Finite Group Databasebeta

← C2×#20254244 #27086935

Subgroups — C2×#20254244 #27086935

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×#15689703C211yesmaximal, characteristic, complemented
2C2×#15689690C211yesmaximal, characteristic, complemented
3#20254244C2116yesmaximal, direct product factor
4C2×#15689440C211yesmaximal, characteristic, complemented
5C2×#15689461C211yesmaximal, characteristic, complemented
6C2×#15689448C211yesmaximal, characteristic, complemented
7C2×#15689435C211yesmaximal, characteristic, complemented
8C2×#15689375C211yesmaximal, characteristic, complemented
9C2×#15689366C211yesmaximal, characteristic, complemented
10C2×#15689358C211yesmaximal, characteristic, complemented
11C2×#15689349C211yesmaximal, characteristic, complemented
12C2×#15689267C211yesmaximal, characteristic, complemented
13C2×#15689267C211yesmaximal, characteristic, complemented
14C2×#15689257C211yesmaximal, characteristic, complemented
15C2×#15689088C211yesmaximal, characteristic, complemented
16C2×C47×#450C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic, complemented
18C22×#10625350C2211yescharacteristic
19C22×#10625334C2211yescharacteristic
20C22×#10625334C2211yescharacteristic
21C22×#10625324C2211yescharacteristic, complemented
22C22×C8×D47C2211yescharacteristic, complemented
23#15689703—24no—
24#15689703C2218yescomplemented
25#15689690—24no—
26#15689690C2218yescomplemented
27C2×#13094020—21no—
28C2×#13094011—21no—
29C2×#13094002—21no—
30C2×#13094000C2211yescharacteristic, complemented
31C2×#13093999—21no—
32C2×#13093999C2211yescharacteristic, complemented
33C2×#13093998C2211yescharacteristic
34C2×#13093997—21no—
35C2×#13093997—21no—
36C2×#13093995C2211yescharacteristic
37C2×#13093995C2211yescharacteristic
38C2×#13093995C2211yescharacteristic
39C2×#13093995C2211yescharacteristic
40C2×#13093993—21no—
41C2×#13093993—21no—
42C2×#13093983C2211yescharacteristic
43C2×C4⋊C4×D47C2211yescharacteristic, complemented
44#15689461C2218yescomplemented
45#15689448C2218yescomplemented
46#15689440C2218yescomplemented
47#15689435C2218yescomplemented
48#15689375C2218yescomplemented
49#15689366C2218yescomplemented
50#15689358C2218yescomplemented
51#15689349C2218yescomplemented
52#15689267C2218yescomplemented
53#15689267C2218yescomplemented
54#15689257C2218yescomplemented
55C2×#13093958C2211yescharacteristic, complemented
56C2×#13093957C2211yescharacteristic, complemented
57C2×#13093956C2211yescharacteristic, complemented
58C2×#13093955C2211yescharacteristic, complemented
59C2×#13093948C2211yescharacteristic, complemented
60C2×#13093948C2211yescharacteristic, complemented
61C2×#13093946C2211yescharacteristic, complemented
62C2×#13093946C2211yescharacteristic, complemented
63C2×#13093945C2211yescharacteristic
64C2×#13093945C2211yescharacteristic
