Finite Group Databasebeta

← #29601580

Subgroups — #29601580

Order 15616.

2666 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D61C211yesmaximal, characteristic
2C2×#16839662C212yesmaximal
3C2×C4×#11758196C212yesmaximal, complemented
4C2×#16839609C211yesmaximal, characteristic, complemented
5#21444057C212yesmaximal, complemented
6#21444056C212yesmaximal, complemented
7#21444047C211yesmaximal, characteristic, complemented
8#21444042C211yesmaximal, characteristic, complemented
9#21444040C211yesmaximal, characteristic, complemented
10#95×Dic61C211yesmaximal, characteristic, complemented
11C2×C4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
12C23×C22⋊D61C2211yescharacteristic
13C23×C4×D61C2211yescharacteristic
14C2×C4×C22⋊D61—28no—
15C2×C4×C22⋊D61C418yescomplemented
16C22×#11758196C2212yes—
17C22×#11758196C2211yescharacteristic
18C22×C22⋊Dic61C2211yescharacteristic
19C22×C22⋊Dic61C2212yes—
20C22×#11758198C2211yescharacteristic
21C22×#11758198C2212yes—
22C22×#11758198C2212yes—
23C22×C4×Dic61C2212yes—
24C22×C4×Dic61C2211yescharacteristic
25C22×C4×Dic61C2212yes—
26#16839662C4116yescomplemented
27C4×#11758196—28no—
28#16839609—24no—
29C2×#14519684C2211yescharacteristic
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2211yescharacteristic
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35C24×C4×C61C2211yescharacteristic
36C22×C22⋊C4×C61C2212yes—
37C22×C42×C61C2212yes—
38C4×C22⋊C4×C61—24no—
39C2×#95×C61C2211yescharacteristic
40C2×#95×C61C2211yescharacteristic
41C24×D61C2311yescharacteristic
42C22×C22⋊D61—24no—
43C22×C22⋊D61—22no—
44C22×C22⋊D61—22no—
45C22×C22⋊D61C2×C414yes—
46C22×C22⋊D61C2×C418yes—
47C23×Dic61C2312yes—
48C23×Dic61C2312yes—
49C23×Dic61C2311yescharacteristic
50C23×Dic61C2311yescharacteristic
51C23×Dic61C2311yescharacteristic
52C22×C4×D61—22no—
53C22×C4×D61—22no—
54C22×C4×D61—24no—
55C22×C4×D61—42no—
56C22×C4×D61C2×C414yes—
57C4×C22⋊D61—232no—
58C2×#11758196—24no—
59C2×#11758196—24no—
60C2×#11758196C2×C414yes—
61C2×#11758196C2×C418yescomplemented
62C2×#11758196D418yes—
63C2×C22⋊Dic61—24no—
64C2×C22⋊Dic61—42no—
65C2×C22⋊Dic61—42no—
66C2×C22⋊Dic61C2×C414yes—
67C2×C22⋊Dic61C2×C418yescomplemented
68C2×#11758198—24no—
69C2×#11758198—24no—
70C2×#11758198—24no—
71C2×#11758198—42no—
72C2×#11758198—42no—
73C2×#11758198C2×C414yes—
74C2×#11758198C2×C418yescomplemented
75C2×#11758198C2×C418yescomplemented
76C2×C4×Dic61—24no—
77C2×C4×Dic61—24no—
78C2×C4×Dic61—24no—
79C2×C4×Dic61—24no—
80C2×C4×Dic61—24no—
81C2×C4×Dic61—42no—
82C2×C4×Dic61C2×C414yes—
83C2×C4×Dic61C2×C418yescomplemented
84#14519684—22no—
85#14519684—24no—
86#14519684—22no—
87#14519684—24no—
88#14519684—24no—
89#14519684—42no—
90C25×C61C2311yescharacteristic
91C23×C4×C61—24no—
92C23×C4×C61—22no—
93C23×C4×C61—22no—
94C23×C4×C61—42no—
95C23×C4×C61C2×C414yes—
96C23×C4×C61C2312yes—
97C23×C4×C61C2311yescharacteristic
98C23×C4×C61C2312yes—
