Finite Group Databasebeta

← C2×#20247211 #26384034

Subgroups — C2×#20247211 #26384034

Order 12032.

3374 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094002C211yesmaximal, characteristic, complemented
2C22×C4×D188C211yesmaximal, characteristic
3#20247211C2116yesmaximal, direct product factor
4C2×#15689065C211yesmaximal, characteristic, complemented
5C2×#15689057C211yesmaximal, characteristic, complemented
6C2×#15689045C211yesmaximal, characteristic, complemented
7C2×#15689036C211yesmaximal, characteristic, complemented
8C2×#15689029C211yesmaximal, characteristic, complemented
9C2×#15689001C211yesmaximal, characteristic
10C2×#15689001C211yesmaximal, characteristic
11C2×#15688997C211yesmaximal, characteristic, complemented
12C2×#15688994C211yesmaximal, characteristic, complemented
13C2×#15688994C211yesmaximal, characteristic, complemented
14C2×#15688982C211yesmaximal, characteristic, complemented
15C2×#95×D47C211yesmaximal, characteristic, complemented
16C2×C47×#387C211yesmaximal, characteristic, complemented
17C23×Dic94C2211yescharacteristic
18C23×D188C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C23×C4×D47C2211yescharacteristic
21C23×C4×D47C2211yescharacteristic
22C23×C4×D47C2211yescharacteristic
23C2×#13094002—28no—
24C2×#13094002C2218yescomplemented
25C2×C4×D188—28no—
26C2×C4×D188C2218yes—
27C22×C4⋊Dic47C2211yescharacteristic
28C22×C4⋊Dic47C2211yescharacteristic
29C22×Dic47⋊C4C2211yescharacteristic
30C22×Dic47⋊C4C2211yescharacteristic
31C22×Dic47⋊C4C2211yescharacteristic
32C22×Dic47⋊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
39C22×(C2×D47)⋊C4C2211yescharacteristic
40C22×(C2×D47)⋊C4C2211yescharacteristic
41#15689065C2218yescomplemented
42#15689057C2218yescomplemented
43#15689045C2218yescomplemented
44#15689036C2218yescomplemented
45#15689029C2218yescomplemented
46#15689001C2218yes—
47#15689001C2218yes—
48#15688997C2218yescomplemented
49#15688994C2218yescomplemented
50#15688994C2218yescomplemented
51#15688982C2218yescomplemented
52C2×C47⋊#95C2211yescharacteristic
53C2×C47⋊#95C2211yescharacteristic
54C2×C47⋊#95C2211yescharacteristic
55C2×C47⋊#95C2211yescharacteristic
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60#95×D47C2218yescomplemented
61C22×C4⋊C4×C47C2211yescharacteristic
62C22×C4⋊C4×C47C2211yescharacteristic
63C22×C42×C47C2211yescharacteristic
64C47×#387C2218yescomplemented
65C2×#95×C47C2211yescharacteristic
66C2×#95×C47C2211yescharacteristic
67C2×#95×C47C2211yescharacteristic
68C2×#95×C47C2211yescharacteristic
69C24×D47C2311yescharacteristic
70C24×D47C2311yescharacteristic
71C22×Dic94—24no—
