Finite Group Databasebeta

← C2×#20254247 #27086938

Subgroups — C2×#20254247 #27086938

Order 12032.

2378 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689704C211yesmaximal, characteristic, complemented
2C2×#15689689C211yesmaximal, characteristic, complemented
3#20254247C2116yesmaximal, direct product factor
4C2×#15689441C211yesmaximal, characteristic, complemented
5C2×#15689466C211yesmaximal, characteristic, complemented
6C2×#15689450C211yesmaximal, characteristic, complemented
7C2×#15689375C211yesmaximal, characteristic, complemented
8C2×#15689370C211yesmaximal, characteristic, complemented
9C2×#15689360C211yesmaximal, characteristic, complemented
10C2×#15689351C211yesmaximal, characteristic, complemented
11C2×#15689270C211yesmaximal, characteristic, complemented
12C2×#15689266C211yesmaximal, characteristic, complemented
13C2×#15689275C211yesmaximal, characteristic, complemented
14C2×#15689258C211yesmaximal, characteristic, complemented
15C2×#15689088C211yesmaximal, characteristic, complemented
16C2×C47×#480C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C22×#10625350C2211yescharacteristic, complemented
19C22×D4×D47C2211yescharacteristic
20C22×#10625325C2211yescharacteristic
21C22×#10625335C2211yescharacteristic
22C22×D376C2211yescharacteristic
23C22×#10625334C2211yescharacteristic
24C22×#10625324C2211yescharacteristic, complemented
25C22×C8×D47C2211yescharacteristic, complemented
26#15689704—24no—
27#15689704C2218yescomplemented
28#15689689—24no—
29#15689689C2218yescomplemented
30C2×#13094020—21no—
31C2×#13094010—21no—
32C2×#13094004—21no—
33C2×#13094004C2211yescharacteristic
34C2×#13094004C2211yescharacteristic, complemented
35C2×#13093999—21no—
36C2×#13093999C2211yescharacteristic
37C2×#13093999C2211yescharacteristic
38C2×#13093999C2211yescharacteristic, complemented
39C2×#13093998—21no—
40C2×#13093998—21no—
41C2×#13093998C2211yescharacteristic
42C2×#13093995C2211yescharacteristic
43C2×#13093994—21no—
44C2×#13093992—21no—
45C2×#13093982C2211yescharacteristic
46#15689466C2218yescomplemented
47#15689450C2218yescomplemented
48#15689441C2218yescomplemented
49#15689375C2218yescomplemented
50#15689370C2218yescomplemented
51#15689360C2218yescomplemented
52#15689351C2218yescomplemented
53#15689275C2218yescomplemented
54#15689270C2218yescomplemented
55#15689266C2218yescomplemented
56#15689258C2218yescomplemented
57C2×#13093955C2211yescharacteristic, complemented
58C2×#13093955C2211yescharacteristic, complemented
59C2×#13093949C2211yescharacteristic, complemented
60C2×#13093947C2211yescharacteristic, complemented
61C2×#13093946C2211yescharacteristic, complemented
62C2×#13093944C2211yescharacteristic