65#15689088C2218yescomplemented
66C2×C22⋊(C47⋊C8)C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
68C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
69C23×D4×C47C2211yescharacteristic
70C22×SD16×C47C2211yescharacteristic
71C22×SD16×C47C2211yescharacteristic
72C2×C22⋊Q8×C47C2211yescharacteristic
73C47×#450C2218yescomplemented
74C2×#102×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×C22⋊C8×C47C2211yescharacteristic
77C2×#10625354—22no—
78C2×#10625354—42no—
79C2×#10625354—42no—
80C2×#10625354C2314yescomplemented
81C2×#10625350—42no—
82C2×#10625350—42no—
83C2×#10625350D414yes—
84C2×#10625350C2314yes—
85C22×Dic94D411yescharacteristic
86C22×D188—21no—
87C22×D188—21no—
88C22×D188D411yescharacteristic
89C22×D188C2311yescharacteristic
90C22×C22⋊D47—21no—
91C22×C22⋊D47—21no—
92C22×C22⋊D47—21no—
93C22×C22⋊D47—21no—
94C22×C22⋊D47—21no—
95C22×C22⋊D47D411yescharacteristic
96C22×C22⋊D47D411yescharacteristic
97C22×C4×D47—21no—
98C22×C4×D47—21no—
99C22×C4×D47C2311yescharacteristic
100C22×C4×D47C2311yescharacteristic
101C2×#10625334—42no—
102C2×#10625334—42no—
103C2×#10625334C2314yes—
104C2×#10625334C2314yes—
105C2×#10625324—42no—
106C2×#10625324C2314yescomplemented
107C22×C47⋊C8C2311yescharacteristic
108C22×C47⋊C8C2311yescharacteristic
109C2×C8×D47—42no—
110C2×C8×D47C2314yescomplemented
111#13094020—28no—
112#13094011—28no—
113#13094002—28no—
114#13094000—22no—
115#13094000C2314yescomplemented
116#13093999—28no—
117#13093999—22no—
118#13093999C2314yescomplemented
119#13093998—22no—
120#13093998C2314yes—
121#13093997—28no—
122#13093997—28no—
123#13093995—22no—
124#13093995—22no—
125#13093995—22no—
126#13093995—22no—
127#13093995C2314yes—
128#13093995C2314yes—
129#13093995C2314yes—
130#13093995C2314yes—
131#13093993—28no—
132#13093993—28no—
133#13093983—22no—
134#13093983C2314yes—
135C2×C4⋊Dic47C2311yescharacteristic
136C2×C4⋊Dic47C2311yescharacteristic
137C2×C4⋊Dic47C2311yescharacteristic
138C2×Dic47⋊C4—21no—
139C2×Dic47⋊C4—21no—
140C4⋊C4×D47—22no—
141C4⋊C4×D47C2314yescomplemented
142C2×C22⋊Dic47—21no—
143C2×C22⋊Dic47—21no—
144C2×C22⋊Dic47—21no—
145C2×C22⋊Dic47—21no—
146C2×C22⋊Dic47—21no—
147C2×(C2×D47)⋊C4—21no—
148C2×(C2×D47)⋊C4—21no—
149C2×(C2×D47)⋊C4—21no—
150C2×C4×Dic47—21no—
151#13093958C2314yescomplemented
152#13093957C2314yescomplemented
153#13093956C2314yescomplemented
154#13093955C2314yescomplemented
155#13093948C2314yescomplemented
156#13093948C2314yescomplemented
157#13093946C2314yescomplemented
158#13093946C2314yescomplemented
159#13093945C2314yes—
160#13093945C2314yes—
161C22⋊(C47⋊C8)C2314yes—
162(C2×D47)⋊C8C2314yescomplemented
163(C2×D47)⋊C8C2314yescomplemented
164C25×C47—21no—
165C22×Q8×C47C2311yescharacteristic
166C22×D4×C47—21no—
167C22×D4×C47—22no—
168C22×D4×C47—42no—
169C22×D4×C47—42no—
