Finite Group Databasebeta

← C2×#20254234 #27086925

Subgroups — C2×#20254234 #27086925

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×#15689687C211yesmaximal, characteristic, complemented
2#20254234C2116yesmaximal, direct product factor
3C2×#15689441C211yesmaximal, characteristic, complemented
4C2×#15689461C211yesmaximal, characteristic, complemented
5C2×#15689444C211yesmaximal, characteristic, complemented
6C2×#15689436C211yesmaximal, characteristic, complemented
7C2×#15689374C211yesmaximal, characteristic, complemented
8C2×#15689371C211yesmaximal, characteristic, complemented
9C2×#15689357C211yesmaximal, characteristic, complemented
10C2×#15689354C211yesmaximal, characteristic, complemented
11C2×#15689268C211yesmaximal, characteristic, complemented
12C2×#15689268C211yesmaximal, characteristic, complemented
13C2×#15689273C211yesmaximal, characteristic, complemented
14C2×#15689256C211yesmaximal, characteristic, complemented
15C2×#15689090C211yesmaximal, characteristic, complemented
16C2×C47×#537C211yesmaximal, characteristic, complemented
17C23×D188C2211yescharacteristic
18C22×#10625336C2211yescharacteristic
19C22×#10625336C2211yescharacteristic
20C22×#10625334C2211yescharacteristic
21C22×#10625334C2211yescharacteristic
22C22×#10625329C2211yescharacteristic, complemented
23C23×C47⋊C8C2211yescharacteristic, complemented
24#15689687—24no—
25#15689687C2218yescomplemented
26C2×#13094020—21no—
27C2×#13094013—21no—
28C2×#13093998C2211yescharacteristic
29C2×#13093998C2211yescharacteristic
30C2×#13093998C2211yescharacteristic
31C2×#13093998C2211yescharacteristic
32C2×#13093992—21no—
33C2×#13093992—21no—
34C2×#13093983C2211yescharacteristic
35#15689461C2218yescomplemented
36#15689444C2218yescomplemented
37#15689441C2218yescomplemented
38#15689436C2218yescomplemented
39#15689374C2218yescomplemented
40#15689371C2218yescomplemented
41#15689357C2218yescomplemented
42#15689354C2218yescomplemented
43#15689273C2218yescomplemented
44#15689268C2218yescomplemented
45#15689268C2218yescomplemented
46#15689256C2218yescomplemented
47C2×#13093957C2211yescharacteristic, complemented
48C2×#13093957C2211yescharacteristic, complemented
49C2×#13093955C2211yescharacteristic, complemented
50C2×#13093955C2211yescharacteristic, complemented
51C2×#13093948C2211yescharacteristic, complemented
52C2×#13093948C2211yescharacteristic, complemented
53C2×#13093945C2211yescharacteristic, complemented
54C2×#13093945C2211yescharacteristic, complemented
55C2×#13093944C2211yescharacteristic
56C2×#13093944C2211yescharacteristic
57C2×#13093944C2211yescharacteristic
58C2×#13093944C2211yescharacteristic
59#15689090C2218yescomplemented
60C2×C22⋊(C47⋊C8)C2211yescharacteristic
61C2×C22⋊(C47⋊C8)C2211yescharacteristic
62C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
63C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
64C22×#41×C47C2211yescharacteristic
65C22×#41×C47C2211yescharacteristic, complemented
