Finite Group Databasebeta

← C2×#20246262 #26375520

Subgroups — C2×#20246262 #26375520

Order 12032.

3094 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D47C211yesmaximal, characteristic
2#20246262C2116yesmaximal, direct product factor
3C2×#15689020C211yesmaximal, characteristic, complemented
4C2×#15689018C211yesmaximal, characteristic, complemented
5C2×#15689009C211yesmaximal, characteristic, complemented
6C2×#15689008C211yesmaximal, characteristic, complemented
7C2×#15689006C211yesmaximal, characteristic, complemented
8C2×#15688982C211yesmaximal, characteristic
9C2×#15688982C211yesmaximal, characteristic
10C2×#15688980C211yesmaximal, characteristic
11C2×C4×Dic47⋊C4C211yesmaximal, characteristic, complemented
12C2×#15688974C211yesmaximal, characteristic, complemented
13C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic
14C2×#15688970C211yesmaximal, characteristic
15C2×#15688970C211yesmaximal, characteristic
16C2×C47×#387C211yesmaximal, characteristic, complemented
17C23×C4×D47C2211yescharacteristic
18C23×C4×D47C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C22×C4⋊Dic47C2211yescharacteristic
21C22×C4⋊Dic47C2211yescharacteristic
22C22×Dic47⋊C4C2211yescharacteristic
23C22×Dic47⋊C4C2211yescharacteristic
24C22×Dic47⋊C4C2211yescharacteristic
25C22×Dic47⋊C4C2211yescharacteristic
26C22×Dic47⋊C4C2211yescharacteristic
27C22×Dic47⋊C4C2211yescharacteristic
28C2×C4⋊C4×D47C4116yescomplemented
29C2×C4⋊C4×D47C2218yes—
30C22×(C2×D47)⋊C4C2211yescharacteristic
31C22×(C2×D47)⋊C4C2211yescharacteristic
32C22×(C2×D47)⋊C4C2211yescharacteristic
33C22×(C2×D47)⋊C4C2211yescharacteristic
34C22×C4×Dic47C2211yescharacteristic
35C22×C4×Dic47C2211yescharacteristic
36C22×C4×Dic47C2211yescharacteristic
37C22×C4×Dic47C2211yescharacteristic
38C22×C4×Dic47C2211yescharacteristic
39#15689020C2218yescomplemented
40#15689018C2218yescomplemented
41#15689009C2218yescomplemented
42#15689008C2218yescomplemented
43#15689006C2218yescomplemented
44#15688982C2218yes—
45#15688982C2218yes—
46#15688980C2218yes—
47C4×Dic47⋊C4C2218yescomplemented
48#15688974C2218yescomplemented
49C4×(C2×D47)⋊C4C2218yes—
50#15688970C2218yes—
51#15688970C2218yes—
52C2×C47⋊#95C2211yescharacteristic
53C2×C47⋊#95C2211yescharacteristic
54C2×C47⋊#95C2211yescharacteristic
55C2×C47⋊#95C2211yescharacteristic
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C22×C4⋊C4×C47C2211yescharacteristic
61C22×C4⋊C4×C47C2211yescharacteristic
62C22×C42×C47C2211yescharacteristic
63C47×#387C2218yescomplemented
64C2×#95×C47C2211yescharacteristic
65C2×#95×C47C2211yescharacteristic
66C2×#95×C47C2211yescharacteristic
67C2×#95×C47C2211yescharacteristic
68C24×D47C2311yescharacteristic
69C23×Dic47C2311yescharacteristic
70C23×Dic47C2311yescharacteristic
71C23×Dic47C2311yescharacteristic
72C23×Dic47C2311yescharacteristic
