Finite Group Databasebeta

← C2×#21457350 #30555016

Subgroups — C2×#21457350 #30555016

Order 15616.

2914 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519804C211yesmaximal, characteristic, complemented
2C22×#14519798C211yesmaximal, characteristic, complemented
3C2×#16840415C211yesmaximal, characteristic, complemented
4C2×#16840407C211yesmaximal, characteristic, complemented
5#21457350C2116yesmaximal, direct product factor
6C2×#16840154C211yesmaximal, characteristic, complemented
7C2×#16840019C211yesmaximal, characteristic, complemented
8C2×#16839994C211yesmaximal, characteristic, complemented
9C2×#16839978C211yesmaximal, characteristic, complemented
10C2×#16839927C211yesmaximal, characteristic, complemented
11C2×#16839921C211yesmaximal, characteristic, complemented
12C2×#16839910C211yesmaximal, characteristic, complemented
13C2×#16839911C211yesmaximal, characteristic, complemented
14C2×#16839872C211yesmaximal, characteristic, complemented
15C2×#16839832C211yesmaximal, characteristic, complemented
16C2×C61×#461C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×#11758226C2211yescharacteristic, complemented
19C22×#11758224C2211yescharacteristic
20C22×D4×D61C2211yescharacteristic
21C2×#14519804—28no—
22C2×#14519804C2218yescomplemented
23C2×#14519798—28no—
24C2×#14519798C2218yescomplemented
25C22×#11758202C2211yescharacteristic, complemented
26C22×#11758202C2211yescharacteristic, complemented
27C22×#11758190C2211yescharacteristic, complemented
28C22×#11758201C2211yescharacteristic
29C22×#11758201C2211yescharacteristic
30C22×D488C2211yescharacteristic
31C22×#11758199C2211yescharacteristic
32C22×#11758189C2211yescharacteristic
33C22×C8×D61C2211yescharacteristic, complemented
34#16840415—24no—
35#16840415C2218yescomplemented
36#16840407—24no—
37#16840407C2218yescomplemented
38C2×#14519765C2211yescharacteristic
39C2×#14519762—21no—
40C2×#14519762—21no—
41C2×#14519761—21no—
42C2×#14519757C2211yescharacteristic
43C2×#14519753C2211yescharacteristic
44C2×#14519753C2211yescharacteristic, complemented
45C2×#14519752—21no—
46C2×#14519752C2211yescharacteristic
47C2×#14519751—21no—
48C2×#14519747—21no—
49C2×C4×D244C2211yescharacteristic
50C2×C4×D244C2211yescharacteristic, complemented
51C2×C4⋊C4×D61—21no—
52C22×#11758198—21no—
53#16840154C2218yescomplemented
54#16840019C2218yescomplemented
55#16839994C2218yescomplemented
56#16839978C2218yescomplemented
57#16839927C2218yescomplemented
58#16839921C2218yescomplemented
59#16839911C2218yescomplemented
60#16839910C2218yescomplemented
61#16839872C2218yescomplemented
62#16839832C2218yescomplemented
63C2×#14519708C2211yescharacteristic, complemented
64C2×#14519702C2211yescharacteristic, complemented
65C2×#14519699C2211yescharacteristic
66C2×#14519698C2211yescharacteristic
