Finite Group Databasebeta

← C2×#20245929 #26374748

Subgroups — C2×#20245929 #26374748

Order 12032.

3790 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094010C211yesmaximal, characteristic
2C22×#13093989C211yesmaximal, characteristic, complemented
3C22×(C22⋊D47)⋊C4C211yesmaximal, characteristic
4#20245929C2116yesmaximal, direct product factor
5C2×#15689027C211yesmaximal, characteristic, complemented
6C2×#15689023C211yesmaximal, characteristic
7C2×#15689017C211yesmaximal, characteristic, complemented
8C2×#15689014C211yesmaximal, characteristic, complemented
9C2×#15689013C211yesmaximal, characteristic, complemented
10C2×#15688987C211yesmaximal, characteristic, complemented
11C2×C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
12C2×C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
13C2×#15688970C211yesmaximal, characteristic, complemented
14C2×#15688970C211yesmaximal, characteristic, complemented
15C2×C42×Dic47C211yesmaximal, characteristic, complemented
16C2×C47×#388C211yesmaximal, characteristic, complemented
17C23×Dic94C2211yescharacteristic
18C23×C22⋊D47C2211yescharacteristic
19C24×Dic47C2211yescharacteristic
20C23×C4×D47C2211yescharacteristic
21C2×#13094010C4116yescomplemented
22C2×#13094010C2218yes—
23C2×#13093989—28no—
24C2×#13093989C2218yescomplemented
25C2×(C22⋊D47)⋊C4—28no—
26C2×(C22⋊D47)⋊C4C2218yes—
27C22×Dic47⋊C4C2211yescharacteristic
28C22×Dic47⋊C4C2211yescharacteristic
29C22×Dic47⋊C4C2211yescharacteristic
30C22×C22⋊Dic47C2211yescharacteristic
31C22×C22⋊Dic47C2211yescharacteristic
32C22×(C2×D47)⋊C4C2211yescharacteristic
33C22×(C2×D47)⋊C4C2211yescharacteristic
34C22×(C2×D47)⋊C4C2211yescharacteristic
35C22×(C2×D47)⋊C4C2211yescharacteristic
36C22×(C2×D47)⋊C4C2211yescharacteristic
37C22×C4×Dic47C2211yescharacteristic
38C22×C4×Dic47C2211yescharacteristic
39C22×C4×Dic47C2211yescharacteristic
40C22×C4×Dic47C2211yescharacteristic
41C22×C4×Dic47C2211yescharacteristic
42C22×C4×Dic47C2211yescharacteristic
43C22×C4×Dic47C2211yescharacteristic
44C22×C4×Dic47C2211yescharacteristic
45#15689027C2218yescomplemented
46#15689023C2218yes—
47#15689017C2218yescomplemented
48#15689014C2218yescomplemented
49#15689013C2218yescomplemented
50#15688987C2218yescomplemented
51C22⋊C4×Dic47C2218yescomplemented
52C22⋊C4×Dic47C2218yescomplemented
53#15688970C2218yescomplemented
54#15688970C2218yescomplemented
55C2×C47⋊#95C2211yescharacteristic
56C2×C47⋊#95C2211yescharacteristic
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×Dic94—24no—
72C22×Dic94—24no—
73C22×Dic94C2×C418yescomplemented
74C22×Dic94C2314yes—
75C22×C22⋊D47—24no—
76C22×C22⋊D47—24no—
