Finite Group Databasebeta

← #30550756

Subgroups — #30550756

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
2#21456633C214yesmaximal, complemented
3#21456625C212yesmaximal, complemented
4#21456616C212yesmaximal, complemented
5#21456584C214yesmaximal, complemented
6#21456576C212yesmaximal, complemented
7#21456567C212yesmaximal, complemented
8#21455755C212yesmaximal, complemented
9#21455742C212yesmaximal, complemented
10#21455434C214yesmaximal, complemented
11#21455069C212yesmaximal, complemented
12#21455046C212yesmaximal, complemented
13C2×#16839726C211yesmaximal, characteristic, complemented
14C22×#121×C61C211yesmaximal, characteristic, complemented
15C22×#11758222C2211yescharacteristic, complemented
16C2×#14519803C2214yescomplemented
17C22×#11758194C2212yescomplemented
18#16840273—21no—
19#16840273—21no—
20#16840273—21no—
21#16840273—21no—
22#16840273C2212yes—
23#16840273C2212yescomplemented
24#16840273C2212yescomplemented
25#16840273C2212yescomplemented
26C2×#14519760—21no—
27C2×#14519756C2211yescharacteristic, complemented
28C2×#14519756C2211yescharacteristic, complemented
29C2×#14519751C2211yescharacteristic, complemented
30C2×#14519751C2211yescharacteristic, complemented
31C2×#14519746—21no—
32C2×C4×C22⋊D61—21no—
33C2×C4×C22⋊D61—21no—
34C2×#14519736C2211yescharacteristic, complemented
35#16840097C2214yescomplemented
36#16840092C2214yescomplemented
37#16840083C2218yescomplemented
38#16840080C2214yescomplemented
39#16840078C2214yescomplemented
40#16840075C2214yescomplemented
41#16840073C2214yescomplemented
42#16840013C2218yescomplemented
43#16840006C2218yescomplemented
44#16839996C2218yescomplemented
45#16839989C2218yescomplemented
46#16839913C2214yescomplemented
47#16839913C2214yescomplemented
48#16839905C2218yescomplemented
49#16839900C2214yescomplemented
50#16839896C2214yescomplemented
51#16839896C2214yescomplemented
52#16839895C2214yescomplemented
53#16839802C2214yescomplemented
54#16839767C2214yescomplemented
55#16839761C2214yescomplemented
56#16839726C2212yescomplemented
57#16839726C2212yescomplemented
58#16839726C2212yescomplemented
59#16839726C2212yescomplemented
60C2×C22⋊#92418C2212yescomplemented
61C2×C22⋊#92418C2212yescomplemented
62C23×D4×C61—21no—
63C23×D4×C61C2211yescharacteristic, complemented
64C24×C4×C61C2211yescharacteristic
65C2×#121×C61—21no—
66C2×#121×C61—21no—
67C2×#121×C61—21no—
68C2×#121×C61—21no—
69C2×#121×C61—21no—
70C2×#121×C61—21no—
71C2×#121×C61C2212yes—
72C2×#121×C61C2212yes—
73C2×#121×C61C2212yes—
74C2×#121×C61C2212yescomplemented
75C2×#121×C61C2212yescomplemented
76C2×#121×C61C2212yescomplemented
77C22×C4⋊C4×C61C2211yescharacteristic, complemented
78C22×C22⋊C4×C61—21no—
79C2×#11758222—21no—
80C2×#11758222—21no—
81C2×#11758222—44no—
82C2×#11758222C2312yes—
83C2×#11758222C2312yescomplemented
84C22×Dic122C2311yescharacteristic, complemented