72C22×Dic94—24no—
73C22×Dic94—42no—
74C22×Dic94C2314yes—
75C22×D188—24no—
76C22×D188—24no—
77C22×D188Q818yescomplemented
78C22×D188C2314yes—
79C23×Dic47C2311yescharacteristic
80C23×Dic47C2311yescharacteristic
81C23×Dic47C2311yescharacteristic
82C23×Dic47C2311yescharacteristic
83C23×Dic47C2311yescharacteristic
84C23×Dic47C2311yescharacteristic
85C22×C4×D47—24no—
86C22×C4×D47—24no—
87C22×C4×D47—24no—
88C22×C4×D47—24no—
89C22×C4×D47—24no—
90C22×C4×D47—24no—
91C22×C4×D47—24no—
92C22×C4×D47—42no—
93C22×C4×D47—42no—
94C22×C4×D47—42no—
95C22×C4×D47—42no—
96C22×C4×D47—42no—
97C22×C4×D47C2314yes—
98C22×C4×D47C2314yes—
99C22×C4×D47C2314yes—
100C22×C4×D47C2314yes—
101#13094002—232no—
102C4×D188—232no—
103C2×C4⋊Dic47—24no—
104C2×C4⋊Dic47—42no—
105C2×C4⋊Dic47C2314yes—
106C2×C4⋊Dic47C2314yes—
107C2×Dic47⋊C4—24no—
108C2×Dic47⋊C4—24no—
109C2×Dic47⋊C4—42no—
110C2×Dic47⋊C4—42no—
111C2×Dic47⋊C4C2314yes—
112C2×Dic47⋊C4C2314yes—
113C2×Dic47⋊C4C2314yes—
114C2×Dic47⋊C4C2314yes—
115C2×(C2×D47)⋊C4—24no—
116C2×(C2×D47)⋊C4—24no—
117C2×(C2×D47)⋊C4—24no—
118C2×(C2×D47)⋊C4—24no—
119C2×(C2×D47)⋊C4—42no—
120C2×(C2×D47)⋊C4—42no—
121C2×(C2×D47)⋊C4—42no—
122C2×(C2×D47)⋊C4D418yes—
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—
131C47⋊#95C2314yes—
132C47⋊#95C2314yes—
133C47⋊#95C2314yes—
134C47⋊#95C2314yes—
135C47⋊#95C2314yes—
136C47⋊#95C2314yes—
137C47⋊#95C2314yes—
138C47⋊#95C2314yes—
139C23×C4×C47C2311yescharacteristic
140C23×C4×C47C2311yescharacteristic
141C23×C4×C47C2311yescharacteristic
142C23×C4×C47C2311yescharacteristic
143C23×C4×C47C2311yescharacteristic
144C23×C4×C47C2311yescharacteristic
145C23×C4×C47C2311yescharacteristic
146C2×C4⋊C4×C47—24no—
147C2×C4⋊C4×C47—24no—
148C2×C4⋊C4×C47C2314yes—
149C2×C4⋊C4×C47C2314yes—
150C2×C42×C47—24no—
151C2×C42×C47C2314yes—
152#95×C47C2314yes—
153#95×C47C2314yes—
154#95×C47C2314yes—
155#95×C47C2314yes—
156C24×C47C2411yescharacteristic
157C23×D47—22no—
158C23×D47—22no—
159C23×D47—22no—
160C23×D47—22no—
161C23×D47—22no—
162C23×D47—22no—
163C23×D47—22no—
164C23×D47—22no—
165C23×D47—22no—
166C23×D47—22no—
167C23×D47C2×D414yes—
168C23×D47C2×Q814yes—
169C23×D47C2×Q814yes—
170C23×D47#4114yes—
171C23×D47C2412yes—
172C23×D47C2412yes—
173C22×C4×C47—22no—
174C22×C4×C47—22no—
175C22×C4×C47—22no—
176C22×C4×C47—22no—
177C22×C4×C47—22no—
178C22×C4×C47—22no—
179C22×C4×C47—22no—
180C22×C4×C47—22no—
181C22×C4×C47—22no—
182C22×C4×C47—22no—
183C22×C4×C47—22no—
184C22×C4×C47—22no—
185C22×C4×C47—22no—
186C22×C4×C47—22no—
187C22×C4×C47—22no—
188C22×C4×C47—22no—
189C22×C4×C47—22no—
190C22×C4×C47—22no—
191C22×C4×C47C2×D414yes—
