Finite Group Databasebeta

← C2×#20254243 #27086934

Subgroups — C2×#20254243 #27086934

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#20254243C2116yesmaximal, direct product factor
4C2×#15689443C211yesmaximal, characteristic, complemented
5C2×#15689463C211yesmaximal, characteristic, complemented
6C2×#15689449C211yesmaximal, characteristic, complemented
7C2×#15689435C211yesmaximal, characteristic, complemented
8C2×#15689374C211yesmaximal, characteristic, complemented
9C2×#15689371C211yesmaximal, characteristic, complemented
10C2×#15689359C211yesmaximal, characteristic, complemented
11C2×#15689271C211yesmaximal, characteristic, complemented
12C2×#15689267C211yesmaximal, characteristic, complemented
13C2×#15689272C211yesmaximal, characteristic, complemented
14C2×#15689258C211yesmaximal, characteristic, complemented
15C2×#15689089C211yesmaximal, characteristic, complemented
16C2×C47×#465C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic, complemented
18C22×#10625350C2211yescharacteristic
19C22×D4×D47C2211yescharacteristic
20C22×#10625336C2211yescharacteristic
21C22×D376C2211yescharacteristic
22C22×#10625334C2211yescharacteristic
23C22×#10625329C2211yescharacteristic, 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#15689463C2218yescomplemented
45#15689449C2218yescomplemented
46#15689443C2218yescomplemented
47#15689435C2218yescomplemented
48#15689374C2218yescomplemented
49#15689371C2218yescomplemented
50#15689359C2218yescomplemented
51#15689272C2218yescomplemented
52#15689271C2218yescomplemented
53#15689267C2218yescomplemented
54#15689258C2218yescomplemented
55C2×#13093958C2211yescharacteristic, complemented
56C2×#13093957C2211yescharacteristic, complemented
57C2×#13093955C2211yescharacteristic, complemented
58C2×#13093948C2211yescharacteristic, complemented
59C2×#13093946C2211yescharacteristic
60C2×#13093946C2211yescharacteristic, complemented
61C2×#13093945C2211yescharacteristic
62C2×#13093944C2211yescharacteristic
63C2×#13093944C2211yescharacteristic, complemented
64#15689089C2218yescomplemented
65C2×(C2×D47)⋊C8C2211yescharacteristic
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
68C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
69C22×SD16×C47C2211yescharacteristic
70C23×C8×C47C2211yescharacteristic, complemented
71C2×C22⋊Q8×C47C2211yescharacteristic, complemented
72C2×#121×C47C2211yescharacteristic
73C47×#465C2218yescomplemented
74C2×#106×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—
113C2×#10625329—42no—
114C2×#10625329C2314yescomplemented
115C22×C47⋊C8C2311yescharacteristic
116C22×C47⋊C8C2311yescharacteristic
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#13093958C2314yescomplemented
154#13093957C2314yescomplemented
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—
172C22×C8×C47—42no—
173C22×C8×C47C2311yescharacteristic
174C22×C8×C47C2311yescharacteristic
175C22×C8×C47C2314yescomplemented
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#106×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—
273C2×C8×C47—22no—
274C2×C8×C47—22no—
275C2×C8×C47—44no—
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—
301#10625329—44no—
302C2×C47⋊C8—22no—
303C2×C47⋊C8—22no—
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×#468—471no—
445C2×#466—471no—
446C2×#465D4711yescharacteristic, complemented
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×M16—471no—
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—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#468—478no—
499#466—478no—
500#465C2×D4718yescomplemented
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×#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—474no—
566C2×M16—1882no—
567C22×C8—42no—
568C22×C8—471no—
569C22×C8—471no—
570C22×C8C22×D4711yescharacteristic
571C22×C8C22×D4711yescharacteristic
572C22×C8C22×D4714yescomplemented
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#107—474no—
620#106—474no—
621#106C22×D4714yescomplemented
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—1884no—
723C2×C8—22no—
724C2×C8—22no—
725C2×C8—44no—
726C2×C8—472no—
727C2×C8—472no—
728C2×C8—942no—
729C2×C8—942no—
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#1568992512yes—
868C22#1568992912yes—
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#2025424314yesdirect product factor
888C2C2×#1568968111yescharacteristic
889C2C2×#1568992511yescharacteristic
890C2C2×#1568992911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#465C2
socleC23×C47C22×D4
hypercenterC2×#465D47
hypocenterC47C2×#3198
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#15689703C2semidirect
2. C2×#15689689C2semidirect
3. #20254243C2direct (N × H)
4. C2×#15689443C2semidirect
5. C2×#15689463C2semidirect
6. C2×#15689449C2semidirect
7. C2×#15689435C2semidirect
8. C2×#15689374C2semidirect
9. C2×#15689371C2semidirect
10. C2×#15689359C2semidirect
11. C2×#15689271C2semidirect
12. C2×#15689267C2semidirect
13. C2×#15689272C2semidirect
14. C2×#15689258C2semidirect
15. C2×#15689089C2semidirect
16. C2×C47×#465C2semidirect
17. C22×#10625354C22semidirect
23. C22×#10625329C22semidirect
25. #15689703C22semidirect
27. #15689689C22semidirect
36. C2×#13093998C22semidirect
43. C2×C4⋊C4×D47C22semidirect
44. #15689463C22semidirect
45. #15689449C22semidirect
46. #15689443C22semidirect
47. #15689435C22semidirect
48. #15689374C22semidirect
49. #15689371C22semidirect
50. #15689359C22semidirect
51. #15689272C22semidirect
52. #15689271C22semidirect
53. #15689267C22semidirect
54. #15689258C22semidirect
55. C2×#13093958C22semidirect
56. C2×#13093957C22semidirect
57. C2×#13093955C22semidirect
58. C2×#13093948C22semidirect
60. C2×#13093946C22semidirect
63. C2×#13093944C22semidirect
64. #15689089C22semidirect
67. C2×(C2×D47)⋊C8C22semidirect
68. C2×(C2×D47)⋊C8C22semidirect
70. C23×C8×C47C22semidirect
71. C2×C22⋊Q8×C47C22semidirect
73. C47×#465C22semidirect
74. C2×#106×C47C22semidirect
75. C2×#103×C47C22semidirect
81. C2×#10625354C23semidirect
114. C2×#10625329C23semidirect
130. #13093998C23semidirect
144. C4⋊C4×D47C23semidirect
153. #13093958C23semidirect
154. #13093957C23semidirect
155. #13093955C23semidirect
156. #13093948C23semidirect
158. #13093946C23semidirect
161. #13093944C23semidirect
164. (C2×D47)⋊C8C23semidirect
165. (C2×D47)⋊C8C23semidirect
175. C22×C8×C47C23semidirect
177. C22⋊Q8×C47C23semidirect
185. #106×C47C23semidirect
186. #103×C47C23semidirect
446. C2×#465D47semidirect
454. C2×C47#3198semidirect
470. C23×C8C2×D47semidirect
479. C2×C22⋊Q8C2×D47semidirect
500. #465C2×D47semidirect
508. C2×#106C2×D47semidirect
510. C2×#103C2×D47semidirect
522. C47C2×#3198semidirect
572. C22×C8C22×D47semidirect
579. C22⋊Q8C22×D47semidirect
621. #106C22×D47semidirect
623. #103C22×D47semidirect
887. C2#20254243direct (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
#202542432
C2×#156894432
C2×#156894632
C2×#156894492
C2×#156894352
C2×#156893742
C2×#156893712
C2×#156893592
C2×#156892712
C2×#156892672
C2×#156892722
C2×#156892582
C2×#156890892
C2×C47×#4652
C2×#319847