99C23×C4×C61C2311yescharacteristic
100C2×C22⋊C4×C61—24no—
101C2×C22⋊C4×C61—24no—
102C2×C22⋊C4×C61C2×C418yescomplemented
103C2×C42×C61—24no—
104C2×C42×C61—24no—
105C2×C42×C61—42no—
106#95×C61—22no—
107#95×C61D414yescomplemented
108C24×C61—22no—
109C24×C61—21no—
110C24×C61—21no—
111C24×C61—21no—
112C24×C61—22no—
113C24×C61—21no—
114C24×C61—22no—
115C24×C61—21no—
116C24×C61—21no—
117C24×C61C22×C414yes—
118C24×C61C22×C412yes—
119C24×C61C2411yescharacteristic
120C23×D61—22no—
121C23×D61—21no—
122C23×D61—21no—
123C23×D61—21no—
124C23×D61—21no—
125C23×D61—22no—
126C23×D61—22no—
127C23×D61—21no—
128C23×D61—21no—
129C23×D61C22×C412yes—
130C23×D61C22×C414yes—
131C22×C4×C61—22no—
132C22×C4×C61—21no—
133C22×C4×C61—22no—
134C22×C4×C61—21no—
135C22×C4×C61—22no—
136C22×C4×C61—22no—
137C22×C4×C61—22no—
138C22×C4×C61—22no—
139C22×C4×C61—22no—
140C22×C4×C61—22no—
141C22×C4×C61—22no—
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61—22no—
145C22×C4×C61—22no—
146C22×C4×C61—28no—
147C22×C4×C61—28no—
148C22×C4×C61—44no—
149C22×C4×C61—48no—
150C22×C4×C61—48no—
151C22×C4×C61C22×C414yes—
152C22×C4×C61C22×C412yes—
153C22×C4×C61C22×C412yes—
154C22×C4×C61C22×C414yes—
155C22×C4×C61C2×D414yes—
156C22×C4×C61C2×D412yes—
157C22×C4×C61C2×D414yes—
158C22×C4×C61#4112yes—
159C22×C4×C61#4114yes—
160C2×C22⋊D61—28no—
161C2×C22⋊D61—28no—
162C2×C22⋊D61—216no—
163C2×C22⋊D61—216no—
164C2×C22⋊D61C42116yescomplemented
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—22no—
168C22×Dic61—22no—
169C22×Dic61—22no—
170C22×Dic61—22no—
171C22×Dic61—22no—
172C22×Dic61—22no—
173C22×Dic61—22no—
174C22×Dic61—22no—
175C22×Dic61—22no—
176C22×Dic61—22no—
177C22×Dic61—22no—
178C22×Dic61—21no—
179C22×Dic61—22no—
180C22×Dic61—22no—
181C22×Dic61—22no—
182C22×Dic61—22no—
183C22×Dic61—21no—
184C22×Dic61C22×C412yes—
185C22×Dic61C22×C414yes—
186C22×Dic61C22×C414yes—
187C22×Dic61C22×C412yes—
188C22×Dic61C22×C412yes—
189C22×Dic61C22×C414yes—
190C22×Dic61C2×D414yes—
191C22×Dic61C2×D414yes—
192C22×Dic61#4112yes—
193C22×Dic61#4112yes—
194C2×C4×D61—28no—
195C2×C4×D61—28no—
196C2×C4×D61—44no—
197C2×C4×D61—48no—
198C2×C4×D61—48no—
199C22⋊C4×C61—216no—
200C42×C61—48no—
201C22⋊Dic61—28no—
202C22⋊Dic61—48no—
203#11758198—28no—
204#11758198—216no—
205#11758198—48no—
206#11758196—216no—
207#11758196C22⋊C4116yescomplemented
208C4×Dic61—28no—
209C4×Dic61—216no—
210C4×Dic61—48no—
211C23×C61—22no—
212C23×C61—22no—
213C23×C61—24no—
214C23×C61—24no—
215C23×C61—24no—
216C23×C61—22no—
217C23×C61—22no—
218C23×C61—24no—
219C23×C61—24no—
220C23×C61—22no—
221C23×C61—22no—
222C23×C61—24no—
223C23×C61—42no—
224C23×C61—42no—
225C23×C61—41no—
226C23×C61—42no—
227C23×C61—42no—
228C23×C61—41no—
229C23×C61—42no—
230C23×C61—41no—
231C23×C61—41no—
232C23×C61—42no—
233C23×C61C2×C4214yes—
234C23×C61C23×C411yescharacteristic
235C23×C61C23×C412yes—
236C23×C61C22×D412yes—
237C23×C61C22×D411yescharacteristic
