Finite Group Databasebeta

← #26232722

Subgroups — #26232722

Order 12032.

1154 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689831C211yesmaximal, characteristic
2C2×#15689199C211yesmaximal, characteristic
3#20246332C211yesmaximal, characteristic
4#20244347C211yesmaximal, characteristic, complemented
5#20244334C211yesmaximal, characteristic, complemented
6#20243818C211yesmaximal, characteristic, complemented
7#20243701C211yesmaximal, characteristic, complemented
8#20243697C211yesmaximal, characteristic, complemented
9#20243473C211yesmaximal, characteristic, complemented
10#20243472C211yesmaximal, characteristic, complemented
11#20243391C211yesmaximal, characteristic, complemented
12#103×Dic47C211yesmaximal, characteristic, complemented
13#20243108C211yesmaximal, characteristic, complemented
14#20243106C211yesmaximal, characteristic, complemented
15C47×#1894C211yesmaximal, characteristic, complemented
16C22×#10625324C2211yescharacteristic
17#15689831—24no—
18#15689831C418yescomplemented
19C2×#13094023C2211yescharacteristic
20C2×#13094014—21no—
21C2×#13094004—21no—
22C2×#13094001—21no—
23C2×#13094000C2211yescharacteristic
24C2×Q8×Dic47C2211yescharacteristic
25C2×C4×C22⋊D47C2211yescharacteristic
26C2×(C22⋊D47)⋊C4—21no—
27C2×#13093983C2211yescharacteristic
28C2×#13093982C2211yescharacteristic
29C22×C4⋊Dic47C2211yescharacteristic
30C2×C4⋊C4×D47C2211yescharacteristic
31#15689199—24no—
32C2×Dic47⋊C8C2211yescharacteristic
33C2×#13093948C2211yescharacteristic
34C2×#13093948C2211yescharacteristic
35C2×C22⋊(C47⋊C8)C2211yescharacteristic
36C2×(C2×D47)⋊C8C2211yescharacteristic
37C2×C8×Dic47C2211yescharacteristic
38#15689023—21no—
39#15689017—21no—
40#15689012—21no—
41#15688992C2211yescharacteristic
42#15688980C2211yescharacteristic
43C4⋊C4×Dic47C2211yescharacteristic
44#15688974—21no—
45#15688886C2211yescharacteristic
46#15688886C2211yescharacteristic
47#15688886C2211yescharacteristic
48#15688886C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688885C2211yescharacteristic
51#15688885C2211yescharacteristic
52#15688885C2211yescharacteristic
53#15688885C2211yescharacteristic
54#15688885C2211yescharacteristic
55C22×M16×C47C2211yescharacteristic
56C2×C22⋊Q8×C47C2211yescharacteristic
57C2×#103×C47C2211yescharacteristic
58C2×#103×C47C2211yescharacteristic
59C47×#380C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C22×Dic94—21no—
63C22×C22⋊D47D411yescharacteristic
64C23×Dic47—21no—
65C22×C4×D47—21no—
66C22×C4×D47C2311yescharacteristic
67C2×#10625324—22no—
68C2×#10625324—22no—
69C2×#10625324—41no—
70C22×C47⋊C8C2311yescharacteristic
71C22×C47⋊C8C2311yescharacteristic
72#13094023—22no—
73#13094023C2×C414yes—
74#13094014—28no—
