Finite Group Databasebeta

← C2×#20254294 #27086991

Subgroups — C2×#20254294 #27086991

Order 12032.

2250 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689701C211yesmaximal, characteristic, complemented
2#20254294C2116yesmaximal, direct product factor
3C2×#15689441C211yesmaximal, characteristic, complemented
4C2×#15689439C211yesmaximal, characteristic, complemented
5C2×#15689453C211yesmaximal, characteristic, complemented
6C2×#15689451C211yesmaximal, characteristic, complemented
7C2×#15689379C211yesmaximal, characteristic, complemented
8C2×#15689374C211yesmaximal, characteristic, complemented
9C2×#15689354C211yesmaximal, characteristic, complemented
10C2×#15689350C211yesmaximal, characteristic, complemented
11C2×#15689285C211yesmaximal, characteristic, complemented
12C2×#15689283C211yesmaximal, characteristic, complemented
13C2×#15689268C211yesmaximal, characteristic, complemented
14C2×#15689266C211yesmaximal, characteristic, complemented
15C2×#15689090C211yesmaximal, characteristic, complemented
16C2×C47×#537C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C22×#10625337C2211yescharacteristic
19C22×#10625335C2211yescharacteristic
20C22×#10625336C2211yescharacteristic
21C22×#10625334C2211yescharacteristic
22C22×#10625329C2211yescharacteristic
23C23×C47⋊C8C2211yescharacteristic
24#15689701—24no—
25#15689701C2218yescomplemented
26C2×#13094003C2211yescharacteristic
27C2×#13094003C2211yescharacteristic
28C2×#13094000—21no—
29C2×#13093998C2211yescharacteristic
30C2×#13093998C2211yescharacteristic
31C2×#13093996—21no—
32C2×#13093996—21no—
33C2×#13093995—21no—
34C22×C4⋊Dic47C2211yescharacteristic
35#15689453C2218yescomplemented
36#15689451C2218yescomplemented
37#15689441C2218yescomplemented
38#15689439C2218yescomplemented
39#15689379C2218yescomplemented
40#15689374C2218yescomplemented
41#15689354C2218yescomplemented
42#15689350C2218yescomplemented
43#15689285C2218yescomplemented
44#15689283C2218yescomplemented
45#15689268C2218yescomplemented
46#15689266C2218yescomplemented
47C2×#13093955C2211yescharacteristic
48C2×#13093955C2211yescharacteristic
49C2×#13093955C2211yescharacteristic
50C2×#13093955C2211yescharacteristic
51C2×#13093948C2211yescharacteristic
52C2×#13093948C2211yescharacteristic
53C2×#13093947C2211yescharacteristic
54C2×#13093947C2211yescharacteristic
55C2×#13093945C2211yescharacteristic
56C2×#13093945C2211yescharacteristic
57C2×#13093944C2211yescharacteristic
58C2×#13093944C2211yescharacteristic
59#15689090C2218yescomplemented
60C2×C22⋊(C47⋊C8)C2211yescharacteristic
61C2×C22⋊(C47⋊C8)C2211yescharacteristic
62C2×C22⋊(C47⋊C8)C2211yescharacteristic
