Finite Group Databasebeta

← #30550758

Subgroups — #30550758

Order 15616.

2686 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840273C211yesmaximal, characteristic, complemented
2C22×#14519751C211yesmaximal, characteristic, complemented
3#21456635C214yesmaximal, complemented
4#21456626C212yesmaximal, complemented
5#21456619C212yesmaximal, complemented
6#21456586C214yesmaximal, complemented
7#21456577C212yesmaximal, complemented
8#21456570C212yesmaximal, complemented
9#21455760C212yesmaximal, complemented
10#21455744C212yesmaximal, complemented
11#21455438C214yesmaximal, complemented
12#21455073C212yesmaximal, complemented
13#21455049C212yesmaximal, complemented
14C2×C61×#407C211yesmaximal, characteristic, complemented
15C22×#11758222C2211yescharacteristic, complemented
16C23×D244C2211yescharacteristic, complemented
17C23×C22⋊D61—21no—
18C2×#14519805C2214yescomplemented
19#16840273—21no—
20#16840273—21no—
21#16840273—21no—
22#16840273—21no—
23#16840273C2212yes—
24#16840273C2212yescomplemented
25#16840273C2212yescomplemented
26#16840273C2212yescomplemented
27C2×#14519760—21no—
28C2×#14519756C2211yescharacteristic, complemented
29C2×#14519756C2211yescharacteristic, complemented
30C2×#14519751—21no—
31C2×#14519751—21no—
32C2×#14519751—21no—
33C2×#14519751—21no—
34C2×#14519751—21no—
35C2×#14519751—21no—
36C2×#14519751C2212yes—
37C2×#14519751C2212yes—
38C2×#14519751C2212yes—
39C2×#14519751C2212yescomplemented
40C2×#14519751C2212yescomplemented
41C2×#14519751C2212yescomplemented
42C2×#14519751C2211yescharacteristic, complemented
43C2×#14519751C2211yescharacteristic, complemented
44C2×#14519746—21no—
45C2×C4×C22⋊D61—21no—
46C2×C4×C22⋊D61—21no—
47C2×#14519736C2211yescharacteristic, complemented
48C22×C4⋊Dic61C2211yescharacteristic, complemented
49C22×#11758198—21no—
50#16840098C2214yescomplemented
51#16840093C2214yescomplemented
52#16840087C2218yescomplemented
53#16840081C2214yescomplemented
54#16840081C2214yescomplemented
55#16840076C2214yescomplemented
56#16840076C2214yescomplemented
57#16840015C2218yescomplemented
58#16840008C2218yescomplemented
59#16839998C2218yescomplemented
60#16839991C2218yescomplemented
61#16839915C2214yescomplemented
62#16839915C2214yescomplemented
63#16839909C2218yescomplemented
64#16839903C2214yescomplemented
65#16839898C2214yescomplemented
66#16839898C2214yescomplemented
67#16839898C2214yescomplemented
68#16839804C2214yescomplemented
69#16839768C2214yescomplemented
70#16839764C2214yescomplemented
71C24×C4×C61C2211yescharacteristic
72C22×M16×C61C2212yescomplemented
73C61×#407C2212yescomplemented
74C61×#407C2212yescomplemented
75C61×#407C2212yescomplemented
76C61×#407C2212yescomplemented
77C2×C22⋊C8×C61C2212yescomplemented
78C2×C22⋊C8×C61C2212yescomplemented
79C24×D61—21no—
80C2×#11758222—21no—
81C2×#11758222—21no—
82C2×#11758222—44no—
83C2×#11758222C2312yes—
84C2×#11758222C2312yescomplemented
85C22×Dic122C2311yescharacteristic, complemented
86C22×D244—21no—
87C22×D244—21no—
88C22×D244—21no—
89C22×D244—44no—
90C22×D244C2312yes—
91C22×D244C2312yes—
92C22×D244C2312yes—
93C22×D244C2311yescharacteristic, complemented
94C22×C22⋊D61—21no—
95C22×C22⋊D61—21no—
96C22×C22⋊D61—21no—