67C2×#14519697C2211yescharacteristic, complemented
68C2×#14519689C2211yescharacteristic
69C2×#14519689C2211yescharacteristic, complemented
70C2×#14519688C2211yescharacteristic, complemented
71C22×SD16×C61C2211yescharacteristic
72C22×SD16×C61C2211yescharacteristic
73C2×C4⋊Q8×C61C2211yescharacteristic, complemented
74C2×C4×D4×C61C2211yescharacteristic
75C61×#461C2218yescomplemented
76C2×C4⋊C8×C61C2211yescharacteristic, complemented
77C2×#103×C61C2211yescharacteristic, complemented
78C2×#103×C61C2211yescharacteristic, complemented
79C24×D61—21no—
80C2×#11758226—22no—
81C2×#11758226—22no—
82C2×#11758226—24no—
83C2×#11758226—24no—
84C2×#11758226—42no—
85C2×#11758226—42no—
86C2×#11758226C2314yes—
87C2×#11758226C2314yescomplemented
88C2×#11758224—24no—
89C2×#11758224—22no—
90C2×#11758224—42no—
91C2×#11758224C2314yes—
92C22×Dic122C2311yescharacteristic
93C22×D244—21no—
94C22×D244—21no—
95C22×D244—21no—
96C22×D244D411yescharacteristic
97C22×D244C2311yescharacteristic
98C22×D244C2311yescharacteristic
99C22×C22⋊D61—21no—
100C22×C22⋊D61—21no—
101C2×D4×D61—24no—
102C2×D4×D61—22no—
103C2×D4×D61—42no—
104C2×D4×D61C2314yes—
105C23×Dic61—21no—
106C22×C4×D61—21no—
107C22×C4×D61—21no—
108C22×C4×D61—21no—
109C22×C4×D61C2311yescharacteristic
110C22×C4×D61C2311yescharacteristic
111#14519804—232no—
112#14519798—232no—
113C2×#11758202—24no—
114C2×#11758202—42no—
115C2×#11758202C2314yescomplemented
116C2×#11758202C2314yescomplemented
117C2×#11758190—24no—
118C2×#11758190C2314yescomplemented
119C2×#11758201—24no—
120C2×#11758201—42no—
121C2×#11758201C2314yes—
122C2×#11758201C2314yes—
123C2×D488—24no—
124C2×D488C2314yes—
125C2×#11758199D418yescomplemented
126C2×#11758199C2314yes—
127C2×#11758189—24no—
128C2×#11758189C2314yes—
129C22×#92418C2311yescharacteristic
130C22×#92418C2311yescharacteristic
131C2×C8×D61—24no—
132C2×C8×D61C2314yescomplemented
133#14519765—22no—
134#14519765C2314yes—
135#14519762—28no—
136#14519762—28no—
137#14519761—28no—
138#14519757—22no—
139#14519757C2314yes—
140#14519753—22no—
141#14519753—22no—
142#14519753C2314yes—
143#14519753C2314yescomplemented
144#14519752—28no—
145#14519752—22no—
146#14519752C2314yes—
147#14519751—28no—
148#14519747—28no—
149C4×D244—22no—
150C4×D244D414yes—
151C4×D244C2314yes—
152C4×D244C2314yescomplemented
153C2×C4⋊Dic61—21no—
154C2×C4⋊Dic61D411yescharacteristic
155C2×C4⋊Dic61C2311yescharacteristic
156C2×#11758196—21no—
157C2×#11758196—21no—
158C4⋊C4×D61—28no—
159C2×#11758198—21no—
160C2×#11758198—21no—
161C2×#11758198—21no—
162C2×#11758198—21no—
163C2×#11758198—21no—
164C2×#11758198—21no—
165C2×#11758198—21no—
166C2×#11758198—28no—
167C2×#11758198D411yescharacteristic
168C2×#11758198D411yescharacteristic
169#14519708C2314yescomplemented
170#14519702C2314yescomplemented
171#14519699C2314yes—
172#14519698C2314yes—