75#13094004—28no—
76#13094001—28no—
77#13094000—22no—
78#13094000C2×C414yes—
79Q8×Dic47—22no—
80Q8×Dic47C2×C414yes—
81C4×C22⋊D47C2×C414yes—
82C4×C22⋊D47D414yes—
83(C22⋊D47)⋊C4—28no—
84#13093983—22no—
85#13093983—41no—
86#13093982—22no—
87#13093982—41no—
88C2×C4⋊Dic47—22no—
89C2×C4⋊Dic47—21no—
90C2×C4⋊Dic47—21no—
91C2×C4⋊Dic47C2×C414yes—
92C2×C4⋊Dic47C2311yescharacteristic
93C2×C4⋊Dic47C2311yescharacteristic
94C2×C4⋊Dic47C2311yescharacteristic
95C2×C4⋊Dic47C2311yescharacteristic
96C2×Dic47⋊C4—21no—
97C2×Dic47⋊C4—21no—
98C2×Dic47⋊C4—21no—
99C2×Dic47⋊C4—21no—
100C2×Dic47⋊C4—21no—
101C2×Dic47⋊C4D411yescharacteristic
102C4⋊C4×D47—22no—
103C4⋊C4×D47C2×C414yes—
104C2×C22⋊Dic47—21no—
105C2×C22⋊Dic47D411yescharacteristic
106C2×(C2×D47)⋊C4—21no—
107C2×(C2×D47)⋊C4—21no—
108C2×(C2×D47)⋊C4—21no—
109C2×(C2×D47)⋊C4D411yescharacteristic
110C2×C4×Dic47—21no—
111C2×C4×Dic47—21no—
112C2×C4×Dic47—21no—
113C2×C4×Dic47—21no—
114C2×C4×Dic47C2311yescharacteristic
115Dic47⋊C8—22no—
116#13093948—22no—
117#13093948—41no—
118C22⋊(C47⋊C8)—22no—
119(C2×D47)⋊C8—22no—
120C8×Dic47—22no—
121C47⋊#95—21no—
122C47⋊#95—21no—
123C22×Q8×C47C2311yescharacteristic
124C23×C4×C47C2311yescharacteristic
125C2×M16×C47—22no—
126C2×M16×C47—22no—
127C2×M16×C47—41no—
128C22×C8×C47C2311yescharacteristic
129C22×C8×C47C2311yescharacteristic
130C22⋊Q8×C47—22no—
131C22⋊Q8×C47C2×C414yes—
132C2×C4⋊C4×C47—21no—
133C2×C4⋊C4×C47C2311yescharacteristic
134C2×C4⋊C4×C47C2311yescharacteristic
135C2×C4⋊C4×C47C2311yescharacteristic
136C2×C22⋊C4×C47—21no—
137C2×C22⋊C4×C47—21no—
138#103×C47—22no—
139#103×C47—41no—
140#95×C47—21no—
141C24×C47C2×D411yescharacteristic
142C23×D47C2×D411yescharacteristic
143C2×Q8×C47—21no—
144C2×Q8×C47—21no—
145C2×Q8×C47—21no—
146C2×Q8×C47—21no—
147C2×Q8×C47—21no—
148C2×Q8×C47C22×C412yes—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47—21no—
157C22×C4×C47C22×C412yes—
158C22×C4×C47C2×D411yescharacteristic
159C22×C4×C47C2×D412yes—
160C22×C4×C47C2411yescharacteristic
161C2×C22⋊D47—22no—
162C2×C22⋊D47—22no—
163C2×C22⋊D47C22⋊C414yes—
164C22×Dic47—21no—
165C22×Dic47—21no—
166C22×Dic47—21no—
167C22×Dic47—24no—
168C22×Dic47—21no—
169C22×Dic47—81no—
170C22×Dic47—81no—
171C22×Dic47C2×D411yescharacteristic
172C22×Dic47C2×D411yescharacteristic
173C22×Dic47C2×D411yescharacteristic
174C2×C4×D47—21no—
175C2×C4×D47—21no—
176C2×C4×D47—21no—
177C2×C4×D47—21no—
178C2×C4×D47—24no—
179C2×C4×D47—81no—
180C2×C4×D47—81no—
181C2×C4×D47C22×C412yes—
182C2×C4×D47C2×D412yes—
183C2×Dic94—24no—
184C2×Dic94—81no—
185C2×Dic94—81no—
186M16×C47—44no—
187C2×C8×C47—21no—
188C2×C8×C47—21no—
189C2×C8×C47—21no—
190C2×C8×C47—21no—
191C2×C8×C47—21no—
192C2×C8×C47#4112yes—
193C4⋊C4×C47—24no—
194C4⋊C4×C47—21no—