238C23×C61C2×#4111yescharacteristic
239C23×C61C2×#4111yescharacteristic
240C23×C61C2×#4111yescharacteristic
241C23×C61C2×#4112yes—
242C23×C61H(5,𝔽2)12yes—
243C23×C61H(5,𝔽2)11yescharacteristic
244C23×C612−1+411yescharacteristic
245C22×D61—22no—
246C22×D61—22no—
247C22×D61—24no—
248C22×D61—22no—
249C22×D61—24no—
250C22×D61—24no—
251C22×D61—22no—
252C22×D61—24no—
253C22×D61—24no—
254C22×D61—22no—
255C22×D61—22no—
256C22×D61—24no—
257C22×D61—42no—
258C22×D61—42no—
259C22×D61—41no—
260C22×D61—42no—
261C22×D61—42no—
262C22×D61—41no—
263C22×D61—42no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—42no—
267C22×D61C2×C4214yes—
268C2×C4×C61—22no—
269C2×C4×C61—24no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—24no—
274C2×C4×C61—24no—
275C2×C4×C61—24no—
276C2×C4×C61—24no—
277C2×C4×C61—24no—
278C2×C4×C61—24no—
279C2×C4×C61—24no—
280C2×C4×C61—24no—
281C2×C4×C61—24no—
282C2×C4×C61—24no—
283C2×C4×C61—24no—
284C2×C4×C61—24no—
285C2×C4×C61—416no—
286C2×C4×C61—42no—
287C2×C4×C61—42no—
288C2×C4×C61—42no—
289C2×C4×C61—42no—
290C2×C4×C61C2×C22⋊C414yes—
291C2×C4×C61C4×D414yes—
292C2×C4×C61C4×D418yescomplemented
293C22⋊D61—232no—
294C2×Dic61—22no—
295C2×Dic61—22no—
296C2×Dic61—24no—
297C2×Dic61—24no—
298C2×Dic61—22no—
299C2×Dic61—24no—
300C2×Dic61—24no—
301C2×Dic61—24no—
302C2×Dic61—22no—
303C2×Dic61—24no—
304C2×Dic61—24no—
305C2×Dic61—24no—
306C2×Dic61—22no—
307C2×Dic61—42no—
308C2×Dic61—42no—
309C2×Dic61—42no—
310C2×Dic61—42no—
311C2×Dic61—42no—
312C2×Dic61—42no—
313C2×Dic61—42no—
314C2×Dic61—42no—
315C2×Dic61—42no—
316C2×Dic61—42no—
317C2×Dic61C2×C4214yes—
318C2×Dic61C2×C22⋊C414yes—
319C2×Dic61C2×C22⋊C414yes—
320C2×Dic61#11714yes—
321C2×Dic61C4×D418yes—
322C2×Dic61C4×D418yes—
323C4×D61—416no—
324#13820—611nomaximal, Sylow
325C22×C61—24no—
326C22×C61—24no—
327C22×C61—24no—
328C22×C61—42no—
329C22×C61—42no—
330C22×C61—42no—
331C22×C61—42no—
332C22×C61—44no—
333C22×C61—44no—
334C22×C61—44no—
335C22×C61—44no—
336C22×C61C22×C4211yescharacteristic
337C22×C61C22×C22⋊C411yescharacteristic
338C22×C61C2×#11711yescharacteristic
339C22×C61C2×C4×D412yes—
340C22×C61C2×C4×D412yes—
341C22×C61C2×C4×D411yescharacteristic
342C22×C61C2×C4×D412yes—
343C22×C61C4×#4111yescharacteristic
344C22×C61C4×#4112yes—
345C22×C61#51812yes—
346C22×C61#51811yescharacteristic
347C22×C61#52012yes—
348C22×C61#52011yescharacteristic
349C22×C61D4212yes—
350C22×C61#54612yes—
351C22×C61#54711yescharacteristic
352C22×C61#54812yes—
353C22×C61#55011yescharacteristic
354C22×C61#55012yes—
355C22×C61#55312yes—
356C22×C61#55511yescharacteristic
357C22×C61#55611yescharacteristic
358C22×C61#55912yes—
359C2×D61—24no—
360C2×D61—24no—
361C2×D61—24no—
362C2×D61—42no—
363C2×D61—42no—
364C2×D61—42no—
365C2×D61—42no—
366C2×D61—44no—
367C2×D61—44no—
368C2×D61—44no—
369C2×D61—44no—
370C4×C61—24no—
371C4×C61—24no—
372C4×C61—28no—
373C4×C61—44no—
374Dic61—24no—
375Dic61—42no—