173#14519697C2314yescomplemented
174#14519689C2314yes—
175#14519689C2314yescomplemented
176#14519688C2314yescomplemented
177C22×Q8×C61C2311yescharacteristic
178C22×Q8×C61C2311yescharacteristic
179C22×D4×C61C2311yescharacteristic
180C23×C4×C61—21no—
181C2×SD16×C61—24no—
182C2×SD16×C61—24no—
183C2×SD16×C61C2314yes—
184C2×SD16×C61C2314yes—
185C22×C8×C61C2311yescharacteristic
186C22×C8×C61C2311yescharacteristic
187C4⋊Q8×C61—22no—
188C4⋊Q8×C61C2314yescomplemented
189C4×D4×C61—22no—
190C4×D4×C61C2314yes—
191C2×C4⋊C4×C61—21no—
192C2×C4⋊C4×C61—21no—
193C2×C4⋊C4×C61C2311yescharacteristic
194C2×C22⋊C4×C61—21no—
195C2×C42×C61C2311yescharacteristic
196C4⋊C8×C61C2314yescomplemented
197#103×C61C2314yescomplemented
198#103×C61C2314yescomplemented
199C24×C61—21no—
200C23×D61—21no—
201C23×D61—21no—
202C23×D61—24no—
203C23×D61—44no—
204C23×D61—44no—
205C23×D61—82no—
206C23×D61C2×D411yescharacteristic
207C23×D61C2×D411yescharacteristic
208C2×Q8×C61—21no—
209C2×Q8×C61—21no—
210C2×Q8×C61—22no—
211C2×Q8×C61—22no—
212C2×Q8×C61—22no—
213C2×Q8×C61—22no—
214C2×Q8×C61C2412yes—
215C2×Q8×C61C2412yes—
216C2×D4×C61—21no—
217C2×D4×C61—22no—
218C2×D4×C61C2×D414yes—
219C2×D4×C61C2412yes—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—24no—
224C22×C4×C61—82no—
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2411yescharacteristic
228C2×C22⋊D61—24no—
229C2×C22⋊D61—24no—
230C2×C22⋊D61—44no—
231C2×C22⋊D61—44no—
232C22×Dic61—21no—
233C22×Dic61—21no—
234C22×Dic61—24no—
235C22×Dic61—44no—
236C22×Dic61C2×D411yescharacteristic
237C22×Dic61C2×D411yescharacteristic
238#11758226—28no—
239#11758226—28no—
240#11758226—44no—
241#11758226—44no—
242#11758226—48no—
243#11758226—48no—
244#11758224—28no—
245#11758224—44no—
246#11758224—48no—
247D4×D61—28no—
248D4×D61—44no—
249D4×D61—48no—
250C2×D244—21no—
251C2×D244—22no—
252C2×D244—22no—
253C2×D244—22no—
254C2×D244—24no—
255C2×D244—24no—
256C2×D244—21no—
257C2×D244—24no—
258C2×D244—42no—
259C2×D244—44no—
260C2×D244—44no—
261C2×D244—82no—
262C2×D244C2×D414yes—
263C2×D244C2×D414yes—
264C2×D244C2412yes—
265C2×D244C2412yes—
266C2×C4×D61—22no—
267C2×C4×D61—22no—
268C2×C4×D61—22no—
269C2×C4×D61—22no—
270C2×C4×D61—24no—
271C2×C4×D61—24no—
272C2×C4×D61—24no—
273C2×C4×D61—44no—
274C2×C4×D61—44no—
275C2×C4×D61—44no—
276C2×C4×D61C2×D412yes—
277C2×C4×D61C2×D412yes—
278C2×C4×D61C2412yes—
279C2×C4×D61C2412yes—
280C2×Dic122—22no—
281C2×Dic122—22no—
282C2×Dic122—21no—
283C2×Dic122C2412yes—
284SD16×C61—28no—
285SD16×C61—28no—
286C2×C8×C61—22no—
287C2×C8×C61—22no—
288C2×C8×C61C2412yes—
289C2×C8×C61C2412yes—
290C4⋊C4×C61—24no—
291C4⋊C4×C61—24no—
292C4⋊C4×C61—21no—
293C4⋊C4×C61C2412yes—
294C22⋊C4×C61—24no—
295C42×C61C2×D412yes—
296C42×C61C2412yes—
297#11758202—28no—
298#11758202—44no—
299#11758201—28no—
300#11758201—44no—
301#11758199C2×D4116yescomplemented