85C22×D244C2311yescharacteristic, complemented
86C22×C22⋊D61—21no—
87C22×C22⋊D61—21no—
88C22×C22⋊D61—21no—
89C22×C4×D61—21no—
90#14519803—48no—
91C2×#11758200C2318yescomplemented
92C2×#11758199C2318yescomplemented
93C2×#11758194—44no—
94C2×#11758194C2314yes—
95C2×#11758194C2314yescomplemented
96C22×#92418C2314yescomplemented
97#14519760—22no—
98#14519760—22no—
99#14519760—22no—
100#14519760—22no—
101#14519756—21no—
102#14519756—21no—
103#14519756—21no—
104#14519756—21no—
105#14519756C2312yes—
106#14519756C2312yes—
107#14519756C2312yescomplemented
108#14519756C2312yescomplemented
109#14519751—21no—
110#14519751—21no—
111#14519751—21no—
112#14519751—21no—
113#14519751C2312yes—
114#14519751C2312yes—
115#14519751C2312yescomplemented
116#14519751C2312yescomplemented
117#14519746—22no—
118#14519746—22no—
119#14519746—22no—
120#14519746—22no—
121C4×C22⋊D61—22no—
122C4×C22⋊D61—22no—
123C4×C22⋊D61—22no—
124C4×C22⋊D61—22no—
125C4×C22⋊D61—22no—
126C4×C22⋊D61—22no—
127C4×C22⋊D61—22no—
128C4×C22⋊D61—22no—
129#14519736—21no—
130#14519736—21no—
131#14519736C2312yes—
132#14519736C2312yescomplemented
133C2×C4⋊Dic61C2311yescharacteristic, complemented
134C2×C4⋊Dic61C2311yescharacteristic, complemented
135C2×#11758196—21no—
136C2×#11758196—21no—
137C2×C22⋊Dic61—21no—
138C2×C22⋊Dic61—21no—
139C2×C22⋊Dic61—21no—
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×C4×Dic61—21no—
143#14519710C2318yescomplemented
144#14519708C2318yescomplemented
145#14519700C2318yescomplemented
146#14519698C2318yescomplemented
147#14519698C2318yescomplemented
148#14519697C2318yescomplemented
149C22⋊#92418C2314yes—
150C22⋊#92418C2314yes—
151C22⋊#92418C2314yescomplemented
152C22⋊#92418C2314yescomplemented
153C25×C61—21no—
154C25×C61D411yescharacteristic
155C22×D4×C61—22no—
156C22×D4×C61—22no—
157C22×D4×C61—22no—
158C22×D4×C61—22no—
159C22×D4×C61—22no—
160C22×D4×C61—22no—
161C22×D4×C61—21no—
162C22×D4×C61—21no—
163C22×D4×C61—21no—
164C22×D4×C61—44no—
165C22×D4×C61—48no—
166C22×D4×C61C2312yes—
167C22×D4×C61C2312yes—
168C22×D4×C61C2312yes—
169C23×C4×C61—21no—
170C23×C4×C61—44no—
171C23×C4×C61D411yescharacteristic
172C23×C4×C61D411yescharacteristic
173C23×C4×C61D411yescharacteristic
174C23×C4×C61D411yescharacteristic
175C23×C4×C61D411yescharacteristic
176C23×C4×C61D411yescharacteristic
177C23×C4×C61D411yescharacteristic
178C23×C4×C61C2311yescharacteristic
179C23×C4×C61C2311yescharacteristic
180C23×C4×C61C2311yescharacteristic
181C23×C4×C61C2311yescharacteristic
182C23×C4×C61C2311yescharacteristic
183C23×C4×C61C2311yescharacteristic
184C23×C4×C61C2311yescharacteristic
185#121×C61—22no—
186#121×C61—22no—
187#121×C61—22no—
188#121×C61—22no—
189#121×C61—22no—
190#121×C61—22no—
191#121×C61—22no—
192#121×C61—22no—
193#121×C61—22no—
194#121×C61—22no—
195#121×C61—22no—
196#121×C61—22no—
197#121×C61C2314yes—
198#121×C61C2314yes—
199#121×C61C2314yes—
200#121×C61C2314yes—
