Finite Group Databasebeta

← C2×#20254235 #27086926

Subgroups — C2×#20254235 #27086926

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×#15689702C211yesmaximal, characteristic, complemented
2C2×#15689689C211yesmaximal, characteristic, complemented
3#20254235C2116yesmaximal, direct product factor
4C2×#15689443C211yesmaximal, characteristic, complemented
5C2×#15689467C211yesmaximal, characteristic, complemented
6C2×#15689445C211yesmaximal, characteristic, complemented
7C2×#15689435C211yesmaximal, characteristic, complemented
8C2×#15689369C211yesmaximal, characteristic, complemented
9C2×#15689357C211yesmaximal, characteristic, complemented
10C2×#15689350C211yesmaximal, characteristic, complemented
11C2×#15689269C211yesmaximal, characteristic, complemented
12C2×#15689265C211yesmaximal, characteristic, complemented
13C2×#15689275C211yesmaximal, characteristic, complemented
14C2×#15689255C211yesmaximal, characteristic, complemented
15C2×#15689091C211yesmaximal, characteristic, complemented
16C2×C47×#469C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C22×#10625352C2211yescharacteristic, complemented
19C22×D4×D47C2211yescharacteristic
20C22×#10625325C2211yescharacteristic
21C22×#10625335C2211yescharacteristic
22C22×#10625334C2211yescharacteristic
23C23×C47⋊C8C2211yescharacteristic, complemented
24#15689702—24no—
25#15689702C2218yescomplemented
26#15689689—24no—
27#15689689C2218yescomplemented
28C2×#13094020—21no—
29C2×#13094010—21no—
30C2×#13094004C2211yescharacteristic
31C2×#13094003C2211yescharacteristic, complemented
32C2×#13094001—21no—
33C2×#13093999C2211yescharacteristic
34C2×#13093998C2211yescharacteristic
35C2×#13093997—21no—
36C2×#13093996—21no—
37C2×#13093995—21no—
38C2×#13093995C2211yescharacteristic
39C2×#13093995C2211yescharacteristic
40C2×#13093994—21no—
41C2×#13093992—21no—
42C2×#13093982C2211yescharacteristic
43C2×C4⋊C4×D47C2211yescharacteristic, complemented
44#15689467C2218yescomplemented
45#15689445C2218yescomplemented
46#15689443C2218yescomplemented
47#15689435C2218yescomplemented
48#15689369C2218yescomplemented
49#15689357C2218yescomplemented
50#15689350C2218yescomplemented
51#15689275C2218yescomplemented
52#15689269C2218yescomplemented
53#15689265C2218yescomplemented
54#15689255C2218yescomplemented
55C2×#13093958C2211yescharacteristic, complemented
56C2×#13093957C2211yescharacteristic, complemented
57C2×#13093955C2211yescharacteristic, complemented
58C2×#13093949C2211yescharacteristic, complemented
59C2×#13093947C2211yescharacteristic, complemented
60C2×#13093946C2211yescharacteristic
61C2×#13093945C2211yescharacteristic
62C2×#13093945C2211yescharacteristic, complemented
63C2×#13093944C2211yescharacteristic
64#15689091C2218yescomplemented
65C2×(C2×D47)⋊C8C2211yescharacteristic
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
