Finite Group Databasebeta

← C2×#20254242 #27086933

Subgroups — C2×#20254242 #27086933

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×#15689687C211yesmaximal, characteristic, complemented
3#20254242C2116yesmaximal, direct product factor
4C2×#15689442C211yesmaximal, characteristic, complemented
5C2×#15689465C211yesmaximal, characteristic, complemented
6C2×#15689448C211yesmaximal, characteristic, complemented
7C2×#15689437C211yesmaximal, characteristic, complemented
8C2×#15689376C211yesmaximal, characteristic, complemented
9C2×#15689369C211yesmaximal, characteristic, complemented
10C2×#15689359C211yesmaximal, characteristic, complemented
11C2×#15689352C211yesmaximal, characteristic, complemented
12C2×#15689270C211yesmaximal, characteristic, complemented
13C2×#15689270C211yesmaximal, characteristic, complemented
14C2×#15689276C211yesmaximal, characteristic, complemented
15C2×#15689259C211yesmaximal, characteristic, complemented
16C2×C47×#408C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic, complemented
18C23×D188C2211yescharacteristic
19C22×#10625325C2211yescharacteristic
20C22×#10625325C2211yescharacteristic
21C22×D376C2211yescharacteristic
22C22×D376C2211yescharacteristic
23#15689701—24no—
24#15689701C2218yescomplemented
25#15689687—24no—
26#15689687C2218yescomplemented
27C2×#13094020—21no—
28C2×#13094013—21no—
29C2×#13094003C2211yescharacteristic
30C2×#13094003C2211yescharacteristic, complemented
31C2×#13094000—21no—
32C2×#13093998C2211yescharacteristic
33C2×#13093998C2211yescharacteristic
34C2×#13093998C2211yescharacteristic
35C2×#13093998C2211yescharacteristic
36C2×#13093998C2211yescharacteristic
37C2×#13093998C2211yescharacteristic, complemented
38C2×#13093996—21no—
39C2×#13093996—21no—
40C2×#13093995—21no—
41C2×#13093992—21no—
42C2×#13093992—21no—
43C2×#13093983C2211yescharacteristic
44C22×C4⋊Dic47C2211yescharacteristic, complemented
45#15689465C2218yescomplemented
46#15689448C2218yescomplemented
47#15689442C2218yescomplemented
48#15689437C2218yescomplemented
49#15689376C2218yescomplemented
50#15689369C2218yescomplemented
51#15689359C2218yescomplemented
52#15689352C2218yescomplemented
53#15689276C2218yescomplemented
54#15689270C2218yescomplemented
55#15689270C2218yescomplemented
56#15689259C2218yescomplemented
57C2×#13093958C2211yescharacteristic, complemented
58C2×#13093958C2211yescharacteristic, complemented
59C2×#13093956C2211yescharacteristic, complemented
60C2×#13093956C2211yescharacteristic, complemented
61C2×#13093949C2211yescharacteristic, complemented
62C2×#13093949C2211yescharacteristic, complemented
63C2×#13093946C2211yescharacteristic
64C2×#13093946C2211yescharacteristic
65C2×#13093946C2211yescharacteristic
66C2×#13093946C2211yescharacteristic
67C2×#13093946C2211yescharacteristic, complemented
68C2×#13093946C2211yescharacteristic, complemented
69C22×#41×C47C2211yescharacteristic
