Finite Group Databasebeta

← C2×#20255598 #27093085

Subgroups — C2×#20255598 #27093085

Order 12032.

2254 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689769C211yesmaximal, characteristic
2#20255598C2116yesmaximal, direct product factor
3C2×#15689480C211yesmaximal, characteristic, complemented
4C2×#15689441C211yesmaximal, characteristic, complemented
5C2×#15689464C211yesmaximal, characteristic, complemented
6C2×#15689420C211yesmaximal, characteristic, complemented
7C2×#15689379C211yesmaximal, characteristic, complemented
8C2×#15689371C211yesmaximal, characteristic, complemented
9C2×#15689345C211yesmaximal, characteristic, complemented
10C2×#15689283C211yesmaximal, characteristic, complemented
11C2×#15689273C211yesmaximal, characteristic, complemented
12C2×C4×#10625336C211yesmaximal, characteristic, complemented
13C2×#15689201C211yesmaximal, characteristic, complemented
14C2×#15689122C211yesmaximal, characteristic, complemented
15C2×#15689127C211yesmaximal, characteristic, complemented
16C2×C47×#552C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C23×D188C2211yescharacteristic
19C22×#10625337C2211yescharacteristic, complemented
20C22×#10625336C2211yescharacteristic
21C22×#10625336C2211yescharacteristic
22C22×#10625329C2211yescharacteristic
23C22×#10625329C2211yescharacteristic, complemented
24#15689769—24no—
25#15689769C2218yes—
26C2×#13094012C2211yescharacteristic
27C2×#13094009—21no—
28C2×#13094003C2211yescharacteristic
29C2×#13093998C2211yescharacteristic
30C2×#13093997—21no—
31C2×#13093992—21no—
32C2×C4×D188C2211yescharacteristic
33C2×C22⋊C4×D47—21no—
34#15689480C2218yescomplemented
35#15689464C2218yescomplemented
36#15689441C2218yescomplemented
37#15689420C2218yescomplemented
38#15689379C2218yescomplemented
39#15689371C2218yescomplemented
40#15689345C2218yescomplemented
41#15689283C2218yescomplemented
42#15689273C2218yescomplemented
43C4×#10625336C2218yescomplemented
44#15689201C2218yescomplemented
45C2×#13093957C2211yescharacteristic, complemented
46C2×#13093955C2211yescharacteristic, complemented
47C2×#13093955C2211yescharacteristic, complemented
48C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
49#15689127C2218yescomplemented
50#15689122C2218yescomplemented
51C2×#13093948C2211yescharacteristic, complemented
52C2×#13093947C2211yescharacteristic, complemented
53C2×#13093947C2211yescharacteristic, complemented
54C2×#13093947C2211yescharacteristic, complemented
55C2×#13093944C2211yescharacteristic
56C2×#13093944C2211yescharacteristic
57C2×#13093944C2211yescharacteristic
58C2×#13093944C2211yescharacteristic
59C2×#13093944C2211yescharacteristic
60C2×#13093944C2211yescharacteristic
61C2×C22⋊(C47⋊C8)C2211yescharacteristic
62C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
63C2×C4×C47⋊C8C2211yescharacteristic, complemented
64C47×#552—24no—
65C47×#552C2218yescomplemented
66C2×#126×C47—21no—
67C2×#125×C47—21no—
