Finite Group Databasebeta

← C4×#16839948 #29685993

Subgroups — C4×#16839948 #29685993

Order 15616.

1910 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519822C211yesmaximal, characteristic, complemented
2C2×#16839948C211yesmaximal, characteristic
3C4×#14519746C212yesmaximal, complemented
4#21446228C211yesmaximal, characteristic, complemented
5#21446224C212yesmaximal, complemented
6#21446099C211yesmaximal, characteristic, complemented
7#21446098C212yesmaximal, complemented
8#21445766C211yesmaximal, characteristic, complemented
9C4×#14519691C212yesmaximal, complemented
10C4×#14519692C211yesmaximal, characteristic, complemented
11C4×#120×C61C211yesmaximal, characteristic, complemented
12C2×#14519822C2211yescharacteristic
13C2×#14519746C2212yes—
14#16840243—21no—
15#16840241—22no—
16#16840237C2211yescharacteristic
17#16840235—21no—
18#16840235C2212yes—
19#16840234—22no—
20C4×#11758222—21no—
21C4×#11758224—22no—
22C2×C4×C22⋊D61—21no—
23C2×C4×C22⋊D61—22no—
24C2×C4×C22⋊D61C2212yes—
25C4×D4×D61—22no—
26#16839948C418yesdirect product factor
27C2×#14519692C2211yescharacteristic
28C2×#14519692C2211yescharacteristic
29C2×#14519691C2212yes—
30C2×#14519691C2212yes—
31#16839641—22no—
32#16839641C2212yes—
33#16839635—22no—
34#16839635C2212yescomplemented
35#16839618C2212yescomplemented
36C4×C22⋊Dic61—22no—
37C4×C22⋊Dic61C2212yescomplemented
38#16839529C2212yescomplemented
39#16839528C2212yescomplemented
40#16839528C2212yescomplemented
41C24×C4×C61C2211yescharacteristic, complemented
42C2×#120×C61C2211yescharacteristic
43C2×C4×D4×C61—21no—
44C2×C4×D4×C61C2211yescharacteristic
45C61×#386—21no—
46C61×#386C2211yescharacteristic
47C61×#385—21no—
48C61×#385C2211yescharacteristic, complemented
49C61×#379C2211yescharacteristic, complemented
50C4×C22⋊C4×C61—21no—
51C4×C22⋊C4×C61C2211yescharacteristic, complemented
52#14519822—22no—
53#14519822—24no—
54#14519822C2×C414yescomplemented
55C2×#11758222—21no—
56C2×#11758224—22no—
57C22×C22⋊D61—21no—
58C22×C22⋊D61—22no—
59C22×C22⋊D61C2312yes—
60C2×D4×D61—22no—
61C22×C4×D61—21no—
62C22×C4×D61D412yescomplemented
63#14519746—24no—
64#14519746C2×C418yescomplemented
65C4×Dic122—21no—
66C4×Dic122—21no—
67#14519742—22no—
68C4×D244—21no—
69C4×D244—21no—
70D4×Dic61—22no—
71D4×Dic61—22no—
72#14519739—22no—
73C4×C22⋊D61—22no—
74C4×C22⋊D61—22no—
75C4×C22⋊D61—22no—
76C4×C22⋊D61—22no—
77C4×C22⋊D61—22no—
78C4×C22⋊D61—22no—
79C4×C22⋊D61—22no—
80C4×C22⋊D61—22no—
81C4×C22⋊D61—48no—
82#14519737—22no—
83#14519737—22no—
84#14519737—22no—
85#14519737—22no—
86#14519736—21no—
87#14519735—22no—
88#14519734—22no—
89#14519733—22no—
90#14519733—22no—
91C2×#11758196—21no—
92C2×#11758196—22no—
93C2×#11758196D412yescomplemented
94C4⋊C4×D61—22no—
95C2×C22⋊Dic61—21no—
96C2×C22⋊Dic61—22no—
97C2×C22⋊Dic61—22no—