70C22×M16×C47C2211yescharacteristic, complemented
71C23×C8×C47C2211yescharacteristic, complemented
72C47×#408C2218yescomplemented
73C2×C22⋊C8×C47C2211yescharacteristic
74C2×C22⋊C8×C47C2211yescharacteristic
75C2×C22⋊C8×C47C2211yescharacteristic, complemented
76C2×C22⋊C8×C47C2211yescharacteristic, complemented
77C24×D47—21no—
78C2×#10625350—22no—
79C2×#10625350—42no—
80C2×#10625350—42no—
81C2×#10625350C2314yescomplemented
82C22×Dic94C2311yescharacteristic
83C22×D188—21no—
84C22×D188—22no—
85C22×D188—42no—
86C22×D188—42no—
87C22×D188C2311yescharacteristic
88C22×D188C2311yescharacteristic
89C22×D188C2311yescharacteristic
90C22×D188C2314yes—
91C22×C22⋊D47—21no—
92C22×C22⋊D47—21no—
93C22×C22⋊D47—21no—
94C22×C22⋊D47—21no—
95C22×C22⋊D47—21no—
96C22×C22⋊D47—21no—
97C22×C22⋊D47—21no—
98C23×Dic47—21no—
99C22×C4×D47—21no—
100C2×#10625325—42no—
101C2×#10625325—42no—
102C2×#10625325C2314yes—
103C2×#10625325C2314yes—
104C2×D376—42no—
105C2×D376—42no—
106C2×D376C2314yes—
107C2×D376C2314yes—
108#13094020—28no—
109#13094013—28no—
110#13094003—22no—
111#13094003—22no—
112#13094003C2314yes—
113#13094003C2314yescomplemented
114#13094000—28no—
115#13093998—22no—
116#13093998—22no—
117#13093998—22no—
118#13093998—22no—
119#13093998—22no—
120#13093998—22no—
121#13093998C2314yes—
122#13093998C2314yes—
123#13093998C2314yes—
124#13093998C2314yes—
125#13093998C2314yes—
126#13093998C2314yescomplemented
127#13093996—28no—
128#13093996—28no—
129#13093995—28no—
130#13093992—28no—
131#13093992—28no—
132#13093983—22no—
133#13093983C2314yes—
134C2×C4⋊Dic47—21no—
135C2×C4⋊Dic47—22no—
136C2×C4⋊Dic47C2311yescharacteristic
137C2×C4⋊Dic47C2311yescharacteristic
138C2×C4⋊Dic47C2311yescharacteristic
139C2×C4⋊Dic47C2311yescharacteristic
140C2×C4⋊Dic47C2314yescomplemented
141C2×Dic47⋊C4—21no—
142C2×Dic47⋊C4—21no—
143C2×C22⋊Dic47—21no—
144C2×C22⋊Dic47—21no—
145C2×C22⋊Dic47—21no—
146C2×(C2×D47)⋊C4—21no—
147C2×(C2×D47)⋊C4—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#13093958C2314yescomplemented
155#13093956C2314yescomplemented
156#13093956C2314yescomplemented
157#13093949C2314yescomplemented
158#13093949C2314yescomplemented
159#13093946C2314yes—
160#13093946C2314yes—
161#13093946C2314yes—
162#13093946C2314yes—
163#13093946C2314yescomplemented
164#13093946C2314yescomplemented
165C2×#41×C47—42no—
166C2×#41×C47—42no—
167C2×#41×C47D414yes—
168C2×#41×C47C2314yes—
169C22×Q8×C47D411yescharacteristic
170C22×D4×C47D411yescharacteristic
171C22×D4×C47D411yescharacteristic
172C22×D4×C47D411yescharacteristic
173C23×C4×C47C2311yescharacteristic
174C23×C4×C47C2311yescharacteristic
175C23×C4×C47C2311yescharacteristic
176C2×M16×C47—42no—
177C2×M16×C47C2314yescomplemented
178C22×C8×C47—42no—
179C22×C8×C47C2311yescharacteristic
180C22×C8×C47C2311yescharacteristic
181C22×C8×C47C2311yescharacteristic
182C22×C8×C47C2311yescharacteristic
183C22×C8×C47C2314yescomplemented
