Finite Group Databasebeta

← C2×#21457774 #30556517

Subgroups — C2×#21457774 #30556517

Order 15616.

2514 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840408C211yesmaximal, characteristic, complemented
2#21457774C2116yesmaximal, direct product factor
3C2×#16840124C211yesmaximal, characteristic, complemented
4C2×#16840080C211yesmaximal, characteristic, complemented
5C2×#16840092C211yesmaximal, characteristic, complemented
6C2×#16840049C211yesmaximal, characteristic, complemented
7C2×#16840013C211yesmaximal, characteristic, complemented
8C2×#16839989C211yesmaximal, characteristic, complemented
9C2×#16839977C211yesmaximal, characteristic, complemented
10C2×#16839905C211yesmaximal, characteristic, complemented
11C2×#16839895C211yesmaximal, characteristic, complemented
12C2×#16839872C211yesmaximal, characteristic, complemented
13C2×#16839834C211yesmaximal, characteristic, complemented
14C2×#16839761C211yesmaximal, characteristic, complemented
15C22×#14519697C211yesmaximal, characteristic, complemented
16C2×C61×#547C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C23×D244C2211yescharacteristic
19C22×#11758200C2211yescharacteristic, complemented
20C22×#11758199C2211yescharacteristic
21C22×#11758199C2211yescharacteristic
22C22×#11758194C2211yescharacteristic, complemented
23C23×#92418C2211yescharacteristic
24#16840408—24no—
25#16840408C2218yescomplemented
26C2×#14519765C2211yescharacteristic
27C2×#14519762—21no—
28C2×#14519756C2211yescharacteristic
29C2×#14519751C2211yescharacteristic
30C2×#14519750—21no—
31C2×#14519745—21no—
32C2×C4×D244C2211yescharacteristic
33C2×C22⋊C4×D61—21no—
34#16840124C2218yescomplemented
35#16840092C2218yescomplemented
36#16840080C2218yescomplemented
37#16840049C2218yescomplemented
38#16840013C2218yescomplemented
39#16839989C2218yescomplemented
40#16839977C2218yescomplemented
41#16839905C2218yescomplemented
42#16839895C2218yescomplemented
43#16839872C2218yescomplemented
44#16839834C2218yescomplemented
45C2×#14519708C2211yescharacteristic, complemented
46C2×#14519708C2211yescharacteristic, complemented
47C2×#14519708C2211yescharacteristic, complemented
48C2×C4⋊#92418C2211yescharacteristic, complemented
49#16839761C2218yescomplemented
50C2×#14519700C2211yescharacteristic, complemented
51C2×#14519700C2211yescharacteristic, complemented
52C2×#14519700C2211yescharacteristic, complemented
53C2×#14519698C2211yescharacteristic, complemented
54C2×#14519697C2211yescharacteristic
55C2×#14519697C2211yescharacteristic
56C2×#14519697C2211yescharacteristic
57C2×#14519697C2211yescharacteristic
58C2×#14519697C2211yescharacteristic
59C2×#14519697C2211yescharacteristic
60C2×#14519697C2218yescomplemented
61C2×C22⋊#92418C2211yescharacteristic
62C2×C22⋊#92418C2211yescharacteristic, complemented
63C2×#14519688C2211yescharacteristic, complemented
64C22×#41×C61—21no—
65C61×#547—24no—
66C61×#547C2218yescomplemented
67C2×C4⋊Q8×C61C2211yescharacteristic, complemented
68C2×#123×C61—21no—
69C2×#123×C61—21no—
70C2×C22⋊Q8×C61—21no—