192C22×C4×C47C2×Q814yes—
193C22×C4×C47#4114yes—
194C22×C4×C47C2412yes—
195C22×C4×C47C2412yes—
196C22×C4×C47C2412yes—
197C22×C4×C47C2412yes—
198C22×C4×C47C2412yes—
199C22×C4×C47C2412yes—
200C22×C4×C47C2412yes—
201C22×Dic47—22no—
202C22×Dic47—22no—
203C22×Dic47—22no—
204C22×Dic47—22no—
205C22×Dic47—22no—
206C22×Dic47—22no—
207C22×Dic47—22no—
208C22×Dic47—22no—
209C22×Dic47—22no—
210C22×Dic47—22no—
211C22×Dic47—22no—
212C22×Dic47—22no—
213C22×Dic47—22no—
214C22×Dic47—22no—
215C22×Dic47—22no—
216C22×Dic47—22no—
217C22×Dic47C2×D414yes—
218C22×Dic47#4114yes—
219C22×Dic47C2412yes—
220C22×Dic47C2412yes—
221C22×Dic47C2412yes—
222C22×Dic47C2412yes—
223C22×Dic47C2412yes—
224C22×Dic47C2412yes—
225C2×D188—232no—
226C2×D188—28no—
227C2×D188—28no—
228C2×D188C2×Q8116yescomplemented
229C2×C4×D47—28no—
230C2×C4×D47—28no—
231C2×C4×D47—28no—
232C2×C4×D47—28no—
233C2×C4×D47—28no—
234C2×C4×D47—28no—
235C2×C4×D47—28no—
236C2×C4×D47—44no—
237C2×C4×D47—44no—
238C2×C4×D47—44no—
239C2×C4×D47—44no—
240C2×C4×D47—44no—
241C2×C4×D47—416no—
242C2×C4×D47—416no—
243C2×C4×D47—416no—
244C2×C4×D47—416no—
245C2×Dic94—28no—
246C2×Dic94—28no—
247C2×Dic94—44no—
248C2×Dic94—416no—
249C4⋊C4×C47—28no—
250C4⋊C4×C47—28no—
251C42×C47—28no—
252(C2×D47)⋊C4—28no—
253(C2×D47)⋊C4—28no—
254(C2×D47)⋊C4—28no—
255(C2×D47)⋊C4—28no—
256(C2×D47)⋊C4—44no—
257(C2×D47)⋊C4—44no—
258(C2×D47)⋊C4—44no—
259(C2×D47)⋊C4C2×D4116yes—
260C4⋊Dic47—28no—
261C4⋊Dic47—44no—
262Dic47⋊C4—28no—
263Dic47⋊C4—28no—
264Dic47⋊C4—44no—
265Dic47⋊C4—44no—
266C23×C47C22×D412yes—
267C23×C47C22×Q812yes—
268C23×C47C2×#4112yes—
269C23×C47C2×#4112yes—
270C23×C47C2×#4112yes—
271C23×C47H(5,𝔽2)12yes—
272C23×C47H(5,𝔽2)12yes—
273C23×C47C2511yescharacteristic
274C22×D47—28no—
275C22×D47—28no—
276C22×D47—28no—
277C22×D47—28no—
278C22×D47—28no—
279C22×D47—28no—
280C22×D47—22no—
281C22×D47—22no—
282C22×D47—22no—
283C22×D47—22no—
284C22×D47—28no—
285C22×D47—28no—
286C22×D47—28no—
287C22×D47—22no—
288C22×D47—22no—
289C22×D47—22no—
290C22×D47—22no—
291C22×D47—22no—
292C22×D47—22no—
293C22×D47—44no—
294C22×D47—44no—
295C22×D47—44no—
296C22×D47—44no—
297C22×D47C22⋊Q8116yes—
298C22×D47C22×D414yes—
299C22×D47C22×Q814yes—
300C22×D47C22×Q814yes—
301C22×D47C2×#4114yes—
302C2×C4×C47—28no—
303C2×C4×C47—28no—
304C2×C4×C47—28no—
305C2×C4×C47—22no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—22no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—22no—
313C2×C4×C47—22no—
314C2×C4×C47—22no—
315C2×C4×C47—22no—
316C2×C4×C47—22no—
317C2×C4×C47—22no—
318C2×C4×C47—22no—
319C2×C4×C47—22no—
320C2×C4×C47—22no—
321C2×C4×C47—22no—
322C2×C4×C47—22no—
