—22no—
330C22×D47—22no—
331C22×D47—22no—
332C22×D47—22no—
333C22×D47—22no—
334C22×D47—22no—
335C22×D47—22no—
336C22×D47—22no—
337C22×D47—22no—
338C22×D47—22no—
339C22×D47—22no—
340C22×D47—22no—
341C22×D47—22no—
342C22×D47—416no—
343C22×D47—416no—
344C22×D47—416no—
345C22×D47—4128no—
346C22×D47—416no—
347C22×D47—416no—
348C22×D47—416no—
349C22×D47—416no—
350C22×D47—44no—
351C22×D47—44no—
352C22×D47—44no—
353C22×D47—44no—
354C22×D47—44no—
355C22×D47—44no—
356C22×D47—44no—
357C22×D47—44no—
358C22×D47—44no—
359C22×D47—44no—
360C22×D47—44no—
361C22×D47—44no—
362C22×D47C23×C414yes—
363C22×D47C23×C414yes—
364C22×D47C23×C414yes—
365C2×C4×C47—28no—
366C2×C4×C47—28no—
367C2×C4×C47—22no—
368C2×C4×C47—22no—
369C2×C4×C47—22no—
370C2×C4×C47—22no—
371C2×C4×C47—22no—
372C2×C4×C47—22no—
373C2×C4×C47—22no—
374C2×C4×C47—22no—
375C2×C4×C47—22no—
376C2×C4×C47—22no—
377C2×C4×C47—22no—
378C2×C4×C47—22no—
379C2×C4×C47—22no—
380C2×C4×C47—22no—
381C2×C4×C47—22no—
382C2×C4×C47—22no—
383C2×C4×C47—44no—
384C2×C4×C47—44no—
385C2×C4×C47—44no—
386C2×C4×C47—44no—
387C2×C4×C47C23×C414yes—
388C2×C4×C47C23×C414yes—
389C22⋊D47—416no—
390C2×Dic47—28no—
391C2×Dic47—22no—
392C2×Dic47—22no—
393C2×Dic47—22no—
394C2×Dic47—22no—
395C2×Dic47—22no—
396C2×Dic47—22no—
397C2×Dic47—22no—
398C2×Dic47—22no—
399C2×Dic47—22no—
400C2×Dic47—22no—
401C2×Dic47—22no—
402C2×Dic47—22no—
403C2×Dic47—22no—
404C2×Dic47—22no—
405C2×Dic47—44no—
406C2×Dic47—44no—
407C2×Dic47—44no—
408C2×Dic47—44no—
409C2×Dic47C23×C414yes—
410D188—416no—
411D188—416no—
412C4×D47—416no—
413C2×#2375—471nomaximal, Sylow
414C22×C47—24no—
415C22×C47—24no—
416C22×C47—24no—
417C22×C47—416no—
418C22×C47—42no—
419C22×C47—42no—
420C22×C47—42no—
421C22×C47—42no—
422C22×C47#51814yes—
423C22×C47#51814yes—
424C22×C47#51814yes—
425C22×C47#56014yes—
426C22×C47#56014yes—
427C22×C47#56014yes—
428C22×C47H(3,𝔽4)14yes—
429C22×C47C24×C411yescharacteristic
430C22×C47C2×H(5,𝔽2)11yescharacteristic
431C22×C47C2×H(5,𝔽2)11yescharacteristic
432C22×C47C2×H(5,𝔽2)11yescharacteristic
433C22×C47C2×H(5,𝔽2)11yescharacteristic
434C22×C47C2×H(5,𝔽2)11yescharacteristic
435C22×C47C2×H(5,𝔽2)11yescharacteristic
436C2×D47—24no—
437C2×D47—24no—
438C2×D47—24no—
439C2×D47—24no—
440C2×D47—24no—
441C2×D47—24no—
442C2×D47—24no—
443C2×D47—24no—
444C2×D47—24no—
445C2×D47—464no—
446C2×D47—416no—
447C2×D47—416no—
448C2×D47—416no—
449C2×D47—42no—
450C2×D47—42no—
451C2×D47—42no—
452C2×D47—42no—
453C2×D47—42no—
454C2×D47—42no—
455C2×D47—42no—
456C2×D47—42no—
457C2×D47—42no—
458C2×D47—42no—
459C2×D47—42no—
460C2×D47—42no—
461C4×C47—24no—
462C4×C47—24no—
463C4×C47—42no—
464C4×C47—42no—
465C4×C47—42no—
466C4×C47—42no—
467Dic47—24no—
468Dic47—42no—
469Dic47—42no—
470Dic47—42no—
471Dic47—42no—
472C22×#120—471no—
473#2375—4716no—
474C2×#390—471no—
475C2×#390—471no—
476C2×#390—471no—
477C2×#388—471no—
478C2×#388—471no—
479C2×#388—471no—
480C2×#388—471no—
481C2×#388—471no—
