Finite Group Databasebeta

← C2×#20251522 #26422605

Subgroups — C2×#20251522 #26422605

Order 12032.

2434 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251522C2116yesmaximal, direct product factor
2C2×#15689060C211yesmaximal, characteristic, complemented
3C2×#15689056C211yesmaximal, characteristic, complemented
4C2×#15689052C211yesmaximal, characteristic, complemented
5C2×#15689049C211yesmaximal, characteristic, complemented
6C2×#15689045C211yesmaximal, characteristic, complemented
7C2×#15689040C211yesmaximal, characteristic, complemented
8C2×#15689039C211yesmaximal, characteristic, complemented
9C2×#15689039C211yesmaximal, characteristic, complemented
10C2×#15689038C211yesmaximal, characteristic, complemented
11C2×#15689038C211yesmaximal, characteristic, complemented
12C2×#15689032C211yesmaximal, characteristic
13C2×#15689024C211yesmaximal, characteristic, complemented
14C2×#15689016C211yesmaximal, characteristic, complemented
15C2×#15689009C211yesmaximal, characteristic, complemented
16C2×C47×#396C211yesmaximal, characteristic, complemented
17C23×D188C2211yescharacteristic
18C23×C22⋊D47C2211yescharacteristic
19C23×C22⋊D47C2211yescharacteristic
20C22×C4⋊Dic47C2211yescharacteristic
21C22×C4⋊Dic47C2211yescharacteristic
22C22×C4⋊Dic47C2211yescharacteristic
23C22×Dic47⋊C4C2211yescharacteristic
24C22×Dic47⋊C4C2211yescharacteristic
25C22×C22⋊Dic47C2211yescharacteristic
26C22×C22⋊Dic47C2211yescharacteristic
27C22×(C2×D47)⋊C4C2211yescharacteristic
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×C4×Dic47C2211yescharacteristic
38#15689060C2218yescomplemented
39#15689056C2218yescomplemented
40#15689052C2218yescomplemented
41#15689049C2218yescomplemented
42#15689045C2218yescomplemented
43#15689040C2218yescomplemented
44#15689039C2218yescomplemented
45#15689039C2218yescomplemented
46#15689038C2218yescomplemented
47#15689038C2218yescomplemented
48#15689032C2218yes—
49#15689024C2218yescomplemented
50#15689016C2218yescomplemented
51#15689009C2218yescomplemented
52C2×C47⋊#95C2211yescharacteristic
53C2×C47⋊#95C2211yescharacteristic
54C2×C47⋊#95C2211yescharacteristic
55C2×C47⋊#95C2211yescharacteristic
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C22×C4⋊C4×C47C2211yescharacteristic
60C22×C4⋊C4×C47C2211yescharacteristic
61C22×C4⋊C4×C47C2211yescharacteristic
62C22×C22⋊C4×C47C2211yescharacteristic
63C22×C22⋊C4×C47C2211yescharacteristic
64C22×C22⋊C4×C47C2211yescharacteristic
65C47×#396C2218yescomplemented
66C2×#95×C47C2211yescharacteristic
67C24×D47C2311yescharacteristic
68C24×D47C2311yescharacteristic
69C22×D188—24no—
70C22×D188—42no—
71C22×D188—42no—
72C22×D188C2314yes—
73C22×C22⋊D47—42no—
74C22×C22⋊D47—42no—
75C22×C22⋊D47—42no—
76C22×C22⋊D47—42no—
77C22×C22⋊D47—42no—
78C22×C22⋊D47—42no—
79C22×C22⋊D47C2314yes—
80C22×C22⋊D47C2314yes—
81C23×Dic47C2311yescharacteristic
82C23×Dic47C2311yescharacteristic