63C2×#13093944C2211yescharacteristic
64C2×#13093944C2211yescharacteristic, complemented
65#15689088C2218yescomplemented
66C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×(C2×D47)⋊C8C2211yescharacteristic
69C2×#121×C47C2211yescharacteristic
70C22×C4⋊C4×C47C2211yescharacteristic, complemented
71C47×#480C2218yescomplemented
72C2×#107×C47C2211yescharacteristic, complemented
73C2×#107×C47C2211yescharacteristic, complemented
74C2×#102×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×C22⋊C8×C47C2211yescharacteristic, complemented
77C24×D47—21no—
78C2×#10625350—22no—
79C2×#10625350—42no—
80C2×#10625350—42no—
81C2×#10625350—42no—
82C2×#10625350—42no—
83C2×#10625350D414yes—
84C2×#10625350C2314yes—
85C2×#10625350C2314yescomplemented
86C22×Dic94D411yescharacteristic
87C22×Dic94C2311yescharacteristic
88C22×D188—21no—
89C22×D188—21no—
90C22×D188—21no—
91C22×D188D411yescharacteristic
92C22×D188C2311yescharacteristic
93C22×D188C2311yescharacteristic
94C22×C22⋊D47—21no—
95C22×C22⋊D47—21no—
96C22×C22⋊D47—21no—
97C22×C22⋊D47—21no—
98C22×C22⋊D47D411yescharacteristic
99C22×C22⋊D47D411yescharacteristic
100C2×D4×D47—22no—
101C2×D4×D47—42no—
102C2×D4×D47—42no—
103C2×D4×D47C2314yes—
104C22×C4×D47—21no—
105C22×C4×D47C2311yescharacteristic
106C22×C4×D47C2311yescharacteristic
107C2×#10625325—42no—
108C2×#10625325C2314yes—
109C2×#10625335—42no—
110C2×#10625335C2314yes—
111C2×D376—42no—
112C2×D376C2314yes—
113C2×#10625334—42no—
114C2×#10625334C2314yes—
115C2×#10625324—42no—
116C2×#10625324C2314yescomplemented
117C22×C47⋊C8C2311yescharacteristic
118C22×C47⋊C8C2311yescharacteristic
119C2×C8×D47—42no—
120C2×C8×D47C2314yescomplemented
121#13094020—28no—
122#13094010—28no—
123#13094004—22no—
124#13094004—22no—
125#13094004—28no—
126#13094004C2314yes—
127#13094004C2314yescomplemented
128#13093999—28no—
129#13093999—22no—
130#13093999—22no—
131#13093999—22no—
132#13093999C2314yes—
133#13093999C2314yes—
134#13093999C2314yescomplemented
135#13093998—22no—
136#13093998—28no—
137#13093998—28no—
138#13093998C2314yes—
139#13093995—22no—
140#13093995C2314yes—
141#13093994—28no—
142#13093992—28no—
143#13093982—22no—
144#13093982C2314yes—
145C2×C4⋊Dic47—21no—
146C2×C4⋊Dic47—21no—
147C2×C4⋊Dic47C2311yescharacteristic
148C2×C22⋊Dic47—21no—
149C2×(C2×D47)⋊C4—21no—
150C2×(C2×D47)⋊C4—21no—
151C2×(C2×D47)⋊C4—21no—
152C2×(C2×D47)⋊C4—21no—
153C2×(C2×D47)⋊C4—21no—
154C2×(C2×D47)⋊C4—21no—
155C2×(C2×D47)⋊C4—21no—
156C2×C4×Dic47—21no—
157#13093955C2314yescomplemented
158#13093955C2314yescomplemented
159#13093949C2314yescomplemented
160#13093947C2314yescomplemented
161#13093946C2314yescomplemented
162#13093944C2314yes—
163#13093944C2314yes—
164#13093944C2314yescomplemented
