Finite Group Databasebeta

← #26222073

Subgroups — #26222073

Order 12032.

1344 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689601C211yesmaximal, characteristic
2C2×#15689230C211yesmaximal, characteristic, complemented
3C2×Q16×Dic47C211yesmaximal, characteristic, complemented
4#20246072C211yesmaximal, characteristic
5#20243731C211yesmaximal, characteristic, complemented
6#20243731C211yesmaximal, characteristic, complemented
7#20243701C211yesmaximal, characteristic
8#20243658C211yesmaximal, characteristic, complemented
9#20243644C211yesmaximal, characteristic, complemented
10#20243589C211yesmaximal, characteristic
11#20243323C211yesmaximal, characteristic
12#20243220C211yesmaximal, characteristic, complemented
13#103×Dic47C211yesmaximal, characteristic, complemented
14#20243156C211yesmaximal, characteristic
15C2×C47×#451C211yesmaximal, characteristic
16#15689601—24no—
17#15689601—24no—
18C2×Q8×Dic47—21no—
19C2×Q8×Dic47—21no—
20C2×Q8×Dic47C2211yescharacteristic
21C2×Q8×Dic47C2211yescharacteristic
22C2×Q8×Dic47C2211yescharacteristic
23C2×Q8×Dic47C2211yescharacteristic
24C2×Q8×Dic47C2211yescharacteristic
25C2×#13093983—21no—
26C2×#13093983—21no—
27C2×#13093983C2211yescharacteristic
28C2×#13093983C2211yescharacteristic
29#15689230—24no—
30Q16×Dic47—24no—
31C2×#13093958C2211yescharacteristic
32C2×#13093956C2211yescharacteristic
33C2×#13093948C2211yescharacteristic
34C2×#13093948C2211yescharacteristic
35C2×#13093948C2211yescharacteristic
36C2×#13093948C2211yescharacteristic
37C2×#13093948C2211yescharacteristic
38C2×#13093948C2211yescharacteristic
39C2×C22⋊(C47⋊C8)C2211yescharacteristic
40C2×#13093934C2211yescharacteristic
41C2×C8×Dic47C2211yescharacteristic
42#15689030C2211yescharacteristic
43#15689022—21no—
44#15689022C2211yescharacteristic
45#15689016—21no—
46#15689016—21no—
47#15689009—21no—
48#15688983C2211yescharacteristic
49C4⋊C4×Dic47C2211yescharacteristic
50#15688886C2211yescharacteristic
51#15688886C2211yescharacteristic
52#15688885C2211yescharacteristic
53#15688885C2211yescharacteristic
54#15688877C2211yescharacteristic
55#15688877C2211yescharacteristic
56C23×Q8×C47C2211yescharacteristic
57C22×Q16×C47C2211yescharacteristic
58C22×Q16×C47C2211yescharacteristic
59C2×C22⋊Q8×C47C2211yescharacteristic
60C47×#451C418yescomplemented
61C2×#103×C47C2211yescharacteristic
62C2×#103×C47C2211yescharacteristic
63C2×C22⋊C8×C47C2211yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66Q8×Dic47—28no—
67Q8×Dic47—28no—
68Q8×Dic47—22no—
69Q8×Dic47—22no—
70Q8×Dic47—22no—
71Q8×Dic47—22no—
72Q8×Dic47—22no—
73Q8×Dic47—22no—
74Q8×Dic47—22no—
75Q8×Dic47—22no—
76Q8×Dic47D414yes—
77Q8×Dic47D414yes—
