Finite Group Databasebeta

← #26232488

Subgroups — #26232488

Order 12032.

1474 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689774C211yesmaximal, characteristic
2C2×C8×C22⋊D47C211yesmaximal, characteristic, complemented
3C4⋊C4×C22⋊D47C211yesmaximal, characteristic, complemented
4#20244347C211yesmaximal, characteristic, complemented
5#20244338C211yesmaximal, characteristic, complemented
6#20243816C211yesmaximal, characteristic, complemented
7#20243815C211yesmaximal, characteristic, complemented
8#20243705C211yesmaximal, characteristic, complemented
9#20243704C211yesmaximal, characteristic, complemented
10#20243474C211yesmaximal, characteristic, complemented
11#20243473C211yesmaximal, characteristic, complemented
12#20243387C211yesmaximal, characteristic, complemented
13#20243202C211yesmaximal, characteristic, complemented
14#340×D47C211yesmaximal, characteristic, complemented
15C2×C47×#340C211yesmaximal, characteristic, complemented
16C22×#10625350—21no—
17C22×C8×D47C2211yescharacteristic
18#15689774—24no—
19#15689774C418yescomplemented
20C2×#13094023C2211yescharacteristic
21C2×#13094009—21no—
22C2×#13094007—21no—
23C2×#13094002—21no—
24C2×#13093999C2211yescharacteristic
25C2×#13093998C2211yescharacteristic
26C2×#13093986C2211yescharacteristic
27C2×C4×C22⋊D47—21no—
28C2×C4×C22⋊D47C2211yescharacteristic
29C2×C4⋊C4×D47C2211yescharacteristic
30C2×C4⋊C4×D47C2211yescharacteristic
31C8×C22⋊D47—24no—
32C2×Dic47⋊C8C2211yescharacteristic
33C2×#13093946C2211yescharacteristic
34C2×#13093946C2211yescharacteristic
35C2×#13093944C2211yescharacteristic
36C2×#13093944C2211yescharacteristic
37C2×C22⋊(C47⋊C8)C2211yescharacteristic
38C2×(C2×D47)⋊C8C2211yescharacteristic
39C2×C8×Dic47C2211yescharacteristic
40#15689018—21no—
41#15688996—21no—
42#15688994—21no—
43#15688992C2211yescharacteristic
44#15688983C2211yescharacteristic
45#15688980C2211yescharacteristic
46C4⋊C4×Dic47C2211yescharacteristic
47#15688886C2211yescharacteristic
48#15688886C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688885C2211yescharacteristic
51#15688885C2211yescharacteristic
52#15688885C2211yescharacteristic
53#15688885C2211yescharacteristic
54#15688885C2211yescharacteristic
55C23×C8×C47C2211yescharacteristic
56C22×C4⋊C4×C47C2211yescharacteristic
57C22×C4⋊C4×C47C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C2×#10625350—28no—
63C2×#10625350—44no—
64C2×#10625350—44no—
65C22×Dic94—21no—
66C22×D188—21no—
67C22×D188C2311yescharacteristic
68C22×C22⋊D47—21no—
69C22×C22⋊D47D411yescharacteristic
70C22×C4×D47—21no—
71C22×C4×D47—21no—
72C22×C4×D47—21no—
73C22×C4×D47C2311yescharacteristic
74C22×C47⋊C8C2311yescharacteristic
75C22×C47⋊C8C2311yescharacteristic
76C2×C8×D47—22no—
77C2×C8×D47—22no—
78C2×C8×D47—41no—
79#13094023—22no—
80#13094023C2×C414yescomplemented
81#13094009—28no—
82#13094007—28no—
83#13094002—28no—
84#13093999—22no—
85#13093999C2×C414yescomplemented