482C2×#388D4711yescharacteristic, complemented
483C2×#386—471no—
484C2×#386—471no—
485C2×#386—471no—
486C2×#379—471no—
487C2×#379—471no—
488C2×C47—44no—
489C2×C47#237518yescomplemented
490C2×C47C2×#51811yescharacteristic
491C2×C47C2×#51811yescharacteristic
492C2×C47C2×#51811yescharacteristic
493C2×C47C2×#56011yescharacteristic
494C2×C47C2×#56011yescharacteristic
495C2×C47C2×#56011yescharacteristic
496C2×C47C2×H(3,𝔽4)11yescharacteristic
497D47—44no—
498D47—44no—
499D47—44no—
500C26—471no—
501C23×D4—471no—
502C23×D4—471no—
503C23×D4—471no—
504C24×C4—471no—
505C2×#120—4716no—
506C2×#120—478no—
507C22×C4⋊C4—471no—
508C22×C4⋊C4—471no—
509C22×C4⋊C4C2×D4711yescharacteristic, complemented
510C22×C22⋊C4—471no—
511C22×C22⋊C4—471no—
512C22×C22⋊C4—471no—
513C22×C22⋊C4—471no—
514C22×C22⋊C4—471no—
515C22×C22⋊C4—471no—
516C22×C22⋊C4—471no—
517C22×C22⋊C4—471no—
518C22×C22⋊C4—471no—
519C22×C22⋊C4—471no—
520C22×C22⋊C4—471no—
521C22×C22⋊C4—471no—
522C22×C22⋊C4—471no—
523C22×C22⋊C4—471no—
524C22×C22⋊C4—471no—
525C22×C22⋊C4C2×D4711yescharacteristic
526C22×C22⋊C4C2×D4711yescharacteristic
527C22×C22⋊C4C2×D4711yescharacteristic
528C22×C42—471no—
529C22×C42—471no—
530C22×C42C2×D4711yescharacteristic, complemented
531#390—478no—
532#390—478no—
533#390—478no—
534#388—478no—
535#388—478no—
536#388—478no—
537#388—478no—
538#388—478no—
539#388C2×D4718yescomplemented
540#386—478no—
541#386—478no—
542#386—478no—
543#379—478no—
544#379—478no—
545C2×#95—471no—
546C2×#95—471no—
547C2×#95—471no—
548C2×#95—471no—
549C2×#95C2×D4711yescharacteristic, complemented
550C2×#95C2×D4711yescharacteristic, complemented
551C47C2×#237511yescharacteristic, complemented, Sylow
552C25—471no—
553C25—471no—
554C25—471no—
555C25—478no—
556C25—474no—
557C25—1882no—
558C25—1882no—
559C25—1882no—
560C25—1882no—
561C25—1882no—
562C25—1882no—
563C25C22×D4711yescharacteristic
564C22×D4—478no—
565C22×D4—474no—
566C22×D4—478no—
567C22×D4—478no—
568C22×D4—474no—
569C22×D4—474no—
570C22×D4—1882no—
571C22×D4—1882no—
572C22×D4—1882no—
573C22×D4—1882no—
574C22×D4—1882no—
575C22×D4—1882no—
576C23×C4—471no—
577C23×C4—471no—
578C23×C4—471no—
579C23×C4—471no—
580C23×C4—471no—
581C23×C4—474no—
582C23×C4—1882no—
583C23×C4—1882no—
584C23×C4—1882no—
585C23×C4C22×D4711yescharacteristic
586C23×C4C22×D4711yescharacteristic
587C23×C4C22×D4711yescharacteristic
588C23×C4C22×D4711yescharacteristic
589C23×C4C22×D4711yescharacteristic
590C23×C4C22×D4711yescharacteristic
591#120—4764no—
592C2×C4⋊C4—42no—
593C2×C4⋊C4—474no—
594C2×C4⋊C4—474no—
595C2×C4⋊C4—1882no—
596C2×C4⋊C4—1882no—
597C2×C4⋊C4C22×D4714yescomplemented
598C2×C22⋊C4—42no—
599C2×C22⋊C4—42no—
600C2×C22⋊C4—478no—
601C2×C22⋊C4—478no—
602C2×C22⋊C4—474no—
603C2×C22⋊C4—474no—
604C2×C22⋊C4—474no—
605C2×C22⋊C4—474no—
606C2×C22⋊C4—474no—
607C2×C22⋊C4—474no—
608C2×C22⋊C4—474no—
609C2×C22⋊C4—474no—
610C2×C22⋊C4—474no—
611C2×C22⋊C4—474no—
612C2×C22⋊C4—474no—