98C2×C22⋊Dic61—22no—
99C2×C22⋊Dic61C2312yes—
100C2×C22⋊Dic61C2312yes—
101C2×C22⋊Dic61C2312yes—
102C2×#11758198—21no—
103C2×#11758198—22no—
104C2×#11758198D412yescomplemented
105C22⋊C4×D61—22no—
106C22⋊C4×D61—22no—
107C2×C4×Dic61—21no—
108C2×C4×Dic61—22no—
109C2×C4×Dic61D412yescomplemented
110C42×D61—22no—
111#14519692—22no—
112#14519692C2×C414yescomplemented
113#14519691—24no—
114#14519691C2×C418yescomplemented
115#14519684—22no—
116#14519684—22no—
117#14519684—22no—
118C25×C61C2311yescharacteristic
119C22×D4×C61—21no—
120C22×D4×C61C2311yescharacteristic
121C23×C4×C61—22no—
122C23×C4×C61—21no—
123C23×C4×C61—21no—
124C23×C4×C61—22no—
125C23×C4×C61—44no—
126C23×C4×C61D411yescharacteristic, complemented
127C23×C4×C61C2311yescharacteristic
128C23×C4×C61C2311yescharacteristic
129#120×C61—22no—
130#120×C61C2×C414yescomplemented
131C4×D4×C61—22no—
132C4×D4×C61—22no—
133C4×D4×C61—44no—
134C2×C4⋊C4×C61—21no—
135C2×C4⋊C4×C61D411yescharacteristic, complemented
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61—21no—
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61D411yescharacteristic, complemented
141C2×C22⋊C4×C61C2311yescharacteristic
142C2×C22⋊C4×C61C2311yescharacteristic
143C2×C22⋊C4×C61C2311yescharacteristic
144C2×C42×C61—21no—
145C2×C42×C61D411yescharacteristic, complemented
146#95×C61—21no—
147#95×C61—21no—
148#95×C61—21no—
149C24×C61—22no—
150C24×C61—21no—
151C24×C61—21no—
152C24×C61—22no—
153C24×C61—42no—
154C24×C61—42no—
155C24×C61C22×C412yescomplemented
156C24×C61C2×D411yescharacteristic
157C24×C61C2411yescharacteristic
158C23×D61—21no—
159C23×D61C2×D412yes—
160C2×D4×C61—22no—
161C2×D4×C61—22no—
162C2×D4×C61—24no—
163C2×D4×C61—42no—
164C2×D4×C61—42no—
165C2×D4×C61C22×C412yes—
166C2×D4×C61#4112yes—
167C22×C4×C61—24no—
168C22×C4×C61—28no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—22no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—42no—
176C22×C4×C61—42no—
177C22×C4×C61—44no—
178C22×C4×C61—42no—
179C22×C4×C61—44no—
180C22×C4×C61—42no—
181C22×C4×C61—42no—
182C22×C4×C61—44no—
183C22×C4×C61—42no—
184C22×C4×C61—42no—
185C22×C4×C61—41no—
186C22×C4×C61—41no—
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D412yes—
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2×D412yes—
193C22×C4×C61C2×D411yescharacteristic
194C2×C22⋊D61—22no—
195C2×C22⋊D61—24no—
196C2×C22⋊D61—24no—
197C2×C22⋊D61—22no—
198C2×C22⋊D61—22no—
199C2×C22⋊D61—22no—
200C2×C22⋊D61—22no—
201C2×C22⋊D61—28no—
202C2×C22⋊D61—44no—
203C2×C22⋊D61—44no—
204C2×C22⋊D61C22×C414yes—
205C2×C22⋊D61#4114yes—
206C22×Dic61—21no—
207C22×Dic61—22no—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—22no—
211C22×Dic61C2×D412yes—
212C22×Dic61C2×D412yes—
213C22×Dic61C2×D412yes—
214#11758224—28no—
215#11758224—28no—
216D4×D61—28no—
217D4×D61—28no—