66C47×#537—24no—
67C47×#537C2218yescomplemented
68C2×C22⋊Q8×C47—21no—
69C2×C22⋊Q8×C47C2211yescharacteristic
70C2×C22⋊Q8×C47C2211yescharacteristic, complemented
71C2×#121×C47—21no—
72C2×#121×C47—21no—
73C2×#121×C47—21no—
74C2×#121×C47C2211yescharacteristic
75C2×#121×C47C2211yescharacteristic, complemented
76C22×C4⋊C4×C47C2211yescharacteristic, complemented
77C24×D47—21no—
78C22×D188—21no—
79C22×D188—22no—
80C22×D188—42no—
81C22×D188—42no—
82C22×D188C2311yescharacteristic
83C22×D188C2311yescharacteristic
84C22×D188C2314yes—
85C22×C22⋊D47—21no—
86C22×C22⋊D47—21no—
87C22×C22⋊D47—21no—
88C22×C22⋊D47—21no—
89C2×#10625336—42no—
90C2×#10625336—42no—
91C2×#10625336C2314yes—
92C2×#10625336C2314yes—
93C2×#10625334—42no—
94C2×#10625334—42no—
95C2×#10625334C2314yes—
96C2×#10625334C2314yes—
97C2×#10625329—42no—
98C2×#10625329C2314yescomplemented
99C22×C47⋊C8—42no—
100C22×C47⋊C8C2311yescharacteristic
101C22×C47⋊C8C2311yescharacteristic
102C22×C47⋊C8C2311yescharacteristic
103C22×C47⋊C8C2311yescharacteristic
104C22×C47⋊C8C2314yescomplemented
105#13094020—28no—
106#13094013—28no—
107#13093998—22no—
108#13093998—22no—
109#13093998—22no—
110#13093998—22no—
111#13093998C2314yes—
112#13093998C2314yes—
113#13093998C2314yes—
114#13093998C2314yes—
115#13093992—28no—
116#13093992—28no—
117#13093983—22no—
118#13093983C2314yes—
119C2×C4⋊Dic47C2311yescharacteristic
120C2×C4⋊Dic47C2311yescharacteristic
121C2×C22⋊Dic47—21no—
122C2×(C2×D47)⋊C4—21no—
123C2×(C2×D47)⋊C4—21no—
124C2×(C2×D47)⋊C4—21no—
125C2×(C2×D47)⋊C4—21no—
126C2×C4×Dic47—21no—
127#13093957C2314yescomplemented
128#13093957C2314yescomplemented
129#13093955C2314yescomplemented
130#13093955C2314yescomplemented
131#13093948C2314yescomplemented
132#13093948C2314yescomplemented
133#13093945C2314yescomplemented
134#13093945C2314yescomplemented
135#13093944C2314yes—
136#13093944C2314yes—
137#13093944C2314yes—
138#13093944C2314yes—
139C22⋊(C47⋊C8)C2314yes—
140C22⋊(C47⋊C8)C2314yes—
141C22⋊(C47⋊C8)C2314yescomplemented
142C22⋊(C47⋊C8)C2314yescomplemented
143C2×#41×C47—22no—
144C2×#41×C47—42no—
145C2×#41×C47—42no—
146C2×#41×C47—42no—
147C2×#41×C47—42no—
148C2×#41×C47D414yes—
149C2×#41×C47C2314yes—
150C2×#41×C47C2314yescomplemented
151C22×Q8×C47D411yescharacteristic
152C22×Q8×C47C2311yescharacteristic
153C22×D4×C47—21no—
154C22×D4×C47—21no—
155C22×D4×C47—21no—
156C22×D4×C47D411yescharacteristic
157C22×D4×C47D411yescharacteristic
158C22×D4×C47D411yescharacteristic
159C22×D4×C47C2311yescharacteristic
160C23×C4×C47—21no—
161C23×C4×C47—21no—
162C23×C4×C47C2311yescharacteristic
163C23×C4×C47C2311yescharacteristic
164C23×C4×C47C2311yescharacteristic
165C22⋊Q8×C47—28no—
166C22⋊Q8×C47—22no—
167C22⋊Q8×C47—22no—
168C22⋊Q8×C47C2314yes—
169C22⋊Q8×C47C2314yescomplemented
170#121×C47—28no—
171#121×C47—28no—
172#121×C47—28no—
173#121×C47—22no—
174#121×C47—22no—
175#121×C47C2314yes—
176#121×C47C2314yescomplemented