201C2×C4⋊C4×C61—21no—
202C2×C4⋊C4×C61—21no—
203C2×C4⋊C4×C61—21no—
204C2×C4⋊C4×C61C2312yes—
205C2×C4⋊C4×C61C2312yes—
206C2×C4⋊C4×C61C2312yes—
207C2×C22⋊C4×C61—22no—
208C2×C22⋊C4×C61—22no—
209C2×C22⋊C4×C61—22no—
210C2×C22⋊C4×C61—22no—
211C2×C22⋊C4×C61—22no—
212C2×C22⋊C4×C61—22no—
213C24×C61—24no—
214C24×C61—22no—
215C24×C61—22no—
216C24×C61—22no—
217C24×C61—42no—
218C24×C61—42no—
219C24×C61—44no—
220C24×C61—44no—
221C24×C61—44no—
222C24×C61C2×D411yescharacteristic
223C24×C61C2×D411yescharacteristic
224C24×C61C2×D411yescharacteristic
225C24×C61C2×D411yescharacteristic
226C24×C61C2×D411yescharacteristic
227C24×C61C2×D411yescharacteristic
228C24×C61C2×D411yescharacteristic
229C23×D61—21no—
230C2×D4×C61—24no—
231C2×D4×C61—24no—
232C2×D4×C61—24no—
233C2×D4×C61—24no—
234C2×D4×C61—22no—
235C2×D4×C61—22no—
236C2×D4×C61—22no—
237C2×D4×C61—28no—
238C2×D4×C61—44no—
239C2×D4×C61—44no—
240C2×D4×C61—44no—
241C2×D4×C61—44no—
242C2×D4×C61—44no—
243C2×D4×C61—48no—
244C2×D4×C61—48no—
245C2×D4×C61—48no—
246C2×D4×C61—48no—
247C2×D4×C61—48no—
248C2×D4×C61—48no—
249C2×D4×C61C2414yes—
250C22×C4×C61—24no—
251C22×C4×C61—24no—
252C22×C4×C61—24no—
253C22×C4×C61—22no—
254C22×C4×C61—22no—
255C22×C4×C61—22no—
256C22×C4×C61—42no—
257C22×C4×C61—42no—
258C22×C4×C61—42no—
259C22×C4×C61—42no—
260C22×C4×C61—42no—
261C22×C4×C61—42no—
262C22×C4×C61—42no—
263C22×C4×C61—42no—
264C22×C4×C61—42no—
265C22×C4×C61—42no—
266C22×C4×C61—42no—
267C22×C4×C61—44no—
268C22×C4×C61C2×D411yescharacteristic
269C22×C4×C61C2×D411yescharacteristic
270C22×C4×C61C2×D411yescharacteristic
271C22×C4×C61C2×D411yescharacteristic
272C22×C4×C61C2×D411yescharacteristic
273C22×C4×C61C2×D411yescharacteristic
274C22×C4×C61C2×D411yescharacteristic
275C22×C4×C61C2×D411yescharacteristic
276C22×C4×C61C2×D411yescharacteristic
277C22×C4×C61C2×D411yescharacteristic
278C22×C4×C61C2×D411yescharacteristic
279C22×C4×C61C2×D411yescharacteristic
280C22×C4×C61C2×D411yescharacteristic
281C22×C4×C61C2×D411yescharacteristic
282C22×C4×C61C2×D411yescharacteristic
283C22×C4×C61C2×D411yescharacteristic
284C22×C4×C61C2×D411yescharacteristic
285C22×C4×C61C2×D411yescharacteristic
286C22×C4×C61C2×D411yescharacteristic
287C22×C4×C61C2×D411yescharacteristic
288C22×C4×C61C2×D411yescharacteristic
289C22×C4×C61C2411yescharacteristic
290C22×C4×C61C2411yescharacteristic
291C22×C4×C61C2411yescharacteristic
292C22×C4×C61C2411yescharacteristic
293C22×C4×C61C2411yescharacteristic
294C22×C4×C61C2411yescharacteristic
295C22×C4×C61C2411yescharacteristic
296C2×C22⋊D61—22no—
297C2×C22⋊D61—22no—
298C2×C22⋊D61—22no—
299C2×C22⋊D61—22no—
300C2×C22⋊D61—22no—
301C2×C22⋊D61—22no—
302C2×C22⋊D61—44no—
303C2×C22⋊D61—44no—
304C2×C22⋊D61—44no—
305C22×Dic61—21no—
306C22×Dic61—21no—
307C22×Dic61—21no—
308#11758222—28no—
309#11758222—44no—
310#11758222—44no—
311#11758222—44no—
312C2×D244—21no—
313C2×D244—42no—
314C2×D244C2412yes—