218#11758222—24no—
219#11758222—24no—
220C2×D244—21no—
221C2×C4×D61—22no—
222C2×C4×D61—22no—
223C2×C4×D61—22no—
224C2×C4×D61—22no—
225C2×C4×D61—22no—
226C2×C4×D61—44no—
227C2×C4×D61—82no—
228C2×Dic122—21no—
229C4⋊C4×C61—22no—
230C4⋊C4×C61—42no—
231C22⋊C4×C61—22no—
232C22⋊C4×C61—21no—
233C22⋊C4×C61—24no—
234C22⋊C4×C61—22no—
235C22⋊C4×C61—22no—
236C22⋊C4×C61—42no—
237C22⋊C4×C61—42no—
238C22⋊C4×C61—42no—
239C22⋊C4×C61C22×C412yescomplemented
240C42×C61—21no—
241C42×C61—21no—
242C42×C61—42no—
243C22⋊Dic61—22no—
244C22⋊Dic61—22no—
245C22⋊Dic61—22no—
246C22⋊Dic61—22no—
247C22⋊Dic61—28no—
248C22⋊Dic61—22no—
249C22⋊Dic61—22no—
250C22⋊Dic61—44no—
251C22⋊Dic61—44no—
252C22⋊Dic61C22×C414yescomplemented
253#11758198—22no—
254#11758198—22no—
255#11758198—22no—
256#11758198—22no—
257#11758198—44no—
258C4⋊Dic61—21no—
259C4⋊Dic61—21no—
260#11758196—22no—
261#11758196—22no—
262#11758196—22no—
263#11758196—22no—
264#11758196—44no—
265C4×Dic61—22no—
266C4×Dic61—22no—
267C4×Dic61—22no—
268C4×Dic61—22no—
269C4×Dic61—22no—
270C4×Dic61—44no—
271C23×C61—24no—
272C23×C61—24no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—24no—
276C23×C61—22no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—41no—
280C23×C61—44no—
281C23×C61—41no—
282C23×C61—42no—
283C23×C61—41no—
284C23×C61—42no—
285C23×C61—41no—
286C23×C61—48no—
287C23×C61—44no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—42no—
293C23×C61C4×D412yescomplemented
294C23×C61C23×C411yescharacteristic
295C23×C61C22×D412yes—
296C23×C61C22×D411yescharacteristic
297C23×C61C2×#4112yes—
298C23×C61C2×#4111yescharacteristic
299C22×D61—22no—
300C22×D61—24no—
301C22×D61—22no—
302C22×D61—42no—
303C22×D61—42no—
304C22×D61—81no—
305C22×D61—81no—
306C22×D61C4×D414yescomplemented
307D4×C61—24no—
308D4×C61—24no—
309D4×C61—48no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—24no—
313C2×C4×C61—22no—
314C2×C4×C61—24no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—41no—
320C2×C4×C61—42no—
321C2×C4×C61—48no—
322C2×C4×C61—44no—
323C2×C4×C61—41no—
324C2×C4×C61—42no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61—42no—
329C2×C4×C61—44no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—81no—
336C2×C4×C61C4×D412yescomplemented
337C2×C4×C61#12012yes—
338C2×C4×C61#12011yescharacteristic
339C2×C4×C61#12011yescharacteristic
340C22⋊D61—28no—
341C22⋊D61—24no—
342C22⋊D61—24no—
343C22⋊D61—24no—
344C22⋊D61—24no—
345C22⋊D61—416no—
346C2×Dic61—24no—
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—24no—
350C2×Dic61—22no—
351C2×Dic61—22no—
352C2×Dic61—42no—
353C2×Dic61—42no—
354C2×Dic61—42no—
355C2×Dic61—42no—
356C2×Dic61—42no—
357C2×Dic61—42no—
358C2×Dic61—42no—
359C2×Dic61—81no—
360C2×Dic61—81no—
361C2×Dic61C4×D414yescomplemented
362D244—24no—
363C4×D61—28no—
364C4×D61—44no—