184C22⋊C8×C47C2314yes—
185C22⋊C8×C47C2314yes—
186C22⋊C8×C47C2314yescomplemented
187C22⋊C8×C47C2314yescomplemented
188C24×C47C2×D411yescharacteristic
189C24×C47C2×D411yescharacteristic
190C24×C47C2×D411yescharacteristic
191C23×D47—21no—
192C23×D47—21no—
193C23×D47—21no—
194C23×D47—24no—
195C23×D47—44no—
196C23×D47—82no—
197C23×D47—82no—
198#41×C47—48no—
199#41×C47—44no—
200#41×C47—44no—
201C2×Q8×C47—42no—
202C2×Q8×C47C2×D414yes—
203C2×D4×C47—42no—
204C2×D4×C47—42no—
205C2×D4×C47—42no—
206C2×D4×C47C2×D414yes—
207C2×D4×C47C2×D414yes—
208C2×D4×C47C2×D414yes—
209C22×C4×C47—22no—
210C22×C4×C47—22no—
211C22×C4×C47—22no—
212C22×C4×C47—22no—
213C22×C4×C47—22no—
214C22×C4×C47—22no—
215C22×C4×C47C2×D411yescharacteristic
216C22×C4×C47C2×D411yescharacteristic
217C22×C4×C47C2×D411yescharacteristic
218C22×C4×C47C2×D412yes—
219C22×C4×C47C2×D412yes—
220C22×C4×C47C2×D412yes—
221C22×C4×C47C2412yes—
222C22×C4×C47C2412yes—
223C22×C4×C47C2412yes—
224C22×C4×C47C2411yescharacteristic
225C2×C22⋊D47—24no—
226C2×C22⋊D47—24no—
227C2×C22⋊D47—24no—
228C2×C22⋊D47—24no—
229C2×C22⋊D47—24no—
230C2×C22⋊D47—24no—
231C2×C22⋊D47—24no—
232C2×C22⋊D47—44no—
233C2×C22⋊D47—82no—
234C2×C22⋊D47—82no—
235C2×C22⋊D47—82no—
236C2×C22⋊D47—82no—
237C2×C22⋊D47—82no—
238C2×C22⋊D47—82no—
239C22×Dic47—21no—
240C22×Dic47—21no—
241C22×Dic47—21no—
242C22×Dic47—21no—
243C22×Dic47—21no—
244C22×Dic47—24no—
245C22×Dic47—82no—
246#10625350—44no—
247#10625350—44no—
248#10625350—48no—
249C2×D188—22no—
250C2×D188—22no—
251C2×D188—22no—
252C2×D188—22no—
253C2×D188—22no—
254C2×D188—22no—
255C2×D188—21no—
256C2×D188—21no—
257C2×D188—21no—
258C2×D188—24no—
259C2×D188—44no—
260C2×D188—44no—
261C2×D188—44no—
262C2×D188—48no—
263C2×D188C2412yes—
264C2×D188C2412yes—
265C2×D188C2412yes—
266C2×C4×D47—24no—
267C2×C4×D47—44no—
268C2×Dic94—22no—
269C2×Dic94—22no—
270C2×Dic94—21no—
271C2×Dic94C2412yes—
272M16×C47—44no—
273C2×C8×C47—22no—
274C2×C8×C47—22no—
275C2×C8×C47—22no—
276C2×C8×C47—22no—
277C2×C8×C47—44no—
278C2×C8×C47C2412yes—
279C2×C8×C47C2412yes—
280C2×C8×C47C2412yes—
281C2×C8×C47C2412yes—
282C22⋊Dic47—24no—
283C22⋊Dic47—24no—
284C22⋊Dic47—24no—
285(C2×D47)⋊C4—24no—
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⋊Dic47—21no—
296C4⋊Dic47C2412yes—
297C4⋊Dic47C2412yes—
298C4⋊Dic47C2412yes—
299C4⋊Dic47C2412yes—
300Dic47⋊C4—24no—
301Dic47⋊C4—24no—
302C4×Dic47—24no—
303D376—44no—
304D376—44no—
305#10625325—44no—
306#10625325—44no—
307C23×C47—22no—
308C23×C47—22no—
309C23×C47—22no—
310C23×C47—22no—
311C23×C47—22no—
312C23×C47—22no—
313C23×C47—22no—
314C23×C47—22no—
315C23×C47—22no—
316C23×C47C22×D412yes—
317C23×C47C22×D412yes—
318C23×C47C22×D412yes—
319C23×C47C22×D411yescharacteristic
320C22×D47—22no—
321C22×D47—22no—
322C22×D47—22no—
323C22×D47—48no—
324C22×D47—42no—
325C22×D47—42no—
326C22×D47—42no—
327C22×D47—42no—
328C22×D47—42no—
329C22×D47—42no—
