Finite Group Databasebeta

← C2×#21455271 #30546830

Subgroups — C2×#21455271 #30546830

Order 15616.

2874 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519798C211yesmaximal, characteristic, complemented
2C22×#14519796C211yesmaximal, characteristic, complemented
3C2×#16840311C211yesmaximal, characteristic, complemented
4C2×C4×#11758224C211yesmaximal, characteristic, complemented
5#21455271C2116yesmaximal, direct product factor
6C2×#16839985C211yesmaximal, characteristic, complemented
7C2×#16839981C211yesmaximal, characteristic, complemented
8C2×#16839971C211yesmaximal, characteristic, complemented
9C2×#16839961C211yesmaximal, characteristic, complemented
10C2×#16839977C211yesmaximal, characteristic, complemented
11C2×#16839965C211yesmaximal, characteristic, complemented
12C2×#16839955C211yesmaximal, characteristic, complemented
13C2×C4⋊C8×D61C211yesmaximal, characteristic, complemented
14C2×#16839757C211yesmaximal, characteristic, complemented
15C2×#16839755C211yesmaximal, characteristic, complemented
16C2×C61×#463C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×#11758224C2211yescharacteristic
19C22×#11758224C2211yescharacteristic
20C2×#14519798—28no—
21C2×#14519798C2218yescomplemented
22C2×#14519796—28no—
23C2×#14519796C2218yescomplemented
24C22×Dic244C2211yescharacteristic
25C22×#11758202C2211yescharacteristic
26C22×#11758190C2211yescharacteristic
27C22×#11758200C2211yescharacteristic
28C22×#11758200C2211yescharacteristic
29C22×#11758199C2211yescharacteristic
30C22×C8×D61C2211yescharacteristic
31C22×C8×D61C2211yescharacteristic
32#16840311—24no—
33#16840311C2218yescomplemented
34C2×#14519775C2211yescharacteristic
35C2×#14519773C2211yescharacteristic
36C2×#14519765C2211yescharacteristic
37C2×#14519750—21no—
38C2×#14519750—21no—
39C4×#11758224—24no—
40C4×#11758224C2218yescomplemented
41C2×C4×Dic122C2211yescharacteristic
42C2×#14519742C2211yescharacteristic
43C2×D4×Dic61C2211yescharacteristic
44C2×C4×C22⋊D61—21no—
45C2×#14519737—21no—
46C2×#14519737—21no—
47C2×#14519737—21no—
48C2×#14519735C2211yescharacteristic
49C2×#14519733—21no—
50C22×C4×Dic61—21no—
51C2×C42×D61C2211yescharacteristic
52#16839985C2218yescomplemented
53#16839981C2218yescomplemented
54#16839977C2218yescomplemented
55#16839971C2218yescomplemented
56#16839965C2218yescomplemented
57#16839961C2218yescomplemented
58#16839955C2218yescomplemented
59C2×C4⋊#92418C2211yescharacteristic
60C2×#14519706C2211yescharacteristic
61C2×#14519706C2211yescharacteristic
62C4⋊C8×D61C2218yescomplemented
63#16839757C2218yescomplemented
64#16839755C2218yescomplemented
65C2×#14519702C2211yescharacteristic
66C2×#14519701C2211yescharacteristic
67C2×#14519700C2211yescharacteristic
68C2×#14519699C2211yescharacteristic
69C2×#14519698C2211yescharacteristic
70C2×#14519697C2211yescharacteristic
71C22×SD16×C61C2211yescharacteristic
72C22×D8×C61C2211yescharacteristic