365C4×D61—82no—
366C4×D61—82no—
367C4×D61—82no—
368Dic122—24no—
369C4×B(4,𝔽2)—611nomaximal, Sylow
370C22×C61—22no—
371C22×C61—21no—
372C22×C61—22no—
373C22×C61—21no—
374C22×C61—28no—
375C22×C61—24no—
376C22×C61—22no—
377C22×C61—41no—
378C22×C61—42no—
379C22×C61—41no—
380C22×C61—42no—
381C22×C61—44no—
382C22×C61—44no—
383C22×C61—44no—
384C22×C61—42no—
385C22×C61—42no—
386C22×C61—42no—
387C22×C61—41no—
388C22×C61—42no—
389C22×C61—41no—
390C22×C61—42no—
391C22×C61—42no—
392C22×C61—81no—
393C22×C61C2×C4×D412yes—
394C22×C61C2×C4×D411yescharacteristic
395C22×C61C2×#12011yescharacteristic
396C22×C61#52511yescharacteristic
397C22×C61#52512yes—
398C2×D61—24no—
399C2×D61—42no—
400C2×D61—42no—
401C2×D61—44no—
402C2×D61—82no—
403C2×D61—84no—
404C4×C61—22no—
405C4×C61—21no—
406C4×C61—22no—
407C4×C61—42no—
408C4×C61—41no—
409C4×C61—42no—
410C4×C61—41no—
411C4×C61—81no—
412C4×C61B(4,𝔽2)12yescomplemented
413Dic61—24no—
414Dic61—44no—
415Dic61—42no—
416Dic61—42no—
417Dic61—82no—
418C4×H(5,𝔽2)—611no—
419C2×B(4,𝔽2)—611no—
420C4×#120—612no—
421C4×#120D6111yescharacteristic, complemented
422#1889—612no—
423#1889—611no—
424#1867—611no—
425#1867—612no—
426#1790—611no—
427C4×#99—612no—
428C4×#99—611no—
429C2×C61—22no—
430C2×C61—22no—
431C2×C61—21no—
432C2×C61—21no—
433C2×C61—42no—
434C2×C61—44no—
435C2×C61C4×#12011yescharacteristic
436C2×C61C2×B(4,𝔽2)11yescharacteristic
437C2×C61#302511yescharacteristic
438D61—44no—
439C2×H(5,𝔽2)—611no—
440C24×C4C2×D6111yescharacteristic, complemented
441C2×#120—612no—
442C2×#120C2×D6111yescharacteristic
443#520—1222no—
444#520—1221no—
445#518—611no—
446#518—612no—
447#518—1222no—
448#518—1221no—
449C4×#41—1222no—
450C4×#41—1221no—
451C2×C4×D4—21no—
452C2×C4×D4—612no—
453C2×C4×D4—1222no—
454C2×C4×D4—1221no—
455C2×C4×D4—1222no—
456C2×C4×D4C2×D6111yescharacteristic
457B(4,𝔽2)—618no—
458C2×#99—611no—
459C2×#99—612no—
460C2×#99—611no—
461C2×#99—612no—
462#386—21no—
463#386—612no—
464#386—1222no—
465#386C2×D6111yescharacteristic
466#385—21no—
467#385—612no—
468#385—1222no—
469#385C2×D6111yescharacteristic, complemented
470#379—612no—
471#379C2×D6111yescharacteristic, complemented
472C4×C22⋊C4—21no—
473C4×C22⋊C4—612no—
474C4×C22⋊C4—1222no—
475C4×C22⋊C4C2×D6111yescharacteristic, complemented
476#342—612no—
477#342—612no—
478#342—612no—
479C61C4×B(4,𝔽2)11yescharacteristic, complemented, Sylow
480C25C22×D6111yescharacteristic
481H(5,𝔽2)—614no—
482H(5,𝔽2)—1224no—
483H(5,𝔽2)—1222no—
484C2×#41—1222no—
485C2×#41—1221no—
486C22×D4—21no—
487C22×D4—612no—
488C22×D4—1222no—
489C22×D4—1221no—
490C22×D4—1222no—
491C22×D4C22×D6111yescharacteristic
492C23×C4—22no—
493C23×C4—21no—
494C23×C4—22no—
495C23×C4—21no—
496C23×C4—44no—
497C23×C4—612no—
498C23×C4—1221no—
499C23×C4C22⋊D6111yescharacteristic, complemented