71C2×#121×C61C2211yescharacteristic
72C2×#121×C61C2211yescharacteristic, complemented
73C2×C4×D4×C61C2211yescharacteristic
74C2×C4×D4×C61C2211yescharacteristic, complemented
75C22×C4⋊C4×C61C2211yescharacteristic
76C22×C4⋊C4×C61C2211yescharacteristic, complemented
77C24×D61—21no—
78C2×#11758222—22no—
79C2×#11758222—24no—
80C2×#11758222—42no—
81C2×#11758222C2314yes—
82C22×Dic122C2311yescharacteristic
83C22×D244—24no—
84C22×D244—21no—
85C22×D244—22no—
86C22×D244—42no—
87C22×D244C2311yescharacteristic
88C22×D244C2314yes—
89C22×D244C2311yescharacteristic
90C22×C22⋊D61—21no—
91C22×C22⋊D61—21no—
92C22×C4×D61—21no—
93C22×C4×D61—21no—
94C2×#11758200—42no—
95C2×#11758200C2314yescomplemented
96C2×#11758199—24no—
97C2×#11758199—42no—
98C2×#11758199C2314yes—
99C2×#11758199C2314yes—
100C2×#11758194—42no—
101C2×#11758194C2314yescomplemented
102C22×#92418—42no—
103C22×#92418C2311yescharacteristic
104C22×#92418C2311yescharacteristic
105C22×#92418C2311yescharacteristic
106C22×#92418C2311yescharacteristic
107C22×#92418C2314yes—
108#14519765—22no—
109#14519765C2314yes—
110#14519762—28no—
111#14519756—22no—
112#14519756C2314yes—
113#14519751—22no—
114#14519751C2314yes—
115#14519750—28no—
116#14519745—28no—
117C4×D244—22no—
118C4×D244C2314yes—
119C2×C4⋊Dic61C2311yescharacteristic
120C2×#11758196—21no—
121C2×C22⋊Dic61—21no—
122C2×#11758198—21no—
123C2×#11758198—21no—
124C2×#11758198—21no—
125C2×#11758198—21no—
126C22⋊C4×D61—28no—
127#14519708C2314yescomplemented
128#14519708C2314yescomplemented
129#14519708C2314yescomplemented
130C4⋊#92418C2314yescomplemented
131#14519700C2314yescomplemented
132#14519700C2314yescomplemented
133#14519700C2314yescomplemented
134#14519698C2314yescomplemented
135#14519697C2314yes—
136#14519697C2314yes—
137#14519697C2314yes—
138#14519697C2314yes—
139#14519697C2314yes—
140#14519697C2314yes—
141C22⋊#92418C2314yes—
142C22⋊#92418C2314yescomplemented
143#14519688C2314yescomplemented
144C2×#41×C61—28no—
145C2×#41×C61—48no—
146C22×Q8×C61—21no—
147C22×D4×C61—21no—
148C22×D4×C61—21no—
149C22×D4×C61D411yescharacteristic
150C22×D4×C61C2311yescharacteristic
151C23×C4×C61—21no—
152C23×C4×C61—21no—
153C23×C4×C61—21no—
154C23×C4×C61C2311yescharacteristic
155C23×C4×C61C2311yescharacteristic
156C4⋊Q8×C61—22no—
157C4⋊Q8×C61C2314yescomplemented
158#123×C61—28no—
159#123×C61—28no—
160C22⋊Q8×C61—28no—
161#121×C61—22no—
162#121×C61—22no—
163#121×C61C2314yes—
164#121×C61C2314yescomplemented
165C4×D4×C61—22no—
166C4×D4×C61D414yes—
167C4×D4×C61C2314yes—
168C4×D4×C61C2314yescomplemented
169C2×C4⋊C4×C61—21no—
170C2×C4⋊C4×C61—22no—
171C2×C4⋊C4×C61—22no—
172C2×C4⋊C4×C61—21no—
173C2×C4⋊C4×C61—21no—
174C2×C4⋊C4×C61D411yescharacteristic
175C2×C4⋊C4×C61C2311yescharacteristic
176C2×C4⋊C4×C61C2311yescharacteristic
177C2×C4⋊C4×C61C2314yes—
178C2×C4⋊C4×C61C2311yescharacteristic
179C2×C4⋊C4×C61C2314yescomplemented
180C2×C22⋊C4×C61—21no—
181C2×C22⋊C4×C61—21no—
182C2×C22⋊C4×C61—21no—
183C2×C22⋊C4×C61D411yescharacteristic
184C2×C22⋊C4×C61D411yescharacteristic
185C2×C42×C61C2311yescharacteristic