330C22×D47—42no—
331C22×D47—42no—
332C22×D47—42no—
333C22×D47—84no—
334C22×D47—84no—
335C22×D47—816no—
336Q8×C47—44no—
337D4×C47—44no—
338D4×C47—44no—
339D4×C47—44no—
340C2×C4×C47—22no—
341C2×C4×C47—22no—
342C2×C4×C47—22no—
343C2×C4×C47—24no—
344C2×C4×C47—24no—
345C2×C4×C47—24no—
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×C47C22×D412yes—
353C2×C4×C47C22×D412yes—
354C2×C4×C47C22×D412yes—
355C2×C4×C47C22×D411yescharacteristic
356C2×C4×C47H(5,𝔽2)12yes—
357C2×C4×C47H(5,𝔽2)12yes—
358C2×C4×C47C2511yescharacteristic
359C22⋊D47—48no—
360C22⋊D47—84no—
361C22⋊D47—84no—
362C22⋊D47—84no—
363C22⋊D47—84no—
364C22⋊D47—84no—
365C22⋊D47—84no—
366C2×Dic47—22no—
367C2×Dic47—22no—
368C2×Dic47—22no—
369C2×Dic47—22no—
370C2×Dic47—22no—
371C2×Dic47—42no—
372C2×Dic47—42no—
373C2×Dic47—42no—
374C2×Dic47—42no—
375C2×Dic47—42no—
376C2×Dic47—84no—
377D188—22no—
378D188—22no—
379D188—22no—
380D188—22no—
381D188—22no—
382D188—22no—
383D188—48no—
384D188—42no—
385D188—42no—
386D188—42no—
387C4×D47—48no—
388Dic94—22no—
389Dic94—22no—
390Dic94—42no—
391C8×C47—22no—
392C8×C47—22no—
393C8×C47—22no—
394C8×C47—22no—
395C2×#3198—471nomaximal, Sylow
396C22×C47—22no—
397C22×C47—22no—
398C22×C47—22no—
399C22×C47—22no—
400C22×C47—22no—
401C22×C47—22no—
402C22×C47—22no—
403C22×C47—22no—
404C22×C47—22no—
405C22×C47—44no—
406C22×C47—44no—
407C22×C47—44no—
408C22×C47#53412yes—
409C22×C47#57612yes—
410C22×C47#57712yes—
411C22×C47C23×D411yescharacteristic
412C2×D47—42no—
413C2×D47—42no—
414C2×D47—42no—
415C2×D47—42no—
416C2×D47—42no—
417C2×D47—42no—
418C2×D47—42no—
419C2×D47—42no—
420C2×D47—42no—
421C2×D47—816no—
422C2×D47—84no—
423C2×D47—84no—
424C2×D47—84no—
425C4×C47—22no—
426C4×C47—22no—
427C4×C47—22no—
428C4×C47#53412yes—
429C4×C47C2×H(5,𝔽2)11yescharacteristic
430C4×C47C2×H(5,𝔽2)11yescharacteristic
431Dic47—42no—
432Dic47—42no—
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×#449—471no—
449C2×#450—471no—
450C2×#447—471no—
451C2×#408D4711yescharacteristic, complemented
452C2×C47—42no—
453C2×C47—42no—
454C2×C47—42no—
455C2×C47#319814yescomplemented
456C2×C47C2×#53411yescharacteristic
457C2×C47C2×#57611yescharacteristic
458C2×C47C2×#57711yescharacteristic
459D47—82no—
460D47—82no—
461D47—82no—
462C22×#41—471no—
463C22×#41C2×D4711yescharacteristic
464C23×D4—471no—
465C22×SD16—471no—
466C22×SD16—471no—
467C22×D8—471no—
468C22×D8—471no—
469C22×M16C2×D4711yescharacteristic, complemented
470C23×C8C2×D4711yescharacteristic, complemented
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—471no—
486C2×#121—941no—
487C2×#121—941no—
488C2×#121—941no—
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#449—478no—
504#447—478no—
505C2×#107—471no—
506C2×#107—471no—
507C2×#106—471no—
508C2×#106—471no—
509C2×#103—471no—
510C2×#103—471no—
511C2×#102—471no—
512C2×#102—471no—
513C2×#102—471no—
514C2×#102—471no—
515C2×#102—471no—
516C2×#102—471no—