63C2×C22⋊(C47⋊C8)C2211yescharacteristic
64C22×#41×C47C2211yescharacteristic
65C22×#41×C47C2211yescharacteristic
66C47×#537—24no—
67C47×#537C2218yescomplemented
68C2×C22⋊Q8×C47—21no—
69C2×C22⋊Q8×C47C2211yescharacteristic
70C2×C22⋊Q8×C47C2211yescharacteristic
71C2×#121×C47—21no—
72C2×#121×C47—21no—
73C2×#121×C47—21no—
74C2×#121×C47C2211yescharacteristic
75C2×#121×C47C2211yescharacteristic
76C22×C4⋊C4×C47C2211yescharacteristic
77C2×#10625350—22no—
78C2×#10625350—42no—
79C2×#10625350—42no—
80C2×#10625350C2314yes—
81C22×Dic94C2311yescharacteristic
82C22×D188C2311yescharacteristic
83C22×C22⋊D47—21no—
84C22×C22⋊D47—21no—
85C22×C22⋊D47—21no—
86C23×Dic47—21no—
87C22×C4×D47—21no—
88C2×#10625337—42no—
89C2×#10625337C2314yes—
90C2×#10625335—42no—
91C2×#10625335C2314yes—
92C2×#10625336—42no—
93C2×#10625336C2314yes—
94C2×#10625334—42no—
95C2×#10625334C2314yes—
96C2×#10625329—42no—
97C2×#10625329C2314yes—
98C22×C47⋊C8—42no—
99C22×C47⋊C8C2311yescharacteristic
100C22×C47⋊C8C2311yescharacteristic
101C22×C47⋊C8C2311yescharacteristic
102C22×C47⋊C8C2311yescharacteristic
103C22×C47⋊C8C2314yes—
104#13094003—22no—
105#13094003—22no—
106#13094003C2314yes—
107#13094003C2314yes—
108#13094000—28no—
109#13093998—22no—
110#13093998—22no—
111#13093998C2314yes—
112#13093998C2314yes—
113#13093996—28no—
114#13093996—28no—
115#13093995—28no—
116C2×C4⋊Dic47—21no—
117C2×C4⋊Dic47—22no—
118C2×C4⋊Dic47C2311yescharacteristic
119C2×C4⋊Dic47C2311yescharacteristic
120C2×C4⋊Dic47C2314yes—
121C2×Dic47⋊C4—21no—
122C2×Dic47⋊C4—21no—
123C2×C22⋊Dic47—21no—
124C2×C22⋊Dic47—21no—
125C2×(C2×D47)⋊C4—21no—
126C2×(C2×D47)⋊C4—21no—
127#13093955C2314yes—
128#13093955C2314yes—
129#13093955C2314yes—
130#13093955C2314yes—
131#13093948C2314yes—
132#13093948C2314yes—
133#13093947C2314yes—
134#13093947C2314yes—
135#13093945C2314yes—
136#13093945C2314yes—
137#13093944C2314yes—
138#13093944C2314yes—
139C22⋊(C47⋊C8)C2314yes—
140C22⋊(C47⋊C8)C2314yes—
141C22⋊(C47⋊C8)C2314yes—
142C22⋊(C47⋊C8)C2314yes—
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×C47C2314yes—
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×C47C2314yes—
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×C47C2314yes—
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×C47C2314yes—
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—
193#41×C47—48no—
194#41×C47—44no—
195#41×C47—44no—
196#41×C47—44no—
197#41×C47—44no—
198#41×C47—48no—
199C2×Q8×C47—21no—
200C2×Q8×C47—22no—
201C2×Q8×C47—22no—
202C2×Q8×C47—42no—
203C2×Q8×C47C2×D414yes—
204C2×Q8×C47C2412yes—
205C2×D4×C47—24no—
206C2×D4×C47—24no—
207C2×D4×C47—24no—
208C2×D4×C47—21no—
209C2×D4×C47—22no—
