Finite Group Databasebeta

← #29601316

Subgroups — #29601316

Order 15616.

2470 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D61C211yesmaximal, characteristic
2C2×#16839662C212yesmaximal
3C2×#16839613C211yesmaximal, characteristic, complemented
4C2×#16839607C211yesmaximal, characteristic, complemented
5#21444056C212yesmaximal, complemented
6#21444055C212yesmaximal, complemented
7#21444047C212yesmaximal, complemented
8#21444042C211yesmaximal, characteristic, complemented
9#21444040C211yesmaximal, characteristic, complemented
10#21444040C211yesmaximal, characteristic, complemented
11C61×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C22⋊D61C2211yescharacteristic
13C23×C4×D61C2211yescharacteristic
14C2×C4×C22⋊D61—24no—
15C2×C4×C22⋊D61—24no—
16C2×C4×C22⋊D61C418yescomplemented
17C22×#11758196C2211yescharacteristic
18C22×#11758196C2212yes—
19C22×C22⋊Dic61C2211yescharacteristic
20C22×C22⋊Dic61C2212yes—
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2212yes—
23C22×#11758198C2212yes—
24C22×C4×Dic61C2212yes—
25C22×C4×Dic61C2212yes—
26C22×C4×Dic61C2211yescharacteristic
27#16839662C4116yescomplemented
28#16839613—24no—
29#16839607—24no—
30C2×#14519684C2211yescharacteristic
31C2×#14519684C2211yescharacteristic
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35C2×#14519684C2212yes—
36C24×C4×C61C2211yescharacteristic
37C22×C22⋊C4×C61C2212yes—
38C2×#95×C61C2211yescharacteristic
39C2×#95×C61C2211yescharacteristic
40C2×#95×C61C2212yes—
41C24×D61C2311yescharacteristic
42C22×C22⋊D61—22no—
43C22×C22⋊D61—22no—
44C22×C22⋊D61—24no—
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—42no—
55C22×C4×D61—42no—
56C22×C4×D61C2×C414yes—
57C4×C22⋊D61—232no—
58C2×#11758196—22no—
59C2×#11758196—22no—
60C2×#11758196—24no—
61C2×#11758196—24no—
62C2×#11758196C2×C414yes—
63C2×#11758196C2×C418yescomplemented
64C2×C22⋊Dic61—22no—
65C2×C22⋊Dic61—22no—
66C2×C22⋊Dic61—42no—
67C2×C22⋊Dic61—42no—
68C2×C22⋊Dic61C2×C414yes—
69C2×C22⋊Dic61C2×C418yescomplemented
70C2×#11758198—22no—
71C2×#11758198—22no—
72C2×#11758198—42no—
73C2×#11758198—42no—
74C2×#11758198—42no—
75C2×#11758198—42no—
76C2×#11758198C2×C414yes—
77C2×#11758198C2×C418yescomplemented
78C2×#11758198C2×C418yescomplemented
79C2×C4×Dic61—24no—
80C2×C4×Dic61—24no—
81C2×C4×Dic61—24no—
82C2×C4×Dic61—42no—
83C2×C4×Dic61—42no—
84C2×C4×Dic61C2×C414yes—
85C2×C4×Dic61C2×C418yescomplemented
86C2×C4×Dic61D414yes—
87C2×C4×Dic61D414yes—
88#14519684—22no—
89#14519684—22no—
90#14519684—24no—
91#14519684—42no—
92#14519684—42no—
93#14519684—42no—
94C25×C61C2311yescharacteristic
95C23×C4×C61—22no—
96C23×C4×C61—22no—
97C23×C4×C61—42no—
98C23×C4×C61—42no—
99C23×C4×C61C2×C414yes—
100C23×C4×C61C2312yes—
101C23×C4×C61C2312yes—
102C23×C4×C61C2311yescharacteristic
103C23×C4×C61C2311yescharacteristic
104C2×C22⋊C4×C61—42no—
105C2×C22⋊C4×C61—42no—
106C2×C22⋊C4×C61C2×C418yescomplemented
107#95×C61—22no—
108#95×C61—22no—
109#95×C61—42no—
110C24×C61—21no—
111C24×C61—21no—
112C24×C61—22no—
113C24×C61—21no—
114C24×C61—22no—
115C24×C61—22no—
116C24×C61—21no—