376Dic61—44no—
377Dic61—44no—
378Dic61C4×C22⋊C418yescomplemented
379C22×C4×D4—611no—
380C2×#390—612no—
381C2×C4×C4⋊C4—612no—
382C2×C4×C22⋊C4—611no—
383C2×C4×C22⋊C4D6111yescharacteristic, complemented
384#1437—612no—
385#1437—612no—
386C4⋊#95—611no—
387C22⋊#95—611no—
388C22⋊#95—611no—
389C4×#95—611no—
390C2×C61—44no—
391C2×C61C2×C4×C22⋊C411yescharacteristic
392C2×C61C42×D411yescharacteristic
393C2×C61#227511yescharacteristic
394C2×C61D4×C22⋊C411yescharacteristic
395C2×C61#234111yescharacteristic
396C2×C61#235411yescharacteristic
397C2×C61#235711yescharacteristic
398C2×C61#236112yes—
399C2×C61#236312yes—
400C2×C61#236612yes—
401C2×C61#236712yes—
402D61—44no—
403C23×D4—611no—
404C24×C4—611no—
405C24×C4C2×D6111yescharacteristic
406C2×C4×D4—618no—
407C2×C4×D4—1228no—
408C22×C4⋊C4—611no—
409C22×C4⋊C4—612no—
410C22×C22⋊C4—611no—
411C22×C22⋊C4—611no—
412C22×C22⋊C4—612no—
413C22×C22⋊C4—612no—
414C22×C22⋊C4—612no—
415C22×C22⋊C4C2×D6112yes—
416C22×C42—611no—
417C22×C42—612no—
418C22×C42—612no—
419C22×C42C2×D6112yes—
420#390—6116no—
421C4×C4⋊C4—1228no—
422C4×C22⋊C4—24no—
423C4×C22⋊C4—1224no—
424C2×#95—611no—
425C2×#95—612no—
426C2×#95—611no—
427C2×#95—612no—
428C2×#95—612no—
429C2×#95—612no—
430C2×#95C2×D6111yescharacteristic
431C2×#95C2×D6111yescharacteristic
432C61#1382011yescharacteristic, complemented, Sylow
433C25—611no—
434C25C22×D6111yescharacteristic
435C22×D4—614no—
436C22×D4—618no—
437C22×D4—1224no—
438C22×D4—1222no—
439C22×D4—1222no—
440C23×C4—22no—
441C23×C4—24no—
442C23×C4—22no—
443C23×C4—42no—
444C23×C4—611no—
445C23×C4—611no—
446C23×C4—612no—
447C23×C4—612no—
448C23×C4—611no—
449C23×C4—614no—
450C23×C4—1224no—
451C23×C4—1222no—
452C23×C4—1222no—
453C23×C4—2442no—
454C23×C4C4×D6114yes—
455C23×C4C22×D6112yes—
456C23×C4C22×D6112yes—
457C23×C4C22×D6111yescharacteristic
458C23×C4C22×D6111yescharacteristic
459C4×D4—12232no—
460C2×C4⋊C4—614no—
461C2×C4⋊C4—618no—
462C2×C4⋊C4—618no—
463C2×C4⋊C4—1224no—
464C2×C4⋊C4—1224no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—614no—
468C2×C22⋊C4—614no—
469C2×C22⋊C4—618no—
470C2×C22⋊C4—618no—
471C2×C22⋊C4—618no—
472C2×C22⋊C4—1224no—
473C2×C22⋊C4—1224no—
474C2×C22⋊C4—1224no—
475C2×C22⋊C4—1224no—
476C2×C22⋊C4—2442no—
477C2×C22⋊C4—2442no—
478C2×C22⋊C4—2442no—
479C2×C22⋊C4—2442no—
480C2×C22⋊C4C4×D6118yescomplemented
481C2×C42—24no—
482C2×C42—24no—
483C2×C42—42no—
484C2×C42—614no—
485C2×C42—618no—
486C2×C42—1224no—
487C2×C42—1224no—
488C2×C42—1224no—
489C2×C42—1224no—
490C2×C42—1224no—
491C2×C42—2442no—
492#95—22no—
493#95—1224no—
494#95—1222no—
495#95—1224no—
496#95—1224no—
497#95—1222no—
498#95—2442no—
499#95C22⋊D6114yescomplemented
500C24—22no—
501C24—21no—
502C24—21no—
503C24—21no—
504C24—22no—
505C24—21no—
506C24—22no—
507C24—21no—
508C24—21no—
509C24—614no—
510C24—612no—
511C24—1222no—
512C24—1221no—
513C24—1221no—
514C24—1221no—
515C24—1222no—
516C24—1221no—