73C23×Dic47C2311yescharacteristic
74C23×Dic47C2311yescharacteristic
75C23×Dic47C2311yescharacteristic
76C22×C4×D47—24no—
77C22×C4×D47—24no—
78C22×C4×D47—42no—
79C22×C4×D47—42no—
80C22×C4×D47—42no—
81C22×C4×D47—42no—
82C22×C4×D47C2×C418yes—
83C22×C4×D47C2×C418yes—
84C22×C4×D47C2×C418yes—
85C22×C4×D47C2314yes—
86C22×C4×D47C2314yes—
87C22×C4×D47C2314yes—
88C2×C4⋊Dic47—42no—
89C2×C4⋊Dic47C2×C418yes—
90C2×C4⋊Dic47C2314yes—
91C2×C4⋊Dic47C2314yes—
92C2×Dic47⋊C4—24no—
93C2×Dic47⋊C4—24no—
94C2×Dic47⋊C4—42no—
95C2×Dic47⋊C4—42no—
96C2×Dic47⋊C4C2×C418yes—
97C2×Dic47⋊C4C2×C418yes—
98C2×Dic47⋊C4C2314yes—
99C2×Dic47⋊C4C2314yes—
100C2×Dic47⋊C4C2314yes—
101C2×Dic47⋊C4C2314yes—
102C2×Dic47⋊C4C2314yes—
103C2×Dic47⋊C4C2314yes—
104C4⋊C4×D47C2×C4164yescomplemented
105C2×(C2×D47)⋊C4—24no—
106C2×(C2×D47)⋊C4—24no—
107C2×(C2×D47)⋊C4—24no—
108C2×(C2×D47)⋊C4Q818yes—
109C2×(C2×D47)⋊C4C2314yes—
110C2×(C2×D47)⋊C4C2314yes—
111C2×(C2×D47)⋊C4C2314yes—
112C2×(C2×D47)⋊C4C2314yes—
113C2×C4×Dic47—24no—
114C2×C4×Dic47—24no—
115C2×C4×Dic47—42no—
116C2×C4×Dic47—42no—
117C2×C4×Dic47—42no—
118C2×C4×Dic47C2314yes—
119C2×C4×Dic47C2314yes—
120C2×C4×Dic47C2314yes—
121C2×C4×Dic47C2314yes—
122C2×C4×Dic47C2314yes—
123C47⋊#95C2314yes—
124C47⋊#95C2314yes—
125C47⋊#95C2314yes—
126C47⋊#95C2314yes—
127C47⋊#95C2314yes—
128C47⋊#95C2314yes—
129C47⋊#95C2314yes—
130C47⋊#95C2314yes—
131C23×C4×C47C2311yescharacteristic
132C23×C4×C47C2311yescharacteristic
133C23×C4×C47C2311yescharacteristic
134C23×C4×C47C2311yescharacteristic
135C23×C4×C47C2311yescharacteristic
136C23×C4×C47C2311yescharacteristic
137C23×C4×C47C2311yescharacteristic
138C2×C4⋊C4×C47—42no—
139C2×C4⋊C4×C47C2×C418yes—
140C2×C4⋊C4×C47C2314yes—
141C2×C4⋊C4×C47C2314yes—
142C2×C42×C47—42no—
143C2×C42×C47C2314yes—
144#95×C47C2314yes—
145#95×C47C2314yes—
146#95×C47C2314yes—
147#95×C47C2314yes—
148C24×C47C2411yescharacteristic
149C23×D47—22no—
150C23×D47—22no—
151C23×D47—22no—
152C23×D47—22no—
153C23×D47C22×C414yes—
154C23×D47C2×Q814yes—
155C23×D47#4114yes—
156C23×D47C2412yes—
157C22×C4×C47—22no—
158C22×C4×C47—22no—
159C22×C4×C47—22no—
160C22×C4×C47—22no—
161C22×C4×C47—22no—
162C22×C4×C47—22no—
163C22×C4×C47—22no—
164C22×C4×C47—22no—
165C22×C4×C47—22no—
166C22×C4×C47—22no—
167C22×C4×C47—22no—
168C22×C4×C47—22no—
169C22×C4×C47—22no—
170C22×C4×C47—22no—
171C22×C4×C47—22no—
172C22×C4×C47—22no—
173C22×C4×C47—22no—
174C22×C4×C47C22×C414yes—
175C22×C4×C47C22×C414yes—
176C22×C4×C47C22×C414yes—
177C22×C4×C47C2×Q814yes—
178C22×C4×C47C2412yes—
179C22×C4×C47C2412yes—
180C22×C4×C47C2412yes—
181C22×C4×C47C2412yes—
182C22×C4×C47C2412yes—
183C22×C4×C47C2412yes—
184C22×C4×C47C2412yes—
185C22×Dic47—22no—
186C22×Dic47—22no—
187C22×Dic47—22no—
188C22×Dic47—22no—
189C22×Dic47—22no—
190C22×Dic47—22no—
191C22×Dic47—22no—
192C22×Dic47—22no—
193C22×Dic47—22no—
194C22×Dic47—22no—
