Finite Group Databasebeta

← C2×#20246462 #26375888

Subgroups — C2×#20246462 #26375888

Order 12032.

3678 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×C4×Dic94C211yesmaximal, characteristic, complemented
3C22×(C22⋊D47)⋊C4C211yesmaximal, characteristic
4#20246462C2116yesmaximal, direct product factor
5C2×#15689027C211yesmaximal, characteristic, complemented
6C2×#15689023C211yesmaximal, characteristic
7C2×#15689017C211yesmaximal, characteristic, complemented
8C2×#15689015C211yesmaximal, characteristic, complemented
9C2×#15689013C211yesmaximal, characteristic, complemented
10C2×#15688998C211yesmaximal, characteristic, complemented
11C2×#15688997C211yesmaximal, characteristic, complemented
12C2×C4⋊C4×Dic47C211yesmaximal, characteristic, complemented
13C2×#15688974C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
16C2×C47×#388C211yesmaximal, characteristic, complemented
17C23×Dic94C2211yescharacteristic
18C23×C22⋊D47C2211yescharacteristic
19C24×Dic47C2211yescharacteristic
20C23×C4×D47C2211yescharacteristic
21C2×#13094010C4116yescomplemented
22C2×#13094010C2218yes—
23C2×C4×Dic94—28no—
24C2×C4×Dic94C2218yescomplemented
25C2×(C22⋊D47)⋊C4—28no—
26C2×(C22⋊D47)⋊C4C2218yes—
27C22×C4⋊Dic47C2211yescharacteristic
28C22×C4⋊Dic47C2211yescharacteristic
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
45#15689027C2218yescomplemented
46#15689023C2218yes—
47#15689017C2218yescomplemented
48#15689015C2218yescomplemented
49#15689013C2218yescomplemented
50#15688998C2218yescomplemented
51#15688997C2218yescomplemented
52C4⋊C4×Dic47C2218yescomplemented
53#15688974C2218yescomplemented
54C22⋊C4×Dic47C2218yescomplemented
55C4×(C2×D47)⋊C4C2218yescomplemented
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C2×C47⋊#95C2211yescharacteristic
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—42no—
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—42no—
93C22×C4×D47C2314yes—
94#13094010C2×C4164yescomplemented
95C4×Dic94—232no—
96(C22⋊D47)⋊C4—232no—
97C2×C4⋊Dic47—24no—
98C2×C4⋊Dic47—24no—
99C2×C4⋊Dic47C2314yes—
100C2×C4⋊Dic47C2314yes—
101C2×Dic47⋊C4—24no—
102C2×Dic47⋊C4—24no—
103C2×Dic47⋊C4D418yes—
104C2×Dic47⋊C4C2314yes—
105C2×Dic47⋊C4C2314yes—
106C2×Dic47⋊C4C2314yes—
107C2×C22⋊Dic47—42no—
108C2×C22⋊Dic47C2×C418yescomplemented
109C2×C22⋊Dic47C2314yes—
110C2×C22⋊Dic47C2314yes—
111C2×(C2×D47)⋊C4—24no—
112C2×(C2×D47)⋊C4—24no—
113C2×(C2×D47)⋊C4—42no—
114C2×(C2×D47)⋊C4C2×C418yescomplemented
115C2×(C2×D47)⋊C4C2×C418yescomplemented
116C2×(C2×D47)⋊C4C2314yes—
117C2×(C2×D47)⋊C4C2314yes—
118C2×(C2×D47)⋊C4C2314yes—
119C2×(C2×D47)⋊C4C2314yes—
120C2×(C2×D47)⋊C4C2314yes—
121C2×C4×Dic47—24no—
122C2×C4×Dic47—24no—
123C2×C4×Dic47—24no—
124C2×C4×Dic47—42no—
125C2×C4×Dic47—42no—
126C2×C4×Dic47C2×C418yescomplemented
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—22no—
216C22×Dic47—22no—
