Finite Group Databasebeta

← C2×#20254246 #27086937

Subgroups — C2×#20254246 #27086937

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×#15689703C211yesmaximal, characteristic, complemented
2C2×#15689692C211yesmaximal, characteristic, complemented
3#20254246C2116yesmaximal, direct product factor
4C2×#15689443C211yesmaximal, characteristic, complemented
5C2×#15689447C211yesmaximal, characteristic, complemented
6C2×#15689438C211yesmaximal, characteristic, complemented
7C2×#15689377C211yesmaximal, characteristic, complemented
8C2×#15689372C211yesmaximal, characteristic, complemented
9C2×#15689360C211yesmaximal, characteristic, complemented
10C2×#15689355C211yesmaximal, characteristic, complemented
11C2×#15689271C211yesmaximal, characteristic, complemented
12C2×#15689271C211yesmaximal, characteristic, complemented
13C2×#15689273C211yesmaximal, characteristic, complemented
14C2×#15689259C211yesmaximal, characteristic, complemented
15C2×#15689088C211yesmaximal, characteristic, complemented
16C2×C47×#485C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic, complemented
18C22×#10625350C2211yescharacteristic
19C23×D188C2211yescharacteristic
20C22×#10625336C2211yescharacteristic
21C22×#10625336C2211yescharacteristic
22C22×D376C2211yescharacteristic
23C22×D376C2211yescharacteristic
24C22×#10625324C2211yescharacteristic, complemented
25C22×C8×D47C2211yescharacteristic, complemented
26#15689703—24no—
27#15689703C2218yescomplemented
28#15689692—24no—
29#15689692C2218yescomplemented
30C2×#13094021—21no—
31C2×#13094012—21no—
32C2×#13094002—21no—
33C2×#13094000C2211yescharacteristic, complemented
34C2×#13093999—21no—
35C2×#13093999C2211yescharacteristic
36C2×#13093999C2211yescharacteristic
37C2×#13093999C2211yescharacteristic
38C2×#13093999C2211yescharacteristic
39C2×#13093999C2211yescharacteristic, complemented
40C2×#13093998C2211yescharacteristic
41C2×#13093997—21no—
42C2×#13093997—21no—
43C2×#13093994—21no—
44C2×#13093994—21no—
45C2×C4⋊C4×D47C2211yescharacteristic, complemented
46#15689447C2218yescomplemented
47#15689443C2218yescomplemented
48#15689438C2218yescomplemented
49#15689377C2218yescomplemented
50#15689372C2218yescomplemented
51#15689360C2218yescomplemented
52#15689355C2218yescomplemented
53#15689273C2218yescomplemented
54#15689271C2218yescomplemented
55#15689271C2218yescomplemented
56#15689259C2218yescomplemented
57C2×#13093957C2211yescharacteristic, complemented
58C2×#13093955C2211yescharacteristic, complemented
59C2×#13093946C2211yescharacteristic
60C2×#13093946C2211yescharacteristic
61C2×#13093944C2211yescharacteristic
62C2×#13093944C2211yescharacteristic
63C2×#13093944C2211yescharacteristic, complemented
64C2×#13093944C2211yescharacteristic, complemented
65#15689088C2218yescomplemented
66C2×C22⋊(C47⋊C8)C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
68C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
69C2×C22⋊Q8×C47C2211yescharacteristic
70C2×#117×C47C2211yescharacteristic
71C47×#485C2218yescomplemented
72C2×#107×C47C2211yescharacteristic, complemented
73C2×#106×C47C2211yescharacteristic, complemented
74C2×#103×C47C2211yescharacteristic, complemented
