Finite Group Databasebeta

← #29685354

Subgroups — #29685354

Order 15616.

1678 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840273C211yesmaximal, characteristic
2C2×C4×C22⋊Dic61C211yesmaximal, characteristic, complemented
3#21446803C212yesmaximal, complemented
4#21446654C212yesmaximal, complemented
5#21446270C214yesmaximal, complemented
6C4×#14519691C214yesmaximal, complemented
7C61×#2280C211yesmaximal, characteristic, complemented
8C22×#11758222C411yescharacteristic, complemented
9#16840273—21no—
10#16840273—21no—
11#16840273—21no—
12#16840273—21no—
13#16840273—21no—
14#16840273—21no—
15#16840273—21no—
16#16840273—21no—
17C2×#14519760C412yescomplemented
18C2×#14519756C411yescharacteristic, complemented
19C2×#14519756C2211yescharacteristic
20C2×#14519751C411yescharacteristic, complemented
21C2×#14519751C2211yescharacteristic
22C2×#14519746C2212yes—
23C2×C4×C22⋊D61C412yescomplemented
24C2×C4×C22⋊D61C2212yes—
25C2×#14519736C411yescharacteristic, complemented
26C22×C22⋊Dic61C2212yes—
27C22×C4×Dic61—21no—
28C2×#14519691C2218yes—
29C4×C22⋊Dic61—21no—
30C4×C22⋊Dic61—21no—
31C4×C22⋊Dic61C2212yes—
32C4×C22⋊Dic61C2212yes—
33C2×#14519684—21no—
34#16839528C2218yes—
35C24×C4×C61C2211yescharacteristic
36C2×#117×C61—21no—
37C61×#381—21no—
38C61×#380—21no—
39C61×#380C2212yes—
40C61×#379C2212yes—
41C4×C22⋊C4×C61—21no—
42C4×C22⋊C4×C61C2212yes—
43C2×#11758222—21no—
44C2×#11758222—21no—
45C2×#11758222—21no—
46C2×#11758222—21no—
47C2×#11758222—44no—
48C22×Dic122C2×C411yescharacteristic, complemented
49C22×D244C2×C411yescharacteristic, complemented
50C22×C22⋊D61C2×C412yes—
51C22×C22⋊D61C2×C412yes—
52C22×C22⋊D61C2312yes—
53C23×Dic61—22no—
54C22×C4×D61C2×C412yescomplemented
55#14519760—22no—
56#14519760—22no—
57#14519760—22no—
58#14519760—22no—
59#14519756—21no—
60#14519756—21no—
61#14519756—21no—
62#14519756—21no—
63#14519756—21no—
64#14519756—21no—
65#14519756—21no—
66#14519756—21no—
67#14519751—21no—
68#14519751—21no—
69#14519751—21no—
70#14519751—21no—
71#14519751—21no—
72#14519751—21no—
73#14519751—21no—
74#14519751—21no—
75#14519746—22no—
76#14519746—22no—
77#14519746—22no—
78#14519746—22no—
79C4×C22⋊D61—22no—
80C4×C22⋊D61—22no—
81C4×C22⋊D61—22no—
82C4×C22⋊D61—22no—
83C4×C22⋊D61—22no—
84C4×C22⋊D61—22no—
85C4×C22⋊D61—22no—
86C4×C22⋊D61—22no—
87#14519736—21no—
88#14519736—21no—
89#14519736—21no—
90#14519736—21no—
91C2×C4⋊Dic61C2×C411yescharacteristic, complemented
92C2×C4⋊Dic61C2×C411yescharacteristic, complemented
93C2×#11758196C2×C412yescomplemented
94C2×#11758196C2×C412yescomplemented
95C2×C22⋊Dic61—22no—
96C2×C22⋊Dic61—28no—
97C2×C22⋊Dic61C2×C412yes—
98C2×C22⋊Dic61C2×C412yes—
99C2×C22⋊Dic61C2312yes—
100C2×C22⋊Dic61C2314yes—
101C2×#11758198C2×C412yescomplemented
102C2×#11758198C2×C412yescomplemented
103C2×C4×Dic61—22no—
104C2×C4×Dic61—22no—
105C2×C4×Dic61—44no—
