Finite Group Databasebeta

← C2×#20245848 #26374635

Subgroups — C2×#20245848 #26374635

Order 12032.

3790 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D47)⋊C4C211yesmaximal, characteristic
2C22×#13093982C211yesmaximal, characteristic, complemented
3C22×#13093980C211yesmaximal, characteristic, complemented
4#20245848C2116yesmaximal, direct product factor
5C2×#15689023C211yesmaximal, characteristic
6C2×#15689023C211yesmaximal, characteristic
7C2×#15689020C211yesmaximal, characteristic, complemented
8C2×#15689018C211yesmaximal, characteristic, complemented
9C2×#15689016C211yesmaximal, characteristic, complemented
10C2×#15689014C211yesmaximal, characteristic, complemented
11C2×#15689012C211yesmaximal, characteristic, complemented
12C2×#15688974C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
14C2×#15688970C211yesmaximal, characteristic, complemented
15C2×C42×Dic47C211yesmaximal, characteristic, complemented
16C2×C47×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D47C2211yescharacteristic
18C24×Dic47C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C2×(C22⋊D47)⋊C4C4116yescomplemented
21C2×(C22⋊D47)⋊C4C2218yes—
22C2×#13093982—28no—
23C2×#13093982C2218yescomplemented
24C2×#13093980—28no—
25C2×#13093980C2218yescomplemented
26C22×C4⋊Dic47C2211yescharacteristic
27C22×Dic47⋊C4C2211yescharacteristic
28C22×Dic47⋊C4C2211yescharacteristic
29C22×Dic47⋊C4C2211yescharacteristic
30C22×Dic47⋊C4C2211yescharacteristic
31C22×Dic47⋊C4C2211yescharacteristic
32C22×C22⋊Dic47C2211yescharacteristic
33C22×C22⋊Dic47C2211yescharacteristic
34C22×(C2×D47)⋊C4C2211yescharacteristic
35C22×(C2×D47)⋊C4C2211yescharacteristic
36C22×(C2×D47)⋊C4C2211yescharacteristic
37C22×(C2×D47)⋊C4C2211yescharacteristic
38C22×(C2×D47)⋊C4C2211yescharacteristic
39C22×C4×Dic47C2211yescharacteristic
40C22×C4×Dic47C2211yescharacteristic
41C22×C4×Dic47C2211yescharacteristic
42C22×C4×Dic47C2211yescharacteristic
43C22×C4×Dic47C2211yescharacteristic
44C22×C4×Dic47C2211yescharacteristic
45C22×C4×Dic47C2211yescharacteristic
46C22×C4×Dic47C2211yescharacteristic
47#15689023C2218yes—
48#15689023C2218yes—
49#15689020C2218yescomplemented
50#15689018C2218yescomplemented
51#15689016C2218yescomplemented
52#15689014C2218yescomplemented
53#15689012C2218yescomplemented
54#15688974C2218yescomplemented
55C22⋊C4×Dic47C2218yescomplemented
56#15688970C2218yescomplemented
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C42×Dic47C2218yescomplemented
62C22×C4⋊C4×C47C2211yescharacteristic
63C22×C22⋊C4×C47C2211yescharacteristic
64C22×C22⋊C4×C47C2211yescharacteristic