186C24×C61—21no—
187C24×C61C2×D411yescharacteristic
188C24×C61C2×D411yescharacteristic
189C23×D61—21no—
190C23×D61—21no—
191C23×D61—24no—
192C23×D61—44no—
193C23×D61—44no—
194C23×D61—82no—
195#41×C61—432no—
196C2×Q8×C61—24no—
197C2×Q8×C61—44no—
198C2×D4×C61—24no—
199C2×D4×C61—24no—
200C2×D4×C61—24no—
201C2×D4×C61—21no—
202C2×D4×C61—22no—
203C2×D4×C61—22no—
204C2×D4×C61—44no—
205C2×D4×C61—44no—
206C2×D4×C61C2×D414yes—
207C2×D4×C61C2412yes—
208C22×C4×C61—22no—
209C22×C4×C61—22no—
210C22×C4×C61—22no—
211C22×C4×C61—22no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—24no—
216C22×C4×C61—24no—
217C22×C4×C61—24no—
218C22×C4×C61—44no—
219C22×C4×C61—44no—
220C22×C4×C61—44no—
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D412yes—
225C22×C4×C61C2×D412yes—
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2412yes—
228C22×C4×C61C2412yes—
229C22×C4×C61C2411yescharacteristic
230C2×C22⋊D61—24no—
231C2×C22⋊D61—24no—
232C2×C22⋊D61—44no—
233C2×C22⋊D61—82no—
234C22×Dic61—21no—
235C22×Dic61—21no—
236#11758222—28no—
237#11758222—44no—
238#11758222—48no—
239C2×D244—21no—
240C2×D244—22no—
241C2×D244—22no—
242C2×D244—22no—
243C2×D244—28no—
244C2×D244—24no—
245C2×D244—21no—
246C2×D244—44no—
247C2×D244—48no—
248C2×D244—44no—
249C2×D244#4114yescomplemented
250C2×D244C2412yes—
251C2×D244C2412yes—
252C2×C4×D61—24no—
253C2×C4×D61—24no—
254C2×C4×D61—44no—
255C2×C4×D61—82no—
256C2×Dic122—22no—
257C2×Dic122—22no—
258C2×Dic122—21no—
259C2×Dic122C2412yes—
260C4⋊C4×C61—21no—
261C4⋊C4×C61—21no—
262C4⋊C4×C61—21no—
263C4⋊C4×C61—24no—
264C4⋊C4×C61—24no—
265C4⋊C4×C61—24no—
266C4⋊C4×C61C2×D414yes—
267C4⋊C4×C61C2412yes—
268C4⋊C4×C61C2412yes—
269C4⋊C4×C61C2412yes—
270C22⋊C4×C61—24no—
271C22⋊C4×C61—24no—
272C22⋊C4×C61—24no—
273C22⋊C4×C61C2×D414yes—
274C22⋊C4×C61C2×D414yes—
275C42×C61C2×D412yes—
276C42×C61C2412yes—
277C22⋊Dic61—24no—
278#11758200—44no—
279#11758199—28no—
280#11758199—44no—
281#11758198—24no—
282#11758198—24no—
283#11758198—24no—
284#11758198—24no—
285C4⋊Dic61—21no—
286C4⋊Dic61C2412yes—
287#11758196—24no—
288#11758194—44no—
289C2×#92418—22no—
290C2×#92418—22no—
291C2×#92418—22no—
292C2×#92418—22no—
293C2×#92418—44no—
294C2×#92418C2412yes—
295C2×#92418C2412yes—
296C2×#92418C2412yes—
297C2×#92418C2412yes—
298C23×C61—22no—
299C23×C61—22no—
300C23×C61—22no—
301C23×C61—22no—
302C23×C61—22no—
303C23×C61—22no—
304C23×C61—42no—
305C23×C61—42no—
306C23×C61—42no—
307C23×C61AGL(1,ℤ/8)14yes—
308C23×C61C22×D412yes—
309C23×C61C22×D412yes—
310C23×C61C22×D411yescharacteristic
311C22×D61—24no—
312C22×D61—22no—
313C22×D61—22no—
314C22×D61—48no—
315C22×D61—42no—
316C22×D61—42no—
317C22×D61—42no—
318C22×D61—48no—
319C22×D61—42no—
320C22×D61—42no—
321C22×D61—84no—
322C22×D61—816no—
323Q8×C61—48no—
324D4×C61—28no—
325D4×C61—22no—
326D4×C61—22no—
327D4×C61—48no—
328D4×C61—48no—
329D4×C61—42no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—24no—
335C2×C4×C61—24no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—48no—
344C2×C4×C61—48no—
345C2×C4×C61—42no—
346C2×C4×C61—42no—