315C2×C4×D61—22no—
316C2×C4×D61—22no—
317C2×C4×D61—44no—
318C2×Dic122—21no—
319C2×Dic122—42no—
320C2×Dic122C2412yes—
321C4⋊C4×C61—22no—
322C4⋊C4×C61—22no—
323C4⋊C4×C61—22no—
324C4⋊C4×C61C2414yes—
325C22⋊C4×C61—24no—
326C22⋊C4×C61—24no—
327C22⋊C4×C61—24no—
328C22⋊C4×C61—24no—
329C22⋊Dic61—22no—
330C22⋊Dic61—22no—
331C22⋊Dic61—22no—
332C22⋊Dic61—22no—
333C22⋊Dic61—22no—
334C22⋊Dic61—22no—
335#11758200—48no—
336#11758199—48no—
337#11758198—22no—
338#11758198—22no—
339#11758198—22no—
340#11758198—22no—
341C4⋊Dic61—21no—
342C4⋊Dic61—21no—
343C4⋊Dic61C2412yes—
344C4⋊Dic61C2412yes—
345#11758196—22no—
346#11758196—22no—
347#11758196—22no—
348#11758196—22no—
349C4×Dic61—22no—
350C4×Dic61—22no—
351#11758194—28no—
352#11758194—44no—
353C2×#92418—44no—
354C2×#92418C2418yes—
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—24no—
368C23×C61—41no—
369C23×C61—41no—
370C23×C61—41no—
371C23×C61—41no—
372C23×C61—41no—
373C23×C61—41no—
374C23×C61—41no—
375C23×C61—41no—
376C23×C61—416no—
377C23×C61—44no—
378C23×C61—44no—
379C23×C61—44no—
380C23×C61—44no—
381C23×C61—44no—
382C23×C61—44no—
383C23×C61—44no—
384C23×C61—44no—
385C23×C61—44no—
386C23×C61—816no—
387C23×C61AGL(1,ℤ/8)14yescomplemented
388C23×C61C22×D411yescharacteristic
389C23×C61C22×D411yescharacteristic
390C23×C61C22×D411yescharacteristic
391C23×C61C22×D411yescharacteristic
392C23×C61C22×D411yescharacteristic
393C23×C61C22×D411yescharacteristic
394C23×C61C22×D411yescharacteristic
395C22×D61—22no—
396C22×D61—42no—
397C22×D61—42no—
398C22×D61—42no—
399D4×C61—28no—
400D4×C61—44no—
401D4×C61—44no—
402D4×C61—48no—
403D4×C61—48no—
404D4×C61—48no—
405D4×C61—48no—
406D4×C61—44no—
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—22no—
415C2×C4×C61—22no—
416C2×C4×C61—22no—
417C2×C4×C61—22no—
418C2×C4×C61—22no—
419C2×C4×C61—22no—
420C2×C4×C61—22no—
421C2×C4×C61—22no—
422C2×C4×C61—24no—
423C2×C4×C61—41no—
424C2×C4×C61—41no—
425C2×C4×C61—41no—
426C2×C4×C61—41no—
427C2×C4×C61—41no—
428C2×C4×C61—41no—
429C2×C4×C61—41no—
430C2×C4×C61—41no—
431C2×C4×C61—41no—
432C2×C4×C61—41no—
433C2×C4×C61—41no—
434C2×C4×C61—41no—
435C2×C4×C61—44no—
436C2×C4×C61—44no—
437C2×C4×C61—44no—
438C2×C4×C61C22×D411yescharacteristic
439C2×C4×C61C22×D411yescharacteristic
440C2×C4×C61C22×D411yescharacteristic
441C2×C4×C61C22×D411yescharacteristic
442C2×C4×C61C22×D411yescharacteristic
443C2×C4×C61C22×D411yescharacteristic
444C2×C4×C61C22×D411yescharacteristic
445C2×C4×C61H(5,𝔽2)14yes—
446C2×C4×C61C2511yescharacteristic
447C22⋊D61—44no—
448C22⋊D61—44no—
449C22⋊D61—44no—
450C22⋊D61—44no—
451C22⋊D61—44no—
452C22⋊D61—44no—
453C2×Dic61—22no—
454C2×Dic61—22no—
455C2×Dic61—22no—
456C2×Dic61—42no—
457C2×Dic61—42no—
458C2×Dic61—42no—
459D244—24no—
460D244—42no—
461C4×D61—44no—
462C4×D61—44no—
463Dic122—24no—
464Dic122—42no—
465#92418—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—44no—