65C22×C22⋊C4×C47C2211yescharacteristic
66C22×C42×C47C2211yescharacteristic
67C47×#388C2218yescomplemented
68C2×#95×C47C2211yescharacteristic
69C2×#95×C47C2211yescharacteristic
70C24×D47C2311yescharacteristic
71C22×C22⋊D47—24no—
72C22×C22⋊D47—24no—
73C22×C22⋊D47C2×C418yes—
74C22×C22⋊D47C2314yes—
75C23×Dic47—24no—
76C23×Dic47—24no—
77C23×Dic47C2×C418yes—
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2311yescharacteristic
80C23×Dic47C2311yescharacteristic
81C23×Dic47C2314yes—
82C23×Dic47C2311yescharacteristic
83C23×Dic47C2311yescharacteristic
84C23×Dic47C2311yescharacteristic
85C23×Dic47C2311yescharacteristic
86C22×C4×D47—24no—
87C22×C4×D47—24no—
88C22×C4×D47C2×C418yes—
89C22×C4×D47C2314yes—
90(C22⋊D47)⋊C4C2×C4164yescomplemented
91#13093982—232no—
92#13093980—232no—
93C2×C4⋊Dic47—24no—
94C2×C4⋊Dic47C2314yes—
95C2×Dic47⋊C4—24no—
96C2×Dic47⋊C4—24no—
97C2×Dic47⋊C4—24no—
98C2×Dic47⋊C4—24no—
99C2×Dic47⋊C4C2×C418yes—
100C2×Dic47⋊C4C2314yes—
101C2×Dic47⋊C4C2314yes—
102C2×Dic47⋊C4C2314yes—
103C2×Dic47⋊C4C2314yes—
104C2×Dic47⋊C4C2314yes—
105C2×C22⋊Dic47—24no—
106C2×C22⋊Dic47—24no—
107C2×C22⋊Dic47C2314yes—
108C2×C22⋊Dic47C2314yes—
109C2×(C2×D47)⋊C4—24no—
110C2×(C2×D47)⋊C4—24no—
111C2×(C2×D47)⋊C4—24no—
112C2×(C2×D47)⋊C4—24no—
113C2×(C2×D47)⋊C4C2×C418yes—
114C2×(C2×D47)⋊C4C2314yes—
115C2×(C2×D47)⋊C4C2314yes—
116C2×(C2×D47)⋊C4C2314yes—
117C2×(C2×D47)⋊C4C2314yes—
118C2×(C2×D47)⋊C4C2314yes—
119C2×C4×Dic47—24no—
120C2×C4×Dic47—24no—
121C2×C4×Dic47—24no—
122C2×C4×Dic47—24no—
123C2×C4×Dic47—24no—
124C2×C4×Dic47—24no—
125C2×C4×Dic47C2×C418yes—
126C2×C4×Dic47D418yescomplemented
127C2×C4×Dic47C2314yes—
128C2×C4×Dic47C2314yes—
129C2×C4×Dic47C2314yes—
130C2×C4×Dic47C2314yes—
131C2×C4×Dic47C2314yes—
132C2×C4×Dic47C2314yes—
133C2×C4×Dic47C2314yes—
134C2×C4×Dic47C2314yes—
135C47⋊#95C2314yes—
136C47⋊#95C2314yes—
137C47⋊#95C2314yes—
138C47⋊#95C2314yes—
139C25×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×C47C2314yes—
148C2×C22⋊C4×C47—24no—
149C2×C22⋊C4×C47—24no—
150C2×C22⋊C4×C47C2×C418yes—
151C2×C22⋊C4×C47C2314yes—
152C2×C22⋊C4×C47C2314yes—
153C2×C22⋊C4×C47C2314yes—
154C2×C42×C47—24no—
155C2×C42×C47C2314yes—
156#95×C47C2314yes—
157#95×C47C2314yes—
158C24×C47—22no—
159C24×C47—22no—
160C24×C47—22no—
161C24×C47—22no—
162C24×C47—22no—
163C24×C47—22no—
164C24×C47C22×C414yes—
165C24×C47C2412yes—
166C24×C47C2411yescharacteristic
167C23×D47—22no—
168C23×D47—22no—
169C23×D47—22no—
170C23×D47—22no—
171C23×D47—22no—
172C23×D47—22no—
173C23×D47C22×C414yes—
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×C47C22×C414yes—
190C22×C4×C47C22×C414yes—
