Finite Group Databasebeta

← C2×#20254239 #27086930

Subgroups — C2×#20254239 #27086930

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×#15689701C211yesmaximal, characteristic, complemented
2C2×#15689689C211yesmaximal, characteristic, complemented
3#20254239C2116yesmaximal, direct product factor
4C2×#15689442C211yesmaximal, characteristic, complemented
5C2×#15689462C211yesmaximal, characteristic, complemented
6C2×#15689446C211yesmaximal, characteristic, complemented
7C2×#15689434C211yesmaximal, characteristic, complemented
8C2×#15689373C211yesmaximal, characteristic, complemented
9C2×#15689372C211yesmaximal, characteristic, complemented
10C2×#15689358C211yesmaximal, characteristic, complemented
11C2×#15689349C211yesmaximal, characteristic, complemented
12C2×#15689268C211yesmaximal, characteristic, complemented
13C2×#15689272C211yesmaximal, characteristic, complemented
14C2×#15689255C211yesmaximal, characteristic, complemented
15C2×#15689088C211yesmaximal, characteristic, complemented
16C2×C47×#449C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C22×D4×D47C2211yescharacteristic
19C22×#10625336C2211yescharacteristic
20C22×#10625334C2211yescharacteristic
21C22×#10625324C2211yescharacteristic, complemented
22C22×C8×D47C2211yescharacteristic, complemented
23#15689701—24no—
24#15689701C2218yescomplemented
25#15689689—24no—
26#15689689C2218yescomplemented
27C2×#13094020—21no—
28C2×#13094010—21no—
29C2×#13094003—21no—
30C2×#13094000C2211yescharacteristic
31C2×#13094000C2211yescharacteristic, complemented
32C2×#13093999C2211yescharacteristic
33C2×#13093998—21no—
34C2×#13093998C2211yescharacteristic
35C2×#13093996—21no—
36C2×#13093996—21no—
37C2×#13093995C2211yescharacteristic
38C2×#13093995C2211yescharacteristic
39C2×#13093995C2211yescharacteristic, complemented
40C2×#13093994—21no—
41C2×#13093992—21no—
42C2×#13093982C2211yescharacteristic
43C22×C4⋊Dic47C2211yescharacteristic, complemented
44#15689462C2218yescomplemented
45#15689446C2218yescomplemented
46#15689442C2218yescomplemented
47#15689434C2218yescomplemented
48#15689373C2218yescomplemented
49#15689372C2218yescomplemented
50#15689358C2218yescomplemented
51#15689349C2218yescomplemented
52#15689272C2218yescomplemented
53#15689268C2218yescomplemented
54#15689255C2218yescomplemented
55C2×#13093957C2211yescharacteristic, complemented
56C2×#13093957C2211yescharacteristic, complemented
57C2×#13093956C2211yescharacteristic, complemented
58C2×#13093956C2211yescharacteristic, complemented
59C2×#13093948C2211yescharacteristic, complemented
60C2×#13093946C2211yescharacteristic
61C2×#13093946C2211yescharacteristic
62C2×#13093945C2211yescharacteristic
63C2×#13093945C2211yescharacteristic
64C2×#13093945C2211yescharacteristic, complemented
65#15689088C2218yescomplemented
66C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×(C2×D47)⋊C8C2211yescharacteristic
69C22×#41×C47C2211yescharacteristic, complemented
70C22×SD16×C47C2211yescharacteristic