347C2×C4×C61—42no—
348C2×C4×C61—48no—
349C2×C4×C61C22×D412yes—
350C2×C4×C61C22×D412yes—
351C2×C4×C61C22×D412yes—
352C2×C4×C61C22×D412yes—
353C2×C4×C61C22×D411yescharacteristic
354C2×C4×C61C2×#4112yes—
355C2×C4×C61H(5,𝔽2)12yes—
356C2×C4×C61C2511yescharacteristic
357C22⋊D61—48no—
358C22⋊D61—84no—
359C2×Dic61—22no—
360C2×Dic61—22no—
361C2×Dic61—42no—
362C2×Dic61—42no—
363D244—24no—
364D244—22no—
365D244—22no—
366D244—22no—
367D244—48no—
368D244—42no—
369D244C2×#4114yescomplemented
370C4×D61—48no—
371C4×D61—84no—
372Dic122—22no—
373Dic122—22no—
374Dic122—42no—
375#92418—22no—
376#92418—22no—
377#92418—22no—
378#92418—22no—
379C2×#3306—611nomaximal, Sylow
380C22×C61—22no—
381C22×C61—28no—
382C22×C61—22no—
383C22×C61—22no—
384C22×C61—22no—
385C22×C61—22no—
386C22×C61—44no—
387C22×C61—42no—
388C22×C61—42no—
389C22×C61—42no—
390C22×C61—84no—
391C22×C61#54612yes—
392C22×C61C2×AGL(1,ℤ/8)14yes—
393C22×C61C2×AGL(1,ℤ/8)12yes—
394C22×C61#57712yes—
395C22×C61C23×D411yescharacteristic
396C2×D61—24no—
397C2×D61—48no—
398C2×D61—42no—
399C2×D61—42no—
400C2×D61—42no—
401C2×D61—42no—
402C2×D61—42no—
403C2×D61—816no—
404C2×D61—84no—
405C4×C61—22no—
406C4×C61—22no—
407C4×C61—22no—
408C4×C61—22no—
409C4×C61—42no—
410C4×C61—42no—
411C4×C61—42no—
412C4×C61#54612yes—
413C4×C61C22×#4111yescharacteristic
414C4×C61C2×H(5,𝔽2)11yescharacteristic
415Dic61—42no—
416Dic61—42no—
417C2×#547D6111yescharacteristic, complemented
418C2×#546—611no—
419#3306—6116no—
420C2×#489—611no—
421C2×#481—611no—
422C2×#483—611no—
423C2×#476—611no—
424C2×#469—611no—
425C2×#465—611no—
426C2×#463—611no—
427C2×#449—611no—
428C2×#447—611no—
429C2×#442—611no—
430C2×#435—611no—
431C2×#417—611no—
432C22×#102—611no—
433C2×C61—24no—
434C2×C61—42no—
435C2×C61—82no—
436C2×C61#330614yescomplemented
437C2×C61C2×#54611yescharacteristic
438C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
439C2×C61C2×#57711yescharacteristic
440D61—44no—
441D61—82no—
442C22×#41—21no—
443C22×#41—611no—
444C23×D4—611no—
445C22×SD16—611no—
446C22×D8—611no—
447C22×D8—611no—
448C22×M16—611no—
449C23×C8—611no—
450#547—24no—
451#547C2×D6118yescomplemented
452#546—618no—
453#546—1224no—
454C2×C4⋊Q8C2×D6111yescharacteristic, complemented
455C2×#124—611no—
456C2×#123—21no—
457C2×#123—21no—
458C2×#123—1221no—
459C2×C22⋊Q8—21no—
460C2×C22⋊Q8—611no—
461C2×#121—611no—
462C2×#121—1221no—
463C2×#121C2×D6111yescharacteristic
464C2×#121C2×D6111yescharacteristic, complemented
465C2×#120—1221no—
466C2×C4×D4—611no—
467C2×C4×D4C2×D6111yescharacteristic
468C2×C4×D4C2×D6111yescharacteristic, complemented
469C22×C4⋊C4C2×D6111yescharacteristic
470C22×C4⋊C4C2×D6111yescharacteristic, complemented
471C22×C22⋊C4—1221no—
472#489—618no—
473#483—618no—
474#481—618no—
475#476—618no—
476#469—618no—
477#465—618no—
478#463—618no—
479#449—618no—
480#447—618no—
481#442—618no—
482#435—618no—
483C2×#106—611no—
484C2×#106—611no—
485C2×#106—611no—
486C2×C4⋊C8—611no—
487#417—618no—
488C2×#103—611no—
489C2×#103—611no—
490C2×#103—611no—
491C2×#102—611no—