217C22×Dic47—28no—
218C22×Dic47—28no—
219C22×Dic47—44no—
220C22×Dic47—416no—
221C22×Dic47C22×C414yes—
222C22×Dic47C22×C414yes—
223C22×Dic47C22×C414yes—
224C22×Dic47C2×D414yes—
225C22×Dic47C2×D414yes—
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—44no—
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—44no—
249C22⋊Dic47C22×C4116yescomplemented
250(C2×D47)⋊C4—28no—
251(C2×D47)⋊C4—28no—
252(C2×D47)⋊C4—44no—
253(C2×D47)⋊C4C22×C4116yescomplemented
254(C2×D47)⋊C4C22×C4116yescomplemented
255C4⋊Dic47—28no—
256C4⋊Dic47—28no—
257Dic47⋊C4—28no—
258Dic47⋊C4—28no—
259Dic47⋊C4C2×D4116yes—
260C4×Dic47—28no—
261C4×Dic47—28no—
262C4×Dic47—28no—
263C4×Dic47—44no—
264C4×Dic47—44no—
265C4×Dic47C22×C4116yescomplemented
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×C47H(5,𝔽2)12yes—
286C23×C472−1+412yes—
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—28no—
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—22no—
343C2×Dic47—22no—
344C2×Dic47—22no—
345C2×Dic47—416no—
346C2×Dic47—44no—
347C2×Dic47—44no—
348C2×Dic47C4×D4116yes—
349C2×Dic47C23×C414yes—
350C2×Dic47C23×C414yes—
351C2×Dic47C23×C414yes—
352C2×Dic47C22×D414yes—
353C2×Dic47C22×D414yes—
354C2×Dic47C2×#4114yes—
355C2×Dic47C2×#4114yes—
356C4×D47—416no—
357Dic94—232no—
358C2×#2367—471nomaximal, Sylow
359C22×C47—24no—
360C22×C47—24no—
361C22×C47—24no—
362C22×C47—416no—
363C22×C47—42no—
364C22×C47—42no—
365C22×C47—42no—
366C22×C47—42no—
367C22×C47C2×C4×D414yes—
368C22×C47C4×#4114yes—
369C22×C47#52014yes—
370C22×C47#54614yes—
371C22×C47#54814yes—
372C22×C47#55614yes—
373C22×C47#55914yes—
374C22×C47C24×C411yescharacteristic
375C22×C47C23×D411yescharacteristic
376C22×C47C22×#4111yescharacteristic
377C22×C47C22×#4111yescharacteristic
378C22×C47C22×#4111yescharacteristic
379C22×C47C2×H(5,𝔽2)11yescharacteristic
380C22×C47C2×2−1+411yescharacteristic
381C2×D47—24no—
382C2×D47—24no—
383C2×D47—24no—
384C2×D47—416no—
385C2×D47—42no—
386C2×D47—42no—
387C2×D47—42no—
388C2×D47—42no—
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—24no—
399Dic47—42no—
400Dic47—42no—
401Dic47C2×C4×D418yes—
402C22×#124—471no—
403C22×C4×Q8—471no—
404C22×C4×D4—471no—
405#2367—4716no—
406C2×#391—471no—
407C2×#390—471no—
408C2×#388—471no—
409C2×#388—471no—
410C2×#388—471no—
411C2×#388D4711yescharacteristic, complemented
412C2×#385—471no—
413C2×#385—471no—
414C2×C4×C4⋊C4—471no—
415C2×C4×C4⋊C4—471no—
416C2×C4×C22⋊C4—471no—
417C2×C4×C22⋊C4—471no—
418C2×C47—44no—
419C2×C47#236718yescomplemented
420C2×C47C22×C4×D411yescharacteristic
421C2×C47C2×C4×#4111yescharacteristic
422C2×C47C2×#52011yescharacteristic
423C2×C47C2×#54611yescharacteristic
424C2×C47C2×#54811yescharacteristic
425C2×C47C2×#55611yescharacteristic
426C2×C47C2×#55911yescharacteristic
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⋊C4—471no—
442C22×C4⋊C4—471no—
443C22×C4⋊C4C2×D4711yescharacteristic