71C22×D8×C47C2211yescharacteristic
72C2×#121×C47C2211yescharacteristic
73C47×#449C2218yescomplemented
74C2×#103×C47C2211yescharacteristic, complemented
75C2×#102×C47C2211yescharacteristic, complemented
76C2×C22⋊C8×C47C2211yescharacteristic, complemented
77C24×D47—21no—
78C2×#10625350—42no—
79C2×#10625350—42no—
80C2×#10625350D414yes—
81C2×#10625350C2314yes—
82C22×Dic94D411yescharacteristic
83C22×D188—21no—
84C22×D188D411yescharacteristic
85C22×D188C2311yescharacteristic
86C22×C22⋊D47—21no—
87C22×C22⋊D47—21no—
88C22×C22⋊D47—21no—
89C22×C22⋊D47—21no—
90C22×C22⋊D47—21no—
91C22×C22⋊D47D411yescharacteristic
92C22×C22⋊D47D411yescharacteristic
93C2×D4×D47—22no—
94C2×D4×D47—42no—
95C2×D4×D47—42no—
96C2×D4×D47C2314yes—
97C23×Dic47—21no—
98C22×C4×D47C2311yescharacteristic
99C22×C4×D47C2311yescharacteristic
100C2×#10625336—42no—
101C2×#10625336C2314yes—
102C2×#10625334—42no—
103C2×#10625334C2314yes—
104C2×#10625324—42no—
105C2×#10625324C2314yescomplemented
106C22×C47⋊C8C2311yescharacteristic
107C22×C47⋊C8C2311yescharacteristic
108C2×C8×D47—42no—
109C2×C8×D47C2314yescomplemented
110#13094020—28no—
111#13094010—28no—
112#13094003—28no—
113#13094000—22no—
114#13094000—22no—
115#13094000C2314yes—
116#13094000C2314yescomplemented
117#13093999—22no—
118#13093999C2314yes—
119#13093998—22no—
120#13093998—28no—
121#13093998C2314yes—
122#13093996—28no—
123#13093996—28no—
124#13093995—22no—
125#13093995—22no—
126#13093995—22no—
127#13093995C2314yes—
128#13093995C2314yes—
129#13093995C2314yescomplemented
130#13093994—28no—
131#13093992—28no—
132#13093982—22no—
133#13093982C2314yes—
134C2×C4⋊Dic47—21no—
135C2×C4⋊Dic47—22no—
136C2×C4⋊Dic47C2311yescharacteristic
137C2×C4⋊Dic47C2311yescharacteristic
138C2×C4⋊Dic47C2311yescharacteristic
139C2×C4⋊Dic47C2314yescomplemented
140C2×Dic47⋊C4—21no—
141C2×Dic47⋊C4—21no—
142C2×C22⋊Dic47—21no—
143C2×C22⋊Dic47—21no—
144C2×C22⋊Dic47—21no—
145C2×(C2×D47)⋊C4—21no—
146C2×(C2×D47)⋊C4—21no—
147C2×(C2×D47)⋊C4—21no—
148C2×(C2×D47)⋊C4—21no—
149C2×(C2×D47)⋊C4—21no—
150C2×C4×Dic47—21no—
151#13093957C2314yescomplemented
152#13093957C2314yescomplemented
153#13093956C2314yescomplemented
154#13093956C2314yescomplemented
155#13093948C2314yescomplemented
156#13093946C2314yes—
157#13093946C2314yes—
158#13093945C2314yes—
159#13093945C2314yes—
160#13093945C2314yescomplemented
161C22⋊(C47⋊C8)C2314yescomplemented
162(C2×D47)⋊C8C2314yes—
163(C2×D47)⋊C8C2314yes—
164C2×#41×C47—22no—
165C2×#41×C47—42no—
166C2×#41×C47—42no—
167C2×#41×C47C2314yescomplemented
168C22×Q8×C47C2311yescharacteristic
169C22×D4×C47—21no—
170C22×D4×C47—21no—
171C22×D4×C47C2311yescharacteristic
172C22×D4×C47C2311yescharacteristic
173C23×C4×C47—21no—
174C23×C4×C47C2311yescharacteristic
175C2×SD16×C47—42no—
176C2×SD16×C47C2314yes—
177C2×D8×C47—42no—
178C2×D8×C47C2314yes—
179C22×C8×C47C2311yescharacteristic
180C22×C8×C47C2311yescharacteristic
181#121×C47—22no—
182#121×C47C2314yes—
183C2×C4⋊C4×C47C2311yescharacteristic