97C22×C22⋊D61—22no—
98C22×C22⋊D61—22no—
99C22×C22⋊D61—22no—
100C22×C22⋊D61—22no—
101C22×C22⋊D61—22no—
102C22×C22⋊D61—22no—
103C22×C22⋊D61—48no—
104C23×Dic61—21no—
105C22×C4×D61—21no—
106#14519805—48no—
107C2×#11758190C2318yescomplemented
108C2×D488C2318yescomplemented
109#14519760—22no—
110#14519760—22no—
111#14519760—22no—
112#14519760—22no—
113#14519756—21no—
114#14519756—21no—
115#14519756—21no—
116#14519756—21no—
117#14519756C2312yes—
118#14519756C2312yes—
119#14519756C2312yescomplemented
120#14519756C2312yescomplemented
121#14519751—22no—
122#14519751—22no—
123#14519751—22no—
124#14519751—22no—
125#14519751—22no—
126#14519751—22no—
127#14519751—22no—
128#14519751—22no—
129#14519751—22no—
130#14519751—22no—
131#14519751—22no—
132#14519751—22no—
133#14519751—21no—
134#14519751—21no—
135#14519751—21no—
136#14519751—21no—
137#14519751C2314yes—
138#14519751C2314yes—
139#14519751C2314yes—
140#14519751C2314yes—
141#14519751C2312yes—
142#14519751C2312yes—
143#14519751C2312yescomplemented
144#14519751C2312yescomplemented
145#14519746—22no—
146#14519746—22no—
147#14519746—22no—
148#14519746—22no—
149C4×C22⋊D61—22no—
150C4×C22⋊D61—22no—
151C4×C22⋊D61—22no—
152C4×C22⋊D61—22no—
153C4×C22⋊D61—22no—
154C4×C22⋊D61—22no—
155C4×C22⋊D61—22no—
156C4×C22⋊D61—22no—
157#14519736—21no—
158#14519736—21no—
159#14519736C2312yes—
160#14519736C2312yescomplemented
161C2×C4⋊Dic61—21no—
162C2×C4⋊Dic61—21no—
163C2×C4⋊Dic61—21no—
164C2×C4⋊Dic61C2312yes—
165C2×C4⋊Dic61C2312yes—
166C2×C4⋊Dic61C2312yes—
167C2×C4⋊Dic61C2311yescharacteristic, complemented
168C2×C4⋊Dic61C2311yescharacteristic, complemented
169C2×#11758196—21no—
170C2×#11758196—21no—
171C2×C22⋊Dic61—21no—
172C2×C22⋊Dic61—21no—
173C2×C22⋊Dic61—21no—
174C2×#11758198—22no—
175C2×#11758198—22no—
176C2×#11758198—22no—
177C2×#11758198—22no—
178C2×#11758198—22no—
179C2×#11758198—22no—
180C2×#11758198—21no—
181C2×#11758198—21no—
182C2×C4×Dic61—21no—
183#14519711C2318yescomplemented
184#14519709C2318yescomplemented
185#14519702C2318yescomplemented
186#14519699C2318yescomplemented
187#14519699C2318yescomplemented
188#14519699C2318yescomplemented
189C25×C61D411yescharacteristic
190C23×C4×C61—44no—
191C23×C4×C61D411yescharacteristic
192C23×C4×C61D411yescharacteristic
193C23×C4×C61D411yescharacteristic
194C23×C4×C61D411yescharacteristic
195C23×C4×C61D411yescharacteristic
196C23×C4×C61D411yescharacteristic
197C23×C4×C61D411yescharacteristic
198C23×C4×C61C2311yescharacteristic
199C23×C4×C61C2311yescharacteristic
200C23×C4×C61C2311yescharacteristic
201C23×C4×C61C2311yescharacteristic
202C23×C4×C61C2311yescharacteristic
203C23×C4×C61C2311yescharacteristic
204C23×C4×C61C2311yescharacteristic
205C2×M16×C61—44no—
206C2×M16×C61C2314yes—
207C2×M16×C61C2314yescomplemented
208C22×C8×C61C2314yescomplemented
209C22⋊C8×C61C2314yes—
210C22⋊C8×C61C2314yes—
211C22⋊C8×C61C2314yescomplemented
212C22⋊C8×C61C2314yescomplemented
213C24×C61—24no—
214C24×C61—42no—
215C24×C61—42no—
216C24×C61C2×D411yescharacteristic
217C24×C61C2×D411yescharacteristic
218C24×C61C2×D411yescharacteristic
219C24×C61C2×D411yescharacteristic
220C24×C61C2×D411yescharacteristic
221C24×C61C2×D411yescharacteristic
222C24×C61C2×D411yescharacteristic