86#13093998—22no—
87#13093998C2×C414yescomplemented
88#13093986—22no—
89#13093986C2×C414yescomplemented
90C4×C22⋊D47—44no—
91C4×C22⋊D47C2×C414yes—
92C4×C22⋊D47D414yes—
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×D47—22no—
104C4⋊C4×D47—41no—
105C4⋊C4×D47C2×C414yescomplemented
106C2×C22⋊Dic47—21no—
107C2×C22⋊Dic47D411yescharacteristic
108C2×(C2×D47)⋊C4—21no—
109C2×(C2×D47)⋊C4—21no—
110C2×(C2×D47)⋊C4—21no—
111C2×(C2×D47)⋊C4—21no—
112C2×(C2×D47)⋊C4D411yescharacteristic
113C2×C4×Dic47—21no—
114C2×C4×Dic47C2311yescharacteristic
115Dic47⋊C8—22no—
116#13093946—22no—
117#13093946—41no—
118#13093944—22no—
119#13093944—41no—
120C22⋊(C47⋊C8)—22no—
121(C2×D47)⋊C8—22no—
122C8×Dic47—22no—
123C47⋊#95—21no—
124C47⋊#95—21no—
125C47⋊#95—21no—
126C23×C4×C47—21no—
127C23×C4×C47—21no—
128C23×C4×C47C2311yescharacteristic
129C22×C8×C47—22no—
130C22×C8×C47—22no—
131C22×C8×C47—41no—
132C22×C8×C47C2311yescharacteristic
133C22×C8×C47C2311yescharacteristic
134C2×C4⋊C4×C47—22no—
135C2×C4⋊C4×C47—21no—
136C2×C4⋊C4×C47—22no—
137C2×C4⋊C4×C47—21no—
138C2×C4⋊C4×C47—41no—
139C2×C4⋊C4×C47C2×C414yescomplemented
140C2×C4⋊C4×C47C2311yescharacteristic
141C2×C4⋊C4×C47C2311yescharacteristic
142C2×C4⋊C4×C47C2311yescharacteristic
143C2×C4⋊C4×C47C2311yescharacteristic
144C24×C47C2×D411yescharacteristic
145C23×D47—21no—
146C23×D47C2×D411yescharacteristic
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—24no—
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47—42no—
157C22×C4×C47—42no—
158C22×C4×C47—42no—
159C22×C4×C47—42no—
160C22×C4×C47—81no—
161C22×C4×C47C22×C412yes—
162C22×C4×C47C2×D411yescharacteristic
163C22×C4×C47C2×D412yes—
164C22×C4×C47C2411yescharacteristic
165C2×C22⋊D47—24no—
166C2×C22⋊D47—42no—
167C2×C22⋊D47—42no—
168C2×C22⋊D47C22⋊C414yes—
169C2×C22⋊D47D814yes—
170C2×C22⋊D47SD1614yes—
171C22×Dic47—21no—
172C22×Dic47—21no—
173C22×Dic47—21no—
174C22×Dic47C2×D411yescharacteristic
175C22×Dic47C2×D411yescharacteristic
176C22×Dic47C2×D411yescharacteristic
177#10625350—432no—
178C2×D188—21no—
179C2×D188—21no—
180C2×D188—21no—
181C2×D188—21no—
182C2×D188—24no—
183C2×D188—21no—
184C2×D188—42no—
185C2×D188—42no—
186C2×D188C22×C412yes—
187C2×C4×D47—21no—
188C2×C4×D47—21no—
189C2×C4×D47—21no—
190C2×C4×D47—21no—
191C2×C4×D47—24no—
192C2×C4×D47—24no—
193C2×C4×D47—42no—
194C2×C4×D47—42no—
195C2×C4×D47—42no—
196C2×C4×D47—42no—
197C2×C4×D47—42no—
198C2×C4×D47—42no—
199C2×C4×D47—81no—
200C2×C4×D47C22×C412yes—
201C2×C4×D47C2×D412yes—
202C2×Dic94—24no—
203C2×Dic94—42no—
204C2×Dic94—42no—
205C2×C8×C47—21no—
206C2×C8×C47—21no—
207C2×C8×C47—21no—
208C2×C8×C47—21no—
209C2×C8×C47—21no—
210C2×C8×C47—44no—
211C2×C8×C47#4112yescomplemented
212C4⋊C4×C47—24no—
213C4⋊C4×C47—21no—
214C4⋊C4×C47—21no—
215C4⋊C4×C47—21no—
216C4⋊C4×C47—21no—
217C4⋊C4×C47—21no—
218C4⋊C4×C47—42no—
219C4⋊C4×C47C22×C412yes—
220C4⋊C4×C47C22×C412yes—
221C4⋊C4×C47#4112yescomplemented
222C22⋊Dic47—42no—
223C22⋊Dic47C22⋊C414yes—