191C22×C4×C47C2×D414yes—
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—232no—
200C2×C22⋊D47—28no—
201C2×C22⋊D47—28no—
202C2×C22⋊D47C22×C4116yes—
203C22×Dic47—22no—
204C22×Dic47—22no—
205C22×Dic47—22no—
206C22×Dic47—22no—
207C22×Dic47—22no—
208C22×Dic47—22no—
209C22×Dic47—232no—
210C22×Dic47—28no—
211C22×Dic47—28no—
212C22×Dic47—22no—
213C22×Dic47—22no—
214C22×Dic47—22no—
215C22×Dic47—22no—
216C22×Dic47—22no—
217C22×Dic47—22no—
218C22×Dic47C22×C414yes—
219C22×Dic47C22×C4116yes—
220C22×Dic47C22×C414yes—
221C22×Dic47C22×C414yes—
222C22×Dic47C2×D414yes—
223C22×Dic47C2×D414yes—
224C22×Dic47#4114yes—
225C22×Dic47#4114yes—
226C22×Dic47#4114yes—
227C22×Dic47#4114yes—
228C22×Dic47C2412yes—
229C22×Dic47C2412yes—
230C22×Dic47C2412yes—
231C22×Dic47C2412yes—
232C22×Dic47C2412yes—
233C22×Dic47C2412yes—
234C22×Dic47C2412yes—
235C2×C4×D47—232no—
236C2×C4×D47—28no—
237C2×C4×D47—28no—
238C2×C4×D47C22×C4116yes—
239C4⋊C4×C47—28no—
240C22⋊C4×C47—28no—
241C22⋊C4×C47—28no—
242C22⋊C4×C47C22×C4116yes—
243C42×C47—28no—
244C22⋊Dic47—28no—
245C22⋊Dic47—28no—
246(C2×D47)⋊C4—28no—
247(C2×D47)⋊C4—28no—
248(C2×D47)⋊C4—28no—
249(C2×D47)⋊C4—28no—
250(C2×D47)⋊C4C22×C4116yes—
251C4⋊Dic47—28no—
252Dic47⋊C4—28no—
253Dic47⋊C4—28no—
254Dic47⋊C4—28no—
255Dic47⋊C4—28no—
256Dic47⋊C4C22×C4116yes—
257C4×Dic47—28no—
258C4×Dic47—28no—
259C4×Dic47—28no—
260C4×Dic47—28no—
261C4×Dic47—28no—
262C4×Dic47—28no—
263C4×Dic47C22×C4116yes—
264C4×Dic47C2×D4116yescomplemented
265C23×C47—28no—
266C23×C47—28no—
267C23×C47—28no—
268C23×C47—22no—
269C23×C47—22no—
270C23×C47—22no—
271C23×C47—22no—
272C23×C47—22no—
273C23×C47—22no—
274C23×C47—44no—
275C23×C47—44no—
276C23×C47—44no—
277C23×C47—44no—
278C23×C47C23×C414yes—
279C23×C47C23×C412yes—
280C23×C47C22×D412yes—
281C23×C47C2×#4112yes—
282C23×C47C2×#4112yes—
283C23×C47C2×#4112yes—
284C23×C47C2×#4112yes—
285C23×C47C2×#4112yes—
286C23×C47C2511yescharacteristic
287C22×D47—28no—
288C22×D47—28no—
289C22×D47—28no—
290C22×D47—22no—
291C22×D47—22no—
292C22×D47—22no—
293C22×D47—22no—
294C22×D47—22no—
295C22×D47—22no—
296C22×D47—44no—
297C22×D47—44no—
298C22×D47—44no—
299C22×D47—44no—
300C22×D47C23×C414yes—
301C2×C4×C47—28no—
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—44no—
320C2×C4×C47—44no—
321C2×C4×C47C23×C414yes—
322C2×C4×C47C23×C414yes—
323C2×C4×C47C22×D414yes—
324C2×C4×C47C2×#4114yes—
325C22⋊D47—232no—
326C2×Dic47—28no—
327C2×Dic47—28no—
328C2×Dic47—28no—
329C2×Dic47—22no—
330C2×Dic47—22no—
331C2×Dic47—22no—
332C2×Dic47—22no—
333C2×Dic47—22no—
334C2×Dic47—22no—
335C2×Dic47—232no—
336C2×Dic47—22no—