302#11758198—24no—
303#11758198—24no—
304#11758198—24no—
305#11758198—24no—
306#11758198—24no—
307#11758198—24no—
308#11758198—24no—
309#11758198C2×D414yes—
310#11758198C2×D414yes—
311C4⋊Dic61—21no—
312C4⋊Dic61—24no—
313C4⋊Dic61C2×D414yes—
314C4⋊Dic61C2412yes—
315#11758196—24no—
316#11758196—24no—
317C2×#92418—22no—
318C2×#92418C2×D414yes—
319C2×#92418C2412yes—
320C2×#92418C2412yes—
321D488—28no—
322#11758190—28no—
323#11758189—28no—
324C8×D61—28no—
325C23×C61—24no—
326C23×C61—22no—
327C23×C61—42no—
328C23×C61—42no—
329C23×C61C22×D411yescharacteristic
330C22×D61—22no—
331C22×D61—22no—
332C22×D61—24no—
333C22×D61—22no—
334C22×D61—22no—
335C22×D61—22no—
336C22×D61—22no—
337C22×D61—22no—
338C22×D61—22no—
339C22×D61—48no—
340C22×D61—48no—
341C22×D61—42no—
342C22×D61—42no—
343C22×D61—42no—
344C22×D61—42no—
345C22×D61—42no—
346C22×D61—84no—
347C22×D61—816no—
348C22×D61C22×D412yes—
349C22×D61C22×D412yes—
350Q8×C61—22no—
351Q8×C61—22no—
352Q8×C61—22no—
353Q8×C61—22no—
354Q8×C61—42no—
355Q8×C61—42no—
356D4×C61—24no—
357D4×C61—22no—
358D4×C61C22×D414yes—
359C2×C4×C61—22no—
360C2×C4×C61—22no—
361C2×C4×C61—22no—
362C2×C4×C61—22no—
363C2×C4×C61—22no—
364C2×C4×C61—42no—
365C2×C4×C61—42no—
366C2×C4×C61—42no—
367C2×C4×C61—84no—
368C2×C4×C61C22×D412yes—
369C2×C4×C61C22×D412yes—
370C2×C4×C61C22×D411yescharacteristic
371C2×C4×C61C22×D412yes—
372C2×C4×C61H(5,𝔽2)12yes—
373C2×C4×C61C2511yescharacteristic
374C22⋊D61—48no—
375C22⋊D61—48no—
376C2×Dic61—22no—
377C2×Dic61—22no—
378C2×Dic61—22no—
379C2×Dic61—22no—
380C2×Dic61—48no—
381C2×Dic61—42no—
382C2×Dic61—42no—
383C2×Dic61C22×D412yes—
384C2×Dic61C22×D412yes—
385D244—24no—
386D244—22no—
387D244—22no—
388D244—22no—
389D244—44no—
390D244—48no—
391D244—48no—
392D244—42no—
393D244—84no—
394D244C22×D414yes—
395C4×D61—24no—
396C4×D61—24no—
397C4×D61—22no—
398C4×D61—22no—
399C4×D61—22no—
400C4×D61—22no—
401C4×D61—48no—
402C4×D61—48no—
403C4×D61—48no—
404Dic122—22no—
405Dic122—22no—
406Dic122—42no—
407C8×C61—22no—
408C8×C61—22no—
409#92418—22no—
410#92418C22×D414yes—
411C2×#3267—611nomaximal, Sylow
412C22×C61—24no—
413C22×C61—48no—
414C22×C61—42no—
415C22×C61—42no—
416C22×C61D4212yes—
417C22×C61#57512yes—
418C22×C61#57712yes—
419C22×C61C23×D411yescharacteristic
420C2×D61—22no—
421C2×D61—22no—
422C2×D61—24no—
423C2×D61—22no—
424C2×D61—22no—
425C2×D61—22no—
426C2×D61—22no—
427C2×D61—44no—
428C2×D61—44no—
429C2×D61—48no—
430C2×D61—42no—
431C2×D61—42no—
432C2×D61—42no—
433C2×D61—42no—
434C2×D61—42no—
435C2×D61—816no—
436C2×D61—84no—
437C4×C61—22no—
438C4×C61—22no—
439C4×C61—42no—
440C4×C61—42no—
441C4×C61—42no—
442C4×C61D4212yes—
443C4×C61C23×D411yescharacteristic
444C4×C61C2×H(5,𝔽2)11yescharacteristic
445Dic61—22no—
446Dic61—22no—
447Dic61—42no—
448Dic61—42no—
449C22×AGL(1,ℤ/8)—611no—
450C22×#135—611no—