224(C2×D47)⋊C4—24no—
225(C2×D47)⋊C4—24no—
226(C2×D47)⋊C4—24no—
227(C2×D47)⋊C4—42no—
228(C2×D47)⋊C4C22⋊C414yes—
229C4⋊Dic47—21no—
230C4⋊Dic47—21no—
231C4⋊Dic47—21no—
232C4⋊Dic47—21no—
233C4⋊Dic47—21no—
234C4⋊Dic47C22×C412yes—
235Dic47⋊C4—24no—
236Dic47⋊C4—24no—
237Dic47⋊C4—42no—
238Dic47⋊C4—42no—
239Dic47⋊C4—81no—
240Dic47⋊C4C22⋊C414yes—
241C4×Dic47—42no—
242C4×Dic47C22×C412yes—
243C4×Dic47C2×D412yes—
244C2×C47⋊C8—21no—
245C2×C47⋊C8—21no—
246C2×C47⋊C8—21no—
247C2×C47⋊C8—21no—
248C2×C47⋊C8—21no—
249C2×C47⋊C8—21no—
250C8×D47—44no—
251C23×C47—21no—
252C23×C47—21no—
253C23×C47—21no—
254C23×C47—21no—
255C23×C47C2×C22⋊C412yes—
256C23×C47C2×D812yes—
257C23×C47C2×SD1612yes—
258C23×C47C22×D411yescharacteristic
259C22×D47—21no—
260C22×D47—21no—
261C22×D47—21no—
262C22×D47—21no—
263C22×D47—22no—
264C22×D47—41no—
265C22×D47—41no—
266C22×D47—41no—
267C22×D47—41no—
268C22×D47—41no—
269C22×D47—41no—
270C22×D47C2×C22⋊C412yes—
271C22×D47C2×D812yes—
272C22×D47C2×SD1612yes—
273C2×C4×C47—21no—
274C2×C4×C47—21no—
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—41no—
283C2×C4×C47—41no—
284C2×C4×C47—41no—
285C2×C4×C47—41no—
286C2×C4×C47—41no—
287C2×C4×C47—41no—
288C2×C4×C47—48no—
289C2×C4×C47—41no—
290C2×C4×C47—41no—
291C2×C4×C47—41no—
292C2×C4×C47—84no—
293C2×C4×C47C2×C22⋊C412yes—
294C2×C4×C47C23×C411yescharacteristic
295C2×C4×C47C22×D411yescharacteristic
296C2×C4×C47C2×#4111yescharacteristic
297C2×C4×C47C2×#4111yescharacteristic
298C2×C4×C47H(5,𝔽2)11yescharacteristic
299C2×C4×C472−1+411yescharacteristic
300C22⋊D47—48no—
301C22⋊D47#102116yescomplemented
302C2×Dic47—21no—
303C2×Dic47—21no—
304C2×Dic47—21no—
305C2×Dic47—21no—
306C2×Dic47—22no—
307C2×Dic47—41no—
308C2×Dic47—41no—
309C2×Dic47—41no—
310C2×Dic47—41no—
311C2×Dic47—41no—
312C2×Dic47—41no—
313C2×Dic47—41no—
314C2×Dic47—41no—
315C2×Dic47C2×C22⋊C412yes—
316C2×Dic47C2×C22⋊C412yes—
317C2×Dic47C2×C22⋊C412yes—
318C2×Dic47C2×D812yes—
319C2×Dic47C2×SD1612yes—
320D188—22no—
321D188—22no—
322D188—48no—
323D188—41no—
324D188—41no—
325C4×D47—22no—
326C4×D47—22no—
327C4×D47—22no—
328C4×D47—22no—
329C4×D47—48no—
330C4×D47—48no—
331C4×D47—84no—
332Dic94—48no—
333C8×C47—22no—
334C8×C47—41no—
335C47⋊C8—41no—
336C47⋊C8—41no—
337#22485—471nomaximal, Sylow
338C22×C47—22no—
339C22×C47—22no—
340C22×C47—22no—
341C22×C47—22no—
342C22×C47—22no—
343C22×C47—22no—
344C22×C47C2×#10214yes—
345C22×C47C22×C22⋊C411yescharacteristic
346C22×C47#54611yescharacteristic
347C22×C47#54711yescharacteristic
348C22×C47C22×D811yescharacteristic
349C22×C47C22×SD1611yescharacteristic
350C22×C47#57711yescharacteristic
351C22×C47#57811yescharacteristic
352C2×D47—22no—
353C2×D47—22no—
354C2×D47—22no—
355C2×D47—22no—
356C2×D47—22no—
357C2×D47—22no—
358C2×D47—42no—
359C2×D47—42no—
360C2×D47—42no—
361C2×D47—81no—
362C2×D47—81no—
363C2×D47—81no—
364C2×D47—81no—
365C2×D47C2×#10214yes—
366C4×C47—22no—
367C4×C47—42no—
368C4×C47—42no—