337C2×Dic47—22no—
338C2×Dic47—22no—
339C2×Dic47—22no—
340C2×Dic47—22no—
341C2×Dic47—22no—
342C2×Dic47—44no—
343C2×Dic47—44no—
344C2×Dic47#117116yescomplemented
345C2×Dic47C4×D4116yes—
346C2×Dic47C23×C414yes—
347C2×Dic47C23×C414yes—
348C2×Dic47C23×C414yes—
349C2×Dic47C22×D414yes—
350C2×Dic47C22×D414yes—
351C2×Dic47C2×#4114yes—
352C2×Dic47C2×#4114yes—
353C2×Dic47C2×#4114yes—
354C2×Dic47C2×#4114yes—
355C4×D47—232no—
356C2×#2293—471nomaximal, Sylow
357C22×C47—24no—
358C22×C47—24no—
359C22×C47—24no—
360C22×C47—42no—
361C22×C47—42no—
362C22×C47—42no—
363C22×C47—42no—
364C22×C47—416no—
365C22×C47C2×#11714yes—
366C22×C47C2×C4×D414yes—
367C22×C47C4×#4114yes—
368C22×C47#52914yes—
369C22×C47#52914yes—
370C22×C47#53214yes—
371C22×C47#53214yes—
372C22×C47C24×C411yescharacteristic
373C22×C47C23×D411yescharacteristic
374C22×C47C22×#4111yescharacteristic
375C22×C47C22×#4111yescharacteristic
376C22×C47C22×#4111yescharacteristic
377C22×C47C22×#4111yescharacteristic
378C22×C47C22×#4111yescharacteristic
379C2×D47—24no—
380C2×D47—24no—
381C2×D47—24no—
382C2×D47—42no—
383C2×D47—42no—
384C2×D47—42no—
385C2×D47—42no—
386C2×D47—416no—
387C4×C47—24no—
388C4×C47—24no—
389C4×C47—24no—
390C4×C47—24no—
391C4×C47—42no—
392C4×C47—42no—
393Dic47—24no—
394Dic47—24no—
395Dic47—24no—
396Dic47—42no—
397Dic47—42no—
398Dic47C2×#11718yescomplemented
399Dic47C2×C4×D418yes—
400C22×C4×D4—471no—
401C22×#117—471no—
402C22×#117—471no—
403#2293—4716no—
404C2×#390—471no—
405C2×#390—471no—
406C2×#389—471no—
407C2×#389—471no—
408C2×#388—471no—
409C2×#388—471no—
410C2×#388—471no—
411C2×#388D4711yescharacteristic, complemented
412C2×C4×C4⋊C4—471no—
413C2×C4×C22⋊C4—471no—
414C2×C4×C22⋊C4—471no—
415C2×C43—471no—
416C2×C47—44no—
417C2×C47#229318yescomplemented
418C2×C47C22×#11711yescharacteristic
419C2×C47C22×C4×D411yescharacteristic
420C2×C47C2×C4×#4111yescharacteristic
421C2×C47C2×#52911yescharacteristic
422C2×C47C2×#52911yescharacteristic
423C2×C47C2×#53211yescharacteristic
424C2×C47C2×#53211yescharacteristic
425D47—44no—
426C23×D4—471no—
427C24×C4—471no—
428C24×C4—471no—
429C2×C4×D4—4716no—
430C2×C4×D4—478no—
431C2×#117—478no—
432C2×#117—478no—
433C2×#117—948no—
434C2×#117—948no—
435C22×C4⋊C4—471no—
436C22×C4⋊C4—471no—
437C22×C4⋊C4—471no—
438C22×C4⋊C4—471no—
439C22×C4⋊C4—471no—
440C22×C4⋊C4—471no—
441C22×C4⋊C4C2×D4711yescharacteristic
442C22×C22⋊C4—471no—
443C22×C22⋊C4—471no—
444C22×C22⋊C4—471no—
445C22×C22⋊C4—471no—
446C22×C22⋊C4—471no—
447C22×C22⋊C4—471no—
448C22×C22⋊C4—471no—
449C22×C22⋊C4C2×D4711yescharacteristic
450C22×C22⋊C4C2×D4711yescharacteristic