613C2×C22⋊C4—474no—
614C2×C22⋊C4—474no—
615C2×C22⋊C4—474no—
616C2×C22⋊C4—474no—
617C2×C22⋊C4—1882no—
618C2×C22⋊C4—1882no—
619C2×C22⋊C4—1882no—
620C2×C22⋊C4—1882no—
621C2×C22⋊C4—1882no—
622C2×C22⋊C4—1882no—
623C2×C22⋊C4—1882no—
624C2×C22⋊C4—1882no—
625C2×C22⋊C4—1882no—
626C2×C22⋊C4—1882no—
627C2×C22⋊C4—1882no—
628C2×C22⋊C4—1882no—
629C2×C22⋊C4—1882no—
630C2×C22⋊C4C4×D4718yescomplemented
631C2×C22⋊C4C22×D4714yes—
632C2×C22⋊C4C22×D4714yes—
633C2×C22⋊C4C22×D4714yes—
634C2×C42—42no—
635C2×C42—474no—
636C2×C42—474no—
637C2×C42—1882no—
638C2×C42—1882no—
639C2×C42C22×D4714yescomplemented
640#95—474no—
641#95—474no—
642#95—474no—
643#95—474no—
644#95C22×D4714yescomplemented
645#95C22×D4714yescomplemented
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—474no—
653C24—474no—
654C24—474no—
655C24—472no—
656C24—472no—
657C24—472no—
658C24—4716no—
659C24—942no—
660C24—942no—
661C24—942no—
662C24—942no—
663C24—942no—
664C24—942no—
665C24—942no—
666C24—942no—
667C24—942no—
668C24—942no—
669C24—942no—
670C24—942no—
671C24—942no—
672C24—942no—
673C24—942no—
674C24—942no—
675C24—942no—
676C24—942no—
677C24—18816no—
678C24—18816no—
679C24—18816no—
680C24—1884no—
681C24—1884no—
682C24—1884no—
683C24—1884no—
684C24—1884no—
685C24—1884no—
686C24—18816no—
687C24—18816no—
688C24—18816no—
689C24—18816no—
690C24C2×C4×D4714yes—
691C24C23×D4712yes—
692C24C23×D4711yescharacteristic
693C2×D4—4716no—
694C2×D4—4716no—
695C2×D4—4716no—
696C2×D4—18816no—
697C2×D4—18816no—
698C2×D4—1884no—
699C2×D4—1884no—
700C2×D4—1884no—
701C2×D4—1884no—
702C2×D4—18816no—
703C2×D4—1884no—
704C2×D4—1884no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—474no—
722C22×C4—472no—
723C22×C4—472no—
724C22×C4—472no—
725C22×C4—472no—
726C22×C4—472no—
727C22×C4—942no—
728C22×C4—942no—
729C22×C4—942no—
730C22×C4—942no—
731C22×C4—942no—
732C22×C4—942no—
733C22×C4—942no—
734C22×C4—942no—
735C22×C4—942no—
736C22×C4—942no—
737C22×C4—942no—
738C22×C4—942no—
739C22×C4—942no—
740C22×C4—942no—
741C22×C4—1884no—
742C22×C4—1884no—
743C22×C4—1884no—
744C22×C4—18816no—
745C22×C4C2×C4×D4714yes—
746C22×C4C2×C4×D4714yes—
747C22×C4C23×D4712yes—
748C22×C4C23×D4712yes—
749C22×C4C23×D4712yes—
750C22×C4C23×D4712yes—
751C22×C4C23×D4712yes—
752C22×C4C23×D4712yes—
753C4⋊C4—44no—
754C4⋊C4—1884no—
755C4⋊C4—1884no—
756C22⋊C4—44no—
757C22⋊C4—44no—
758C22⋊C4—4716no—
759C22⋊C4—4716no—
760C22⋊C4—1884no—
761C22⋊C4—1884no—
762C22⋊C4—1884no—
763C22⋊C4—1884no—
764C22⋊C4—1884no—
765C22⋊C4—1884no—
766C22⋊C4—1884no—
767C22⋊C4—1884no—
768C22⋊C4—1884no—
769C22⋊C4—1884no—
770C22⋊C4—1884no—
771C22⋊C4—1884no—
772C22⋊C4—1884no—
773C22⋊C4C2×C4×D47116yescomplemented
774C42—44no—
775C42—1884no—
776C42—1884no—
777C23—28no—
778C23—28no—
779C23—28no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—44no—
787C23—44no—
788C23—44no—
789C23—44no—
790C23—474no—
791C23—474no—
792C23—474no—
793C23—948no—
794C23—948no—