73C2×#124×C61C2211yescharacteristic
74C2×C4×D4×C61C2211yescharacteristic
75C61×#463C2218yescomplemented
76C2×C4⋊C8×C61C2211yescharacteristic
77C2×#103×C61C2211yescharacteristic
78C2×#102×C61C2211yescharacteristic
79C2×#11758226—22no—
80C2×#11758226—24no—
81C2×#11758226—24no—
82C2×#11758226C2314yes—
83C2×#11758224—22no—
84C2×#11758224—24no—
85C2×#11758224—22no—
86C2×#11758224—24no—
87C2×#11758224—24no—
88C2×#11758224D418yescomplemented
89C2×#11758224C2314yes—
90C2×#11758224C2314yes—
91C22×Dic122C2311yescharacteristic
92C22×Dic122C2311yescharacteristic
93C22×D244—21no—
94C22×D244C2311yescharacteristic
95C22×C22⋊D61—21no—
96C22×C22⋊D61—21no—
97C22×C22⋊D61—21no—
98C22×C22⋊D61—21no—
99C23×Dic61—21no—
100C23×Dic61—21no—
101C23×Dic61—21no—
102C22×C4×D61—21no—
103C22×C4×D61D411yescharacteristic
104C22×C4×D61D411yescharacteristic
105C22×C4×D61C2311yescharacteristic
106#14519798—232no—
107#14519796—232no—
108C2×Dic244—24no—
109C2×Dic244C2314yes—
110C2×#11758202—24no—
111C2×#11758202C2314yes—
112C2×#11758190—24no—
113C2×#11758190C2314yes—
114C2×#11758200—24no—
115C2×#11758200—24no—
116C2×#11758200C2314yes—
117C2×#11758200C2314yes—
118C2×#11758199—24no—
119C2×#11758199C2314yes—
120C22×#92418C2311yescharacteristic
121C22×#92418C2311yescharacteristic
122C2×C8×D61—24no—
123C2×C8×D61—24no—
124C2×C8×D61C2314yes—
125C2×C8×D61C2314yes—
126#14519775—22no—
127#14519775C2314yes—
128#14519773—22no—
129#14519773C2314yes—
130#14519765—22no—
131#14519765C2314yes—
132#14519750—28no—
133#14519750—28no—
134C4×Dic122—22no—
135C4×Dic122C2314yes—
136#14519742—22no—
137#14519742C2314yes—
138D4×Dic61—22no—
139D4×Dic61C2314yes—
140C4×C22⋊D61—28no—
141#14519737—28no—
142#14519737—28no—
143#14519737—28no—
144#14519735—22no—
145#14519735C2314yes—
146#14519733—28no—
147C2×C4⋊Dic61C2311yescharacteristic
148C2×#11758196—21no—
149C2×#11758196—21no—
150C2×#11758196—21no—
151C2×#11758196—21no—
152C2×C22⋊Dic61—21no—
153C2×#11758198—21no—
154C2×#11758198—21no—
155C2×#11758198—21no—
156C2×C4×Dic61—21no—
157C2×C4×Dic61—21no—
158C2×C4×Dic61—21no—
159C2×C4×Dic61—28no—
160C2×C4×Dic61D411yescharacteristic
161C2×C4×Dic61D411yescharacteristic
162C2×C4×Dic61C2311yescharacteristic
163C42×D61D414yes—
164C42×D61C2314yes—
165C4⋊#92418C2314yes—
166#14519706C2314yes—
167#14519706C2314yes—
168#14519702C2314yes—
169#14519701C2314yes—
170#14519700C2314yes—
171#14519699C2314yes—
172#14519698C2314yes—
173#14519697C2314yes—
174C22×Q8×C61C2311yescharacteristic
175C22×D4×C61C2311yescharacteristic
176C22×D4×C61C2311yescharacteristic
177C23×C4×C61—21no—
178C2×SD16×C61—24no—
179C2×SD16×C61C2314yes—
180C2×D8×C61—24no—
181C2×D8×C61C2314yes—
182C22×C8×C61C2311yescharacteristic
183C22×C8×C61C2311yescharacteristic
184#124×C61—22no—
185#124×C61C2314yes—
186C4×D4×C61—22no—
187C4×D4×C61C2314yes—
188C2×C4⋊C4×C61C2311yescharacteristic
189C2×C22⋊C4×C61—21no—