195C4⋊C4×C47—21no—
196C4⋊C4×C47—21no—
197C4⋊C4×C47—21no—
198C4⋊C4×C47—21no—
199C4⋊C4×C47C22×C412yes—
200C22⋊C4×C47—24no—
201C22⋊C4×C47—81no—
202C22⋊Dic47—42no—
203C22⋊Dic47C22⋊C414yes—
204(C2×D47)⋊C4—24no—
205(C2×D47)⋊C4—42no—
206(C2×D47)⋊C4—81no—
207(C2×D47)⋊C4C22⋊C414yes—
208C4⋊Dic47—24no—
209C4⋊Dic47—21no—
210C4⋊Dic47—21no—
211C4⋊Dic47—21no—
212C4⋊Dic47—24no—
213C4⋊Dic47—21no—
214C4⋊Dic47—21no—
215C4⋊Dic47C22×C412yes—
216C4⋊Dic47C22×C412yes—
217C4⋊Dic47#4112yes—
218Dic47⋊C4—24no—
219Dic47⋊C4—24no—
220Dic47⋊C4—24no—
221Dic47⋊C4—42no—
222Dic47⋊C4—81no—
223Dic47⋊C4C22⋊C414yes—
224C4×Dic47—24no—
225C4×Dic47—42no—
226C4×Dic47—42no—
227C4×Dic47—42no—
228C4×Dic47C22×C412yes—
229C4×Dic47C2×D412yes—
230C2×C47⋊C8—21no—
231C2×C47⋊C8—21no—
232C2×C47⋊C8—21no—
233C2×C47⋊C8—21no—
234C2×C47⋊C8—21no—
235C2×C47⋊C8—21no—
236#10625324—44no—
237C23×C47—21no—
238C23×C47—21no—
239C23×C47—21no—
240C23×C47—21no—
241C23×C47—21no—
242C23×C47—21no—
243C23×C47C2×C22⋊C412yes—
244C23×C47C22×D411yescharacteristic
245C22×D47—21no—
246C22×D47—21no—
247C22×D47—21no—
248C22×D47—21no—
249C22×D47—21no—
250C22×D47—21no—
251C22×D47C2×C22⋊C412yes—
252Q8×C47—22no—
253Q8×C47—22no—
254Q8×C47—41no—
255Q8×C47—41no—
256C2×C4×C47—21no—
257C2×C4×C47—21no—
258C2×C4×C47—22no—
259C2×C4×C47—22no—
260C2×C4×C47—22no—
261C2×C4×C47—22no—
262C2×C4×C47—22no—
263C2×C4×C47—22no—
264C2×C4×C47—41no—
265C2×C4×C47—41no—
266C2×C4×C47—41no—
267C2×C4×C47—41no—
268C2×C4×C47—41no—
269C2×C4×C47—41no—
270C2×C4×C47—41no—
271C2×C4×C47—41no—
272C2×C4×C47—41no—
273C2×C4×C47—41no—
274C2×C4×C47C2×C22⋊C412yes—
275C2×C4×C47C23×C411yescharacteristic
276C2×C4×C47C22×D411yescharacteristic
277C2×C4×C47C2×#4111yescharacteristic
278C2×C4×C47C2×#4111yescharacteristic
279C2×C4×C47H(5,𝔽2)11yescharacteristic
280C2×C4×C472−1+411yescharacteristic
281C22⋊D47—28no—
282C2×Dic47—21no—
283C2×Dic47—21no—
284C2×Dic47—21no—
285C2×Dic47—21no—
286C2×Dic47—22no—
287C2×Dic47—22no—
288C2×Dic47—22no—
289C2×Dic47—41no—
290C2×Dic47—41no—
291C2×Dic47—41no—
292C2×Dic47—41no—
293C2×Dic47—41no—
294C2×Dic47—41no—
295C2×Dic47—41no—
296C2×Dic47—41no—
297C2×Dic47—41no—
298C2×Dic47—84no—
299C2×Dic47C2×C22⋊C412yes—
300C2×Dic47C2×C22⋊C412yes—
301C2×Dic47C2×C22⋊C412yes—
302C2×Dic47#13712yes—
303C2×Dic47#13712yes—
304C4×D47—22no—
305C4×D47—22no—
306C4×D47—22no—
307C4×D47—22no—
308C4×D47—84no—
309Dic94—84no—
310C8×C47—22no—
311C8×C47—41no—
312C47⋊C8—41no—
313C47⋊C8—41no—
314#22502—471nomaximal, Sylow
315C22×C47—22no—
316C22×C47—22no—
317C22×C47—22no—
318C22×C47—41no—
319C22×C47—41no—
320C22×C47—41no—
321C22×C47—41no—
322C22×C47C22×C22⋊C411yescharacteristic
323C22×C47#54611yescharacteristic
324C22×C47#54711yescharacteristic
