Finite Group Databasebeta

← C2×#20254270 #27086964

Subgroups — C2×#20254270 #27086964

Order 12032.

2186 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689701C211yesmaximal, characteristic
2#20254270C2116yesmaximal, direct product factor
3C2×#15689456C211yesmaximal, characteristic, complemented
4C2×#15689464C211yesmaximal, characteristic, complemented
5C2×#15689447C211yesmaximal, characteristic, complemented
6C2×#15689451C211yesmaximal, characteristic, complemented
7C2×#15689379C211yesmaximal, characteristic, complemented
8C2×#15689371C211yesmaximal, characteristic, complemented
9C2×#15689362C211yesmaximal, characteristic, complemented
10C2×#15689354C211yesmaximal, characteristic, complemented
11C2×#15689283C211yesmaximal, characteristic, complemented
12C2×#15689283C211yesmaximal, characteristic, complemented
13C2×#15689279C211yesmaximal, characteristic, complemented
14C2×#15689262C211yesmaximal, characteristic, complemented
15C2×#15689090C211yesmaximal, characteristic, complemented
16C2×C47×#536C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C22×#10625337C2211yescharacteristic
19C22×#10625337C2211yescharacteristic
20C22×#10625336C2211yescharacteristic
21C22×#10625336C2211yescharacteristic
22C22×#10625329C2211yescharacteristic
23C23×C47⋊C8C2211yescharacteristic
24#15689701—24no—
25#15689701C2218yes—
26C2×#13094003C2211yescharacteristic
27C2×#13094003C2211yescharacteristic
28C2×#13094000—21no—
29C2×#13093998C2211yescharacteristic
30C2×#13093998C2211yescharacteristic
31C2×#13093996—21no—
32C2×#13093996—21no—
33C2×#13093995—21no—
34C22×C4⋊Dic47C2211yescharacteristic
35#15689464C2218yescomplemented
36#15689456C2218yescomplemented
37#15689451C2218yescomplemented
38#15689447C2218yescomplemented
39#15689379C2218yescomplemented
40#15689371C2218yescomplemented
41#15689362C2218yescomplemented
42#15689354C2218yescomplemented
43#15689283C2218yescomplemented
44#15689283C2218yescomplemented
45#15689279C2218yescomplemented
46#15689262C2218yescomplemented
47C2×#13093957C2211yescharacteristic
48C2×#13093957C2211yescharacteristic
49C2×#13093955C2211yescharacteristic
50C2×#13093955C2211yescharacteristic
51C2×#13093948C2211yescharacteristic
52C2×#13093948C2211yescharacteristic
53C2×#13093948C2211yescharacteristic
54C2×#13093948C2211yescharacteristic
55C2×#13093947C2211yescharacteristic
56C2×#13093947C2211yescharacteristic
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
65C23×Q8×C47C2211yescharacteristic
66C47×#536—24no—
67C47×#536C2218yescomplemented
68C2×C4⋊Q8×C47—21no—
69C2×#124×C47—21no—
70C2×#123×C47—21no—
71C2×#123×C47—21no—
72C2×C22⋊Q8×C47C2211yescharacteristic
73C2×C22⋊Q8×C47C2211yescharacteristic
74C2×C22⋊Q8×C47C2211yescharacteristic
75C2×C22⋊Q8×C47C2211yescharacteristic
76C2×#117×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×#10625337—42no—
90C2×#10625337C2314yes—
91C2×#10625337C2314yes—
92C2×#10625336—42no—
93C2×#10625336—42no—
94C2×#10625336C2314yes—
95C2×#10625336C2314yes—