190C2×C22⋊C4×C61—21no—
191C2×C22⋊C4×C61—21no—
192C2×C42×C61C2311yescharacteristic
193C4⋊C8×C61C2314yes—
194#103×C61C2314yes—
195#102×C61C2314yes—
196C24×C61—21no—
197C24×C61—21no—
198C23×D61—21no—
199C23×D61C2×D411yescharacteristic
200C2×Q8×C61—21no—
201C2×Q8×C61—22no—
202C2×Q8×C61—22no—
203C2×Q8×C61C2412yes—
204C2×D4×C61—21no—
205C2×D4×C61—22no—
206C2×D4×C61—21no—
207C2×D4×C61—22no—
208C2×D4×C61—22no—
209C2×D4×C61C2×D414yes—
210C2×D4×C61C2412yes—
211C2×D4×C61C2412yes—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—24no—
215C22×C4×C61—44no—
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2411yescharacteristic
219C2×C22⋊D61—28no—
220C2×C22⋊D61—24no—
221C2×C22⋊D61—24no—
222C2×C22⋊D61—24no—
223C2×C22⋊D61—24no—
224C2×C22⋊D61—44no—
225C2×C22⋊D61—44no—
226C2×C22⋊D61—44no—
227C22×Dic61—21no—
228C22×Dic61—28no—
229C22×Dic61—24no—
230C22×Dic61—21no—
231C22×Dic61—21no—
232C22×Dic61—24no—
233C22×Dic61—24no—
234C22×Dic61—44no—
235C22×Dic61—44no—
236C22×Dic61C2×D411yescharacteristic
237C22×Dic61C2×D411yescharacteristic
238C22×Dic61C2×D411yescharacteristic
239#11758226—28no—
240#11758226—28no—
241#11758226—48no—
242#11758224—216no—
243#11758224—28no—
244#11758224—28no—
245#11758224—28no—
246#11758224—48no—
247#11758224C2×D4116yescomplemented
248C2×D244—22no—
249C2×D244—22no—
250C2×D244—24no—
251C2×D244—21no—
252C2×D244—44no—
253C2×D244C2412yes—
254C2×C4×D61—24no—
255C2×C4×D61—24no—
256C2×C4×D61—42no—
257C2×C4×D61—44no—
258C2×C4×D61C2×D414yes—
259C2×C4×D61C2×D414yes—
260C2×C4×D61C2×D412yes—
261C2×C4×D61C2×D414yes—
262C2×C4×D61#4114yes—
263C2×C4×D61C2412yes—
264C2×Dic122—21no—
265C2×Dic122—22no—
266C2×Dic122—22no—
267C2×Dic122—22no—
268C2×Dic122—21no—
269C2×Dic122C2×D414yes—
270C2×Dic122C2412yes—
271C2×Dic122C2412yes—
272SD16×C61—28no—
273D8×C61—28no—
274C2×C8×C61—22no—
275C2×C8×C61—22no—
276C2×C8×C61C2412yes—
277C2×C8×C61C2412yes—
278C4⋊C4×C61—21no—
279C4⋊C4×C61C2412yes—
280C22⋊C4×C61—24no—
281C22⋊C4×C61—24no—
282C22⋊C4×C61—24no—
283C42×C61C2×D412yes—
284C42×C61C2412yes—
285C22⋊Dic61—24no—
286#11758202—28no—
287#11758200—28no—
288#11758200—28no—
289#11758199—28no—
290#11758198—24no—
291#11758198—24no—
292#11758198—24no—
293C4⋊Dic61—21no—
294C4⋊Dic61C2412yes—
295#11758196—24no—
296#11758196—24no—
297#11758196—24no—
298#11758196—24no—
299C4×Dic61—24no—
300C4×Dic61—24no—
301C4×Dic61—24no—
302C4×Dic61C2×D412yes—
303C4×Dic61C2×D414yes—
304C4×Dic61C2×D414yes—
305C4×Dic61C2412yes—
306C2×#92418—22no—
307C2×#92418—22no—
308C2×#92418C2412yes—
309C2×#92418C2412yes—
310Dic244—28no—
311#11758190—28no—
312C8×D61—28no—
313C8×D61—28no—
314C23×C61—24no—
315C23×C61—22no—
316C23×C61—22no—
317C23×C61—42no—
318C23×C61—42no—
319C23×C61—42no—
320C23×C61—42no—
321C23×C61—42no—
322C23×C61C22×D411yescharacteristic
323C22×D61—22no—
324C22×D61—22no—
325C22×D61—22no—
326C22×D61—42no—
327C22×D61—42no—
328C22×D61—42no—
329C22×D61#12114yes—