184C2×C22⋊C4×C47—21no—
185#103×C47C2314yescomplemented
186#102×C47C2314yescomplemented
187C22⋊C8×C47C2314yescomplemented
188C24×C47—21no—
189C24×C47—21no—
190C24×C47C2×D411yescharacteristic
191C23×D47—21no—
192C23×D47—24no—
193C23×D47—44no—
194C23×D47—82no—
195C23×D47—82no—
196C23×D47C2×D411yescharacteristic
197C23×D47C2×D411yescharacteristic
198#41×C47—44no—
199#41×C47—44no—
200#41×C47—48no—
201C2×Q8×C47—21no—
202C2×Q8×C47—22no—
203C2×Q8×C47—22no—
204C2×Q8×C47C2412yes—
205C2×D4×C47—24no—
206C2×D4×C47—24no—
207C2×D4×C47—21no—
208C2×D4×C47—21no—
209C2×D4×C47—22no—
210C2×D4×C47—22no—
211C2×D4×C47—22no—
212C2×D4×C47—22no—
213C2×D4×C47—44no—
214C2×D4×C47—82no—
215C2×D4×C47C2412yes—
216C2×D4×C47C2412yes—
217C22×C4×C47—22no—
218C22×C4×C47—22no—
219C22×C4×C47—21no—
220C22×C4×C47—21no—
221C22×C4×C47—24no—
222C22×C4×C47—44no—
223C22×C4×C47C2×D411yescharacteristic
224C22×C4×C47C2×D412yes—
225C22×C4×C47C2412yes—
226C22×C4×C47C2411yescharacteristic
227C2×C22⋊D47—24no—
228C2×C22⋊D47—24no—
229C2×C22⋊D47—24no—
230C2×C22⋊D47—24no—
231C2×C22⋊D47—24no—
232C2×C22⋊D47—42no—
233C2×C22⋊D47—42no—
234C2×C22⋊D47—44no—
235C2×C22⋊D47—82no—
236C2×C22⋊D47—82no—
237C2×C22⋊D47—82no—
238C2×C22⋊D47—82no—
239C2×C22⋊D47C2×D414yes—
240C2×C22⋊D47C2×D414yes—
241C22×Dic47—21no—
242C22×Dic47—21no—
243C22×Dic47—21no—
244C22×Dic47—24no—
245C22×Dic47—82no—
246C22×Dic47C2×D411yescharacteristic
247C22×Dic47C2×D411yescharacteristic
248D4×D47—44no—
249D4×D47—44no—
250D4×D47—48no—
251#10625350—48no—
252#10625350—44no—
253#10625350—44no—
254C2×D188—22no—
255C2×D188—22no—
256C2×D188—21no—
257C2×D188—24no—
258C2×D188—42no—
259C2×D188—82no—
260C2×D188C2×D414yes—
261C2×D188C2412yes—
262C2×C4×D47—22no—
263C2×C4×D47—22no—
264C2×C4×D47—22no—
265C2×C4×D47—22no—
266C2×C4×D47C2×D412yes—
267C2×C4×D47C2×D412yes—
268C2×C4×D47C2412yes—
269C2×C4×D47C2412yes—
270C2×Dic94—42no—
271C2×Dic94C2×D414yes—
272SD16×C47—44no—
273D8×C47—44no—
274C2×C8×C47—22no—
275C2×C8×C47—22no—
276C2×C8×C47C2412yes—
277C2×C8×C47C2412yes—
278C4⋊C4×C47—21no—
279C4⋊C4×C47C2412yes—
280C22⋊C4×C47—24no—
281C22⋊Dic47—24no—
282C22⋊Dic47—24no—
283C22⋊Dic47—24no—
284#10625336—44no—
285#10625334—44no—
286(C2×D47)⋊C4—24no—
287(C2×D47)⋊C4—24no—
288(C2×D47)⋊C4—24no—
289(C2×D47)⋊C4—24no—
290(C2×D47)⋊C4—24no—
291C4⋊Dic47—21no—
292C4⋊Dic47—21no—
293C4⋊Dic47—24no—
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—42no—
313C23×C47—42no—
314C23×C47—42no—
315C23×C47—42no—
316C23×C47—42no—
317C23×C47—42no—
318C23×C47C22×D412yes—
319C23×C47C22×D411yescharacteristic
320C22×D47—22no—
321C22×D47—22no—
322C22×D47—22no—
323C22×D47—22no—
324C22×D47—22no—
325C22×D47—22no—
326C22×D47—22no—
327C22×D47—48no—
328C22×D47—42no—
329C22×D47—42no—
330C22×D47—42no—
331C22×D47—84no—
332C22×D47—84no—
333C22×D47—816no—
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—
346D4×C47—84no—
347C2×C4×C47—22no—
348C2×C4×C47—24no—
349C2×C4×C47—22no—
350C2×C4×C47—22no—
351C2×C4×C47—22no—
352C2×C4×C47—22no—
353C2×C4×C47—48no—