106C2×C4×Dic61C2×C412yescomplemented
107#14519691—216no—
108#14519684—22no—
109#14519684—22no—
110C25×C61C2311yescharacteristic
111C23×C4×C61—44no—
112C23×C4×C61C2×C411yescharacteristic
113C23×C4×C61C2×C411yescharacteristic
114C23×C4×C61C2×C411yescharacteristic
115C23×C4×C61C2×C411yescharacteristic
116C23×C4×C61D411yescharacteristic
117C23×C4×C61D411yescharacteristic
118C23×C4×C61D411yescharacteristic
119C23×C4×C61D411yescharacteristic
120C23×C4×C61D411yescharacteristic
121C23×C4×C61D411yescharacteristic
122C23×C4×C61D411yescharacteristic
123C23×C4×C61D411yescharacteristic
124C23×C4×C61C2311yescharacteristic
125C23×C4×C61C2311yescharacteristic
126#117×C61—44no—
127C2×C4⋊C4×C61—22no—
128C2×C22⋊C4×C61—22no—
129C2×C22⋊C4×C61—22no—
130C2×C22⋊C4×C61C2314yes—
131C2×C42×C61—22no—
132#95×C61—22no—
133#95×C61—22no—
134C24×C61—24no—
135C24×C61—42no—
136C24×C61—42no—
137C24×C61C22×C411yescharacteristic
138C24×C61C22×C411yescharacteristic
139C24×C61C2×D411yescharacteristic
140C24×C61C2×D411yescharacteristic
141C24×C61C2×D411yescharacteristic
142C24×C61C2×D411yescharacteristic
143C24×C61C2411yescharacteristic
144C23×D61C22×C412yes—
145C22×C4×C61—24no—
146C22×C4×C61—24no—
147C22×C4×C61—24no—
148C22×C4×C61—24no—
149C22×C4×C61—42no—
150C22×C4×C61—42no—
151C22×C4×C61—42no—
152C22×C4×C61—42no—
153C22×C4×C61—42no—
154C22×C4×C61—42no—
155C22×C4×C61—42no—
156C22×C4×C61—42no—
157C22×C4×C61—42no—
158C22×C4×C61—42no—
159C22×C4×C61—42no—
160C22×C4×C61C22⋊C411yescharacteristic
161C22×C4×C61C22⋊C411yescharacteristic
162C22×C4×C61C22⋊C411yescharacteristic
163C22×C4×C61C22⋊C411yescharacteristic
164C22×C4×C61C22⋊C411yescharacteristic
165C22×C4×C61C22⋊C411yescharacteristic
166C22×C4×C61C22⋊C411yescharacteristic
167C22×C4×C61C22⋊C411yescharacteristic
168C22×C4×C61C22⋊C411yescharacteristic
169C22×C4×C61C22⋊C411yescharacteristic
170C22×C4×C61C22⋊C411yescharacteristic
171C22×C4×C61C22⋊C411yescharacteristic
172C22×C4×C61C22⋊C411yescharacteristic
173C22×C4×C61C22⋊C411yescharacteristic
174C22×C4×C61C22⋊C411yescharacteristic
175C22×C4×C61C22⋊C411yescharacteristic
176C22×C4×C61C22×C411yescharacteristic
177C22×C4×C61C22×C411yescharacteristic
178C22×C4×C61C22×C411yescharacteristic
179C22×C4×C61C22×C411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C2×C22⋊D61—22no—
189C2×C22⋊D61—22no—
190C2×C22⋊D61—22no—
191C2×C22⋊D61—22no—
192C2×C22⋊D61—22no—
193C2×C22⋊D61—22no—
194C2×C22⋊D61—28no—
195C2×C22⋊D61—44no—
196C2×C22⋊D61—44no—
197C22×Dic61—28no—
198C22×Dic61—24no—
199C22×Dic61—44no—
200C22×Dic61—44no—
201C22×Dic61C22×C412yes—
202C22×Dic61C22×C412yes—
203C22×Dic61C22×C412yes—
204#11758222—44no—
205#11758222—44no—
206#11758222—44no—
207#11758222—44no—
208C2×D244—21no—
209C2×D244—21no—
210C2×D244—42no—
211C2×C4×D61—22no—
212C2×C4×D61—22no—
213C2×C4×D61—44no—
214C2×Dic122—21no—
215C2×Dic122—21no—
216C2×Dic122—42no—
217C4⋊C4×C61—44no—