492C2×#102—611no—
493C2×#102—611no—
494C2×#102—611no—
495C2×#102—611no—
496C2×#102—611no—
497C2×#102—611no—
498C2×#102—618no—
499C2×C22⋊C8—611no—
500C2×C22⋊C8—611no—
501C2×#97—611no—
502C61C2×#330611yescharacteristic, complemented, Sylow
503C25—1221no—
504C2×#41—28no—
505C2×#41—48no—
506C2×#41—614no—
507C2×#41—1224no—
508C2×#41—1222no—
509C2×#41—2442no—
510C22×Q8—21no—
511C22×Q8—611no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—611no—
515C22×D4—611no—
516C22×D4—614no—
517C22×D4—1224no—
518C22×D4—1221no—
519C22×D4—1221no—
520C22×D4—1221no—
521C22×D4—1222no—
522C22×D4—2442no—
523C22×D4C22⋊D6111yescharacteristic
524C22×D4C22×D6111yescharacteristic
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—1221no—
529C23×C4—1221no—
530C23×C4C22×D6111yescharacteristic
531C23×C4C22×D6111yescharacteristic
532C2×SD16—614no—
533C2×SD16—2442no—
534C2×D8—614no—
535C2×D8—614no—
536C2×D8—1224no—
537C2×D8—2442no—
538C2×M16—614no—
539C2×M16—2442no—
540C22×C8—611no—
541C22×C8—611no—
542C22×C8—611no—
543C22×C8—611no—
544C22×C8—614no—
545C22×C8—2442no—
546C4⋊Q8—22no—
547C4⋊Q8C22×D6114yescomplemented
548#124—614no—
549#124—1222no—
550#123—28no—
551#123—28no—
552#123—1228no—
553C22⋊Q8—28no—
554C22⋊Q8—614no—
555C22⋊Q8—1222no—
556#121—22no—
557#121—22no—
558#121—614no—
559#121—1222no—
560#121—1228no—
561#121C22×D6114yes—
562#121C22×D6114yescomplemented
563#120—1228no—
564C4×D4—22no—
565C4×D4—614no—
566C4×D4—1222no—
567C4×D4C22⋊D6114yes—
568C4×D4C22×D6114yes—
569C4×D4C22×D6114yescomplemented
570C2×C4⋊C4—21no—
571C2×C4⋊C4—22no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—611no—
576C2×C4⋊C4—1221no—
577C2×C4⋊C4C22⋊D6111yescharacteristic
578C2×C4⋊C4C22×D6111yescharacteristic
579C2×C4⋊C4C22×D6111yescharacteristic
580C2×C4⋊C4C22×D6114yes—
581C2×C4⋊C4C22×D6111yescharacteristic
582C2×C4⋊C4C22×D6114yescomplemented
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—1221no—
587C2×C22⋊C4—1221no—
588C2×C22⋊C4—1221no—
589C2×C22⋊C4—1221no—
590C2×C22⋊C4—1221no—
591C2×C22⋊C4—1228no—
592C2×C22⋊C4C22⋊D6111yescharacteristic
593C2×C22⋊C4C22⋊D6111yescharacteristic
594C2×C42C22×D6111yescharacteristic
595#106—614no—
596#106—614no—
597#106—614no—
598C4⋊C8—614no—
599#103—614no—
600#103—614no—
601#103—614no—
602#102—614no—
603#102—614no—
604#102—614no—
605#102—614no—
606#102—614no—
607#102—614no—
608#102—614no—
609C22⋊C8—614no—
610C22⋊C8—614no—
611#97—614no—
612C24—21no—
613C24—1221no—
614C24—1224no—
615C24—1221no—
616C24—4882no—
617C24—2444no—
618C24—2444no—
619C24C2×C22⋊D6111yescharacteristic
620C24C2×C22⋊D6111yescharacteristic
621#41—432no—
622#41—1228no—
623#41—2444no—
624#41—2448no—
625C2×Q8—24no—
626C2×Q8—44no—
627C2×Q8—612no—
628C2×Q8—1221no—
629C2×Q8—1222no—
630C2×Q8—1222no—
631C2×D4—24no—
632C2×D4—24no—
633C2×D4—24no—
634C2×D4—21no—
635C2×D4—22no—
636C2×D4—22no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—614no—
640C2×D4—612no—
641C2×D4—612no—
642C2×D4—1228no—
643C2×D4—1224no—
644C2×D4—1224no—
645C2×D4—1221no—
646C2×D4—1224no—
647C2×D4—1221no—
648C2×D4—1222no—