369C4×C47—42no—
370C4×C47—81no—
371C4×C47C4×#4111yescharacteristic
372C4×C47#52011yescharacteristic
373C4×C47#54611yescharacteristic
374C4×C47#54711yescharacteristic
375Dic47—22no—
376Dic47—22no—
377Dic47—42no—
378Dic47—81no—
379Dic47—81no—
380Dic47C2×#10214yes—
381C2×#547—471no—
382C2×C8×D4—471no—
383D4×C4⋊C4—471no—
384#1990—471no—
385#1988—471no—
386#1893—471no—
387#1893—471no—
388#1874—471no—
389#1874—471no—
390#1823—471no—
391#1823—471no—
392#1802—471no—
393C4×#102—471no—
394C2×#340—471no—
395C2×#340D4711yescharacteristic, complemented
396C2×C47—24no—
397C2×C47#233911yescharacteristic
398C2×C47C22×#10211yescharacteristic
399C2×C47#289811yescharacteristic
400C2×C47#329411yescharacteristic
401C2×C47#329811yescharacteristic
402C2×C47#333411yescharacteristic
403C2×C47#333511yescharacteristic
404D47—24no—
405D47—82no—
406C22×#41—941no—
407C23×C8—471no—
408C23×C8C2×D4711yescharacteristic
409#547—478no—
410#547—944no—
411C2×C4⋊Q8—471no—
412C2×#123—941no—
413C2×#123—941no—
414C2×C22⋊Q8—941no—
415C2×#121—471no—
416C2×#121—471no—
417C2×C4×D4—471no—
418C2×C4×D4—471no—
419C2×C4×D4—941no—
420C22×C4⋊C4—471no—
421C22×C4⋊C4—471no—
422C22×C4⋊C4C2×D4711yescharacteristic
423C22×C4⋊C4C2×D4711yescharacteristic
424C8×D4—944no—
425C2×C4⋊C8—471no—
426C2×#102—471no—
427C2×#102—471no—
428C2×#102—471no—
429C2×#102—471no—
430C2×C22⋊C8—471no—
431C2×C22⋊C8—471no—
432C2×C4×C8—471no—
433#389—941no—
434#385—941no—
435#385—941no—
436#384—471no—
437#380—471no—
438#380—471no—
439C4×C4⋊C4—471no—
440#340—471no—
441#340—471no—
442#340—471no—
443#340—471no—
444#340—471no—
445#340—471no—
446#340—471no—
447#340—471no—
448#340C2×D4711yescharacteristic
449#340C2×D4711yescharacteristic
450#340C2×D4711yescharacteristic
451#340C2×D4711yescharacteristic
452C47#2248511yescharacteristic, complemented, Sylow
453C2×#41—948no—
454C2×#41—1884no—
455C2×#41—1884no—
456C22×Q8—941no—
457C22×D4—471no—
458C22×D4—471no—
459C22×D4—941no—
460C22×D4—941no—
461C23×C4—21no—
462C23×C4—21no—
463C23×C4—471no—
464C23×C4—941no—
465C23×C4—941no—
466C23×C4—941no—
467C23×C4C22×D4711yescharacteristic
468C22×C8—22no—
469C22×C8—22no—
470C22×C8—41no—
471C22×C8—471no—
472C22×C8—471no—
473C22×C8—942no—
474C22×C8—942no—
475C22×C8—1881no—
476C22×C8C22×D4711yescharacteristic
477C22×C8C22×D4711yescharacteristic
478C4⋊Q8—474no—
479C4⋊Q8—942no—
480#123—948no—
481#123—948no—
482C22⋊Q8—948no—
483#121—474no—
484#121—474no—
485#121—942no—
486#121—942no—
487C4×D4—474no—
488C4×D4—474no—
489C4×D4—474no—
490C4×D4—942no—
491C4×D4—1884no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—41no—
497C2×C4⋊C4—471no—
498C2×C4⋊C4—471no—
499C2×C4⋊C4—474no—
500C2×C4⋊C4—471no—
501C2×C4⋊C4—471no—
502C2×C4⋊C4—942no—
503C2×C4⋊C4—941no—
504C2×C4⋊C4—941no—
505C2×C4⋊C4—942no—
506C2×C4⋊C4—941no—
507C2×C4⋊C4—941no—
508C2×C4⋊C4—941no—
509C2×C4⋊C4—1881no—
510C2×C4⋊C4C4×D4714yescomplemented
511C2×C4⋊C4C22×D4711yescharacteristic