451C22×C22⋊C4C2×D4711yescharacteristic
452C22×C42—471no—
453C22×C42—471no—
454C22×C42—471no—
455C22×C42—471no—
456C22×C42—471no—
457C22×C42—471no—
458C22×C42—471no—
459C22×C42—471no—
460C22×C42C2×D4711yescharacteristic
461#390—478no—
462#390—478no—
463#389—478no—
464#389—478no—
465#388—478no—
466#388—478no—
467#388—478no—
468#388C2×D4718yescomplemented
469C4×C4⋊C4—478no—
470C4×C22⋊C4—478no—
471C4×C22⋊C4—478no—
472C2×#95—471no—
473C2×#95—471no—
474C2×#95—471no—
475C2×#95—471no—
476C2×#95C2×D4711yescharacteristic
477C2×#95C2×D4711yescharacteristic
478C43—478no—
479C47C2×#229311yescharacteristic, complemented, Sylow
480C25—471no—
481C25C22×D4711yescharacteristic
482C22×D4—478no—
483C22×D4—474no—
484C22×D4—944no—
485C22×D4—944no—
486C23×C4—471no—
487C23×C4—471no—
488C23×C4—478no—
489C23×C4—474no—
490C23×C4—471no—
491C23×C4—471no—
492C23×C4—471no—
493C23×C4—478no—
494C23×C4—474no—
495C23×C4—471no—
496C23×C4—471no—
497C23×C4—944no—
498C23×C4—944no—
499C23×C4—944no—
500C23×C4—944no—
501C23×C4C22×D4711yescharacteristic
502C23×C4C22×D4711yescharacteristic
503C23×C4C22×D4711yescharacteristic
504C23×C4C22×D4711yescharacteristic
505C23×C4C22×D4711yescharacteristic
506C23×C4C22×D4711yescharacteristic
507C4×D4—4764no—
508#117—9432no—
509#117—9432no—
510C2×C4⋊C4—24no—
511C2×C4⋊C4—478no—
512C2×C4⋊C4—474no—
513C2×C4⋊C4—474no—
514C2×C4⋊C4—474no—
515C2×C4⋊C4—474no—
516C2×C4⋊C4—474no—
517C2×C4⋊C4—474no—
518C2×C4⋊C4—944no—
519C2×C4⋊C4—944no—
520C2×C4⋊C4—944no—
521C2×C4⋊C4—944no—
522C2×C4⋊C4—944no—
523C2×C4⋊C4C22×D4714yes—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—478no—
527C2×C22⋊C4—474no—
528C2×C22⋊C4—474no—
529C2×C22⋊C4—474no—
530C2×C22⋊C4—474no—
531C2×C22⋊C4—474no—
532C2×C22⋊C4—474no—
533C2×C22⋊C4—474no—
534C2×C22⋊C4—944no—
535C2×C22⋊C4—944no—
536C2×C22⋊C4—944no—
537C2×C22⋊C4—944no—
538C2×C22⋊C4—944no—
539C2×C22⋊C4—944no—
540C2×C22⋊C4C4×D4718yes—
541C2×C22⋊C4C22×D4714yes—
542C2×C22⋊C4C22×D4714yes—
543C2×C22⋊C4C22×D4714yes—
544C2×C42—24no—
545C2×C42—478no—
546C2×C42—478no—
547C2×C42—474no—
548C2×C42—474no—
549C2×C42—474no—
550C2×C42—474no—
551C2×C42—474no—
552C2×C42—474no—
553C2×C42—474no—
554C2×C42—474no—
555C2×C42—944no—
556C2×C42—944no—
557C2×C42—944no—
558C2×C42—944no—
559C2×C42—944no—
560C2×C42—944no—
561C2×C42C22×D4714yes—
562#95—474no—
563#95—474no—
564#95—474no—
565#95—474no—
566#95C22×D4714yes—
567#95C22×D4714yes—
568C24—22no—
569C24—22no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—474no—
575C24—472no—
576C24—942no—
577C24—942no—
578C24—942no—
579C24—942no—
580C24—942no—
581C24—942no—
582C24C2×C4×D4714yes—