117C24×C61—21no—
118C24×C61—21no—
119C24×C61C22×C414yes—
120C24×C61C22×C412yes—
121C24×C61C2411yescharacteristic
122C23×D61—21no—
123C23×D61—21no—
124C23×D61—22no—
125C23×D61—22no—
126C23×D61—22no—
127C23×D61—21no—
128C23×D61—21no—
129C23×D61—21no—
130C23×D61—21no—
131C23×D61C22×C412yes—
132C23×D61C22×C414yes—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61—22no—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
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—22no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—28no—
152C22×C4×C61—44no—
153C22×C4×C61—44no—
154C22×C4×C61—48no—
155C22×C4×C61—48no—
156C22×C4×C61C22×C414yes—
157C22×C4×C61C22×C414yes—
158C22×C4×C61C22×C412yes—
159C22×C4×C61C22×C412yes—
160C22×C4×C61C2×D412yes—
161C22×C4×C61C2×D412yes—
162C2×C22⋊D61—28no—
163C2×C22⋊D61—28no—
164C2×C22⋊D61—216no—
165C2×C22⋊D61—216no—
166C2×C22⋊D61C42116yescomplemented
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61—22no—
174C22×Dic61—22no—
175C22×Dic61—22no—
176C22×Dic61—22no—
177C22×Dic61—22no—
178C22×Dic61—22no—
179C22×Dic61—22no—
180C22×Dic61—22no—
181C22×Dic61—22no—
182C22×Dic61—22no—
183C22×Dic61—22no—
184C22×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61C22×C412yes—
188C22×Dic61C22×C414yes—
189C22×Dic61C22×C414yes—
190C22×Dic61C22×C412yes—
191C22×Dic61C22×C412yes—
192C22×Dic61C22×C414yes—
193C22×Dic61C2×D412yes—
194C22×Dic61C2×D412yes—
195C22×Dic61C2×D412yes—
196C22×Dic61C2×D412yes—
197C22×Dic61#4114yes—
198C2×C4×D61—28no—
199C2×C4×D61—44no—
200C2×C4×D61—44no—
201C2×C4×D61—48no—
202C2×C4×D61—48no—
203C22⋊C4×C61—48no—
204C22⋊Dic61—28no—
205C22⋊Dic61—48no—
206#11758198—28no—
207#11758198—48no—
208#11758198—48no—
209#11758196—28no—
210#11758196—216no—
211C4×Dic61—216no—
212C4×Dic61—48no—
213C4×Dic61C22⋊C4116yescomplemented
214C23×C61—22no—
215C23×C61—22no—
216C23×C61—24no—
217C23×C61—24no—
218C23×C61—24no—
219C23×C61—24no—
220C23×C61—22no—
221C23×C61—22no—
222C23×C61—22no—
223C23×C61—22no—
224C23×C61—24no—
225C23×C61—24no—
226C23×C61—42no—
227C23×C61—42no—
228C23×C61—41no—
229C23×C61—41no—
230C23×C61—41no—
231C23×C61—41no—
232C23×C61—42no—
233C23×C61—42no—
234C23×C61—42no—
235C23×C61—42no—
236C23×C61C2×C4214yes—
237C23×C61C23×C411yescharacteristic
238C23×C61C23×C412yes—
239C23×C61C22×D411yescharacteristic
240C23×C61C22×D411yescharacteristic
241C23×C61C2×#4112yes—
242C23×C61H(5,𝔽2)12yes—
243C23×C61H(5,𝔽2)12yes—
244C23×C61H(5,𝔽2)11yescharacteristic
245C23×C61H(5,𝔽2)11yescharacteristic
246C23×C612−1+411yescharacteristic
247C23×C612−1+411yescharacteristic
248C22×D61—22no—
249C22×D61—22no—
250C22×D61—24no—
251C22×D61—24no—
252C22×D61—24no—
253C22×D61—24no—
254C22×D61—22no—
255C22×D61—22no—
256C22×D61—22no—
257C22×D61—22no—
258C22×D61—24no—
259C22×D61—24no—
260C22×D61—42no—
261C22×D61—42no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—42no—
267C22×D61—42no—
268C22×D61—42no—
269C22×D61—42no—
270C22×D61C2×C4214yes—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—24no—
274C2×C4×C61—24no—
275C2×C4×C61—22no—
276C2×C4×C61—24no—