68C2×#125×C47C2211yescharacteristic, complemented
69C2×#123×C47—21no—
70C2×C22⋊Q8×C47C2211yescharacteristic
71C2×C22⋊Q8×C47C2211yescharacteristic, complemented
72C2×C4×Q8×C47C2211yescharacteristic, complemented
73C2×C4×D4×C47C2211yescharacteristic
74C2×#117×C47—21no—
75C2×#117×C47C2211yescharacteristic
76C22×C4⋊C4×C47C2211yescharacteristic, complemented
77C24×D47—21no—
78C2×#10625350—22no—
79C2×#10625350—24no—
80C2×#10625350—42no—
81C2×#10625350C2314yes—
82C22×Dic94C2311yescharacteristic
83C22×D188—24no—
84C22×D188—22no—
85C22×D188—21no—
86C22×D188—42no—
87C22×D188C2311yescharacteristic
88C22×D188C2314yes—
89C22×D188C2311yescharacteristic
90C22×C22⋊D47—21no—
91C22×C22⋊D47—21no—
92C22×C4×D47—21no—
93C22×C4×D47—21no—
94C2×#10625337—42no—
95C2×#10625337C2314yescomplemented
96C2×#10625336—24no—
97C2×#10625336—42no—
98C2×#10625336C2314yes—
99C2×#10625336C2314yes—
100C2×#10625329—42no—
101C2×#10625329—42no—
102C2×#10625329C2314yes—
103C2×#10625329C2314yescomplemented
104C22×C47⋊C8C2311yescharacteristic
105C22×C47⋊C8C2311yescharacteristic
106C22×C47⋊C8C2311yescharacteristic
107C22×C47⋊C8C2311yescharacteristic
108#13094012—22no—
109#13094012C2314yes—
110#13094009—28no—
111#13094003—22no—
112#13094003C2314yes—
113#13093998—22no—
114#13093998C2314yes—
115#13093997—28no—
116#13093992—28no—
117C4×D188—22no—
118C4×D188C2314yes—
119C2×C4⋊Dic47C2311yescharacteristic
120C2×Dic47⋊C4—21no—
121C2×C22⋊Dic47—21no—
122C2×(C2×D47)⋊C4—21no—
123C2×(C2×D47)⋊C4—21no—
124C2×(C2×D47)⋊C4—21no—
125C2×(C2×D47)⋊C4—21no—
126C22⋊C4×D47—28no—
127#13093957C2314yescomplemented
128#13093955C2314yescomplemented
129#13093955C2314yescomplemented
130C4⋊(C47⋊C8)C2314yescomplemented
131#13093948C2314yescomplemented
132#13093947C2314yescomplemented
133#13093947C2314yescomplemented
134#13093947C2314yescomplemented
135#13093944C2314yes—
136#13093944C2314yes—
137#13093944C2314yes—
138#13093944C2314yes—
139#13093944C2314yes—
140#13093944C2314yes—
141C22⋊(C47⋊C8)C2314yes—
142C22⋊(C47⋊C8)C2314yescomplemented
143C4×C47⋊C8C2314yescomplemented
144C22×Q8×C47C2311yescharacteristic
145C22×D4×C47D411yescharacteristic
146C23×C4×C47—21no—
147C23×C4×C47C2311yescharacteristic
148C23×C4×C47C2311yescharacteristic
149#126×C47—28no—
150#125×C47—28no—
151#125×C47—22no—
152#125×C47C2314yescomplemented
153#123×C47—28no—
154C22⋊Q8×C47—22no—
155C22⋊Q8×C47—22no—
156C22⋊Q8×C47C2314yes—
157C22⋊Q8×C47C2314yescomplemented
158C4×Q8×C47—22no—
159C4×Q8×C47C2314yescomplemented
160C4×D4×C47D414yes—
161C4×D4×C47C2314yes—
162#117×C47—22no—
163#117×C47—28no—
164#117×C47C2314yes—
165C2×C4⋊C4×C47—21no—
166C2×C4⋊C4×C47—22no—
167C2×C4⋊C4×C47—21no—
168C2×C4⋊C4×C47—21no—
169C2×C4⋊C4×C47—21no—
170C2×C4⋊C4×C47—21no—
171C2×C4⋊C4×C47—21no—
172C2×C4⋊C4×C47D411yescharacteristic
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C4⋊C4×C47C2311yescharacteristic
176C2×C4⋊C4×C47C2314yescomplemented
177C2×C22⋊C4×C47—21no—
178C2×C22⋊C4×C47—21no—