77C22×C22⋊D47C2×C418yes—
78C22×C22⋊D47C2314yes—
79C23×Dic47—24no—
80C23×Dic47—24no—
81C23×Dic47—24no—
82C23×Dic47C2311yescharacteristic
83C23×Dic47C2311yescharacteristic
84C23×Dic47C2314yes—
85C23×Dic47C2311yescharacteristic
86C23×Dic47C2311yescharacteristic
87C23×Dic47C2311yescharacteristic
88C23×Dic47C2311yescharacteristic
89C23×Dic47C2311yescharacteristic
90C22×C4×D47—24no—
91C22×C4×D47—24no—
92C22×C4×D47—24no—
93C22×C4×D47C2314yes—
94#13094010C2×C4164yescomplemented
95#13093989—232no—
96(C22⋊D47)⋊C4—232no—
97C2×Dic47⋊C4—24no—
98C2×Dic47⋊C4—24no—
99C2×Dic47⋊C4—24no—
100C2×Dic47⋊C4C2314yes—
101C2×Dic47⋊C4C2314yes—
102C2×Dic47⋊C4C2314yes—
103C2×C22⋊Dic47—24no—
104C2×C22⋊Dic47C2×C418yescomplemented
105C2×C22⋊Dic47C2314yes—
106C2×C22⋊Dic47C2314yes—
107C2×(C2×D47)⋊C4—24no—
108C2×(C2×D47)⋊C4—24no—
109C2×(C2×D47)⋊C4—24no—
110C2×(C2×D47)⋊C4C2×C418yescomplemented
111C2×(C2×D47)⋊C4C2×C418yescomplemented
112C2×(C2×D47)⋊C4C2314yes—
113C2×(C2×D47)⋊C4C2314yes—
114C2×(C2×D47)⋊C4C2314yes—
115C2×(C2×D47)⋊C4C2314yes—
116C2×(C2×D47)⋊C4C2314yes—
117C2×C4×Dic47—24no—
118C2×C4×Dic47—24no—
119C2×C4×Dic47—24no—
120C2×C4×Dic47—24no—
121C2×C4×Dic47—24no—
122C2×C4×Dic47—24no—
123C2×C4×Dic47C2×C418yescomplemented
124C2×C4×Dic47D418yes—
125C2×C4×Dic47C2314yes—
126C2×C4×Dic47C2314yes—
127C2×C4×Dic47C2314yes—
128C2×C4×Dic47C2314yes—
129C2×C4×Dic47C2314yes—
130C2×C4×Dic47C2314yes—
131C2×C4×Dic47C2314yes—
132C2×C4×Dic47C2314yes—
133C47⋊#95C2314yes—
134C47⋊#95C2314yes—
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×C418yescomplemented
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—22no—
210C22×Dic47—22no—
211C22×Dic47—22no—
212C22×Dic47—22no—
213C22×Dic47—22no—
214C22×Dic47—22no—
215C22×Dic47—28no—
216C22×Dic47—28no—
217C22×Dic47—28no—
218C22×Dic47—416no—
219C22×Dic47C22×C414yes—
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—28no—
236C2×C4×D47—28no—
237C2×C4×D47—28no—
238C2×C4×D47—416no—
239C2×Dic94—232no—
240C2×Dic94—28no—
241C2×Dic94—28no—
242C2×Dic94C22×C4116yescomplemented
243C4⋊C4×C47—28no—
244C22⋊C4×C47—28no—
245C22⋊C4×C47—28no—
246C22⋊C4×C47C22×C4116yescomplemented
247C42×C47—28no—
248C22⋊Dic47—28no—
249C22⋊Dic47C22×C4116yescomplemented
250(C2×D47)⋊C4—28no—
251(C2×D47)⋊C4—28no—
252(C2×D47)⋊C4—28no—
253(C2×D47)⋊C4C22×C4116yescomplemented
254(C2×D47)⋊C4C22×C4116yescomplemented
255Dic47⋊C4—28no—
256Dic47⋊C4—28no—
257Dic47⋊C4—28no—
258C4×Dic47—28no—
259C4×Dic47—28no—
260C4×Dic47—28no—
261C4×Dic47—28no—
262C4×Dic47—28no—
263C4×Dic47—28no—
264C4×Dic47C22×C4116yescomplemented
265C4×Dic47C2×D4116yes—
266C23×C47—28no—
267C23×C47—28no—
268C23×C47—28no—
269C23×C47—22no—