68C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
69C22×D8×C47C2211yescharacteristic
70C22×M16×C47C2211yescharacteristic, complemented
71C2×#121×C47C2211yescharacteristic
72C2×#121×C47C2211yescharacteristic, complemented
73C47×#469C2218yescomplemented
74C2×#106×C47C2211yescharacteristic, complemented
75C2×#102×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic, complemented
77C24×D47—21no—
78C2×#10625350—42no—
79C2×#10625350—42no—
80C2×#10625350D414yes—
81C2×#10625350C2314yes—
82C2×#10625352—22no—
83C2×#10625352—42no—
84C2×#10625352—42no—
85C2×#10625352C2314yescomplemented
86C22×Dic94D411yescharacteristic
87C22×Dic94C2311yescharacteristic
88C22×D188—21no—
89C22×D188D411yescharacteristic
90C22×D188C2311yescharacteristic
91C22×C22⋊D47—21no—
92C22×C22⋊D47—21no—
93C22×C22⋊D47—21no—
94C22×C22⋊D47—21no—
95C22×C22⋊D47—21no—
96C22×C22⋊D47D411yescharacteristic
97C22×C22⋊D47D411yescharacteristic
98C2×D4×D47—22no—
99C2×D4×D47—42no—
100C2×D4×D47—42no—
101C2×D4×D47C2314yes—
102C23×Dic47—21no—
103C22×C4×D47—21no—
104C22×C4×D47C2311yescharacteristic
105C22×C4×D47C2311yescharacteristic
106C2×#10625325—42no—
107C2×#10625325C2314yes—
108C2×#10625335—42no—
109C2×#10625335C2314yes—
110C2×#10625334—42no—
111C2×#10625334C2314yes—
112C22×C47⋊C8—42no—
113C22×C47⋊C8C2311yescharacteristic
114C22×C47⋊C8C2311yescharacteristic
115C22×C47⋊C8C2314yescomplemented
116#13094020—28no—
117#13094010—28no—
118#13094004—22no—
119#13094004C2314yes—
120#13094003—22no—
121#13094003C2314yescomplemented
122#13094001—28no—
123#13093999—22no—
124#13093999C2314yes—
125#13093998—22no—
126#13093998C2314yes—
127#13093997—28no—
128#13093996—28no—
129#13093995—28no—
130#13093995—22no—
131#13093995—22no—
132#13093995C2314yes—
133#13093995C2314yes—
134#13093994—28no—
135#13093992—28no—
136#13093982—22no—
137#13093982C2314yes—
138C2×C4⋊Dic47—21no—
139C2×C4⋊Dic47C2311yescharacteristic
140C2×C4⋊Dic47C2311yescharacteristic
141C2×Dic47⋊C4—21no—
142C2×Dic47⋊C4—21no—
143C4⋊C4×D47—22no—
144C4⋊C4×D47C2314yescomplemented
145C2×C22⋊Dic47—21no—
146C2×C22⋊Dic47—21no—
147C2×C22⋊Dic47—21no—
148C2×(C2×D47)⋊C4—21no—
149C2×(C2×D47)⋊C4—21no—
150C2×(C2×D47)⋊C4—21no—
151C2×(C2×D47)⋊C4—21no—
152C2×C4×Dic47—21no—
153#13093958C2314yescomplemented
154#13093957C2314yescomplemented
155#13093955C2314yescomplemented
156#13093949C2314yescomplemented
157#13093947C2314yescomplemented
158#13093946C2314yes—
159#13093945C2314yes—
160#13093945C2314yescomplemented
161#13093944C2314yes—
162(C2×D47)⋊C8C2314yes—
163(C2×D47)⋊C8C2314yes—
164(C2×D47)⋊C8C2314yescomplemented
165(C2×D47)⋊C8C2314yescomplemented
166C22×D4×C47—21no—
167C22×D4×C47—21no—
168C22×D4×C47C2311yescharacteristic
169C22×D4×C47C2311yescharacteristic
170C23×C4×C47C2311yescharacteristic
171C2×D8×C47—42no—
172C2×D8×C47C2314yes—
173C2×M16×C47—42no—
174C2×M16×C47C2314yescomplemented
175C22×C8×C47C2311yescharacteristic