170C22×D4×C47C2311yescharacteristic
171C22×D4×C47C2311yescharacteristic
172C22×D4×C47C2314yes—
173C23×C4×C47C2311yescharacteristic
174C2×SD16×C47—42no—
175C2×SD16×C47—42no—
176C2×SD16×C47C2314yes—
177C2×SD16×C47C2314yes—
178C22×C8×C47C2311yescharacteristic
179C22×C8×C47C2311yescharacteristic
180C22⋊Q8×C47—22no—
181C22⋊Q8×C47C2314yes—
182C2×C4⋊C4×C47—21no—
183C2×C4⋊C4×C47C2311yescharacteristic
184C2×C22⋊C4×C47—21no—
185#102×C47C2314yes—
186#102×C47C2314yes—
187C22⋊C8×C47C2314yes—
188C24×C47—21no—
189C24×C47—21no—
190C24×C47—24no—
191C24×C47—44no—
192C24×C47—82no—
193C24×C47—82no—
194C24×C47C2×D411yescharacteristic
195C23×D47—21no—
196C23×D47C2×D411yescharacteristic
197C23×D47C2×D411yescharacteristic
198C2×Q8×C47—21no—
199C2×Q8×C47—22no—
200C2×Q8×C47—22no—
201C2×Q8×C47C2412yes—
202C2×D4×C47—21no—
203C2×D4×C47—21no—
204C2×D4×C47—24no—
205C2×D4×C47—22no—
206C2×D4×C47—22no—
207C2×D4×C47—22no—
208C2×D4×C47—22no—
209C2×D4×C47—44no—
210C2×D4×C47—44no—
211C2×D4×C47—44no—
212C2×D4×C47—48no—
213C2×D4×C47C2412yes—
214C2×D4×C47C2412yes—
215C22×C4×C47—22no—
216C22×C4×C47—22no—
217C22×C4×C47—21no—
218C22×C4×C47—21no—
219C22×C4×C47C2×D411yescharacteristic
220C22×C4×C47C2×D412yes—
221C22×C4×C47C2412yes—
222C22×C4×C47C2411yescharacteristic
223C2×C22⋊D47—24no—
224C2×C22⋊D47—24no—
225C2×C22⋊D47—24no—
226C2×C22⋊D47—24no—
227C2×C22⋊D47—24no—
228C2×C22⋊D47—42no—
229C2×C22⋊D47—42no—
230C2×C22⋊D47—82no—
231C2×C22⋊D47—82no—
232C2×C22⋊D47—82no—
233C2×C22⋊D47—82no—
234C2×C22⋊D47—82no—
235C2×C22⋊D47C2×D414yes—
236C2×C22⋊D47C2×D414yes—
237C22×Dic47—21no—
238C22×Dic47—21no—
239C22×Dic47—21no—
240C22×Dic47C2×D411yescharacteristic
241C22×Dic47C2×D411yescharacteristic
242#10625354—44no—
243#10625354—44no—
244#10625354—48no—
245#10625350—48no—
246#10625350—44no—
247#10625350—44no—
248C2×D188—22no—
249C2×D188—22no—
250C2×D188—24no—
251C2×D188—21no—
252C2×D188—24no—
253C2×D188—42no—
254C2×D188—44no—
255C2×D188—82no—
256C2×D188C2×D414yes—
257C2×D188C2412yes—
258C2×C4×D47—22no—
259C2×C4×D47—22no—
260C2×C4×D47—22no—
261C2×C4×D47—22no—
262C2×C4×D47—24no—
263C2×C4×D47—24no—
264C2×C4×D47—44no—
265C2×C4×D47—82no—
266C2×C4×D47C2×D412yes—
267C2×C4×D47C2×D412yes—
268C2×C4×D47C2412yes—
269C2×C4×D47C2412yes—
270C2×Dic94—42no—
271C2×Dic94C2×D414yes—
272SD16×C47—44no—
273SD16×C47—44no—
274C2×C8×C47—22no—
275C2×C8×C47—22no—
276C2×C8×C47C2412yes—
277C2×C8×C47C2412yes—
278C4⋊C4×C47—24no—
279C4⋊C4×C47—21no—
280C4⋊C4×C47C2412yes—
281C22⋊C4×C47—24no—
282C22⋊Dic47—24no—
283C22⋊Dic47—24no—
284C22⋊Dic47—24no—
285C22⋊Dic47—24no—
286C22⋊Dic47—24no—
287#10625334—44no—
288#10625334—44no—
289(C2×D47)⋊C4—24no—
290(C2×D47)⋊C4—24no—
291(C2×D47)⋊C4—24no—
292C4⋊Dic47—21no—
293C4⋊Dic47—21no—
294C4⋊Dic47—21no—
295C4⋊Dic47C2412yes—
296C4⋊Dic47C2412yes—
297C4⋊Dic47C2412yes—
298Dic47⋊C4—24no—
