Finite Group Databasebeta

← C2×#20254241 #27086932

Subgroups — C2×#20254241 #27086932

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×#15689689C211yesmaximal, characteristic, complemented
3#20254241C2116yesmaximal, direct product factor
4C2×#15689440C211yesmaximal, characteristic, complemented
5C2×#15689462C211yesmaximal, characteristic, complemented
6C2×#15689450C211yesmaximal, characteristic, complemented
7C2×#15689438C211yesmaximal, characteristic, complemented
8C2×#15689376C211yesmaximal, characteristic, complemented
9C2×#15689357C211yesmaximal, characteristic, complemented
10C2×#15689354C211yesmaximal, characteristic, complemented
11C2×#15689271C211yesmaximal, characteristic, complemented
12C2×#15689267C211yesmaximal, characteristic, complemented
13C2×#15689272C211yesmaximal, characteristic, complemented
14C2×#15689258C211yesmaximal, characteristic, complemented
15C2×#15689091C211yesmaximal, characteristic, complemented
16C2×C47×#468C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic, complemented
18C22×#10625350C2211yescharacteristic
19C22×D4×D47C2211yescharacteristic
20C22×#10625336C2211yescharacteristic
21C22×D376C2211yescharacteristic
22C22×#10625334C2211yescharacteristic
23C23×C47⋊C8C2211yescharacteristic, complemented
24#15689703—24no—
25#15689703C2218yescomplemented
26#15689689—24no—
27#15689689C2218yescomplemented
28C2×#13094020—21no—
29C2×#13094010—21no—
30C2×#13094002—21no—
31C2×#13094000C2211yescharacteristic
32C2×#13093999—21no—
33C2×#13093999C2211yescharacteristic
34C2×#13093999C2211yescharacteristic
35C2×#13093998C2211yescharacteristic
36C2×#13093998C2211yescharacteristic, complemented
37C2×#13093997—21no—
38C2×#13093997—21no—
39C2×#13093995C2211yescharacteristic
40C2×#13093994—21no—
41C2×#13093992—21no—
42C2×#13093982C2211yescharacteristic
43C2×C4⋊C4×D47C2211yescharacteristic, complemented
44#15689462C2218yescomplemented
45#15689450C2218yescomplemented
46#15689440C2218yescomplemented
47#15689438C2218yescomplemented
48#15689376C2218yescomplemented
49#15689357C2218yescomplemented
50#15689354C2218yescomplemented
51#15689272C2218yescomplemented
52#15689271C2218yescomplemented
53#15689267C2218yescomplemented
54#15689258C2218yescomplemented
55C2×#13093957C2211yescharacteristic, complemented
56C2×#13093956C2211yescharacteristic, complemented
57C2×#13093955C2211yescharacteristic, complemented
58C2×#13093948C2211yescharacteristic, complemented
59C2×#13093946C2211yescharacteristic
60C2×#13093946C2211yescharacteristic, complemented
61C2×#13093945C2211yescharacteristic
62C2×#13093944C2211yescharacteristic
63C2×#13093944C2211yescharacteristic, complemented
64#15689091C2218yescomplemented
65C2×(C2×D47)⋊C8C2211yescharacteristic
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
68C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
69C22×SD16×C47C2211yescharacteristic
70C22×M16×C47C2211yescharacteristic, complemented
71C2×C22⋊Q8×C47C2211yescharacteristic, complemented
72C2×#121×C47C2211yescharacteristic
73C47×#468C2218yescomplemented
74C2×#107×C47C2211yescharacteristic, complemented
75C2×#103×C47C2211yescharacteristic, complemented
76C2×#102×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—21no—
90C22×D188D411yescharacteristic
91C22×D188C2311yescharacteristic
92C22×D188C2311yescharacteristic
93C22×C22⋊D47—21no—
94C22×C22⋊D47—21no—
95C22×C22⋊D47—21no—
96C22×C22⋊D47—21no—