78#13093983—28no—
79#13093983—28no—
80#13093983—22no—
81#13093983—22no—
82#13093983—22no—
83#13093983—22no—
84C2×C4⋊Dic47—21no—
85C2×C4⋊Dic47—21no—
86C2×C4⋊Dic47—21no—
87C2×C4⋊Dic47—21no—
88C2×C4⋊Dic47—21no—
89C2×C4⋊Dic47—21no—
90C2×C4⋊Dic47D411yescharacteristic
91C2×C4⋊Dic47D411yescharacteristic
92C2×C4⋊Dic47C2311yescharacteristic
93C2×C4⋊Dic47C2311yescharacteristic
94C2×C4⋊Dic47C2311yescharacteristic
95C2×C4⋊Dic47C2311yescharacteristic
96C2×C22⋊Dic47—21no—
97C2×C22⋊Dic47—21no—
98C2×C22⋊Dic47D411yescharacteristic
99C2×C22⋊Dic47D411yescharacteristic
100C2×C4×Dic47—21no—
101C2×C4×Dic47—21no—
102C2×C4×Dic47—21no—
103C2×C4×Dic47—21no—
104C2×C4×Dic47—21no—
105C2×C4×Dic47—21no—
106C2×C4×Dic47—21no—
107C2×C4×Dic47C2311yescharacteristic
108C2×C4×Dic47C2311yescharacteristic
109#13093958—22no—
110#13093956—22no—
111#13093948—22no—
112#13093948—22no—
113#13093948—22no—
114#13093948—22no—
115#13093948—22no—
116#13093948—22no—
117C22⋊(C47⋊C8)—22no—
118#13093934—22no—
119C8×Dic47—22no—
120C47⋊#95—21no—
121C47⋊#95—21no—
122C47⋊#95—21no—
123C47⋊#95—21no—
124C47⋊#95—21no—
125C22×Q8×C47—22no—
126C22×Q8×C47—22no—
127C22×Q8×C47—22no—
128C22×Q8×C47—22no—
129C22×Q8×C47—21no—
130C22×Q8×C47—22no—
131C22×Q8×C47C2×C414yes—
132C22×Q8×C47C2311yescharacteristic
133C22×Q8×C47C2311yescharacteristic
134C22×Q8×C47C2311yescharacteristic
135C23×C4×C47—21no—
136C23×C4×C47C2311yescharacteristic
137C2×Q16×C47—22no—
138C2×Q16×C47—22no—
139C2×Q16×C47—22no—
140C2×Q16×C47—22no—
141C2×Q16×C47C2×C414yes—
142C2×Q16×C47C2×C414yes—
143C22×C8×C47C2311yescharacteristic
144C22×C8×C47C2311yescharacteristic
145C22⋊Q8×C47—22no—
146C22⋊Q8×C47C2×C414yes—
147C2×C4⋊C4×C47—21no—
148C2×C4⋊C4×C47C2311yescharacteristic
149C2×C22⋊C4×C47—21no—
150#103×C47C2×C414yes—
151#103×C47C2×C414yes—
152C22⋊C8×C47C2×C414yes—
153C24×C47C2×D411yescharacteristic
154C2×Q8×C47—28no—
155C2×Q8×C47—28no—
156C2×Q8×C47—24no—
157C2×Q8×C47—24no—
158C2×Q8×C47—28no—
159C2×Q8×C47—28no—
160C2×Q8×C47—24no—
161C2×Q8×C47—21no—
162C2×Q8×C47—21no—
163C2×Q8×C47—21no—
164C2×Q8×C47—21no—
165C2×Q8×C47—21no—
166C2×Q8×C47—21no—
167C2×Q8×C47—21no—
168C2×Q8×C47—21no—
169C2×Q8×C47—21no—
170C2×Q8×C47—21no—
171C2×Q8×C47—21no—
172C2×Q8×C47C22×C412yes—
173C2×Q8×C47C22×C412yes—
174C2×Q8×C47C22×C412yes—
175C2×Q8×C47C2×D412yes—
176C2×Q8×C47C2×D412yes—
177C2×Q8×C47#4112yes—
178C2×Q8×C47#4112yes—
179C22×C4×C47—24no—
180C22×C4×C47—24no—
181C22×C4×C47—24no—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47C22×C412yes—
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47#4112yes—
193C22×C4×C47C2411yescharacteristic
194C22×Dic47—21no—
195C22×Dic47—21no—
196C22×Dic47—21no—