795C23—948no—
796C23—948no—
797C23—948no—
798C23—948no—
799C23—948no—
800C23—948no—
801C23—948no—
802C23—942no—
803C23—942no—
804C23—942no—
805C23—942no—
806C23—942no—
807C23—942no—
808C23—942no—
809C23—942no—
810C23—942no—
811C23—942no—
812C23—942no—
813C23—942no—
814C23—942no—
815C23—942no—
816C23—942no—
817C23—942no—
818C23—942no—
819C23—942no—
820C23—18816no—
821C23—18816no—
822C23—18816no—
823C23—188128no—
824C23—18816no—
825C23—18816no—
826C23—18816no—
827C23—18816no—
828C23—1884no—
829C23—1884no—
830C23—1884no—
831C23—1884no—
832C23—1884no—
833C23—1884no—
834C23—1884no—
835C23—1884no—
836C23—1884no—
837C23—1884no—
838C23—1884no—
839C23—1884no—
840C23C22×C4×D4714yes—
841C23C22×C4×D4712yes—
842C23#1309406912yes—
843C23#1309406912yes—
844C23#1309407012yes—
845C23#1309407012yes—
846C23#1309407012yes—
847C23#1309407012yes—
848C23C24×D4711yescharacteristic
849D4—18816no—
850D4—18816no—
851D4—18816no—
852C2×C4—28no—
853C2×C4—28no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—44no—
871C2×C4—44no—
872C2×C4—44no—
873C2×C4—44no—
874C2×C4—474no—
875C2×C4—948no—
876C2×C4—942no—
877C2×C4—942no—
878C2×C4—942no—
879C2×C4—942no—
880C2×C4—942no—
881C2×C4—942no—
882C2×C4—942no—
883C2×C4—942no—
884C2×C4—942no—
885C2×C4—942no—
886C2×C4—942no—
887C2×C4—942no—
888C2×C4—942no—
889C2×C4—942no—
890C2×C4—18816no—
891C2×C4—1884no—
892C2×C4—1884no—
893C2×C4—1884no—
894C2×C4—1884no—
895C2×C4C22×C4×D4714yes—
896C2×C4C22×C4×D4714yes—
897C22—24no—
898C22—24no—
899C22—24no—
900C22—416no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—944no—
906C22—944no—
907C22—944no—
908C22—944no—
909C22—944no—
910C22—944no—
911C22—944no—
912C22—944no—
913C22—944no—
914C22—18864no—
915C22—18816no—
916C22—18816no—
917C22—18816no—
918C22—1882no—
919C22—1882no—
920C22—1882no—
921C22—1882no—
922C22—1882no—
923C22—1882no—
924C22—1882no—
925C22—1882no—
926C22—1882no—
927C22—1882no—
928C22—1882no—
929C22—1882no—
930C22#1568959514yes—
931C22#1568959514yes—
932C22#1568959714yes—
933C22#1568986114yes—
934C22#1568986314yes—
935C22#1568986414yes—
936C22#1568986514yes—
937C22C23×C4×D4711yescharacteristic
938C22C2×#1309406911yescharacteristic
939C22C2×#1309406911yescharacteristic
940C22C2×#1309407011yescharacteristic
941C22C2×#1309407011yescharacteristic
942C22C2×#1309407011yescharacteristic
943C22C2×#1309407011yescharacteristic
944C4—24no—
945C4—24no—
946C4—42no—
947C4—42no—
948C4—42no—
949C4—42no—
950C4—944no—
951C4—1882no—
952C4—1882no—
953C4—1882no—
954C4—1882no—
955C2—44no—
956C2—1884no—
957C2—1884no—
958C2—1884no—
959C2#2024652818yesdirect product factor
960C2C2×#1568959511yescharacteristic
961C2C2×#1568959511yescharacteristic
962C2C2×#1568959711yescharacteristic
963C2C2×#1568986111yescharacteristic
964C2C2×#1568986311yescharacteristic
965C2C2×#1568986411yescharacteristic
966C2C2×#1568986511yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#388C2
socleC24×C47C24