165C22⋊(C47⋊C8)C2314yescomplemented
166(C2×D47)⋊C8C2314yes—
167(C2×D47)⋊C8C2314yes—
168C22×D4×C47—21no—
169C22×D4×C47C2311yescharacteristic
170C23×C4×C47—21no—
171C23×C4×C47C2311yescharacteristic
172C22×C8×C47C2311yescharacteristic
173C22×C8×C47C2311yescharacteristic
174#121×C47—22no—
175#121×C47C2314yes—
176C2×C4⋊C4×C47—21no—
177C2×C4⋊C4×C47—22no—
178C2×C4⋊C4×C47C2311yescharacteristic
179C2×C4⋊C4×C47C2311yescharacteristic
180C2×C4⋊C4×C47C2311yescharacteristic
181C2×C4⋊C4×C47C2314yescomplemented
182C2×C22⋊C4×C47—21no—
183#107×C47C2314yescomplemented
184#107×C47C2314yescomplemented
185#102×C47C2314yes—
186#102×C47C2314yes—
187C22⋊C8×C47C2314yescomplemented
188C24×C47—21no—
189C24×C47C2×D411yescharacteristic
190C23×D47—21no—
191C23×D47—21no—
192C23×D47—24no—
193C23×D47—44no—
194C23×D47—82no—
195C23×D47—82no—
196C23×D47C2×D411yescharacteristic
197C23×D47C2×D411yescharacteristic
198C2×D4×C47—24no—
199C2×D4×C47—21no—
200C2×D4×C47—22no—
201C2×D4×C47—22no—
202C2×D4×C47—82no—
203C2×D4×C47C2412yes—
204C22×C4×C47—22no—
205C22×C4×C47—22no—
206C22×C4×C47—21no—
207C22×C4×C47—21no—
208C22×C4×C47—21no—
209C22×C4×C47—24no—
210C22×C4×C47—82no—
211C22×C4×C47C2×D411yescharacteristic
212C22×C4×C47C2×D412yes—
213C22×C4×C47C2412yes—
214C22×C4×C47C2411yescharacteristic
215C2×C22⋊D47—24no—
216C2×C22⋊D47—24no—
217C2×C22⋊D47—24no—
218C2×C22⋊D47—24no—
219C2×C22⋊D47—42no—
220C2×C22⋊D47—42no—
221C2×C22⋊D47—44no—
222C2×C22⋊D47—44no—
223C2×C22⋊D47—82no—
224C2×C22⋊D47—82no—
225C2×C22⋊D47C2×D414yes—
226C2×C22⋊D47C2×D414yes—
227C22×Dic47—21no—
228C22×Dic47—21no—
229C22×Dic47C2×D411yescharacteristic
230C22×Dic47C2×D411yescharacteristic
231D4×D47—44no—
232D4×D47—44no—
233D4×D47—48no—
234#10625350—44no—
235#10625350—44no—
236#10625350—48no—
237#10625350—44no—
238#10625350—44no—
239#10625350—48no—
240C2×D188—22no—
241C2×D188—22no—
242C2×D188—22no—
243C2×D188—22no—
244C2×D188—21no—
245C2×D188—21no—
246C2×D188—24no—
247C2×D188—24no—
248C2×D188—24no—
249C2×D188—42no—
250C2×D188—82no—
251C2×D188—82no—
252C2×D188—82no—
253C2×D188C2×D414yes—
254C2×D188C2412yes—
255C2×D188C2412yes—
256C2×C4×D47—22no—
257C2×C4×D47—22no—
258C2×C4×D47—22no—
259C2×C4×D47—22no—
260C2×C4×D47—24no—
261C2×C4×D47—44no—
262C2×C4×D47C2×D412yes—
263C2×C4×D47C2×D412yes—
264C2×C4×D47C2412yes—
265C2×C4×D47C2412yes—
266C2×Dic94—22no—
267C2×Dic94—22no—
268C2×Dic94—21no—
269C2×Dic94—42no—
270C2×Dic94C2×D414yes—
271C2×Dic94C2412yes—
272C2×C8×C47—22no—
273C2×C8×C47—22no—
274C2×C8×C47C2412yes—
275C2×C8×C47C2412yes—
276C4⋊C4×C47—21no—
277C4⋊C4×C47—21no—
278C4⋊C4×C47—24no—
279C4⋊C4×C47—21no—
280C4⋊C4×C47C2412yes—
281C4⋊C4×C47C2412yes—
282C4⋊C4×C47C2412yes—
283C22⋊C4×C47—24no—
284C22⋊Dic47—24no—
285#10625335—44no—