451C2×#547—611no—
452C2×#546—611no—
453#3267—6116no—
454C2×#497—611no—
455C2×#470—611no—
456C2×#465—611no—
457C2×#463—611no—
458C2×#461D6111yescharacteristic, complemented
459C2×#452—611no—
460C2×#452—611no—
461C2×#449—611no—
462C2×#450—611no—
463C2×#442—611no—
464C2×#435—611no—
465C2×C61—44no—
466C2×C61#326714yescomplemented
467C2×C61C2×D4211yescharacteristic
468C2×C61C2×#57511yescharacteristic
469C2×C61C2×#57711yescharacteristic
470D61—42no—
471D61—42no—
472D61—44no—
473D61—82no—
474C22×#41—611no—
475C22×#41—611no—
476C22×#41—611no—
477C23×D4—611no—
478C2×AGL(1,ℤ/8)—618no—
479C2×AGL(1,ℤ/8)—1228no—
480C2×#135—618no—
481C2×#135—1228no—
482C22×Q16—611no—
483C22×Q16—611no—
484C22×SD16—611no—
485C22×SD16—611no—
486C22×SD16—611no—
487C22×SD16C2×D6111yescharacteristic
488C22×SD16C2×D6111yescharacteristic
489C22×D8—611no—
490C22×D8—611no—
491C22×M16—611no—
492C23×C8—611no—
493#547—618no—
494#547—1224no—
495#546—618no—
496#546—1224no—
497C2×C4⋊Q8C2×D6111yescharacteristic, complemented
498C2×#124—611no—
499C2×#123—1221no—
500C2×#123—1221no—
501C2×#123—1221no—
502C2×C22⋊Q8—611no—
503C2×C22⋊Q8—611no—
504C2×C22⋊Q8—611no—
505C2×#121—611no—
506C2×#121—1221no—
507C2×#121—1221no—
508C2×#120—1221no—
509C2×C4×D4—611no—
510C2×C4×D4—611no—
511C2×C4×D4C2×D6111yescharacteristic
512C22×C4⋊C4—1221no—
513C22×C22⋊C4—1221no—
514#497—618no—
515#470—618no—
516#465—618no—
517#463—618no—
518#461C2×D6118yescomplemented
519#452—618no—
520#452—618no—
521#450—618no—
522#449—618no—
523#442—618no—
524#435—618no—
525C2×#106—611no—
526C2×C4⋊C8C2×D6111yescharacteristic, complemented
527C2×#103—611no—
528C2×#103C2×D6111yescharacteristic, complemented
529C2×#103C2×D6111yescharacteristic, complemented
530C2×#102—611no—
531C2×#102—611no—
532C2×#102—611no—
533C2×C22⋊C8—611no—
534C2×C22⋊C8—611no—
535C2×#97—611no—
536C61C2×#326711yescharacteristic, complemented, Sylow
537C25—1221no—
538C2×#41—614no—
539C2×#41—614no—
540C2×#41—614no—
541C2×#41—1222no—
542C2×#41—1222no—
543C2×#41—1222no—
544C2×#41—1224no—
545C2×#41—1224no—
546C2×#41—1224no—
547C2×#41—2442no—
548C2×#41—2442no—
549C2×#41—2442no—
550C22×Q8—611no—
551C22×Q8C22×D6111yescharacteristic
552C22×Q8C22×D6111yescharacteristic
553C22×D4—614no—
554C22×D4—611no—
555C22×D4—611no—
556C22×D4—611no—
557C22×D4—1221no—
558C22×D4—1221no—
559C22×D4—1221no—
560C22×D4—1222no—
561C22×D4—1221no—
562C22×D4—1224no—
563C22×D4—1221no—
564C22×D4—2442no—
565C22×D4C22×D6111yescharacteristic
566C23×C4—21no—
567C23×C4—611no—
568C23×C4—611no—
569C23×C4—1221no—
570C23×C4—1221no—
571C23×C4—1221no—
572C23×C4—1221no—
573AGL(1,ℤ/8)—12232no—
574#135—12232no—
575C2×Q16—614no—
576C2×Q16—614no—
577C2×Q16—1224no—
578C2×Q16—2442no—
579C2×SD16—24no—
580C2×SD16—24no—
581C2×SD16—614no—
582C2×SD16—614no—
583C2×SD16—614no—
584C2×SD16—1224no—
585C2×SD16—1224no—