325C22×C47C2×#13711yescharacteristic
326C22×C47C2×#13711yescharacteristic
327C22×C47#57611yescharacteristic
328C22×C47#57711yescharacteristic
329C2×D47—22no—
330C2×D47—22no—
331C2×D47—22no—
332C2×D47—41no—
333C2×D47—41no—
334C2×D47—41no—
335C2×D47—41no—
336C4×C47—22no—
337C4×C47—42no—
338C4×C47—42no—
339C4×C47—81no—
340C4×C47—81no—
341C4×C47C4×#4111yescharacteristic
342C4×C47#52011yescharacteristic
343C4×C47#54611yescharacteristic
344C4×C47#54711yescharacteristic
345Dic47—22no—
346Dic47—22no—
347Dic47—42no—
348Dic47—42no—
349Dic47—42no—
350Dic47—81no—
351Dic47#41914yes—
352C2×#554—471no—
353C2×#436—471no—
354#2354—471no—
355#1990—471no—
356#1987—471no—
357#1894—471no—
358#1894D4711yescharacteristic, complemented
359#1873—471no—
360#1873—471no—
361#1823—471no—
362#1823—471no—
363#1803—471no—
364C4×#103—471no—
365#1736—471no—
366#1736—471no—
367C2×C47—42no—
368C2×C47#233911yescharacteristic
369C2×C47C2×#41911yescharacteristic
370C2×C47#289711yescharacteristic
371C2×C47#333111yescharacteristic
372C2×C47#333311yescharacteristic
373C2×C47#335611yescharacteristic
374C2×C47#335711yescharacteristic
375D47—42no—
376C22×M16—471no—
377C22×M16C2×D4711yescharacteristic
378#554—478no—
379#554—944no—
380C2×C4⋊Q8—471no—
381C2×#125—941no—
382C2×C22⋊Q8—471no—
383C2×C22⋊Q8—941no—
384C2×C22⋊Q8—941no—
385C2×C22⋊Q8C2×D4711yescharacteristic
386C2×C4×Q8—471no—
387C2×C4×D4—471no—
388C2×C4×D4—941no—
389C2×#117—471no—
390C2×#117—471no—
391C22×C4⋊C4—471no—
392C22×C4⋊C4—471no—
393#436—944no—
394C2×C4⋊C8—471no—
395C2×#103—471no—
396C2×#103—471no—
397C2×#103C2×D4711yescharacteristic
398C2×#103C2×D4711yescharacteristic
399C2×C22⋊C8—471no—
400C2×C22⋊C8—471no—
401C2×C4×C8—471no—
402#390—941no—
403#388—941no—
404#388—941no—
405#384—471no—
406#380—471no—
407#380C2×D4711yescharacteristic
408C4×C4⋊C4—471no—
409C4×C4⋊C4—941no—
410#340—471no—
411#340—471no—
412#340—471no—
413#340—471no—
414#340—471no—
415#340—471no—
416#340—471no—
417#340—471no—
418#340—471no—
419#340—471no—
420#340C2×D4711yescharacteristic
421#340C2×D4711yescharacteristic
422C47#2250211yescharacteristic, complemented, Sylow
423C22×Q8—941no—
424C22×Q8C22×D4711yescharacteristic
425C22×D4—471no—
426C23×C4—471no—
427C23×C4—941no—
428C23×C4—941no—
429C23×C4C22×D4711yescharacteristic
430C2×M16—22no—
431C2×M16—22no—
432C2×M16—41no—
433C2×M16—942no—
434C2×M16—942no—
435C2×M16—1881no—
436C22×C8—471no—
437C22×C8—471no—
438C22×C8C22×D4711yescharacteristic
439C22×C8C22×D4711yescharacteristic
440C4⋊Q8—474no—
441C4⋊Q8—942no—
442#125—948no—
443C22⋊Q8—22no—
444C22⋊Q8—474no—
445C22⋊Q8—948no—
446C22⋊Q8—948no—
447C22⋊Q8—942no—
448C22⋊Q8C4×D4714yes—
449C4×Q8—474no—
450C4×Q8—942no—
451C4×D4—474no—
452C4×D4—474no—
453C4×D4—948no—