649C2×D4—1222no—
650C2×D4—1222no—
651C2×D4—4882no—
652C2×D4—2444no—
653C2×D4—2448no—
654C2×D4—2444no—
655C2×D4—2444no—
656C2×D4C2×C22⋊D6114yes—
657C2×D4C23×D6112yes—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—24no—
663C22×C4—24no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—24no—
668C22×C4—44no—
669C22×C4—44no—
670C22×C4—44no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—1224no—
674C22×C4—1224no—
675C22×C4—4882no—
676C22×C4—2444no—
677C22×C4C2×C22⋊D6112yes—
678C22×C4C2×C22⋊D6112yes—
679C22×C4C2×C22⋊D6111yescharacteristic
680C22×C4C2×C22⋊D6111yescharacteristic
681C22×C4C2×C22⋊D6111yescharacteristic
682C22×C4C2×C22⋊D6111yescharacteristic
683C22×C4C23×D6112yes—
684C22×C4C23×D6112yes—
685C22×C4C23×D6111yescharacteristic
686SD16—2444no—
687D8—1228no—
688D8—2444no—
689M16—2444no—
690C2×C8—612no—
691C2×C8—612no—
692C2×C8—612no—
693C2×C8—612no—
694C2×C8—1222no—
695C2×C8—1222no—
696C2×C8—1222no—
697C2×C8—1222no—
698C2×C8—2444no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—24no—
703C4⋊C4—24no—
704C4⋊C4—24no—
705C4⋊C4—612no—
706C4⋊C4—1221no—
707C4⋊C4—1224no—
708C4⋊C4C2×C22⋊D6114yes—
709C4⋊C4C23×D6112yes—
710C4⋊C4C23×D6112yes—
711C4⋊C4C23×D6112yes—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—1224no—
716C22⋊C4—1224no—
717C22⋊C4—1224no—
718C22⋊C4—1224no—
719C22⋊C4—1224no—
720C22⋊C4C2×C22⋊D6114yes—
721C22⋊C4C2×C22⋊D6114yes—
722C42C2×C22⋊D6112yes—
723C42C23×D6112yes—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—1222no—
734C23—1224no—
735C23—1222no—
736C23—48816no—
737C23—4884no—
738C23—2448no—
739C23—2448no—
740C23—2442no—
741C23—2442no—
742C23—2442no—
743C23—2442no—
744C23—2442no—
745C23#1451980314yes—
746C23C22×C22⋊D6112yes—
747C23C22×C22⋊D6112yes—
748C23C22×C22⋊D6111yescharacteristic
749Q8—48no—
750Q8—1222no—
751Q8—1222no—
752Q8—2442no—
753D4—28no—
754D4—22no—
755D4—22no—
756D4—48no—
757D4—48no—
758D4—42no—
759D4—614no—
760D4—1222no—
761D4—1222no—
762D4—1222no—
763D4—1224no—
764D4—4884no—
765D4—2448no—
766D4—2448no—
767D4—2442no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—48no—
782C2×C4—48no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—48no—
787C2×C4—1222no—
788C2×C4—1222no—
789C2×C4—4884no—
790C2×C4—2448no—
791C2×C4—2442no—
792C2×C4—2442no—
793C2×C4C22×C22⋊D6112yes—
794C2×C4C22×C22⋊D6112yes—
795C2×C4C22×C22⋊D6112yes—
796C2×C4C22×C22⋊D6112yes—
797C2×C4C22×C22⋊D6111yescharacteristic
798C2×C4#41×D6112yes—
799C2×C4#1451982312yes—
800C2×C4C24×D6111yescharacteristic
801C8—1222no—
802C8—1222no—
803C8—1222no—
804C8—1222no—
805C22—22no—
806C22—22no—
807C22—28no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—44no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—84no—
816C22—1224no—
817C22—48816no—
818C22—4884no—
819C22—2442no—
820C22—2442no—
821C22—2442no—
822C22—2442no—
823C22—2442no—
824C22—2448no—
825C22#1684040012yes—
826C22C2×#1451980314yes—
827C22C2×#1451980312yes—
828C22#1684057012yes—
829C22C23×C22⋊D6111yescharacteristic
830C4—22no—
831C4—22no—
832C4—22no—
833C4—22no—
834C4—42no—
835C4—42no—