299Dic47⋊C4—24no—
300C4×Dic47—24no—
301C2×C47⋊C8—22no—
302C2×C47⋊C8—22no—
303C2×C47⋊C8C2412yes—
304C2×C47⋊C8C2412yes—
305#10625324—44no—
306C8×D47—44no—
307C23×C47—22no—
308C23×C47—22no—
309C23×C47—22no—
310C23×C47—22no—
311C23×C47—22no—
312C23×C47—48no—
313C23×C47—42no—
314C23×C47—42no—
315C23×C47—42no—
316C23×C47—42no—
317C23×C47—42no—
318C23×C47—42no—
319C23×C47—84no—
320C23×C47—84no—
321C23×C47—816no—
322C23×C47C22×D412yes—
323C23×C47C22×D411yescharacteristic
324C22×D47—22no—
325C22×D47—22no—
326C22×D47—22no—
327C22×D47—22no—
328C22×D47—22no—
329C22×D47—22no—
330C22×D47—22no—
331C22×D47—42no—
332C22×D47—42no—
333C22×D47—42no—
334C22×D47C22×D412yes—
335C22×D47C22×D412yes—
336Q8×C47—22no—
337Q8×C47—22no—
338Q8×C47—42no—
339D4×C47—22no—
340D4×C47—22no—
341D4×C47—22no—
342D4×C47—22no—
343D4×C47—48no—
344D4×C47—42no—
345D4×C47—42no—
346C2×C4×C47—22no—
347C2×C4×C47—24no—
348C2×C4×C47—22no—
349C2×C4×C47—22no—
350C2×C4×C47—22no—
351C2×C4×C47—22no—
352C2×C4×C47—42no—
353C2×C4×C47—42no—
354C2×C4×C47C22×D412yes—
355C2×C4×C47C22×D411yescharacteristic
356C2×C4×C47H(5,𝔽2)12yes—
357C2×C4×C47H(5,𝔽2)12yes—
358C2×C4×C47C2511yescharacteristic
359C22⋊D47—44no—
360C22⋊D47—44no—
361C22⋊D47—84no—
362C22⋊D47—84no—
363C22⋊D47—84no—
364C22⋊D47—84no—
365C22⋊D47—84no—
366C2×Dic47—22no—
367C2×Dic47—22no—
368C2×Dic47—22no—
369C2×Dic47—22no—
370C2×Dic47—22no—
371C2×Dic47—42no—
372C2×Dic47—42no—
373C2×Dic47—42no—
374C2×Dic47C22×D412yes—
375C2×Dic47C22×D412yes—
376D188—22no—
377D188—22no—
378D188—44no—
379D188—48no—
380D188—42no—
381D188—84no—
382C4×D47—24no—
383C4×D47—24no—
384C4×D47—22no—
385C4×D47—22no—
386C4×D47—22no—
387C4×D47—22no—
388C4×D47—48no—
389C4×D47—84no—
390Dic94—44no—
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—42no—
404C22×C47—42no—
405C22×C47—42no—
406C22×C47—816no—
407C22×C47—84no—
408C22×C47—84no—
409C22×C47#53412yes—
410C22×C47#57612yes—
411C22×C47#57712yes—
412C22×C47C23×D411yescharacteristic
413C2×D47—22no—
414C2×D47—22no—
415C2×D47—22no—
416C2×D47—22no—
417C2×D47—22no—
418C2×D47—22no—
419C2×D47—44no—
420C2×D47—44no—
421C2×D47—42no—
422C2×D47—42no—
423C2×D47—42no—
424C2×D47—84no—
425C4×C47—22no—
426C4×C47—42no—
427C4×C47—42no—
428C4×C47#53412yes—
429C4×C47C2×H(5,𝔽2)11yescharacteristic
430C4×C47C2×H(5,𝔽2)11yescharacteristic
431Dic47—22no—
432Dic47—22no—
433Dic47—42no—
434Dic47—42no—
435Dic47—42no—
436C2×#537—471no—
437C2×#535—471no—
438#3198—4716no—
439C2×#481—471no—
440C2×#485—471no—
441C2×#482—471no—
442C2×#480—471no—
443C2×#469—471no—
444C2×#468—471no—
445C2×#466—471no—
446C2×#465—471no—
447C2×#449—471no—
448C2×#449—471no—
449C2×#450D4711yescharacteristic, complemented
450C2×#447—471no—
451C2×#408—471no—
452C2×C47—42no—
453C2×C47—82no—
454C2×C47—82no—
455C2×C47#319814yescomplemented
456C2×C47C2×#53411yescharacteristic