517#408C2×D4718yescomplemented
518C2×C22⋊C8C2×D4711yescharacteristic
519C2×C22⋊C8C2×D4711yescharacteristic
520C2×C22⋊C8C2×D4711yescharacteristic, complemented
521C2×C22⋊C8C2×D4711yescharacteristic, complemented
522C47C2×#319811yescharacteristic, complemented, Sylow
523C25—941no—
524C2×#41—42no—
525C2×#41—42no—
526C2×#41—474no—
527C2×#41—942no—
528C2×#41—1882no—
529C2×#41—1882no—
530C2×#41D18814yes—
531C2×#41C22×D4714yes—
532C22×Q8—471no—
533C22×Q8D18811yescharacteristic
534C22×D4—471no—
535C22×D4—471no—
536C22×D4—471no—
537C22×D4—474no—
538C22×D4—941no—
539C22×D4—941no—
540C22×D4—941no—
541C22×D4—941no—
542C22×D4—941no—
543C22×D4—941no—
544C22×D4—941no—
545C22×D4—941no—
546C22×D4—942no—
547C22×D4—1882no—
548C22×D4—1882no—
549C22×D4D18811yescharacteristic
550C22×D4D18811yescharacteristic
551C22×D4D18811yescharacteristic
552C23×C4—941no—
553C23×C4—941no—
554C23×C4C22×D4711yescharacteristic
555C23×C4C22×D4711yescharacteristic
556C23×C4C22×D4711yescharacteristic
557C2×SD16—474no—
558C2×SD16—474no—
559C2×SD16—1882no—
560C2×SD16—1882no—
561C2×D8—474no—
562C2×D8—474no—
563C2×D8—1882no—
564C2×D8—1882no—
565C2×M16—42no—
566C2×M16C22×D4714yescomplemented
567C22×C8—42no—
568C22×C8C22×D4711yescharacteristic
569C22×C8C22×D4711yescharacteristic
570C22×C8C22×D4711yescharacteristic
571C22×C8C22×D4711yescharacteristic
572C22×C8C22×D4714yescomplemented
573#127—948no—
574#124—948no—
575C22⋊Q8—474no—
576C22⋊Q8—474no—
577C22⋊Q8—948no—
578C22⋊Q8—942no—
579C22⋊Q8—942no—
580#121—474no—
581#121—474no—
582#121—474no—
583#121—474no—
584#121—474no—
585#121—474no—
586#121—948no—
587#121—948no—
588#121—948no—
589#121—942no—
590#121—942no—
591#121—942no—
592#121—942no—
593#121—942no—
594#121—942no—
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—471no—
604C2×C4⋊C4—941no—
605C2×C4⋊C4—942no—
606C2×C4⋊C4—941no—
607C2×C4⋊C4—941no—
608C2×C22⋊C4—941no—
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#103—474no—
624#102—474no—
625#102—474no—
626#102—474no—
627#102—474no—
628#102—474no—
629#102—474no—
630C22⋊C8C22×D4714yes—
631C22⋊C8C22×D4714yes—
632C22⋊C8C22×D4714yescomplemented
633C22⋊C8C22×D4714yescomplemented
634C24—944no—
635C24—941no—
636C24—941no—
637C24—941no—
638C24—3762no—
639C24—3762no—
640C24—1884no—
641C24C2×D18811yescharacteristic
642C24C2×D18811yescharacteristic
643C24C2×D18811yescharacteristic
644#41—48no—
645#41—44no—
646#41—44no—
647#41—1884no—
648#41—1884no—
649#41—1888no—
650C2×Q8—42no—
651C2×Q8—472no—
652C2×Q8—941no—
653C2×Q8—942no—
654C2×Q8—942no—
655C2×Q8C2×D18814yes—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4—42no—
659C2×D4—472no—
660C2×D4—472no—
661C2×D4—472no—
662C2×D4—944no—
663C2×D4—944no—
664C2×D4—944no—
665C2×D4—944no—
666C2×D4—944no—
667C2×D4—944no—
668C2×D4—944no—
669C2×D4—941no—
670C2×D4—941no—
671C2×D4—941no—
672C2×D4—944no—
673C2×D4—942no—
674C2×D4—942no—
675C2×D4—942no—
676C2×D4—942no—