97C22×C22⋊D47D411yescharacteristic
98C22×C22⋊D47D411yescharacteristic
99C2×D4×D47—22no—
100C2×D4×D47—42no—
101C2×D4×D47—42no—
102C2×D4×D47C2314yes—
103C22×C4×D47—21no—
104C22×C4×D47—21no—
105C22×C4×D47C2311yescharacteristic
106C22×C4×D47C2311yescharacteristic
107C2×#10625336—42no—
108C2×#10625336C2314yes—
109C2×D376—42no—
110C2×D376C2314yes—
111C2×#10625334—42no—
112C2×#10625334C2314yes—
113C22×C47⋊C8—42no—
114C22×C47⋊C8C2311yescharacteristic
115C22×C47⋊C8C2311yescharacteristic
116C22×C47⋊C8C2314yescomplemented
117#13094020—28no—
118#13094010—28no—
119#13094002—28no—
120#13094000—22no—
121#13094000C2314yes—
122#13093999—28no—
123#13093999—22no—
124#13093999—22no—
125#13093999C2314yes—
126#13093999C2314yes—
127#13093998—22no—
128#13093998—22no—
129#13093998C2314yes—
130#13093998C2314yescomplemented
131#13093997—28no—
132#13093997—28no—
133#13093995—22no—
134#13093995C2314yes—
135#13093994—28no—
136#13093992—28no—
137#13093982—22no—
138#13093982C2314yes—
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×(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#13093957C2314yescomplemented
154#13093956C2314yescomplemented
155#13093955C2314yescomplemented
156#13093948C2314yescomplemented
157#13093946C2314yes—
158#13093946C2314yescomplemented
159#13093945C2314yes—
160#13093944C2314yes—
161#13093944C2314yescomplemented
162(C2×D47)⋊C8C2314yes—
163(C2×D47)⋊C8C2314yes—
164(C2×D47)⋊C8C2314yescomplemented
165(C2×D47)⋊C8C2314yescomplemented
166C22×Q8×C47C2311yescharacteristic
167C22×D4×C47—21no—
168C22×D4×C47C2311yescharacteristic
169C23×C4×C47C2311yescharacteristic
170C2×SD16×C47—42no—
171C2×SD16×C47C2314yes—
172C2×M16×C47—42no—
173C2×M16×C47C2314yescomplemented
174C22×C8×C47C2311yescharacteristic
175C22×C8×C47C2311yescharacteristic
176C22⋊Q8×C47—22no—
177C22⋊Q8×C47C2314yescomplemented
178#121×C47—22no—
179#121×C47C2314yes—
180C2×C4⋊C4×C47—21no—
181C2×C4⋊C4×C47C2311yescharacteristic
182C2×C4⋊C4×C47C2311yescharacteristic
183C2×C22⋊C4×C47—21no—
184C2×C22⋊C4×C47—21no—
185#107×C47C2314yescomplemented
186#103×C47C2314yescomplemented
187#102×C47C2314yes—
188C24×C47—21no—
189C24×C47C2×D411yescharacteristic
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—
202C2×D4×C47—24no—
203C2×D4×C47—21no—
204C2×D4×C47—22no—
205C2×D4×C47—22no—
206C2×D4×C47—82no—
207C2×D4×C47C2412yes—
208C22×C4×C47—22no—
209C22×C4×C47—22no—
210C22×C4×C47—21no—
211C22×C4×C47—21no—
212C22×C4×C47—21no—
213C22×C4×C47C2×D411yescharacteristic
214C22×C4×C47C2×D412yes—
215C22×C4×C47C2412yes—
216C22×C4×C47C2411yescharacteristic
217C2×C22⋊D47—24no—
218C2×C22⋊D47—24no—
219C2×C22⋊D47—24no—
220C2×C22⋊D47—24no—
221C2×C22⋊D47—42no—
222C2×C22⋊D47—42no—
223C2×C22⋊D47—44no—
224C2×C22⋊D47—82no—
225C2×C22⋊D47—82no—
226C2×C22⋊D47—82no—
227C2×C22⋊D47C2×D414yes—
228C2×C22⋊D47C2×D414yes—
229C22×Dic47—21no—
230C22×Dic47—21no—
231C22×Dic47C2×D411yescharacteristic
232C22×Dic47C2×D411yescharacteristic
233#10625354—44no—
234#10625354—44no—
235#10625354—48no—
236D4×D47—44no—
237D4×D47—44no—
238D4×D47—48no—
239#10625350—48no—
240#10625350—44no—
241#10625350—44no—
242C2×D188—22no—
243C2×D188—22no—
244C2×D188—22no—
245C2×D188—22no—
246C2×D188—24no—
247C2×D188—21no—
248C2×D188—21no—
249C2×D188—24no—
250C2×D188—24no—
251C2×D188—42no—
252C2×D188—44no—
253C2×D188—82no—
254C2×D188—82no—
255C2×D188C2×D414yes—
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—