223C23×D61—21no—
224C23×D61—22no—
225C23×D61—22no—
226C23×D61—22no—
227C23×D61—44no—
228C23×D61—44no—
229C23×D61—44no—
230C22×C4×C61—24no—
231C22×C4×C61—24no—
232C22×C4×C61—24no—
233C22×C4×C61—42no—
234C22×C4×C61—42no—
235C22×C4×C61—42no—
236C22×C4×C61—42no—
237C22×C4×C61—42no—
238C22×C4×C61—42no—
239C22×C4×C61—42no—
240C22×C4×C61—42no—
241C22×C4×C61—42no—
242C22×C4×C61—42no—
243C22×C4×C61—42no—
244C22×C4×C61C2×D411yescharacteristic
245C22×C4×C61C2×D411yescharacteristic
246C22×C4×C61C2×D411yescharacteristic
247C22×C4×C61C2×D411yescharacteristic
248C22×C4×C61C2×D411yescharacteristic
249C22×C4×C61C2×D411yescharacteristic
250C22×C4×C61C2×D411yescharacteristic
251C22×C4×C61C2×D411yescharacteristic
252C22×C4×C61C2×D411yescharacteristic
253C22×C4×C61C2×D411yescharacteristic
254C22×C4×C61C2×D411yescharacteristic
255C22×C4×C61C2×D411yescharacteristic
256C22×C4×C61C2×D411yescharacteristic
257C22×C4×C61C2×D411yescharacteristic
258C22×C4×C61C2×D411yescharacteristic
259C22×C4×C61C2×D411yescharacteristic
260C22×C4×C61C2×D411yescharacteristic
261C22×C4×C61C2×D411yescharacteristic
262C22×C4×C61C2×D411yescharacteristic
263C22×C4×C61C2×D411yescharacteristic
264C22×C4×C61C2×D411yescharacteristic
265C22×C4×C61C2411yescharacteristic
266C22×C4×C61C2411yescharacteristic
267C22×C4×C61C2411yescharacteristic
268C22×C4×C61C2411yescharacteristic
269C22×C4×C61C2411yescharacteristic
270C22×C4×C61C2411yescharacteristic
271C22×C4×C61C2411yescharacteristic
272C2×C22⋊D61—24no—
273C2×C22⋊D61—24no—
274C2×C22⋊D61—24no—
275C2×C22⋊D61—24no—
276C2×C22⋊D61—22no—
277C2×C22⋊D61—22no—
278C2×C22⋊D61—22no—
279C2×C22⋊D61—22no—
280C2×C22⋊D61—22no—
281C2×C22⋊D61—22no—
282C2×C22⋊D61—44no—
283C2×C22⋊D61—48no—
284C2×C22⋊D61—48no—
285C2×C22⋊D61—48no—
286C2×C22⋊D61—48no—
287C2×C22⋊D61—48no—
288C2×C22⋊D61—44no—
289C2×C22⋊D61—44no—
290C2×C22⋊D61—48no—
291C22×Dic61—21no—
292C22×Dic61—22no—
293C22×Dic61—22no—
294C22×Dic61—22no—
295C22×Dic61—21no—
296C22×Dic61—21no—
297C22×Dic61—44no—
298#11758222—28no—
299#11758222—44no—
300#11758222—44no—
301#11758222—44no—
302C2×D244—28no—
303C2×D244—22no—
304C2×D244—22no—
305C2×D244—22no—
306C2×D244—21no—
307C2×D244—44no—
308C2×D244—44no—
309C2×D244—42no—
310C2×D244—44no—
311C2×D244—44no—
312C2×D244—44no—
313C2×D244C2414yes—
314C2×D244C2412yes—
315C2×C4×D61—22no—
316C2×C4×D61—22no—
317C2×C4×D61—44no—
318C2×Dic122—21no—
319C2×Dic122—42no—
320C2×Dic122C2412yes—
321M16×C61—28no—
322M16×C61—44no—
323C2×C8×C61—44no—
324C2×C8×C61C2418yes—
325C22⋊Dic61—22no—
326C22⋊Dic61—22no—
327C22⋊Dic61—22no—
328C22⋊Dic61—22no—
329C22⋊Dic61—22no—
330C22⋊Dic61—22no—
331#11758198—24no—
332#11758198—24no—
333#11758198—24no—
334#11758198—24no—
335#11758198—22no—
336#11758198—22no—
337#11758198—22no—
338#11758198—22no—
339C4⋊Dic61—22no—
340C4⋊Dic61—22no—
341C4⋊Dic61—22no—
342C4⋊Dic61—21no—
343C4⋊Dic61—21no—
344C4⋊Dic61C2412yes—
345C4⋊Dic61C2412yes—
346C4⋊Dic61C2414yes—
347#11758196—22no—
348#11758196—22no—
349#11758196—22no—
350#11758196—22no—
351C4×Dic61—22no—
352C4×Dic61—22no—
353D488—48no—
354#11758190—48no—
355C23×C61—22no—
356C23×C61—22no—
357C23×C61—22no—
358C23×C61—22no—
359C23×C61—22no—
360C23×C61—22no—
361C23×C61—22no—
362C23×C61—22no—