586C2×SD16—2442no—
587C2×SD16C22×D6114yes—
588C2×SD16C22×D6114yes—
589C2×D8—618no—
590C2×D8—614no—
591C2×D8—614no—
592C2×D8—1224no—
593C2×M16—614no—
594C2×M16—1224no—
595C22×C8—611no—
596C22×C8—611no—
597C22×C8—614no—
598C22×C8—1224no—
599C22×C8C22×D6111yescharacteristic
600C22×C8C22×D6111yescharacteristic
601C4⋊Q8—22no—
602C4⋊Q8C22×D6114yescomplemented
603#124—614no—
604#124—1222no—
605#123—1228no—
606#123—1228no—
607#123—1228no—
608C22⋊Q8—614no—
609C22⋊Q8—614no—
610C22⋊Q8—614no—
611C22⋊Q8—1222no—
612C22⋊Q8—1222no—
613C22⋊Q8—1222no—
614#121—614no—
615#121—1228no—
616#121—1222no—
617#121—1228no—
618#120—1228no—
619C4×D4—22no—
620C4×D4—614no—
621C4×D4—614no—
622C4×D4—614no—
623C4×D4—1222no—
624C4×D4C22×D6114yes—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—611no—
628C2×C4⋊C4—611no—
629C2×C4⋊C4—1228no—
630C2×C4⋊C4—1221no—
631C2×C4⋊C4—1221no—
632C2×C4⋊C4—1221no—
633C2×C4⋊C4C22×D6111yescharacteristic
634C2×C22⋊C4—21no—
635C2×C22⋊C4—611no—
636C2×C22⋊C4—611no—
637C2×C22⋊C4—1228no—
638C2×C22⋊C4—1221no—
639C2×C22⋊C4—1221no—
640C2×C22⋊C4—1221no—
641C2×C22⋊C4—1221no—
642C2×C22⋊C4—1221no—
643C2×C22⋊C4—1221no—
644C2×C22⋊C4—1221no—
645C2×C42C22×D6111yescharacteristic
646#106—614no—
647C4⋊C8C22×D6114yescomplemented
648#103—614no—
649#103C22×D6114yescomplemented
650#103C22×D6114yescomplemented
651#102—614no—
652#102—614no—
653#102—614no—
654C22⋊C8—614no—
655C22⋊C8—614no—
656#97—614no—
657C24—21no—
658C24—611no—
659C24—611no—
660C24—1224no—
661C24—1221no—
662C24—1221no—
663C24—4882no—
664C24—2444no—
665C24—2444no—
666#41—1228no—
667#41—1228no—
668#41—1228no—
669#41—2444no—
670#41—2448no—
671#41—2444no—
672#41—2444no—
673#41—2448no—
674#41—2448no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8—22no—
678C2×Q8—22no—
679C2×Q8—22no—
680C2×Q8—22no—
681C2×Q8—612no—
682C2×Q8—1221no—
683C2×Q8—1222no—
684C2×Q8—1222no—
685C2×Q8C23×D6112yes—
686C2×Q8C23×D6112yes—
687C2×D4—21no—
688C2×D4—22no—
689C2×D4—614no—
690C2×D4—614no—
691C2×D4—612no—
692C2×D4—612no—
693C2×D4—1224no—
694C2×D4—1224no—
695C2×D4—1224no—
696C2×D4—1224no—
697C2×D4—1228no—
698C2×D4—1224no—
699C2×D4—1221no—
700C2×D4—1222no—
701C2×D4—1221no—
702C2×D4—1222no—
703C2×D4—1222no—
704C2×D4—4882no—
705C2×D4—2442no—
706C2×D4—2444no—
707C2×D4—2444no—
708C2×D4—2444no—
709C2×D4—2448no—
710C2×D4—2444no—
711C2×D4—2444no—
712C2×D4D4×D6114yes—
713C2×D4C23×D6112yes—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—24no—
718C22×C4—82no—
719C22×C4—611no—
720C22×C4—611no—
721C22×C4—612no—
722C22×C4—612no—
723C22×C4—612no—
724C22×C4—612no—
725C22×C4—1224no—
726C22×C4—1224no—
727C22×C4—1224no—
728C22×C4—1222no—
729C22×C4—1222no—
730C22×C4—1222no—
731C22×C4—1222no—
732C22×C4—1221no—
733C22×C4—1221no—
734C22×C4—1224no—
735C22×C4—2444no—
736C22×C4—2444no—
737C22×C4—2444no—
738C22×C4—2444no—