457C2×C47C2×#57611yescharacteristic
458C2×C47C2×#57711yescharacteristic
459D47—42no—
460D47—42no—
461D47—82no—
462C22×#41—471no—
463C22×#41—471no—
464C23×D4C2×D4711yescharacteristic
465C22×SD16C2×D4711yescharacteristic
466C22×SD16C2×D4711yescharacteristic
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—941no—
479C2×C22⋊Q8C2×D4711yescharacteristic
480C2×#121—471no—
481C2×#121—471no—
482C2×#121—471no—
483C2×#121—471no—
484C2×#121—471no—
485C2×#121—471no—
486C2×#121—941no—
487C2×#121—941no—
488C2×#121—941no—
489C2×#120—941no—
490C2×#120—941no—
491C2×#117—471no—
492C22×C4⋊C4—471no—
493#485—478no—
494#482—478no—
495#481—478no—
496#480—478no—
497#469—478no—
498#468—478no—
499#466—478no—
500#465—478no—
501#450C2×D4718yescomplemented
502#449—478no—
503#449—478no—
504#447—478no—
505C2×#107—471no—
506C2×#107—471no—
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
522C47C2×#319811yescharacteristic, complemented, Sylow
523C25—21no—
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×Q8C22×D4711yescharacteristic
534C22×D4—21no—
535C22×D4—22no—
536C22×D4—42no—
537C22×D4—42no—
538C22×D4—471no—
539C22×D4—471no—
540C22×D4—471no—
541C22×D4—471no—
542C22×D4—941no—
543C22×D4—941no—
544C22×D4—941no—
545C22×D4—941no—
546C22×D4—941no—
547C22×D4—941no—
548C22×D4—941no—
549C22×D4C22×D4711yescharacteristic
550C22×D4C22×D4711yescharacteristic
551C22×D4C22×D4714yes—
552C23×C4—471no—
553C23×C4—471no—
554C23×C4—941no—
555C23×C4—941no—
556C23×C4C22×D4711yescharacteristic
557C2×SD16—42no—
558C2×SD16—42no—
559C2×SD16C22×D4714yes—
560C2×SD16C22×D4714yes—
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—22no—
576C22⋊Q8—474no—
577C22⋊Q8—948no—
578C22⋊Q8—942no—
579C22⋊Q8C22×D4714yes—
580#121—474no—
581#121—474no—
582#121—474no—
583#121—474no—
584#121—474no—
585#121—474no—
586#121—948no—
587#121—948no—
588#121—942no—
589#121—948no—
590#121—942no—
591#121—942no—
592#121—942no—
593#121—942no—
594#121—942no—
595#120—948no—
596#120—948no—
597#117—474no—
598#117—942no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—471no—
601C2×C4⋊C4—471no—
602C2×C4⋊C4—471no—
603C2×C4⋊C4—474no—
604C2×C4⋊C4—942no—
605C2×C4⋊C4—941no—
606C2×C4⋊C4—941no—
607C2×C4⋊C4C22×D4711yescharacteristic
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#107—474no—
619#107—474no—
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×D4714yes—
634C24—21no—
635C24—21no—
636C24—24no—
637C24—44no—
638C24—82no—
639C24—82no—
640C24—471no—
641C24—471no—
642C24—941no—
643C24D4×D4711yescharacteristic
644#41—1888no—
645#41—1884no—
646#41—1884no—
647#41—1884no—
648#41—1884no—
649#41—1888no—
650C2×Q8—21no—
651C2×Q8—22no—
652C2×Q8—22no—
653C2×Q8—474no—
654C2×Q8—1882no—
655C2×Q8C23×D4712yes—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—24no—