195C22×Dic47—22no—
196C22×Dic47—22no—
197C22×Dic47—22no—
198C22×Dic47—22no—
199C22×Dic47—22no—
200C22×Dic47C22×C414yes—
201C22×Dic47C22×C414yes—
202C22×Dic47C22×C414yes—
203C22×Dic47C2×Q814yes—
204C22×Dic47#4114yes—
205C22×Dic47#4114yes—
206C22×Dic47C2412yes—
207C22×Dic47C2412yes—
208C22×Dic47C2412yes—
209C22×Dic47C2412yes—
210C22×Dic47C2412yes—
211C22×Dic47C2412yes—
212C22×Dic47C2412yes—
213C2×C4×D47—232no—
214C2×C4×D47—28no—
215C2×C4×D47—28no—
216C2×C4×D47—416no—
217C2×C4×D47—416no—
218C2×C4×D47—44no—
219C2×C4×D47—44no—
220C2×C4×D47—44no—
221C2×C4×D47—44no—
222C2×C4×D47C22×C4116yes—
223C2×C4×D47C22×C4116yes—
224C2×C4×D47C22×C4116yes—
225C4⋊C4×C47—44no—
226C4⋊C4×C47C22×C4116yes—
227C42×C47—44no—
228(C2×D47)⋊C4—28no—
229(C2×D47)⋊C4—28no—
230(C2×D47)⋊C4—28no—
231(C2×D47)⋊C4C2×Q8116yes—
232C4⋊Dic47—44no—
233C4⋊Dic47C22×C4116yes—
234Dic47⋊C4—28no—
235Dic47⋊C4—28no—
236Dic47⋊C4—44no—
237Dic47⋊C4—44no—
238Dic47⋊C4C22×C4116yes—
239Dic47⋊C4C22×C4116yes—
240C4×Dic47—28no—
241C4×Dic47—28no—
242C4×Dic47—44no—
243C4×Dic47—44no—
244C4×Dic47—44no—
245C23×C47C23×C412yes—
246C23×C47C22×Q812yes—
247C23×C47C2×#4112yes—
248C23×C47C2×#4112yes—
249C23×C47C2×#4112yes—
250C23×C47H(5,𝔽2)12yes—
251C23×C47H(5,𝔽2)12yes—
252C23×C47C2511yescharacteristic
253C22×D47—28no—
254C22×D47—28no—
255C22×D47—28no—
256C22×D47—28no—
257C22×D47—28no—
258C22×D47—28no—
259C22×D47—22no—
260C22×D47—22no—
261C22×D47—22no—
262C22×D47—22no—
263C22×D47C4×Q8116yes—
264C22×D47C23×C414yes—
265C22×D47C22×Q814yes—
266C22×D47C2×#4114yes—
267C2×C4×C47—28no—
268C2×C4×C47—28no—
269C2×C4×C47—28no—
270C2×C4×C47—28no—
271C2×C4×C47—22no—
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—44no—
289C2×C4×C47—44no—
290C2×C4×C47—44no—
291C2×C4×C47C23×C414yes—
292C2×C4×C47C23×C414yes—
293C2×C4×C47C23×C414yes—
294C2×C4×C47C22×Q814yes—
295C2×Dic47—28no—
296C2×Dic47—28no—
297C2×Dic47—28no—
298C2×Dic47—22no—
299C2×Dic47—22no—
300C2×Dic47—22no—
301C2×Dic47—22no—
302C2×Dic47—22no—
303C2×Dic47—22no—
304C2×Dic47—22no—
305C2×Dic47—22no—
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—44no—
314C2×Dic47—44no—
315C2×Dic47—44no—
316C2×Dic47#117116yes—
317C2×Dic47C23×C414yes—
318C2×Dic47C23×C414yes—
319C2×Dic47C23×C414yes—
320C2×Dic47C22×Q814yes—
321C2×Dic47C2×#4114yes—
322C2×Dic47C2×#4114yes—
323C4×D47—232no—
324C4×D47—416no—
325C4×D47—416no—
326C2×#2345—471nomaximal, Sylow
327C22×C47C2×#11714yes—
328C22×C47C2×C4×Q814yes—
329C22×C47#51814yes—
330C22×C47#55314yes—
331C22×C47#55314yes—
332C22×C47#55414yes—
333C22×C47#55414yes—
334C22×C47C24×C411yescharacteristic
335C22×C47C23×Q811yescharacteristic
336C22×C47C22×#4111yescharacteristic
337C22×C47C22×#4111yescharacteristic
338C22×C47C22×#4111yescharacteristic
339C22×C47C2×H(5,𝔽2)11yescharacteristic
340C22×C47C2×H(5,𝔽2)11yescharacteristic
341C2×D47—232no—
342C2×D47—24no—