210C2×D4×C47—22no—
211C2×D4×C47—42no—
212C2×D4×C47—42no—
213C2×D4×C47—42no—
214C2×D4×C47—44no—
215C2×D4×C47—82no—
216C2×D4×C47—82no—
217C2×D4×C47C2×D414yes—
218C2×D4×C47C2×D414yes—
219C2×D4×C47C2×D414yes—
220C2×D4×C47C2412yes—
221C22×C4×C47—22no—
222C22×C4×C47—22no—
223C22×C4×C47—22no—
224C22×C4×C47—22no—
225C22×C4×C47—22no—
226C22×C4×C47—22no—
227C22×C4×C47—21no—
228C22×C4×C47—21no—
229C22×C4×C47—21no—
230C22×C4×C47—24no—
231C22×C4×C47—24no—
232C22×C4×C47—44no—
233C22×C4×C47—82no—
234C22×C4×C47C2×D411yescharacteristic
235C22×C4×C47C2×D411yescharacteristic
236C22×C4×C47C2×D411yescharacteristic
237C22×C4×C47C2×D412yes—
238C22×C4×C47C2×D412yes—
239C22×C4×C47C2×D412yes—
240C22×C4×C47C2412yes—
241C22×C4×C47C2412yes—
242C22×C4×C47C2412yes—
243C22×C4×C47C2411yescharacteristic
244C2×C22⋊D47—24no—
245C2×C22⋊D47—24no—
246C2×C22⋊D47—24no—
247C2×C22⋊D47—44no—
248C2×C22⋊D47—82no—
249C2×C22⋊D47—82no—
250C22×Dic47—21no—
251C22×Dic47—21no—
252C22×Dic47—21no—
253C22×Dic47—24no—
254C22×Dic47—82no—
255#10625350—44no—
256#10625350—44no—
257#10625350—48no—
258C2×D188—22no—
259C2×D188—22no—
260C2×D188—21no—
261C2×D188C2412yes—
262C2×C4×D47—24no—
263C2×C4×D47—44no—
264C2×Dic94—22no—
265C2×Dic94—22no—
266C2×Dic94—21no—
267C2×Dic94C2412yes—
268C4⋊C4×C47—24no—
269C4⋊C4×C47—21no—
270C4⋊C4×C47—21no—
271C4⋊C4×C47—24no—
272C4⋊C4×C47—24no—
273C4⋊C4×C47C2412yes—
274C4⋊C4×C47C2412yes—
275C22⋊C4×C47—24no—
276C22⋊C4×C47—24no—
277C22⋊C4×C47—24no—
278C22⋊C4×C47—24no—
279C22⋊Dic47—24no—
280C22⋊Dic47—24no—
281#10625337—44no—
282#10625336—44no—
283#10625335—44no—
284#10625334—44no—
285(C2×D47)⋊C4—24no—
286(C2×D47)⋊C4—24no—
287C4⋊Dic47—24no—
288C4⋊Dic47—21no—
289C4⋊Dic47—21no—
290C4⋊Dic47C2412yes—
291C4⋊Dic47C2412yes—
292Dic47⋊C4—24no—
293Dic47⋊C4—24no—
294#10625329—44no—
295C2×C47⋊C8—22no—
296C2×C47⋊C8—22no—
297C2×C47⋊C8—22no—
298C2×C47⋊C8—22no—
299C2×C47⋊C8—44no—
300C2×C47⋊C8C2412yes—
301C2×C47⋊C8C2412yes—
302C2×C47⋊C8C2412yes—
303C2×C47⋊C8C2412yes—
304C23×C47—22no—
305C23×C47—22no—
306C23×C47—22no—
307C23×C47—22no—
308C23×C47—22no—
309C23×C47—22no—
310C23×C47—22no—
311C23×C47—22no—
312C23×C47—22no—
313C23×C47—22no—
314C23×C47—42no—
315C23×C47—42no—
316C23×C47—42no—
317C23×C47C22×D412yes—
318C23×C47C22×D412yes—
319C23×C47C22×D412yes—
320C23×C47C22×D411yescharacteristic
321C22×D47—22no—
322C22×D47—42no—
323C22×D47—42no—
324C22×D47—42no—
325Q8×C47—22no—
326Q8×C47—22no—
327Q8×C47—44no—
328Q8×C47—42no—
329D4×C47—22no—
330D4×C47—22no—
331D4×C47—44no—
332D4×C47—44no—
333D4×C47—44no—
334D4×C47—48no—
335D4×C47—42no—
336D4×C47—84no—
337D4×C47—84no—
338C2×C4×C47—22no—
339C2×C4×C47—22no—
340C2×C4×C47—22no—
341C2×C4×C47—24no—