177C2×C4⋊C4×C47—21no—
178C2×C4⋊C4×C47—22no—
179C2×C4⋊C4×C47—21no—
180C2×C4⋊C4×C47—21no—
181C2×C4⋊C4×C47C2311yescharacteristic
182C2×C4⋊C4×C47C2311yescharacteristic
183C2×C4⋊C4×C47C2314yescomplemented
184C2×C22⋊C4×C47—21no—
185C2×C22⋊C4×C47—21no—
186C2×C22⋊C4×C47—21no—
187C2×C22⋊C4×C47—21no—
188C24×C47—21no—
189C24×C47C2×D411yescharacteristic
190C24×C47C2×D411yescharacteristic
191C24×C47C2×D411yescharacteristic
192C23×D47—21no—
193C23×D47—21no—
194C23×D47—24no—
195C23×D47—44no—
196C23×D47—82no—
197C23×D47—82no—
198#41×C47—48no—
199#41×C47—44no—
200#41×C47—44no—
201#41×C47—44no—
202#41×C47—44no—
203#41×C47—48no—
204C2×Q8×C47—21no—
205C2×Q8×C47—22no—
206C2×Q8×C47—22no—
207C2×Q8×C47—42no—
208C2×Q8×C47C2×D414yes—
209C2×Q8×C47C2412yes—
210C2×D4×C47—24no—
211C2×D4×C47—24no—
212C2×D4×C47—24no—
213C2×D4×C47—21no—
214C2×D4×C47—22no—
215C2×D4×C47—22no—
216C2×D4×C47—42no—
217C2×D4×C47—42no—
218C2×D4×C47—42no—
219C2×D4×C47—44no—
220C2×D4×C47—82no—
221C2×D4×C47—82no—
222C2×D4×C47C2×D414yes—
223C2×D4×C47C2×D414yes—
224C2×D4×C47C2×D414yes—
225C2×D4×C47C2412yes—
226C22×C4×C47—22no—
227C22×C4×C47—22no—
228C22×C4×C47—22no—
229C22×C4×C47—22no—
230C22×C4×C47—22no—
231C22×C4×C47—22no—
232C22×C4×C47—21no—
233C22×C4×C47—21no—
234C22×C4×C47—21no—
235C22×C4×C47—24no—
236C22×C4×C47—24no—
237C22×C4×C47—44no—
238C22×C4×C47—82no—
239C22×C4×C47C2×D411yescharacteristic
240C22×C4×C47C2×D411yescharacteristic
241C22×C4×C47C2×D411yescharacteristic
242C22×C4×C47C2×D412yes—
243C22×C4×C47C2×D412yes—
244C22×C4×C47C2×D412yes—
245C22×C4×C47C2412yes—
246C22×C4×C47C2412yes—
247C22×C4×C47C2412yes—
248C22×C4×C47C2411yescharacteristic
249C2×C22⋊D47—24no—
250C2×C22⋊D47—24no—
251C2×C22⋊D47—24no—
252C2×C22⋊D47—24no—
253C2×C22⋊D47—82no—
254C2×C22⋊D47—82no—
255C2×C22⋊D47—82no—
256C2×C22⋊D47—82no—
257C22×Dic47—21no—
258C22×Dic47—21no—
259C2×D188—22no—
260C2×D188—22no—
261C2×D188—22no—
262C2×D188—22no—
263C2×D188—21no—
264C2×D188—21no—
265C2×D188—24no—
266C2×D188—44no—
267C2×D188—44no—
268C2×D188—44no—
269C2×D188—48no—
270C2×D188C2412yes—
271C2×D188C2412yes—
272C4⋊C4×C47—21no—
273C4⋊C4×C47—21no—
274C4⋊C4×C47—24no—
275C4⋊C4×C47—24no—
276C4⋊C4×C47—24no—
277C4⋊C4×C47C2412yes—
278C4⋊C4×C47C2412yes—
279C22⋊C4×C47—24no—
280C22⋊C4×C47—24no—
281C22⋊C4×C47—24no—
282C22⋊C4×C47—24no—
283C22⋊Dic47—24no—
284#10625336—44no—
285#10625336—44no—
286#10625334—44no—
287#10625334—44no—
288(C2×D47)⋊C4—24no—
289(C2×D47)⋊C4—24no—
290(C2×D47)⋊C4—24no—
291(C2×D47)⋊C4—24no—
292C4⋊Dic47—21no—
293C4⋊Dic47—21no—
294C4⋊Dic47C2412yes—
295C4⋊Dic47C2412yes—
296C4×Dic47—24no—
297#10625329—44no—
298C2×C47⋊C8—22no—
299C2×C47⋊C8—22no—
300C2×C47⋊C8—22no—
301C2×C47⋊C8—22no—
302C2×C47⋊C8—44no—
303C2×C47⋊C8C2412yes—
304C2×C47⋊C8C2412yes—
305C2×C47⋊C8C2412yes—
306C2×C47⋊C8C2412yes—
307C23×C47—22no—
308C23×C47—22no—
309C23×C47—22no—
310C23×C47—22no—
311C23×C47—22no—
312C23×C47—22no—
313C23×C47—22no—
314C23×C47—22no—
315C23×C47—22no—
316C23×C47—22no—
