Finite Group Databasebeta

← C2×#20246065 #26375015

Subgroups — C2×#20246065 #26375015

Order 12032.

3198 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094002C211yesmaximal, characteristic
2C22×#13093989C211yesmaximal, characteristic, complemented
3C22×#13093982C211yesmaximal, characteristic
4#20246065C2116yesmaximal, direct product factor
5C2×#15689027C211yesmaximal, characteristic, complemented
6C2×#15689018C211yesmaximal, characteristic, complemented
7C2×#15689018C211yesmaximal, characteristic, complemented
8C2×#15689014C211yesmaximal, characteristic
9C2×#15689013C211yesmaximal, characteristic
10C2×#15689013C211yesmaximal, characteristic
11C2×#15689012C211yesmaximal, characteristic
12C2×#15689010C211yesmaximal, characteristic, complemented
13C2×#15689009C211yesmaximal, characteristic, complemented
14C2×#15688982C211yesmaximal, characteristic
15C2×C4×Dic47⋊C4C211yesmaximal, characteristic, complemented
16C2×C47×#389C211yesmaximal, characteristic, complemented
17C23×Dic94C2211yescharacteristic
18C23×C4×D47C2211yescharacteristic
19C2×#13094002C4116yescomplemented
20C2×#13094002C2218yes—
21C2×#13093989—28no—
22C2×#13093989C2218yescomplemented
23C2×#13093982—28no—
24C2×#13093982C2218yes—
25C22×C4⋊Dic47C2211yescharacteristic
26C22×Dic47⋊C4C2211yescharacteristic
27C22×Dic47⋊C4C2211yescharacteristic
28C22×Dic47⋊C4C2211yescharacteristic
29C22×Dic47⋊C4C2211yescharacteristic
30C22×Dic47⋊C4C2211yescharacteristic
31C22×Dic47⋊C4C2211yescharacteristic
32C22×(C2×D47)⋊C4C2211yescharacteristic
33C22×(C2×D47)⋊C4C2211yescharacteristic
34C22×(C2×D47)⋊C4C2211yescharacteristic
35C22×(C2×D47)⋊C4C2211yescharacteristic
36C22×(C2×D47)⋊C4C2211yescharacteristic
37C22×(C2×D47)⋊C4C2211yescharacteristic
38C22×C4×Dic47C2211yescharacteristic
39C22×C4×Dic47C2211yescharacteristic
40C22×C4×Dic47C2211yescharacteristic
41C22×C4×Dic47C2211yescharacteristic
42C22×C4×Dic47C2211yescharacteristic
43#15689027C2218yescomplemented
44#15689018C2218yescomplemented
45#15689018C2218yescomplemented
46#15689014C2218yes—
47#15689013C2218yes—
48#15689013C2218yes—
49#15689012C2218yes—
50#15689010C2218yescomplemented
51#15689009C2218yescomplemented
52#15688982C2218yes—
53C4×Dic47⋊C4C2218yescomplemented
54C2×C47⋊#95C2211yescharacteristic
55C2×C47⋊#95C2211yescharacteristic
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C2×C47⋊#95C2211yescharacteristic
62C22×C4⋊C4×C47C2211yescharacteristic
63C22×C4⋊C4×C47C2211yescharacteristic
64C22×C4⋊C4×C47C2211yescharacteristic
65C22×C4⋊C4×C47C2211yescharacteristic
66C22×C42×C47C2211yescharacteristic
67C47×#389C2218yescomplemented
68C2×#95×C47C2211yescharacteristic
69C2×#95×C47C2211yescharacteristic
70C24×D47C2311yescharacteristic
71C22×Dic94—24no—
72C22×Dic94—24no—
73C22×Dic94C2×C418yes—