286#10625334—44no—
287(C2×D47)⋊C4—24no—
288(C2×D47)⋊C4—24no—
289(C2×D47)⋊C4—24no—
290(C2×D47)⋊C4—24no—
291(C2×D47)⋊C4—24no—
292(C2×D47)⋊C4—24no—
293(C2×D47)⋊C4—24no—
294C4⋊Dic47—21no—
295C4⋊Dic47—24no—
296C4⋊Dic47—24no—
297C4⋊Dic47C2412yes—
298C4×Dic47—24no—
299C2×C47⋊C8—22no—
300C2×C47⋊C8—22no—
301C2×C47⋊C8C2412yes—
302C2×C47⋊C8C2412yes—
303D376—44no—
304#10625325—44no—
305#10625324—44no—
306C8×D47—44no—
307C23×C47—22no—
308C23×C47—22no—
309C23×C47—22no—
310C23×C47—22no—
311C23×C47—42no—
312C23×C47—42no—
313C23×C47—42no—
314C23×C47C22×D412yes—
315C23×C47C22×D411yescharacteristic
316C22×D47—22no—
317C22×D47—22no—
318C22×D47—22no—
319C22×D47—22no—
320C22×D47—22no—
321C22×D47—22no—
322C22×D47—22no—
323C22×D47—22no—
324C22×D47—48no—
325C22×D47—42no—
326C22×D47—42no—
327C22×D47—42no—
328C22×D47—42no—
329C22×D47—42no—
330C22×D47—42no—
331C22×D47—84no—
332C22×D47—84no—
333C22×D47—816no—
334C22×D47C22×D412yes—
335C22×D47C22×D412yes—
336D4×C47—22no—
337D4×C47—22no—
338D4×C47—42no—
339D4×C47—84no—
340C2×C4×C47—22no—
341C2×C4×C47—24no—
342C2×C4×C47—22no—
343C2×C4×C47—22no—
344C2×C4×C47—22no—
345C2×C4×C47—22no—
346C2×C4×C47—22no—
347C2×C4×C47—42no—
348C2×C4×C47—42no—
349C2×C4×C47—42no—
350C2×C4×C47—84no—
351C2×C4×C47C22×D412yes—
352C2×C4×C47C22×D411yescharacteristic
353C2×C4×C47H(5,𝔽2)12yes—
354C2×C4×C47H(5,𝔽2)12yes—
355C2×C4×C47C2511yescharacteristic
356C22⋊D47—44no—
357C22⋊D47—44no—
358C22⋊D47—48no—
359C22⋊D47—48no—
360C22⋊D47—84no—
361C22⋊D47—84no—
362C2×Dic47—22no—
363C2×Dic47—22no—
364C2×Dic47—22no—
365C2×Dic47—22no—
366C2×Dic47—42no—
367C2×Dic47—42no—
368C2×Dic47C22×D412yes—
369C2×Dic47C22×D412yes—
370D188—22no—
371D188—22no—
372D188—22no—
373D188—22no—
374D188—44no—
375D188—42no—
376D188—42no—
377D188—84no—
378D188—84no—
379D188—84no—
380C4×D47—24no—
381C4×D47—24no—
382C4×D47—22no—
383C4×D47—22no—
384C4×D47—22no—
385C4×D47—22no—
386C4×D47—48no—
387Dic94—22no—
388Dic94—22no—
389Dic94—44no—
390Dic94—42no—
391C8×C47—22no—
392C8×C47—22no—
393C47⋊C8—22no—
394C47⋊C8—22no—
395C2×#3198—471nomaximal, Sylow
396C22×C47—22no—
397C22×C47—22no—
398C22×C47—22no—
399C22×C47—44no—
400C22×C47—42no—
401C22×C47—42no—
402C22×C47—42no—
403C22×C47—84no—
404C22×C47#53412yes—
405C22×C47#57612yes—
406C22×C47#57712yes—
407C22×C47C23×D411yescharacteristic
408C2×D47—22no—
409C2×D47—22no—
410C2×D47—22no—
411C2×D47—22no—
412C2×D47—22no—
413C2×D47—22no—
414C2×D47—44no—
415C2×D47—44no—
416C2×D47—42no—
417C2×D47—42no—
418C2×D47—42no—
419C2×D47—42no—
420C2×D47—42no—
421C2×D47—42no—
422C2×D47—816no—
423C2×D47—84no—
424C2×D47—84no—
425C4×C47—22no—
426C4×C47—42no—
427C4×C47—42no—
428C4×C47—42no—
429C4×C47#53412yes—
430C4×C47C2×H(5,𝔽2)11yescharacteristic