517C24—1222no—
518C24—1221no—
519C24—1221no—
520C24C2×C4×D6114yes—
521C24C2×C4×D6112yes—
522C24C23×D6111yescharacteristic
523C2×D4—6116no—
524C2×D4—1228no—
525C2×D4—1228no—
526C2×D4—12216no—
527C2×D4—12216no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—28no—
544C22×C4—28no—
545C22×C4—44no—
546C22×C4—48no—
547C22×C4—48no—
548C22×C4—612no—
549C22×C4—614no—
550C22×C4—614no—
551C22×C4—612no—
552C22×C4—612no—
553C22×C4—612no—
554C22×C4—614no—
555C22×C4—612no—
556C22×C4—614no—
557C22×C4—614no—
558C22×C4—1228no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1222no—
562C22×C4—1222no—
563C22×C4—1222no—
564C22×C4—1222no—
565C22×C4—1222no—
566C22×C4—1222no—
567C22×C4—1222no—
568C22×C4—1222no—
569C22×C4—1222no—
570C22×C4—1222no—
571C22×C4—1222no—
572C22×C4—1222no—
573C22×C4—1222no—
574C22×C4—1221no—
575C22×C4—1222no—
576C22×C4—1222no—
577C22×C4—1221no—
578C22×C4—1228no—
579C22×C4—2444no—
580C22×C4—2448no—
581C22×C4—2448no—
582C22×C4C2×C4×D6114yes—
583C22×C4C2×C4×D6112yes—
584C22×C4C2×C4×D6112yes—
585C22×C4C2×C4×D6114yes—
586C22×C4#1175822212yes—
587C22×C4#1175822214yes—
588C22×C4D4×D6114yes—
589C22×C4C2×C22⋊D6112yes—
590C22×C4C2×C22⋊D6114yes—
591C4⋊C4—6116no—
592C4⋊C4—12216no—
593C22⋊C4—216no—
594C22⋊C4—1228no—
595C22⋊C4—1228no—
596C22⋊C4—12216no—
597C22⋊C4—2448no—
598C22⋊C4—2448no—
599C42—48no—
600C42—12216no—
601C42—1228no—
602C42—2448no—
603C23—22no—
604C23—22no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—22no—
609C23—22no—
610C23—24no—
611C23—24no—
612C23—22no—
613C23—24no—
614C23—22no—
615C23—42no—
616C23—41no—
617C23—41no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—41no—
622C23—42no—
623C23—41no—
624C23—42no—
625C23—614no—
626C23—1222no—
627C23—1222no—
628C23—1224no—
629C23—1224no—
630C23—1224no—
631C23—1222no—
632C23—1222no—
633C23—1224no—
634C23—1224no—
635C23—1222no—
636C23—1224no—
637C23—1222no—
638C23—2442no—
639C23—2441no—
640C23—2441no—
641C23—2442no—
642C23—2442no—
643C23—2442no—
644C23—2441no—
645C23—2442no—
646C23—2441no—
647C23—2442no—
648C23C42×D6114yes—
649C23C22×C4×D6111yescharacteristic
650C23C22×C4×D6112yes—
651C23C2×D4×D6112yes—
652C23C22×C22⋊D6111yescharacteristic
653C23#41×D6111yescharacteristic
654C23#41×D6111yescharacteristic
655C23C2×#1175822212yes—
656C23C2×#1175822211yescharacteristic
657C23#1451982212yes—
658C23#1451982311yescharacteristic
659C23#1451982411yescharacteristic
660D4—12232no—
661C2×C4—24no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—416no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—614no—
684C2×C4—614no—
685C2×C4—614no—
686C2×C4—618no—
687C2×C4—618no—
688C2×C4—614no—
689C2×C4—1222no—
690C2×C4—1222no—
691C2×C4—1224no—
692C2×C4—1224no—
693C2×C4—1222no—
694C2×C4—1224no—
695C2×C4—1224no—
696C2×C4—1224no—
697C2×C4—1224no—
698C2×C4—1222no—
699C2×C4—1224no—
700C2×C4—1224no—
701C2×C4—1222no—
702C2×C4—24416no—
703C2×C4—2442no—
704C2×C4—2442no—