583C24C23×D4712yes—
584C24C23×D4711yescharacteristic
585C2×D4—4716no—
586C2×D4—9432no—
587C2×D4—948no—
588C2×D4—948no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
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—474no—
604C22×C4—474no—
605C22×C4—474no—
606C22×C4—474no—
607C22×C4—474no—
608C22×C4—474no—
609C22×C4—472no—
610C22×C4—472no—
611C22×C4—474no—
612C22×C4—4716no—
613C22×C4—474no—
614C22×C4—474no—
615C22×C4—472no—
616C22×C4—472no—
617C22×C4—472no—
618C22×C4—4716no—
619C22×C4—472no—
620C22×C4—472no—
621C22×C4—948no—
622C22×C4—9432no—
623C22×C4—948no—
624C22×C4—948no—
625C22×C4—9432no—
626C22×C4—948no—
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×C4C2×C4×D4714yes—
640C22×C4C2×C4×D4714yes—
641C22×C4D4×D4714yes—
642C22×C4#1062535214yes—
643C22×C4C23×D4712yes—
644C22×C4C23×D4712yes—
645C22×C4C23×D4712yes—
646C22×C4C23×D4712yes—
647C22×C4C23×D4712yes—
648C22×C4C23×D4712yes—
649C4⋊C4—28no—
650C4⋊C4—4716no—
651C4⋊C4—948no—
652C4⋊C4—948no—
653C4⋊C4—948no—
654C4⋊C4—948no—
655C4⋊C4—948no—
656C22⋊C4—28no—
657C22⋊C4—28no—
658C22⋊C4—4716no—
659C22⋊C4—948no—
660C22⋊C4—948no—
661C22⋊C4—948no—
662C22⋊C4—948no—
663C22⋊C4—948no—
664C22⋊C4—948no—
665C22⋊C4C2×C4×D47116yes—
666C42—28no—
667C42—4716no—
668C42—4716no—
669C42—948no—
670C42—948no—
671C42—948no—
672C42—948no—
673C42—948no—
674C42—948no—
675C23—28no—
676C23—28no—
677C23—28no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23—44no—
688C23—474no—
689C23—948no—
690C23—948no—
691C23—948no—
692C23—942no—
693C23—942no—
694C23—942no—
695C23—942no—
696C23—942no—
697C23—942no—
698C23—1884no—
699C23—1884no—
700C23—1884no—
701C23—1884no—
702C23C22×C4×D4714yes—
703C23C22×C4×D4712yes—
704C23C2×D4×D4712yes—
705C23#41×D4712yes—
706C23#41×D4712yes—
707C23#41×D4712yes—
708C23#41×D4712yes—
709C23C2×#1062535212yes—
710C23C24×D4711yescharacteristic
711D4—9432no—
712C2×C4—28no—
713C2×C4—28no—
714C2×C4—28no—
715C2×C4—28no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
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—44no—
731C2×C4—44no—
732C2×C4—4716no—
733C2×C4—4716no—
734C2×C4—474no—
735C2×C4—474no—
736C2×C4—474no—
737C2×C4—474no—
738C2×C4—474no—
739C2×C4—474no—
740C2×C4—474no—
741C2×C4—474no—
742C2×C4—474no—
743C2×C4—9432no—
744C2×C4—9432no—
745C2×C4—948no—
746C2×C4—948no—
747C2×C4—948no—
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—1884no—
761C2×C4—1884no—
762C2×C4C22×C4×D4714yes—
763C2×C4C22×C4×D4714yes—
764C2×C4C2×D4×D4714yes—
765C2×C4C2×#1062535214yes—
766C22—24no—
767C22—24no—
768C22—24no—
769C22—416no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—944no—