342C2×C4×C47—24no—
343C2×C4×C47—24no—
344C2×C4×C47—22no—
345C2×C4×C47—22no—
346C2×C4×C47—22no—
347C2×C4×C47—22no—
348C2×C4×C47—22no—
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×C47—42no—
357C2×C4×C47—84no—
358C2×C4×C47C22×D412yes—
359C2×C4×C47C22×D412yes—
360C2×C4×C47C22×D412yes—
361C2×C4×C47C22×D411yescharacteristic
362C2×C4×C47H(5,𝔽2)12yes—
363C2×C4×C47H(5,𝔽2)12yes—
364C2×C4×C47C2511yescharacteristic
365C22⋊D47—48no—
366C22⋊D47—84no—
367C22⋊D47—84no—
368C2×Dic47—22no—
369C2×Dic47—22no—
370C2×Dic47—22no—
371C2×Dic47—42no—
372C2×Dic47—42no—
373C2×Dic47—42no—
374C2×Dic47—84no—
375D188—22no—
376D188—22no—
377D188—42no—
378C4×D47—48no—
379Dic94—22no—
380Dic94—22no—
381Dic94—42no—
382C47⋊C8—22no—
383C47⋊C8—22no—
384C47⋊C8—22no—
385C47⋊C8—22no—
386C2×#3204—471nomaximal, Sylow
387C22×C47—22no—
388C22×C47—22no—
389C22×C47—22no—
390C22×C47—22no—
391C22×C47—22no—
392C22×C47—22no—
393C22×C47—22no—
394C22×C47—22no—
395C22×C47—22no—
396C22×C47—44no—
397C22×C47—44no—
398C22×C47—44no—
399C22×C47—42no—
400C22×C47—42no—
401C22×C47—42no—
402C22×C47—84no—
403C22×C47#53412yes—
404C22×C47#57712yes—
405C22×C47#57712yes—
406C22×C47C23×D411yescharacteristic
407C2×D47—42no—
408C2×D47—42no—
409C2×D47—42no—
410C2×D47—84no—
411C4×C47—22no—
412C4×C47—22no—
413C4×C47—22no—
414C4×C47—42no—
415C4×C47—42no—
416C4×C47—42no—
417C4×C47#53412yes—
418C4×C47C2×H(5,𝔽2)11yescharacteristic
419C4×C47C2×H(5,𝔽2)11yescharacteristic
420Dic47—42no—
421Dic47—42no—
422Dic47—42no—
423C2×#537—471no—
424C2×#537D4711yescharacteristic, complemented
425#3204—4716no—
426C2×#481—471no—
427C2×#481—471no—
428C2×#483—471no—
429C2×#483—471no—
430C2×#470—471no—
431C2×#469—471no—
432C2×#465—471no—
433C2×#465—471no—
434C2×#452—471no—
435C2×#452—471no—
436C2×#449—471no—
437C2×#449—471no—
438C2×#408—471no—
439C2×C47—42no—
440C2×C47—42no—
441C2×C47—42no—
442C2×C47—82no—
443C2×C47#320414yescomplemented
444C2×C47C2×#53411yescharacteristic
445C2×C47C2×#57711yescharacteristic
446C2×C47C2×#57711yescharacteristic
447D47—82no—
448C22×#41—471no—
449C22×#41C2×D4711yescharacteristic
450C22×#41C2×D4711yescharacteristic
451C22×Q16—471no—
452C22×SD16—471no—
453C22×SD16—471no—
454C22×D8—471no—
455C22×M16—471no—
456C23×C8—471no—
457#537—24no—
458#537—478no—
459#537—944no—
460#537C2×D4718yescomplemented
461C2×C22⋊Q8—21no—
462C2×C22⋊Q8—471no—
463C2×C22⋊Q8—471no—
464C2×C22⋊Q8—941no—
465C2×C22⋊Q8C2×D4711yescharacteristic
466C2×C22⋊Q8C2×D4711yescharacteristic
467C2×#121—21no—
468C2×#121—21no—
469C2×#121—21no—
470C2×#121—471no—
471C2×#121—471no—
472C2×#121—941no—
473C2×#121—941no—
474C2×#121—941no—
475C2×#121C2×D4711yescharacteristic