431C4×C47C2×H(5,𝔽2)11yescharacteristic
432Dic47—22no—
433Dic47—22no—
434Dic47—42no—
435Dic47—42no—
436C2×#537—471no—
437C2×#535—471no—
438#3198—4716no—
439C2×#481—471no—
440C2×#485—471no—
441C2×#482—471no—
442C2×#480D4711yescharacteristic, complemented
443C2×#469—471no—
444C2×#468—471no—
445C2×#466—471no—
446C2×#465—471no—
447C2×#449—471no—
448C2×#449—471no—
449C2×#450—471no—
450C2×#447—471no—
451C2×#408—471no—
452C2×C47—42no—
453C2×C47—82no—
454C2×C47#319814yescomplemented
455C2×C47C2×#53411yescharacteristic
456C2×C47C2×#57611yescharacteristic
457C2×C47C2×#57711yescharacteristic
458D47—42no—
459D47—42no—
460D47—82no—
461D47—82no—
462C22×#41—471no—
463C22×#41—471no—
464C23×D4—471no—
465C22×SD16—471no—
466C22×SD16—471no—
467C22×D8—471no—
468C22×D8—471no—
469C22×M16—471no—
470C23×C8—471no—
471#537—478no—
472#537—944no—
473#535—478no—
474#535—944no—
475C2×#127—941no—
476C2×#124—941no—
477C2×C22⋊Q8—471no—
478C2×C22⋊Q8—471no—
479C2×C22⋊Q8—941no—
480C2×#121—471no—
481C2×#121—471no—
482C2×#121—471no—
483C2×#121—471no—
484C2×#121—471no—
485C2×#121—941no—
486C2×#121—941no—
487C2×#121—941no—
488C2×#121C2×D4711yescharacteristic
489C2×#120—941no—
490C2×#120—941no—
491C2×#117—471no—
492C22×C4⋊C4C2×D4711yescharacteristic, complemented
493#485—478no—
494#482—478no—
495#481—478no—
496#480C2×D4718yescomplemented
497#469—478no—
498#468—478no—
499#466—478no—
500#465—478no—
501#450—478no—
502#449—478no—
503#449—478no—
504#447—478no—
505C2×#107C2×D4711yescharacteristic, complemented
506C2×#107C2×D4711yescharacteristic, complemented
507C2×#106—471no—
508C2×#106—471no—
509C2×#103—471no—
510C2×#103—471no—
511C2×#102—471no—
512C2×#102—471no—
513C2×#102—471no—
514C2×#102—471no—
515C2×#102C2×D4711yescharacteristic
516C2×#102C2×D4711yescharacteristic
517#408—478no—
518C2×C22⋊C8—471no—
519C2×C22⋊C8—471no—
520C2×C22⋊C8—471no—
521C2×C22⋊C8C2×D4711yescharacteristic, complemented
522C47C2×#319811yescharacteristic, complemented, Sylow
523C25—941no—
524C2×#41—474no—
525C2×#41—474no—
526C2×#41—474no—
527C2×#41—942no—
528C2×#41—1882no—
529C2×#41—1882no—
530C2×#41—1882no—
531C2×#41—1882no—
532C22×Q8—471no—
533C22×Q8—471no—
534C22×D4—21no—
535C22×D4—471no—
536C22×D4—471no—
537C22×D4—474no—
538C22×D4—471no—
539C22×D4—471no—
540C22×D4—471no—
541C22×D4—941no—
542C22×D4—941no—
543C22×D4—941no—
544C22×D4—942no—
545C22×D4—941no—
546C22×D4—941no—
547C22×D4—941no—
548C22×D4—941no—
549C22×D4—1882no—
550C22×D4—1882no—
551C22×D4C22×D4711yescharacteristic
552C23×C4—21no—
553C23×C4—471no—
554C23×C4—471no—
555C23×C4—941no—
556C23×C4C22×D4711yescharacteristic
557C2×SD16—474no—
558C2×SD16—474no—
559C2×SD16—1882no—
560C2×SD16—1882no—
561C2×D8—474no—
562C2×D8—474no—
563C2×D8—1882no—
564C2×D8—1882no—