272SD16×C47—44no—
273M16×C47—44no—
274C2×C8×C47—22no—
275C2×C8×C47—22no—
276C2×C8×C47C2412yes—
277C2×C8×C47C2412yes—
278C4⋊C4×C47—24no—
279C4⋊C4×C47—21no—
280C4⋊C4×C47—21no—
281C4⋊C4×C47C2412yes—
282C4⋊C4×C47C2412yes—
283C22⋊C4×C47—24no—
284C22⋊C4×C47—24no—
285C22⋊Dic47—24no—
286#10625336—44no—
287#10625334—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—
294C4⋊Dic47—21no—
295C4⋊Dic47—21no—
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—
306D376—44no—
307C23×C47—22no—
308C23×C47—22no—
309C23×C47—22no—
310C23×C47—22no—
311C23×C47—42no—
312C23×C47—42no—
313C23×C47—42no—
314C23×C47C22×D412yes—
315C23×C47C22×D411yescharacteristic
316C22×D47—22no—
317C22×D47—22no—
318C22×D47—22no—
319C22×D47—22no—
320C22×D47—22no—
321C22×D47—22no—
322C22×D47—22no—
323C22×D47—22no—
324C22×D47—48no—
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—
339D4×C47—22no—
340D4×C47—22no—
341D4×C47—42no—
342D4×C47—84no—
343C2×C4×C47—22no—
344C2×C4×C47—24no—
345C2×C4×C47—22no—
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×C47—42no—
353C2×C4×C47C22×D412yes—
354C2×C4×C47C22×D411yescharacteristic
355C2×C4×C47H(5,𝔽2)12yes—
356C2×C4×C47H(5,𝔽2)12yes—
357C2×C4×C47C2511yescharacteristic
358C22⋊D47—44no—
359C22⋊D47—44no—
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—42no—
369C2×Dic47—42no—
370C2×Dic47C22×D412yes—
371C2×Dic47C22×D412yes—
372D188—22no—
373D188—22no—
374D188—22no—
375D188—22no—
376D188—44no—
377D188—48no—
378D188—42no—
379D188—42no—
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—42no—
401C22×C47—42no—
402C22×C47—42no—
403C22×C47—84no—
404C22×C47#53412yes—
405C22×C47#57612yes—
406C22×C47#57712yes—
407C22×C47C23×D411yescharacteristic
408C2×D47—22no—
409C2×D47—22no—
410C2×D47—22no—
411C2×D47—22no—
412C2×D47—22no—
413C2×D47—22no—
414C2×D47—44no—
415C2×D47—44no—
416C2×D47—42no—
417C2×D47—42no—
418C2×D47—42no—
419C2×D47—42no—
420C2×D47—42no—
421C2×D47—42no—
422C2×D47—816no—
423C2×D47—84no—
424C2×D47—84no—
425C4×C47—22no—
426C4×C47—42no—
427C4×C47—42no—
428C4×C47—42no—
429C4×C47#53412yes—
430C4×C47C2×H(5,𝔽2)11yescharacteristic
431C4×C47C2×H(5,𝔽2)11yescharacteristic
432Dic47—22no—
433Dic47—22no—
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×#468D4711yescharacteristic, complemented
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#319814yescomplemented
455C2×C47C2×#53411yescharacteristic
456C2×C47C2×#57611yescharacteristic
457C2×C47C2×#57711yescharacteristic
458D47—42no—
459D47—42no—
460D47—82no—
461D47—82no—
462C22×#41—471no—
463C22×#41—471no—
464C23×D4—471no—
465C22×SD16—471no—
466C22×SD16C2×D4711yescharacteristic
467C22×D8—471no—
468C22×D8—471no—
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—941no—
479C2×C22⋊Q8C2×D4711yescharacteristic, complemented
480C2×#121—471no—
481C2×#121—471no—
482C2×#121—471no—
483C2×#121—471no—
484C2×#121—471no—
485C2×#121—941no—
486C2×#121—941no—
487C2×#121—941no—
488C2×#121C2×D4711yescharacteristic
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#468C2×D4718yescomplemented
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×#106—471no—
509C2×#103—471no—
510C2×#103C2×D4711yescharacteristic, complemented
511C2×#102—471no—
512C2×#102—471no—
513C2×#102—471no—
514C2×#102—471no—
515C2×#102—471no—
516C2×#102C2×D4711yescharacteristic
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×Q8C22×D4711yescharacteristic
534C22×D4—21no—
535C22×D4—471no—