179C2×C22⋊C4×C47—21no—
180C2×C22⋊C4×C47D411yescharacteristic
181C2×C22⋊C4×C47D411yescharacteristic
182C2×C42×C47—21no—
183C2×C42×C47—21no—
184C2×C42×C47C2311yescharacteristic
185C24×C47C2×D411yescharacteristic
186C24×C47C2×D411yescharacteristic
187C23×D47—21no—
188C23×D47—21no—
189C23×D47—24no—
190C23×D47—44no—
191C23×D47—44no—
192C23×D47—82no—
193C2×Q8×C47—21no—
194C2×Q8×C47—22no—
195C2×Q8×C47—22no—
196C2×Q8×C47C2412yes—
197C2×D4×C47—42no—
198C2×D4×C47C2×D414yes—
199C22×C4×C47—22no—
200C22×C4×C47—22no—
201C22×C4×C47—22no—
202C22×C4×C47—22no—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47—24no—
208C22×C4×C47—44no—
209C22×C4×C47C2×D411yescharacteristic
210C22×C4×C47C2×D411yescharacteristic
211C22×C4×C47C2×D411yescharacteristic
212C22×C4×C47C2×D411yescharacteristic
213C22×C4×C47C2×D412yes—
214C22×C4×C47C2×D412yes—
215C22×C4×C47C2412yes—
216C22×C4×C47C2412yes—
217C22×C4×C47C2411yescharacteristic
218C2×C22⋊D47—24no—
219C2×C22⋊D47—24no—
220C2×C22⋊D47—44no—
221C2×C22⋊D47—82no—
222C22×Dic47—21no—
223C22×Dic47—21no—
224#10625350—28no—
225#10625350—44no—
226#10625350—48no—
227C2×D188—21no—
228C2×D188—22no—
229C2×D188—22no—
230C2×D188—22no—
231C2×D188—28no—
232C2×D188—24no—
233C2×D188—21no—
234C2×D188—44no—
235C2×D188—48no—
236C2×D188—44no—
237C2×D188#4114yes—
238C2×D188C2412yes—
239C2×D188C2412yes—
240C2×C4×D47—24no—
241C2×C4×D47—24no—
242C2×C4×D47—44no—
243C2×C4×D47—82no—
244C2×Dic94—22no—
245C2×Dic94—22no—
246C2×Dic94—21no—
247C2×Dic94C2412yes—
248C4⋊C4×C47—21no—
249C4⋊C4×C47—21no—
250C4⋊C4×C47—24no—
251C4⋊C4×C47—24no—
252C4⋊C4×C47—24no—
253C4⋊C4×C47—24no—
254C4⋊C4×C47—24no—
255C4⋊C4×C47—24no—
256C4⋊C4×C47—21no—
257C4⋊C4×C47C2×D414yes—
258C4⋊C4×C47C2412yes—
259C4⋊C4×C47C2412yes—
260C4⋊C4×C47C2412yes—
261C22⋊C4×C47—24no—
262C22⋊C4×C47—24no—
263C22⋊C4×C47—24no—
264C22⋊C4×C47C2×D414yes—
265C22⋊C4×C47C2×D414yes—
266C42×C47—24no—
267C42×C47—24no—
268C42×C47C2×D412yes—
269C42×C47C2412yes—
270C22⋊Dic47—24no—
271#10625337—44no—
272#10625336—28no—
273#10625336—44no—
274(C2×D47)⋊C4—24no—
275(C2×D47)⋊C4—24no—
276(C2×D47)⋊C4—24no—
277(C2×D47)⋊C4—24no—
278C4⋊Dic47—21no—
279C4⋊Dic47C2412yes—
280Dic47⋊C4—24no—
281#10625329—44no—
282#10625329—44no—
283C2×C47⋊C8—22no—
284C2×C47⋊C8—22no—
285C2×C47⋊C8—22no—
286C2×C47⋊C8—22no—
287C2×C47⋊C8C2412yes—
288C2×C47⋊C8C2412yes—
289C2×C47⋊C8C2412yes—
290C2×C47⋊C8C2412yes—
291C23×C47—22no—
292C23×C47—22no—
293C23×C47—22no—
294C23×C47—22no—
295C23×C47—22no—
296C23×C47—22no—
297C23×C47C22×D412yes—
298C23×C47C22×D412yes—
299C23×C47C22×D411yescharacteristic
300C22×D47—24no—
301C22×D47—22no—
302C22×D47—22no—
303C22×D47—48no—
304C22×D47—42no—
305C22×D47—42no—
306C22×D47—48no—
307C22×D47—42no—
308C22×D47—42no—
309C22×D47—42no—
310C22×D47—84no—
311C22×D47—816no—
312Q8×C47—22no—
313Q8×C47—22no—
314Q8×C47—42no—
315D4×C47—44no—
316C2×C4×C47—22no—
317C2×C4×C47—22no—
318C2×C4×C47—22no—
319C2×C4×C47—22no—
320C2×C4×C47—24no—