500C23×C4C22×D6111yescharacteristic
501C23×C4C22×D6111yescharacteristic
502#120—22no—
503#120—618no—
504#120—1224no—
505#120C4×D6114yescomplemented
506C4×Q8—1221no—
507C4×Q8—1221no—
508C4×Q8—1222no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—44no—
512C4×D4—1221no—
513C4×D4—1221no—
514C4×D4—1222no—
515C4×D4—1222no—
516C4×D4—1222no—
517C4×D4—1222no—
518C4×D4—1222no—
519C4×D4—1222no—
520C4×D4—1222no—
521C4×D4—1222no—
522C4×D4—1222no—
523C4×D4—1222no—
524C4×D4—1222no—
525C4×D4—1222no—
526C4×D4—1222no—
527C4×D4—1222no—
528C4×D4—1222no—
529C4×D4—2448no—
530#117—1222no—
531#117—1222no—
532#117—1222no—
533#117—1222no—
534#117—1221no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—612no—
537C2×C4⋊C4—1222no—
538C2×C4⋊C4—1221no—
539C2×C4⋊C4—1222no—
540C2×C4⋊C4C22⋊D6111yescharacteristic, complemented
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—612no—
546C2×C22⋊C4—612no—
547C2×C22⋊C4—612no—
548C2×C22⋊C4—612no—
549C2×C22⋊C4—1222no—
550C2×C22⋊C4—1222no—
551C2×C22⋊C4—1221no—
552C2×C22⋊C4—1222no—
553C2×C22⋊C4—1221no—
554C2×C22⋊C4—1222no—
555C2×C22⋊C4—1222no—
556C2×C22⋊C4—1222no—
557C2×C22⋊C4C22⋊D6111yescharacteristic, complemented
558C2×C22⋊C4C22×D6111yescharacteristic
559C2×C22⋊C4C22×D6111yescharacteristic
560C2×C22⋊C4C22×D6111yescharacteristic
561C2×C42—21no—
562C2×C42—612no—
563C2×C42—1222no—
564C2×C42—1221no—
565C2×C42—1222no—
566C2×C42C22⋊D6111yescharacteristic, complemented
567#99—614no—
568#99—618no—
569#99—1224no—
570#99—1222no—
571#95—21no—
572#95—21no—
573#95—21no—
574#95—1222no—
575#95—1222no—
576#95—1222no—
577C24—22no—
578C24—21no—
579C24—22no—
580C24—21no—
581C24—42no—
582C24—42no—
583C24—612no—
584C24—1221no—
585C24C2×C4×D6112yescomplemented
586C24C2×C22⋊D6111yescharacteristic
587C24C23×D6111yescharacteristic
588#41—1224no—
589#41—1228no—
590#41—1228no—
591#41—1224no—
592C2×Q8—1221no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—24no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—614no—
599C2×D4—614no—
600C2×D4—1221no—
601C2×D4—1228no—
602C2×D4—1228no—
603C2×D4—1222no—
604C2×D4—1224no—
605C2×D4—1222no—
606C2×D4—1222no—
607C2×D4—1222no—
608C2×D4—1222no—
609C2×D4—1224no—
610C2×D4—1228no—
611C2×D4—2444no—
612C2×D4—2444no—
613C2×D4C2×C4×D6112yes—
614C2×D4#1175822212yes—
615C22×C4—24no—
616C22×C4—28no—
617C22×C4—22no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—44no—
627C22×C4—42no—
628C22×C4—44no—
629C22×C4—42no—
630C22×C4—44no—
631C22×C4—42no—
632C22×C4—41no—
633C22×C4—42no—
634C22×C4—41no—
635C22×C4—612no—
636C22×C4—612no—
637C22×C4—612no—
638C22×C4—1222no—
639C22×C4—1222no—
640C22×C4—1222no—
641C22×C4—1221no—
642C22×C4—1221no—
643C22×C4—1221no—
644C22×C4—1222no—
645C22×C4—1222no—
646C22×C4—1222no—
647C22×C4—1222no—
648C22×C4—4882no—
649C22×C4—2444no—
650C22×C4D4×D6112yes—