491C22×C61—44no—
492C22×C61—44no—
493C22×C61—88no—
494C22×C61—88no—
495C22×C61—88no—
496C22×C61#53412yes—
497C22×C61C2×AGL(1,ℤ/8)12yes—
498C22×C61C2×AGL(1,ℤ/8)12yes—
499C22×C61C2×AGL(1,ℤ/8)12yes—
500C22×C61#57512yes—
501C22×C61C23×D411yescharacteristic
502C2×D61—42no—
503C2×D61—42no—
504C2×D61—42no—
505C2×D61—84no—
506C4×C61—21no—
507C4×C61—21no—
508C4×C61—21no—
509C4×C61—21no—
510C4×C61—21no—
511C4×C61—21no—
512C4×C61—44no—
513C4×C61#53412yes—
514C4×C61C2×H(5,𝔽2)12yes—
515Dic61—42no—
516Dic61—42no—
517Dic61—42no—
518C2×#525—611no—
519C22×#121D6111yescharacteristic, complemented
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×#407—611no—
532C2×C61—22no—
533C2×C61—22no—
534C2×C61—22no—
535C2×C61—22no—
536C2×C61—22no—
537C2×C61—41no—
538C2×C61—41no—
539C2×C61—84no—
540C2×C61C2×#53411yescharacteristic
541C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
542C2×C61C2×#57511yescharacteristic
543D61—82no—
544C22×#41—611no—
545C23×D4—21no—
546C23×D4C2×D6111yescharacteristic, complemented
547C24×C4C2×D6111yescharacteristic
548C2×AGL(1,ℤ/8)—614no—
549C22×M16—612no—
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—21no—
562C2×#121—21no—
563C2×#121—21no—
564C2×#121—21no—
565C2×#121—21no—
566C2×#121—21no—
567C2×#121—611no—
568C2×#121—611no—
569C2×#121C2×D6112yes—
570C2×#121C2×D6112yes—
571C2×#121C2×D6112yes—
572C2×#121C2×D6112yescomplemented
573C2×#121C2×D6112yescomplemented
574C2×#121C2×D6112yescomplemented
575C2×#120—1221no—
576C2×C4×D4—1221no—
577C2×C4×D4—1221no—
578C2×#117—611no—
579C22×C4⋊C4C2×D6111yescharacteristic, complemented
580C22×C22⋊C4—21no—
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#407—612no—
603#407—612no—
604#407—612no—
605#407—612no—
606C2×C22⋊C8—612no—
607C2×C22⋊C8—612no—
608C61#6075011yescharacteristic, complemented, Sylow
609C25—21no—
610C25C22⋊D6111yescharacteristic
611C2×#41—612no—
612C2×#41—612no—
613C2×#41—1221no—
614C2×#41—1221no—
615C2×#41—2444no—
616C22×Q8—611no—
617C22×D4—22no—
618C22×D4—22no—
619C22×D4—22no—
620C22×D4—22no—
621C22×D4—22no—
622C22×D4—22no—
623C22×D4—21no—
624C22×D4—21no—
625C22×D4—21no—
626C22×D4—44no—
627C22×D4—48no—
628C22×D4—611no—
629C22×D4—1221no—
630C22×D4—1221no—
631C22×D4—1221no—
632C22×D4C22×D6112yes—
633C22×D4C22×D6112yes—
634C22×D4C22×D6112yes—
635C23×C4—21no—
636C23×C4—44no—
637C23×C4—1221no—
638C23×C4C22⋊D6111yescharacteristic
639C23×C4C22⋊D6111yescharacteristic
640C23×C4C22⋊D6111yescharacteristic
641C23×C4C22⋊D6111yescharacteristic
642C23×C4C22⋊D6111yescharacteristic
643C23×C4C22⋊D6111yescharacteristic
644C23×C4C22⋊D6111yescharacteristic
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—614no—
656C2×M16—614no—
657C2×M16—2444no—
658C22×C8—614no—
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—22no—
672#121—22no—
673#121—22no—
674#121—22no—
675#121—22no—
676#121—22no—
677#121—22no—
678#121—22no—
679#121—22no—
680#121—22no—