197C22×Dic47—21no—
198C22×Dic47C2×D411yescharacteristic
199C22×Dic47C2×D411yescharacteristic
200C22×Dic47C2×D411yescharacteristic
201C22×Dic47C2×D411yescharacteristic
202Q16×C47—28no—
203Q16×C47—28no—
204C2×C8×C47—21no—
205C2×C8×C47—21no—
206C2×C8×C47—21no—
207C2×C8×C47—21no—
208C2×C8×C47C22×C412yes—
209C2×C8×C47C22×C412yes—
210C4⋊C4×C47—24no—
211C4⋊C4×C47—21no—
212C4⋊C4×C47C22×C412yes—
213C22⋊C4×C47—24no—
214C22⋊Dic47—24no—
215C22⋊Dic47—22no—
216C22⋊Dic47—22no—
217C22⋊Dic47—81no—
218C4⋊Dic47—24no—
219C4⋊Dic47—24no—
220C4⋊Dic47—21no—
221C4⋊Dic47—21no—
222C4⋊Dic47—24no—
223C4⋊Dic47—24no—
224C4⋊Dic47—22no—
225C4⋊Dic47—22no—
226C4⋊Dic47—21no—
227C4⋊Dic47—21no—
228C4⋊Dic47—21no—
229C4⋊Dic47—21no—
230C4⋊Dic47—42no—
231C4⋊Dic47—81no—
232C4⋊Dic47C2×D412yes—
233C4⋊Dic47C2×D412yes—
234C4×Dic47—24no—
235C4×Dic47—24no—
236C4×Dic47—24no—
237C4×Dic47—21no—
238C4×Dic47—21no—
239C4×Dic47—24no—
240C4×Dic47—24no—
241C4×Dic47—42no—
242C4×Dic47—81no—
243C4×Dic47C2×D412yes—
244C4×Dic47C2×D412yes—
245C2×C47⋊C8—21no—
246C2×C47⋊C8—21no—
247C2×C47⋊C8—21no—
248C2×C47⋊C8—21no—
249C2×C47⋊C8—21no—
250C2×C47⋊C8—21no—
251C23×C47—21no—
252C23×C47—21no—
253C23×C47—21no—
254C23×C47—21no—
255C23×C47—21no—
256C23×C47—21no—
257C23×C47C4×D412yes—
258C23×C47C22×D411yescharacteristic
259Q8×C47—216no—
260Q8×C47—22no—
261Q8×C47—22no—
262Q8×C47—22no—
263Q8×C47—22no—
264Q8×C47—22no—
265Q8×C47—22no—
266Q8×C47—22no—
267Q8×C47—22no—
268Q8×C47—41no—
269Q8×C47—41no—
270Q8×C47C4×D414yes—
271Q8×C47C4×D414yes—
272C2×C4×C47—216no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—21no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—21no—
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—41no—
288C2×C4×C47—41no—
289C2×C4×C47—41no—
290C2×C4×C47—41no—
291C2×C4×C47C4×D412yes—
292C2×C4×C47C23×C411yescharacteristic
293C2×C4×C47C22×D411yescharacteristic
294C2×C4×C47C22×D411yescharacteristic
295C2×C4×C47C2×#4111yescharacteristic
296C2×C4×C47C2×#4111yescharacteristic
297C2×C4×C47C2×#4111yescharacteristic
298C2×Dic47—21no—
299C2×Dic47—21no—
300C2×Dic47—21no—
301C2×Dic47—21no—
302C2×Dic47—21no—
303C2×Dic47—21no—
304C2×Dic47—22no—
305C2×Dic47—22no—
306C2×Dic47—21no—
307C2×Dic47—21no—
308C2×Dic47—21no—
309C2×Dic47—21no—
310C2×Dic47—41no—
311C2×Dic47—41no—
312C2×Dic47—41no—
313C2×Dic47—41no—
314C2×Dic47—41no—
315C2×Dic47—41no—
316C2×Dic47—41no—
317C2×Dic47—41no—
318C2×Dic47—41no—
319C2×Dic47—41no—
320C2×Dic47#12012yes—
321C2×Dic47#12012yes—
322C8×C47—22no—
323C8×C47—22no—
324C47⋊C8—41no—
325C47⋊C8—41no—
326#21463—471nomaximal, Sylow
327C22×C47—22no—
328C22×C47—22no—
329C22×C47—22no—
330C22×C47—41no—
331C22×C47—41no—
332C22×C47—41no—