651C22×C4D4×D6112yes—
652C22×C4C2×C22⋊D6111yescharacteristic
653C22×C4C2×C22⋊D6111yescharacteristic
654C22×C4C2×C22⋊D6111yescharacteristic
655C22×C4C2×C22⋊D6111yescharacteristic
656C22×C4C2×C22⋊D6111yescharacteristic
657C4⋊C4—22no—
658C4⋊C4—42no—
659C4⋊C4—1222no—
660C4⋊C4—1221no—
661C4⋊C4—1222no—
662C4⋊C4—1221no—
663C4⋊C4—1222no—
664C4⋊C4—1222no—
665C4⋊C4—2444no—
666C22⋊C4—22no—
667C22⋊C4—21no—
668C22⋊C4—24no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—614no—
675C22⋊C4—1222no—
676C22⋊C4—1222no—
677C22⋊C4—1228no—
678C22⋊C4—1222no—
679C22⋊C4—1222no—
680C22⋊C4—1222no—
681C22⋊C4—1222no—
682C22⋊C4—1222no—
683C22⋊C4—1222no—
684C22⋊C4—1222no—
685C22⋊C4—1222no—
686C22⋊C4—2444no—
687C22⋊C4—2444no—
688C22⋊C4—2444no—
689C22⋊C4C2×C4×D6112yescomplemented
690C42—21no—
691C42—21no—
692C42—42no—
693C42—1222no—
694C42—1222no—
695C42—1222no—
696C42—1222no—
697C42—1222no—
698C42—2444no—
699C23—22no—
700C23—22no—
701C23—24no—
702C23—24no—
703C23—24no—
704C23—22no—
705C23—21no—
706C23—21no—
707C23—41no—
708C23—44no—
709C23—41no—
710C23—41no—
711C23—42no—
712C23—41no—
713C23—42no—
714C23—44no—
715C23—48no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—42no—
721C23—614no—
722C23—1224no—
723C23—1222no—
724C23—1222no—
725C23—4881no—
726C23—4881no—
727C23—2442no—
728C23—2442no—
729C23C4×C22⋊D6112yescomplemented
730C23C22×C4×D6111yescharacteristic
731C23C2×D4×D6112yes—
732C23C22×C22⋊D6111yescharacteristic
733C23#41×D6112yes—
734C23C2×#1175822211yescharacteristic
735Q8—1224no—
736D4—24no—
737D4—24no—
738D4—48no—
739D4—1224no—
740D4—1228no—
741D4—1224no—
742D4—1224no—
743D4—1224no—
744D4—1224no—
745D4—24416no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—22no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—42no—
756C2×C4—41no—
757C2×C4—44no—
758C2×C4—48no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—44no—
765C2×C4—42no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—81no—
772C2×C4—614no—
773C2×C4—1228no—
774C2×C4—1224no—
775C2×C4—1222no—
776C2×C4—1222no—
777C2×C4—1224no—
778C2×C4—1222no—
779C2×C4—1222no—
780C2×C4—4882no—
781C2×C4—4882no—
782C2×C4—4882no—
783C2×C4—4881no—
784C2×C4—4881no—
785C2×C4—2442no—
786C2×C4—2442no—
787C2×C4—2442no—
788C2×C4—2442no—
789C2×C4—2442no—
790C2×C4—2444no—
791C2×C4—2442no—
792C2×C4—2442no—
793C2×C4C4×C22⋊D6112yescomplemented
794C2×C4#1451974511yescharacteristic
795C2×C4#1451974512yes—
796C2×C4#1451974511yescharacteristic
797C22—21no—
798C22—22no—
799C22—21no—
800C22—22no—
801C22—24no—
802C22—28no—
803C22—22no—
804C22—41no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—44no—
812C22—44no—
813C22—44no—
814C22—42no—
815C22—41no—
816C22—41no—
817C22—42no—
818C22—42no—
819C22—81no—
820C22—1224no—
821C22—4882no—
822C22—4884no—
823C22—2444no—
824C22—2442no—