836C4—42no—
837C4—2442no—
838C4—2442no—
839C4#1684040012yes—
840C4C2×#41×D6111yescharacteristic
841C4C2×#1451982311yescharacteristic
842C2—24no—
843C2—42no—
844C2—82no—
845C2—4882no—
846C2—2444no—
847C2#2145777414yesdirect product factor
848C2C2×#1684040011yescharacteristic
849C2C22×#1451980311yescharacteristic
850C2C2×#1684057011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#547C2
socleC23×C61C22×D4
hypercenterC2×#547D61
hypocenterC61C2×#3306
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#16840408C2semidirect
2. #21457774C2direct (N × H)
3. C2×#16840124C2semidirect
4. C2×#16840080C2semidirect
5. C2×#16840092C2semidirect
6. C2×#16840049C2semidirect
7. C2×#16840013C2semidirect
8. C2×#16839989C2semidirect
9. C2×#16839977C2semidirect
10. C2×#16839905C2semidirect
11. C2×#16839895C2semidirect
12. C2×#16839872C2semidirect
13. C2×#16839834C2semidirect
14. C2×#16839761C2semidirect
15. C22×#14519697C2semidirect
16. C2×C61×#547C2semidirect
19. C22×#11758200C22semidirect
22. C22×#11758194C22semidirect
25. #16840408C22semidirect
34. #16840124C22semidirect
35. #16840092C22semidirect
36. #16840080C22semidirect
37. #16840049C22semidirect
38. #16840013C22semidirect
39. #16839989C22semidirect
40. #16839977C22semidirect
41. #16839905C22semidirect
42. #16839895C22semidirect
43. #16839872C22semidirect
44. #16839834C22semidirect
45. C2×#14519708C22semidirect
46. C2×#14519708C22semidirect
47. C2×#14519708C22semidirect
48. C2×C4⋊#92418C22semidirect
49. #16839761C22semidirect
50. C2×#14519700C22semidirect
51. C2×#14519700C22semidirect
52. C2×#14519700C22semidirect
53. C2×#14519698C22semidirect
60. C2×#14519697C22semidirect
62. C2×C22⋊#92418C22semidirect
63. C2×#14519688C22semidirect
66. C61×#547C22semidirect
67. C2×C4⋊Q8×C61C22semidirect
72. C2×#121×C61C22semidirect
74. C2×C4×D4×C61C22semidirect
76. C22×C4⋊C4×C61C22semidirect
95. C2×#11758200C23semidirect
101. C2×#11758194C23semidirect
127. #14519708C23semidirect
128. #14519708C23semidirect
129. #14519708C23semidirect
130. C4⋊#92418C23semidirect
131. #14519700C23semidirect
132. #14519700C23semidirect
133. #14519700C23semidirect
134. #14519698C23semidirect
142. C22⋊#92418C23semidirect
143. #14519688C23semidirect
157. C4⋊Q8×C61C23semidirect
164. #121×C61C23semidirect
168. C4×D4×C61C23semidirect
179. C2×C4⋊C4×C61C23semidirect
249. C2×D244#41semidirect
369. D244C2×#41semidirect
417. C2×#547D61semidirect
436. C2×C61#3306semidirect
451. #547C2×D61semidirect
454. C2×C4⋊Q8C2×D61semidirect
464. C2×#121C2×D61semidirect
468. C2×C4×D4C2×D61semidirect
470. C22×C4⋊C4C2×D61semidirect
502. C61C2×#3306semidirect
547. C4⋊Q8C22×D61semidirect
562. #121C22×D61semidirect
569. C4×D4C22×D61semidirect
582. C2×C4⋊C4C22×D61semidirect
847. C2#21457774direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404082
#214577742
C2×#168401242
C2×#168400802
C2×#168400922
C2×#168400492
C2×#168400132
C2×#168399892
C2×#168399772
C2×#168399052
C2×#168398952
C2×#168398722
C2×#168398342
C2×#168397612
C22×#145196972
C2×C61×#5472
C2×#330661