476C2×#121C2×D4711yescharacteristic
477C22×C4⋊C4—471no—
478C22×C4⋊C4C2×D4711yescharacteristic
479#483—478no—
480#483—478no—
481#481—478no—
482#481—478no—
483#470—478no—
484#469—478no—
485#465—478no—
486#465—478no—
487#452—478no—
488#452—478no—
489#449—478no—
490#449—478no—
491C2×#106—471no—
492C2×#106—471no—
493C2×#106—471no—
494C2×#106—471no—
495C2×#103—471no—
496C2×#103—471no—
497C2×#103—471no—
498C2×#103—471no—
499C2×#102—471no—
500C2×#102—471no—
501C2×#102—471no—
502C2×#102—471no—
503#408—478no—
504C2×C22⋊C8—471no—
505C2×C22⋊C8—471no—
506C2×C22⋊C8—471no—
507C2×C22⋊C8—471no—
508C47C2×#320411yescharacteristic, complemented, Sylow
509C2×#41—22no—
510C2×#41—42no—
511C2×#41—42no—
512C2×#41—42no—
513C2×#41—42no—
514C2×#41—474no—
515C2×#41—942no—
516C2×#41—1882no—
517C2×#41—1882no—
518C2×#41C22⋊D4714yes—
519C2×#41C22×D4714yes—
520C2×#41C22×D4714yes—
521C22×Q8—471no—
522C22×Q8C22⋊D4711yescharacteristic
523C22×Q8C22×D4711yescharacteristic
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—471no—
528C22×D4—941no—
529C22×D4—941no—
530C22×D4—941no—
531C22×D4C22⋊D4711yescharacteristic
532C22×D4C22⋊D4711yescharacteristic
533C22×D4C22⋊D4711yescharacteristic
534C22×D4C22×D4711yescharacteristic
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—941no—
538C23×C4—941no—
539C23×C4C22×D4711yescharacteristic
540C23×C4C22×D4711yescharacteristic
541C23×C4C22×D4711yescharacteristic
542C2×Q16—474no—
543C2×Q16—1882no—
544C2×SD16—474no—
545C2×SD16—474no—
546C2×SD16—1882no—
547C2×SD16—1882no—
548C2×D8—474no—
549C2×D8—1882no—
550C2×M16—474no—
551C2×M16—1882no—
552C22×C8—471no—
553C22×C8—471no—
554C22×C8—471no—
555C22×C8—471no—
556C22×C8—474no—
557C22×C8—1882no—
558C22⋊Q8—28no—
559C22⋊Q8—22no—
560C22⋊Q8—22no—
561C22⋊Q8—474no—
562C22⋊Q8—474no—
563C22⋊Q8—948no—
564C22⋊Q8—942no—
565C22⋊Q8—942no—
566C22⋊Q8C22×D4714yes—
567C22⋊Q8C22×D4714yes—
568#121—28no—
569#121—28no—
570#121—28no—
571#121—22no—
572#121—22no—
573#121—474no—
574#121—474no—
575#121—948no—
576#121—948no—
577#121—948no—
578#121—942no—
579#121—942no—
580#121C22×D4714yes—
581#121C22×D4714yes—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—471no—
587C2×C4⋊C4—471no—
588C2×C4⋊C4—474no—
589C2×C4⋊C4—941no—
590C2×C4⋊C4—942no—
591C2×C4⋊C4—941no—
592C2×C4⋊C4—941no—
593C2×C4⋊C4C22×D4711yescharacteristic
594C2×C4⋊C4C22×D4711yescharacteristic
595C2×C4⋊C4C22×D4714yes—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—941no—
601C2×C22⋊C4—941no—
602C2×C22⋊C4—941no—
603C2×C22⋊C4—941no—
604#106—474no—
605#106—474no—
606#106—474no—
607#106—474no—
608#103—474no—
609#103—474no—
610#103—474no—
611#103—474no—
612#102—474no—
613#102—474no—