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#13093957C2314yes—
128#13093957C2314yes—
129#13093955C2314yes—
130#13093955C2314yes—
131#13093948C2314yes—
132#13093948C2314yes—
133#13093948C2314yes—
134#13093948C2314yes—
135#13093947C2314yes—
136#13093947C2314yes—
137#13093944C2314yes—
138#13093944C2314yes—
139C22⋊(C47⋊C8)C2314yes—
140C22⋊(C47⋊C8)C2314yes—
141C22⋊(C47⋊C8)C2314yes—
142C22⋊(C47⋊C8)C2314yes—
143C2×#41×C47—42no—
144C2×#41×C47—42no—
145C2×#41×C47D414yes—
146C2×#41×C47C2314yes—
147C22×Q8×C47—21no—
148C22×Q8×C47—22no—
149C22×Q8×C47—42no—
150C22×Q8×C47—42no—
151C22×Q8×C47D411yescharacteristic
152C22×Q8×C47C2311yescharacteristic
153C22×Q8×C47C2311yescharacteristic
154C22×Q8×C47C2314yes—
155C22×D4×C47D411yescharacteristic
156C22×D4×C47D411yescharacteristic
157C22×D4×C47D411yescharacteristic
158C23×C4×C47—21no—
159C23×C4×C47C2311yescharacteristic
160C23×C4×C47C2311yescharacteristic
161C23×C4×C47C2311yescharacteristic
162C4⋊Q8×C47—28no—
163#124×C47—28no—
164#123×C47—28no—
165#123×C47—28no—
166C22⋊Q8×C47—22no—
167C22⋊Q8×C47—22no—
168C22⋊Q8×C47—22no—
169C22⋊Q8×C47—22no—
170C22⋊Q8×C47C2314yes—
171C22⋊Q8×C47C2314yes—
172C22⋊Q8×C47C2314yes—
173C22⋊Q8×C47C2314yes—
174#117×C47—22no—
175#117×C47C2314yes—
176C2×C4⋊C4×C47—21no—
177C2×C4⋊C4×C47—21no—
178C2×C4⋊C4×C47—21no—
179C2×C4⋊C4×C47—21no—
180C2×C4⋊C4×C47C2311yescharacteristic
181C2×C4⋊C4×C47C2311yescharacteristic
182C2×C22⋊C4×C47—21no—
183C2×C22⋊C4×C47—21no—
184C2×C22⋊C4×C47—21no—
185C2×C22⋊C4×C47—21no—
186C2×C22⋊C4×C47—21no—
187C2×C42×C47—21no—
188C24×C47C2×D411yescharacteristic
189C24×C47C2×D411yescharacteristic
190C24×C47C2×D411yescharacteristic
191C23×D47—21no—
192#41×C47—48no—
193#41×C47—44no—
194#41×C47—44no—
195C2×Q8×C47—21no—
196C2×Q8×C47—21no—
197C2×Q8×C47—24no—
198C2×Q8×C47—22no—
199C2×Q8×C47—22no—
200C2×Q8×C47—22no—
201C2×Q8×C47—22no—
202C2×Q8×C47—42no—
203C2×Q8×C47—44no—
204C2×Q8×C47—44no—
205C2×Q8×C47—44no—
206C2×Q8×C47—48no—
207C2×Q8×C47C2×D414yes—
208C2×Q8×C47C2412yes—
209C2×Q8×C47C2412yes—
210C2×D4×C47—42no—
211C2×D4×C47—42no—
212C2×D4×C47—42no—
213C2×D4×C47C2×D414yes—
214C2×D4×C47C2×D414yes—
215C2×D4×C47C2×D414yes—
216C22×C4×C47—22no—
217C22×C4×C47—22no—
218C22×C4×C47—22no—
219C22×C4×C47—22no—
220C22×C4×C47—22no—
221C22×C4×C47—22no—
222C22×C4×C47—21no—
223C22×C4×C47—21no—
224C22×C4×C47—21no—
225C22×C4×C47—21no—
226C22×C4×C47—24no—
227C22×C4×C47—44no—
228C22×C4×C47C2×D411yescharacteristic
229C22×C4×C47C2×D411yescharacteristic
230C22×C4×C47C2×D411yescharacteristic
231C22×C4×C47C2×D412yes—
232C22×C4×C47C2×D412yes—
233C22×C4×C47C2×D412yes—
234C22×C4×C47C2412yes—
235C22×C4×C47C2412yes—
236C22×C4×C47C2412yes—
237C22×C4×C47C2411yescharacteristic
238C2×C22⋊D47—24no—
239C2×C22⋊D47—24no—
240C2×C22⋊D47—24no—
241C2×C22⋊D47—44no—
242C2×C22⋊D47—82no—
243C2×C22⋊D47—82no—
244C22×Dic47—21no—
245C22×Dic47—21no—
246C22×Dic47—21no—
247C22×Dic47—24no—
248C22×Dic47—82no—
249#10625350—44no—
250#10625350—44no—
251#10625350—48no—
252C2×D188—22no—