75C2×#103×C47C2211yescharacteristic, complemented
76C2×C22⋊C8×C47C2211yescharacteristic
77C24×D47—21no—
78C2×#10625354—22no—
79C2×#10625354—42no—
80C2×#10625354—42no—
81C2×#10625354C2314yescomplemented
82C2×#10625350—42no—
83C2×#10625350—42no—
84C2×#10625350D414yes—
85C2×#10625350C2314yes—
86C22×Dic94D411yescharacteristic
87C22×D188—21no—
88C22×D188—21no—
89C22×D188—22no—
90C22×D188—21no—
91C22×D188—21no—
92C22×D188—21no—
93C22×D188—21no—
94C22×D188—21no—
95C22×D188—42no—
96C22×D188—42no—
97C22×D188D411yescharacteristic
98C22×D188C2311yescharacteristic
99C22×D188C2311yescharacteristic
100C22×D188C2311yescharacteristic
101C22×D188C2314yes—
102C22×C22⋊D47—21no—
103C22×C22⋊D47D411yescharacteristic
104C22×C22⋊D47D411yescharacteristic
105C22×C4×D47—21no—
106C22×C4×D47—21no—
107C22×C4×D47C2311yescharacteristic
108C22×C4×D47C2311yescharacteristic
109C2×#10625336—42no—
110C2×#10625336—42no—
111C2×#10625336C2314yes—
112C2×#10625336C2314yes—
113C2×D376—42no—
114C2×D376—42no—
115C2×D376C2314yes—
116C2×D376C2314yes—
117C2×#10625324—42no—
118C2×#10625324C2314yescomplemented
119C22×C47⋊C8C2311yescharacteristic
120C22×C47⋊C8C2311yescharacteristic
121C2×C8×D47—42no—
122C2×C8×D47C2314yescomplemented
123#13094021—28no—
124#13094012—28no—
125#13094002—28no—
126#13094000—22no—
127#13094000C2314yescomplemented
128#13093999—28no—
129#13093999—22no—
130#13093999—22no—
131#13093999—22no—
132#13093999—22no—
133#13093999—22no—
134#13093999C2314yes—
135#13093999C2314yes—
136#13093999C2314yes—
137#13093999C2314yes—
138#13093999C2314yescomplemented
139#13093998—22no—
140#13093998C2314yes—
141#13093997—28no—
142#13093997—28no—
143#13093994—28no—
144#13093994—28no—
145C2×C4⋊Dic47C2311yescharacteristic
146C2×Dic47⋊C4—21no—
147C2×Dic47⋊C4—21no—
148C4⋊C4×D47—22no—
149C4⋊C4×D47C2314yescomplemented
150C2×(C2×D47)⋊C4—21no—
151C2×(C2×D47)⋊C4—21no—
152C2×(C2×D47)⋊C4—21no—
153C2×(C2×D47)⋊C4—21no—
154C2×(C2×D47)⋊C4—21no—
155C2×(C2×D47)⋊C4—21no—
156C2×(C2×D47)⋊C4—21no—
157#13093957C2314yescomplemented
158#13093955C2314yescomplemented
159#13093946C2314yes—
160#13093946C2314yes—
161#13093944C2314yes—
162#13093944C2314yes—
163#13093944C2314yescomplemented
164#13093944C2314yescomplemented
165C22⋊(C47⋊C8)C2314yes—
166(C2×D47)⋊C8C2314yescomplemented
167(C2×D47)⋊C8C2314yescomplemented
168C22×Q8×C47C2311yescharacteristic
169C23×C4×C47C2311yescharacteristic
170C22×C8×C47C2311yescharacteristic
171C22×C8×C47C2311yescharacteristic
172C22⋊Q8×C47—22no—
173C22⋊Q8×C47C2314yes—
174#117×C47—22no—
175#117×C47C2314yes—
176C2×C4⋊C4×C47—21no—
177C2×C4⋊C4×C47C2311yescharacteristic
178C2×C4⋊C4×C47C2311yescharacteristic
179C2×C4⋊C4×C47C2311yescharacteristic
180C2×C22⋊C4×C47—21no—
181C2×C22⋊C4×C47—21no—
182C2×C42×C47—21no—
183#107×C47C2314yescomplemented
184#106×C47C2314yescomplemented
185#103×C47C2314yescomplemented
186#103×C47C2314yescomplemented
187C22⋊C8×C47C2314yes—
188C24×C47C2×D411yescharacteristic
189C23×D47—21no—
190C23×D47—21no—
191C23×D47—21no—
192C23×D47—24no—
193C23×D47—44no—
194C23×D47—82no—
195C23×D47—82no—
196C23×D47C2×D411yescharacteristic
197C23×D47C2×D411yescharacteristic
198C2×Q8×C47—21no—
199C2×Q8×C47—22no—
200C2×Q8×C47—22no—