321C2×C4×C47—24no—
322C2×C4×C47—22no—
323C2×C4×C47—22no—
324C2×C4×C47—22no—
325C2×C4×C47—22no—
326C2×C4×C47—22no—
327C2×C4×C47—22no—
328C2×C4×C47—22no—
329C2×C4×C47—22no—
330C2×C4×C47—48no—
331C2×C4×C47—42no—
332C2×C4×C47—42no—
333C2×C4×C47—42no—
334C2×C4×C47—42no—
335C2×C4×C47C22×D412yes—
336C2×C4×C47C22×D412yes—
337C2×C4×C47C22×D412yes—
338C2×C4×C47C22×D412yes—
339C2×C4×C47C22×D411yescharacteristic
340C2×C4×C47C2×#4112yes—
341C2×C4×C47H(5,𝔽2)12yes—
342C2×C4×C47C2511yescharacteristic
343C22⋊D47—48no—
344C22⋊D47—84no—
345C2×Dic47—22no—
346C2×Dic47—22no—
347C2×Dic47—42no—
348C2×Dic47—42no—
349D188—24no—
350D188—22no—
351D188—22no—
352D188—22no—
353D188—48no—
354D188—42no—
355D188C2×#4114yes—
356C4×D47—48no—
357C4×D47—84no—
358Dic94—22no—
359Dic94—22no—
360Dic94—42no—
361C47⋊C8—22no—
362C47⋊C8—22no—
363C47⋊C8—22no—
364C47⋊C8—22no—
365C2×#3323—471nomaximal, Sylow
366C22×C47—22no—
367C22×C47—22no—
368C22×C47—22no—
369C22×C47—22no—
370C22×C47—22no—
371C22×C47—22no—
372C22×C47—44no—
373C22×C47—44no—
374C22×C47#54612yes—
375C22×C47#57512yes—
376C22×C47#57712yes—
377C22×C47C23×D411yescharacteristic
378C2×D47—24no—
379C2×D47—48no—
380C2×D47—42no—
381C2×D47—42no—
382C2×D47—42no—
383C2×D47—42no—
384C2×D47—42no—
385C2×D47—816no—
386C2×D47—84no—
387C4×C47—22no—
388C4×C47—22no—
389C4×C47—22no—
390C4×C47—22no—
391C4×C47—42no—
392C4×C47—42no—
393C4×C47—42no—
394C4×C47—42no—
395C4×C47#54612yes—
396C4×C47C22×#4111yescharacteristic
397C4×C47C2×H(5,𝔽2)11yescharacteristic
398Dic47—42no—
399Dic47—42no—
400C2×#552D4711yescharacteristic, complemented
401C2×#546—471no—
402#3323—4716no—
403C2×#488—471no—
404C2×#481—471no—
405C2×#485—471no—
406C2×#478—471no—
407C2×#470—471no—
408C2×#468—471no—
409C2×#464—471no—
410C2×#452—471no—
411C2×#450—471no—
412C2×C4×SD16—471no—
413C2×#436—471no—
414C2×#417—471no—
415C2×#418—471no—
416C2×C47—42no—
417C2×C47—42no—
418C2×C47#332314yescomplemented
419C2×C47C2×#54611yescharacteristic
420C2×C47C2×#57511yescharacteristic
421C2×C47C2×#57711yescharacteristic
422D47—44no—
423D47—82no—
424C22×#41—471no—
425C23×D4—471no—
426C22×Q16—471no—
427C22×SD16—471no—
428C22×SD16—471no—
429C22×M16—471no—
430C22×M16—471no—
431#552—24no—
432#552C2×D4718yescomplemented
433#546—478no—
434#546—944no—
435C2×#126—21no—
436C2×#125—21no—
437C2×#125C2×D4711yescharacteristic, complemented
438C2×#124—471no—
439C2×#123—21no—
440C2×#123—941no—
441C2×C22⋊Q8—471no—
442C2×C22⋊Q8C2×D4711yescharacteristic
443C2×C22⋊Q8C2×D4711yescharacteristic, complemented
444C2×#121—471no—
445C2×#121—941no—
446C2×#120—941no—
447C2×C4×Q8C2×D4711yescharacteristic, complemented
448C2×C4×D4—471no—
449C2×C4×D4C2×D4711yescharacteristic
450C2×#117—21no—
451C2×#117C2×D4711yescharacteristic
452C22×C4⋊C4C2×D4711yescharacteristic, complemented
453C22×C22⋊C4—941no—
454#488—478no—
455#485—478no—
456#481—478no—
457#478—478no—
458#470—478no—
459#468—478no—
460#464—478no—
461#452—478no—
462#450—478no—