74C22×Dic94C2314yes—
75C23×Dic47C2311yescharacteristic
76C23×Dic47C2311yescharacteristic
77C23×Dic47C2311yescharacteristic
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2311yescharacteristic
80C23×Dic47C2311yescharacteristic
81C23×Dic47C2311yescharacteristic
82C22×C4×D47—24no—
83C22×C4×D47—24no—
84C22×C4×D47C2×C418yes—
85C22×C4×D47C2314yes—
86#13094002C2×C4164yescomplemented
87#13093989—232no—
88#13093982—232no—
89C2×C4⋊Dic47—24no—
90C2×C4⋊Dic47C2314yes—
91C2×Dic47⋊C4—24no—
92C2×Dic47⋊C4—24no—
93C2×Dic47⋊C4—24no—
94C2×Dic47⋊C4—42no—
95C2×Dic47⋊C4C2×C418yes—
96C2×Dic47⋊C4C2×C418yes—
97C2×Dic47⋊C4C2314yes—
98C2×Dic47⋊C4C2314yes—
99C2×Dic47⋊C4C2314yes—
100C2×Dic47⋊C4C2314yes—
101C2×Dic47⋊C4C2314yes—
102C2×Dic47⋊C4C2314yes—
103C2×(C2×D47)⋊C4—24no—
104C2×(C2×D47)⋊C4—24no—
105C2×(C2×D47)⋊C4—42no—
106C2×(C2×D47)⋊C4—42no—
107C2×(C2×D47)⋊C4C2×C418yes—
108C2×(C2×D47)⋊C4C2×C418yes—
109C2×(C2×D47)⋊C4C2314yes—
110C2×(C2×D47)⋊C4C2314yes—
111C2×(C2×D47)⋊C4C2314yes—
112C2×(C2×D47)⋊C4C2314yes—
113C2×(C2×D47)⋊C4C2314yes—
114C2×(C2×D47)⋊C4C2314yes—
115C2×C4×Dic47—24no—
116C2×C4×Dic47—24no—
117C2×C4×Dic47—24no—
118C2×C4×Dic47—42no—
119C2×C4×Dic47D418yes—
120C2×C4×Dic47C2314yes—
121C2×C4×Dic47C2314yes—
122C2×C4×Dic47C2314yes—
123C2×C4×Dic47C2314yes—
124C2×C4×Dic47C2314yes—
125C47⋊#95C2314yes—
126C47⋊#95C2314yes—
127C47⋊#95C2314yes—
128C47⋊#95C2314yes—
129C47⋊#95C2314yes—
130C47⋊#95C2314yes—
131C47⋊#95C2314yes—
132C47⋊#95C2314yes—
133C23×C4×C47C2311yescharacteristic
134C23×C4×C47C2311yescharacteristic
135C23×C4×C47C2311yescharacteristic
136C23×C4×C47C2311yescharacteristic
137C23×C4×C47C2311yescharacteristic
138C23×C4×C47C2311yescharacteristic
139C23×C4×C47C2311yescharacteristic
140C2×C4⋊C4×C47—24no—
141C2×C4⋊C4×C47—24no—
142C2×C4⋊C4×C47—42no—
143C2×C4⋊C4×C47C2×C418yes—
144C2×C4⋊C4×C47C2314yes—
145C2×C4⋊C4×C47C2314yes—
146C2×C4⋊C4×C47C2314yes—
147C2×C4⋊C4×C47C2314yes—
148C2×C42×C47—42no—
149C2×C42×C47C2314yes—
150#95×C47C2314yes—
151#95×C47C2314yes—
152C24×C47C2411yescharacteristic
153C23×D47—22no—
154C23×D47—22no—
155C23×D47—22no—
156C23×D47—22no—
157C23×D47—22no—
158C23×D47—22no—
159C23×D47C22×C414yes—
160C23×D47C2412yes—
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×C47—22no—
175C22×C4×C47—22no—
176C22×C4×C47—22no—
177C22×C4×C47—22no—
178C22×C4×C47C22×C414yes—
179C22×C4×C47C22×C414yes—
180C22×C4×C47C22×C414yes—
181C22×C4×C47C2×D414yes—
182C22×C4×C47C2412yes—
183C22×C4×C47C2412yes—
184C22×C4×C47C2412yes—
185C22×C4×C47C2412yes—
186C22×C4×C47C2412yes—
187C22×C4×C47C2412yes—
188C22×C4×C47C2412yes—
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×Dic47—22no—
201C22×Dic47—22no—
202C22×Dic47—22no—
203C22×Dic47—22no—
204C22×Dic47C22×C414yes—
205C22×Dic47C22×C414yes—
206C22×Dic47C22×C414yes—
207C22×Dic47C2×D414yes—