253C2×D188—22no—
254C2×D188—21no—
255C2×D188C2412yes—
256C2×C4×D47—24no—
257C2×C4×D47—44no—
258C2×Dic94—22no—
259C2×Dic94—22no—
260C2×Dic94—21no—
261C2×Dic94C2412yes—
262C4⋊C4×C47—24no—
263C4⋊C4×C47—24no—
264C4⋊C4×C47—24no—
265C4⋊C4×C47—24no—
266C4⋊C4×C47—21no—
267C4⋊C4×C47—21no—
268C4⋊C4×C47C2412yes—
269C4⋊C4×C47C2412yes—
270C22⋊C4×C47—24no—
271C22⋊C4×C47—24no—
272C22⋊C4×C47—24no—
273C22⋊C4×C47—24no—
274C22⋊C4×C47—24no—
275C42×C47—24no—
276C22⋊Dic47—24no—
277C22⋊Dic47—24no—
278#10625337—44no—
279#10625337—44no—
280#10625336—44no—
281#10625336—44no—
282(C2×D47)⋊C4—24no—
283(C2×D47)⋊C4—24no—
284C4⋊Dic47—24no—
285C4⋊Dic47—21no—
286C4⋊Dic47—21no—
287C4⋊Dic47C2412yes—
288C4⋊Dic47C2412yes—
289Dic47⋊C4—24no—
290Dic47⋊C4—24no—
291#10625329—44no—
292C2×C47⋊C8—22no—
293C2×C47⋊C8—22no—
294C2×C47⋊C8—22no—
295C2×C47⋊C8—22no—
296C2×C47⋊C8—44no—
297C2×C47⋊C8C2412yes—
298C2×C47⋊C8C2412yes—
299C2×C47⋊C8C2412yes—
300C2×C47⋊C8C2412yes—
301C23×C47—22no—
302C23×C47—22no—
303C23×C47—22no—
304C23×C47—22no—
305C23×C47—22no—
306C23×C47—22no—
307C23×C47—22no—
308C23×C47—22no—
309C23×C47—22no—
310C23×C47C22×D412yes—
311C23×C47C22×D412yes—
312C23×C47C22×D412yes—
313C23×C47C22×D411yescharacteristic
314C22×D47—22no—
315C22×D47—42no—
316C22×D47—42no—
317C22×D47—42no—
318Q8×C47—22no—
319Q8×C47—22no—
320Q8×C47—22no—
321Q8×C47—22no—
322Q8×C47—44no—
323Q8×C47—48no—
324Q8×C47—42no—
325Q8×C47—42no—
326D4×C47—44no—
327D4×C47—44no—
328D4×C47—44no—
329C2×C4×C47—22no—
330C2×C4×C47—22no—
331C2×C4×C47—22no—
332C2×C4×C47—24no—
333C2×C4×C47—24no—
334C2×C4×C47—24no—
335C2×C4×C47—22no—
336C2×C4×C47—22no—
337C2×C4×C47—22no—
338C2×C4×C47—22no—
339C2×C4×C47—22no—
340C2×C4×C47—22no—
341C2×C4×C47—22no—
342C2×C4×C47—22no—
343C2×C4×C47—22no—
344C2×C4×C47—22no—
345C2×C4×C47—48no—
346C2×C4×C47—42no—
347C2×C4×C47—42no—
348C2×C4×C47—42no—
349C2×C4×C47—42no—
350C2×C4×C47C22×D412yes—
351C2×C4×C47C22×D412yes—
352C2×C4×C47C22×D412yes—
353C2×C4×C47C22×D411yescharacteristic
354C2×C4×C47H(5,𝔽2)12yes—
355C2×C4×C47H(5,𝔽2)12yes—
356C2×C4×C47C2511yescharacteristic
357C22⋊D47—48no—
358C22⋊D47—84no—
359C22⋊D47—84no—
360C2×Dic47—22no—
361C2×Dic47—22no—
362C2×Dic47—22no—
363C2×Dic47—42no—
364C2×Dic47—42no—
365C2×Dic47—42no—
366C2×Dic47—84no—
367D188—22no—
368D188—22no—
369D188—42no—
370C4×D47—48no—
371Dic94—22no—
372Dic94—22no—
373Dic94—42no—
374C47⋊C8—22no—
375C47⋊C8—22no—
376C47⋊C8—22no—
377C47⋊C8—22no—
378C2×#3201—471nomaximal, Sylow
379C22×C47—22no—
380C22×C47—22no—
381C22×C47—22no—
382C22×C47—22no—
383C22×C47—22no—
384C22×C47—22no—
385C22×C47—22no—
386C22×C47—22no—
387C22×C47—22no—
388C22×C47—44no—
389C22×C47—44no—
390C22×C47—44no—
391C22×C47#53412yes—
392C22×C47#57712yes—
393C22×C47#57812yes—
394C22×C47C23×D411yescharacteristic
395C2×D47—42no—
396C2×D47—42no—
397C2×D47—42no—
398C2×D47—84no—
399C4×C47—22no—
400C4×C47—22no—
401C4×C47—22no—
402C4×C47—42no—
403C4×C47—42no—
404C4×C47—42no—
405C4×C47—42no—
406C4×C47#53412yes—
407C4×C47C2×H(5,𝔽2)11yescharacteristic