363C23×C61—22no—
364C23×C61—22no—
365C23×C61—22no—
366C23×C61—22no—
367C23×C61—41no—
368C23×C61—41no—
369C23×C61—41no—
370C23×C61—41no—
371C23×C61—41no—
372C23×C61—41no—
373C23×C61—41no—
374C23×C61—41no—
375C23×C61—416no—
376C23×C61AGL(1,ℤ/8)14yescomplemented
377C23×C61C22×D411yescharacteristic
378C23×C61C22×D411yescharacteristic
379C23×C61C22×D411yescharacteristic
380C23×C61C22×D411yescharacteristic
381C23×C61C22×D411yescharacteristic
382C23×C61C22×D411yescharacteristic
383C23×C61C22×D411yescharacteristic
384C22×D61—22no—
385C22×D61—24no—
386C22×D61—42no—
387C22×D61—44no—
388C22×D61—44no—
389C22×D61—44no—
390C22×D61—44no—
391C22×D61—42no—
392C22×D61—44no—
393C22×D61—44no—
394C22×D61—44no—
395C22×D61—44no—
396C22×D61—42no—
397C22×D61—44no—
398C22×D61—816no—
399C2×C4×C61—22no—
400C2×C4×C61—22no—
401C2×C4×C61—22no—
402C2×C4×C61—22no—
403C2×C4×C61—22no—
404C2×C4×C61—22no—
405C2×C4×C61—22no—
406C2×C4×C61—22no—
407C2×C4×C61—22no—
408C2×C4×C61—22no—
409C2×C4×C61—22no—
410C2×C4×C61—22no—
411C2×C4×C61—22no—
412C2×C4×C61—22no—
413C2×C4×C61—22no—
414C2×C4×C61—41no—
415C2×C4×C61—41no—
416C2×C4×C61—41no—
417C2×C4×C61—41no—
418C2×C4×C61—41no—
419C2×C4×C61—41no—
420C2×C4×C61—41no—
421C2×C4×C61—41no—
422C2×C4×C61—41no—
423C2×C4×C61—41no—
424C2×C4×C61—41no—
425C2×C4×C61—41no—
426C2×C4×C61C22×D411yescharacteristic
427C2×C4×C61C22×D411yescharacteristic
428C2×C4×C61C22×D411yescharacteristic
429C2×C4×C61C22×D411yescharacteristic
430C2×C4×C61C22×D411yescharacteristic
431C2×C4×C61C22×D411yescharacteristic
432C2×C4×C61C22×D411yescharacteristic
433C2×C4×C61H(5,𝔽2)14yes—
434C2×C4×C61C2511yescharacteristic
435C22⋊D61—44no—
436C22⋊D61—44no—
437C22⋊D61—48no—
438C22⋊D61—48no—
439C22⋊D61—44no—
440C22⋊D61—44no—
441C22⋊D61—44no—
442C22⋊D61—48no—
443C22⋊D61—48no—
444C22⋊D61—44no—
445C2×Dic61—22no—
446C2×Dic61—22no—
447C2×Dic61—22no—
448C2×Dic61—24no—
449C2×Dic61—42no—
450C2×Dic61—44no—
451C2×Dic61—44no—
452C2×Dic61—42no—
453C2×Dic61—44no—
454C2×Dic61—42no—
455D244—28no—
456D244—24no—
457D244—44no—
458D244—44no—
459D244—42no—
460D244—44no—
461C4×D61—44no—
462C4×D61—44no—
463Dic122—24no—
464Dic122—42no—
465C8×C61—28no—
466#60750—611nomaximal, Sylow
467C22×C61—28no—
468C22×C61—21no—
469C22×C61—21no—
470C22×C61—21no—
471C22×C61—21no—
472C22×C61—21no—
473C22×C61—21no—
474C22×C61—21no—
475C22×C61—21no—
476C22×C61—21no—
477C22×C61—21no—
478C22×C61—21no—
479C22×C61—21no—
480C22×C61—21no—
481C22×C61—21no—
482C22×C61—21no—
483C22×C61—21no—
484C22×C61—44no—
485C22×C61—44no—
486C22×C61—44no—
487C22×C61—44no—
488C22×C61—44no—
489C22×C61—44no—
490C22×C61#53412yes—
491C22×C61C2×AGL(1,ℤ/8)12yes—
492C22×C61C2×AGL(1,ℤ/8)12yes—
493C22×C61C2×AGL(1,ℤ/8)12yes—
494C22×C61#57512yes—
495C22×C61C23×D411yescharacteristic
496C2×D61—42no—
497C2×D61—44no—
498C2×D61—44no—
499C2×D61—42no—
500C2×D61—42no—
501C2×D61—44no—
502C2×D61—84no—
503C2×D61—88no—
504C2×D61—88no—
505C2×D61—88no—
506C4×C61—21no—
507C4×C61—21no—
508C4×C61—21no—
509C4×C61—21no—
510C4×C61—21no—
511C4×C61—21no—
512C4×C61#53412yes—
513C4×C61C2×H(5,𝔽2)12yes—
514Dic61—42no—
515Dic61—44no—
516Dic61—42no—
517Dic61—42no—
518C2×#525—611no—
519C22×#121—611no—
520#3194—614no—
521#3193—612no—
522#3192—612no—