565C2×M16—474no—
566C2×M16—1882no—
567C22×C8—471no—
568C22×C8—471no—
569C22×C8—474no—
570C22×C8—1882no—
571C22×C8C22×D4711yescharacteristic
572C22×C8C22×D4711yescharacteristic
573#127—948no—
574#124—948no—
575C22⋊Q8—474no—
576C22⋊Q8—474no—
577C22⋊Q8—942no—
578C22⋊Q8—942no—
579C22⋊Q8—948no—
580#121—22no—
581#121—474no—
582#121—474no—
583#121—474no—
584#121—474no—
585#121—474no—
586#121—942no—
587#121—942no—
588#121—942no—
589#121—948no—
590#121—948no—
591#121—948no—
592#121—942no—
593#121—942no—
594#121C22×D4714yes—
595#120—948no—
596#120—948no—
597#117—474no—
598#117—942no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—471no—
602C2×C4⋊C4—941no—
603C2×C4⋊C4—941no—
604C2×C4⋊C4C22×D4711yescharacteristic
605C2×C4⋊C4C22×D4711yescharacteristic
606C2×C4⋊C4C22×D4711yescharacteristic
607C2×C4⋊C4C22×D4714yescomplemented
608C2×C22⋊C4—21no—
609C2×C22⋊C4—941no—
610C2×C22⋊C4—941no—
611C2×C22⋊C4—941no—
612C2×C22⋊C4—941no—
613C2×C22⋊C4—941no—
614C2×C22⋊C4—941no—
615C2×C22⋊C4—941no—
616C2×C22⋊C4—941no—
617C2×C42—941no—
618#107C22×D4714yescomplemented
619#107C22×D4714yescomplemented
620#106—474no—
621#106—474no—
622#103—474no—
623#103—474no—
624#102—474no—
625#102—474no—
626#102—474no—
627#102—474no—
628#102C22×D4714yes—
629#102C22×D4714yes—
630C22⋊C8—474no—
631C22⋊C8—474no—
632C22⋊C8—474no—
633C22⋊C8C22×D4714yescomplemented
634C24—21no—
635C24—471no—
636C24—471no—
637C24—944no—
638C24—941no—
639C24—941no—
640C24—3762no—
641C24—3762no—
642C24—1884no—
643C24D4×D4711yescharacteristic
644#41—1888no—
645#41—1884no—
646#41—1884no—
647#41—1884no—
648#41—1884no—
649#41—1888no—
650C2×Q8—474no—
651C2×Q8—472no—
652C2×Q8—941no—
653C2×Q8—942no—
654C2×Q8—942no—
655C2×Q8—1882no—
656C2×D4—24no—
657C2×D4—21no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—82no—
661C2×D4—474no—
662C2×D4—474no—
663C2×D4—474no—
664C2×D4—472no—
665C2×D4—472no—
666C2×D4—944no—
667C2×D4—944no—
668C2×D4—944no—
669C2×D4—944no—
670C2×D4—944no—
671C2×D4—944no—
672C2×D4—944no—
673C2×D4—941no—
674C2×D4—941no—
675C2×D4—942no—
676C2×D4—942no—
677C2×D4—942no—
678C2×D4—942no—
679C2×D4—3762no—
680C2×D4—3762no—
681C2×D4—3762no—
682C2×D4—3762no—
683C2×D4—3762no—
684C2×D4—1882no—
685C2×D4—1884no—
686C2×D4—1884no—
687C2×D4—1888no—
688C2×D4—1882no—
689C2×D4—1882no—
690C2×D4—1884no—
691C2×D4—1884no—
692C2×D4C23×D4712yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—24no—
699C22×C4—82no—
700C22×C4—471no—
701C22×C4—471no—
702C22×C4—472no—
703C22×C4—472no—
704C22×C4—472no—
705C22×C4—472no—
706C22×C4—942no—
707C22×C4—942no—
708C22×C4—942no—
709C22×C4—942no—
710C22×C4—941no—
711C22×C4—941no—
712C22×C4—944no—
713C22×C4—1884no—
714C22×C4D4×D4712yes—
715C22×C4D4×D4711yescharacteristic