354C2×C4×C47—42no—
355C2×C4×C47—42no—
356C2×C4×C47C22×D412yes—
357C2×C4×C47C22×D411yescharacteristic
358C2×C4×C47H(5,𝔽2)12yes—
359C2×C4×C47H(5,𝔽2)12yes—
360C2×C4×C47C2511yescharacteristic
361C22⋊D47—44no—
362C22⋊D47—44no—
363C22⋊D47—48no—
364C22⋊D47—84no—
365C22⋊D47—84no—
366C22⋊D47—84no—
367C22⋊D47—84no—
368C2×Dic47—22no—
369C2×Dic47—22no—
370C2×Dic47—22no—
371C2×Dic47—22no—
372C2×Dic47—22no—
373C2×Dic47—42no—
374C2×Dic47—42no—
375C2×Dic47—42no—
376C2×Dic47—84no—
377C2×Dic47C22×D412yes—
378C2×Dic47C22×D412yes—
379D188—22no—
380D188—22no—
381D188—44no—
382D188—42no—
383D188—84no—
384C4×D47—24no—
385C4×D47—24no—
386C4×D47—22no—
387C4×D47—22no—
388C4×D47—22no—
389C4×D47—22no—
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—84no—
407C22×C47—84no—
408C22×C47#53412yes—
409C22×C47#57612yes—
410C22×C47#57712yes—
411C22×C47C23×D411yescharacteristic
412C2×D47—22no—
413C2×D47—22no—
414C2×D47—22no—
415C2×D47—22no—
416C2×D47—22no—
417C2×D47—22no—
418C2×D47—44no—
419C2×D47—44no—
420C2×D47—42no—
421C2×D47—42no—
422C2×D47—42no—
423C2×D47—816no—
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×#449D4711yescharacteristic, complemented
449C2×#450—471no—
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×#41C2×D4711yescharacteristic, complemented
464C23×D4—471no—
465C22×SD16—471no—
466C22×SD16C2×D4711yescharacteristic
467C22×D8—471no—
468C22×D8C2×D4711yescharacteristic
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⋊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#450—478no—
502#449—478no—
503#449C2×D4718yescomplemented
504#447—478no—
505C2×#107—471no—
506C2×#107—471no—
507C2×#106—471no—
508C2×#106—471no—
509C2×#103—471no—
510C2×#103C2×D4711yescharacteristic, complemented
511C2×#102—471no—
512C2×#102—471no—
513C2×#102—471no—
514C2×#102—471no—
515C2×#102—471no—
516C2×#102C2×D4711yescharacteristic, complemented
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—22no—
525C2×#41—42no—
526C2×#41—42no—
527C2×#41—474no—
528C2×#41—474no—
529C2×#41—1882no—
530C2×#41—1882no—
531C2×#41C22×D4714yescomplemented
532C22×Q8—471no—
533C22×Q8C22×D4711yescharacteristic
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—471no—
537C22×D4—471no—
538C22×D4—474no—
539C22×D4—471no—
540C22×D4—471no—
541C22×D4—941no—
542C22×D4—942no—
543C22×D4—941no—
544C22×D4—941no—
545C22×D4—941no—
546C22×D4—941no—
547C22×D4—941no—
548C22×D4—1882no—
549C22×D4—1882no—
550C22×D4C22×D4711yescharacteristic
551C22×D4C22×D4711yescharacteristic
552C23×C4—21no—
553C23×C4—471no—
554C23×C4—471no—
555C23×C4—941no—
556C23×C4C22×D4711yescharacteristic
557C2×SD16—42no—
558C2×SD16—474no—
559C2×SD16—1882no—
560C2×SD16C22×D4714yes—
561C2×D8—42no—
562C2×D8—474no—
563C2×D8—1882no—
564C2×D8C22×D4714yes—
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—948no—
578C22⋊Q8—942no—
579C22⋊Q8—942no—
580#121—22no—
581#121—474no—
582#121—474no—
583#121—474no—
584#121—474no—
585#121—474no—
586#121—942no—
587#121—948no—
588#121—942no—