201C2×Q8×C47C2412yes—
202C22×C4×C47—22no—
203C22×C4×C47—22no—
204C22×C4×C47—21no—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47—21no—
208C22×C4×C47C2×D411yescharacteristic
209C22×C4×C47C2×D412yes—
210C22×C4×C47C2412yes—
211C22×C4×C47C2411yescharacteristic
212C2×C22⋊D47—24no—
213C2×C22⋊D47—42no—
214C2×C22⋊D47—42no—
215C2×C22⋊D47—82no—
216C2×C22⋊D47C2×D414yes—
217C2×C22⋊D47C2×D414yes—
218C22×Dic47—21no—
219C22×Dic47C2×D411yescharacteristic
220C22×Dic47C2×D411yescharacteristic
221#10625354—44no—
222#10625354—44no—
223#10625354—48no—
224#10625350—48no—
225#10625350—44no—
226#10625350—44no—
227C2×D188—22no—
228C2×D188—22no—
229C2×D188—22no—
230C2×D188—22no—
231C2×D188—22no—
232C2×D188—22no—
233C2×D188—24no—
234C2×D188—21no—
235C2×D188—21no—
236C2×D188—21no—
237C2×D188—24no—
238C2×D188—24no—
239C2×D188—24no—
240C2×D188—24no—
241C2×D188—24no—
242C2×D188—24no—
243C2×D188—44no—
244C2×D188—44no—
245C2×D188—42no—
246C2×D188—44no—
247C2×D188—48no—
248C2×D188—44no—
249C2×D188—82no—
250C2×D188—82no—
251C2×D188—82no—
252C2×D188—82no—
253C2×D188—82no—
254C2×D188C2×D414yes—
255C2×D188C2412yes—
256C2×D188C2412yes—
257C2×D188C2412yes—
258C2×C4×D47—22no—
259C2×C4×D47—22no—
260C2×C4×D47—22no—
261C2×C4×D47—22no—
262C2×C4×D47—24no—
263C2×C4×D47—24no—
264C2×C4×D47—44no—
265C2×C4×D47—82no—
266C2×C4×D47C2×D412yes—
267C2×C4×D47C2×D412yes—
268C2×C4×D47C2412yes—
269C2×C4×D47C2412yes—
270C2×Dic94—42no—
271C2×Dic94C2×D414yes—
272C2×C8×C47—22no—
273C2×C8×C47—22no—
274C2×C8×C47C2412yes—
275C2×C8×C47C2412yes—
276C4⋊C4×C47—24no—
277C4⋊C4×C47—21no—
278C4⋊C4×C47—21no—
279C4⋊C4×C47—21no—
280C4⋊C4×C47C2412yes—
281C4⋊C4×C47C2412yes—
282C4⋊C4×C47C2412yes—
283C22⋊C4×C47—24no—
284C22⋊C4×C47—24no—
285C42×C47—24no—
286#10625336—44no—
287#10625336—44no—
288(C2×D47)⋊C4—24no—
289(C2×D47)⋊C4—24no—
290(C2×D47)⋊C4—24no—
291(C2×D47)⋊C4—24no—
292(C2×D47)⋊C4—24no—
293(C2×D47)⋊C4—24no—
294(C2×D47)⋊C4—24no—
295C4⋊Dic47—21no—
296C4⋊Dic47C2412yes—
297Dic47⋊C4—24no—
298Dic47⋊C4—24no—
299C2×C47⋊C8—22no—
300C2×C47⋊C8—22no—
301C2×C47⋊C8C2412yes—
302C2×C47⋊C8C2412yes—
303D376—44no—
304D376—44no—
305#10625324—44no—
306C8×D47—44no—
307C23×C47—22no—
308C23×C47—22no—
309C23×C47—22no—
310C23×C47C22×D412yes—
311C23×C47C22×D411yescharacteristic
312C22×D47—22no—
313C22×D47—22no—
314C22×D47—22no—
315C22×D47—22no—
316C22×D47—22no—
317C22×D47—22no—
318C22×D47—22no—
319C22×D47—22no—
320C22×D47—22no—
321C22×D47—48no—
322C22×D47—42no—
323C22×D47—42no—
324C22×D47—42no—
325C22×D47—42no—
326C22×D47—42no—
327C22×D47—42no—
328C22×D47—42no—
329C22×D47—42no—
330C22×D47—42no—
331C22×D47—84no—
332C22×D47—84no—
333C22×D47—816no—
334C22×D47C22×D412yes—
335C22×D47C22×D412yes—
336Q8×C47—22no—
337Q8×C47—22no—
338Q8×C47—42no—
339C2×C4×C47—22no—
340C2×C4×C47—24no—
341C2×C4×C47—22no—
342C2×C4×C47—22no—
343C2×C4×C47—22no—
344C2×C4×C47—22no—
345C2×C4×C47—22no—
346C2×C4×C47—22no—
347C2×C4×C47—42no—
348C2×C4×C47—42no—
349C2×C4×C47—42no—
350C2×C4×C47—42no—
351C2×C4×C47C22×D412yes—
352C2×C4×C47C22×D411yescharacteristic
353C2×C4×C47H(5,𝔽2)12yes—
354C2×C4×C47H(5,𝔽2)12yes—
355C2×C4×C47C2511yescharacteristic
356C22⋊D47—44no—
357C22⋊D47—44no—
358C22⋊D47—84no—
359C2×Dic47—22no—