716C22×C4C23×D4712yes—
717C22×C4C23×D4711yescharacteristic
718SD16—1884no—
719SD16—1884no—
720D8—1884no—
721D8—1884no—
722M16—1884no—
723C2×C8—22no—
724C2×C8—22no—
725C2×C8—472no—
726C2×C8—472no—
727C2×C8—942no—
728C2×C8—942no—
729C2×C8—1884no—
730C2×C8C23×D4712yes—
731C2×C8C23×D4712yes—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—24no—
735C4⋊C4—21no—
736C4⋊C4—472no—
737C4⋊C4—944no—
738C4⋊C4—944no—
739C4⋊C4—941no—
740C4⋊C4C23×D4712yes—
741C4⋊C4C23×D4712yes—
742C4⋊C4C23×D4712yes—
743C22⋊C4—24no—
744C22⋊C4—944no—
745C22⋊C4—944no—
746C22⋊C4—944no—
747C22⋊C4—944no—
748C22⋊C4—944no—
749C22⋊C4—944no—
750C22⋊C4—944no—
751C22⋊C4—944no—
752C42—944no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—472no—
761C23—472no—
762C23—942no—
763C23—942no—
764C23—942no—
765C23—942no—
766C23—942no—
767C23—942no—
768C23—942no—
769C23—942no—
770C23—3764no—
771C23—3764no—
772C23—37616no—
773C23—1888no—
774C23—1882no—
775C23—1882no—
776C23—1882no—
777C23—1882no—
778C23—1882no—
779C23—1882no—
780C23C2×D4×D4712yes—
781C23C2×D4×D4711yescharacteristic
782Q8—942no—
783Q8—942no—
784Q8—1884no—
785Q8—1882no—
786D4—22no—
787D4—22no—
788D4—42no—
789D4—84no—
790D4—942no—
791D4—942no—
792D4—942no—
793D4—942no—
794D4—3764no—
795D4—3764no—
796D4—3764no—
797D4—3764no—
798D4—3764no—
799D4—1884no—
800D4—1884no—
801D4—1884no—
802D4—1888no—
803D4—1888no—
804D4—1882no—
805D4—1882no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—84no—
817C2×C4—472no—
818C2×C4—472no—
819C2×C4—942no—
820C2×C4—942no—
821C2×C4—944no—
822C2×C4—944no—
823C2×C4—942no—
824C2×C4—942no—
825C2×C4—942no—
826C2×C4—942no—
827C2×C4—942no—
828C2×C4—942no—
829C2×C4—1888no—
830C2×C4—1882no—
831C2×C4—1882no—
832C2×C4C2×D4×D4712yes—
833C2×C4C2×D4×D4711yescharacteristic
834C2×C4#1309407012yes—
835C2×C4#1309407012yes—
836C2×C4C24×D4711yescharacteristic
837C8—22no—
838C8—22no—
839C8—942no—
840C8—942no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—44no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—84no—
849C22—942no—
850C22—942no—
851C22—942no—
852C22—942no—
853C22—942no—
854C22—942no—
855C22—37616no—
856C22—3764no—
857C22—3764no—
858C22—1882no—
859C22—1882no—
860C22—1882no—
861C22—1882no—
862C22—1882no—
863C22—1882no—
864C22—1884no—
865C22—1884no—
866C22#1568968412yes—
867C22#1568992412yes—
868C22#1568993212yes—
869C22C22×D4×D4711yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—942no—
875C4—942no—
876C4—1882no—
877C4—1882no—
878C4#1568968412yes—
879C4C2×#1309407011yescharacteristic
880C4C2×#1309407011yescharacteristic
881C2—42no—
882C2—82no—
883C2—3762no—
884C2—3762no—
885C2—1882no—
886C2—1882no—
887C2#2025424714yesdirect product factor
888C2C2×#1568968411yescharacteristic