330C22×D61C22×D412yes—
331Q8×C61—22no—
332Q8×C61—22no—
333Q8×C61—42no—
334D4×C61—24no—
335D4×C61—22no—
336D4×C61—22no—
337D4×C61—22no—
338D4×C61—42no—
339D4×C61C22×D414yes—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—48no—
345C2×C4×C61—42no—
346C2×C4×C61—42no—
347C2×C4×C61C22×D412yes—
348C2×C4×C61C22×D412yes—
349C2×C4×C61C22×D411yescharacteristic
350C2×C4×C61C22×D412yes—
351C2×C4×C61C2×#4112yes—
352C2×C4×C61C2511yescharacteristic
353C22⋊D61—216no—
354C22⋊D61—48no—
355C22⋊D61—48no—
356C22⋊D61—48no—
357C2×Dic61—24no—
358C2×Dic61—22no—
359C2×Dic61—22no—
360C2×Dic61—216no—
361C2×Dic61—22no—
362C2×Dic61—22no—
363C2×Dic61—42no—
364C2×Dic61—42no—
365C2×Dic61—48no—
366C2×Dic61—48no—
367C2×Dic61#12114yes—
368C2×Dic61#13514yescomplemented
369C2×Dic61C22×D412yes—
370C2×Dic61C22×D412yes—
371C2×Dic61C22×D412yes—
372D244—22no—
373D244—22no—
374D244—48no—
375D244—42no—
376C4×D61—28no—
377C4×D61—44no—
378C4×D61—48no—
379C4×D61#12118yes—
380C4×D61C22×D414yes—
381C4×D61C2×#4114yes—
382Dic122—24no—
383Dic122—22no—
384Dic122—22no—
385Dic122—22no—
386Dic122—42no—
387Dic122C22×D414yes—
388C8×C61—22no—
389C8×C61—22no—
390#92418—22no—
391#92418—22no—
392C2×#3035—611nomaximal, Sylow
393C22×C61—24no—
394C22×C61—48no—
395C22×C61—42no—
396C22×C61—42no—
397C22×C61—42no—
398C22×C61—42no—
399C22×C61—42no—
400C22×C61—84no—
401C22×C61C2×#12112yes—
402C22×C61C2×#13512yes—
403C22×C61#57512yes—
404C22×C61C23×D411yescharacteristic
405C2×D61—28no—
406C2×D61—22no—
407C2×D61—22no—
408C2×D61—42no—
409C2×D61—42no—
410C2×D61—42no—
411C2×D61—84no—
412C2×D61C2×#12114yes—
413C4×C61—22no—
414C4×C61—22no—
415C4×C61—42no—
416C4×C61—42no—
417C4×C61C2×#12112yes—
418C4×C61C23×D411yescharacteristic
419C4×C61C22×#4111yescharacteristic
420Dic61—24no—
421Dic61—22no—
422Dic61—42no—
423Dic61—42no—
424Dic61C2×#12114yes—
425Dic61C2×#13514yescomplemented
426C22×#135—611no—
427C22×#135—611no—
428C2×#532—611no—
429C2×C4×#41—611no—
430#3035—6116no—
431C2×#464—611no—
432C2×#464—611no—
433C2×#462—611no—
434C2×#460—611no—
435C2×#463—611no—
436C2×#463D6111yescharacteristic, complemented
437C2×#461—611no—
438C2×#459—611no—
439C22×C4⋊C8—611no—
440C2×#416—611no—
441C2×#416—611no—
442C2×C61—44no—
443C2×C61—82no—
444C2×C61#303514yescomplemented
445C2×C61C22×#12111yescharacteristic
446C2×C61C22×#13511yescharacteristic
447C2×C61C2×#57511yescharacteristic
448D61—24no—
449D61—82no—
450C22×#41—611no—
451C22×#41—611no—
452C22×#41—611no—
453C2×#135—618no—
454C2×#135—618no—
455C2×#135—1228no—
456C2×#135—1228no—
457C22×Q16—611no—
458C22×Q16—611no—
459C22×SD16—611no—
460C22×SD16—611no—
461C22×SD16—611no—
462C22×SD16C2×D6111yescharacteristic
463C22×D8—611no—
464C22×D8C2×D6111yescharacteristic
465C23×C8—611no—
466C23×C8—611no—
467#532—618no—
468#532—1224no—
469C2×C4⋊Q8—611no—
470C2×#127—611no—
471C2×#124—611no—
472C2×#124C2×D6111yescharacteristic
473C2×#121—1221no—