277C2×C4×C61—24no—
278C2×C4×C61—24no—
279C2×C4×C61—24no—
280C2×C4×C61—24no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—24no—
284C2×C4×C61—416no—
285C2×C4×C61—42no—
286C2×C4×C61—42no—
287C2×C4×C61—42no—
288C2×C4×C61—42no—
289C2×C4×C61—42no—
290C2×C4×C61—42no—
291C2×C4×C61—42no—
292C2×C4×C61—42no—
293C2×C4×C61—42no—
294C2×C4×C61—42no—
295C2×C4×C61C2×C22⋊C414yes—
296C22⋊D61—232no—
297C2×Dic61—22no—
298C2×Dic61—22no—
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61—22no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—24no—
305C2×Dic61—24no—
306C2×Dic61—24no—
307C2×Dic61—24no—
308C2×Dic61—24no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—24no—
312C2×Dic61—42no—
313C2×Dic61—42no—
314C2×Dic61—42no—
315C2×Dic61—42no—
316C2×Dic61—42no—
317C2×Dic61—42no—
318C2×Dic61—42no—
319C2×Dic61—42no—
320C2×Dic61—42no—
321C2×Dic61—42no—
322C2×Dic61C2×C4214yes—
323C2×Dic61C2×C22⋊C414yes—
324C2×Dic61C2×C22⋊C414yes—
325C2×Dic61#11714yes—
326C2×Dic61C4×D418yes—
327C2×Dic61C4×D418yes—
328C4×D61—416no—
329#13785—611nomaximal, Sylow
330C22×C61—24no—
331C22×C61—24no—
332C22×C61—24no—
333C22×C61—42no—
334C22×C61—42no—
335C22×C61—42no—
336C22×C61—42no—
337C22×C61—44no—
338C22×C61—44no—
339C22×C61—44no—
340C22×C61—44no—
341C22×C61C22×C4211yescharacteristic
342C22×C61C22×C22⋊C411yescharacteristic
343C22×C61C2×#11711yescharacteristic
344C22×C61C2×C4×D412yes—
345C22×C61C2×C4×D412yes—
346C22×C61#51812yes—
347C22×C61#51811yescharacteristic
348C22×C61#51811yescharacteristic
349C22×C61#51812yes—
350C22×C61#52012yes—
351C22×C61#52011yescharacteristic
352C22×C61#52011yescharacteristic
353C22×C61#52012yes—
354C22×C61#53512yes—
355C22×C61#53512yes—
356C22×C61#53511yescharacteristic
357C22×C61#53611yescharacteristic
358C22×C61#53711yescharacteristic
359C22×C61#53711yescharacteristic
360C22×C61#54012yes—
361C22×C61#54012yes—
362C22×C61#54212yes—
363C22×C61#54212yes—
364C2×D61—24no—
365C2×D61—24no—
366C2×D61—24no—
367C2×D61—42no—
368C2×D61—42no—
369C2×D61—42no—
370C2×D61—42no—
371C2×D61—44no—
372C2×D61—44no—
373C2×D61—44no—
374C2×D61—44no—
375C4×C61—24no—
376C4×C61—42no—
377C4×C61—44no—
378C4×C61—44no—
379Dic61—24no—
380Dic61—42no—
381Dic61—44no—
382Dic61—44no—
383Dic61C4×C22⋊C418yes—
384C22×C4×D4—611no—
385C2×#390—612no—
386C2×C4×C4⋊C4—611no—
387C2×#376—611no—
388#1437—612no—
389#1437—612no—
390C4⋊#95—612no—
391C22⋊#95—611no—
392C22⋊#95—611no—
393C22⋊#95—611no—
394C22⋊#95D6111yescharacteristic, complemented
395C2×C61—44no—
396C2×C61C2×C4×C22⋊C411yescharacteristic
397C2×C61#227511yescharacteristic
398C2×C61#227511yescharacteristic
399C2×C61#230911yescharacteristic
400C2×C61#231111yescharacteristic
401C2×C61#231911yescharacteristic
402C2×C61#231911yescharacteristic
403C2×C61#232412yes—
404C2×C61#232412yes—
405C2×C61#232612yes—
406C2×C61#232812yes—
407D61—44no—
408C23×D4—611no—
409C24×C4—611no—
410C24×C4C2×D6111yescharacteristic
411C2×C4×D4—618no—
412C2×C4×D4—1224no—
413C2×C4×D4—1224no—
414C22×C4⋊C4—611no—
415C22×C4⋊C4—612no—
416C22×C22⋊C4—611no—
417C22×C22⋊C4—611no—
418C22×C22⋊C4—612no—