775C22—944no—
776C22—944no—
777C22—18816no—
778C22—1882no—
779C22—1882no—
780C22—1882no—
781C22—1882no—
782C22#117×D4714yes—
783C22C4×D4×D4714yes—
784C22C4×#1062535214yes—
785C22#1568965014yes—
786C22#1568965614yes—
787C22#1568966814yes—
788C22#1568967214yes—
789C22C23×C4×D4711yescharacteristic
790C22C22×D4×D4711yescharacteristic
791C22C2×#41×D4711yescharacteristic
792C22C2×#41×D4711yescharacteristic
793C22C2×#41×D4711yescharacteristic
794C22C2×#41×D4711yescharacteristic
795C22C22×#1062535211yescharacteristic
796C4—24no—
797C4—24no—
798C4—24no—
799C4—24no—
800C4—42no—
801C4—42no—
802C4—478no—
803C4—478no—
804C4—944no—
805C4—944no—
806C4—944no—
807C4—1882no—
808C4—1882no—
809C2—44no—
810C2—1884no—
811C2#2024584818yesdirect product factor
812C2C2×#117×D4711yescharacteristic
813C2C2×C4×D4×D4711yescharacteristic
814C2C2×C4×#1062535211yescharacteristic
815C2C2×#1568965011yescharacteristic
816C2C2×#1568965611yescharacteristic
817C2C2×#1568966811yescharacteristic
818C2C2×#1568967211yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#388C2
socleC24×C47C24
prime radicalC23×C22⋊D47C22
cosocleC23×C47C25
hypercenterC2×#388D47
hypocenterC47C2×#2293
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×#13093982C2semidirect
3. C22×#13093980C2semidirect
4. #20245848C2direct (N × H)
7. C2×#15689020C2semidirect
8. C2×#15689018C2semidirect
9. C2×#15689016C2semidirect
10. C2×#15689014C2semidirect
11. C2×#15689012C2semidirect
12. C2×#15688974C2semidirect
13. C2×C22⋊C4×Dic47C2semidirect
14. C2×#15688970C2semidirect
15. C2×C42×Dic47C2semidirect
16. C2×C47×#388C2semidirect
20. C2×(C22⋊D47)⋊C4C4semidirect
23. C2×#13093982C22semidirect
25. C2×#13093980C22semidirect
49. #15689020C22semidirect
50. #15689018C22semidirect
51. #15689016C22semidirect
52. #15689014C22semidirect
53. #15689012C22semidirect
54. #15688974C22semidirect
55. C22⋊C4×Dic47C22semidirect
56. #15688970C22semidirect
61. C42×Dic47C22semidirect
67. C47×#388C22semidirect
90. (C22⋊D47)⋊C4C2×C4semidirect
126. C2×C4×Dic47D4semidirect
264. C4×Dic47C2×D4semidirect
344. C2×Dic47#117semidirect
398. Dic47C2×#117semidirect
411. C2×#388D47semidirect
417. C2×C47#2293semidirect
468. #388C2×D47semidirect
479. C47C2×#2293semidirect
811. C2#20245848direct (N × H)

Maximal subgroups

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

subgroupindex
C22×(C22⋊D47)⋊C42
C22×#130939822
C22×#130939802
#202458482
C2×#156890232
C2×#156890202
C2×#156890182
C2×#156890162
C2×#156890142
C2×#156890122
C2×#156889742
C2×C22⋊C4×Dic472
C2×#156889702
C2×C42×Dic472
C2×C47×#3882
C2×#229347