323C2×C4×C47—44no—
324C2×C4×C47—44no—
325C2×C4×C47—44no—
326C2×C4×C47—44no—
327C2×C4×C47C22×D414yes—
328C2×C4×C47C22×Q814yes—
329C2×C4×C47C2×#4114yes—
330C2×Dic47—28no—
331C2×Dic47—28no—
332C2×Dic47—22no—
333C2×Dic47—22no—
334C2×Dic47—22no—
335C2×Dic47—22no—
336C2×Dic47—22no—
337C2×Dic47—22no—
338C2×Dic47—22no—
339C2×Dic47—22no—
340C2×Dic47—22no—
341C2×Dic47—22no—
342C2×Dic47—22no—
343C2×Dic47—22no—
344C2×Dic47—22no—
345C2×Dic47—22no—
346C2×Dic47—22no—
347C2×Dic47—22no—
348C2×Dic47—44no—
349C2×Dic47—44no—
350C2×Dic47—44no—
351C2×Dic47—44no—
352C2×Dic47C22×D414yes—
353C2×Dic47C2×#4114yes—
354D188—232no—
355C4×D47—416no—
356C4×D47—416no—
357C4×D47—416no—
358C4×D47—416no—
359Dic94—416no—
360C2×#2450—471nomaximal, Sylow
361C22×C47C2×C22⋊Q814yes—
362C22×C47#52914yes—
363C22×C47#53814yes—
364C22×C47#54614yes—
365C22×C47#54614yes—
366C22×C47#55414yes—
367C22×C47#55414yes—
368C22×C47C23×D411yescharacteristic
369C22×C47C23×Q811yescharacteristic
370C22×C47C22×#4111yescharacteristic
371C22×C47C22×#4111yescharacteristic
372C22×C47C22×#4111yescharacteristic
373C22×C47C2×H(5,𝔽2)11yescharacteristic
374C22×C47C2×H(5,𝔽2)11yescharacteristic
375C2×D47—24no—
376C2×D47—24no—
377C2×D47—24no—
378C2×D47—24no—
379C2×D47—24no—
380C2×D47—24no—
381C2×D47—232no—
382C2×D47—24no—
383C2×D47—24no—
384C2×D47—24no—
385C2×D47—42no—
386C2×D47—42no—
387C2×D47—42no—
388C2×D47—42no—
389C2×D47—416no—
390C2×D47C2×C22⋊Q818yes—
391C4×C47—24no—
392C4×C47—24no—
393C4×C47—24no—
394C4×C47—42no—
395C4×C47—42no—
396C4×C47—42no—
397C4×C47—42no—
398Dic47—24no—
399Dic47—24no—
400Dic47—42no—
401Dic47—42no—
402Dic47—42no—
403Dic47—42no—
404C22×C22⋊Q8—471no—
405C22×C4×D4—471no—
406#2450—4716no—
407C2×#400—471no—
408C2×#398—471no—
409C2×#396—471no—
410C2×#393—471no—
411C2×#391—471no—
412C2×#387D4711yescharacteristic, complemented
413C2×#386—471no—
414C2×#386—471no—
415C2×#385—471no—
416C2×#385—471no—
417C2×#385—471no—
418C2×#380—471no—
419C22×#95—471no—
420C2×C47#245018yescomplemented
421C2×C47C22×C22⋊Q811yescharacteristic
422C2×C47C2×#52911yescharacteristic
423C2×C47C2×#53811yescharacteristic
424C2×C47C2×#54611yescharacteristic
425C2×C47C2×#54611yescharacteristic
426C2×C47C2×#55411yescharacteristic
427C2×C47C2×#55411yescharacteristic
428D47—28no—
429D47—44no—
430C23×Q8—471no—
431C23×D4—471no—
432C24×C4—471no—
433C24×C4—471no—
434C24×C4—471no—
435C24×C4—471no—
436C2×C22⋊Q8—478no—
437C2×C22⋊Q8—948no—
438C2×C4×D4—478no—
439C2×C4×D4—948no—
440C22×C4⋊C4—471no—
441C22×C4⋊C4—471no—
442C22×C4⋊C4—471no—
443C22×C4⋊C4—471no—
444C22×C4⋊C4—471no—
445C22×C4⋊C4—471no—
446C22×C4⋊C4C2×D4711yescharacteristic