408C4×C47C2×H(5,𝔽2)11yescharacteristic
409Dic47—42no—
410Dic47—42no—
411Dic47—42no—
412C2×#537—471no—
413C2×#536D4711yescharacteristic, complemented
414#3201—4716no—
415C2×#484—471no—
416C2×#485—471no—
417C2×#482—471no—
418C2×#483—471no—
419C2×#470—471no—
420C2×#468—471no—
421C2×#467—471no—
422C2×#465—471no—
423C2×#452—471no—
424C2×#452—471no—
425C2×#451—471no—
426C2×#448—471no—
427C2×#408—471no—
428C2×C47—42no—
429C2×C47—42no—
430C2×C47—42no—
431C2×C47#320114yescomplemented
432C2×C47C2×#53411yescharacteristic
433C2×C47C2×#57711yescharacteristic
434C2×C47C2×#57811yescharacteristic
435D47—82no—
436C22×#41—471no—
437C22×#41C2×D4711yescharacteristic
438C23×Q8C2×D4711yescharacteristic
439C22×Q16—471no—
440C22×Q16—471no—
441C22×SD16—471no—
442C22×SD16—471no—
443C22×M16—471no—
444C23×C8—471no—
445#537—478no—
446#537—944no—
447#536—24no—
448#536C2×D4718yescomplemented
449C2×C4⋊Q8—21no—
450C2×#124—21no—
451C2×#123—21no—
452C2×#123—21no—
453C2×C22⋊Q8—471no—
454C2×C22⋊Q8—471no—
455C2×C22⋊Q8—941no—
456C2×C22⋊Q8C2×D4711yescharacteristic
457C2×C22⋊Q8C2×D4711yescharacteristic
458C2×C22⋊Q8C2×D4711yescharacteristic
459C2×C22⋊Q8C2×D4711yescharacteristic
460C2×#121—471no—
461C2×#121—471no—
462C2×#121—941no—
463C2×#121—941no—
464C2×#121—941no—
465C2×#117C2×D4711yescharacteristic
466C22×C4⋊C4—471no—
467#485—478no—
468#484—478no—
469#483—478no—
470#482—478no—
471#470—478no—
472#468—478no—
473#467—478no—
474#465—478no—
475#452—478no—
476#452—478no—
477#451—478no—
478#448—478no—
479C2×#107—471no—
480C2×#107—471no—
481C2×#106—471no—
482C2×#106—471no—
483C2×#103—471no—
484C2×#103—471no—
485C2×#103—471no—
486C2×#103—471no—
487C2×#103—471no—
488C2×#103—471no—
489C2×#102—471no—
490C2×#102—471no—
491#408—478no—
492C2×C22⋊C8—471no—
493C2×C22⋊C8—471no—
494C2×C22⋊C8—471no—
495C2×C22⋊C8—471no—
496C47C2×#320111yescharacteristic, complemented, Sylow
497C2×#41—42no—
498C2×#41—42no—
499C2×#41—474no—
500C2×#41—942no—
501C2×#41—1882no—
502C2×#41—1882no—
503C2×#41C22⋊D4714yes—
504C2×#41C22×D4714yes—
505C22×Q8—21no—
506C22×Q8—22no—
507C22×Q8—42no—
508C22×Q8—42no—
509C22×Q8—471no—
510C22×Q8C22⋊D4711yescharacteristic
511C22×Q8C22×D4711yescharacteristic
512C22×Q8C22×D4711yescharacteristic
513C22×Q8C22×D4714yes—
514C22×D4—471no—
515C22×D4—941no—
516C22×D4—941no—
517C22×D4—941no—
518C22×D4C22⋊D4711yescharacteristic
519C22×D4C22⋊D4711yescharacteristic
520C22×D4C22⋊D4711yescharacteristic
521C23×C4—21no—
522C23×C4—941no—
523C23×C4—941no—
524C23×C4C22×D4711yescharacteristic
525C23×C4C22×D4711yescharacteristic
526C23×C4C22×D4711yescharacteristic
527C2×Q16—474no—
528C2×Q16—474no—
529C2×Q16—1882no—
530C2×Q16—1882no—
531C2×SD16—474no—
532C2×SD16—474no—
533C2×SD16—1882no—
534C2×SD16—1882no—
535C2×M16—474no—
536C2×M16—1882no—
537C22×C8—471no—
538C22×C8—471no—
539C22×C8—471no—
540C22×C8—471no—
541C22×C8—474no—
542C22×C8—1882no—
543C4⋊Q8—28no—
544#124—28no—
545#123—28no—
546#123—28no—
547C22⋊Q8—22no—
548C22⋊Q8—22no—
549C22⋊Q8—22no—