444C22×C22⋊C4—471no—
445C22×C22⋊C4—471no—
446C22×C22⋊C4—471no—
447C22×C22⋊C4—471no—
448C22×C22⋊C4—471no—
449C22×C22⋊C4—471no—
450C22×C22⋊C4—471no—
451C22×C22⋊C4C2×D4711yescharacteristic
452C22×C22⋊C4C2×D4711yescharacteristic
453C22×C22⋊C4C2×D4711yescharacteristic
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#385—478no—
468#385—478no—
469C4×C4⋊C4—478no—
470C4×C4⋊C4—478no—
471C4×C22⋊C4—478no—
472C4×C22⋊C4—478no—
473C2×#95—471no—
474C2×#95—471no—
475C2×#95—471no—
476C2×#95—471no—
477C2×#95—471no—
478C2×#95—471no—
479C2×#95C2×D4711yescharacteristic
480C2×#95C2×D4711yescharacteristic
481C47C2×#236711yescharacteristic, 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—471no—
498C23×C4—471no—
499C23×C4—474no—
500C23×C4—474no—
501C23×C4—944no—
502C23×C4—944no—
503C23×C4—944no—
504C23×C4—944no—
505C23×C4—1882no—
506C23×C4—1882no—
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—478no—
518C2×C4⋊C4—474no—
519C2×C4⋊C4—474no—
520C2×C4⋊C4—474no—
521C2×C4⋊C4—474no—
522C2×C4⋊C4—474no—
523C2×C4⋊C4—944no—
524C2×C4⋊C4—944no—
525C2×C4⋊C4—944no—
526C2×C4⋊C4—944no—
527C2×C4⋊C4C22×D4714yes—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—478no—
531C2×C22⋊C4—474no—
532C2×C22⋊C4—478no—
533C2×C22⋊C4—478no—
534C2×C22⋊C4—474no—
535C2×C22⋊C4—474no—
536C2×C22⋊C4—474no—
537C2×C22⋊C4—474no—
538C2×C22⋊C4—474no—
539C2×C22⋊C4—474no—
540C2×C22⋊C4—944no—
541C2×C22⋊C4—944no—
542C2×C22⋊C4—1882no—
543C2×C22⋊C4—1882no—
544C2×C22⋊C4C4×D4718yescomplemented
545C2×C22⋊C4C22×D4714yes—
546C2×C22⋊C4C22×D4714yes—
547C2×C22⋊C4C22×D4714yes—
548C2×C42—24no—
549C2×C42—478no—
550C2×C42—474no—
551C2×C42—474no—
552C2×C42—474no—
553C2×C42—474no—
554C2×C42—474no—
555C2×C42—474no—
556C2×C42—944no—
557C2×C42—944no—
558C2×C42—944no—
559C2×C42—1882no—
560C2×C42—1882no—
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—472no—
613C22×C4—474no—
614C22×C4—474no—
615C22×C4—474no—
616C22×C4—474no—
617C22×C4—472no—
618C22×C4—472no—
619C22×C4—472no—
620C22×C4—472no—
621C22×C4—472no—
622C22×C4—472no—
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—948no—
641C22×C4—1884no—
642C22×C4—18816no—
643C22×C4—1884no—
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—4716no—
657C4⋊C4—948no—
658C4⋊C4—948no—
659C4⋊C4—948no—
660C4⋊C4—948no—
661C22⋊C4—28no—
662C22⋊C4—28no—
663C22⋊C4—4716no—
664C22⋊C4—4716no—
665C22⋊C4—4716no—
666C22⋊C4—948no—
667C22⋊C4—948no—
668C22⋊C4—1884no—
669C22⋊C4—1884no—
670C22⋊C4C2×C4×D47116yescomplemented
671C42—28no—
672C42—4716no—
673C42—948no—
674C42—948no—
675C42—948no—
676C42—1884no—
677C42—1884no—
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—
710C23C2×#1062535212yes—
711C23#1309407012yes—
712C23#1309407112yes—
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—474no—
738C2×C4—474no—
739C2×C4—474no—
740C2×C4—474no—
741C2×C4—474no—
742C2×C4—474no—
743C2×C4—474no—