463C4×SD16—478no—
464#436—478no—
465C2×#107—471no—
466C2×#106—471no—
467C2×#106—471no—
468C2×C4⋊C8—471no—
469#418—478no—
470#417—478no—
471C2×#103—471no—
472C2×#103—471no—
473C2×#103—471no—
474C2×#103—471no—
475C2×#102—471no—
476C2×#102—471no—
477C2×#102—471no—
478C2×#102—471no—
479C2×#102—471no—
480C2×#102—471no—
481C2×C22⋊C8—471no—
482C2×C22⋊C8—471no—
483C2×C4×C8—471no—
484C47C2×#332311yescharacteristic, complemented, Sylow
485C25—941no—
486C2×#41—474no—
487C2×#41—944no—
488C2×#41—942no—
489C2×#41—1882no—
490C22×Q8—471no—
491C22×Q8C22×D4711yescharacteristic
492C22×D4—471no—
493C22×D4—471no—
494C22×D4—474no—
495C22×D4—944no—
496C22×D4—941no—
497C22×D4—941no—
498C22×D4—941no—
499C22×D4—942no—
500C22×D4—1882no—
501C22×D4C22⋊D4711yescharacteristic
502C23×C4—21no—
503C23×C4—941no—
504C23×C4—941no—
505C23×C4C22×D4711yescharacteristic
506C23×C4C22×D4711yescharacteristic
507C2×Q16—474no—
508C2×Q16—1882no—
509C2×SD16—474no—
510C2×SD16—474no—
511C2×SD16—944no—
512C2×SD16—1882no—
513C2×M16—474no—
514C2×M16—474no—
515C2×M16—1882no—
516C2×M16—1882no—
517C22×C8—471no—
518C22×C8—471no—
519C22×C8—471no—
520C22×C8—471no—
521#126—28no—
522#125—28no—
523#125—22no—
524#125C22×D4714yescomplemented
525#124—474no—
526#124—942no—
527#123—28no—
528#123—948no—
529C22⋊Q8—22no—
530C22⋊Q8—22no—
531C22⋊Q8—474no—
532C22⋊Q8—942no—
533C22⋊Q8C22×D4714yes—
534C22⋊Q8C22×D4714yescomplemented
535#121—474no—
536#121—942no—
537#121—948no—
538#120—948no—
539C4×Q8—22no—
540C4×Q8C22×D4714yescomplemented
541C4×D4—474no—
542C4×D4—942no—
543C4×D4C22⋊D4714yes—
544C4×D4C22×D4714yes—
545#117—22no—
546#117—28no—
547#117C22×D4714yes—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—22no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—471no—
556C2×C4⋊C4—941no—
557C2×C4⋊C4C22⋊D4711yescharacteristic
558C2×C4⋊C4C22×D4711yescharacteristic
559C2×C4⋊C4C22×D4711yescharacteristic
560C2×C4⋊C4C22×D4711yescharacteristic
561C2×C4⋊C4C22×D4714yescomplemented
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—941no—
566C2×C22⋊C4—941no—
567C2×C22⋊C4—941no—
568C2×C22⋊C4—941no—
569C2×C22⋊C4—941no—
570C2×C22⋊C4—948no—
571C2×C22⋊C4C22⋊D4711yescharacteristic
572C2×C22⋊C4C22⋊D4711yescharacteristic
573C2×C42—21no—
574C2×C42—21no—
575C2×C42C22×D4711yescharacteristic
576#107—474no—
577#106—474no—
578#106—474no—
579C4⋊C8—474no—
580#103—474no—
581#103—474no—
582#103—474no—
583#103—474no—
584#102—474no—
585#102—474no—
586#102—474no—
587#102—474no—
588#102—474no—
589#102—474no—
590C22⋊C8—474no—
591C22⋊C8—474no—
592C4×C8—474no—
593C24—941no—
594C24—944no—
595C24—941no—
596C24—3762no—
597C24—1884no—
598C24—1884no—
599C24C2×C22⋊D4711yescharacteristic
600C24C2×C22⋊D4711yescharacteristic
601#41—948no—
602#41—1884no—
603#41—1888no—
604C2×Q8—21no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—472no—
608C2×Q8—941no—
609C2×Q8—942no—
610C2×Q8—942no—
611C2×Q8C23×D4712yes—
612C2×D4—42no—
613C2×D4—474no—
614C2×D4—472no—