550C22⋊Q8—22no—
551C22⋊Q8—474no—
552C22⋊Q8—474no—
553C22⋊Q8—948no—
554C22⋊Q8—942no—
555C22⋊Q8—942no—
556C22⋊Q8C22×D4714yes—
557C22⋊Q8C22×D4714yes—
558C22⋊Q8C22×D4714yes—
559C22⋊Q8C22×D4714yes—
560#121—474no—
561#121—474no—
562#121—948no—
563#121—948no—
564#121—948no—
565#121—942no—
566#121—942no—
567#117—22no—
568#117C22×D4714yes—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—471no—
574C2×C4⋊C4—471no—
575C2×C4⋊C4—474no—
576C2×C4⋊C4—941no—
577C2×C4⋊C4—942no—
578C2×C4⋊C4—941no—
579C2×C4⋊C4—941no—
580C2×C4⋊C4C22×D4711yescharacteristic
581C2×C4⋊C4C22×D4711yescharacteristic
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—941no—
588C2×C22⋊C4—941no—
589C2×C22⋊C4—941no—
590C2×C22⋊C4—941no—
591C2×C42—21no—
592#107—474no—
593#107—474no—
594#106—474no—
595#106—474no—
596#103—474no—
597#103—474no—
598#103—474no—
599#103—474no—
600#103—474no—
601#103—474no—
602#102—474no—
603#102—474no—
604C22⋊C8—474no—
605C22⋊C8—474no—
606C22⋊C8—474no—
607C22⋊C8—474no—
608C24—941no—
609C24C2×C22⋊D4711yescharacteristic
610C24C2×C22⋊D4711yescharacteristic
611C24C2×C22⋊D4711yescharacteristic
612#41—48no—
613#41—44no—
614#41—44no—
615#41—1884no—
616#41—1884no—
617#41—1888no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—24no—
621C2×Q8—22no—
622C2×Q8—22no—
623C2×Q8—22no—
624C2×Q8—22no—
625C2×Q8—42no—
626C2×Q8—44no—
627C2×Q8—44no—
628C2×Q8—44no—
629C2×Q8—48no—
630C2×Q8—472no—
631C2×Q8—941no—
632C2×Q8—942no—
633C2×Q8—942no—
634C2×Q8C2×C22⋊D4714yes—
635C2×Q8C23×D4712yes—
636C2×Q8C23×D4712yes—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—472no—
641C2×D4—944no—
642C2×D4—944no—
643C2×D4—944no—
644C2×D4—941no—
645C2×D4—942no—
646C2×D4—942no—
647C2×D4—3762no—
648C2×D4—3762no—
649C2×D4—1884no—
650C2×D4C2×C22⋊D4714yes—
651C2×D4C2×C22⋊D4714yes—
652C2×D4C2×C22⋊D4714yes—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—24no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—44no—
665C22×C4—944no—
666C22×C4—941no—
667C22×C4—941no—
668C22×C4—941no—
669C22×C4—944no—
670C22×C4—3762no—
671C22×C4—1884no—
672C22×C4C2×C22⋊D4712yes—
673C22×C4C2×C22⋊D4712yes—
674C22×C4C2×C22⋊D4712yes—
675C22×C4C2×C22⋊D4711yescharacteristic
676C22×C4C2×C22⋊D4711yescharacteristic
677C22×C4C2×C22⋊D4711yescharacteristic
678C22×C4C23×D4712yes—
679C22×C4C23×D4712yes—
680C22×C4C23×D4712yes—
681C22×C4C23×D4711yescharacteristic
682Q16—1884no—
683Q16—1884no—
684SD16—1884no—
685SD16—1884no—
686M16—1884no—
687C2×C8—472no—
688C2×C8—472no—
689C2×C8—472no—
690C2×C8—472no—
691C2×C8—942no—
692C2×C8—942no—
693C2×C8—942no—
694C2×C8—942no—
695C2×C8—1884no—
696C4⋊C4—24no—
697C4⋊C4—24no—
698C4⋊C4—24no—
699C4⋊C4—24no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—472no—
703C4⋊C4—472no—
704C4⋊C4—944no—
705C4⋊C4—944no—
706C4⋊C4—944no—
707C4⋊C4—941no—
708C4⋊C4—941no—
709C4⋊C4C23×D4712yes—
710C4⋊C4C23×D4712yes—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—944no—
717C22⋊C4—944no—
718C22⋊C4—944no—
719C22⋊C4—944no—