270C23×C47—22no—
271C23×C47—22no—
272C23×C47—22no—
273C23×C47—22no—
274C23×C47—22no—
275C23×C47—44no—
276C23×C47—44no—
277C23×C47—44no—
278C23×C47—44no—
279C23×C47C23×C414yes—
280C23×C47C23×C412yes—
281C23×C47C22×D412yes—
282C23×C47C2×#4112yes—
283C23×C47C2×#4112yes—
284C23×C47C2×#4112yes—
285C23×C47C2×#4112yes—
286C23×C47C2×#4112yes—
287C23×C47C2511yescharacteristic
288C22×D47—28no—
289C22×D47—28no—
290C22×D47—28no—
291C22×D47—22no—
292C22×D47—22no—
293C22×D47—22no—
294C22×D47—22no—
295C22×D47—22no—
296C22×D47—22no—
297C22×D47—44no—
298C22×D47—44no—
299C22×D47—44no—
300C22×D47—44no—
301C22×D47C23×C414yes—
302C2×C4×C47—28no—
303C2×C4×C47—28no—
304C2×C4×C47—28no—
305C2×C4×C47—28no—
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—44no—
321C2×C4×C47—44no—
322C2×C4×C47C23×C414yes—
323C2×C4×C47C23×C414yes—
324C2×C4×C47C22×D414yes—
325C2×C4×C47C2×#4114yes—
326C22⋊D47—232no—
327C2×Dic47—28no—
328C2×Dic47—28no—
329C2×Dic47—28no—
330C2×Dic47—22no—
331C2×Dic47—22no—
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—44no—
343C2×Dic47—44no—
344C2×Dic47—416no—
345C2×Dic47C4×D4116yes—
346C2×Dic47#124116yescomplemented
347C2×Dic47C23×C414yes—
348C2×Dic47C23×C414yes—
349C2×Dic47C23×C414yes—
350C2×Dic47C22×D414yes—
351C2×Dic47C22×D414yes—
352C2×Dic47C2×#4114yes—
353C2×Dic47C2×#4114yes—
354C2×Dic47C2×#4114yes—
355C2×Dic47C2×#4114yes—
356C4×D47—416no—
357Dic94—232no—
358C2×C4×#124—471nomaximal, Sylow
359C22×C47—24no—
360C22×C47—24no—
361C22×C47—24no—
362C22×C47—42no—
363C22×C47—42no—
364C22×C47—42no—
365C22×C47—42no—
366C22×C47—416no—
367C22×C47C2×C4×D414yes—
368C22×C47C4×#4114yes—
369C22×C47C4×#4114yes—
370C22×C47C2×#12414yes—
371C22×C47#52914yes—
372C22×C47#52914yes—
373C22×C47#53214yes—
374C22×C47C24×C411yescharacteristic
375C22×C47C23×D411yescharacteristic
376C22×C47C22×#4111yescharacteristic
377C22×C47C22×#4111yescharacteristic
378C22×C47C22×#4111yescharacteristic
379C22×C47C22×#4111yescharacteristic
380C22×C47C22×#4111yescharacteristic
381C2×D47—24no—
382C2×D47—24no—
383C2×D47—24no—
384C2×D47—42no—
385C2×D47—42no—
386C2×D47—42no—
387C2×D47—42no—
388C2×D47—416no—
389C4×C47—24no—
390C4×C47—24no—
391C4×C47—24no—
392C4×C47—24no—
393C4×C47—42no—
394C4×C47—42no—
395Dic47—24no—
396Dic47—24no—
397Dic47—24no—
398Dic47—42no—
399Dic47—42no—
400Dic47C2×C4×D418yes—
401Dic47C2×#12418yescomplemented
402C22×#124—471no—
403C22×C4×Q8—471no—
404C22×C4×D4—471no—
405C4×#124—4716no—
406C2×#391—471no—
407C2×#390—471no—
408C2×#388—471no—
409C2×#388—471no—
410C2×#388—471no—
411C2×#388D4711yescharacteristic, complemented
412C2×#382—471no—
413C2×C4×C22⋊C4—471no—
414C2×C4×C22⋊C4—471no—