317C23×C47—42no—
318C23×C47—42no—
319C23×C47—42no—
320C23×C47C22×D412yes—
321C23×C47C22×D412yes—
322C23×C47C22×D412yes—
323C23×C47C22×D411yescharacteristic
324C22×D47—22no—
325C22×D47—22no—
326C22×D47—48no—
327C22×D47—42no—
328C22×D47—42no—
329C22×D47—42no—
330C22×D47—42no—
331C22×D47—42no—
332C22×D47—42no—
333C22×D47—84no—
334C22×D47—84no—
335C22×D47—816no—
336Q8×C47—22no—
337Q8×C47—22no—
338Q8×C47—44no—
339Q8×C47—42no—
340D4×C47—22no—
341D4×C47—22no—
342D4×C47—44no—
343D4×C47—44no—
344D4×C47—44no—
345D4×C47—48no—
346D4×C47—42no—
347D4×C47—84no—
348D4×C47—84no—
349C2×C4×C47—22no—
350C2×C4×C47—22no—
351C2×C4×C47—22no—
352C2×C4×C47—24no—
353C2×C4×C47—24no—
354C2×C4×C47—24no—
355C2×C4×C47—22no—
356C2×C4×C47—22no—
357C2×C4×C47—22no—
358C2×C4×C47—22no—
359C2×C4×C47—22no—
360C2×C4×C47—22no—
361C2×C4×C47—22no—
362C2×C4×C47—22no—
363C2×C4×C47—22no—
364C2×C4×C47—48no—
365C2×C4×C47—42no—
366C2×C4×C47—42no—
367C2×C4×C47—42no—
368C2×C4×C47—84no—
369C2×C4×C47C22×D412yes—
370C2×C4×C47C22×D412yes—
371C2×C4×C47C22×D412yes—
372C2×C4×C47C22×D411yescharacteristic
373C2×C4×C47H(5,𝔽2)12yes—
374C2×C4×C47H(5,𝔽2)12yes—
375C2×C4×C47C2511yescharacteristic
376C22⋊D47—84no—
377C22⋊D47—84no—
378C22⋊D47—84no—
379C22⋊D47—84no—
380C2×Dic47—22no—
381C2×Dic47—22no—
382C2×Dic47—42no—
383C2×Dic47—42no—
384D188—22no—
385D188—22no—
386D188—22no—
387D188—22no—
388D188—48no—
389D188—42no—
390D188—42no—
391C47⋊C8—22no—
392C47⋊C8—22no—
393C47⋊C8—22no—
394C47⋊C8—22no—
395C2×#3198—471nomaximal, Sylow
396C22×C47—22no—
397C22×C47—22no—
398C22×C47—22no—
399C22×C47—22no—
400C22×C47—22no—
401C22×C47—22no—
402C22×C47—22no—
403C22×C47—22no—
404C22×C47—22no—
405C22×C47—44no—
406C22×C47—44no—
407C22×C47—44no—
408C22×C47—42no—
409C22×C47—42no—
410C22×C47—42no—
411C22×C47—84no—
412C22×C47#53412yes—
413C22×C47#57612yes—
414C22×C47#57712yes—
415C22×C47C23×D411yescharacteristic
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—22no—
427C4×C47—22no—
428C4×C47—42no—
429C4×C47—42no—
430C4×C47—42no—
431C4×C47#53412yes—
432C4×C47C2×H(5,𝔽2)11yescharacteristic
433C4×C47C2×H(5,𝔽2)11yescharacteristic
434Dic47—42no—
435Dic47—42no—
436C2×#537D4711yescharacteristic, complemented
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×#450—471no—
450C2×#447—471no—
451C2×#408—471no—
452C2×C47—42no—
453C2×C47—42no—
454C2×C47—42no—
455C2×C47—82no—
456C2×C47#319814yescomplemented
457C2×C47C2×#53411yescharacteristic
458C2×C47C2×#57611yescharacteristic
459C2×C47C2×#57711yescharacteristic
460D47—82no—
461D47—82no—
462C22×#41C2×D4711yescharacteristic
463C22×#41C2×D4711yescharacteristic, complemented
464C23×D4—471no—
465C22×SD16—471no—
466C22×SD16—471no—
467C22×D8—471no—
468C22×D8—471no—
469C22×M16—471no—
470C23×C8—471no—
471#537—24no—
472#537C2×D4718yescomplemented
473#535—478no—
474#535—944no—
475C2×#127—941no—
476C2×#124—941no—
477C2×C22⋊Q8—21no—
478C2×C22⋊Q8C2×D4711yescharacteristic
479C2×C22⋊Q8C2×D4711yescharacteristic, complemented