343C2×D47—24no—
344C2×D47—24no—
345C2×D47—24no—
346C2×D47—24no—
347C2×D47—24no—
348C2×D47C2×C4×Q818yes—
349C4×C47—24no—
350C4×C47—24no—
351C4×C47—24no—
352C4×C47—24no—
353C4×C47—42no—
354C4×C47—42no—
355C4×C47—42no—
356Dic47—24no—
357Dic47—24no—
358Dic47—24no—
359Dic47—42no—
360Dic47—42no—
361Dic47—42no—
362Dic47C2×#11718yes—
363C23×C4⋊C4—471no—
364#2345—4716no—
365C2×#389—471no—
366C2×#389—471no—
367C2×#387—471no—
368C2×#387—471no—
369C2×#387—471no—
370C2×#387D4711yescharacteristic, complemented
371C2×#380—471no—
372C2×#380—471no—
373C2×#380—471no—
374C2×C4×C4⋊C4—471no—
375C2×C4×C4⋊C4—471no—
376C2×C4×C22⋊C4—471no—
377C2×C4×C22⋊C4—471no—
378C2×C4×C22⋊C4—471no—
379C2×C47#234518yescomplemented
380C2×C47C22×#11711yescharacteristic
381C2×C47C22×C4×Q811yescharacteristic
382C2×C47C2×#51811yescharacteristic
383C2×C47C2×#55311yescharacteristic
384C2×C47C2×#55311yescharacteristic
385C2×C47C2×#55411yescharacteristic
386C2×C47C2×#55411yescharacteristic
387D47—28no—
388C24×C4—471no—
389C24×C4—471no—
390C24×C4—471no—
391C22×C4⋊C4—471no—
392C22×C4⋊C4—471no—
393C22×C4⋊C4—471no—
394C22×C4⋊C4—4716no—
395C22×C4⋊C4—478no—
396C22×C4⋊C4—471no—
397C22×C4⋊C4—471no—
398C22×C4⋊C4—471no—
399C22×C4⋊C4—471no—
400C22×C4⋊C4—471no—
401C22×C4⋊C4C2×D4711yescharacteristic
402C22×C4⋊C4C2×D4711yescharacteristic
403C22×C22⋊C4—471no—
404C22×C22⋊C4—471no—
405C22×C22⋊C4—471no—
406C22×C22⋊C4—471no—
407C22×C42—471no—
408C22×C42—471no—
409C22×C42—471no—
410C22×C42—471no—
411C22×C42—471no—
412C22×C42C2×D4711yescharacteristic
413#389—478no—
414#389—478no—
415#387—478no—
416#387—478no—
417#387—478no—
418#387C2×D4718yescomplemented
419#380—478no—
420#380—478no—
421#380—478no—
422C4×C4⋊C4—478no—
423C4×C4⋊C4—478no—
424C4×C22⋊C4—478no—
425C4×C22⋊C4—478no—
426C4×C22⋊C4—478no—
427C2×#95—471no—
428C2×#95—471no—
429C2×#95—471no—
430C2×#95—471no—
431C2×#95—471no—
432C2×#95—471no—
433C2×#95—471no—
434C2×#95—471no—
435C2×#95C2×D4711yescharacteristic
436C2×#95C2×D4711yescharacteristic
437C2×#95C2×D4711yescharacteristic
438C2×#95C2×D4711yescharacteristic
439C47C2×#234511yescharacteristic, complemented, Sylow
440C25—471no—
441C23×C4—471no—
442C23×C4—471no—
443C23×C4—471no—
444C23×C4—471no—
445C23×C4—478no—
446C23×C4—474no—
447C23×C4—478no—
448C23×C4—478no—
449C23×C4—474no—
450C23×C4—474no—
451C23×C4—471no—
452C23×C4—471no—
453C23×C4—471no—
454C23×C4—944no—
455C23×C4—944no—
456C23×C4—1882no—
457C23×C4—1882no—
458C23×C4—1882no—
459C23×C4—1882no—
460C23×C4C22×D4711yescharacteristic
461C23×C4C22×D4711yescharacteristic
462C23×C4C22×D4711yescharacteristic
463C23×C4C22×D4711yescharacteristic
464C23×C4C22×D4711yescharacteristic
465C23×C4C22×D4711yescharacteristic
466C23×C4C22×D4711yescharacteristic
467C2×C4⋊C4—42no—
468C2×C4⋊C4—478no—
469C2×C4⋊C4—478no—
470C2×C4⋊C4—478no—
471C2×C4⋊C4—474no—
472C2×C4⋊C4—474no—