415C2×C4×C22⋊C4—471no—
416C2×C4×C22⋊C4—471no—
417C2×C43—471no—
418C2×C47—44no—
419C2×C47C4×#12418yescomplemented
420C2×C47C22×C4×D411yescharacteristic
421C2×C47C2×C4×#4111yescharacteristic
422C2×C47C2×C4×#4111yescharacteristic
423C2×C47C22×#12411yescharacteristic
424C2×C47C2×#52911yescharacteristic
425C2×C47C2×#52911yescharacteristic
426C2×C47C2×#53211yescharacteristic
427D47—44no—
428C23×Q8—471no—
429C23×D4—471no—
430C24×C4—471no—
431C24×C4—471no—
432C2×#124—4716no—
433C2×#124—478no—
434C2×C4×Q8—478no—
435C2×C4×Q8—948no—
436C2×C4×D4—478no—
437C2×C4×D4—948no—
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#391—478no—
462#390—478no—
463#388—478no—
464#388—478no—
465#388—478no—
466#388C2×D4718yescomplemented
467#382—478no—
468C4×C22⋊C4—478no—
469C4×C22⋊C4—478no—
470C4×C22⋊C4—478no—
471C4×C22⋊C4—478no—
472C2×#95—471no—
473C2×#95—471no—
474C2×#95—471no—
475C2×#95—471no—
476C2×#95—471no—
477C2×#95—471no—
478C2×#95C2×D4711yescharacteristic
479C2×#95C2×D4711yescharacteristic
480C43—478no—
481C47C2×C4×#12411yescharacteristic, complemented, Sylow
482C25—471no—
483C25C22×D4711yescharacteristic
484C22×Q8—478no—
485C22×Q8—474no—
486C22×Q8—944no—
487C22×Q8—944no—
488C22×D4—478no—
489C22×D4—474no—
490C22×D4—944no—
491C22×D4—944no—
492C23×C4—471no—
493C23×C4—471no—
494C23×C4—471no—
495C23×C4—471no—
496C23×C4—471no—
497C23×C4—474no—
498C23×C4—471no—
499C23×C4—471no—
500C23×C4—474no—
501C23×C4—944no—
502C23×C4—944no—
503C23×C4—944no—
504C23×C4—944no—
505C23×C4—944no—
506C23×C4—944no—
507C23×C4C22×D4711yescharacteristic
508C23×C4C22×D4711yescharacteristic
509C23×C4C22×D4711yescharacteristic
510C23×C4C22×D4711yescharacteristic
511C23×C4C22×D4711yescharacteristic
512C23×C4C22×D4711yescharacteristic
513#124—4764no—
514C4×Q8—9432no—
515C4×D4—9432no—
516C2×C4⋊C4—24no—
517C2×C4⋊C4—474no—
518C2×C4⋊C4—474no—
519C2×C4⋊C4—474no—
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—478no—
529C2×C22⋊C4—478no—
530C2×C22⋊C4—474no—
531C2×C22⋊C4—474no—
532C2×C22⋊C4—474no—
533C2×C22⋊C4—474no—
534C2×C22⋊C4—474no—
535C2×C22⋊C4—474no—
536C2×C22⋊C4—944no—
537C2×C22⋊C4—944no—
538C2×C22⋊C4—944no—
539C2×C22⋊C4—944no—
540C2×C22⋊C4C4×D4718yescomplemented
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#95—474no—
567#95—474no—
568#95C22×D4714yes—
569#95C22×D4714yes—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—474no—
577C24—472no—
578C24—942no—
579C24—942no—
580C24—942no—
581C24—942no—
582C24—942no—
583C24—942no—
584C24C2×C4×D4714yes—
585C24C23×D4712yes—
586C24C23×D4711yescharacteristic
587C2×Q8—4716no—
588C2×Q8—948no—
589C2×Q8—9432no—
590C2×Q8—948no—