360C2×Dic47—22no—
361C2×Dic47—22no—
362C2×Dic47—42no—
363C2×Dic47C22×D412yes—
364C2×Dic47C22×D412yes—
365D188—22no—
366D188—22no—
367D188—22no—
368D188—22no—
369D188—22no—
370D188—22no—
371D188—44no—
372D188—48no—
373D188—48no—
374D188—42no—
375D188—42no—
376D188—42no—
377D188—84no—
378D188—84no—
379D188—84no—
380D188—84no—
381D188—84no—
382C4×D47—24no—
383C4×D47—24no—
384C4×D47—22no—
385C4×D47—22no—
386C4×D47—22no—
387C4×D47—22no—
388C4×D47—48no—
389C4×D47—84no—
390Dic94—44no—
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#53412yes—
401C22×C47#57612yes—
402C22×C47#57712yes—
403C22×C47C23×D411yescharacteristic
404C2×D47—22no—
405C2×D47—22no—
406C2×D47—22no—
407C2×D47—22no—
408C2×D47—22no—
409C2×D47—22no—
410C2×D47—44no—
411C2×D47—44no—
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—42no—
427C4×C47—42no—
428C4×C47—42no—
429C4×C47—42no—
430C4×C47#53412yes—
431C4×C47C2×H(5,𝔽2)11yescharacteristic
432C4×C47C2×H(5,𝔽2)11yescharacteristic
433Dic47—22no—
434Dic47—22no—
435Dic47—42no—
436C2×#537—471no—
437C2×#535—471no—
438#3198—4716no—
439C2×#481—471no—
440C2×#485D4711yescharacteristic, complemented
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×#408—471no—
452C2×C47—42no—
453C2×C47#319814yescomplemented
454C2×C47C2×#53411yescharacteristic
455C2×C47C2×#57611yescharacteristic
456C2×C47C2×#57711yescharacteristic
457D47—42no—
458D47—42no—
459D47—82no—
460D47—82no—
461D47—82no—
462C22×#41—471no—
463C22×#41—471no—
464C23×D4—471no—
465C22×SD16—471no—
466C22×SD16—471no—
467C22×D8—471no—
468C22×D8—471no—
469C22×M16—471no—
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—941no—
479C2×C22⋊Q8C2×D4711yescharacteristic
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×#117C2×D4711yescharacteristic
492C22×C4⋊C4—471no—
493#485C2×D4718yescomplemented
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×#107C2×D4711yescharacteristic, complemented
507C2×#106—471no—
508C2×#106C2×D4711yescharacteristic, complemented
509C2×#103C2×D4711yescharacteristic, complemented
510C2×#103C2×D4711yescharacteristic, complemented
511C2×#102—471no—
512C2×#102—471no—
513C2×#102—471no—
514C2×#102—471no—
515C2×#102—471no—
516C2×#102—471no—
517#408—478no—
518C2×C22⋊C8—471no—
519C2×C22⋊C8—471no—
520C2×C22⋊C8—471no—
521C2×C22⋊C8C2×D4711yescharacteristic
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×Q8C22×D4711yescharacteristic
534C22×D4—471no—
535C22×D4—471no—
536C22×D4—471no—
537C22×D4—471no—
538C22×D4—471no—
539C22×D4—471no—
540C22×D4—474no—
541C22×D4—941no—
542C22×D4—941no—
543C22×D4—941no—
544C22×D4—941no—
545C22×D4—941no—
546C22×D4—941no—
547C22×D4—941no—
548C22×D4—941no—
549C22×D4—942no—
550C22×D4—1882no—
551C22×D4—1882no—
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—474no—
562C2×D8—474no—
563C2×D8—1882no—
564C2×D8—1882no—
565C2×M16—474no—
566C2×M16—1882no—
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—22no—
576C22⋊Q8—474no—
577C22⋊Q8—948no—
578C22⋊Q8—942no—
579C22⋊Q8C22×D4714yes—
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—942no—
589#121—942no—
590#121—942no—
591#121—942no—
592#121—942no—
593#121—948no—
594#121—942no—
595#120—948no—
596#120—948no—