218C22⋊C4×C61—28no—
219C22⋊C4×C61—44no—
220C22⋊C4×C61—44no—
221C42×C61—44no—
222C22⋊Dic61—28no—
223C22⋊Dic61—22no—
224C22⋊Dic61—22no—
225C22⋊Dic61—22no—
226C22⋊Dic61—22no—
227C22⋊Dic61—22no—
228C22⋊Dic61—22no—
229C22⋊Dic61—24no—
230C22⋊Dic61#4118yescomplemented
231#11758198—22no—
232#11758198—22no—
233#11758198—22no—
234#11758198—22no—
235C4⋊Dic61—21no—
236C4⋊Dic61—21no—
237C4⋊Dic61—21no—
238C4⋊Dic61—21no—
239#11758196—22no—
240#11758196—22no—
241#11758196—22no—
242#11758196—22no—
243C4×Dic61—22no—
244C4×Dic61—22no—
245C4×Dic61—44no—
246C4×Dic61—44no—
247C23×C61—22no—
248C23×C61—22no—
249C23×C61—22no—
250C23×C61—22no—
251C23×C61—22no—
252C23×C61—22no—
253C23×C61—22no—
254C23×C61—22no—
255C23×C61—22no—
256C23×C61—22no—
257C23×C61—22no—
258C23×C61—22no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—416no—
268C23×C61C2×C22⋊C411yescharacteristic
269C23×C61C2×C22⋊C411yescharacteristic
270C23×C61C2×C22⋊C411yescharacteristic
271C23×C61C2×C22⋊C411yescharacteristic
272C23×C61C23×C411yescharacteristic
273C23×C61C22×D411yescharacteristic
274C23×C61C22×D411yescharacteristic
275C23×C61C2×#4114yes—
276C22×D61—22no—
277C22×D61—24no—
278C22×D61—42no—
279C22×D61—42no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—44no—
308C2×C4×C61—44no—
309C2×C4×C61—44no—
310C2×C4×C61#9914yescomplemented
311C2×C4×C61C2×C22⋊C411yescharacteristic
312C2×C4×C61C2×C22⋊C411yescharacteristic
313C2×C4×C61C2×C22⋊C411yescharacteristic
314C2×C4×C61C2×C22⋊C411yescharacteristic
315C2×C4×C61C2×C22⋊C411yescharacteristic
316C2×C4×C61C2×C22⋊C411yescharacteristic
317C2×C4×C61C2×C22⋊C411yescharacteristic
318C2×C4×C61C2×C22⋊C411yescharacteristic
319C22⋊D61—44no—
320C22⋊D61—44no—
321C22⋊D61—44no—
322C22⋊D61—44no—
323C22⋊D61—44no—
324C22⋊D61—44no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—24no—
329C2×Dic61—28no—
330C2×Dic61—44no—
331C2×Dic61—416no—
332C2×Dic61—44no—
333C2×Dic61—42no—
334C2×Dic61—42no—
335D244—42no—
336D244—42no—
337C4×D61—44no—
338C4×D61—44no—
339Dic122—42no—
340Dic122—42no—
341#21420—611nomaximal, Sylow
342C22×C61—28no—
343C22×C61—21no—
344C22×C61—21no—
345C22×C61—21no—
346C22×C61—21no—
347C22×C61—21no—
348C22×C61—21no—
349C22×C61—21no—
350C22×C61—21no—
351C22×C61—21no—
352C22×C61—21no—
353C22×C61—21no—
354C22×C61—21no—
355C22×C61—21no—
356C22×C61—21no—
357C22×C61—21no—
358C22×C61—21no—
359C22×C61—44no—
360C22×C61—44no—
361C22×C61—44no—
362C22×C61—44no—
363C22×C61—44no—
364C22×C61—44no—
365C22×C61C2×#9912yes—
366C22×C61#41012yes—
367C22×C61C22×C22⋊C411yescharacteristic
368C22×C61C4×#4112yes—
369C22×C61#52512yes—
370C22×C61#53212yes—
371C2×D61—42no—
372C2×D61—42no—
373C2×D61—42no—
374C2×D61—84no—
375C4×C61—21no—
376C4×C61—21no—
377C4×C61—21no—
378C4×C61—21no—
379C4×C61—21no—
380C4×C61—21no—
381C4×C61—84no—
382C4×C61C2×#9912yes—
383C4×C61C2×#9912yes—
384Dic61—48no—
385Dic61—42no—
386Dic61—42no—