705C2×C4—2442no—
706C2×C4—2442no—
707C2×C4—2442no—
708C2×C4—2442no—
709C2×C4—2442no—
710C2×C4—2442no—
711C2×C4—2442no—
712C2×C4—2442no—
713C2×C4C22⋊C4×D6114yes—
714C2×C4C4×C22⋊D6114yes—
715C2×C4C4×C22⋊D6118yescomplemented
716C22—24no—
717C22—24no—
718C22—24no—
719C22—42no—
720C22—42no—
721C22—44no—
722C22—44no—
723C22—44no—
724C22—44no—
725C22—42no—
726C22—42no—
727C22—1224no—
728C22—1224no—
729C22—1224no—
730C22—2442no—
731C22—2442no—
732C22—2444no—
733C22—2444no—
734C22—2444no—
735C22—2444no—
736C22—2442no—
737C22—2442no—
738C22C2×C42×D6111yescharacteristic
739C22C2×C22⋊C4×D6111yescharacteristic
740C22#117×D6111yescharacteristic
741C22C4×D4×D6112yes—
742C22C4×D4×D6112yes—
743C22C2×C4×C22⋊D6111yescharacteristic
744C22C2×C4×C22⋊D6112yes—
745C22C4×#1175822211yescharacteristic
746C22C4×#1175822212yes—
747C22#1684023412yes—
748C22#1684023511yescharacteristic
749C22#1684024112yes—
750C22#1684024211yescharacteristic
751C22D4×C22⋊D6112yes—
752C22#1684040212yes—
753C22#1684041111yescharacteristic
754C22#1684042112yes—
755C22#1684043111yescharacteristic
756C22#1684043312yes—
757C22#1684046112yes—
758C22#1684047511yescharacteristic
759C22#1684048011yescharacteristic
760C22#1684049512yes—
761C4—28no—
762C4—24no—
763C4—24no—
764C4—44no—
765C4—618no—
766C4—1224no—
767C4—2444no—
768C4—2444no—
769C4—2442no—
770C2—44no—
771C2—2444no—
772C2C4×C22⋊C4×D6111yescharacteristic
773C2C42×C22⋊D6111yescharacteristic
774C2#2144817811yescharacteristic
775C2C22⋊C4×C22⋊D6111yescharacteristic
776C2#2144865911yescharacteristic
777C2#2144876911yescharacteristic
778C2#2144879311yescharacteristic
779C2#2144883612yes—
780C2#2144885812yes—
781C2#2144888112yes—
782C2#2144889112yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC22×C61C22×C42
FittingC2×C4×C22⋊C4×C61C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC2×C4×C22⋊C4D61
hypocenterC61#13820
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×#11758196C2semidirect
4. C2×#16839609C2semidirect
5. #21444057C2semidirect
6. #21444056C2semidirect
7. #21444047C2semidirect
8. #21444042C2semidirect
9. #21444040C2semidirect
10. #95×Dic61C2semidirect
11. C2×C4×C22⋊C4×C61C2semidirect
15. C2×C4×C22⋊D61C4semidirect
26. #16839662C4semidirect
61. C2×#11758196C2×C4semidirect
67. C2×C22⋊Dic61C2×C4semidirect
74. C2×#11758198C2×C4semidirect
75. C2×#11758198C2×C4semidirect
83. C2×C4×Dic61C2×C4semidirect
102. C2×C22⋊C4×C61C2×C4semidirect
107. #95×C61D4semidirect
164. C2×C22⋊D61C42semidirect
207. #11758196C22⋊C4semidirect
292. C2×C4×C61C4×D4semidirect
378. Dic61C4×C22⋊C4semidirect
383. C2×C4×C22⋊C4D61semidirect
432. C61#13820semidirect
480. C2×C22⋊C4C4×D61semidirect
499. #95C22⋊D61semidirect
715. C2×C4C4×C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D612
C2×#168396622
C2×C4×#117581962
C2×#168396092
#214440572
#214440562
#214440472
#214440422
#214440402
#95×Dic612
C2×C4×C22⋊C4×C612
#1382061