523#3188—614no—
524#3187—612no—
525#3186—612no—
526#3094—612no—
527#3092—612no—
528#3055—614no—
529#3006—612no—
530#3003—612no—
531C2×#407D6111yescharacteristic, complemented
532C2×C61—22no—
533C2×C61—22no—
534C2×C61—22no—
535C2×C61—22no—
536C2×C61—22no—
537C2×C61—41no—
538C2×C61—41no—
539C2×C61C2×#53411yescharacteristic
540C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
541C2×C61C2×#57511yescharacteristic
542D61—82no—
543D61—84no—
544C22×#41—611no—
545C23×D4—611no—
546C23×D4—1221no—
547C24×C4C2×D6111yescharacteristic
548C2×AGL(1,ℤ/8)—614no—
549C22×M16C2×D6112yescomplemented
550#525—612no—
551#525—612no—
552#525—612no—
553#525—612no—
554#525—1221no—
555#525—1221no—
556#525—1221no—
557#525—1221no—
558C2×#123—1221no—
559C2×C22⋊Q8—611no—
560C2×C22⋊Q8—611no—
561C2×#121—612no—
562C2×#121—612no—
563C2×#121—612no—
564C2×#121—612no—
565C2×#121—612no—
566C2×#121—612no—
567C2×#121—611no—
568C2×#121—611no—
569C2×#121—1221no—
570C2×#121—1221no—
571C2×#121—1221no—
572C2×#121—1221no—
573C2×#121—1221no—
574C2×#121—1221no—
575C2×#120—1221no—
576C2×C4×D4—1221no—
577C2×C4×D4—1221no—
578C2×#117—611no—
579C22×C4⋊C4—611no—
580C22×C22⋊C4—1221no—
581#484—614no—
582#483—614no—
583#482—618no—
584#481—614no—
585#481—614no—
586#480—614no—
587#480—614no—
588#469—618no—
589#468—618no—
590#466—618no—
591#465—618no—
592#450—614no—
593#450—614no—
594#449—618no—
595#448—614no—
596#447—614no—
597#447—614no—
598#447—614no—
599#428—614no—
600#418—614no—
601#417—614no—
602#407C2×D6112yescomplemented
603#407C2×D6112yescomplemented
604#407C2×D6112yescomplemented
605#407C2×D6112yescomplemented
606C2×C22⋊C8C2×D6112yescomplemented
607C2×C22⋊C8C2×D6112yescomplemented
608C61#6075011yescharacteristic, complemented, Sylow
609C25—1221no—
610C25D24411yescharacteristic
611C2×#41—612no—
612C2×#41—612no—
613C2×#41—1221no—
614C2×#41—1221no—
615C2×#41—2444no—
616C22×Q8—611no—
617C22×D4—612no—
618C22×D4—612no—
619C22×D4—612no—
620C22×D4—611no—
621C22×D4—1221no—
622C22×D4—1221no—
623C22×D4—1221no—
624C22×D4—1222no—
625C22×D4—1222no—
626C22×D4—1222no—
627C22×D4—1222no—
628C22×D4—1222no—
629C22×D4—1222no—
630C22×D4—1221no—
631C22×D4—1221no—
632C22×D4—1221no—
633C22×D4—2444no—
634C22×D4—2448no—
635C23×C4—44no—
636C23×C4—1221no—
637C23×C4—1221no—
638C23×C4D24411yescharacteristic
639C23×C4D24411yescharacteristic
640C23×C4D24411yescharacteristic
641C23×C4D24411yescharacteristic
642C23×C4D24411yescharacteristic
643C23×C4D24411yescharacteristic
644C23×C4D24411yescharacteristic
645C23×C4C22×D6111yescharacteristic
646C23×C4C22×D6111yescharacteristic
647C23×C4C22×D6111yescharacteristic
648C23×C4C22×D6111yescharacteristic
649C23×C4C22×D6111yescharacteristic
650C23×C4C22×D6111yescharacteristic
651C23×C4C22×D6111yescharacteristic
652AGL(1,ℤ/8)—2448no—
653C2×SD16—618no—
654C2×D8—618no—
655C2×M16—44no—
656C2×M16C22×D6114yes—
657C2×M16C22×D6114yescomplemented
658C22×C8C22×D6114yescomplemented
659#123—1222no—
660#123—1222no—
661#123—1222no—
662#123—1222no—
663C22⋊Q8—612no—
664C22⋊Q8—612no—
665C22⋊Q8—612no—
666C22⋊Q8—612no—
667C22⋊Q8—1221no—
668C22⋊Q8—1221no—
669C22⋊Q8—1221no—
670C22⋊Q8—1221no—
671#121—614no—
672#121—614no—
673#121—614no—
674#121—614no—
675#121—612no—