83C23×Dic47C2311yescharacteristic
84C23×Dic47C2311yescharacteristic
85C23×Dic47C2311yescharacteristic
86C23×Dic47C2311yescharacteristic
87C2×C4⋊Dic47—42no—
88C2×C4⋊Dic47—42no—
89C2×C4⋊Dic47—42no—
90C2×C4⋊Dic47C2314yes—
91C2×C4⋊Dic47C2314yes—
92C2×C4⋊Dic47C2314yes—
93C2×Dic47⋊C4—42no—
94C2×Dic47⋊C4—42no—
95C2×Dic47⋊C4C2314yes—
96C2×Dic47⋊C4C2314yes—
97C2×C22⋊Dic47—42no—
98C2×C22⋊Dic47—42no—
99C2×C22⋊Dic47C2314yes—
100C2×C22⋊Dic47C2314yes—
101C2×(C2×D47)⋊C4—42no—
102C2×(C2×D47)⋊C4—42no—
103C2×(C2×D47)⋊C4—42no—
104C2×(C2×D47)⋊C4—42no—
105C2×(C2×D47)⋊C4—42no—
106C2×(C2×D47)⋊C4—42no—
107C2×(C2×D47)⋊C4—42no—
108C2×(C2×D47)⋊C4—42no—
109C2×(C2×D47)⋊C4—42no—
110C2×(C2×D47)⋊C4—42no—
111C2×(C2×D47)⋊C4C2314yes—
112C2×(C2×D47)⋊C4C2314yes—
113C2×(C2×D47)⋊C4C2314yes—
114C2×(C2×D47)⋊C4C2314yes—
115C2×(C2×D47)⋊C4C2314yes—
116C2×(C2×D47)⋊C4C2314yes—
117C2×(C2×D47)⋊C4C2314yes—
118C2×(C2×D47)⋊C4C2314yes—
119C2×(C2×D47)⋊C4C2314yes—
120C2×(C2×D47)⋊C4C2314yes—
121C2×C4×Dic47—42no—
122C2×C4×Dic47C2314yes—
123C47⋊#95C2314yes—
124C47⋊#95C2314yes—
125C47⋊#95C2314yes—
126C47⋊#95C2314yes—
127C47⋊#95C2314yes—
128C47⋊#95C2314yes—
129C47⋊#95C2314yes—
130C25×C47C2311yescharacteristic
131C23×C4×C47C2311yescharacteristic
132C23×C4×C47C2311yescharacteristic
133C23×C4×C47C2311yescharacteristic
134C23×C4×C47C2311yescharacteristic
135C23×C4×C47C2311yescharacteristic
136C23×C4×C47C2311yescharacteristic
137C2×C4⋊C4×C47—24no—
138C2×C4⋊C4×C47—42no—
139C2×C4⋊C4×C47—42no—
140C2×C4⋊C4×C47C2314yes—
141C2×C4⋊C4×C47C2314yes—
142C2×C4⋊C4×C47C2314yes—
143C2×C22⋊C4×C47—24no—
144C2×C22⋊C4×C47—42no—
145C2×C22⋊C4×C47—42no—
146C2×C22⋊C4×C47C2314yes—
147C2×C22⋊C4×C47C2314yes—
148C2×C22⋊C4×C47C2314yes—
149#95×C47C2314yes—
150C24×C47—22no—
151C24×C47—22no—
152C24×C47—22no—
153C24×C47—22no—
154C24×C47—22no—
155C24×C47—22no—
156C24×C47—22no—
157C24×C47C2412yes—
158C24×C47C2411yescharacteristic
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×D47—22no—
168C23×D47—22no—
169C23×D47—22no—
170C23×D47—22no—
171C23×D47—22no—
172C23×D47—22no—
173C23×D47C2412yes—
174C23×D47C2412yes—
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×C47—22no—
192C22×C4×C47#4114yes—
193C22×C4×C47C2412yes—
194C22×C4×C47C2412yes—
195C22×C4×C47C2412yes—
196C22×C4×C47C2412yes—
197C22×C4×C47C2412yes—
198C22×C4×C47C2412yes—
199C2×C22⋊D47—44no—
200C2×C22⋊D47—44no—
201C2×C22⋊D47—44no—
202C2×C22⋊D47—44no—
203C2×C22⋊D47—44no—
204C2×C22⋊D47—44no—
205C2×C22⋊D47—416no—
206C2×C22⋊D47—416no—
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×Dic47—22no—
218C22×Dic47—22no—
219C22×Dic47—22no—
220C22×Dic47—22no—
221C22×Dic47—22no—
222C22×Dic47—22no—
223C22×Dic47—22no—
224C22×Dic47—22no—
225C22×Dic47C2412yes—
226C22×Dic47C2412yes—
227C22×Dic47C2412yes—
228C22×Dic47C2412yes—
229C22×Dic47C2412yes—
230C22×Dic47C2412yes—
231C2×D188—28no—
232C2×D188—44no—
233C2×D188—44no—