473C2×C4⋊C4—474no—
474C2×C4⋊C4—4764no—
475C2×C4⋊C4—474no—
476C2×C4⋊C4—474no—
477C2×C4⋊C4—474no—
478C2×C4⋊C4—474no—
479C2×C4⋊C4—474no—
480C2×C4⋊C4—944no—
481C2×C4⋊C4—944no—
482C2×C4⋊C4—1882no—
483C2×C4⋊C4—1882no—
484C2×C4⋊C4—1882no—
485C2×C4⋊C4C4×D4718yes—
486C2×C4⋊C4C22×D4714yes—
487C2×C4⋊C4C22×D4714yes—
488C2×C22⋊C4—478no—
489C2×C22⋊C4—474no—
490C2×C22⋊C4—474no—
491C2×C22⋊C4—474no—
492C2×C22⋊C4—474no—
493C2×C22⋊C4—944no—
494C2×C22⋊C4—944no—
495C2×C22⋊C4—944no—
496C2×C42—42no—
497C2×C42—474no—
498C2×C42—474no—
499C2×C42—474no—
500C2×C42—474no—
501C2×C42—474no—
502C2×C42—944no—
503C2×C42—944no—
504C2×C42—1882no—
505C2×C42—1882no—
506C2×C42—1882no—
507C2×C42C22×D4714yes—
508#95—474no—
509#95—474no—
510#95—474no—
511#95—474no—
512#95—474no—
513#95—474no—
514#95—474no—
515#95—474no—
516#95C22×D4714yes—
517#95C22×D4714yes—
518#95C22×D4714yes—
519#95C22×D4714yes—
520C24—474no—
521C24—474no—
522C24—474no—
523C24—472no—
524C24—942no—
525C24—942no—
526C24—942no—
527C24—942no—
528C24C23×D4711yescharacteristic
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—474no—
547C22×C4—474no—
548C22×C4—474no—
549C22×C4—472no—
550C22×C4—474no—
551C22×C4—474no—
552C22×C4—474no—
553C22×C4—472no—
554C22×C4—472no—
555C22×C4—472no—
556C22×C4—4716no—
557C22×C4—4716no—
558C22×C4—4716no—
559C22×C4—472no—
560C22×C4—472no—
561C22×C4—472no—
562C22×C4—9432no—
563C22×C4—948no—
564C22×C4—948no—
565C22×C4—942no—
566C22×C4—942no—
567C22×C4—942no—
568C22×C4—942no—
569C22×C4—942no—
570C22×C4—942no—
571C22×C4—942no—
572C22×C4—942no—
573C22×C4—942no—
574C22×C4—942no—
575C22×C4—942no—
576C22×C4—942no—
577C22×C4—942no—
578C22×C4—942no—
579C22×C4—942no—
580C22×C4—18816no—
581C22×C4—18816no—
582C22×C4—1884no—
583C22×C4—1884no—
584C22×C4—1884no—
585C22×C4—1884no—
586C22×C4C2×C4×D4714yes—
587C22×C4C2×C4×D4714yes—
588C22×C4C2×C4×D4714yes—
589C22×C4Q8×D4714yes—
590C22×C4C23×D4712yes—
591C22×C4C23×D4712yes—
592C22×C4C23×D4712yes—
593C22×C4C23×D4712yes—
594C22×C4C23×D4712yes—
595C22×C4C23×D4712yes—
596C22×C4C23×D4712yes—
597C4⋊C4—44no—
598C4⋊C4—4716no—
599C4⋊C4—4716no—
600C4⋊C4—4716no—
601C4⋊C4—948no—
602C4⋊C4—948no—
603C4⋊C4—1884no—
604C4⋊C4—1884no—
605C4⋊C4—1884no—
606C4⋊C4C2×C4×D47116yes—
607C22⋊C4—4716no—
608C22⋊C4—948no—
609C22⋊C4—948no—
610C22⋊C4—948no—
611C42—44no—
612C42—948no—
613C42—948no—
614C42—1884no—
615C42—1884no—
616C42—1884no—
617C23—4716no—
618C23—474no—
619C23—474no—
620C23—474no—
621C23—948no—
622C23—948no—
623C23—948no—
624C23—948no—
625C23—948no—
626C23—948no—
627C23—942no—
628C23—942no—
629C23—942no—
630C23—942no—
631C23C22×C4×D4712yes—
632C23C2×Q8×D4712yes—
633C23#41×D4712yes—
634C23#41×D4712yes—
635C23#41×D4712yes—
636C23#1309406912yes—
637C23#1309407012yes—
638C23C24×D4711yescharacteristic
639C2×C4—28no—
640C2×C4—28no—
641C2×C4—28no—
642C2×C4—28no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—44no—