676#121—612no—
677#121—612no—
678#121—612no—
679#121—1222no—
680#121—1222no—
681#121—1222no—
682#121—1222no—
683#121—1222no—
684#121—1222no—
685#121—1222no—
686#121—1222no—
687#121—1222no—
688#121—1222no—
689#121—1222no—
690#121—1222no—
691#121—1221no—
692#121—1221no—
693#121—1221no—
694#121—1221no—
695#120—1222no—
696#120—1222no—
697#120—1222no—
698#120—1222no—
699C4×D4—1222no—
700C4×D4—1222no—
701C4×D4—1222no—
702C4×D4—1222no—
703C4×D4—1222no—
704C4×D4—1222no—
705C4×D4—1222no—
706C4×D4—1222no—
707#117—612no—
708#117—612no—
709#117—1221no—
710#117—1221no—
711C2×C4⋊C4—612no—
712C2×C4⋊C4—612no—
713C2×C4⋊C4—612no—
714C2×C4⋊C4—611no—
715C2×C4⋊C4—611no—
716C2×C4⋊C4—1221no—
717C2×C4⋊C4—1221no—
718C2×C4⋊C4—1221no—
719C2×C4⋊C4—1221no—
720C2×C4⋊C4—1221no—
721C2×C22⋊C4—1221no—
722C2×C22⋊C4—1221no—
723C2×C22⋊C4—1221no—
724C2×C22⋊C4—1222no—
725C2×C22⋊C4—1222no—
726C2×C22⋊C4—1222no—
727C2×C22⋊C4—1222no—
728C2×C22⋊C4—1222no—
729C2×C22⋊C4—1222no—
730C2×C22⋊C4—1221no—
731C2×C22⋊C4—1221no—
732C2×C42—1221no—
733#107—618no—
734#106—618no—
735#103—618no—
736#102—618no—
737#102—618no—
738#102—618no—
739C22⋊C8C22×D6114yes—
740C22⋊C8C22×D6114yes—
741C22⋊C8C22×D6114yescomplemented
742C22⋊C8C22×D6114yescomplemented
743C24—24no—
744C24—42no—
745C24—42no—
746C24—1221no—
747C24—1222no—
748C24—1222no—
749C24—1222no—
750C24—2444no—
751C24—2444no—
752C24—2444no—
753C24C2×D24411yescharacteristic
754C24C2×D24411yescharacteristic
755C24C2×D24411yescharacteristic
756C24C2×D24411yescharacteristic
757C24C2×D24411yescharacteristic
758C24C2×D24411yescharacteristic
759C24C2×D24411yescharacteristic
760#41—1228no—
761#41—2444no—
762#41—2444no—
763#41—2444no—
764C2×Q8—612no—
765C2×Q8—1221no—
766C2×Q8—2442no—
767C2×D4—612no—
768C2×D4—614no—
769C2×D4—1222no—
770C2×D4—1222no—
771C2×D4—1222no—
772C2×D4—1222no—
773C2×D4—1222no—
774C2×D4—1222no—
775C2×D4—1224no—
776C2×D4—1224no—
777C2×D4—1224no—
778C2×D4—1224no—
779C2×D4—1222no—
780C2×D4—1222no—
781C2×D4—1222no—
782C2×D4—1221no—
783C2×D4—1228no—
784C2×D4—2444no—
785C2×D4—2444no—
786C2×D4—2442no—
787C2×D4—2444no—
788C2×D4—2444no—
789C2×D4—2444no—
790C2×D4—2448no—
791C2×D4—2448no—
792C2×D4—2448no—
793C2×D4—2448no—
794C2×D4—2448no—
795C2×D4—2444no—
796C2×D4—2444no—
797C2×D4—2448no—
798C2×D4—2444no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—42no—
803C22×C4—42no—
804C22×C4—42no—
805C22×C4—42no—
806C22×C4—42no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—1221no—
814C22×C4—1221no—
815C22×C4—1222no—
816C22×C4—1222no—
817C22×C4—1222no—
818C22×C4—1221no—
819C22×C4—1222no—
820C22×C4—1222no—
821C22×C4—2444no—
822C22×C4—2444no—
823C22×C4C2×D24411yescharacteristic
824C22×C4C2×D24411yescharacteristic
825C22×C4C2×D24411yescharacteristic
826C22×C4C2×D24411yescharacteristic
827C22×C4C2×D24411yescharacteristic
828C22×C4C2×D24411yescharacteristic
829C22×C4C2×D24411yescharacteristic
830C22×C4C2×D24411yescharacteristic
831C22×C4C2×D24411yescharacteristic
832C22×C4C2×D24411yescharacteristic
833C22×C4C2×D24411yescharacteristic
834C22×C4C2×D24411yescharacteristic
835C22×C4C2×D24411yescharacteristic
836C22×C4C2×D24411yescharacteristic
837C22×C4C2×D24411yescharacteristic
838C22×C4C2×D24411yescharacteristic