720C42—24no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—942no—
731C23—1882no—
732C23—1882no—
733C23—1882no—
734C23C22×C22⋊D4712yes—
735C23C22×C22⋊D4712yes—
736C23C22×C22⋊D4712yes—
737C23C22×C22⋊D4711yescharacteristic
738Q8—22no—
739Q8—22no—
740Q8—22no—
741Q8—22no—
742Q8—44no—
743Q8—48no—
744Q8—42no—
745Q8—42no—
746Q8—942no—
747Q8—942no—
748Q8—1882no—
749D4—44no—
750D4—44no—
751D4—44no—
752D4—942no—
753D4—942no—
754D4—3764no—
755D4—3764no—
756D4—1888no—
757D4—1882no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—48no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—942no—
780C2×C4—942no—
781C2×C4—942no—
782C2×C4—3764no—
783C2×C4—1888no—
784C2×C4—1882no—
785C2×C4—1882no—
786C2×C4—1882no—
787C2×C4C22×C22⋊D4712yes—
788C2×C4C22×C22⋊D4712yes—
789C2×C4C22×C22⋊D4712yes—
790C2×C4C22×C22⋊D4711yescharacteristic
791C2×C4#1309406912yes—
792C2×C4#1309406912yes—
793C2×C4C24×D4711yescharacteristic
794C8—942no—
795C8—942no—
796C8—942no—
797C8—942no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—44no—
808C22—44no—
809C22—44no—
810C22—3764no—
811C22—1882no—
812C22—1882no—
813C22—1882no—
814C22#1568968212yes—
815C22#1568993112yes—
816C22#1568993812yes—
817C22C23×C22⋊D4711yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—42no—
825C4—1882no—
826C4—1882no—
827C4—1882no—
828C4#1568968212yes—
829C4C2×#1309406911yescharacteristic
830C4C2×#1309406911yescharacteristic
831C2—42no—
832C2—42no—
833C2—42no—
834C2—3762no—
835C2#2025427014yesdirect product factor
836C2C2×#1568968211yescharacteristic
837C2C2×#1568993111yescharacteristic
838C2C2×#1568993811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#536C2
socleC23×C47C22×D4
prime radicalC2×#15689701C2
hypercenterC2×#536D47
hypocenterC47C2×#3201
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
2. #20254270C2direct (N × H)
3. C2×#15689456C2semidirect
4. C2×#15689464C2semidirect
5. C2×#15689447C2semidirect
6. C2×#15689451C2semidirect
7. C2×#15689379C2semidirect
8. C2×#15689371C2semidirect
9. C2×#15689362C2semidirect
10. C2×#15689354C2semidirect
11. C2×#15689283C2semidirect
12. C2×#15689283C2semidirect
13. C2×#15689279C2semidirect
14. C2×#15689262C2semidirect
15. C2×#15689090C2semidirect
16. C2×C47×#536C2semidirect
35. #15689464C22semidirect
36. #15689456C22semidirect
37. #15689451C22semidirect
38. #15689447C22semidirect
39. #15689379C22semidirect
40. #15689371C22semidirect
41. #15689362C22semidirect
42. #15689354C22semidirect
43. #15689283C22semidirect
44. #15689283C22semidirect
45. #15689279C22semidirect
46. #15689262C22semidirect
59. #15689090C22semidirect
67. C47×#536C22semidirect
413. C2×#536D47semidirect
431. C2×C47#3201semidirect
448. #536C2×D47semidirect
496. C47C2×#3201semidirect
835. C2#20254270direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897012
#202542702
C2×#156894562
C2×#156894642
C2×#156894472
C2×#156894512
C2×#156893792
C2×#156893712
C2×#156893622
C2×#156893542
C2×#156892832
C2×#156892792
C2×#156892622
C2×#156890902
C2×C47×#5362
C2×#320147