589#121—942no—
590#121—942no—
591#121—948no—
592#121—948no—
593#121—942no—
594#121C22×D4714yes—
595#120—948no—
596#120—948no—
597#117—474no—
598#117—942no—
599C2×C4⋊C4—471no—
600C2×C4⋊C4—471no—
601C2×C4⋊C4—474no—
602C2×C4⋊C4—471no—
603C2×C4⋊C4—941no—
604C2×C4⋊C4—941no—
605C2×C4⋊C4—941no—
606C2×C4⋊C4—942no—
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#103C22×D4714yescomplemented
624#102—474no—
625#102—474no—
626#102—474no—
627#102—474no—
628#102—474no—
629#102C22×D4714yescomplemented
630C22⋊C8—474no—
631C22⋊C8—474no—
632C22⋊C8—474no—
633C22⋊C8C22×D4714yescomplemented
634C24—21no—
635C24—21no—
636C24—471no—
637C24—471no—
638C24—944no—
639C24—941no—
640C24—3762no—
641C24—3762no—
642C24—1884no—
643C24D4×D4711yescharacteristic
644#41—44no—
645#41—44no—
646#41—48no—
647#41—1888no—
648#41—1884no—
649#41—1884no—
650C2×Q8—21no—
651C2×Q8—22no—
652C2×Q8—22no—
653C2×Q8—474no—
654C2×Q8—1882no—
655C2×Q8C23×D4712yes—
656C2×D4—24no—
657C2×D4—24no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—22no—
663C2×D4—22no—
664C2×D4—44no—
665C2×D4—82no—
666C2×D4—474no—
667C2×D4—474no—
668C2×D4—474no—
669C2×D4—472no—
670C2×D4—944no—
671C2×D4—944no—
672C2×D4—944no—
673C2×D4—944no—
674C2×D4—944no—
675C2×D4—944no—
676C2×D4—941no—
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×D4C23×D4712yes—
692C2×D4C23×D4712yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—24no—
698C22×C4—44no—
699C22×C4—471no—
700C22×C4—471no—
701C22×C4—472no—
702C22×C4—472no—
703C22×C4—472no—
704C22×C4—472no—
705C22×C4—942no—
706C22×C4—942no—
707C22×C4—942no—
708C22×C4—942no—
709C22×C4—944no—
710C22×C4—941no—
711C22×C4—941no—
712C22×C4—941no—
713C22×C4—3762no—
714C22×C4D4×D4712yes—
715C22×C4D4×D4711yescharacteristic
716C22×C4C23×D4712yes—
717C22×C4C23×D4711yescharacteristic
718SD16—44no—
719SD16—1884no—
720D8—44no—
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—472no—
734C4⋊C4—472no—
735C4⋊C4—472no—
736C4⋊C4—944no—
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—42no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—472no—
765C23—472no—
766C23—942no—
767C23—942no—
768C23—942no—
769C23—942no—
770C23—942no—
771C23—942no—
772C23—942no—
773C23—3764no—
774C23—3764no—
775C23—37616no—
776C23—1888no—
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—84no—
794D4—942no—
795D4—942no—
796D4—3764no—
797D4—3764no—
798D4—3764no—
799D4—3764no—
800D4—3764no—
801D4—1884no—
802D4—1884no—
803D4—1884no—
804D4—1888no—
805D4—1882no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—48no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—472no—
816C2×C4—472no—
817C2×C4—942no—
818C2×C4—942no—
819C2×C4—944no—
820C2×C4—944no—
821C2×C4—942no—
822C2×C4—942no—
823C2×C4—942no—
824C2×C4—942no—
825C2×C4—942no—
826C2×C4—942no—
827C2×C4—942no—
828C2×C4—3764no—
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—84no—
852C22—84no—
853C22—942no—
854C22—942no—
855C22—942no—
856C22—942no—
857C22—942no—
858C22—942no—
859C22—37616no—