614#102—474no—
615#102—474no—
616C22⋊C8—474no—
617C22⋊C8—474no—
618C22⋊C8—474no—
619C22⋊C8—474no—
620C24—21no—
621C24—941no—
622C24C2×C22⋊D4711yescharacteristic
623C24C2×C22⋊D4711yescharacteristic
624C24C2×C22⋊D4711yescharacteristic
625#41—48no—
626#41—44no—
627#41—44no—
628#41—44no—
629#41—44no—
630#41—48no—
631#41—1884no—
632#41—1884no—
633#41—1888no—
634C2×Q8—21no—
635C2×Q8—22no—
636C2×Q8—22no—
637C2×Q8—42no—
638C2×Q8—472no—
639C2×Q8—941no—
640C2×Q8—942no—
641C2×Q8—942no—
642C2×Q8C2×C22⋊D4714yes—
643C2×Q8C23×D4712yes—
644C2×D4—24no—
645C2×D4—24no—
646C2×D4—24no—
647C2×D4—21no—
648C2×D4—22no—
649C2×D4—22no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—44no—
654C2×D4—82no—
655C2×D4—82no—
656C2×D4—472no—
657C2×D4—944no—
658C2×D4—944no—
659C2×D4—944no—
660C2×D4—941no—
661C2×D4—942no—
662C2×D4—942no—
663C2×D4—3762no—
664C2×D4—3762no—
665C2×D4—1884no—
666C2×D4C2×C22⋊D4714yes—
667C2×D4C2×C22⋊D4714yes—
668C2×D4C2×C22⋊D4714yes—
669C2×D4C23×D4712yes—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—24no—
680C22×C4—24no—
681C22×C4—44no—
682C22×C4—82no—
683C22×C4—944no—
684C22×C4—941no—
685C22×C4—941no—
686C22×C4—941no—
687C22×C4—944no—
688C22×C4—3762no—
689C22×C4—1884no—
690C22×C4C2×C22⋊D4712yes—
691C22×C4C2×C22⋊D4712yes—
692C22×C4C2×C22⋊D4712yes—
693C22×C4C2×C22⋊D4711yescharacteristic
694C22×C4C2×C22⋊D4711yescharacteristic
695C22×C4C2×C22⋊D4711yescharacteristic
696C22×C4C23×D4712yes—
697C22×C4C23×D4712yes—
698C22×C4C23×D4712yes—
699C22×C4C23×D4711yescharacteristic
700Q16—1884no—
701SD16—1884no—
702SD16—1884no—
703D8—1884no—
704M16—1884no—
705C2×C8—472no—
706C2×C8—472no—
707C2×C8—472no—
708C2×C8—472no—
709C2×C8—942no—
710C2×C8—942no—
711C2×C8—942no—
712C2×C8—942no—
713C2×C8—1884no—
714C4⋊C4—24no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—24no—
718C4⋊C4—24no—
719C4⋊C4—472no—
720C4⋊C4—472no—
721C4⋊C4—944no—
722C4⋊C4—944no—
723C4⋊C4—944no—
724C4⋊C4—941no—
725C4⋊C4—941no—
726C4⋊C4C23×D4712yes—
727C4⋊C4C23×D4712yes—
728C22⋊C4—24no—
729C22⋊C4—24no—
730C22⋊C4—24no—
731C22⋊C4—24no—
732C22⋊C4—944no—
733C22⋊C4—944no—
734C22⋊C4—944no—
735C22⋊C4—944no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—942no—
750C23—1882no—
751C23—1882no—
752C23—1882no—
753C23C22×C22⋊D4712yes—
754C23C22×C22⋊D4712yes—
755C23C22×C22⋊D4712yes—
756C23C22×C22⋊D4711yescharacteristic
757Q8—22no—
758Q8—22no—
759Q8—44no—
760Q8—42no—
761Q8—942no—
762Q8—942no—
763Q8—1882no—
764D4—22no—
765D4—22no—
766D4—44no—
767D4—44no—
768D4—44no—
769D4—48no—
770D4—42no—
771D4—84no—
772D4—84no—
773D4—942no—
774D4—942no—
775D4—3764no—
776D4—3764no—
777D4—1888no—