447C22×C4⋊C4C2×D4711yescharacteristic
448C22×C22⋊C4—471no—
449C22×C22⋊C4—471no—
450C22×C22⋊C4—471no—
451C22×C22⋊C4—471no—
452C22×C22⋊C4—471no—
453C22×C22⋊C4—471no—
454C22×C22⋊C4—471no—
455C22×C22⋊C4—471no—
456C22×C42C2×D4711yescharacteristic
457#400—478no—
458#398—478no—
459#396—478no—
460#393—478no—
461#391—478no—
462#387C2×D4718yescomplemented
463#386—478no—
464#386—478no—
465#385—478no—
466#385—478no—
467#385—478no—
468#380—478no—
469C2×#95—471no—
470C2×#95—471no—
471C2×#95—471no—
472C2×#95—471no—
473C2×#95—471no—
474C2×#95—471no—
475C2×#95—471no—
476C2×#95—471no—
477C2×#95—478no—
478C2×#95C2×D4711yescharacteristic
479C2×#95C2×D4711yescharacteristic
480C2×#95C2×D4711yescharacteristic
481C2×#95C2×D4711yescharacteristic
482C47C2×#245011yescharacteristic, complemented, Sylow
483C25—471no—
484C25—471no—
485C22×Q8—474no—
486C22×Q8—944no—
487C22×Q8—944no—
488C22×Q8—1882no—
489C22×D4—478no—
490C22×D4—474no—
491C22×D4—944no—
492C22×D4—944no—
493C23×C4—471no—
494C23×C4—471no—
495C23×C4—471no—
496C23×C4—471no—
497C23×C4—471no—
498C23×C4—471no—
499C23×C4—474no—
500C23×C4—474no—
501C23×C4—474no—
502C23×C4—474no—
503C23×C4—944no—
504C23×C4—944no—
505C23×C4—944no—
506C23×C4—944no—
507C23×C4—944no—
508C23×C4—944no—
509C23×C4—944no—
510C23×C4—1882no—
511C23×C4—1882no—
512C23×C4—1882no—
513C23×C4—1882no—
514C23×C4—1882no—
515C23×C4C22×D4711yescharacteristic
516C23×C4C22×D4711yescharacteristic
517C23×C4C22×D4711yescharacteristic
518C23×C4C22×D4711yescharacteristic
519C23×C4C22×D4711yescharacteristic
520C23×C4C22×D4711yescharacteristic
521C23×C4C22×D4711yescharacteristic
522C22⋊Q8—9432no—
523C4×D4—9432no—
524C2×C4⋊C4—24no—
525C2×C4⋊C4—24no—
526C2×C4⋊C4—474no—
527C2×C4⋊C4—474no—
528C2×C4⋊C4—474no—
529C2×C4⋊C4—474no—
530C2×C4⋊C4—474no—
531C2×C4⋊C4—474no—
532C2×C4⋊C4—944no—
533C2×C4⋊C4—944no—
534C2×C4⋊C4—944no—
535C2×C4⋊C4—1882no—
536C2×C4⋊C4—1882no—
537C2×C4⋊C4—1882no—
538C2×C4⋊C4C22×D4714yes—
539C2×C4⋊C4C22×D4714yes—
540C2×C22⋊C4—478no—
541C2×C22⋊C4—474no—
542C2×C22⋊C4—474no—
543C2×C22⋊C4—474no—
544C2×C22⋊C4—474no—
545C2×C22⋊C4—474no—
546C2×C22⋊C4—474no—
547C2×C22⋊C4—474no—
548C2×C22⋊C4—474no—
549C2×C22⋊C4—944no—
550C2×C22⋊C4—944no—
551C2×C22⋊C4—944no—
552C2×C22⋊C4—944no—
553C2×C22⋊C4—1882no—
554C2×C22⋊C4—1882no—
555C2×C22⋊C4—1882no—
556C2×C42—24no—
557C2×C42C22×D4714yes—
558#95—474no—
559#95—474no—
560#95—474no—
561#95—474no—
562#95—474no—
563#95—474no—
564#95—474no—
565#95—474no—
566#95C22×D4714yes—
567#95C22×D4714yes—
568#95C22×D4714yes—
569#95C22×D4714yes—
570C24—474no—
571C24—474no—
572C24—474no—
573C24—472no—
574C24—474no—