839C22×C4C2×D24411yescharacteristic
840C22×C4C2×D24411yescharacteristic
841C22×C4C2×D24411yescharacteristic
842C22×C4C2×D24411yescharacteristic
843C22×C4C2×D24411yescharacteristic
844C22×C4C23×D6111yescharacteristic
845C22×C4C23×D6111yescharacteristic
846C22×C4C23×D6111yescharacteristic
847C22×C4C23×D6111yescharacteristic
848C22×C4C23×D6111yescharacteristic
849C22×C4C23×D6111yescharacteristic
850C22×C4C23×D6111yescharacteristic
851SD16—2448no—
852D8—2448no—
853M16—28no—
854M16—44no—
855C2×C8—44no—
856C2×C8C23×D6118yes—
857C4⋊C4—612no—
858C4⋊C4—612no—
859C4⋊C4—614no—
860C4⋊C4—1222no—
861C4⋊C4—1222no—
862C4⋊C4—1222no—
863C4⋊C4—1221no—
864C4⋊C4—1221no—
865C4⋊C4—1222no—
866C4⋊C4—1222no—
867C4⋊C4—1222no—
868C4⋊C4—1222no—
869C22⋊C4—1222no—
870C22⋊C4—1222no—
871C22⋊C4—1222no—
872C22⋊C4—1222no—
873C22⋊C4—1222no—
874C22⋊C4—1222no—
875C22⋊C4—1224no—
876C22⋊C4—1224no—
877C22⋊C4—1224no—
878C22⋊C4—1224no—
879C22⋊C4—1222no—
880C22⋊C4—1222no—
881C22⋊C4—1222no—
882C22⋊C4—1222no—
883C42—1222no—
884C42—1222no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—416no—
906C23—1222no—
907C23—1224no—
908C23—48816no—
909C23—2442no—
910C23—2444no—
911C23—2444no—
912C23—2444no—
913C23—2444no—
914C23—2442no—
915C23—2444no—
916C23—2444no—
917C23—2444no—
918C23—2442no—
919C23—2444no—
920C23—2444no—
921C23#1451980514yescomplemented
922C23C22×D24411yescharacteristic
923C23C22×D24411yescharacteristic
924C23C22×D24411yescharacteristic
925C23C22×D24411yescharacteristic
926C23C22×D24411yescharacteristic
927C23C22×D24411yescharacteristic
928C23C22×D24411yescharacteristic
929Q8—1224no—
930Q8—2442no—
931D4—1224no—
932D4—1228no—
933D4—2444no—
934D4—2444no—
935D4—2442no—
936D4—2444no—
937D4—2448no—
938D4—2448no—
939D4—2444no—
940D4—2444no—
941D4—2444no—
942D4—2448no—
943D4—2448no—
944D4—2444no—
945D4—2444no—
946D4—2444no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—1222no—
975C2×C4—1222no—
976C2×C4—1224no—
977C2×C4—1222no—
978C2×C4—2444no—
979C2×C4—2444no—
980C2×C4—2444no—
981C2×C4—2442no—
982C2×C4—2442no—
983C2×C4—2444no—
984C2×C4—2442no—
985C2×C4—2444no—
986C2×C4C22×D24411yescharacteristic
987C2×C4C22×D24411yescharacteristic
988C2×C4C22×D24411yescharacteristic
989C2×C4C22×D24411yescharacteristic
990C2×C4C22×D24411yescharacteristic
991C2×C4C22×D24411yescharacteristic
992C2×C4C22×D24411yescharacteristic
993C2×C4#1451982214yes—
994C2×C4C24×D6111yescharacteristic
995C8—28no—
996C22—28no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—44no—
1014C22—44no—
1015C22—44no—
1016C22—44no—
1017C22—44no—
1018C22—44no—
1019C22—4888no—
1020C22—4888no—
1021C22—4888no—
1022C22—4884no—
1023C22—2444no—
1024C22—2442no—
1025C22—2442no—
1026C22—2444no—
1027C22—2442no—
1028C22—2444no—
1029C22#1684032412yes—
1030C22C2×#1451980512yes—
1031C22C2×#1451980512yes—
1032C22C2×#1451980512yes—
1033C22#1684056212yes—
1034C22C23×D24411yescharacteristic
1035C4—21no—
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—21no—
1041C4—2444no—
1042C4—2442no—
1043C4—2442no—
1044C4—2442no—
1045C4#1684032412yes—
1046C4C2×#1451982212yes—
1047C2—22no—
1048C2—22no—
1049C2—22no—
1050C2—22no—
1051C2—22no—
1052C2—41no—
1053C2—41no—
1054C2—4884no—
1055C2—4882no—
1056C2C2×#1684032411yescharacteristic