536C22×D4—471no—
537C22×D4—474no—
538C22×D4—471no—
539C22×D4—471no—
540C22×D4—471no—
541C22×D4—941no—
542C22×D4—941no—
543C22×D4—941no—
544C22×D4—942no—
545C22×D4—941no—
546C22×D4—941no—
547C22×D4—941no—
548C22×D4—941no—
549C22×D4—1882no—
550C22×D4—1882no—
551C22×D4C22×D4711yescharacteristic
552C23×C4—471no—
553C23×C4—471no—
554C23×C4—941no—
555C23×C4—941no—
556C23×C4C22×D4711yescharacteristic
557C2×SD16—42no—
558C2×SD16—474no—
559C2×SD16—1882no—
560C2×SD16C22×D4714yes—
561C2×D8—474no—
562C2×D8—474no—
563C2×D8—1882no—
564C2×D8—1882no—
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—22no—
576C22⋊Q8—474no—
577C22⋊Q8—948no—
578C22⋊Q8—942no—
579C22⋊Q8C22×D4714yescomplemented
580#121—22no—
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—948no—
591#121—942no—
592#121—942no—
593#121—942no—
594#121C22×D4714yes—
595#120—948no—
596#120—948no—
597#117—474no—
598#117—942no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—471no—
601C2×C4⋊C4—471no—
602C2×C4⋊C4—474no—
603C2×C4⋊C4—942no—
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#107C22×D4714yescomplemented
620#106—474no—
621#106—474no—
622#103—474no—
623#103C22×D4714yescomplemented
624#102—474no—
625#102—474no—
626#102—474no—
627#102—474no—
628#102—474no—
629#102C22×D4714yes—
630C22⋊C8—474no—
631C22⋊C8—474no—
632C22⋊C8—474no—
633C22⋊C8—474no—
634C24—21no—
635C24—471no—
636C24—471no—
637C24—944no—
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—24no—
657C2×D4—21no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—82no—
661C2×D4—474no—
662C2×D4—474no—
663C2×D4—474no—
664C2×D4—472no—
665C2×D4—472no—
666C2×D4—944no—
667C2×D4—944no—
668C2×D4—944no—
669C2×D4—944no—
670C2×D4—944no—
671C2×D4—944no—
672C2×D4—944no—
673C2×D4—941no—
674C2×D4—941no—
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—1882no—
685C2×D4—1884no—
686C2×D4—1884no—
687C2×D4—1884no—
688C2×D4—1888no—
689C2×D4—1882no—
690C2×D4—1882no—
691C2×D4—1884no—
692C2×D4C23×D4712yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—471no—
699C22×C4—471no—
700C22×C4—472no—
701C22×C4—472no—
702C22×C4—472no—
703C22×C4—472no—
704C22×C4—944no—
705C22×C4—944no—
706C22×C4—942no—
707C22×C4—942no—
708C22×C4—942no—
709C22×C4—942no—
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—44no—
719SD16—1884no—
720D8—1884no—
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—24no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—472no—
736C4⋊C4—472no—
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—42no—
758C23—42no—
759C23—42no—
760C23—472no—
761C23—472no—
762C23—942no—
763C23—942no—
764C23—942no—
765C23—942no—
766C23—942no—
767C23—942no—
768C23—942no—
769C23—942no—
770C23—3764no—
771C23—3764no—
772C23—37616no—
773C23—1888no—
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—22no—
787D4—22no—
788D4—42no—
789D4—84no—
790D4—942no—
791D4—942no—
792D4—942no—
793D4—942no—
794D4—3764no—
795D4—3764no—
796D4—3764no—
797D4—3764no—
798D4—3764no—
799D4—1884no—
800D4—1888no—
801D4—1884no—
802D4—1884no—
803D4—1888no—
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—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—472no—
817C2×C4—472no—
818C2×C4—942no—
819C2×C4—942no—
820C2×C4—944no—
821C2×C4—944no—
822C2×C4—942no—
823C2×C4—942no—
824C2×C4—942no—
825C2×C4—942no—
826C2×C4—942no—
827C2×C4—942no—
828C2×C4—3764no—
829C2×C4—1888no—
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—84no—