480C2×#121—21no—
481C2×#121—21no—
482C2×#121—21no—
483C2×#121—471no—
484C2×#121—471no—
485C2×#121—471no—
486C2×#121—471no—
487C2×#121C2×D4711yescharacteristic
488C2×#121C2×D4711yescharacteristic, complemented
489C2×#120—941no—
490C2×#120—941no—
491C2×#117—471no—
492C22×C4⋊C4C2×D4711yescharacteristic, complemented
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#450—478no—
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×#102—471no—
516C2×#102—471no—
517#408—478no—
518C2×C22⋊C8—471no—
519C2×C22⋊C8—471no—
520C2×C22⋊C8—471no—
521C2×C22⋊C8—471no—
522C47C2×#319811yescharacteristic, complemented, Sylow
523C25—941no—
524C2×#41—22no—
525C2×#41—42no—
526C2×#41—42no—
527C2×#41—42no—
528C2×#41—42no—
529C2×#41C22⋊D4714yes—
530C2×#41C22×D4714yes—
531C2×#41C22×D4714yescomplemented
532C22×Q8C22⋊D4711yescharacteristic
533C22×Q8C22×D4711yescharacteristic
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—471no—
538C22×D4—471no—
539C22×D4—474no—
540C22×D4—941no—
541C22×D4—941no—
542C22×D4—941no—
543C22×D4—941no—
544C22×D4—941no—
545C22×D4—942no—
546C22×D4—1882no—
547C22×D4—1882no—
548C22×D4C22⋊D4711yescharacteristic
549C22×D4C22⋊D4711yescharacteristic
550C22×D4C22⋊D4711yescharacteristic
551C22×D4C22×D4711yescharacteristic
552C23×C4—21no—
553C23×C4—21no—
554C23×C4C22×D4711yescharacteristic
555C23×C4C22×D4711yescharacteristic
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—471no—
570C22×C8—471no—
571C22×C8—474no—
572C22×C8—1882no—
573#127—948no—
574#124—948no—
575C22⋊Q8—28no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8C22×D4714yes—
579C22⋊Q8C22×D4714yescomplemented
580#121—28no—
581#121—28no—
582#121—28no—
583#121—22no—
584#121—22no—
585#121—474no—
586#121—474no—
587#121—474no—
588#121—474no—
589#121—942no—
590#121—942no—
591#121—942no—
592#121—942no—
593#121C22×D4714yes—
594#121C22×D4714yescomplemented
595#120—948no—
596#120—948no—
597#117—474no—
598#117—942no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—471no—
604C2×C4⋊C4—471no—
605C2×C4⋊C4C22×D4711yescharacteristic
606C2×C4⋊C4C22×D4711yescharacteristic
607C2×C4⋊C4C22×D4714yescomplemented
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
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#102—474no—
629#102—474no—
630C22⋊C8—474no—
631C22⋊C8—474no—
632C22⋊C8—474no—
633C22⋊C8—474no—
634C24—21no—
635C24—944no—
636C24—941no—
637C24—941no—
638C24—3762no—
639C24—3762no—
640C24—1884no—
641C24C2×C22⋊D4711yescharacteristic
642C24C2×C22⋊D4711yescharacteristic
643C24C2×C22⋊D4711yescharacteristic
644#41—48no—
645#41—44no—
646#41—44no—
647#41—44no—
648#41—44no—
649#41—48no—
650C2×Q8—21no—
651C2×Q8—22no—
652C2×Q8—22no—
653C2×Q8—42no—
654C2×Q8C2×C22⋊D4714yes—
655C2×Q8C23×D4712yes—
656C2×D4—24no—
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—21no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—44no—
666C2×D4—82no—
667C2×D4—82no—
668C2×D4—472no—