661C2×C4—44no—
662C2×C4—44no—
663C2×C4—4716no—
664C2×C4—474no—
665C2×C4—474no—
666C2×C4—474no—
667C2×C4—474no—
668C2×C4—474no—
669C2×C4—474no—
670C2×C4—9432no—
671C2×C4—948no—
672C2×C4—948no—
673C2×C4—948no—
674C2×C4—942no—
675C2×C4—942no—
676C2×C4—942no—
677C2×C4—942no—
678C2×C4—942no—
679C2×C4—942no—
680C2×C4—942no—
681C2×C4—942no—
682C2×C4—942no—
683C2×C4—942no—
684C2×C4—942no—
685C2×C4—942no—
686C2×C4—942no—
687C2×C4—942no—
688C2×C4—942no—
689C2×C4—18816no—
690C2×C4—18816no—
691C2×C4—1884no—
692C2×C4—1884no—
693C2×C4—1884no—
694C2×C4C22×C4×D4714yes—
695C2×C4C22×C4×D4714yes—
696C2×C4C22×C4×D4714yes—
697C2×C4C2×Q8×D4714yes—
698C22—478no—
699C22—944no—
700C22—944no—
701C22—944no—
702C22—944no—
703C22—944no—
704C22—944no—
705C22—9432no—
706C22#117×D4714yes—
707C22C4×Q8×D4714yes—
708C22#1568959514yes—
709C22#1568981814yes—
710C22#1568982414yes—
711C22#1568982714yes—
712C22#1568982914yes—
713C22C23×C4×D4711yescharacteristic
714C22C22×Q8×D4711yescharacteristic
715C22C2×#41×D4711yescharacteristic
716C22C2×#41×D4711yescharacteristic
717C22C2×#41×D4711yescharacteristic
718C22C2×#1309406911yescharacteristic
719C22C2×#1309407011yescharacteristic
720C4—24no—
721C4—24no—
722C4—24no—
723C4—24no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—478no—
728C4—944no—
729C4—944no—
730C4—944no—
731C4—1882no—
732C4—1882no—
733C4—1882no—
734C2—948no—
735C2#2024626218yesdirect product factor
736C2C2×#117×D4711yescharacteristic
737C2C2×C4×Q8×D4711yescharacteristic
738C2C2×#1568959511yescharacteristic
739C2C2×#1568981811yescharacteristic
740C2C2×#1568982411yescharacteristic
741C2C2×#1568982711yescharacteristic
742C2C2×#1568982911yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#387C2
socleC24×C47C24
prime radicalC24×D47C23
cosocleC23×C47C25
hypercenterC2×#387D47
hypocenterC47C2×#2345
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #20246262C2direct (N × H)
3. C2×#15689020C2semidirect
4. C2×#15689018C2semidirect
5. C2×#15689009C2semidirect
6. C2×#15689008C2semidirect
7. C2×#15689006C2semidirect
11. C2×C4×Dic47⋊C4C2semidirect
12. C2×#15688974C2semidirect
16. C2×C47×#387C2semidirect
28. C2×C4⋊C4×D47C4semidirect
39. #15689020C22semidirect
40. #15689018C22semidirect
41. #15689009C22semidirect
42. #15689008C22semidirect
43. #15689006C22semidirect
47. C4×Dic47⋊C4C22semidirect
48. #15688974C22semidirect
63. C47×#387C22semidirect
104. C4⋊C4×D47C2×C4semidirect
370. C2×#387D47semidirect
379. C2×C47#2345semidirect
418. #387C2×D47semidirect
439. C47C2×#2345semidirect
735. C2#20246262direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D472
#202462622
C2×#156890202
C2×#156890182
C2×#156890092
C2×#156890082
C2×#156890062
C2×#156889822
C2×#156889802
C2×C4×Dic47⋊C42
C2×#156889742
C2×C4×(C2×D47)⋊C42
C2×#156889702
C2×C47×#3872
C2×#234547