234C2×D188—416no—
235C4⋊C4×C47—28no—
236C4⋊C4×C47—44no—
237C4⋊C4×C47—44no—
238C22⋊C4×C47—28no—
239C22⋊C4×C47—44no—
240C22⋊C4×C47—44no—
241C22⋊Dic47—44no—
242C22⋊Dic47—44no—
243(C2×D47)⋊C4—44no—
244(C2×D47)⋊C4—44no—
245(C2×D47)⋊C4—44no—
246(C2×D47)⋊C4—44no—
247(C2×D47)⋊C4—44no—
248(C2×D47)⋊C4—44no—
249(C2×D47)⋊C4—44no—
250(C2×D47)⋊C4—44no—
251(C2×D47)⋊C4—44no—
252(C2×D47)⋊C4—44no—
253C4⋊Dic47—44no—
254C4⋊Dic47—44no—
255C4⋊Dic47—44no—
256Dic47⋊C4—44no—
257Dic47⋊C4—44no—
258C4×Dic47—44no—
259C23×C47—22no—
260C23×C47—22no—
261C23×C47—22no—
262C23×C47—22no—
263C23×C47—22no—
264C23×C47—22no—
265C23×C47—22no—
266C23×C47—44no—
267C23×C47—44no—
268C23×C47—44no—
269C23×C47—44no—
270C23×C47—44no—
271C23×C47—44no—
272C23×C47—44no—
273C23×C47C2×#4112yes—
274C23×C47H(5,𝔽2)12yes—
275C23×C47H(5,𝔽2)12yes—
276C23×C47H(5,𝔽2)12yes—
277C23×C47H(5,𝔽2)12yes—
278C23×C47H(5,𝔽2)12yes—
279C23×C472−1+412yes—
280C23×C47C2511yescharacteristic
281C22×D47—22no—
282C22×D47—22no—
283C22×D47—22no—
284C22×D47—22no—
285C22×D47—22no—
286C22×D47—22no—
287C22×D47—22no—
288C22×D47—22no—
289C22×D47—22no—
290C22×D47—22no—
291C22×D47—22no—
292C22×D47—22no—
293C22×D47—22no—
294C22×D47—22no—
295C22×D47—44no—
296C22×D47—44no—
297C22×D47—44no—
298C22×D47—44no—
299C22×D47—44no—
300C22×D47—44no—
301C22×D47—44no—
302C22×D47—44no—
303C22×D47—44no—
304C22×D47—44no—
305C22×D47—44no—
306C22×D47—44no—
307C22×D47—44no—
308C22×D47—44no—
309C2×C4×C47—28no—
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—22no—
324C2×C4×C47—22no—
325C2×C4×C47—22no—
326C2×C4×C47—22no—
327C2×C4×C47—44no—
328C2×C4×C47—44no—
329C2×C4×C47—44no—
330C2×C4×C47—44no—
331C2×C4×C47—44no—
332C2×C4×C47C2×#4114yes—
333C22⋊D47—416no—
334C22⋊D47—416no—
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—22no—
349C2×Dic47—22no—
350C2×Dic47—22no—
351C2×Dic47—22no—
352C2×Dic47—22no—
353C2×Dic47—44no—
354C2×Dic47—44no—
355C2×Dic47—44no—
356C2×Dic47—44no—
357C2×Dic47—44no—
358C2×Dic47—44no—
359D188—416no—
360C2×#2829—471nomaximal, Sylow
361C22×C47—42no—
362C22×C47—42no—
363C22×C47—42no—
364C22×C47—42no—
365C22×C47—42no—
366C22×C47—42no—
367C22×C47—42no—
368C22×C47—88no—
369C22×C47#53814yes—
370C22×C47#54014yes—
371C22×C47#54214yes—
372C22×C47#56014yes—
373C22×C47#56014yes—
374C22×C47#56214yes—
375C22×C47#56214yes—
376C22×C47C22×#4111yescharacteristic
377C22×C47C2×H(5,𝔽2)11yescharacteristic
378C22×C47C2×H(5,𝔽2)11yescharacteristic
379C22×C47C2×H(5,𝔽2)11yescharacteristic
380C22×C47C2×H(5,𝔽2)11yescharacteristic
381C22×C47C2×H(5,𝔽2)11yescharacteristic
382C22×C47C2×2−1+411yescharacteristic
383C2×D47—42no—
384C2×D47—42no—
385C2×D47—42no—
386C2×D47—42no—
387C2×D47—42no—
388C2×D47—42no—
389C2×D47—42no—
390C2×D47—42no—
391C2×D47—42no—
392C2×D47—42no—
393C2×D47—42no—
394C2×D47—42no—
395C2×D47—42no—
396C2×D47—42no—
397C2×D47—88no—
398C2×D47—88no—
399C4×C47—24no—
400C4×C47—42no—
401C4×C47—42no—