176C22×C8×C47C2311yescharacteristic
177#121×C47—22no—
178#121×C47—22no—
179#121×C47C2314yes—
180#121×C47C2314yescomplemented
181C2×C4⋊C4×C47C2311yescharacteristic
182C2×C4⋊C4×C47C2311yescharacteristic
183C2×C22⋊C4×C47—21no—
184C2×C22⋊C4×C47—21no—
185#106×C47C2314yescomplemented
186#102×C47C2314yes—
187#102×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
198C2×D4×C47—24no—
199C2×D4×C47—24no—
200C2×D4×C47—21no—
201C2×D4×C47—21no—
202C2×D4×C47—22no—
203C2×D4×C47—22no—
204C2×D4×C47—22no—
205C2×D4×C47—22no—
206C2×D4×C47—82no—
207C2×D4×C47—82no—
208C2×D4×C47C2412yes—
209C2×D4×C47C2412yes—
210C22×C4×C47—22no—
211C22×C4×C47—22no—
212C22×C4×C47—21no—
213C22×C4×C47—21no—
214C22×C4×C47C2×D411yescharacteristic
215C22×C4×C47C2×D412yes—
216C22×C4×C47C2412yes—
217C22×C4×C47C2411yescharacteristic
218C2×C22⋊D47—24no—
219C2×C22⋊D47—24no—
220C2×C22⋊D47—24no—
221C2×C22⋊D47—24no—
222C2×C22⋊D47—24no—
223C2×C22⋊D47—42no—
224C2×C22⋊D47—42no—
225C2×C22⋊D47—44no—
226C2×C22⋊D47—44no—
227C2×C22⋊D47—82no—
228C2×C22⋊D47—82no—
229C2×C22⋊D47—82no—
230C2×C22⋊D47C2×D414yes—
231C2×C22⋊D47C2×D414yes—
232C22×Dic47—21no—
233C22×Dic47—21no—
234C22×Dic47—21no—
235C22×Dic47—24no—
236C22×Dic47—44no—
237C22×Dic47C2×D411yescharacteristic
238C22×Dic47C2×D411yescharacteristic
239#10625352—44no—
240#10625352—44no—
241#10625352—48no—
242D4×D47—44no—
243D4×D47—44no—
244D4×D47—48no—
245#10625350—48no—
246#10625350—44no—
247#10625350—44no—
248C2×D188—22no—
249C2×D188—22no—
250C2×D188—21no—
251C2×D188—24no—
252C2×D188—42no—
253C2×D188—82no—
254C2×D188C2×D414yes—
255C2×D188C2412yes—
256C2×C4×D47—22no—
257C2×C4×D47—22no—
258C2×C4×D47—22no—
259C2×C4×D47—22no—
260C2×C4×D47—24no—
261C2×C4×D47—82no—
262C2×C4×D47C2×D412yes—
263C2×C4×D47C2×D412yes—
264C2×C4×D47C2412yes—
265C2×C4×D47C2412yes—
266C2×Dic94—22no—
267C2×Dic94—22no—
268C2×Dic94—21no—
269C2×Dic94—42no—
270C2×Dic94C2×D414yes—
271C2×Dic94C2412yes—
272D8×C47—44no—
273M16×C47—44no—
274C2×C8×C47—22no—
275C2×C8×C47—22no—
276C2×C8×C47C2412yes—
277C2×C8×C47C2412yes—
278C4⋊C4×C47—21no—
279C4⋊C4×C47—21no—
280C4⋊C4×C47C2412yes—
281C4⋊C4×C47C2412yes—
282C22⋊C4×C47—24no—
283C22⋊C4×C47—24no—
284C22⋊Dic47—24no—
285C22⋊Dic47—24no—
286C22⋊Dic47—24no—
287#10625335—44no—
288#10625334—44no—
289(C2×D47)⋊C4—24no—
290(C2×D47)⋊C4—24no—
291(C2×D47)⋊C4—24no—
292(C2×D47)⋊C4—24no—
293C4⋊Dic47—21no—
294C4⋊Dic47—21no—
295C4⋊Dic47—24no—
296C4⋊Dic47C2412yes—
297C4⋊Dic47C2412yes—
298Dic47⋊C4—24no—
299Dic47⋊C4—24no—
300C4×Dic47—24no—
301C2×C47⋊C8—22no—
302C2×C47⋊C8—22no—
303C2×C47⋊C8—44no—
304C2×C47⋊C8C2412yes—
305C2×C47⋊C8C2412yes—
306#10625325—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—
336D4×C47—22no—
337D4×C47—22no—
338D4×C47—22no—
339D4×C47—22no—
340D4×C47—42no—
341D4×C47—42no—
342D4×C47—84no—
343D4×C47—84no—
344C2×C4×C47—22no—
345C2×C4×C47—24no—
346C2×C4×C47—22no—