208C22×Dic47C2×D414yes—
209C22×Dic47#4114yes—
210C22×Dic47C2412yes—
211C22×Dic47C2412yes—
212C22×Dic47C2412yes—
213C22×Dic47C2412yes—
214C22×Dic47C2412yes—
215C22×Dic47C2412yes—
216C22×Dic47C2412yes—
217C2×C4×D47—232no—
218C2×C4×D47—28no—
219C2×C4×D47—28no—
220C2×C4×D47C22×C4116yes—
221C2×Dic94—232no—
222C2×Dic94—28no—
223C2×Dic94—28no—
224C2×Dic94C22×C4116yes—
225C4⋊C4×C47—28no—
226C4⋊C4×C47—28no—
227C4⋊C4×C47—44no—
228C4⋊C4×C47C22×C4116yes—
229C42×C47—44no—
230(C2×D47)⋊C4—28no—
231(C2×D47)⋊C4—28no—
232(C2×D47)⋊C4—44no—
233(C2×D47)⋊C4—44no—
234(C2×D47)⋊C4C22×C4116yes—
235(C2×D47)⋊C4C22×C4116yes—
236C4⋊Dic47—28no—
237Dic47⋊C4—28no—
238Dic47⋊C4—28no—
239Dic47⋊C4—28no—
240Dic47⋊C4—44no—
241Dic47⋊C4C22×C4116yes—
242Dic47⋊C4C22×C4116yes—
243C4×Dic47—28no—
244C4×Dic47—28no—
245C4×Dic47—28no—
246C4×Dic47—44no—
247C4×Dic47C2×D4116yes—
248C23×C47C23×C412yes—
249C23×C47C22×D412yes—
250C23×C47C2×#4112yes—
251C23×C47H(5,𝔽2)12yes—
252C23×C472−1+412yes—
253C23×C472−1+412yes—
254C23×C472−1+412yes—
255C23×C47C2511yescharacteristic
256C22×D47—28no—
257C22×D47—28no—
258C22×D47—28no—
259C22×D47—22no—
260C22×D47—22no—
261C22×D47—22no—
262C22×D47—22no—
263C22×D47—22no—
264C22×D47—22no—
265C22×D47—44no—
266C22×D47—44no—
267C22×D47—44no—
268C22×D47—44no—
269C22×D47C23×C414yes—
270C2×C4×C47—28no—
271C2×C4×C47—28no—
272C2×C4×C47—28no—
273C2×C4×C47—28no—
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—22no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—44no—
292C2×C4×C47—44no—
293C2×C4×C47—44no—
294C2×C4×C47C23×C414yes—
295C2×C4×C47C23×C414yes—
296C2×C4×C47C23×C414yes—
297C2×C4×C47C22×D414yes—
298C2×Dic47—28no—
299C2×Dic47—28no—
300C2×Dic47—28no—
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—22no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—44no—
317C2×Dic47—44no—
318C2×Dic47—44no—
319C2×Dic47C4×D4116yes—
320C2×Dic47C23×C414yes—
321C2×Dic47C23×C414yes—
322C2×Dic47C23×C414yes—
323C2×Dic47C22×D414yes—
324C2×Dic47C22×D414yes—
325C2×Dic47C2×#4114yes—
326C4×D47—232no—
327Dic94—232no—
328C2×#2323—471nomaximal, Sylow
329C22×C47C2×C4×D414yes—
330C22×C47#51914yes—
331C22×C47#52014yes—
332C22×C47#53614yes—
333C22×C47#53714yes—
334C22×C47#54114yes—
335C22×C47#54214yes—
336C22×C47C24×C411yescharacteristic
337C22×C47C23×D411yescharacteristic
338C22×C47C22×#4111yescharacteristic
339C22×C47C2×H(5,𝔽2)11yescharacteristic
340C22×C47C2×2−1+411yescharacteristic
341C22×C47C2×2−1+411yescharacteristic
342C22×C47C2×2−1+411yescharacteristic
343C2×D47—24no—
344C2×D47—24no—
345C2×D47—24no—
346C2×D47—416no—
347C2×D47—42no—
348C2×D47—42no—
349C2×D47—42no—
350C2×D47—42no—
351C4×C47—24no—
352C4×C47—24no—
353C4×C47—24no—
354C4×C47—24no—
355C4×C47—42no—
356C4×C47—42no—
357C4×C47—42no—
358Dic47—24no—
359Dic47—24no—