454#117—942no—
455#117—942no—
456#117—1881no—
457#117—1881no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—471no—
460C2×C4⋊C4—474no—
461C2×C4⋊C4—471no—
462C2×C4⋊C4—471no—
463C2×C4⋊C4—471no—
464C2×C4⋊C4—474no—
465C2×C4⋊C4—471no—
466C2×C4⋊C4—942no—
467C2×C4⋊C4—941no—
468C2×C4⋊C4—941no—
469C2×C4⋊C4—941no—
470C2×C4⋊C4—941no—
471C2×C4⋊C4—941no—
472C2×C4⋊C4—942no—
473C2×C4⋊C4—941no—
474C2×C4⋊C4—941no—
475C2×C4⋊C4C22×D4711yescharacteristic
476C2×C4⋊C4C22×D4711yescharacteristic
477C2×C4⋊C4C22×D4711yescharacteristic
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—471no—
481C2×C22⋊C4—471no—
482C2×C22⋊C4—941no—
483C2×C22⋊C4—941no—
484C2×C22⋊C4—941no—
485C2×C22⋊C4—941no—
486C2×C42—471no—
487C2×C42—941no—
488C2×C42—941no—
489C2×C42—941no—
490C2×C42—941no—
491C4⋊C8—942no—
492#103—22no—
493#103—41no—
494#103—942no—
495#103—1881no—
496C22⋊C8—942no—
497C22⋊C8—942no—
498C4×C8—942no—
499#95—21no—
500#95—941no—
501#95—941no—
502C24—471no—
503C24D4×D4711yescharacteristic
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—944no—
510C2×Q8—3761no—
511C2×Q8—3761no—
512C2×Q8C2×C4×D4712yes—
513C2×D4—474no—
514C2×D4—942no—
515C2×D4—942no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—471no—
525C22×C4—471no—
526C22×C4—471no—
527C22×C4—472no—
528C22×C4—472no—
529C22×C4—944no—
530C22×C4—941no—
531C22×C4—941no—
532C22×C4—941no—
533C22×C4—941no—
534C22×C4—944no—
535C22×C4—941no—
536C22×C4—941no—
537C22×C4—941no—
538C22×C4—941no—
539C22×C4—3761no—
540C22×C4—3761no—
541C22×C4—3761no—
542C22×C4—3761no—
543C22×C4C2×C4×D4712yes—
544C22×C4D4×D4711yescharacteristic
545C22×C4D4×D4712yes—
546C22×C4C23×D4711yescharacteristic
547M16—44no—
548M16—1884no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—941no—
555C2×C8—941no—
556C2×C8—941no—
557C2×C8—941no—
558C2×C8—941no—
559C2×C8—941no—
560C2×C8#1062535212yes—
561C4⋊C4—24no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—474no—
568C4⋊C4—472no—
569C4⋊C4—472no—
570C4⋊C4—472no—
571C4⋊C4—944no—
572C4⋊C4—944no—
573C4⋊C4—944no—
574C4⋊C4—944no—
575C4⋊C4—944no—
576C4⋊C4—941no—
577C4⋊C4—941no—
578C4⋊C4—941no—
579C4⋊C4—941no—
580C4⋊C4—941no—
581C4⋊C4—3761no—
582C4⋊C4—1882no—
583C4⋊C4C2×C4×D4712yes—
584C22⋊C4—24no—
585C22⋊C4—81no—
586C22⋊C4—474no—
587C22⋊C4—474no—
588C22⋊C4—944no—
589C22⋊C4—3761no—
590C22⋊C4—1882no—
591C22⋊C4—1882no—
592C42—472no—
593C42—472no—
594C42—944no—
595C42—1882no—
596C42—1882no—
597C42—1882no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—472no—
605C23—941no—
606C23—941no—
607C23—941no—
608C23—941no—
609C23—941no—
610C23—941no—
611C23C22⋊C4×D4712yes—
612C23C2×D4×D4711yescharacteristic
613Q8—22no—
614Q8—22no—
615Q8—41no—
616Q8—41no—
617Q8—3764no—