387Dic61—42no—
388C2×#525—611no—
389#2280D6111yescharacteristic, complemented
390C2×C4×C22⋊C4—611no—
391#1996—612no—
392#1964—612no—
393#1898—614no—
394C4×#99—614no—
395C2×C61—22no—
396C2×C61—22no—
397C2×C61—22no—
398C2×C61—22no—
399C2×C61—22no—
400C2×C61—41no—
401C2×C61—41no—
402C2×C61#229711yescharacteristic
403C2×C61C22×#9911yescharacteristic
404C2×C61C2×#41011yescharacteristic
405D61—82no—
406C22×#41—611no—
407C24×C4C2×D6111yescharacteristic
408#525—1221no—
409#525—1221no—
410#525—1221no—
411#525—1221no—
412#525—1221no—
413#525—1221no—
414#525—1221no—
415#525—1221no—
416C2×#123—612no—
417C2×C22⋊Q8—611no—
418C2×C22⋊Q8—611no—
419C2×#121—611no—
420C2×#121—611no—
421C2×#120—612no—
422C2×C4×D4—612no—
423C2×C4×D4—612no—
424C2×#117—21no—
425C2×#117—611no—
426C22×C22⋊C4—612no—
427C22×C42—1221no—
428C2×#99—618no—
429#381—21no—
430#380—21no—
431#380C2×D6112yes—
432#379C2×D6112yes—
433C4×C22⋊C4—21no—
434C4×C22⋊C4—612no—
435C4×C22⋊C4—612no—
436C4×C22⋊C4—1221no—
437C4×C22⋊C4—1221no—
438C4×C22⋊C4C2×D6112yes—
439C2×#95—1221no—
440#342—618no—
441C61#2142011yescharacteristic, complemented, Sylow
442C25C22×D6111yescharacteristic
443C2×#41—1221no—
444C2×#41—1221no—
445C2×#41—1221no—
446C2×#41—1221no—
447C2×#41—2444no—
448C22×Q8—611no—
449C22×D4—612no—
450C22×D4—612no—
451C22×D4—612no—
452C22×D4—611no—
453C23×C4—44no—
454C23×C4—612no—
455C23×C4—1222no—
456C23×C4C4×D6111yescharacteristic
457C23×C4C4×D6111yescharacteristic
458C23×C4C4×D6111yescharacteristic
459C23×C4C4×D6111yescharacteristic
460C23×C4D24411yescharacteristic
461C23×C4D24411yescharacteristic
462C23×C4D24411yescharacteristic
463C23×C4D24411yescharacteristic
464C23×C4C22⋊D6111yescharacteristic
465C23×C4C22⋊D6111yescharacteristic
466C23×C4C22⋊D6111yescharacteristic
467C23×C4C22⋊D6111yescharacteristic
468C23×C4C22×D6111yescharacteristic
469C23×C4C22×D6111yescharacteristic
470#123—1222no—
471#123—1222no—
472#123—1222no—
473#123—1222no—
474C22⋊Q8—1221no—
475C22⋊Q8—1221no—
476C22⋊Q8—1221no—
477C22⋊Q8—1221no—
478C22⋊Q8—1221no—
479C22⋊Q8—1221no—
480C22⋊Q8—1221no—
481C22⋊Q8—1221no—
482#121—1221no—
483#121—1221no—
484#121—1221no—
485#121—1221no—
486#121—1221no—
487#121—1221no—
488#121—1221no—
489#121—1221no—
490#120—1222no—
491#120—1222no—
492#120—1222no—
493#120—1222no—
494C4×D4—1222no—
495C4×D4—1222no—
496C4×D4—1222no—
497C4×D4—1222no—
498C4×D4—1222no—
499C4×D4—1222no—
500C4×D4—1222no—
501C4×D4—1222no—
502#117—44no—
503#117—1221no—
504#117—1221no—
505#117—1221no—
506#117—1221no—
507C2×C4⋊C4—22no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—611no—
510C2×C4⋊C4—612no—
511C2×C4⋊C4—612no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—614no—
515C2×C22⋊C4—612no—
516C2×C22⋊C4—612no—
517C2×C22⋊C4—612no—
518C2×C22⋊C4—612no—
519C2×C22⋊C4—612no—
520C2×C22⋊C4—1228no—
521C2×C22⋊C4—1222no—
522C2×C22⋊C4C22×D6114yes—
523C2×C42—22no—