615C2×D4—472no—
616C2×D4—948no—
617C2×D4—944no—
618C2×D4—944no—
619C2×D4—941no—
620C2×D4—944no—
621C2×D4—941no—
622C2×D4—942no—
623C2×D4—942no—
624C2×D4—942no—
625C2×D4—3762no—
626C2×D4—1884no—
627C2×D4—1888no—
628C2×D4—1884no—
629C2×D4—1884no—
630C2×D4C2×C22⋊D4714yes—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—24no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—44no—
641C22×C4—941no—
642C22×C4—941no—
643C22×C4—944no—
644C22×C4—944no—
645C22×C4—3762no—
646C22×C4—1884no—
647C22×C4C2×C22⋊D4712yes—
648C22×C4C2×C22⋊D4712yes—
649C22×C4C2×C22⋊D4711yescharacteristic
650C22×C4C2×C22⋊D4711yescharacteristic
651C22×C4C2×C22⋊D4711yescharacteristic
652C22×C4C2×C22⋊D4711yescharacteristic
653C22×C4C23×D4712yes—
654C22×C4C23×D4712yes—
655C22×C4C23×D4711yescharacteristic
656Q16—1884no—
657SD16—948no—
658SD16—1884no—
659M16—1884no—
660M16—1884no—
661C2×C8—472no—
662C2×C8—472no—
663C2×C8—472no—
664C2×C8—472no—
665C2×C8—942no—
666C2×C8—942no—
667C2×C8—942no—
668C2×C8—942no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—24no—
676C4⋊C4—24no—
677C4⋊C4—21no—
678C4⋊C4—472no—
679C4⋊C4—944no—
680C4⋊C4—941no—
681C4⋊C4C2×C22⋊D4714yes—
682C4⋊C4C23×D4712yes—
683C4⋊C4C23×D4712yes—
684C4⋊C4C23×D4712yes—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—944no—
689C22⋊C4—944no—
690C22⋊C4—944no—
691C22⋊C4—944no—
692C22⋊C4—944no—
693C22⋊C4C2×C22⋊D4714yes—
694C22⋊C4C2×C22⋊D4714yes—
695C42—24no—
696C42—24no—
697C42C2×C22⋊D4712yes—
698C42C23×D4712yes—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—944no—
706C23—942no—
707C23—942no—
708C23—3764no—
709C23—37616no—
710C23—1888no—
711C23—1888no—
712C23—1882no—
713C23—1882no—
714C23—1882no—
715C23—1882no—
716C23—1882no—
717C23C22×C22⋊D4712yes—
718C23C22×C22⋊D4712yes—
719C23C22×C22⋊D4711yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—42no—
723Q8—942no—
724Q8—942no—
725Q8—1882no—
726D4—44no—
727D4—474no—
728D4—944no—
729D4—942no—
730D4—942no—
731D4—942no—
732D4—3764no—
733D4—1888no—
734D4—1888no—
735D4—1882no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—48no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—942no—
756C2×C4—942no—
757C2×C4—3764no—
758C2×C4—1888no—
759C2×C4—1882no—
760C2×C4—1882no—
761C2×C4C22×C22⋊D4712yes—
762C2×C4C22×C22⋊D4712yes—
763C2×C4C22×C22⋊D4712yes—
764C2×C4C22×C22⋊D4712yes—
765C2×C4C22×C22⋊D4711yescharacteristic
766C2×C4#41×D4712yes—
767C2×C4#1309407012yes—
768C2×C4C24×D4711yescharacteristic
769C8—942no—
770C8—942no—
771C8—942no—
772C8—942no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—44no—
780C22—44no—
781C22—944no—
782C22—37616no—
783C22—3764no—
784C22—1882no—
785C22—1882no—
786C22—1882no—
787C22—1882no—
788C22—1882no—
789C22—1888no—
790C22#1568976112yes—
791C22#1568992112yes—
792C22#1568993112yes—
793C22C23×C22⋊D4711yescharacteristic
794C4—22no—
795C4—22no—
796C4—22no—
797C4—22no—
798C4—42no—
799C4—42no—
800C4—42no—
801C4—42no—
802C4—1882no—