669C2×D4—472no—
670C2×D4—944no—
671C2×D4—944no—
672C2×D4—944no—
673C2×D4—944no—
674C2×D4—941no—
675C2×D4—941no—
676C2×D4—944no—
677C2×D4—942no—
678C2×D4—942no—
679C2×D4—942no—
680C2×D4—942no—
681C2×D4—3762no—
682C2×D4—3762no—
683C2×D4—3762no—
684C2×D4—3762no—
685C2×D4—1884no—
686C2×D4—1884no—
687C2×D4—1884no—
688C2×D4—1888no—
689C2×D4C2×C22⋊D4714yes—
690C2×D4C2×C22⋊D4714yes—
691C2×D4C2×C22⋊D4714yes—
692C2×D4C23×D4712yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—24no—
703C22×C4—24no—
704C22×C4—44no—
705C22×C4—82no—
706C22×C4—941no—
707C22×C4—941no—
708C22×C4C2×C22⋊D4712yes—
709C22×C4C2×C22⋊D4712yes—
710C22×C4C2×C22⋊D4712yes—
711C22×C4C2×C22⋊D4711yescharacteristic
712C22×C4C2×C22⋊D4711yescharacteristic
713C22×C4C2×C22⋊D4711yescharacteristic
714C22×C4C23×D4712yes—
715C22×C4C23×D4712yes—
716C22×C4C23×D4712yes—
717C22×C4C23×D4711yescharacteristic
718SD16—1884no—
719SD16—1884no—
720D8—1884no—
721D8—1884no—
722M16—1884no—
723C2×C8—472no—
724C2×C8—472no—
725C2×C8—472no—
726C2×C8—472no—
727C2×C8—942no—
728C2×C8—942no—
729C2×C8—942no—
730C2×C8—942no—
731C2×C8—1884no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—24no—
735C4⋊C4—24no—
736C4⋊C4—24no—
737C4⋊C4—472no—
738C4⋊C4—472no—
739C4⋊C4—941no—
740C4⋊C4—941no—
741C4⋊C4C23×D4712yes—
742C4⋊C4C23×D4712yes—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—24no—
746C22⋊C4—24no—
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—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23—942no—
767C23—942no—
768C23—3764no—
769C23—3764no—
770C23—37616no—
771C23—1888no—
772C23—1882no—
773C23—1882no—
774C23—1882no—
775C23—1882no—
776C23—1882no—
777C23—1882no—
778C23C22×C22⋊D4712yes—
779C23C22×C22⋊D4712yes—
780C23C22×C22⋊D4712yes—
781C23C22×C22⋊D4711yescharacteristic
782Q8—22no—
783Q8—22no—
784Q8—44no—
785Q8—42no—
786D4—22no—
787D4—22no—
788D4—44no—
789D4—44no—
790D4—44no—
791D4—48no—
792D4—42no—
793D4—84no—
794D4—84no—
795D4—942no—
796D4—942no—
797D4—942no—
798D4—942no—
799D4—3764no—
800D4—3764no—
801D4—3764no—
802D4—3764no—
803D4—1888no—
804D4—1882no—
805D4—1882no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—48no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—84no—
826C2×C4—942no—
827C2×C4—942no—
828C2×C4—1882no—
829C2×C4—1882no—
830C2×C4C22×C22⋊D4712yes—
831C2×C4C22×C22⋊D4712yes—
832C2×C4C22×C22⋊D4712yes—
833C2×C4C22×C22⋊D4711yescharacteristic
834C2×C4#1309406912yes—
835C2×C4#1309406912yes—
836C2×C4C24×D4711yescharacteristic
837C8—942no—
838C8—942no—
839C8—942no—
840C8—942no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—84no—
857C22—37616no—
858C22—3764no—
859C22—3764no—
860C22—1882no—
861C22—1882no—
862C22—1882no—
863C22—1882no—
864C22—1882no—
865C22—1882no—
866C22#1568968212yes—
867C22#1568992612yes—
868C22#1568993112yes—
869C22C23×C22⋊D4711yescharacteristic
870C4—22no—
871C4—22no—
872C4—22no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—1882no—
877C4—1882no—