575C24—472no—
576C24—942no—
577C24—942no—
578C24—942no—
579C24—942no—
580C24—942no—
581C24—942no—
582C24—942no—
583C24—942no—
584C24—942no—
585C24—942no—
586C24C23×D4711yescharacteristic
587C2×Q8—948no—
588C2×Q8—948no—
589C2×Q8—1884no—
590C2×Q8—18816no—
591C2×D4—4716no—
592C2×D4—948no—
593C2×D4—9432no—
594C2×D4—948no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—474no—
614C22×C4—474no—
615C22×C4—472no—
616C22×C4—472no—
617C22×C4—472no—
618C22×C4—472no—
619C22×C4—472no—
620C22×C4—472no—
621C22×C4—948no—
622C22×C4—948no—
623C22×C4—948no—
624C22×C4—948no—
625C22×C4—948no—
626C22×C4—942no—
627C22×C4—942no—
628C22×C4—942no—
629C22×C4—942no—
630C22×C4—942no—
631C22×C4—942no—
632C22×C4—942no—
633C22×C4—942no—
634C22×C4—942no—
635C22×C4—942no—
636C22×C4—942no—
637C22×C4—942no—
638C22×C4—942no—
639C22×C4—942no—
640C22×C4—942no—
641C22×C4—942no—
642C22×C4—948no—
643C22×C4—948no—
644C22×C4—1884no—
645C22×C4—1884no—
646C22×C4—1884no—
647C22×C4—1884no—
648C22×C4—1884no—
649C22×C4—18816no—
650C22×C4—18816no—
651C22×C4—18816no—
652C22×C4—18816no—
653C22×C4#1062535014yes—
654C22×C4D4×D4714yes—
655C22×C4Q8×D4714yes—
656C22×C4C23×D4712yes—
657C22×C4C23×D4712yes—
658C22×C4C23×D4712yes—
659C22×C4C23×D4712yes—
660C22×C4C23×D4712yes—
661C22×C4C23×D4712yes—
662C22×C4C23×D4712yes—
663C4⋊C4—28no—
664C4⋊C4—28no—
665C4⋊C4—948no—
666C4⋊C4—948no—
667C4⋊C4—948no—
668C4⋊C4—1884no—
669C4⋊C4—1884no—
670C4⋊C4—1884no—
671C22⋊C4—4716no—
672C22⋊C4—948no—
673C22⋊C4—948no—
674C22⋊C4—948no—
675C22⋊C4—948no—
676C22⋊C4—1884no—
677C22⋊C4—1884no—
678C22⋊C4—1884no—
679C42—28no—
680C23—4716no—
681C23—474no—
682C23—474no—
683C23—474no—
684C23—474no—
685C23—948no—
686C23—948no—
687C23—948no—
688C23—948no—
689C23—948no—
690C23—942no—
691C23—942no—
692C23—942no—
693C23—942no—
694C23—948no—
695C23—948no—
696C23—948no—
697C23—948no—
698C23—942no—
699C23—942no—
700C23—942no—
701C23—942no—
702C23—942no—
703C23—942no—
704C23—1884no—
705C23—1884no—
706C23—1884no—
707C23—1884no—
708C23C2×D4×D4712yes—
709C23C2×Q8×D4712yes—
710C23#41×D4712yes—
711C23#41×D4712yes—
712C23C2×#1062535012yes—
713C23#1309407012yes—
714C23#1309407012yes—
715C23C24×D4711yescharacteristic
716Q8—18816no—
717D4—9432no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—474no—
744C2×C4—474no—
745C2×C4—948no—
746C2×C4—948no—
747C2×C4—942no—
748C2×C4—942no—
749C2×C4—942no—
750C2×C4—942no—
751C2×C4—942no—
752C2×C4—942no—
753C2×C4—942no—
754C2×C4—942no—
755C2×C4—942no—
756C2×C4—942no—
757C2×C4—942no—
758C2×C4—942no—
759C2×C4—942no—
760C2×C4—942no—
761C2×C4—942no—
762C2×C4—942no—
763C2×C4—18816no—
764C2×C4—18816no—