803C4—1882no—
804C4#1568976112yes—
805C4C2×#41×D4711yescharacteristic
806C4C2×#1309407011yescharacteristic
807C2—42no—
808C2—42no—
809C2—3762no—
810C2—1884no—
811C2#2025559814yesdirect product factor
812C2C2×#1568976111yescharacteristic
813C2C2×#1568992111yescharacteristic
814C2C2×#1568993111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#552C2
socleC23×C47C22×D4
prime radicalC2×#15689769C2
hypercenterC2×#552D47
hypocenterC47C2×#3323
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. #20255598C2direct (N × H)
3. C2×#15689480C2semidirect
4. C2×#15689441C2semidirect
5. C2×#15689464C2semidirect
6. C2×#15689420C2semidirect
7. C2×#15689379C2semidirect
8. C2×#15689371C2semidirect
9. C2×#15689345C2semidirect
10. C2×#15689283C2semidirect
11. C2×#15689273C2semidirect
12. C2×C4×#10625336C2semidirect
13. C2×#15689201C2semidirect
14. C2×#15689122C2semidirect
15. C2×#15689127C2semidirect
16. C2×C47×#552C2semidirect
19. C22×#10625337C22semidirect
23. C22×#10625329C22semidirect
34. #15689480C22semidirect
35. #15689464C22semidirect
36. #15689441C22semidirect
37. #15689420C22semidirect
38. #15689379C22semidirect
39. #15689371C22semidirect
40. #15689345C22semidirect
41. #15689283C22semidirect
42. #15689273C22semidirect
43. C4×#10625336C22semidirect
44. #15689201C22semidirect
45. C2×#13093957C22semidirect
46. C2×#13093955C22semidirect
47. C2×#13093955C22semidirect
48. C2×C4⋊(C47⋊C8)C22semidirect
49. #15689127C22semidirect
50. #15689122C22semidirect
51. C2×#13093948C22semidirect
52. C2×#13093947C22semidirect
53. C2×#13093947C22semidirect
54. C2×#13093947C22semidirect
62. C2×C22⋊(C47⋊C8)C22semidirect
63. C2×C4×C47⋊C8C22semidirect
65. C47×#552C22semidirect
68. C2×#125×C47C22semidirect
71. C2×C22⋊Q8×C47C22semidirect
72. C2×C4×Q8×C47C22semidirect
76. C22×C4⋊C4×C47C22semidirect
95. C2×#10625337C23semidirect
103. C2×#10625329C23semidirect
127. #13093957C23semidirect
128. #13093955C23semidirect
129. #13093955C23semidirect
130. C4⋊(C47⋊C8)C23semidirect
131. #13093948C23semidirect
132. #13093947C23semidirect
133. #13093947C23semidirect
134. #13093947C23semidirect
142. C22⋊(C47⋊C8)C23semidirect
143. C4×C47⋊C8C23semidirect
152. #125×C47C23semidirect
157. C22⋊Q8×C47C23semidirect
159. C4×Q8×C47C23semidirect
176. C2×C4⋊C4×C47C23semidirect
400. C2×#552D47semidirect
418. C2×C47#3323semidirect
432. #552C2×D47semidirect
437. C2×#125C2×D47semidirect
443. C2×C22⋊Q8C2×D47semidirect
447. C2×C4×Q8C2×D47semidirect
452. C22×C4⋊C4C2×D47semidirect
484. C47C2×#3323semidirect
524. #125C22×D47semidirect
534. C22⋊Q8C22×D47semidirect
540. C4×Q8C22×D47semidirect
561. C2×C4⋊C4C22×D47semidirect
811. C2#20255598direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897692
#202555982
C2×#156894802
C2×#156894412
C2×#156894642
C2×#156894202
C2×#156893792
C2×#156893712
C2×#156893452
C2×#156892832
C2×#156892732
C2×C4×#106253362
C2×#156892012
C2×#156891222
C2×#156891272
C2×C47×#5522
C2×#332347