677C2×D4—942no—
678C2×D4—942no—
679C2×D4—3762no—
680C2×D4—3762no—
681C2×D4—3762no—
682C2×D4—3762no—
683C2×D4—3762no—
684C2×D4—3762no—
685C2×D4—1884no—
686C2×D4—1884no—
687C2×D4—1884no—
688C2×D4—1888no—
689C2×D4—1884no—
690C2×D4C2×D18814yes—
691C2×D4C2×D18814yes—
692C2×D4C2×D18814yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—944no—
700C22×C4—941no—
701C22×C4—941no—
702C22×C4—941no—
703C22×C4—941no—
704C22×C4—941no—
705C22×C4—944no—
706C22×C4—3762no—
707C22×C4—1884no—
708C22×C4C2×D18812yes—
709C22×C4C2×D18812yes—
710C22×C4C2×D18812yes—
711C22×C4C2×D18811yescharacteristic
712C22×C4C2×D18811yescharacteristic
713C22×C4C2×D18811yescharacteristic
714C22×C4C23×D4712yes—
715C22×C4C23×D4712yes—
716C22×C4C23×D4712yes—
717C22×C4C23×D4711yescharacteristic
718SD16—1884no—
719SD16—1884no—
720D8—1884no—
721D8—1884no—
722M16—44no—
723C2×C8—22no—
724C2×C8—22no—
725C2×C8—22no—
726C2×C8—22no—
727C2×C8—44no—
728C2×C8C23×D4712yes—
729C2×C8C23×D4712yes—
730C2×C8C23×D4712yes—
731C2×C8C23×D4712yes—
732C4⋊C4—472no—
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⋊C4—941no—
743C22⋊C4—944no—
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—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—942no—
763C23—942no—
764C23—942no—
765C23—3764no—
766C23—3764no—
767C23—37616no—
768C23—1888no—
769C23—1882no—
770C23—1882no—
771C23—1882no—
772C23—1882no—
773C23—1882no—
774C23—1882no—
775C23—1882no—
776C23—1882no—
777C23—1882no—
778C23C22×D18812yes—
779C23C22×D18812yes—
780C23C22×D18812yes—
781C23C22×D18811yescharacteristic
782Q8—44no—
783Q8—942no—
784Q8—942no—
785Q8—1882no—
786D4—44no—
787D4—44no—
788D4—44no—
789D4—942no—
790D4—942no—
791D4—942no—
792D4—942no—
793D4—942no—
794D4—942no—
795D4—3764no—
796D4—3764no—
797D4—3764no—
798D4—3764no—
799D4—3764no—
800D4—3764no—
801D4—1888no—
802D4—1888no—
803D4—1882no—
804D4—1882no—
805D4—1882no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—942no—
819C2×C4—942no—
820C2×C4—942no—
821C2×C4—942no—
822C2×C4—942no—
823C2×C4—3764no—
824C2×C4—1888no—
825C2×C4—1882no—
826C2×C4—1882no—
827C2×C4—1882no—
828C2×C4—1882no—
829C2×C4—1882no—
830C2×C4C22×D18812yes—
831C2×C4C22×D18812yes—
832C2×C4C22×D18812yes—
833C2×C4C22×D18811yescharacteristic
834C2×C4#1309406912yes—
835C2×C4#1309406912yes—
836C2×C4C24×D4711yescharacteristic
837C8—22no—
838C8—22no—
839C8—22no—
840C8—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—37616no—
854C22—3764no—
855C22—3764no—
856C22—3764no—
857C22—1882no—
858C22—1882no—
859C22—1882no—
860C22—1882no—
861C22—1882no—
862C22—1882no—
863C22—1882no—
864C22—1882no—
865C22—1882no—
866C22#1568968512yes—
867C22#1568992812yes—
868C22#1568993512yes—
869C22C23×D18811yescharacteristic
870C4—22no—
871C4—22no—
872C4—22no—
873C4—1882no—
874C4—1882no—
875C4—1882no—
876C4—1882no—
877C4—1882no—
878C4#1568968512yes—
879C4C2×#1309406911yescharacteristic
880C4C2×#1309406911yescharacteristic