778D4—1882no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—48no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—84no—
799C2×C4—942no—
800C2×C4—942no—
801C2×C4—942no—
802C2×C4—3764no—
803C2×C4—1888no—
804C2×C4—1882no—
805C2×C4—1882no—
806C2×C4—1882no—
807C2×C4C22×C22⋊D4712yes—
808C2×C4C22×C22⋊D4712yes—
809C2×C4C22×C22⋊D4712yes—
810C2×C4C22×C22⋊D4711yescharacteristic
811C2×C4#1309406912yes—
812C2×C4#1309406912yes—
813C2×C4C24×D4711yescharacteristic
814C8—942no—
815C8—942no—
816C8—942no—
817C8—942no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—44no—
828C22—44no—
829C22—44no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—84no—
834C22—3764no—
835C22—1882no—
836C22—1882no—
837C22—1882no—
838C22#1568968212yes—
839C22#1568993112yes—
840C22#1568993412yes—
841C22C23×C22⋊D4711yescharacteristic
842C4—22no—
843C4—22no—
844C4—22no—
845C4—42no—
846C4—42no—
847C4—42no—
848C4—1882no—
849C4—1882no—
850C4—1882no—
851C4#1568968212yes—
852C4C2×#1309406911yescharacteristic
853C4C2×#1309406911yescharacteristic
854C2—42no—
855C2—42no—
856C2—42no—
857C2—82no—
858C2—3762no—
859C2#2025429414yesdirect product factor
860C2C2×#1568968211yescharacteristic
861C2C2×#1568993111yescharacteristic
862C2C2×#1568993411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#537C2
socleC23×C47C22×D4
hypercenterC2×#537D47
hypocenterC47C2×#3204
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×#15689701C2semidirect
2. #20254294C2direct (N × H)
3. C2×#15689441C2semidirect
4. C2×#15689439C2semidirect
5. C2×#15689453C2semidirect
6. C2×#15689451C2semidirect
7. C2×#15689379C2semidirect
8. C2×#15689374C2semidirect
9. C2×#15689354C2semidirect
10. C2×#15689350C2semidirect
11. C2×#15689285C2semidirect
12. C2×#15689283C2semidirect
13. C2×#15689268C2semidirect
14. C2×#15689266C2semidirect
15. C2×#15689090C2semidirect
16. C2×C47×#537C2semidirect
25. #15689701C22semidirect
35. #15689453C22semidirect
36. #15689451C22semidirect
37. #15689441C22semidirect
38. #15689439C22semidirect
39. #15689379C22semidirect
40. #15689374C22semidirect
41. #15689354C22semidirect
42. #15689350C22semidirect
43. #15689285C22semidirect
44. #15689283C22semidirect
45. #15689268C22semidirect
46. #15689266C22semidirect
59. #15689090C22semidirect
67. C47×#537C22semidirect
424. C2×#537D47semidirect
443. C2×C47#3204semidirect
460. #537C2×D47semidirect
508. C47C2×#3204semidirect
859. C2#20254294direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897012
#202542942
C2×#156894412
C2×#156894392
C2×#156894532
C2×#156894512
C2×#156893792
C2×#156893742
C2×#156893542
C2×#156893502
C2×#156892852
C2×#156892832
C2×#156892682
C2×#156892662
C2×#156890902
C2×C47×#5372
C2×#320447