474C2×#121—1221no—
475C4×#41—618no—
476C4×#41—1224no—
477C2×C4×Q8—611no—
478C2×C4×Q8—611no—
479C2×C4×D4—611no—
480C2×C4×D4—1221no—
481C2×C4×D4—1221no—
482C2×C4×D4—1221no—
483C2×C4×D4—1221no—
484C2×C4×D4C2×D6111yescharacteristic
485C2×#117—611no—
486C2×#117—1221no—
487C22×C42—611no—
488C22×C42—1221no—
489#464—618no—
490#464—618no—
491#463—618no—
492#463C2×D6118yescomplemented
493#462—618no—
494#461—618no—
495#460—618no—
496#459—618no—
497C2×C4⋊C8—611no—
498C2×C4⋊C8—611no—
499C2×C4⋊C8—611no—
500C2×C4⋊C8—618no—
501C2×C4⋊C8C2×D6111yescharacteristic
502#416—618no—
503#416—618no—
504C2×#103—611no—
505C2×#103—611no—
506C2×#103—611no—
507C2×#103C2×D6111yescharacteristic
508C2×#102—611no—
509C2×#102—611no—
510C2×#102—611no—
511C2×#102C2×D6111yescharacteristic
512C61C2×#303511yescharacteristic, complemented, Sylow
513C2×#41—614no—
514C2×#41—618no—
515C2×#41—614no—
516C2×#41—614no—
517C2×#41—1222no—
518C2×#41—1224no—
519C2×#41—1222no—
520C2×#41—1222no—
521C2×#41—1224no—
522C2×#41—1224no—
523C2×#41—1224no—
524C2×#41—1224no—
525C22×Q8—611no—
526C22×Q8—611no—
527C22×Q8C22×D6111yescharacteristic
528C22×D4—611no—
529C22×D4—1221no—
530C22×D4—1221no—
531C22×D4—1221no—
532C22×D4—1221no—
533C22×D4—1221no—
534C22×D4C22×D6111yescharacteristic
535C22×D4C22×D6111yescharacteristic
536C23×C4—21no—
537C23×C4—611no—
538C23×C4—611no—
539C23×C4—611no—
540C23×C4—1221no—
541C23×C4—1221no—
542C23×C4—1221no—
543C23×C4—1221no—
544#135—12232no—
545#135—12232no—
546C2×Q16—614no—
547C2×Q16—614no—
548C2×Q16—1224no—
549C2×Q16—1224no—
550C2×SD16—24no—
551C2×SD16—614no—
552C2×SD16—614no—
553C2×SD16—614no—
554C2×SD16—1224no—
555C2×SD16—1224no—
556C2×SD16—1224no—
557C2×SD16C22×D6114yes—
558C2×D8—24no—
559C2×D8—614no—
560C2×D8—1224no—
561C2×D8C22×D6114yes—
562C22×C8—611no—
563C22×C8—611no—
564C22×C8—614no—
565C22×C8—614no—
566C22×C8—1224no—
567C22×C8—1224no—
568C22×C8C22×D6111yescharacteristic
569C22×C8C22×D6111yescharacteristic
570C4⋊Q8—614no—
571C4⋊Q8—1222no—
572#127—614no—
573#127—1222no—
574#124—22no—
575#124—614no—
576#124—1222no—
577#124C22×D6114yes—
578#121—1228no—
579#121—1228no—
580C4×Q8—614no—
581C4×Q8—614no—
582C4×Q8—1222no—
583C4×Q8—1222no—
584C4×D4—22no—
585C4×D4—614no—
586C4×D4—1228no—
587C4×D4—1228no—
588C4×D4—1222no—
589C4×D4—1228no—
590C4×D4—1228no—
591C4×D4C22×D6114yes—
592#117—614no—
593#117—1228no—
594#117—1222no—
595C2×C4⋊C4—611no—
596C2×C4⋊C4—1221no—
597C2×C4⋊C4—1221no—
598C2×C4⋊C4—1221no—
599C2×C4⋊C4—1221no—
600C2×C4⋊C4C22×D6111yescharacteristic
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—1221no—
605C2×C22⋊C4—1221no—
606C2×C22⋊C4—1221no—
607C2×C22⋊C4—1221no—
608C2×C42—611no—
609C2×C42—611no—
610C2×C42—611no—
611C2×C42—614no—
612C2×C42—614no—
613C2×C42—1228no—
614C2×C42—1221no—
615C2×C42—1221no—
616C2×C42—1221no—
617C2×C42C22×D6111yescharacteristic
618C4⋊C8—614no—
619C4⋊C8—614no—
620C4⋊C8—614no—
621C4⋊C8C22×D6114yes—