402C4×C47—42no—
403C4×C47—42no—
404C4×C47—42no—
405Dic47—42no—
406Dic47—42no—
407Dic47—42no—
408Dic47—42no—
409Dic47—42no—
410Dic47—42no—
411#2829—4716no—
412C2×#399—471no—
413C2×#398—471no—
414C2×#397—471no—
415C2×#397—471no—
416C2×#396—471no—
417C2×#396D4711yescharacteristic, complemented
418C2×#394—471no—
419C2×#394—471no—
420C2×#394—471no—
421C2×#394—471no—
422C2×#394—471no—
423C2×#392—471no—
424C2×#390—471no—
425C2×#388—471no—
426C2×#387—471no—
427C2×C47—82no—
428C2×C47#282918yescomplemented
429C2×C47C2×#53811yescharacteristic
430C2×C47C2×#54011yescharacteristic
431C2×C47C2×#54211yescharacteristic
432C2×C47C2×#56011yescharacteristic
433C2×C47C2×#56011yescharacteristic
434C2×C47C2×#56211yescharacteristic
435C2×C47C2×#56211yescharacteristic
436D47—82no—
437D47—82no—
438C23×D4—471no—
439C23×D4—471no—
440C23×D4—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×C4⋊C4C2×D4711yescharacteristic
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×C22⋊C4—471no—
457C22×C22⋊C4—471no—
458C22×C22⋊C4—471no—
459C22×C22⋊C4—471no—
460C22×C22⋊C4—471no—
461C22×C22⋊C4C2×D4711yescharacteristic
462C22×C22⋊C4C2×D4711yescharacteristic
463C22×C22⋊C4C2×D4711yescharacteristic
464C22×C42—471no—
465#399—478no—
466#398—478no—
467#397—478no—
468#397—478no—
469#396—478no—
470#396C2×D4718yescomplemented
471#394—478no—
472#394—478no—
473#394—478no—
474#394—478no—
475#394—478no—
476#392—478no—
477#390—478no—
478#388—478no—
479#387—478no—
480C2×#95—471no—
481C2×#95—471no—
482C2×#95—471no—
483C2×#95—471no—
484C2×#95—471no—
485C2×#95—471no—
486C2×#95—471no—
487C2×#95C2×D4711yescharacteristic
488C47C2×#282911yescharacteristic, complemented, Sylow
489C25—471no—
490C25—471no—
491C25C22×D4711yescharacteristic
492C22×D4—474no—
493C22×D4—474no—
494C22×D4—474no—
495C22×D4—944no—
496C22×D4—1882no—
497C22×D4—1882no—
498C22×D4—1882no—
499C22×D4—1882no—
500C22×D4—1882no—
501C22×D4—1882no—
502C22×D4—1882no—
503C22×D4—1882no—
504C23×C4—471no—
505C23×C4—471no—
506C23×C4—471no—
507C23×C4—471no—
508C23×C4—471no—
509C23×C4—471no—
510C23×C4C22×D4711yescharacteristic
511C23×C4C22×D4711yescharacteristic
512C23×C4C22×D4711yescharacteristic
513C23×C4C22×D4711yescharacteristic
514C23×C4C22×D4711yescharacteristic
515C23×C4C22×D4711yescharacteristic
516C2×C4⋊C4—24no—
517C2×C4⋊C4—42no—
518C2×C4⋊C4—42no—
519C2×C4⋊C4—474no—
520C2×C4⋊C4—474no—
521C2×C4⋊C4—474no—
522C2×C4⋊C4—474no—
523C2×C4⋊C4—474no—
524C2×C4⋊C4—1882no—
525C2×C4⋊C4—1882no—
526C2×C4⋊C4—1882no—
527C2×C4⋊C4—1882no—
528C2×C4⋊C4—1882no—
529C2×C4⋊C4C22×D4714yes—
530C2×C4⋊C4C22×D4714yes—
531C2×C4⋊C4C22×D4714yes—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4—474no—
536C2×C22⋊C4—474no—
537C2×C22⋊C4—474no—
538C2×C22⋊C4—474no—
539C2×C22⋊C4—474no—
540C2×C22⋊C4—474no—
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—1882no—
548C2×C22⋊C4—1882no—
549C2×C22⋊C4—1882no—