681#121—22no—
682#121—22no—
683#121—612no—
684#121—612no—
685#121—612no—
686#121—612no—
687#121—1221no—
688#121—1221no—
689#121—1221no—
690#121—1221no—
691#121C22×D6114yes—
692#121C22×D6114yes—
693#121C22×D6114yes—
694#121C22×D6114yes—
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—21no—
712C2×C4⋊C4—21no—
713C2×C4⋊C4—21no—
714C2×C4⋊C4—611no—
715C2×C4⋊C4—611no—
716C2×C4⋊C4—1221no—
717C2×C4⋊C4—1221no—
718C2×C4⋊C4C22×D6112yes—
719C2×C4⋊C4C22×D6112yes—
720C2×C4⋊C4C22×D6112yes—
721C2×C22⋊C4—22no—
722C2×C22⋊C4—22no—
723C2×C22⋊C4—22no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—1221no—
728C2×C22⋊C4—1221no—
729C2×C22⋊C4—1221no—
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⋊C8—614no—
740C22⋊C8—614no—
741C22⋊C8—614no—
742C22⋊C8—614no—
743C24—24no—
744C24—22no—
745C24—22no—
746C24—22no—
747C24—42no—
748C24—42no—
749C24—44no—
750C24—44no—
751C24—44no—
752C24—1221no—
753C24C2×C22⋊D6111yescharacteristic
754C24C2×C22⋊D6111yescharacteristic
755C24C2×C22⋊D6111yescharacteristic
756C24C2×C22⋊D6111yescharacteristic
757C24C2×C22⋊D6111yescharacteristic
758C24C2×C22⋊D6111yescharacteristic
759C24C2×C22⋊D6111yescharacteristic
760#41—1228no—
761#41—2444no—
762#41—2444no—
763#41—2444no—
764C2×Q8—612no—
765C2×Q8—1221no—
766C2×Q8—2442no—
767C2×D4—24no—
768C2×D4—24no—
769C2×D4—24no—
770C2×D4—24no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—22no—
774C2×D4—28no—
775C2×D4—44no—
776C2×D4—44no—
777C2×D4—44no—
778C2×D4—44no—
779C2×D4—44no—
780C2×D4—48no—
781C2×D4—48no—
782C2×D4—48no—
783C2×D4—48no—
784C2×D4—48no—
785C2×D4—48no—
786C2×D4—612no—
787C2×D4—1222no—
788C2×D4—1222no—
789C2×D4—1222no—
790C2×D4—1222no—
791C2×D4—1222no—
792C2×D4—1222no—
793C2×D4—1221no—
794C2×D4—2442no—
795C2×D4—2444no—
796C2×D4—2444no—
797C2×D4—2444no—
798C2×D4C23×D6114yes—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
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—42no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—44no—
817C22×C4—1221no—
818C22×C4—1221no—
819C22×C4—1221no—
820C22×C4—1222no—
821C22×C4—1222no—
822C22×C4—2444no—
823C22×C4C2×C22⋊D6111yescharacteristic
824C22×C4C2×C22⋊D6111yescharacteristic
825C22×C4C2×C22⋊D6111yescharacteristic
826C22×C4C2×C22⋊D6111yescharacteristic
827C22×C4C2×C22⋊D6111yescharacteristic
828C22×C4C2×C22⋊D6111yescharacteristic
829C22×C4C2×C22⋊D6111yescharacteristic
830C22×C4C2×C22⋊D6111yescharacteristic
831C22×C4C2×C22⋊D6111yescharacteristic
832C22×C4C2×C22⋊D6111yescharacteristic
833C22×C4C2×C22⋊D6111yescharacteristic
834C22×C4C2×C22⋊D6111yescharacteristic
835C22×C4C2×C22⋊D6111yescharacteristic
836C22×C4C2×C22⋊D6111yescharacteristic
837C22×C4C2×C22⋊D6111yescharacteristic
838C22×C4C2×C22⋊D6111yescharacteristic
839C22×C4C2×C22⋊D6111yescharacteristic
840C22×C4C2×C22⋊D6111yescharacteristic
841C22×C4C2×C22⋊D6111yescharacteristic
842C22×C4C2×C22⋊D6111yescharacteristic