524C2×C42—612no—
525C2×C42—1222no—
526C2×C42—1222no—
527C2×C42—2444no—
528#99—12216no—
529#95—22no—
530#95—22no—
531#95—1222no—
532#95—1222no—
533C24—24no—
534C24—42no—
535C24—42no—
536C24—612no—
537C24C2×C4×D6111yescharacteristic
538C24C2×C4×D6111yescharacteristic
539C24C2×D24411yescharacteristic
540C24C2×D24411yescharacteristic
541C24C2×C22⋊D6111yescharacteristic
542C24C2×C22⋊D6111yescharacteristic
543C24C23×D6111yescharacteristic
544#41—2444no—
545#41—2444no—
546#41—2444no—
547#41—2444no—
548C2×Q8—1221no—
549C2×Q8—1221no—
550C2×Q8—2442no—
551C2×D4—1222no—
552C2×D4—1222no—
553C2×D4—1228no—
554C2×D4—1222no—
555C2×D4—1222no—
556C2×D4—1222no—
557C2×D4—1222no—
558C2×D4—1221no—
559C2×D4—1221no—
560C2×D4—2442no—
561C2×D4—2444no—
562C2×D4—2444no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—612no—
579C22×C4—612no—
580C22×C4—612no—
581C22×C4—1228no—
582C22×C4—1224no—
583C22×C4—1222no—
584C22×C4—1222no—
585C22×C4—2444no—
586C22×C4—2444no—
587C22×C4—2444no—
588C22×C4#1175819811yescharacteristic
589C22×C4#1175819811yescharacteristic
590C22×C4#1175819811yescharacteristic
591C22×C4#1175819811yescharacteristic
592C22×C4#1175819811yescharacteristic
593C22×C4#1175819811yescharacteristic
594C22×C4#1175819811yescharacteristic
595C22×C4#1175819811yescharacteristic
596C22×C4#1175819811yescharacteristic
597C22×C4#1175819811yescharacteristic
598C22×C4#1175819811yescharacteristic
599C22×C4#1175819811yescharacteristic
600C22×C4#1175819811yescharacteristic
601C22×C4#1175819811yescharacteristic
602C22×C4#1175819811yescharacteristic
603C22×C4#1175819811yescharacteristic
604C22×C4C2×C4×D6111yescharacteristic
605C22×C4C2×C4×D6111yescharacteristic
606C22×C4C2×C4×D6111yescharacteristic
607C22×C4C2×C4×D6111yescharacteristic
608C22×C4C2×D24411yescharacteristic
609C22×C4C2×D24411yescharacteristic
610C22×C4C2×D24411yescharacteristic
611C22×C4C2×D24411yescharacteristic
612C22×C4C2×C22⋊D6111yescharacteristic
613C22×C4C2×C22⋊D6111yescharacteristic
614C22×C4C2×C22⋊D6111yescharacteristic
615C22×C4C2×C22⋊D6111yescharacteristic
616C4⋊C4—44no—
617C4⋊C4—1222no—
618C4⋊C4—1222no—
619C4⋊C4—1222no—
620C4⋊C4—1222no—
621C4⋊C4—1221no—
622C4⋊C4—1221no—
623C4⋊C4—1221no—
624C4⋊C4—1221no—
625C22⋊C4—28no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—618no—
629C22⋊C4—1228no—
630C22⋊C4—1222no—
631C22⋊C4—1222no—
632C22⋊C4—1224no—
633C22⋊C4—1222no—
634C22⋊C4—1222no—
635C22⋊C4—1222no—
636C22⋊C4—1222no—
637C22⋊C4—1222no—
638C22⋊C4—1222no—
639C22⋊C4—1222no—
640C22⋊C4—1222no—
641C42—44no—
642C42—1222no—
643C42—1222no—
644C42—2444no—
645C42—2444no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—416no—
667C23—1224no—
668C23—1222no—
669C23—2442no—
670C23—2442no—
671C23C2×#1175819811yescharacteristic
672C23C2×#1175819811yescharacteristic
673C23C2×#1175819811yescharacteristic
674C23C2×#1175819811yescharacteristic