739C22×C4D4×D6111yescharacteristic
740C22×C4D4×D6111yescharacteristic
741C22×C4C23×D6111yescharacteristic
742Q16—1228no—
743Q16—2444no—
744SD16—28no—
745SD16—28no—
746SD16—1228no—
747SD16—1228no—
748SD16—2444no—
749D8—6116no—
750D8—1228no—
751M16—1228no—
752C2×C8—22no—
753C2×C8—22no—
754C2×C8—614no—
755C2×C8—612no—
756C2×C8—612no—
757C2×C8—1228no—
758C2×C8—1222no—
759C2×C8C23×D6112yes—
760C2×C8C23×D6112yes—
761C4⋊C4—24no—
762C4⋊C4—24no—
763C4⋊C4—21no—
764C4⋊C4—614no—
765C4⋊C4—612no—
766C4⋊C4—1224no—
767C4⋊C4—1224no—
768C4⋊C4—1224no—
769C4⋊C4—1221no—
770C4⋊C4C23×D6112yes—
771C22⋊C4—24no—
772C22⋊C4—614no—
773C22⋊C4—614no—
774C22⋊C4—1224no—
775C22⋊C4—1224no—
776C22⋊C4—1224no—
777C22⋊C4—1224no—
778C22⋊C4—1224no—
779C22⋊C4—1224no—
780C22⋊C4—1224no—
781C42D4×D6112yes—
782C42C23×D6112yes—
783C23—22no—
784C23—24no—
785C23—42no—
786C23—42no—
787C23—612no—
788C23—612no—
789C23—1222no—
790C23—1222no—
791C23—1222no—
792C23—1222no—
793C23—1222no—
794C23—1222no—
795C23—1222no—
796C23—1224no—
797C23—1222no—
798C23—4884no—
799C23—48816no—
800C23—2448no—
801C23—2448no—
802C23—2442no—
803C23—2442no—
804C23—2442no—
805C23—2442no—
806C23—2442no—
807C23C2×D4×D6111yescharacteristic
808Q8—22no—
809Q8—22no—
810Q8—22no—
811Q8—22no—
812Q8—42no—
813Q8—42no—
814Q8—1222no—
815Q8—1222no—
816Q8—2442no—
817D4—22no—
818D4—24no—
819D4—614no—
820D4—1222no—
821D4—1222no—
822D4—1222no—
823D4—1224no—
824D4—4884no—
825D4—2444no—
826D4—2448no—
827D4—2448no—
828D4—2448no—
829D4—2448no—
830D4—2442no—
831D4C2×D4×D6114yes—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—84no—
841C2×C4—612no—
842C2×C4—612no—
843C2×C4—1222no—
844C2×C4—1222no—
845C2×C4—1222no—
846C2×C4—1222no—
847C2×C4—1222no—
848C2×C4—1222no—
849C2×C4—1224no—
850C2×C4—1224no—
851C2×C4—1222no—
852C2×C4—1222no—
853C2×C4—2448no—
854C2×C4—2448no—
855C2×C4—2448no—
856C2×C4—2448no—
857C2×C4—2442no—
858C2×C4—2442no—
859C2×C4C2×D4×D6112yes—
860C2×C4C2×D4×D6112yes—
861C2×C4C2×D4×D6112yes—
862C2×C4C2×D4×D6111yescharacteristic
863C2×C4#1451982312yes—
864C2×C4C24×D6111yescharacteristic
865C8—22no—
866C8—22no—
867C8—614no—
868C8—1222no—
869C22—24no—
870C22—42no—
871C22—42no—
872C22—48no—
873C22—1222no—
874C22—1222no—
875C22—1224no—
876C22—1222no—
877C22—1222no—
878C22—1222no—
879C22—1222no—
880C22—48816no—
881C22—4884no—
882C22—2442no—
883C22—2442no—
884C22—2442no—
885C22—2442no—
886C22—2442no—
887C22—2444no—
888C22—2444no—
889C22—2448no—
890C22#1684039612yes—
891C22#1684056112yes—
892C22#1684056812yes—
893C22C22×D4×D6111yescharacteristic
894C4—22no—
895C4—22no—
896C4—42no—
897C4—42no—
898C4—42no—
899C4—1222no—
900C4—1222no—
901C4—2442no—
902C4—2442no—
903C4#1684039612yes—
904C4C22×D4×D6111yescharacteristic
905C4C2×#1451982311yescharacteristic
906C2—44no—
907C2—4882no—
908C2—2442no—
909C2—2442no—
910C2—2444no—