843C22×C4C2×C22⋊D6111yescharacteristic
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—1228no—
854M16—2444no—
855C2×C8—618no—
856C2×C8—2444no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—612no—
861C4⋊C4—612no—
862C4⋊C4—1221no—
863C4⋊C4—1221no—
864C4⋊C4—1222no—
865C4⋊C4—1222no—
866C4⋊C4—1222no—
867C4⋊C4—1222no—
868C4⋊C4C23×D6114yes—
869C22⋊C4—24no—
870C22⋊C4—24no—
871C22⋊C4—24no—
872C22⋊C4—24no—
873C22⋊C4—1222no—
874C22⋊C4—1222no—
875C22⋊C4—1222no—
876C22⋊C4—1222no—
877C22⋊C4—1222no—
878C22⋊C4—1222no—
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—24no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—416no—
907C23—44no—
908C23—44no—
909C23—44no—
910C23—44no—
911C23—44no—
912C23—44no—
913C23—44no—
914C23—44no—
915C23—44no—
916C23—816no—
917C23—1222no—
918C23—2442no—
919C23—2442no—
920C23—2442no—
921C23#1451980314yescomplemented
922C23C22×C22⋊D6111yescharacteristic
923C23C22×C22⋊D6111yescharacteristic
924C23C22×C22⋊D6111yescharacteristic
925C23C22×C22⋊D6111yescharacteristic
926C23C22×C22⋊D6111yescharacteristic
927C23C22×C22⋊D6111yescharacteristic
928C23C22×C22⋊D6111yescharacteristic
929Q8—1224no—
930Q8—2442no—
931D4—28no—
932D4—44no—
933D4—44no—
934D4—48no—
935D4—48no—
936D4—48no—
937D4—48no—
938D4—44no—
939D4—1224no—
940D4—2442no—
941D4—2444no—
942D4—2444no—
943D4—2444no—
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—24no—
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—41no—
975C2×C4—44no—
976C2×C4—44no—
977C2×C4—44no—
978C2×C4—1222no—
979C2×C4—1222no—
980C2×C4—1222no—
981C2×C4—2444no—
982C2×C4—2442no—
983C2×C4—2442no—
984C2×C4—2442no—
985C2×C4—2444no—
986C2×C4C22×C22⋊D6111yescharacteristic
987C2×C4C22×C22⋊D6111yescharacteristic
988C2×C4C22×C22⋊D6111yescharacteristic
989C2×C4C22×C22⋊D6111yescharacteristic
990C2×C4C22×C22⋊D6111yescharacteristic
991C2×C4C22×C22⋊D6111yescharacteristic
992C2×C4C22×C22⋊D6111yescharacteristic
993C2×C4#1451982214yes—
994C2×C4C24×D6111yescharacteristic
995C8—1228no—
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—44no—
1020C22—44no—
1021C22—44no—
1022C22—88no—
1023C22—88no—
1024C22—88no—
1025C22—4884no—
1026C22—2442no—
1027C22—2442no—
1028C22—2442no—
1029C22#1684032112yes—
1030C22C2×#1451980312yes—
1031C22C2×#1451980312yes—
1032C22C2×#1451980312yes—
1033C22#1684056012yes—
1034C22C23×C22⋊D6111yescharacteristic
1035C4—21no—
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—21no—
1041C4—44no—
1042C4—2442no—
1043C4—2442no—
1044C4—2442no—
1045C4#1684032112yes—
1046C4C2×#1451982212yes—
1047C2—22no—
1048C2—22no—
1049C2—22no—
1050C2—22no—
1051C2—22no—
1052C2—41no—
1053C2—41no—
1054C2—84no—
1055C2—4882no—
1056C2C2×#1684032111yescharacteristic
1057C2C22×#1451980311yescharacteristic
1058C2C2×#1684056011yescharacteristic
subgroupG/H
centerC22C23×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC22×#121×C61C2
socleC22×C61C23×D4
hypercenterC22×#121D61