347C2×C4×C47—22no—
348C2×C4×C47—22no—
349C2×C4×C47—22no—
350C2×C4×C47—42no—
351C2×C4×C47—42no—
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—44no—
358C22⋊D47—44no—
359C22⋊D47—48no—
360C22⋊D47—48no—
361C22⋊D47—84no—
362C22⋊D47—84no—
363C22⋊D47—84no—
364C2×Dic47—22no—
365C2×Dic47—22no—
366C2×Dic47—22no—
367C2×Dic47—22no—
368C2×Dic47—22no—
369C2×Dic47—48no—
370C2×Dic47—42no—
371C2×Dic47—42no—
372C2×Dic47—42no—
373C2×Dic47C22×D412yes—
374C2×Dic47C22×D412yes—
375D188—22no—
376D188—22no—
377D188—44no—
378D188—42no—
379D188—84no—
380C4×D47—24no—
381C4×D47—24no—
382C4×D47—22no—
383C4×D47—22no—
384C4×D47—22no—
385C4×D47—22no—
386C4×D47—84no—
387Dic94—22no—
388Dic94—22no—
389Dic94—44no—
390Dic94—42no—
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×#469D4711yescharacteristic, complemented
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—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×#41—471no—
464C23×D4—471no—
465C22×SD16—471no—
466C22×SD16—471no—
467C22×D8—471no—
468C22×D8C2×D4711yescharacteristic
469C22×M16C2×D4711yescharacteristic, complemented
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—941no—
485C2×#121—941no—
486C2×#121—941no—
487C2×#121C2×D4711yescharacteristic
488C2×#121C2×D4711yescharacteristic, complemented
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#469C2×D4718yescomplemented
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×#106C2×D4711yescharacteristic, complemented
509C2×#103—471no—
510C2×#103—471no—
511C2×#102—471no—
512C2×#102—471no—
513C2×#102—471no—
514C2×#102—471no—
515C2×#102C2×D4711yescharacteristic
516C2×#102C2×D4711yescharacteristic, complemented
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—474no—
525C2×#41—474no—
526C2×#41—474no—
527C2×#41—942no—
528C2×#41—1882no—
529C2×#41—1882no—
530C2×#41—1882no—
531C2×#41—1882no—
532C22×Q8—471no—
533C22×Q8—471no—
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—471no—
553C23×C4—471no—
554C23×C4—941no—
555C23×C4—941no—
556C23×C4C22×D4711yescharacteristic
557C2×SD16—474no—
558C2×SD16—474no—
559C2×SD16—1882no—
560C2×SD16—1882no—
561C2×D8—42no—
562C2×D8—474no—
563C2×D8—1882no—
564C2×D8C22×D4714yes—
565C2×M16—42no—
566C2×M16C22×D4714yescomplemented
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—22no—
582#121—474no—
583#121—474no—
584#121—474no—
585#121—474no—
586#121—948no—
587#121—942no—
588#121—942no—
589#121—942no—
590#121—948no—
591#121—948no—
592#121—942no—
593#121C22×D4714yes—
594#121C22×D4714yescomplemented
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—942no—
603C2×C4⋊C4—941no—
604C2×C4⋊C4—941no—
605C2×C4⋊C4—941no—
606C2×C4⋊C4C22×D4711yescharacteristic
607C2×C4⋊C4C22×D4711yescharacteristic
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
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#106C22×D4714yescomplemented
622#103—474no—