849C22—942no—
850C22—942no—
851C22—942no—
852C22—942no—
853C22—942no—
854C22—942no—
855C22—37616no—
856C22—3764no—
857C22—3764no—
858C22—1882no—
859C22—1882no—
860C22—1882no—
861C22—1882no—
862C22—1882no—
863C22—1882no—
864C22—1884no—
865C22—1884no—
866C22#1568968112yes—
867C22#1568992712yes—
868C22#1568993212yes—
869C22C22×D4×D4711yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—942no—
875C4—942no—
876C4—1882no—
877C4—1882no—
878C4#1568968112yes—
879C4C2×#1309406911yescharacteristic
880C4C2×#1309407011yescharacteristic
881C2—42no—
882C2—82no—
883C2—3762no—
884C2—3762no—
885C2—1882no—
886C2—1882no—
887C2#2025424114yesdirect product factor
888C2C2×#1568968111yescharacteristic
889C2C2×#1568992711yescharacteristic
890C2C2×#1568993211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#468C2
socleC23×C47C22×D4
hypercenterC2×#468D47
hypocenterC47C2×#3198
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#15689703C2semidirect
2. C2×#15689689C2semidirect
3. #20254241C2direct (N × H)
4. C2×#15689440C2semidirect
5. C2×#15689462C2semidirect
6. C2×#15689450C2semidirect
7. C2×#15689438C2semidirect
8. C2×#15689376C2semidirect
9. C2×#15689357C2semidirect
10. C2×#15689354C2semidirect
11. C2×#15689271C2semidirect
12. C2×#15689267C2semidirect
13. C2×#15689272C2semidirect
14. C2×#15689258C2semidirect
15. C2×#15689091C2semidirect
16. C2×C47×#468C2semidirect
17. C22×#10625354C22semidirect
23. C23×C47⋊C8C22semidirect
25. #15689703C22semidirect
27. #15689689C22semidirect
36. C2×#13093998C22semidirect
43. C2×C4⋊C4×D47C22semidirect
44. #15689462C22semidirect
45. #15689450C22semidirect
46. #15689440C22semidirect
47. #15689438C22semidirect
48. #15689376C22semidirect
49. #15689357C22semidirect
50. #15689354C22semidirect
51. #15689272C22semidirect
52. #15689271C22semidirect
53. #15689267C22semidirect
54. #15689258C22semidirect
55. C2×#13093957C22semidirect
56. C2×#13093956C22semidirect
57. C2×#13093955C22semidirect
58. C2×#13093948C22semidirect
60. C2×#13093946C22semidirect
63. C2×#13093944C22semidirect
64. #15689091C22semidirect
67. C2×(C2×D47)⋊C8C22semidirect
68. C2×(C2×D47)⋊C8C22semidirect
70. C22×M16×C47C22semidirect
71. C2×C22⋊Q8×C47C22semidirect
73. C47×#468C22semidirect
74. C2×#107×C47C22semidirect
75. C2×#103×C47C22semidirect
81. C2×#10625354C23semidirect
116. C22×C47⋊C8C23semidirect
130. #13093998C23semidirect
144. C4⋊C4×D47C23semidirect
153. #13093957C23semidirect
154. #13093956C23semidirect
155. #13093955C23semidirect
156. #13093948C23semidirect
158. #13093946C23semidirect
161. #13093944C23semidirect
164. (C2×D47)⋊C8C23semidirect
165. (C2×D47)⋊C8C23semidirect
173. C2×M16×C47C23semidirect
177. C22⋊Q8×C47C23semidirect
185. #107×C47C23semidirect
186. #103×C47C23semidirect
444. C2×#468D47semidirect
454. C2×C47#3198semidirect
469. C22×M16C2×D47semidirect
479. C2×C22⋊Q8C2×D47semidirect
498. #468C2×D47semidirect
506. C2×#107C2×D47semidirect
510. C2×#103C2×D47semidirect
522. C47C2×#3198semidirect
566. C2×M16C22×D47semidirect
579. C22⋊Q8C22×D47semidirect
619. #107C22×D47semidirect
623. #103C22×D47semidirect
887. C2#20254241direct (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×#156896892
#202542412
C2×#156894402
C2×#156894622
C2×#156894502
C2×#156894382
C2×#156893762
C2×#156893572
C2×#156893542
C2×#156892712
C2×#156892672
C2×#156892722
C2×#156892582
C2×#156890912
C2×C47×#4682
C2×#319847