hypocenterC61#60750
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24×C4 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C2×#16840273C2semidirect
2. #21456633C2semidirect
3. #21456625C2semidirect
4. #21456616C2semidirect
5. #21456584C2semidirect
6. #21456576C2semidirect
7. #21456567C2semidirect
8. #21455755C2semidirect
9. #21455742C2semidirect
10. #21455434C2semidirect
11. #21455069C2semidirect
12. #21455046C2semidirect
13. C2×#16839726C2semidirect
14. C22×#121×C61C2semidirect
15. C22×#11758222C22semidirect
16. C2×#14519803C22semidirect
17. C22×#11758194C22semidirect
23. #16840273C22semidirect
24. #16840273C22semidirect
25. #16840273C22semidirect
27. C2×#14519756C22semidirect
28. C2×#14519756C22semidirect
29. C2×#14519751C22semidirect
30. C2×#14519751C22semidirect
34. C2×#14519736C22semidirect
35. #16840097C22semidirect
36. #16840092C22semidirect
37. #16840083C22semidirect
38. #16840080C22semidirect
39. #16840078C22semidirect
40. #16840075C22semidirect
41. #16840073C22semidirect
42. #16840013C22semidirect
43. #16840006C22semidirect
44. #16839996C22semidirect
45. #16839989C22semidirect
46. #16839913C22semidirect
47. #16839913C22semidirect
48. #16839905C22semidirect
49. #16839900C22semidirect
50. #16839896C22semidirect
51. #16839896C22semidirect
52. #16839895C22semidirect
53. #16839802C22semidirect
54. #16839767C22semidirect
55. #16839761C22semidirect
56. #16839726C22semidirect
57. #16839726C22semidirect
58. #16839726C22semidirect
59. #16839726C22semidirect
60. C2×C22⋊#92418C22semidirect
61. C2×C22⋊#92418C22semidirect
63. C23×D4×C61C22semidirect
74. C2×#121×C61C22semidirect
75. C2×#121×C61C22semidirect
76. C2×#121×C61C22semidirect
77. C22×C4⋊C4×C61C22semidirect
83. C2×#11758222C23semidirect
84. C22×Dic122C23semidirect
85. C22×D244C23semidirect
91. C2×#11758200C23semidirect
92. C2×#11758199C23semidirect
95. C2×#11758194C23semidirect
96. C22×#92418C23semidirect
107. #14519756C23semidirect
108. #14519756C23semidirect
115. #14519751C23semidirect
116. #14519751C23semidirect
132. #14519736C23semidirect
133. C2×C4⋊Dic61C23semidirect
134. C2×C4⋊Dic61C23semidirect
143. #14519710C23semidirect
144. #14519708C23semidirect
145. #14519700C23semidirect
146. #14519698C23semidirect
147. #14519698C23semidirect
148. #14519697C23semidirect
151. C22⋊#92418C23semidirect
152. C22⋊#92418C23semidirect
387. C23×C61AGL(1,ℤ/8)semidirect
519. C22×#121D61semidirect
546. C23×D4C2×D61semidirect
572. C2×#121C2×D61semidirect
573. C2×#121C2×D61semidirect
574. C2×#121C2×D61semidirect
579. C22×C4⋊C4C2×D61semidirect
608. C61#60750semidirect
921. C23#14519803semidirect

Maximal subgroups

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

subgroupindex
C2×#168402732
#214566332
#214566252
#214566162
#214565842
#214565762
#214565672
#214557552
#214557422
#214554342
#214550692
#214550462
C2×#168397262
C22×#121×C612
#6075061