prime radicalC22×#13093994C2
cosocleC23×C47C25
hypercenterC2×#388D47
hypocenterC47C2×#2375
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. #20246528C2direct (N × H)
3. C2×#15689025C2semidirect
4. C2×#15689024C2semidirect
5. C2×#15689023C2semidirect
6. C2×#15689016C2semidirect
7. C2×#15689015C2semidirect
8. C2×#15689014C2semidirect
9. C2×#15689013C2semidirect
10. C2×#15689012C2semidirect
11. C2×#15689001C2semidirect
12. C2×#15689001C2semidirect
13. C2×#15688999C2semidirect
14. C2×#15688978C2semidirect
15. C2×#15688978C2semidirect
16. C2×C47×#388C2semidirect
21. C23×C4×D47C22semidirect
22. C2×#13093994C4semidirect
24. C22×C4⋊Dic47C22semidirect
25. C22×Dic47⋊C4C22semidirect
38. C22×(C2×D47)⋊C4C22semidirect
39. C22×(C2×D47)⋊C4C22semidirect
40. C22×(C2×D47)⋊C4C22semidirect
41. C22×C4×Dic47C22semidirect
42. C22×C4×Dic47C22semidirect
43. #15689025C22semidirect
44. #15689024C22semidirect
45. #15689023C22semidirect
46. #15689016C22semidirect
47. #15689015C22semidirect
48. #15689014C22semidirect
49. #15689013C22semidirect
50. #15689012C22semidirect
51. #15689001C22semidirect
52. #15689001C22semidirect
53. #15688999C22semidirect
54. #15688978C22semidirect
55. #15688978C22semidirect
56. C2×C47⋊#95C22semidirect
57. C2×C47⋊#95C22semidirect
58. C2×C47⋊#95C22semidirect
59. C2×C47⋊#95C22semidirect
60. C22×C4⋊C4×C47C22semidirect
64. C22×C42×C47C22semidirect
65. C47×#388C22semidirect
66. C2×#95×C47C22semidirect
67. C2×#95×C47C22semidirect
74. C24×D47C2×C4semidirect
99. C22×C4×D47C23semidirect
100. #13093994C2×C4semidirect
102. C2×C4⋊Dic47C23semidirect
104. C2×Dic47⋊C4C23semidirect
120. C2×(C2×D47)⋊C4C2×C4semidirect
121. C2×(C2×D47)⋊C4C2×C4semidirect
132. C2×(C2×D47)⋊C4C23semidirect
133. C2×(C2×D47)⋊C4C23semidirect
134. C2×(C2×D47)⋊C4C23semidirect
137. C2×C4×Dic47C23semidirect
138. C2×C4×Dic47C23semidirect
139. C47⋊#95C23semidirect
140. C47⋊#95C23semidirect
141. C47⋊#95C23semidirect
142. C47⋊#95C23semidirect
151. C2×C4⋊C4×C47C23semidirect
154. C2×C22⋊C4×C47C2×C4semidirect
159. C2×C42×C47C23semidirect
160. #95×C47C23semidirect
161. #95×C47C23semidirect
205. C23×D47C22×C4semidirect
272. C22⋊C4×C47C22×C4semidirect
287. (C2×D47)⋊C4C22×C4semidirect
288. (C2×D47)⋊C4C22×C4semidirect
482. C2×#388D47semidirect
489. C2×C47#2375semidirect
509. C22×C4⋊C4C2×D47semidirect
530. C22×C42C2×D47semidirect
539. #388C2×D47semidirect
549. C2×#95C2×D47semidirect
550. C2×#95C2×D47semidirect
551. C47C2×#2375semidirect
597. C2×C4⋊C4C22×D47semidirect
630. C2×C22⋊C4C4×D47semidirect
639. C2×C42C22×D47semidirect
644. #95C22×D47semidirect
645. #95C22×D47semidirect
773. C22⋊C4C2×C4×D47semidirect
959. C2#20246528direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130939942
#202465282
C2×#156890252
C2×#156890242
C2×#156890232
C2×#156890162
C2×#156890152
C2×#156890142
C2×#156890132
C2×#156890122
C2×#156890012
C2×#156889992
C2×#156889782
C2×C47×#3882
C2×#237547