623#103—474no—
624#102—474no—
625#102—474no—
626#102—474no—
627#102—474no—
628#102C22×D4714yes—
629#102C22×D4714yescomplemented
630C22⋊C8—474no—
631C22⋊C8—474no—
632C22⋊C8—474no—
633C22⋊C8—474no—
634C24—21no—
635C24—21no—
636C24—471no—
637C24—471no—
638C24—944no—
639C24—941no—
640C24—3762no—
641C24—3762no—
642C24—1884no—
643C24D4×D4711yescharacteristic
644#41—1888no—
645#41—1884no—
646#41—1884no—
647#41—1884no—
648#41—1884no—
649#41—1888no—
650C2×Q8—474no—
651C2×Q8—472no—
652C2×Q8—941no—
653C2×Q8—942no—
654C2×Q8—942no—
655C2×Q8—1882no—
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—82no—
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—1882no—
684C2×D4—1884no—
685C2×D4—1884no—
686C2×D4—1888no—
687C2×D4—1882no—
688C2×D4—1882no—
689C2×D4—1884no—
690C2×D4—1884no—
691C2×D4C23×D4712yes—
692C2×D4C23×D4712yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—471no—
698C22×C4—471no—
699C22×C4—472no—
700C22×C4—472no—
701C22×C4—472no—
702C22×C4—472no—
703C22×C4—944no—
704C22×C4—944no—
705C22×C4—942no—
706C22×C4—942no—
707C22×C4—942no—
708C22×C4—942no—
709C22×C4—941no—
710C22×C4—941no—
711C22×C4—941no—
712C22×C4—3762no—
713C22×C4—1884no—
714C22×C4D4×D4712yes—
715C22×C4D4×D4711yescharacteristic
716C22×C4C23×D4712yes—
717C22×C4C23×D4711yescharacteristic
718SD16—1884no—
719SD16—1884no—
720D8—44no—
721D8—1884no—
722M16—44no—
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—21no—
734C4⋊C4—472no—
735C4⋊C4—472no—
736C4⋊C4—944no—
737C4⋊C4—944no—
738C4⋊C4—944no—
739C4⋊C4—941no—
740C4⋊C4—941no—
741C4⋊C4C23×D4712yes—
742C4⋊C4C23×D4712yes—
743C22⋊C4—24no—
744C22⋊C4—24no—
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—942no—
783Q8—942no—
784Q8—1884no—
785Q8—1882no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—22no—
790D4—42no—
791D4—42no—
792D4—84no—
793D4—84no—
794D4—942no—
795D4—942no—
796D4—3764no—
797D4—3764no—
798D4—3764no—
799D4—3764no—
800D4—1884no—
801D4—1884no—
802D4—1884no—
803D4—1888no—
804D4—1888no—
805D4—1882no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—472no—
815C2×C4—472no—
816C2×C4—942no—
817C2×C4—942no—
818C2×C4—944no—
819C2×C4—944no—
820C2×C4—942no—
821C2×C4—942no—
822C2×C4—942no—
823C2×C4—942no—
824C2×C4—942no—
825C2×C4—942no—
826C2×C4—942no—
827C2×C4—3764no—
828C2×C4—1888no—
829C2×C4—1882no—
830C2×C4—1882no—
831C2×C4—1882no—
832C2×C4C2×D4×D4712yes—
833C2×C4C2×D4×D4711yescharacteristic
834C2×C4#1309406912yes—
835C2×C4#1309407012yes—
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#1568968112yes—
867C22#1568992712yes—
868C22#1568993312yes—
869C22C22×D4×D4711yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—942no—
874C4—942no—
875C4—1882no—
876C4—1882no—
877C4—1882no—
878C4#1568968112yes—
879C4C2×#1309406911yescharacteristic
880C4C2×#1309407011yescharacteristic
881C2—42no—
882C2—82no—
883C2—82no—
884C2—3762no—
885C2—1882no—
886C2—1882no—