878C4#1568968212yes—
879C4C2×#1309406911yescharacteristic
880C4C2×#1309406911yescharacteristic
881C2—42no—
882C2—42no—
883C2—42no—
884C2—82no—
885C2—3762no—
886C2—3762no—
887C2#2025423414yesdirect product factor
888C2C2×#1568968211yescharacteristic
889C2C2×#1568992611yescharacteristic
890C2C2×#1568993111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#537C2
socleC23×C47C22×D4
hypercenterC2×#537D47
hypocenterC47C2×#3198
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C2×#15689687C2semidirect
2. #20254234C2direct (N × H)
3. C2×#15689441C2semidirect
4. C2×#15689461C2semidirect
5. C2×#15689444C2semidirect
6. C2×#15689436C2semidirect
7. C2×#15689374C2semidirect
8. C2×#15689371C2semidirect
9. C2×#15689357C2semidirect
10. C2×#15689354C2semidirect
11. C2×#15689268C2semidirect
12. C2×#15689268C2semidirect
13. C2×#15689273C2semidirect
14. C2×#15689256C2semidirect
15. C2×#15689090C2semidirect
16. C2×C47×#537C2semidirect
22. C22×#10625329C22semidirect
23. C23×C47⋊C8C22semidirect
25. #15689687C22semidirect
35. #15689461C22semidirect
36. #15689444C22semidirect
37. #15689441C22semidirect
38. #15689436C22semidirect
39. #15689374C22semidirect
40. #15689371C22semidirect
41. #15689357C22semidirect
42. #15689354C22semidirect
43. #15689273C22semidirect
44. #15689268C22semidirect
45. #15689268C22semidirect
46. #15689256C22semidirect
47. C2×#13093957C22semidirect
48. C2×#13093957C22semidirect
49. C2×#13093955C22semidirect
50. C2×#13093955C22semidirect
51. C2×#13093948C22semidirect
52. C2×#13093948C22semidirect
53. C2×#13093945C22semidirect
54. C2×#13093945C22semidirect
59. #15689090C22semidirect
62. C2×C22⋊(C47⋊C8)C22semidirect
63. C2×C22⋊(C47⋊C8)C22semidirect
65. C22×#41×C47C22semidirect
67. C47×#537C22semidirect
70. C2×C22⋊Q8×C47C22semidirect
75. C2×#121×C47C22semidirect
76. C22×C4⋊C4×C47C22semidirect
98. C2×#10625329C23semidirect
104. C22×C47⋊C8C23semidirect
127. #13093957C23semidirect
128. #13093957C23semidirect
129. #13093955C23semidirect
130. #13093955C23semidirect
131. #13093948C23semidirect
132. #13093948C23semidirect
133. #13093945C23semidirect
134. #13093945C23semidirect
141. C22⋊(C47⋊C8)C23semidirect
142. C22⋊(C47⋊C8)C23semidirect
150. C2×#41×C47C23semidirect
169. C22⋊Q8×C47C23semidirect
176. #121×C47C23semidirect
183. C2×C4⋊C4×C47C23semidirect
436. C2×#537D47semidirect
456. C2×C47#3198semidirect
463. C22×#41C2×D47semidirect
472. #537C2×D47semidirect
479. C2×C22⋊Q8C2×D47semidirect
488. C2×#121C2×D47semidirect
492. C22×C4⋊C4C2×D47semidirect
522. C47C2×#3198semidirect
531. C2×#41C22×D47semidirect
579. C22⋊Q8C22×D47semidirect
594. #121C22×D47semidirect
607. C2×C4⋊C4C22×D47semidirect
887. C2#20254234direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896872
#202542342
C2×#156894412
C2×#156894612
C2×#156894442
C2×#156894362
C2×#156893742
C2×#156893712
C2×#156893572
C2×#156893542
C2×#156892682
C2×#156892732
C2×#156892562
C2×#156890902
C2×C47×#5372
C2×#319847