333C22×C47—41no—
334C22×C47C2×C4×D411yescharacteristic
335C22×C47C2×#12011yescharacteristic
336C22×C47#52511yescharacteristic
337C22×C47#57711yescharacteristic
338C22×C47#57811yescharacteristic
339C22×C47#57811yescharacteristic
340C22×C47#57811yescharacteristic
341C4×C47—24no—
342C4×C47—24no—
343C4×C47—22no—
344C4×C47—42no—
345C4×C47—42no—
346C4×C47C2×C4×D411yescharacteristic
347C4×C47C2×C4×D411yescharacteristic
348C4×C47#52511yescharacteristic
349C4×C47#52511yescharacteristic
350Dic47—22no—
351Dic47—22no—
352Dic47—41no—
353Dic47—42no—
354Dic47—41no—
355Dic47—42no—
356Dic47—81no—
357Dic47—81no—
358C2×#519—471no—
359C2×#451D4711yescharacteristic
360C2×#441—471no—
361C2×C4×Q16—471no—
362#2323—471no—
363#1878—471no—
364#1878—471no—
365#1873—471no—
366#1865—471no—
367#1863—471no—
368#1854—471no—
369#1787—471no—
370#1763—471no—
371C4×#103—471no—
372#1750—471no—
373C2×C47—42no—
374C2×C47C4×#12011yescharacteristic
375C2×C47#294711yescharacteristic
376C2×C47#295011yescharacteristic
377C2×C47#301111yescharacteristic
378C2×C47#301311yescharacteristic
379C2×C47#312111yescharacteristic
380C2×C47#312711yescharacteristic
381C23×Q8C2×D4711yescharacteristic
382C22×Q16C2×D4711yescharacteristic
383C22×Q16C2×D4711yescharacteristic
384C2×C22⋊Q8C2×D4711yescharacteristic
385#519—944no—
386#519—944no—
387C2×C4×Q8—471no—
388C2×C4×Q8—471no—
389C2×C4×Q8—471no—
390C2×C4×Q8—471no—
391C2×C4×Q8—471no—
392C2×C4×Q8—941no—
393C2×C4×Q8—941no—
394C2×#117—471no—
395C2×#117—471no—
396C2×#117—941no—
397C2×#117—941no—
398#451Dic4718yescomplemented
399#441—944no—
400C4×Q16—944no—
401C2×#107—471no—
402C2×#106—471no—
403C2×#103—471no—
404C2×#103—471no—
405C2×#103—471no—
406C2×#103—471no—
407C2×#103—471no—
408C2×#103—471no—
409C2×#103C2×D4711yescharacteristic
410C2×#103C2×D4711yescharacteristic
411C2×C22⋊C8—471no—
412C2×C22⋊C8C2×D4711yescharacteristic
413C2×#97—471no—
414C2×C4×C8—471no—
415#391—471no—
416#389—471no—
417#389—941no—
418#388—941no—
419#388—941no—
420#387—941no—
421#380—471no—
422C4×C4⋊C4—471no—
423#340—471no—
424#340—471no—
425#340—471no—
426#340—471no—
427#336—471no—
428#336—471no—
429C47#2146311yescharacteristic, complemented, Sylow
430C22×Q8—22no—
431C22×Q8—22no—
432C22×Q8—22no—
433C22×Q8—22no—
434C22×Q8—21no—
435C22×Q8—22no—
436C22×Q8C2×Dic4714yes—
437C22×Q8C22×D4711yescharacteristic
438C22×Q8C22×D4711yescharacteristic
439C22×Q8C22×D4711yescharacteristic
440C23×C4—21no—
441C23×C4C22×D4711yescharacteristic
442C2×Q16—22no—
443C2×Q16—22no—
444C2×Q16—22no—
445C2×Q16—22no—
446C2×Q16C2×Dic4714yes—
447C2×Q16C2×Dic4714yes—
448C22×C8—471no—
449C22×C8—471no—
450C22×C8C22×D4711yescharacteristic
451C22×C8C22×D4711yescharacteristic