360Dic47—24no—
361Dic47—42no—
362Dic47—42no—
363Dic47—42no—
364Dic47C2×C4×D418yes—
365C22×C22⋊Q8—471no—
366C22×C4×Q8—471no—
367C22×#117—471no—
368#2323—4716no—
369C2×#391—471no—
370C2×#389—471no—
371C2×#389—471no—
372C2×#389D4711yescharacteristic, complemented
373C2×#388—471no—
374C2×#388—471no—
375C2×#388—471no—
376C2×#388—471no—
377C2×#387—471no—
378C2×#387—471no—
379C2×#380—471no—
380C2×C4×C4⋊C4—471no—
381C2×C47#232318yescomplemented
382C2×C47C22×C4×D411yescharacteristic
383C2×C47C2×#51911yescharacteristic
384C2×C47C2×#52011yescharacteristic
385C2×C47C2×#53611yescharacteristic
386C2×C47C2×#53711yescharacteristic
387C2×C47C2×#54111yescharacteristic
388C2×C47C2×#54211yescharacteristic
389D47—44no—
390C23×Q8—471no—
391C24×C4—471no—
392C2×C22⋊Q8—4716no—
393C2×C22⋊Q8—478no—
394C2×C4×Q8—478no—
395C2×C4×Q8—948no—
396C2×#117—478no—
397C2×#117—948no—
398C22×C4⋊C4—471no—
399C22×C4⋊C4—471no—
400C22×C4⋊C4—471no—
401C22×C4⋊C4—471no—
402C22×C4⋊C4—471no—
403C22×C4⋊C4—471no—
404C22×C4⋊C4—471no—
405C22×C4⋊C4C2×D4711yescharacteristic
406C22×C4⋊C4C2×D4711yescharacteristic
407C22×C4⋊C4C2×D4711yescharacteristic
408C22×C4⋊C4C2×D4711yescharacteristic
409C22×C22⋊C4—471no—
410C22×C22⋊C4—471no—
411C22×C22⋊C4—471no—
412C22×C22⋊C4—471no—
413C22×C22⋊C4—471no—
414C22×C22⋊C4—471no—
415C22×C42—471no—
416C22×C42—471no—
417C22×C42—471no—
418C22×C42—471no—
419C22×C42—471no—
420C22×C42C2×D4711yescharacteristic
421#391—478no—
422#389—478no—
423#389—478no—
424#389C2×D4718yescomplemented
425#388—478no—
426#388—478no—
427#388—478no—
428#388—478no—
429#387—478no—
430#387—478no—
431#380—478no—
432C4×C4⋊C4—478no—
433C2×#95—471no—
434C2×#95—471no—
435C2×#95—471no—
436C2×#95—471no—
437C2×#95—471no—
438C2×#95—471no—
439C2×#95—471no—
440C2×#95—471no—
441C2×#95C2×D4711yescharacteristic
442C2×#95C2×D4711yescharacteristic
443C47C2×#232311yescharacteristic, complemented, Sylow
444C25—471no—
445C22×Q8—478no—
446C22×Q8—474no—
447C22×Q8—944no—
448C22×Q8—944no—
449C23×C4—471no—
450C23×C4—471no—
451C23×C4—471no—
452C23×C4—471no—
453C23×C4—478no—
454C23×C4—474no—
455C23×C4—471no—
456C23×C4—471no—
457C23×C4—471no—
458C23×C4—944no—
459C23×C4—944no—
460C23×C4C22×D4711yescharacteristic
461C23×C4C22×D4711yescharacteristic
462C23×C4C22×D4711yescharacteristic
463C23×C4C22×D4711yescharacteristic
464C23×C4C22×D4711yescharacteristic
465C23×C4C22×D4711yescharacteristic
466C23×C4C22×D4711yescharacteristic
467C22⋊Q8—4764no—
468C4×Q8—9432no—
469#117—9432no—
470C2×C4⋊C4—24no—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—42no—
473C2×C4⋊C4—478no—
474C2×C4⋊C4—478no—
475C2×C4⋊C4—474no—
476C2×C4⋊C4—474no—
477C2×C4⋊C4—474no—
478C2×C4⋊C4—474no—
479C2×C4⋊C4—474no—
480C2×C4⋊C4—474no—
481C2×C4⋊C4—474no—
482C2×C4⋊C4—944no—
483C2×C4⋊C4—944no—
484C2×C4⋊C4—944no—