622#103—614no—
623#103—614no—
624#103—614no—
625#103C22×D6114yes—
626#102—614no—
627#102—614no—
628#102—614no—
629#102C22×D6114yes—
630C24—21no—
631C24—21no—
632C24—611no—
633C24—1221no—
634#41—6116no—
635#41—12216no—
636#41—1228no—
637#41—1228no—
638#41—1228no—
639#41—1228no—
640#41—1228no—
641#41—2448no—
642#41—2448no—
643C2×Q8—21no—
644C2×Q8—22no—
645C2×Q8—22no—
646C2×Q8—614no—
647C2×Q8—612no—
648C2×Q8—612no—
649C2×Q8—1221no—
650C2×Q8—1221no—
651C2×Q8—1222no—
652C2×Q8—1222no—
653C2×Q8—1222no—
654C2×Q8C23×D6112yes—
655C2×D4—21no—
656C2×D4—22no—
657C2×D4—21no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—612no—
661C2×D4—1224no—
662C2×D4—1224no—
663C2×D4—1224no—
664C2×D4—1224no—
665C2×D4—1228no—
666C2×D4—1224no—
667C2×D4—1222no—
668C2×D4—1221no—
669C2×D4—1222no—
670C2×D4—2444no—
671C2×D4—2444no—
672C2×D4—2444no—
673C2×D4—2444no—
674C2×D4D4×D6114yes—
675C2×D4C23×D6112yes—
676C2×D4C23×D6112yes—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—24no—
680C22×C4—44no—
681C22×C4—611no—
682C22×C4—611no—
683C22×C4—612no—
684C22×C4—614no—
685C22×C4—614no—
686C22×C4—612no—
687C22×C4—611no—
688C22×C4—614no—
689C22×C4—614no—
690C22×C4—1224no—
691C22×C4—1224no—
692C22×C4—1224no—
693C22×C4—1228no—
694C22×C4—1224no—
695C22×C4—1224no—
696C22×C4—1221no—
697C22×C4—1221no—
698C22×C4—1221no—
699C22×C4—2442no—
700C22×C4—2444no—
701C22×C4—2444no—
702C22×C4—2444no—
703C22×C4D4×D6111yescharacteristic
704C22×C4D4×D6111yescharacteristic
705C22×C4C23×D6111yescharacteristic
706Q16—1228no—
707Q16—1228no—
708SD16—28no—
709SD16—1228no—
710SD16—1228no—
711SD16—1228no—
712D8—28no—
713D8—1228no—
714C2×C8—22no—
715C2×C8—22no—
716C2×C8—612no—
717C2×C8—612no—
718C2×C8—1228no—
719C2×C8—1228no—
720C2×C8—1222no—
721C2×C8—1222no—
722C2×C8C23×D6112yes—
723C2×C8C23×D6112yes—
724C4⋊C4—21no—
725C4⋊C4—612no—
726C4⋊C4—1224no—
727C4⋊C4—1224no—
728C4⋊C4—1224no—
729C4⋊C4—1221no—
730C4⋊C4—1224no—
731C4⋊C4C23×D6112yes—
732C22⋊C4—24no—
733C22⋊C4—24no—
734C22⋊C4—24no—
735C22⋊C4—1224no—
736C22⋊C4—1224no—
737C22⋊C4—1224no—
738C22⋊C4—1224no—
739C42—614no—
740C42—614no—
741C42—612no—
742C42—612no—
743C42—1224no—
744C42—1224no—
745C42—1224no—
746C42D4×D6112yes—
747C42C23×D6112yes—
748C23—24no—
749C23—22no—
750C23—22no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—614no—
757C23—612no—
758C23—1222no—
759C23—1222no—
760C23—1222no—
761C23—2442no—
762C23—2442no—
763C23—2442no—
764C23C2×D4×D6111yescharacteristic
765Q8—22no—
766Q8—22no—
767Q8—42no—
768Q8—614no—
769Q8—1224no—
770Q8—1222no—
771Q8—1222no—
772Q8—1222no—
773Q8—2442no—
774D4—24no—
775D4—22no—
776D4—22no—
777D4—22no—
778D4—42no—
779D4—12216no—
780D4—1222no—
781D4—1222no—
782D4—2448no—
783D4—2448no—
784D4—2448no—
785D4—2448no—
786D4—2442no—
787D4C2×D4×D6114yes—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—48no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—614no—