452C22⋊Q8—22no—
453C22⋊Q8C2×Dic4714yes—
454C4×Q8—474no—
455C4×Q8—474no—
456C4×Q8—942no—
457C4×Q8—942no—
458C4×Q8—942no—
459C4×Q8—942no—
460C4×Q8—942no—
461C4×Q8—942no—
462C4×Q8—948no—
463C4×Q8—948no—
464C4×Q8—942no—
465C4×Q8—942no—
466#117—942no—
467#117—942no—
468#117—942no—
469#117—942no—
470#117—948no—
471#117—948no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—471no—
474C2×C4⋊C4—471no—
475C2×C4⋊C4—471no—
476C2×C4⋊C4—471no—
477C2×C4⋊C4—471no—
478C2×C4⋊C4—471no—
479C2×C4⋊C4—941no—
480C2×C4⋊C4—941no—
481C2×C4⋊C4—941no—
482C2×C4⋊C4—941no—
483C2×C4⋊C4—941no—
484C2×C4⋊C4—941no—
485C2×C4⋊C4C22×D4711yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—471no—
488C2×C22⋊C4—471no—
489C2×C22⋊C4—941no—
490C2×C22⋊C4—941no—
491C2×C42—471no—
492C2×C42—471no—
493C2×C42—941no—
494C2×C42—941no—
495C2×C42—941no—
496C2×C42—941no—
497C2×C42—941no—
498C2×C42—941no—
499C2×C42—941no—
500#107—942no—
501#106—942no—
502#103—942no—
503#103—942no—
504#103—942no—
505#103—942no—
506#103—942no—
507#103—942no—
508#103C2×Dic4714yes—
509#103C2×Dic4714yes—
510C22⋊C8—942no—
511C22⋊C8C2×Dic4714yes—
512#97—942no—
513C4×C8—942no—
514#95—941no—
515#95—941no—
516#95—941no—
517#95—941no—
518#95—941no—
519C24D4×D4711yescharacteristic
520C2×Q8—24no—
521C2×Q8—28no—
522C2×Q8—28no—
523C2×Q8—24no—
524C2×Q8—28no—
525C2×Q8—28no—
526C2×Q8—24no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8D4×D4712yes—
539C2×Q8D4×D4712yes—
540C2×Q8#1062535212yes—
541C2×Q8#1062535212yes—
542C2×Q8C22×Dic4712yes—
543C2×Q8C22×Dic4712yes—
544C2×Q8C22×Dic4712yes—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—471no—
557C22×C4—471no—
558C22×C4—471no—
559C22×C4—471no—
560C22×C4—941no—
561C22×C4—941no—
562C22×C4—941no—
563C22×C4—941no—
564C22×C4D4×D4711yescharacteristic
565C22×C4#1062535212yes—
566C22×C4C22×Dic4712yes—
567C22×C4C23×D4711yescharacteristic
568Q16—28no—
569Q16—28no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—941no—
575C2×C8—941no—
576C2×C8—941no—
577C2×C8—941no—
578C2×C8—941no—
579C2×C8—941no—
580C2×C8C22×Dic4712yes—
581C2×C8C22×Dic4712yes—
582C4⋊C4—24no—
583C4⋊C4—21no—
584C4⋊C4—472no—
585C4⋊C4—472no—
586C4⋊C4—942no—
587C4⋊C4—942no—
588C4⋊C4—944no—
589C4⋊C4—944no—
590C4⋊C4—944no—
591C4⋊C4—944no—
592C4⋊C4—941no—
593C4⋊C4—941no—
594C4⋊C4—941no—
595C4⋊C4—941no—
596C4⋊C4—941no—
597C4⋊C4—941no—
598C4⋊C4—3761no—
599C4⋊C4—1882no—
600C4⋊C4C22×Dic4712yes—
601C22⋊C4—24no—
602C22⋊C4—942no—
603C22⋊C4—942no—
604C22⋊C4—944no—
605C22⋊C4—3761no—
606C42—472no—
607C42—472no—
608C42—944no—
609C42—944no—
610C42—944no—
611C42—944no—
612C42—944no—
613C42—941no—
614C42—941no—
615C42—3761no—