889C2C2×#1568992411yescharacteristic
890C2C2×#1568993211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#480C2
socleC23×C47C22×D4
hypercenterC2×#480D47
hypocenterC47C2×#3198
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
1. C2×#15689704C2semidirect
2. C2×#15689689C2semidirect
3. #20254247C2direct (N × H)
4. C2×#15689441C2semidirect
5. C2×#15689466C2semidirect
6. C2×#15689450C2semidirect
7. C2×#15689375C2semidirect
8. C2×#15689370C2semidirect
9. C2×#15689360C2semidirect
10. C2×#15689351C2semidirect
11. C2×#15689270C2semidirect
12. C2×#15689266C2semidirect
13. C2×#15689275C2semidirect
14. C2×#15689258C2semidirect
15. C2×#15689088C2semidirect
16. C2×C47×#480C2semidirect
18. C22×#10625350C22semidirect
24. C22×#10625324C22semidirect
25. C22×C8×D47C22semidirect
27. #15689704C22semidirect
29. #15689689C22semidirect
34. C2×#13094004C22semidirect
38. C2×#13093999C22semidirect
46. #15689466C22semidirect
47. #15689450C22semidirect
48. #15689441C22semidirect
49. #15689375C22semidirect
50. #15689370C22semidirect
51. #15689360C22semidirect
52. #15689351C22semidirect
53. #15689275C22semidirect
54. #15689270C22semidirect
55. #15689266C22semidirect
56. #15689258C22semidirect
57. C2×#13093955C22semidirect
58. C2×#13093955C22semidirect
59. C2×#13093949C22semidirect
60. C2×#13093947C22semidirect
61. C2×#13093946C22semidirect
64. C2×#13093944C22semidirect
65. #15689088C22semidirect
66. C2×C22⋊(C47⋊C8)C22semidirect
70. C22×C4⋊C4×C47C22semidirect
71. C47×#480C22semidirect
72. C2×#107×C47C22semidirect
73. C2×#107×C47C22semidirect
76. C2×C22⋊C8×C47C22semidirect
85. C2×#10625350C23semidirect
116. C2×#10625324C23semidirect
120. C2×C8×D47C23semidirect
127. #13094004C23semidirect
134. #13093999C23semidirect
157. #13093955C23semidirect
158. #13093955C23semidirect
159. #13093949C23semidirect
160. #13093947C23semidirect
161. #13093946C23semidirect
164. #13093944C23semidirect
165. C22⋊(C47⋊C8)C23semidirect
181. C2×C4⋊C4×C47C23semidirect
183. #107×C47C23semidirect
184. #107×C47C23semidirect
187. C22⋊C8×C47C23semidirect
442. C2×#480D47semidirect
454. C2×C47#3198semidirect
492. C22×C4⋊C4C2×D47semidirect
496. #480C2×D47semidirect
505. C2×#107C2×D47semidirect
506. C2×#107C2×D47semidirect
521. C2×C22⋊C8C2×D47semidirect
522. C47C2×#3198semidirect
607. C2×C4⋊C4C22×D47semidirect
618. #107C22×D47semidirect
619. #107C22×D47semidirect
633. C22⋊C8C22×D47semidirect
887. C2#20254247direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897042
C2×#156896892
#202542472
C2×#156894412
C2×#156894662
C2×#156894502
C2×#156893752
C2×#156893702
C2×#156893602
C2×#156893512
C2×#156892702
C2×#156892662
C2×#156892752
C2×#156892582
C2×#156890882
C2×C47×#4802
C2×#319847