597#117—22no—
598#117C22×D4714yes—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—471no—
601C2×C4⋊C4—474no—
602C2×C4⋊C4—942no—
603C2×C4⋊C4—941no—
604C2×C4⋊C4—941no—
605C2×C4⋊C4C22×D4711yescharacteristic
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—21no—
618#107—474no—
619#107C22×D4714yescomplemented
620#106—474no—
621#106C22×D4714yescomplemented
622#103C22×D4714yescomplemented
623#103C22×D4714yescomplemented
624#102—474no—
625#102—474no—
626#102—474no—
627#102—474no—
628#102—474no—
629#102—474no—
630C22⋊C8—474no—
631C22⋊C8—474no—
632C22⋊C8—474no—
633C22⋊C8C22×D4714yes—
634C24—471no—
635C24—471no—
636C24—944no—
637C24—941no—
638C24—941no—
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—21no—
651C2×Q8—22no—
652C2×Q8—22no—
653C2×Q8—474no—
654C2×Q8—1882no—
655C2×Q8C23×D4712yes—
656C2×D4—474no—
657C2×D4—474no—
658C2×D4—474no—
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—1882no—
688C2×D4—1884no—
689C2×D4—1888no—
690C2×D4—1884no—
691C2×D4—1882no—
692C2×D4—1882no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—471no—
700C22×C4—471no—
701C22×C4—472no—
702C22×C4—472no—
703C22×C4—472no—
704C22×C4—472no—
705C22×C4—944no—
706C22×C4—944no—
707C22×C4—942no—
708C22×C4—942no—
709C22×C4—942no—
710C22×C4—942no—
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—1884no—
721D8—1884no—
722M16—1884no—
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—24no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—472no—
737C4⋊C4—944no—
738C4⋊C4—944no—
739C4⋊C4—941no—
740C4⋊C4C23×D4712yes—
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—24no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—472no—
757C23—472no—
758C23—942no—
759C23—942no—
760C23—942no—
761C23—942no—
762C23—942no—
763C23—942no—
764C23—942no—
765C23—942no—
766C23—942no—
767C23—3764no—
768C23—3764no—
769C23—37616no—
770C23—1888no—
771C23—1882no—
772C23—1882no—
773C23—1882no—
774C23—1882no—
775C23—1882no—
776C23—1882no—
777C23—1882no—
778C23—1882no—
779C23—1882no—
780C23C2×D4×D4712yes—
781C23C2×D4×D4711yescharacteristic
782Q8—22no—
783Q8—22no—
784Q8—42no—
785Q8—1884no—
786D4—942no—
787D4—942no—
788D4—942no—
789D4—942no—
790D4—942no—
791D4—942no—
792D4—3764no—
793D4—3764no—
794D4—3764no—
795D4—3764no—
796D4—3764no—
797D4—3764no—
798D4—1884no—
799D4—1888no—
800D4—1888no—
801D4—1884no—
802D4—1884no—
803D4—1882no—
804D4—1882no—
805D4—1882no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—472no—
819C2×C4—472no—
820C2×C4—942no—
821C2×C4—942no—
822C2×C4—944no—
823C2×C4—944no—
824C2×C4—942no—
825C2×C4—942no—
826C2×C4—942no—
827C2×C4—942no—
828C2×C4—942no—
829C2×C4—3764no—
830C2×C4—1888no—
831C2×C4—1882no—
832C2×C4C2×D4×D4712yes—
833C2×C4C2×D4×D4711yescharacteristic
834C2×C4#1309407012yes—
835C2×C4#1309407012yes—
836C2×C4C24×D4711yescharacteristic
837C8—22no—
838C8—22no—
839C8—942no—
840C8—942no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—44no—
845C22—942no—
846C22—942no—
847C22—942no—
848C22—942no—
849C22—942no—
850C22—942no—
851C22—37616no—
852C22—3764no—
853C22—3764no—
854C22—3764no—
855C22—1882no—
856C22—1882no—
857C22—1882no—
858C22—1882no—
859C22—1882no—
860C22—1882no—
861C22—1882no—