616C42—1882no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23D4×Dic4712yes—
624C23C2×D4×D4711yescharacteristic
625Q8—216no—
626Q8—22no—
627Q8—22no—
628Q8—22no—
629Q8—22no—
630Q8—22no—
631Q8—22no—
632Q8—22no—
633Q8—22no—
634Q8—41no—
635Q8—41no—
636Q8D4×Dic4714yes—
637Q8D4×Dic4714yes—
638C2×C4—216no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—472no—
658C2×C4—472no—
659C2×C4—941no—
660C2×C4—941no—
661C2×C4—941no—
662C2×C4—941no—
663C2×C4—942no—
664C2×C4—942no—
665C2×C4—941no—
666C2×C4—941no—
667C2×C4—941no—
668C2×C4—941no—
669C2×C4—941no—
670C2×C4—941no—
671C2×C4—1881no—
672C2×C4—1881no—
673C2×C4—1881no—
674C2×C4—1881no—
675C2×C4—1881no—
676C2×C4—1881no—
677C2×C4—1881no—
678C2×C4—1881no—
679C2×C4—1881no—
680C2×C4—1881no—
681C2×C4D4×Dic4712yes—
682C2×C4C23×Dic4711yescharacteristic
683C2×C4C2×D4×D4711yescharacteristic
684C2×C4C2×D4×D4711yescharacteristic
685C2×C4C2×#1062535211yescharacteristic
686C2×C4C2×#1062535211yescharacteristic
687C2×C4C2×#1062535211yescharacteristic
688C8—22no—
689C8—22no—
690C8—1881no—
691C8—1881no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22C2×D4×Dic4711yescharacteristic
700C22#120×D4711yescharacteristic
701C22#1568962911yescharacteristic
702C22#1568993211yescharacteristic
703C22#1568993611yescharacteristic
704C22#1568993611yescharacteristic
705C22#1568993911yescharacteristic
706C4—24no—
707C4—24no—
708C4—22no—
709C4—42no—
710C4—42no—
711C4—942no—
712C4—942no—
713C4—3761no—
714C4—3761no—
715C4—1881no—
716C4—1882no—
717C4—1881no—
718C4—1882no—
719C4C2×D4×Dic4711yescharacteristic
720C4C2×D4×Dic4711yescharacteristic
721C4#1568962911yescharacteristic
722C4#1568962911yescharacteristic
723C2—42no—
724C2#120×Dic4711yescharacteristic
725C2#2025223211yescharacteristic
726C2#2025225611yescharacteristic
727C2#2025267811yescharacteristic
728C2#2025270411yescharacteristic
729C2#2025361811yescharacteristic
730C2#2025368211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#451C2
socleC23×C47C22×D4
prime radicalC24×C47C2×D4
cosocleC22×C4×C47C24
hypercenterC2×#451D47
hypocenterC47#21463
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
2. C2×#15689230C2semidirect
3. C2×Q16×Dic47C2semidirect
5. #20243731C2semidirect
6. #20243731C2semidirect
8. #20243658C2semidirect
9. #20243644C2semidirect
12. #20243220C2semidirect
13. #103×Dic47C2semidirect
60. C47×#451C4semidirect
398. #451Dic47semidirect
429. C47#21463semidirect

Maximal subgroups

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

subgroupindex
C2×#156896012
C2×#156892302
C2×Q16×Dic472
#202460722
#202437312
#202437012
#202436582
#202436442
#202435892
#202433232
#202432202
#103×Dic472
#202431562
C2×C47×#4512
#2146347