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—474no—
610C22×C4—474no—
611C22×C4—474no—
612C22×C4—474no—
613C22×C4—474no—
614C22×C4—474no—
615C22×C4—472no—
616C22×C4—472no—
617C22×C4—474no—
618C22×C4—474no—
619C22×C4—474no—
620C22×C4—472no—
621C22×C4—472no—
622C22×C4—472no—
623C22×C4—472no—
624C22×C4—472no—
625C22×C4—948no—
626C22×C4—948no—
627C22×C4—948no—
628C22×C4—948no—
629C22×C4—948no—
630C22×C4—948no—
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—942no—
643C22×C4—18816no—
644C22×C4—18816no—
645C22×C4C2×C4×D4714yes—
646C22×C4C2×C4×D4714yes—
647C22×C4D4×D4714yes—
648C22×C4#1062535214yes—
649C22×C4C23×D4712yes—
650C22×C4C23×D4712yes—
651C22×C4C23×D4712yes—
652C22×C4C23×D4712yes—
653C22×C4C23×D4712yes—
654C22×C4C23×D4712yes—
655C4⋊C4—28no—
656C4⋊C4—948no—
657C4⋊C4—948no—
658C4⋊C4—948no—
659C22⋊C4—28no—
660C22⋊C4—28no—
661C22⋊C4—4716no—
662C22⋊C4—4716no—
663C22⋊C4—4716no—
664C22⋊C4—948no—
665C22⋊C4—948no—
666C22⋊C4—948no—
667C22⋊C4—948no—
668C22⋊C4C2×C4×D47116yescomplemented
669C42—28no—
670C42—4716no—
671C42—4716no—
672C42—948no—
673C42—948no—
674C42—948no—
675C42—948no—
676C42—948no—
677C42—948no—
678C23—28no—
679C23—28no—
680C23—28no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—474no—
692C23—948no—
693C23—948no—
694C23—948no—
695C23—942no—
696C23—942no—
697C23—942no—
698C23—942no—
699C23—942no—
700C23—942no—
701C23—1884no—
702C23—1884no—
703C23—1884no—
704C23—1884no—
705C23C22×C4×D4714yes—
706C23C22×C4×D4712yes—
707C23C2×D4×D4712yes—
708C23#41×D4712yes—
709C23#41×D4712yes—
710C23#41×D4712yes—
711C23#41×D4712yes—
712C23C2×#1062535212yes—
713C23C24×D4711yescharacteristic
714Q8—9432no—
715D4—9432no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—28no—
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—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—4716no—
737C2×C4—4716no—
738C2×C4—474no—
739C2×C4—474no—
740C2×C4—474no—
741C2×C4—474no—
742C2×C4—474no—
743C2×C4—474no—
744C2×C4—474no—
745C2×C4—474no—
746C2×C4—474no—
747C2×C4—948no—
748C2×C4—948no—
749C2×C4—948no—
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—18816no—
763C2×C4—18816no—
764C2×C4—1884no—
765C2×C4—1884no—
766C2×C4C22×C4×D4714yes—
767C2×C4C22×C4×D4714yes—
768C2×C4C2×D4×D4714yes—
769C2×C4C2×#1062535214yes—
770C22—24no—
771C22—24no—
772C22—24no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—416no—
778C22—944no—
779C22—944no—
780C22—944no—
781C22—1882no—
782C22—1882no—
783C22—1882no—
784C22—1882no—
785C22—18816no—
786C22C4×D4×D4714yes—
787C22C4×#1062535214yes—
788C22#1568959114yes—
789C22#124×D4714yes—
790C22#1568965014yes—
791C22#1568965614yes—
792C22#1568966814yes—