550C2×C22⋊C4—1882no—
551C2×C22⋊C4—1882no—
552C2×C22⋊C4—1882no—
553C2×C22⋊C4—1882no—
554C2×C22⋊C4—1882no—
555C2×C22⋊C4—1882no—
556C2×C22⋊C4—1882no—
557C2×C22⋊C4—1882no—
558C2×C22⋊C4—1882no—
559C2×C22⋊C4C22×D4714yes—
560C2×C22⋊C4C22×D4714yes—
561C2×C22⋊C4C22×D4714yes—
562C2×C42—474no—
563C2×C42—1882no—
564#95—474no—
565#95—474no—
566#95—474no—
567#95—474no—
568#95—474no—
569#95—474no—
570#95—474no—
571#95C22×D4714yes—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—472no—
580C24—472no—
581C24—942no—
582C24—942no—
583C24—942no—
584C24—942no—
585C24—942no—
586C24—942no—
587C24—942no—
588C24—942no—
589C24—942no—
590C24—942no—
591C24—942no—
592C24—942no—
593C24—942no—
594C24—942no—
595C24C23×D4712yes—
596C24C23×D4711yescharacteristic
597C2×D4—948no—
598C2×D4—1884no—
599C2×D4—1884no—
600C2×D4—18816no—
601C2×D4—1884no—
602C2×D4—1884no—
603C2×D4—1884no—
604C2×D4—1884no—
605C2×D4—1884no—
606C2×D4—1884no—
607C2×D4—18816no—
608C2×D4—18816no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—472no—
627C22×C4—472no—
628C22×C4—472no—
629C22×C4—472no—
630C22×C4—472no—
631C22×C4—472no—
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—942no—
643C22×C4—942no—
644C22×C4—942no—
645C22×C4—942no—
646C22×C4—942no—
647C22×C4—942no—
648C22×C4—942no—
649C22×C4—942no—
650C22×C4#1062535214yes—
651C22×C4C23×D4712yes—
652C22×C4C23×D4712yes—
653C22×C4C23×D4712yes—
654C22×C4C23×D4712yes—
655C22×C4C23×D4712yes—
656C22×C4C23×D4712yes—
657C4⋊C4—28no—
658C4⋊C4—44no—
659C4⋊C4—44no—
660C4⋊C4—1884no—
661C4⋊C4—1884no—
662C4⋊C4—1884no—
663C4⋊C4—1884no—
664C4⋊C4—1884no—
665C22⋊C4—28no—
666C22⋊C4—44no—
667C22⋊C4—44no—
668C22⋊C4—1884no—
669C22⋊C4—1884no—
670C22⋊C4—1884no—
671C22⋊C4—1884no—
672C22⋊C4—1884no—
673C22⋊C4—1884no—
674C22⋊C4—1884no—
675C22⋊C4—1884no—
676C22⋊C4—1884no—
677C22⋊C4—1884no—
678C22⋊C4—1884no—
679C22⋊C4—1884no—
680C42—1884no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—942no—
696C23—942no—
697C23—942no—
698C23—942no—
699C23—942no—
700C23—942no—
701C23—942no—
702C23—942no—
703C23—942no—
704C23—942no—
705C23—942no—
706C23—942no—
707C23—942no—
708C23—942no—
709C23—1884no—
710C23—1884no—
711C23—1884no—
712C23—1884no—
713C23—1884no—
714C23—1884no—
715C23—1884no—
716C23—1884no—
717C23—1884no—
718C23—1884no—
719C23—1884no—
720C23—1884no—
721C23—1884no—
722C23—1884no—
723C23C2×#1062535212yes—
724C23#1309406912yes—
725C23#1309406912yes—
726C23#1309407012yes—
727C23#1309407012yes—
728C23#1309407012yes—
729C23#1309407212yes—
730C23C24×D4711yescharacteristic
731D4—18816no—
732D4—18816no—
733D4—18816no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—28no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—942no—
758C2×C4—942no—
759C2×C4—942no—
760C2×C4—942no—
761C2×C4—942no—
762C2×C4—942no—
763C2×C4—942no—
764C2×C4—942no—
765C2×C4—942no—
766C2×C4—942no—
767C2×C4—942no—
768C2×C4—942no—
769C2×C4—942no—
770C2×C4—942no—