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—22no—
663C2×D4—44no—
664C2×D4—44no—
665C2×D4—44no—
666C2×D4—48no—
667C2×D4—474no—
668C2×D4—474no—
669C2×D4—474no—
670C2×D4—472no—
671C2×D4—944no—
672C2×D4—944no—
673C2×D4—944no—
674C2×D4—944no—
675C2×D4—944no—
676C2×D4—944no—
677C2×D4—944no—
678C2×D4—941no—
679C2×D4—942no—
680C2×D4—942no—
681C2×D4—3762no—
682C2×D4—3762no—
683C2×D4—3762no—
684C2×D4—3762no—
685C2×D4—3762no—
686C2×D4—3762no—
687C2×D4—1882no—
688C2×D4—1884no—
689C2×D4—1882no—
690C2×D4—1882no—
691C2×D4C23×D4712yes—
692C2×D4C23×D4712yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—471no—
698C22×C4—471no—
699C22×C4—472no—
700C22×C4—472no—
701C22×C4—472no—
702C22×C4—472no—
703C22×C4—944no—
704C22×C4—944no—
705C22×C4—942no—
706C22×C4—942no—
707C22×C4—942no—
708C22×C4—942no—
709C22×C4—941no—
710C22×C4—941no—
711C22×C4—941no—
712C22×C4—3762no—
713C22×C4—1884no—
714C22×C4D4×D4712yes—
715C22×C4D4×D4711yescharacteristic
716C22×C4C23×D4712yes—
717C22×C4C23×D4711yescharacteristic
718SD16—44no—
719SD16—44no—
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—24no—
733C4⋊C4—21no—
734C4⋊C4—472no—
735C4⋊C4—472no—
736C4⋊C4—472no—
737C4⋊C4—944no—
738C4⋊C4—944no—
739C4⋊C4—941no—
740C4⋊C4—941no—
741C4⋊C4—941no—
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—22no—
758C23—48no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—84no—
766C23—84no—
767C23—816no—
768C23—472no—
769C23—472no—
770C23—942no—
771C23—942no—
772C23—942no—
773C23—942no—
774C23—942no—
775C23—942no—
776C23—942no—
777C23—1882no—
778C23—1882no—
779C23—1882no—
780C23C2×D4×D4712yes—
781C23C2×D4×D4711yescharacteristic
782Q8—22no—
783Q8—22no—
784Q8—42no—
785Q8—1884no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—22no—
790D4—48no—
791D4—42no—
792D4—42no—
793D4—942no—
794D4—942no—
795D4—3764no—
796D4—3764no—
797D4—3764no—
798D4—3764no—
799D4—3764no—
800D4—3764no—
801D4—1884no—
802D4—1888no—
803D4—1884no—
804D4—1884no—
805D4—1882no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—472no—
815C2×C4—472no—
816C2×C4—942no—
817C2×C4—942no—
818C2×C4—944no—
819C2×C4—944no—
820C2×C4—942no—
821C2×C4—942no—
822C2×C4—942no—
823C2×C4—942no—
824C2×C4—942no—
825C2×C4—942no—
826C2×C4—942no—
827C2×C4—3764no—
828C2×C4—1888no—
829C2×C4—1882no—
830C2×C4—1882no—
831C2×C4—1882no—
832C2×C4C2×D4×D4712yes—
833C2×C4C2×D4×D4711yescharacteristic
834C2×C4#1309406912yes—
835C2×C4#1309406912yes—
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—42no—
849C22—42no—
850C22—42no—
851C22—816no—
852C22—84no—
853C22—84no—
854C22—942no—
855C22—942no—
856C22—942no—
857C22—942no—
858C22—942no—
859C22—942no—
860C22—3764no—
861C22—1882no—
862C22—1882no—
863C22—1882no—
864C22—1884no—
865C22—1884no—
866C22#1568968312yes—
867C22#1568992712yes—
868C22#1568992912yes—