825C22—2442no—
826C22C4×D4×D6112yes—
827C22C2×C4×C22⋊D6111yescharacteristic
828C22C2×#1451974511yescharacteristic
829C22#1684026911yescharacteristic
830C22#1684027112yes—
831C4—21no—
832C4—22no—
833C4—22no—
834C4—42no—
835C4—42no—
836C4—41no—
837C4—41no—
838C4—81no—
839C4—1224no—
840C4—4882no—
841C4—2444no—
842C4—2442no—
843C4—2442no—
844C4#1683994812yesdirect product factor
845C2—21no—
846C2—21no—
847C2—22no—
848C2—22no—
849C2—44no—
850C2—42no—
851C2—2444no—
852C2C4×#1451974511yescharacteristic
853C2C2×#1683994811yescharacteristic
854C2#2145521011yescharacteristic
subgroupG/H
centerC2×C4#14519745
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC4×#120×C61C2
socleC22×C61C2×#120
prime radicalC2×#16839948C2
cosocleC24×C61C24
hypercenterC4×#120D61
hypocenterC61C4×B(4,𝔽2)
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×#120

Complements

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

NH ≅ G/Ntype
1. C4×#14519822C2semidirect
3. C4×#14519746C2semidirect
4. #21446228C2semidirect
5. #21446224C2semidirect
6. #21446099C2semidirect
7. #21446098C2semidirect
8. #21445766C2semidirect
9. C4×#14519691C2semidirect
10. C4×#14519692C2semidirect
11. C4×#120×C61C2semidirect
26. #16839948C4direct (N × H)
34. #16839635C22semidirect
35. #16839618C22semidirect
37. C4×C22⋊Dic61C22semidirect
38. #16839529C22semidirect
39. #16839528C22semidirect
40. #16839528C22semidirect
41. C24×C4×C61C22semidirect
48. C61×#385C22semidirect
49. C61×#379C22semidirect
51. C4×C22⋊C4×C61C22semidirect
54. #14519822C2×C4semidirect
62. C22×C4×D61D4semidirect
64. #14519746C2×C4semidirect
93. C2×#11758196D4semidirect
104. C2×#11758198D4semidirect
109. C2×C4×Dic61D4semidirect
112. #14519692C2×C4semidirect
114. #14519691C2×C4semidirect
126. C23×C4×C61D4semidirect
130. #120×C61C2×C4semidirect
135. C2×C4⋊C4×C61D4semidirect
140. C2×C22⋊C4×C61D4semidirect
145. C2×C42×C61D4semidirect
155. C24×C61C22×C4semidirect
239. C22⋊C4×C61C22×C4semidirect
252. C22⋊Dic61C22×C4semidirect
293. C23×C61C4×D4semidirect
306. C22×D61C4×D4semidirect
336. C2×C4×C61C4×D4semidirect
361. C2×Dic61C4×D4semidirect
412. C4×C61B(4,𝔽2)semidirect
421. C4×#120D61semidirect
440. C24×C4C2×D61semidirect
469. #385C2×D61semidirect
471. #379C2×D61semidirect
475. C4×C22⋊C4C2×D61semidirect
479. C61C4×B(4,𝔽2)semidirect
499. C23×C4C22⋊D61semidirect
505. #120C4×D61semidirect
540. C2×C4⋊C4C22⋊D61semidirect
557. C2×C22⋊C4C22⋊D61semidirect
566. C2×C42C22⋊D61semidirect
585. C24C2×C4×D61semidirect
689. C22⋊C4C2×C4×D61semidirect
729. C23C4×C22⋊D61semidirect
793. C2×C4C4×C22⋊D61semidirect
844. C4#16839948direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#145198222
C2×#168399482
C4×#145197462
#214462282
#214462242
#214460992
#214460982
#214457662
C4×#145196912
C4×#145196922
C4×#120×C612
C4×B(4,𝔽2)61