485C2×C4⋊C4—944no—
486C2×C4⋊C4—1882no—
487C2×C4⋊C4C4×D4718yes—
488C2×C4⋊C4C22×D4714yes—
489C2×C4⋊C4C22×D4714yes—
490C2×C4⋊C4C22×D4714yes—
491C2×C4⋊C4C22×D4714yes—
492C2×C22⋊C4—478no—
493C2×C22⋊C4—478no—
494C2×C22⋊C4—474no—
495C2×C22⋊C4—474no—
496C2×C22⋊C4—474no—
497C2×C22⋊C4—474no—
498C2×C22⋊C4—474no—
499C2×C22⋊C4—474no—
500C2×C22⋊C4—944no—
501C2×C22⋊C4—944no—
502C2×C22⋊C4—1882no—
503C2×C22⋊C4—1882no—
504C2×C42—42no—
505C2×C42—478no—
506C2×C42—474no—
507C2×C42—474no—
508C2×C42—474no—
509C2×C42—474no—
510C2×C42—474no—
511C2×C42—944no—
512C2×C42—944no—
513C2×C42—944no—
514C2×C42—1882no—
515C2×C42C22×D4714yes—
516#95—474no—
517#95—474no—
518#95—474no—
519#95—474no—
520#95—474no—
521#95—474no—
522#95—474no—
523#95—474no—
524#95C22×D4714yes—
525#95C22×D4714yes—
526C24—474no—
527C24—472no—
528C24—942no—
529C24—942no—
530C24—942no—
531C24—942no—
532C24—942no—
533C24—942no—
534C24C23×D4711yescharacteristic
535C2×Q8—4716no—
536C2×Q8—948no—
537C2×Q8—9432no—
538C2×Q8—948no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—474no—
557C22×C4—474no—
558C22×C4—474no—
559C22×C4—472no—
560C22×C4—474no—
561C22×C4—474no—
562C22×C4—474no—
563C22×C4—472no—
564C22×C4—472no—
565C22×C4—472no—
566C22×C4—4716no—
567C22×C4—472no—
568C22×C4—472no—
569C22×C4—472no—
570C22×C4—948no—
571C22×C4—9432no—
572C22×C4—948no—
573C22×C4—942no—
574C22×C4—942no—
575C22×C4—942no—
576C22×C4—942no—
577C22×C4—942no—
578C22×C4—942no—
579C22×C4—942no—
580C22×C4—942no—
581C22×C4—942no—
582C22×C4—942no—
583C22×C4—942no—
584C22×C4—942no—
585C22×C4—942no—
586C22×C4—942no—
587C22×C4—942no—
588C22×C4C2×C4×D4714yes—
589C22×C4C2×C4×D4714yes—
590C22×C4C2×C4×D4714yes—
591C22×C4D4×D4714yes—
592C22×C4C23×D4712yes—
593C22×C4C23×D4712yes—
594C22×C4C23×D4712yes—
595C22×C4C23×D4712yes—
596C22×C4C23×D4712yes—
597C22×C4C23×D4712yes—
598C22×C4C23×D4712yes—
599C4⋊C4—28no—
600C4⋊C4—28no—
601C4⋊C4—44no—
602C4⋊C4—4716no—
603C4⋊C4—4716no—
604C4⋊C4—948no—
605C4⋊C4—948no—
606C4⋊C4—948no—
607C4⋊C4—948no—
608C4⋊C4—1884no—
609C4⋊C4C2×C4×D47116yes—
610C22⋊C4—4716no—
611C22⋊C4—4716no—
612C22⋊C4—948no—
613C22⋊C4—948no—
614C22⋊C4—1884no—
615C22⋊C4—1884no—
616C42—44no—
617C42—4716no—
618C42—948no—
619C42—948no—
620C42—948no—
621C42—1884no—
622C23—474no—
623C23—948no—
624C23—948no—
625C23—948no—
626C23—942no—
627C23—942no—
628C23—942no—
629C23—942no—
630C23—942no—
631C23—942no—
632C23—1884no—
633C23—1884no—
634C23—1884no—
635C23—1884no—
636C23C22×C4×D4712yes—
637C23C2×D4×D4712yes—
638C23#41×D4712yes—
639C23#1309406912yes—
640C23#1309407112yes—
641C23#1309407212yes—
642C23#1309407212yes—
643C23C24×D4711yescharacteristic
644Q8—9432no—
645C2×C4—28no—
646C2×C4—28no—
647C2×C4—28no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—28no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—44no—