796C2×C4—614no—
797C2×C4—612no—
798C2×C4—612no—
799C2×C4—618no—
800C2×C4—614no—
801C2×C4—614no—
802C2×C4—612no—
803C2×C4—1228no—
804C2×C4—12216no—
805C2×C4—1224no—
806C2×C4—1222no—
807C2×C4—1222no—
808C2×C4—1222no—
809C2×C4—1222no—
810C2×C4—2444no—
811C2×C4—2448no—
812C2×C4—2448no—
813C2×C4—2448no—
814C2×C4—2442no—
815C2×C4—2442no—
816C2×C4C2×D4×D6112yes—
817C2×C4C2×D4×D6112yes—
818C2×C4C2×D4×D6111yescharacteristic
819C2×C4C2×D4×D6112yes—
820C2×C4#41×D6112yes—
821C2×C4C24×D6111yescharacteristic
822C8—22no—
823C8—22no—
824C8—1222no—
825C8—1222no—
826C22—24no—
827C22—42no—
828C22—42no—
829C22—48no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—84no—
834C22—614no—
835C22—1222no—
836C22—1222no—
837C22—1228no—
838C22—4884no—
839C22—2442no—
840C22—2442no—
841C22—2442no—
842C22#121×D6112yes—
843C22#135×D6112yes—
844C22#1684055812yes—
845C22C22×D4×D6111yescharacteristic
846C4—22no—
847C4—22no—
848C4—42no—
849C4—42no—
850C4—614no—
851C4—614no—
852C4—1222no—
853C4—1224no—
854C4—2442no—
855C4—2442no—
856C4#121×D6112yes—
857C4C22×D4×D6111yescharacteristic
858C4C2×#41×D6111yescharacteristic
859C2—44no—
860C2—82no—
861C2—1224no—
862C2—4882no—
863C2#2145527114yesdirect product factor
864C2C2×#121×D6111yescharacteristic
865C2C2×#135×D6111yescharacteristic
866C2C2×#1684055811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#463C2
socleC23×C61C22×D4
hypercenterC2×#463D61
hypocenterC61C2×#3035
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C22×#14519798C2semidirect
2. C22×#14519796C2semidirect
3. C2×#16840311C2semidirect
4. C2×C4×#11758224C2semidirect
5. #21455271C2direct (N × H)
6. C2×#16839985C2semidirect
7. C2×#16839981C2semidirect
8. C2×#16839971C2semidirect
9. C2×#16839961C2semidirect
10. C2×#16839977C2semidirect
11. C2×#16839965C2semidirect
12. C2×#16839955C2semidirect
13. C2×C4⋊C8×D61C2semidirect
14. C2×#16839757C2semidirect
15. C2×#16839755C2semidirect
16. C2×C61×#463C2semidirect
21. C2×#14519798C22semidirect
23. C2×#14519796C22semidirect
33. #16840311C22semidirect
40. C4×#11758224C22semidirect
52. #16839985C22semidirect
53. #16839981C22semidirect
54. #16839977C22semidirect
55. #16839971C22semidirect
56. #16839965C22semidirect
57. #16839961C22semidirect
58. #16839955C22semidirect
62. C4⋊C8×D61C22semidirect
63. #16839757C22semidirect
64. #16839755C22semidirect
75. C61×#463C22semidirect
88. C2×#11758224D4semidirect
247. #11758224C2×D4semidirect
368. C2×Dic61#135semidirect
425. Dic61C2×#135semidirect
436. C2×#463D61semidirect
444. C2×C61#3035semidirect
492. #463C2×D61semidirect
512. C61C2×#3035semidirect
863. C2#21455271direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197982
C22×#145197962
C2×#168403112
C2×C4×#117582242
#214552712
C2×#168399852
C2×#168399812
C2×#168399712
C2×#168399612
C2×#168399772
C2×#168399652
C2×#168399552
C2×C4⋊C8×D612
C2×#168397572
C2×#168397552
C2×C61×#4632
C2×#303561