771C2×C4—942no—
772C2×C4—942no—
773C2×C4—942no—
774C2×C4—942no—
775C2×C4—1884no—
776C2×C4—1884no—
777C2×C4—1884no—
778C2×C4—1884no—
779C2×C4—1884no—
780C2×C4—1884no—
781C2×C4C2×#1062535214yes—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—88no—
790C22—3768no—
791C22—3768no—
792C22—1882no—
793C22—1882no—
794C22—1882no—
795C22—1882no—
796C22—1882no—
797C22—1882no—
798C22—1882no—
799C22—1882no—
800C22—1882no—
801C22—1882no—
802C22—1882no—
803C22—1882no—
804C22—1882no—
805C22—1882no—
806C22#1568971014yes—
807C22#1568972614yes—
808C22#1568974614yes—
809C22#1568986114yes—
810C22#1568986414yes—
811C22#1568986914yes—
812C22#1568986914yes—
813C22C22×#1062535211yescharacteristic
814C22C2×#1309406911yescharacteristic
815C22C2×#1309406911yescharacteristic
816C22C2×#1309407011yescharacteristic
817C22C2×#1309407011yescharacteristic
818C22C2×#1309407011yescharacteristic
819C22C2×#1309407211yescharacteristic
820C4—24no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—42no—
825C4—42no—
826C4—1882no—
827C4—1882no—
828C4—1882no—
829C4—1882no—
830C4—1882no—
831C4—1882no—
832C2—82no—
833C2—3762no—
834C2—3762no—
835C2#2025152218yesdirect product factor
836C2C2×#1568971011yescharacteristic
837C2C2×#1568972611yescharacteristic
838C2C2×#1568974611yescharacteristic
839C2C2×#1568986111yescharacteristic
840C2C2×#1568986411yescharacteristic
841C2C2×#1568986911yescharacteristic
842C2C2×#1568986911yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#396C2
socleC24×C47C24
prime radicalC2×#15689032C2
hypercenterC2×#396D47
hypocenterC47C2×#2829
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. #20251522C2direct (N × H)
2. C2×#15689060C2semidirect
3. C2×#15689056C2semidirect
4. C2×#15689052C2semidirect
5. C2×#15689049C2semidirect
6. C2×#15689045C2semidirect
7. C2×#15689040C2semidirect
8. C2×#15689039C2semidirect
9. C2×#15689039C2semidirect
10. C2×#15689038C2semidirect
11. C2×#15689038C2semidirect
13. C2×#15689024C2semidirect
14. C2×#15689016C2semidirect
15. C2×#15689009C2semidirect
16. C2×C47×#396C2semidirect
38. #15689060C22semidirect
39. #15689056C22semidirect
40. #15689052C22semidirect
41. #15689049C22semidirect
42. #15689045C22semidirect
43. #15689040C22semidirect
44. #15689039C22semidirect
45. #15689039C22semidirect
46. #15689038C22semidirect
47. #15689038C22semidirect
49. #15689024C22semidirect
50. #15689016C22semidirect
51. #15689009C22semidirect
65. C47×#396C22semidirect
417. C2×#396D47semidirect
428. C2×C47#2829semidirect
470. #396C2×D47semidirect
488. C47C2×#2829semidirect
835. C2#20251522direct (N × H)

Maximal subgroups

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

subgroupindex
#202515222
C2×#156890602
C2×#156890562
C2×#156890522
C2×#156890492
C2×#156890452
C2×#156890402
C2×#156890392
C2×#156890382
C2×#156890322
C2×#156890242
C2×#156890162
C2×#156890092
C2×C47×#3962
C2×#282947