675C23C22×C4×D6111yescharacteristic
676C23C22×C22⋊D6111yescharacteristic
677C23C22×D24411yescharacteristic
678C23#41×D6114yes—
679Q8—2442no—
680Q8—2442no—
681D4—2442no—
682D4—2444no—
683D4—2444no—
684D4—2444no—
685D4—2444no—
686D4—2444no—
687D4—2444no—
688D4—2442no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—1222no—
720C2×C4—1222no—
721C2×C4—1222no—
722C2×C4—1224no—
723C2×C4—1228no—
724C2×C4—2444no—
725C2×C4—2444no—
726C2×C4—24416no—
727C2×C4—2444no—
728C2×C4—2444no—
729C2×C4—2442no—
730C2×C4—2442no—
731C2×C4#1451969114yescomplemented
732C2×C4C2×#1175819811yescharacteristic
733C2×C4C2×#1175819811yescharacteristic
734C2×C4C2×#1175819811yescharacteristic
735C2×C4C2×#1175819811yescharacteristic
736C2×C4C2×#1175819811yescharacteristic
737C2×C4C2×#1175819811yescharacteristic
738C2×C4C2×#1175819811yescharacteristic
739C2×C4C2×#1175819811yescharacteristic
740C22—28no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—21no—
756C22—21no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—4884no—
764C22—2442no—
765C22—2442no—
766C22—2442no—
767C22C2×#1451969112yes—
768C22#1683973512yes—
769C22C22×#1175819811yescharacteristic
770C22#1684023012yes—
771C22#1684027412yes—
772C22#1684030812yes—
773C4—21no—
774C4—21no—
775C4—21no—
776C4—21no—
777C4—21no—
778C4—21no—
779C4—84no—
780C4—2448no—
781C4—2442no—
782C4—2442no—
783C4—2442no—
784C4C2×#1451969112yes—
785C4C2×#1451969112yes—
786C2—22no—
787C2—22no—
788C2—22no—
789C2—22no—
790C2—22no—
791C2—41no—
792C2—41no—
793C2—4882no—
794C2#2144830711yescharacteristic
795C2C22×#1451969111yescharacteristic
796C2C2×#1683973511yescharacteristic
subgroupG/H
centerC2×C4C2×#11758198
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#2280C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840273C2
cosocleC24×C61C24
hypercenter#2280D61
hypocenterC61#21420
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊Dic61C2semidirect
3. #21446803C2semidirect
4. #21446654C2semidirect
5. #21446270C2semidirect
6. C4×#14519691C2semidirect
7. C61×#2280C2semidirect
8. C22×#11758222C4semidirect
17. C2×#14519760C4semidirect
18. C2×#14519756C4semidirect
20. C2×#14519751C4semidirect
23. C2×C4×C22⋊D61C4semidirect
25. C2×#14519736C4semidirect
48. C22×Dic122C2×C4semidirect
49. C22×D244C2×C4semidirect
54. C22×C4×D61C2×C4semidirect
91. C2×C4⋊Dic61C2×C4semidirect
92. C2×C4⋊Dic61C2×C4semidirect
93. C2×#11758196C2×C4semidirect
94. C2×#11758196C2×C4semidirect
101. C2×#11758198C2×C4semidirect
102. C2×#11758198C2×C4semidirect
106. C2×C4×Dic61C2×C4semidirect
230. C22⋊Dic61#41semidirect
310. C2×C4×C61#99semidirect
389. #2280D61semidirect
441. C61#21420semidirect
731. C2×C4#14519691semidirect

Maximal subgroups

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

subgroupindex
C2×#168402732
C2×C4×C22⋊Dic612
#214468032
#214466542
#214462702
C4×#145196912
C61×#22802
#2142061