512C2×C4⋊C4C22×D4711yescharacteristic
513C2×C4⋊C4C22×D4711yescharacteristic
514C2×C4⋊C4C22×D4711yescharacteristic
515C2×C22⋊C4—471no—
516C2×C22⋊C4—471no—
517C2×C22⋊C4—941no—
518C2×C22⋊C4—941no—
519C2×C22⋊C4—941no—
520C2×C22⋊C4—941no—
521C2×C22⋊C4—941no—
522C2×C42—471no—
523C2×C42—941no—
524C4⋊C8—942no—
525#102—942no—
526#102—942no—
527#102—1881no—
528#102—1881no—
529C22⋊C8—942no—
530C22⋊C8—942no—
531C4×C8—942no—
532#95—941no—
533#95—941no—
534#95—941no—
535C24—471no—
536C24—941no—
537C24D4×D4711yescharacteristic
538#41—18832no—
539C2×Q8—944no—
540C2×Q8—1882no—
541C2×Q8—1882no—
542C2×D4—474no—
543C2×D4—474no—
544C2×D4—474no—
545C2×D4—472no—
546C2×D4—944no—
547C2×D4—944no—
548C2×D4—941no—
549C2×D4—941no—
550C2×D4—941no—
551C2×D4—941no—
552C2×D4—941no—
553C2×D4—1882no—
554C2×D4—1882no—
555C2×D4—1882no—
556C2×D4—1882no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—24no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—81no—
571C22×C4—471no—
572C22×C4—471no—
573C22×C4—471no—
574C22×C4—472no—
575C22×C4—472no—
576C22×C4—944no—
577C22×C4—944no—
578C22×C4—941no—
579C22×C4—941no—
580C22×C4—941no—
581C22×C4—941no—
582C22×C4—941no—
583C22×C4—941no—
584C22×C4—941no—
585C22×C4—3761no—
586C22×C4—1882no—
587C22×C4—1882no—
588C22×C4—1882no—
589C22×C4—1882no—
590C22×C4—1882no—
591C22×C4—1882no—
592C22×C4C2×C4×D4712yes—
593C22×C4D4×D4711yescharacteristic
594C22×C4D4×D4712yes—
595C22×C4C23×D4711yescharacteristic
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—44no—
602C2×C8—941no—
603C2×C8—941no—
604C2×C8—941no—
605C2×C8—941no—
606C2×C8—941no—
607C2×C8—941no—
608C2×C8—1884no—
609C2×C8#1062535012yescomplemented
610C4⋊C4—24no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—42no—
617C4⋊C4—474no—
618C4⋊C4—472no—
619C4⋊C4—944no—
620C4⋊C4—944no—
621C4⋊C4—941no—
622C4⋊C4—941no—
623C4⋊C4—941no—
624C4⋊C4—941no—
625C4⋊C4—941no—
626C4⋊C4—3761no—
627C4⋊C4—1882no—
628C4⋊C4—1882no—
629C4⋊C4C2×C4×D4712yes—
630C4⋊C4C2×C4×D4712yes—
631C4⋊C4#1062535012yescomplemented
632C22⋊C4—474no—
633C22⋊C4—474no—
634C22⋊C4—944no—
635C22⋊C4—944no—
636C22⋊C4—944no—
637C22⋊C4—1882no—
638C22⋊C4—1882no—
639C42—472no—
640C42—472no—
641C42—1882no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—472no—
647C23—472no—
648C23—472no—
649C23—941no—
650C23—941no—
651C23—941no—
652C23—941no—
653C23—942no—
654C23—1881no—
655C23—1881no—
656C23—1881no—
657C23—1881no—
658C23—1881no—
659C23—1881no—
660C23C22⋊C4×D4712yes—
661C23D8×D4712yes—
662C23SD16×D4712yes—
663C23C2×D4×D4711yescharacteristic
664Q8—1888no—
665D4—4716no—
666D4—942no—
667D4—942no—
668D4—1888no—
669D4—1888no—
670D4—1881no—
671D4—1881no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—48no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—84no—
692C2×C4—472no—
693C2×C4—472no—
694C2×C4—472no—
695C2×C4—472no—
696C2×C4—472no—
697C2×C4—941no—
698C2×C4—941no—
699C2×C4—941no—
700C2×C4—941no—
701C2×C4—942no—
702C2×C4—942no—
703C2×C4—942no—