887C2#2025423514yesdirect product factor
888C2C2×#1568968111yescharacteristic
889C2C2×#1568992711yescharacteristic
890C2C2×#1568993311yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#469C2
socleC23×C47C22×D4
hypercenterC2×#469D47
hypocenterC47C2×#3198
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#469

Complements

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

NH ≅ G/Ntype
1. C2×#15689702C2semidirect
2. C2×#15689689C2semidirect
3. #20254235C2direct (N × H)
4. C2×#15689443C2semidirect
5. C2×#15689467C2semidirect
6. C2×#15689445C2semidirect
7. C2×#15689435C2semidirect
8. C2×#15689369C2semidirect
9. C2×#15689357C2semidirect
10. C2×#15689350C2semidirect
11. C2×#15689269C2semidirect
12. C2×#15689265C2semidirect
13. C2×#15689275C2semidirect
14. C2×#15689255C2semidirect
15. C2×#15689091C2semidirect
16. C2×C47×#469C2semidirect
18. C22×#10625352C22semidirect
23. C23×C47⋊C8C22semidirect
25. #15689702C22semidirect
27. #15689689C22semidirect
31. C2×#13094003C22semidirect
43. C2×C4⋊C4×D47C22semidirect
44. #15689467C22semidirect
45. #15689445C22semidirect
46. #15689443C22semidirect
47. #15689435C22semidirect
48. #15689369C22semidirect
49. #15689357C22semidirect
50. #15689350C22semidirect
51. #15689275C22semidirect
52. #15689269C22semidirect
53. #15689265C22semidirect
54. #15689255C22semidirect
55. C2×#13093958C22semidirect
56. C2×#13093957C22semidirect
57. C2×#13093955C22semidirect
58. C2×#13093949C22semidirect
59. C2×#13093947C22semidirect
62. C2×#13093945C22semidirect
64. #15689091C22semidirect
67. C2×(C2×D47)⋊C8C22semidirect
68. C2×(C2×D47)⋊C8C22semidirect
70. C22×M16×C47C22semidirect
72. C2×#121×C47C22semidirect
73. C47×#469C22semidirect
74. C2×#106×C47C22semidirect
76. C2×#102×C47C22semidirect
85. C2×#10625352C23semidirect
115. C22×C47⋊C8C23semidirect
121. #13094003C23semidirect
144. C4⋊C4×D47C23semidirect
153. #13093958C23semidirect
154. #13093957C23semidirect
155. #13093955C23semidirect
156. #13093949C23semidirect
157. #13093947C23semidirect
160. #13093945C23semidirect
164. (C2×D47)⋊C8C23semidirect
165. (C2×D47)⋊C8C23semidirect
174. C2×M16×C47C23semidirect
180. #121×C47C23semidirect
185. #106×C47C23semidirect
187. #102×C47C23semidirect
443. C2×#469D47semidirect
455. C2×C47#3198semidirect
469. C22×M16C2×D47semidirect
488. C2×#121C2×D47semidirect
497. #469C2×D47semidirect
508. C2×#106C2×D47semidirect
516. C2×#102C2×D47semidirect
522. C47C2×#3198semidirect
566. C2×M16C22×D47semidirect
594. #121C22×D47semidirect
621. #106C22×D47semidirect
629. #102C22×D47semidirect
887. C2#20254235direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897022
C2×#156896892
#202542352
C2×#156894432
C2×#156894672
C2×#156894452
C2×#156894352
C2×#156893692
C2×#156893572
C2×#156893502
C2×#156892692
C2×#156892652
C2×#156892752
C2×#156892552
C2×#156890912
C2×C47×#4692
C2×#319847