1057C2C22×#1451980511yescharacteristic
1058C2C2×#1684056211yescharacteristic
subgroupG/H
centerC22C23×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#407C2
socleC22×C61C23×D4
hypercenterC2×#407D61
hypocenterC61#60750
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
1. C2×#16840273C2semidirect
2. C22×#14519751C2semidirect
3. #21456635C2semidirect
4. #21456626C2semidirect
5. #21456619C2semidirect
6. #21456586C2semidirect
7. #21456577C2semidirect
8. #21456570C2semidirect
9. #21455760C2semidirect
10. #21455744C2semidirect
11. #21455438C2semidirect
12. #21455073C2semidirect
13. #21455049C2semidirect
14. C2×C61×#407C2semidirect
15. C22×#11758222C22semidirect
16. C23×D244C22semidirect
18. C2×#14519805C22semidirect
24. #16840273C22semidirect
25. #16840273C22semidirect
26. #16840273C22semidirect
28. C2×#14519756C22semidirect
29. C2×#14519756C22semidirect
39. C2×#14519751C22semidirect
40. C2×#14519751C22semidirect
41. C2×#14519751C22semidirect
42. C2×#14519751C22semidirect
43. C2×#14519751C22semidirect
47. C2×#14519736C22semidirect
48. C22×C4⋊Dic61C22semidirect
50. #16840098C22semidirect
51. #16840093C22semidirect
52. #16840087C22semidirect
53. #16840081C22semidirect
54. #16840081C22semidirect
55. #16840076C22semidirect
56. #16840076C22semidirect
57. #16840015C22semidirect
58. #16840008C22semidirect
59. #16839998C22semidirect
60. #16839991C22semidirect
61. #16839915C22semidirect
62. #16839915C22semidirect
63. #16839909C22semidirect
64. #16839903C22semidirect
65. #16839898C22semidirect
66. #16839898C22semidirect
67. #16839898C22semidirect
68. #16839804C22semidirect
69. #16839768C22semidirect
70. #16839764C22semidirect
72. C22×M16×C61C22semidirect
73. C61×#407C22semidirect
74. C61×#407C22semidirect
75. C61×#407C22semidirect
76. C61×#407C22semidirect
77. C2×C22⋊C8×C61C22semidirect
78. C2×C22⋊C8×C61C22semidirect
84. C2×#11758222C23semidirect
85. C22×Dic122C23semidirect
93. C22×D244C23semidirect
107. C2×#11758190C23semidirect
108. C2×D488C23semidirect
119. #14519756C23semidirect
120. #14519756C23semidirect
143. #14519751C23semidirect
144. #14519751C23semidirect
160. #14519736C23semidirect
167. C2×C4⋊Dic61C23semidirect
168. C2×C4⋊Dic61C23semidirect
183. #14519711C23semidirect
184. #14519709C23semidirect
185. #14519702C23semidirect
186. #14519699C23semidirect
187. #14519699C23semidirect
188. #14519699C23semidirect
207. C2×M16×C61C23semidirect
208. C22×C8×C61C23semidirect
211. C22⋊C8×C61C23semidirect
212. C22⋊C8×C61C23semidirect
376. C23×C61AGL(1,ℤ/8)semidirect
531. C2×#407D61semidirect
549. C22×M16C2×D61semidirect
602. #407C2×D61semidirect
603. #407C2×D61semidirect
604. #407C2×D61semidirect
605. #407C2×D61semidirect
606. C2×C22⋊C8C2×D61semidirect
607. C2×C22⋊C8C2×D61semidirect
608. C61#60750semidirect
657. C2×M16C22×D61semidirect
658. C22×C8C22×D61semidirect
741. C22⋊C8C22×D61semidirect
742. C22⋊C8C22×D61semidirect
921. C23#14519805semidirect

Maximal subgroups

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

subgroupindex
C2×#168402732
C22×#145197512
#214566352
#214566262
#214566192
#214565862
#214565772
#214565702
#214557602
#214557442
#214554382
#214550732
#214550492
C2×C61×#4072
#6075061