869C22C22×D4×D4711yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—942no—
874C4—942no—
875C4—1882no—
876C4—1882no—
877C4—1882no—
878C4#1568968312yes—
879C4C2×#1309406911yescharacteristic
880C4C2×#1309406911yescharacteristic
881C2—42no—
882C2—82no—
883C2—82no—
884C2—3762no—
885C2—1882no—
886C2—1882no—
887C2#2025424414yesdirect product factor
888C2C2×#1568968311yescharacteristic
889C2C2×#1568992711yescharacteristic
890C2C2×#1568992911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#450C2
socleC23×C47C22×D4
hypercenterC2×#450D47
hypocenterC47C2×#3198
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
1. C2×#15689703C2semidirect
2. C2×#15689690C2semidirect
3. #20254244C2direct (N × H)
4. C2×#15689440C2semidirect
5. C2×#15689461C2semidirect
6. C2×#15689448C2semidirect
7. C2×#15689435C2semidirect
8. C2×#15689375C2semidirect
9. C2×#15689366C2semidirect
10. C2×#15689358C2semidirect
11. C2×#15689349C2semidirect
12. C2×#15689267C2semidirect
13. C2×#15689267C2semidirect
14. C2×#15689257C2semidirect
15. C2×#15689088C2semidirect
16. C2×C47×#450C2semidirect
17. C22×#10625354C22semidirect
21. C22×#10625324C22semidirect
22. C22×C8×D47C22semidirect
24. #15689703C22semidirect
26. #15689690C22semidirect
30. C2×#13094000C22semidirect
32. C2×#13093999C22semidirect
43. C2×C4⋊C4×D47C22semidirect
44. #15689461C22semidirect
45. #15689448C22semidirect
46. #15689440C22semidirect
47. #15689435C22semidirect
48. #15689375C22semidirect
49. #15689366C22semidirect
50. #15689358C22semidirect
51. #15689349C22semidirect
52. #15689267C22semidirect
53. #15689267C22semidirect
54. #15689257C22semidirect
55. C2×#13093958C22semidirect
56. C2×#13093957C22semidirect
57. C2×#13093956C22semidirect
58. C2×#13093955C22semidirect
59. C2×#13093948C22semidirect
60. C2×#13093948C22semidirect
61. C2×#13093946C22semidirect
62. C2×#13093946C22semidirect
65. #15689088C22semidirect
67. C2×(C2×D47)⋊C8C22semidirect
68. C2×(C2×D47)⋊C8C22semidirect
73. C47×#450C22semidirect
80. C2×#10625354C23semidirect
106. C2×#10625324C23semidirect
110. C2×C8×D47C23semidirect
115. #13094000C23semidirect
118. #13093999C23semidirect
141. C4⋊C4×D47C23semidirect
151. #13093958C23semidirect
152. #13093957C23semidirect
153. #13093956C23semidirect
154. #13093955C23semidirect
155. #13093948C23semidirect
156. #13093948C23semidirect
157. #13093946C23semidirect
158. #13093946C23semidirect
162. (C2×D47)⋊C8C23semidirect
163. (C2×D47)⋊C8C23semidirect
449. C2×#450D47semidirect
455. C2×C47#3198semidirect
501. #450C2×D47semidirect
522. C47C2×#3198semidirect
887. C2#20254244direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897032
C2×#156896902
#202542442
C2×#156894402
C2×#156894612
C2×#156894482
C2×#156894352
C2×#156893752
C2×#156893662
C2×#156893582
C2×#156893492
C2×#156892672
C2×#156892572
C2×#156890882
C2×C47×#4502
C2×#319847