744C2×C4—948no—
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—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—416no—
777C22—42no—
778C22—944no—
779C22—944no—
780C22—944no—
781C22—1882no—
782C22—1882no—
783C22—1882no—
784C22—18816no—
785C22—1882no—
786C22C4×D4×D4714yes—
787C22C4×#1062535214yes—
788C22#1568960314yes—
789C22#1568976514yes—
790C22#1568977914yes—
791C22#1568984014yes—
792C22#1568985514yes—
793C22C23×C4×D4711yescharacteristic
794C22C22×D4×D4711yescharacteristic
795C22C2×#41×D4711yescharacteristic
796C22C2×#41×D4711yescharacteristic
797C22C22×#1062535211yescharacteristic
798C22C2×#1309407011yescharacteristic
799C22C2×#1309407111yescharacteristic
800C4—24no—
801C4—24no—
802C4—24no—
803C4—24no—
804C4—42no—
805C4—42no—
806C4—478no—
807C4—944no—
808C4—944no—
809C4—944no—
810C4—944no—
811C4—1882no—
812C4—1882no—
813C2—44no—
814C2—1884no—
815C2#2024646218yesdirect product factor
816C2C2×C4×D4×D4711yescharacteristic
817C2C2×C4×#1062535211yescharacteristic
818C2C2×#1568960311yescharacteristic
819C2C2×#1568976511yescharacteristic
820C2C2×#1568977911yescharacteristic
821C2C2×#1568984011yescharacteristic
822C2C2×#1568985511yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#388C2
socleC24×C47C24
prime radicalC23×C22⋊D47C22
cosocleC23×C47C25
hypercenterC2×#388D47
hypocenterC47C2×#2367
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic94C2semidirect
4. #20246462C2direct (N × H)
5. C2×#15689027C2semidirect
7. C2×#15689017C2semidirect
8. C2×#15689015C2semidirect
9. C2×#15689013C2semidirect
10. C2×#15688998C2semidirect
11. C2×#15688997C2semidirect
12. C2×C4⋊C4×Dic47C2semidirect
13. C2×#15688974C2semidirect
14. C2×C22⋊C4×Dic47C2semidirect
15. C2×C4×(C2×D47)⋊C4C2semidirect
16. C2×C47×#388C2semidirect
21. C2×#13094010C4semidirect
24. C2×C4×Dic94C22semidirect
45. #15689027C22semidirect
47. #15689017C22semidirect
48. #15689015C22semidirect
49. #15689013C22semidirect
50. #15688998C22semidirect
51. #15688997C22semidirect
52. C4⋊C4×Dic47C22semidirect
53. #15688974C22semidirect
54. C22⋊C4×Dic47C22semidirect
55. C4×(C2×D47)⋊C4C22semidirect
67. C47×#388C22semidirect
73. C22×Dic94C2×C4semidirect
94. #13094010C2×C4semidirect
108. C2×C22⋊Dic47C2×C4semidirect
114. C2×(C2×D47)⋊C4C2×C4semidirect
115. C2×(C2×D47)⋊C4C2×C4semidirect
126. 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
265. C4×Dic47C22×C4semidirect
411. C2×#388D47semidirect
419. C2×C47#2367semidirect
466. #388C2×D47semidirect
481. C47C2×#2367semidirect
544. C2×C22⋊C4C4×D47semidirect
670. C22⋊C4C2×C4×D47semidirect
815. C2#20246462direct (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×C4×Dic942
C22×(C22⋊D47)⋊C42
#202464622
C2×#156890272
C2×#156890232
C2×#156890172
C2×#156890152
C2×#156890132
C2×#156889982
C2×#156889972
C2×C4⋊C4×Dic472
C2×#156889742
C2×C22⋊C4×Dic472
C2×C4×(C2×D47)⋊C42
C2×C47×#3882
C2×#236747