862C22—1882no—
863C22—1882no—
864C22—1884no—
865C22—1884no—
866C22#1568968412yes—
867C22#1568992512yes—
868C22#1568993212yes—
869C22C22×D4×D4711yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—42no—
875C4—942no—
876C4—942no—
877C4—1882no—
878C4#1568968412yes—
879C4C2×#1309407011yescharacteristic
880C4C2×#1309407011yescharacteristic
881C2—42no—
882C2—3762no—
883C2—3762no—
884C2—3762no—
885C2—1882no—
886C2—1882no—
887C2#2025424614yesdirect product factor
888C2C2×#1568968411yescharacteristic
889C2C2×#1568992511yescharacteristic
890C2C2×#1568993211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#485C2
socleC23×C47C22×D4
hypercenterC2×#485D47
hypocenterC47C2×#3198
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
1. C2×#15689703C2semidirect
2. C2×#15689692C2semidirect
3. #20254246C2direct (N × H)
4. C2×#15689443C2semidirect
5. C2×#15689447C2semidirect
6. C2×#15689438C2semidirect
7. C2×#15689377C2semidirect
8. C2×#15689372C2semidirect
9. C2×#15689360C2semidirect
10. C2×#15689355C2semidirect
11. C2×#15689271C2semidirect
12. C2×#15689271C2semidirect
13. C2×#15689273C2semidirect
14. C2×#15689259C2semidirect
15. C2×#15689088C2semidirect
16. C2×C47×#485C2semidirect
17. C22×#10625354C22semidirect
24. C22×#10625324C22semidirect
25. C22×C8×D47C22semidirect
27. #15689703C22semidirect
29. #15689692C22semidirect
33. C2×#13094000C22semidirect
39. C2×#13093999C22semidirect
45. C2×C4⋊C4×D47C22semidirect
46. #15689447C22semidirect
47. #15689443C22semidirect
48. #15689438C22semidirect
49. #15689377C22semidirect
50. #15689372C22semidirect
51. #15689360C22semidirect
52. #15689355C22semidirect
53. #15689273C22semidirect
54. #15689271C22semidirect
55. #15689271C22semidirect
56. #15689259C22semidirect
57. C2×#13093957C22semidirect
58. C2×#13093955C22semidirect
63. C2×#13093944C22semidirect
64. C2×#13093944C22semidirect
65. #15689088C22semidirect
67. C2×(C2×D47)⋊C8C22semidirect
68. C2×(C2×D47)⋊C8C22semidirect
71. C47×#485C22semidirect
72. C2×#107×C47C22semidirect
73. C2×#106×C47C22semidirect
74. C2×#103×C47C22semidirect
75. C2×#103×C47C22semidirect
81. C2×#10625354C23semidirect
118. C2×#10625324C23semidirect
122. C2×C8×D47C23semidirect
127. #13094000C23semidirect
138. #13093999C23semidirect
149. C4⋊C4×D47C23semidirect
157. #13093957C23semidirect
158. #13093955C23semidirect
163. #13093944C23semidirect
164. #13093944C23semidirect
166. (C2×D47)⋊C8C23semidirect
167. (C2×D47)⋊C8C23semidirect
183. #107×C47C23semidirect
184. #106×C47C23semidirect
185. #103×C47C23semidirect
186. #103×C47C23semidirect
440. C2×#485D47semidirect
453. C2×C47#3198semidirect
493. #485C2×D47semidirect
506. C2×#107C2×D47semidirect
508. C2×#106C2×D47semidirect
509. C2×#103C2×D47semidirect
510. C2×#103C2×D47semidirect
522. C47C2×#3198semidirect
619. #107C22×D47semidirect
621. #106C22×D47semidirect
622. #103C22×D47semidirect
623. #103C22×D47semidirect
887. C2#20254246direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897032
C2×#156896922
#202542462
C2×#156894432
C2×#156894472
C2×#156894382
C2×#156893772
C2×#156893722
C2×#156893602
C2×#156893552
C2×#156892712
C2×#156892732
C2×#156892592
C2×#156890882
C2×C47×#4852
C2×#319847