765C2×C4—18816no—
766C2×C4—18816no—
767C2×C4—1884no—
768C2×C4—1884no—
769C2×C4—1884no—
770C2×C4—1884no—
771C2×C4C2×D4×D4714yes—
772C2×C4C2×Q8×D4714yes—
773C2×C4C2×#1062535014yes—
774C22—478no—
775C22—944no—
776C22—944no—
777C22—944no—
778C22—944no—
779C22—944no—
780C22—9432no—
781C22—944no—
782C22—944no—
783C22—944no—
784C22—944no—
785C22—1882no—
786C22—1882no—
787C22—1882no—
788C22—18816no—
789C22—1882no—
790C22C22⋊Q8×D4714yes—
791C22#1568965114yes—
792C22#1568971214yes—
793C22#1568976514yes—
794C22#1568976914yes—
795C22#1568982914yes—
796C22#1568983314yes—
797C22C22×D4×D4711yescharacteristic
798C22C22×Q8×D4711yescharacteristic
799C22C2×#41×D4711yescharacteristic
800C22C2×#41×D4711yescharacteristic
801C22C22×#1062535011yescharacteristic
802C22C2×#1309407011yescharacteristic
803C22C2×#1309407011yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—42no—
811C4—944no—
812C4—944no—
813C4—1882no—
814C4—1882no—
815C4—1882no—
816C4—1882no—
817C2—948no—
818C2—1884no—
819C2#2024721118yesdirect product factor
820C2C2×C22⋊Q8×D4711yescharacteristic
821C2C2×#1568965111yescharacteristic
822C2C2×#1568971211yescharacteristic
823C2C2×#1568976511yescharacteristic
824C2C2×#1568976911yescharacteristic
825C2C2×#1568982911yescharacteristic
826C2C2×#1568983311yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#387C2
socleC24×C47C24
prime radicalC23×D188C22
hypercenterC2×#387D47
hypocenterC47C2×#2450
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. C22×#13094002C2semidirect
3. #20247211C2direct (N × H)
4. C2×#15689065C2semidirect
5. C2×#15689057C2semidirect
6. C2×#15689045C2semidirect
7. C2×#15689036C2semidirect
8. C2×#15689029C2semidirect
11. C2×#15688997C2semidirect
12. C2×#15688994C2semidirect
13. C2×#15688994C2semidirect
14. C2×#15688982C2semidirect
15. C2×#95×D47C2semidirect
16. C2×C47×#387C2semidirect
24. C2×#13094002C22semidirect
41. #15689065C22semidirect
42. #15689057C22semidirect
43. #15689045C22semidirect
44. #15689036C22semidirect
45. #15689029C22semidirect
48. #15688997C22semidirect
49. #15688994C22semidirect
50. #15688994C22semidirect
51. #15688982C22semidirect
60. #95×D47C22semidirect
64. C47×#387C22semidirect
77. C22×D188Q8semidirect
228. C2×D188C2×Q8semidirect
412. C2×#387D47semidirect
420. C2×C47#2450semidirect
462. #387C2×D47semidirect
482. C47C2×#2450semidirect
819. C2#20247211direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940022
C22×C4×D1882
#202472112
C2×#156890652
C2×#156890572
C2×#156890452
C2×#156890362
C2×#156890292
C2×#156890012
C2×#156889972
C2×#156889942
C2×#156889822
C2×#95×D472
C2×C47×#3872
C2×#245047