669C2×C4—4716no—
670C2×C4—474no—
671C2×C4—474no—
672C2×C4—474no—
673C2×C4—474no—
674C2×C4—474no—
675C2×C4—474no—
676C2×C4—9432no—
677C2×C4—948no—
678C2×C4—948no—
679C2×C4—942no—
680C2×C4—942no—
681C2×C4—942no—
682C2×C4—948no—
683C2×C4—942no—
684C2×C4—942no—
685C2×C4—942no—
686C2×C4—942no—
687C2×C4—942no—
688C2×C4—942no—
689C2×C4—942no—
690C2×C4—942no—
691C2×C4—942no—
692C2×C4—942no—
693C2×C4—942no—
694C2×C4—942no—
695C2×C4—1884no—
696C2×C4—1884no—
697C2×C4—1884no—
698C2×C4C22×C4×D4714yes—
699C2×C4C22×C4×D4714yes—
700C2×C4C22×C4×D4714yes—
701C2×C4C2×D4×D4714yes—
702C22—944no—
703C22—944no—
704C22—944no—
705C22—18816no—
706C22—1882no—
707C22—1882no—
708C22—1882no—
709C22—1882no—
710C22C4×D4×D4714yes—
711C22#1568959914yes—
712C22#1568960414yes—
713C22#1568969814yes—
714C22#1568970014yes—
715C22#1568973214yes—
716C22#1568974314yes—
717C22C23×C4×D4711yescharacteristic
718C22C22×D4×D4711yescharacteristic
719C22C2×#41×D4711yescharacteristic
720C22C2×#1309406911yescharacteristic
721C22C2×#1309407111yescharacteristic
722C22C2×#1309407211yescharacteristic
723C22C2×#1309407211yescharacteristic
724C4—24no—
725C4—24no—
726C4—24no—
727C4—24no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—478no—
732C4—944no—
733C4—944no—
734C4—944no—
735C4—1882no—
736C4—1882no—
737C4—1882no—
738C2—1884no—
739C2#2024606518yesdirect product factor
740C2C2×C4×D4×D4711yescharacteristic
741C2C2×#1568959911yescharacteristic
742C2C2×#1568960411yescharacteristic
743C2C2×#1568969811yescharacteristic
744C2C2×#1568970011yescharacteristic
745C2C2×#1568973211yescharacteristic
746C2C2×#1568974311yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#389C2
socleC24×C47C24
prime radicalC24×D47C23
cosocleC23×C47C25
hypercenterC2×#389D47
hypocenterC47C2×#2323
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C22×#13093989C2semidirect
4. #20246065C2direct (N × H)
5. C2×#15689027C2semidirect
6. C2×#15689018C2semidirect
7. C2×#15689018C2semidirect
12. C2×#15689010C2semidirect
13. C2×#15689009C2semidirect
15. C2×C4×Dic47⋊C4C2semidirect
16. C2×C47×#389C2semidirect
19. C2×#13094002C4semidirect
22. C2×#13093989C22semidirect
43. #15689027C22semidirect
44. #15689018C22semidirect
45. #15689018C22semidirect
50. #15689010C22semidirect
51. #15689009C22semidirect
53. C4×Dic47⋊C4C22semidirect
67. C47×#389C22semidirect
86. #13094002C2×C4semidirect
372. C2×#389D47semidirect
381. C2×C47#2323semidirect
424. #389C2×D47semidirect
443. C47C2×#2323semidirect
739. C2#20246065direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940022
C22×#130939892
C22×#130939822
#202460652
C2×#156890272
C2×#156890182
C2×#156890142
C2×#156890132
C2×#156890122
C2×#156890102
C2×#156890092
C2×#156889822
C2×C4×Dic47⋊C42
C2×C47×#3892
C2×#232347