860C22—3764no—
861C22—1882no—
862C22—1882no—
863C22—1882no—
864C22—1884no—
865C22—1884no—
866C22#1568968312yes—
867C22#1568992712yes—
868C22#1568993012yes—
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#2025423914yesdirect product factor
888C2C2×#1568968311yescharacteristic
889C2C2×#1568992711yescharacteristic
890C2C2×#1568993011yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#449C2
socleC23×C47C22×D4
hypercenterC2×#449D47
hypocenterC47C2×#3198
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#15689701C2semidirect
2. C2×#15689689C2semidirect
3. #20254239C2direct (N × H)
4. C2×#15689442C2semidirect
5. C2×#15689462C2semidirect
6. C2×#15689446C2semidirect
7. C2×#15689434C2semidirect
8. C2×#15689373C2semidirect
9. C2×#15689372C2semidirect
10. C2×#15689358C2semidirect
11. C2×#15689349C2semidirect
12. C2×#15689268C2semidirect
13. C2×#15689272C2semidirect
14. C2×#15689255C2semidirect
15. C2×#15689088C2semidirect
16. C2×C47×#449C2semidirect
21. C22×#10625324C22semidirect
22. C22×C8×D47C22semidirect
24. #15689701C22semidirect
26. #15689689C22semidirect
31. C2×#13094000C22semidirect
39. C2×#13093995C22semidirect
43. C22×C4⋊Dic47C22semidirect
44. #15689462C22semidirect
45. #15689446C22semidirect
46. #15689442C22semidirect
47. #15689434C22semidirect
48. #15689373C22semidirect
49. #15689372C22semidirect
50. #15689358C22semidirect
51. #15689349C22semidirect
52. #15689272C22semidirect
53. #15689268C22semidirect
54. #15689255C22semidirect
55. C2×#13093957C22semidirect
56. C2×#13093957C22semidirect
57. C2×#13093956C22semidirect
58. C2×#13093956C22semidirect
59. C2×#13093948C22semidirect
64. C2×#13093945C22semidirect
65. #15689088C22semidirect
66. C2×C22⋊(C47⋊C8)C22semidirect
69. C22×#41×C47C22semidirect
73. C47×#449C22semidirect
74. C2×#103×C47C22semidirect
75. C2×#102×C47C22semidirect
76. C2×C22⋊C8×C47C22semidirect
105. C2×#10625324C23semidirect
109. C2×C8×D47C23semidirect
116. #13094000C23semidirect
129. #13093995C23semidirect
139. C2×C4⋊Dic47C23semidirect
151. #13093957C23semidirect
152. #13093957C23semidirect
153. #13093956C23semidirect
154. #13093956C23semidirect
155. #13093948C23semidirect
160. #13093945C23semidirect
161. C22⋊(C47⋊C8)C23semidirect
167. C2×#41×C47C23semidirect
185. #103×C47C23semidirect
186. #102×C47C23semidirect
187. C22⋊C8×C47C23semidirect
448. C2×#449D47semidirect
455. C2×C47#3198semidirect
463. C22×#41C2×D47semidirect
503. #449C2×D47semidirect
510. C2×#103C2×D47semidirect
516. C2×#102C2×D47semidirect
521. C2×C22⋊C8C2×D47semidirect
522. C47C2×#3198semidirect
531. C2×#41C22×D47semidirect
623. #103C22×D47semidirect
629. #102C22×D47semidirect
633. C22⋊C8C22×D47semidirect
887. C2#20254239direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897012
C2×#156896892
#202542392
C2×#156894422
C2×#156894622
C2×#156894462
C2×#156894342
C2×#156893732
C2×#156893722
C2×#156893582
C2×#156893492
C2×#156892682
C2×#156892722
C2×#156892552
C2×#156890882
C2×C47×#4492
C2×#319847