911C2#2145735014yesdirect product factor
912C2C2×#1684039611yescharacteristic
913C2C2×#1684056111yescharacteristic
914C2C2×#1684056811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#461C2
socleC23×C61C22×D4
hypercenterC2×#461D61
hypocenterC61C2×#3267
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C22×#14519804C2semidirect
2. C22×#14519798C2semidirect
3. C2×#16840415C2semidirect
4. C2×#16840407C2semidirect
5. #21457350C2direct (N × H)
6. C2×#16840154C2semidirect
7. C2×#16840019C2semidirect
8. C2×#16839994C2semidirect
9. C2×#16839978C2semidirect
10. C2×#16839927C2semidirect
11. C2×#16839921C2semidirect
12. C2×#16839910C2semidirect
13. C2×#16839911C2semidirect
14. C2×#16839872C2semidirect
15. C2×#16839832C2semidirect
16. C2×C61×#461C2semidirect
18. C22×#11758226C22semidirect
22. C2×#14519804C22semidirect
24. C2×#14519798C22semidirect
25. C22×#11758202C22semidirect
26. C22×#11758202C22semidirect
27. C22×#11758190C22semidirect
33. C22×C8×D61C22semidirect
35. #16840415C22semidirect
37. #16840407C22semidirect
44. C2×#14519753C22semidirect
50. C2×C4×D244C22semidirect
53. #16840154C22semidirect
54. #16840019C22semidirect
55. #16839994C22semidirect
56. #16839978C22semidirect
57. #16839927C22semidirect
58. #16839921C22semidirect
59. #16839911C22semidirect
60. #16839910C22semidirect
61. #16839872C22semidirect
62. #16839832C22semidirect
63. C2×#14519708C22semidirect
64. C2×#14519702C22semidirect
67. C2×#14519697C22semidirect
69. C2×#14519689C22semidirect
70. C2×#14519688C22semidirect
73. C2×C4⋊Q8×C61C22semidirect
75. C61×#461C22semidirect
76. C2×C4⋊C8×C61C22semidirect
77. C2×#103×C61C22semidirect
78. C2×#103×C61C22semidirect
87. C2×#11758226C23semidirect
115. C2×#11758202C23semidirect
116. C2×#11758202C23semidirect
118. C2×#11758190C23semidirect
125. C2×#11758199D4semidirect
132. C2×C8×D61C23semidirect
143. #14519753C23semidirect
152. C4×D244C23semidirect
169. #14519708C23semidirect
170. #14519702C23semidirect
173. #14519697C23semidirect
175. #14519689C23semidirect
176. #14519688C23semidirect
188. C4⋊Q8×C61C23semidirect
196. C4⋊C8×C61C23semidirect
197. #103×C61C23semidirect
198. #103×C61C23semidirect
301. #11758199C2×D4semidirect
458. C2×#461D61semidirect
466. C2×C61#3267semidirect
497. C2×C4⋊Q8C2×D61semidirect
518. #461C2×D61semidirect
526. C2×C4⋊C8C2×D61semidirect
528. C2×#103C2×D61semidirect
529. C2×#103C2×D61semidirect
536. C61C2×#3267semidirect
602. C4⋊Q8C22×D61semidirect
647. C4⋊C8C22×D61semidirect
649. #103C22×D61semidirect
650. #103C22×D61semidirect
911. C2#21457350direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198042
C22×#145197982
C2×#168404152
C2×#168404072
#214573502
C2×#168401542
C2×#168400192
C2×#168399942
C2×#168399782
C2×#168399272
C2×#168399212
C2×#168399102
C2×#168399112
C2×#168398722
C2×#168398322
C2×C61×#4612
C2×#326761