618D4—948no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—472no—
638C2×C4—472no—
639C2×C4—472no—
640C2×C4—472no—
641C2×C4—472no—
642C2×C4—941no—
643C2×C4—941no—
644C2×C4—941no—
645C2×C4—941no—
646C2×C4—942no—
647C2×C4—942no—
648C2×C4—942no—
649C2×C4—942no—
650C2×C4—942no—
651C2×C4—942no—
652C2×C4—942no—
653C2×C4—3764no—
654C2×C4—3764no—
655C2×C4—1881no—
656C2×C4—1881no—
657C2×C4—1881no—
658C2×C4—1881no—
659C2×C4—1881no—
660C2×C4—1881no—
661C2×C4—1881no—
662C2×C4—1881no—
663C2×C4—1881no—
664C2×C4C22⋊C4×D4712yes—
665C2×C4C22×C4×D4711yescharacteristic
666C2×C4C2×D4×D4711yescharacteristic
667C2×C4#41×D4711yescharacteristic
668C2×C4C2×#1062535211yescharacteristic
669C2×C4#1309406911yescharacteristic
670C2×C4#1309407111yescharacteristic
671C8—22no—
672C8—41no—
673C8—1881no—
674C8—1881no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—942no—
683C22—942no—
684C22—942no—
685C22—1881no—
686C22—1881no—
687C22—1881no—
688C22—1881no—
689C22C2×C22⋊C4×D4711yescharacteristic
690C22#1568976211yescharacteristic
691C22#1568977311yescharacteristic
692C22#137×D4711yescharacteristic
693C22#137×D4711yescharacteristic
694C22#1568992711yescharacteristic
695C22#1568993211yescharacteristic
696C4—22no—
697C4—42no—
698C4—42no—
699C4—81no—
700C4—81no—
701C4—474no—
702C4—942no—
703C4—942no—
704C4—3761no—
705C4—1882no—
706C4—1882no—
707C4—1882no—
708C4C4×#1062535211yescharacteristic
709C4#1568960211yescharacteristic
710C4#1568976011yescharacteristic
711C4#1568977111yescharacteristic
712C2—42no—
713C2—1882no—
714C2#2024621411yescharacteristic
715C2#419×D4711yescharacteristic
716C2#2025191211yescharacteristic
717C2#2025569911yescharacteristic
718C2#2025572111yescharacteristic
719C2#2025599811yescharacteristic
720C2#2025600911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1894C2
socleC23×C47C22×D4
prime radicalC22×C22⋊D47D4
cosocleC22×C4×C47C24
hypercenter#1894D47
hypocenterC47#22502
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1894

Complements

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

NH ≅ G/Ntype
4. #20244347C2semidirect
5. #20244334C2semidirect
6. #20243818C2semidirect
7. #20243701C2semidirect
8. #20243697C2semidirect
9. #20243473C2semidirect
10. #20243472C2semidirect
11. #20243391C2semidirect
12. #103×Dic47C2semidirect
13. #20243108C2semidirect
14. #20243106C2semidirect
15. C47×#1894C2semidirect
18. #15689831C4semidirect
358. #1894D47semidirect
422. C47#22502semidirect

Maximal subgroups

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

subgroupindex
C2×#156898312
C2×#156891992
#202463322
#202443472
#202443342
#202438182
#202437012
#202436972
#202434732
#202434722
#202433912
#103×Dic472
#202431082
#202431062
C47×#18942
#2250247