881C2—42no—
882C2—42no—
883C2—42no—
884C2—3762no—
885C2—3762no—
886C2—3762no—
887C2#2025424214yesdirect product factor
888C2C2×#1568968511yescharacteristic
889C2C2×#1568992811yescharacteristic
890C2C2×#1568993511yescharacteristic
subgroupG/H
centerC23C22×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#408C2
socleC23×C47C22×D4
hypercenterC2×#408D47
hypocenterC47C2×#3198
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
1. C2×#15689701C2semidirect
2. C2×#15689687C2semidirect
3. #20254242C2direct (N × H)
4. C2×#15689442C2semidirect
5. C2×#15689465C2semidirect
6. C2×#15689448C2semidirect
7. C2×#15689437C2semidirect
8. C2×#15689376C2semidirect
9. C2×#15689369C2semidirect
10. C2×#15689359C2semidirect
11. C2×#15689352C2semidirect
12. C2×#15689270C2semidirect
13. C2×#15689270C2semidirect
14. C2×#15689276C2semidirect
15. C2×#15689259C2semidirect
16. C2×C47×#408C2semidirect
17. C22×#10625350C22semidirect
24. #15689701C22semidirect
26. #15689687C22semidirect
30. C2×#13094003C22semidirect
37. C2×#13093998C22semidirect
44. C22×C4⋊Dic47C22semidirect
45. #15689465C22semidirect
46. #15689448C22semidirect
47. #15689442C22semidirect
48. #15689437C22semidirect
49. #15689376C22semidirect
50. #15689369C22semidirect
51. #15689359C22semidirect
52. #15689352C22semidirect
53. #15689276C22semidirect
54. #15689270C22semidirect
55. #15689270C22semidirect
56. #15689259C22semidirect
57. C2×#13093958C22semidirect
58. C2×#13093958C22semidirect
59. C2×#13093956C22semidirect
60. C2×#13093956C22semidirect
61. C2×#13093949C22semidirect
62. C2×#13093949C22semidirect
67. C2×#13093946C22semidirect
68. C2×#13093946C22semidirect
70. C22×M16×C47C22semidirect
71. C23×C8×C47C22semidirect
72. C47×#408C22semidirect
75. C2×C22⋊C8×C47C22semidirect
76. C2×C22⋊C8×C47C22semidirect
81. C2×#10625350C23semidirect
113. #13094003C23semidirect
126. #13093998C23semidirect
140. C2×C4⋊Dic47C23semidirect
153. #13093958C23semidirect
154. #13093958C23semidirect
155. #13093956C23semidirect
156. #13093956C23semidirect
157. #13093949C23semidirect
158. #13093949C23semidirect
163. #13093946C23semidirect
164. #13093946C23semidirect
177. C2×M16×C47C23semidirect
183. C22×C8×C47C23semidirect
186. C22⋊C8×C47C23semidirect
187. C22⋊C8×C47C23semidirect
451. C2×#408D47semidirect
455. C2×C47#3198semidirect
469. C22×M16C2×D47semidirect
470. C23×C8C2×D47semidirect
517. #408C2×D47semidirect
520. C2×C22⋊C8C2×D47semidirect
521. C2×C22⋊C8C2×D47semidirect
522. C47C2×#3198semidirect
566. C2×M16C22×D47semidirect
572. C22×C8C22×D47semidirect
632. C22⋊C8C22×D47semidirect
633. C22⋊C8C22×D47semidirect
887. C2#20254242direct (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×#156896872
#202542422
C2×#156894422
C2×#156894652
C2×#156894482
C2×#156894372
C2×#156893762
C2×#156893692
C2×#156893592
C2×#156893522
C2×#156892702
C2×#156892762
C2×#156892592
C2×C47×#4082
C2×#319847