793C22C23×C4×D4711yescharacteristic
794C22C22×D4×D4711yescharacteristic
795C22C2×#41×D4711yescharacteristic
796C22C2×#41×D4711yescharacteristic
797C22C2×#41×D4711yescharacteristic
798C22C2×#41×D4711yescharacteristic
799C22C22×#1062535211yescharacteristic
800C4—24no—
801C4—24no—
802C4—24no—
803C4—24no—
804C4—42no—
805C4—42no—
806C4—478no—
807C4—478no—
808C4—944no—
809C4—944no—
810C4—944no—
811C4—1882no—
812C4—1882no—
813C2—44no—
814C2—1884no—
815C2#2024592918yesdirect product factor
816C2C2×C4×D4×D4711yescharacteristic
817C2C2×C4×#1062535211yescharacteristic
818C2C2×#1568959111yescharacteristic
819C2C2×#124×D4711yescharacteristic
820C2C2×#1568965011yescharacteristic
821C2C2×#1568965611yescharacteristic
822C2C2×#1568966811yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#388C2
socleC24×C47C24
prime radicalC23×C22⋊D47C22
cosocleC23×C47C25
hypercenterC2×#388D47
hypocenterC47C2×C4×#124
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×#13093989C2semidirect
4. #20245929C2direct (N × H)
5. C2×#15689027C2semidirect
7. C2×#15689017C2semidirect
8. C2×#15689014C2semidirect
9. C2×#15689013C2semidirect
10. C2×#15688987C2semidirect
11. C2×C22⋊C4×Dic47C2semidirect
12. C2×C22⋊C4×Dic47C2semidirect
13. C2×#15688970C2semidirect
14. C2×#15688970C2semidirect
15. C2×C42×Dic47C2semidirect
16. C2×C47×#388C2semidirect
21. C2×#13094010C4semidirect
24. C2×#13093989C22semidirect
45. #15689027C22semidirect
47. #15689017C22semidirect
48. #15689014C22semidirect
49. #15689013C22semidirect
50. #15688987C22semidirect
51. C22⋊C4×Dic47C22semidirect
52. C22⋊C4×Dic47C22semidirect
53. #15688970C22semidirect
54. #15688970C22semidirect
61. C42×Dic47C22semidirect
67. C47×#388C22semidirect
73. C22×Dic94C2×C4semidirect
94. #13094010C2×C4semidirect
104. C2×C22⋊Dic47C2×C4semidirect
110. C2×(C2×D47)⋊C4C2×C4semidirect
111. C2×(C2×D47)⋊C4C2×C4semidirect
123. C2×C4×Dic47C2×C4semidirect
150. C2×C22⋊C4×C47C2×C4semidirect
242. C2×Dic94C22×C4semidirect
246. C22⋊C4×C47C22×C4semidirect
249. C22⋊Dic47C22×C4semidirect
253. (C2×D47)⋊C4C22×C4semidirect
254. (C2×D47)⋊C4C22×C4semidirect
264. C4×Dic47C22×C4semidirect
346. C2×Dic47#124semidirect
401. Dic47C2×#124semidirect
411. C2×#388D47semidirect
419. C2×C47C4×#124semidirect
466. #388C2×D47semidirect
481. C47C2×C4×#124semidirect
540. C2×C22⋊C4C4×D47semidirect
668. C22⋊C4C2×C4×D47semidirect
815. C2#20245929direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940102
C22×#130939892
C22×(C22⋊D47)⋊C42
#202459292
C2×#156890272
C2×#156890232
C2×#156890172
C2×#156890142
C2×#156890132
C2×#156889872
C2×C22⋊C4×Dic472
C2×#156889702
C2×C42×Dic472
C2×C47×#3882
C2×C4×#12447