704C2×C4—942no—
705C2×C4—942no—
706C2×C4—3764no—
707C2×C4—1888no—
708C2×C4—1888no—
709C2×C4—1881no—
710C2×C4—1881no—
711C2×C4—1881no—
712C2×C4—1881no—
713C2×C4—1881no—
714C2×C4—1881no—
715C2×C4—1881no—
716C2×C4—1881no—
717C2×C4C22⋊C4×D4712yes—
718C2×C4C22×C4×D4711yescharacteristic
719C2×C4C2×D4×D4711yescharacteristic
720C2×C4C2×#1062535011yescharacteristic
721C2×C4C2×#1062535011yescharacteristic
722C2×C4#1309406911yescharacteristic
723C2×C4#1309407211yescharacteristic
724C8—22no—
725C8—41no—
726C8—1881no—
727C8—1881no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—474no—
735C22—942no—
736C22—942no—
737C22—942no—
738C22—942no—
739C22—942no—
740C22—942no—
741C22—3761no—
742C22—3761no—
743C22—3761no—
744C22—3761no—
745C22—1882no—
746C22—1882no—
747C22—1882no—
748C22#102×D4714yes—
749C22C2×C22⋊C4×D4711yescharacteristic
750C22#1568976311yescharacteristic
751C22#1568977411yescharacteristic
752C22C2×D8×D4711yescharacteristic
753C22C2×SD16×D4711yescharacteristic
754C22#1568992911yescharacteristic
755C22#1568993611yescharacteristic
756C4—22no—
757C4—42no—
758C4—42no—
759C4—42no—
760C4—81no—
761C4—474no—
762C4—942no—
763C4—942no—
764C4—3761no—
765C4—3761no—
766C4—1882no—
767C4C4×#1062535011yescharacteristic
768C4#1568960411yescharacteristic
769C4#1568976311yescharacteristic
770C4#1568977411yescharacteristic
771C2—24no—
772C2—944no—
773C2—3762no—
774C2#2024621511yescharacteristic
775C2C2×#102×D4711yescharacteristic
776C2#2025191611yescharacteristic
777C2#2025519711yescharacteristic
778C2#2025524911yescharacteristic
779C2#2025573311yescharacteristic
780C2#2025574111yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#340C2
socleC23×C47C22×D4
prime radicalC2×#15689774C2
cosocleC22×C4×C47C24
hypercenterC2×#340D47
hypocenterC47#22485
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
2. C2×C8×C22⋊D47C2semidirect
3. C4⋊C4×C22⋊D47C2semidirect
4. #20244347C2semidirect
5. #20244338C2semidirect
6. #20243816C2semidirect
7. #20243815C2semidirect
8. #20243705C2semidirect
9. #20243704C2semidirect
10. #20243474C2semidirect
11. #20243473C2semidirect
12. #20243387C2semidirect
13. #20243202C2semidirect
14. #340×D47C2semidirect
15. C2×C47×#340C2semidirect
19. #15689774C4semidirect
80. #13094023C2×C4semidirect
85. #13093999C2×C4semidirect
87. #13093998C2×C4semidirect
89. #13093986C2×C4semidirect
105. C4⋊C4×D47C2×C4semidirect
139. C2×C4⋊C4×C47C2×C4semidirect
211. C2×C8×C47#41semidirect
221. C4⋊C4×C47#41semidirect
301. C22⋊D47#102semidirect
395. C2×#340D47semidirect
452. C47#22485semidirect
510. C2×C4⋊C4C4×D47semidirect
609. C2×C8#10625350semidirect
631. C4⋊C4#10625350semidirect

Maximal subgroups

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

subgroupindex
C2×#156897742
C2×C8×C22⋊D472
C4⋊C4×C22⋊D472
#202443472
#202443382
#202438162
#202438152
#202437052
#202437042
#202434742
#202434732
#202433872
#202432022
#340×D472
C2×C47×#3402
#2248547