419C22×C22⋊C4—612no—
420C22×C22⋊C4—612no—
421C22×C22⋊C4C2×D6112yes—
422C22×C42—611no—
423C22×C42—612no—
424C22×C42—612no—
425#390—6116no—
426C4×C4⋊C4—1224no—
427#376—1224no—
428C2×#95—611no—
429C2×#95—611no—
430C2×#95—612no—
431C2×#95—612no—
432C2×#95—612no—
433C2×#95—612no—
434C2×#95C2×D6111yescharacteristic
435C2×#95C2×D6111yescharacteristic
436C2×#95C2×D6112yes—
437C61#1378511yescharacteristic, complemented, Sylow
438C25—611no—
439C25C22×D6111yescharacteristic
440C22×D4—614no—
441C22×D4—618no—
442C22×D4—1222no—
443C22×D4—1222no—
444C22×D4—1224no—
445C23×C4—22no—
446C23×C4—22no—
447C23×C4—42no—
448C23×C4—42no—
449C23×C4—611no—
450C23×C4—611no—
451C23×C4—612no—
452C23×C4—612no—
453C23×C4—611no—
454C23×C4—614no—
455C23×C4—1222no—
456C23×C4—1222no—
457C23×C4—2442no—
458C23×C4—2442no—
459C23×C4C4×D6114yes—
460C23×C4C22×D6112yes—
461C23×C4C22×D6112yes—
462C23×C4C22×D6111yescharacteristic
463C23×C4C22×D6111yescharacteristic
464C4×D4—12232no—
465C2×C4⋊C4—614no—
466C2×C4⋊C4—618no—
467C2×C4⋊C4—1222no—
468C2×C4⋊C4—1222no—
469C2×C4⋊C4—1224no—
470C2×C4⋊C4—1224no—
471C2×C22⋊C4—42no—
472C2×C22⋊C4—42no—
473C2×C22⋊C4—614no—
474C2×C22⋊C4—614no—
475C2×C22⋊C4—618no—
476C2×C22⋊C4—618no—
477C2×C22⋊C4—618no—
478C2×C22⋊C4—1222no—
479C2×C22⋊C4—1222no—
480C2×C22⋊C4—1222no—
481C2×C22⋊C4—1222no—
482C2×C22⋊C4—2442no—
483C2×C22⋊C4—2442no—
484C2×C22⋊C4—2442no—
485C2×C22⋊C4—2442no—
486C2×C22⋊C4—2442no—
487C2×C22⋊C4—2442no—
488C2×C22⋊C4C4×D6118yescomplemented
489C2×C42—614no—
490C2×C42—614no—
491C2×C42—614no—
492C2×C42—618no—
493C2×C42—1224no—
494C2×C42—1224no—
495C2×C42—1224no—
496C2×C42—2442no—
497C2×C42—2442no—
498#95—22no—
499#95—22no—
500#95—42no—
501#95—1224no—
502#95—1222no—
503#95—1222no—
504#95—2442no—
505#95—2442no—
506#95—2442no—
507C24—21no—
508C24—21no—
509C24—22no—
510C24—21no—
511C24—22no—
512C24—22no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—614no—
517C24—612no—
518C24—1221no—
519C24—1221no—
520C24—1222no—
521C24—1221no—
522C24—1222no—
523C24—1222no—
524C24—1221no—
525C24—1221no—
526C24—1221no—
527C24C2×C4×D6114yes—
528C24C2×C4×D6112yes—
529C24C23×D6111yescharacteristic
530C2×D4—6116no—
531C2×D4—1228no—
532C2×D4—1228no—
533C2×D4—12216no—
534C2×D4—12216no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—28no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—612no—
559C22×C4—614no—
560C22×C4—612no—
561C22×C4—612no—
562C22×C4—614no—
563C22×C4—612no—
564C22×C4—612no—
565C22×C4—612no—
566C22×C4—614no—
567C22×C4—614no—
568C22×C4—612no—
569C22×C4—1221no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4—1222no—
574C22×C4—1222no—
575C22×C4—1221no—
576C22×C4—1221no—
577C22×C4—1222no—
578C22×C4—1222no—
579C22×C4—1222no—
580C22×C4—1222no—
581C22×C4—1222no—
582C22×C4—1222no—
583C22×C4—1222no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—1222no—
587C22×C4—1222no—
588C22×C4—1222no—
589C22×C4—1228no—
590C22×C4—2444no—
591C22×C4—2444no—
592C22×C4—2448no—
593C22×C4—2448no—
594C22×C4C2×C4×D6114yes—
595C22×C4C2×C4×D6114yes—
596C22×C4C2×C4×D6112yes—
597C22×C4C2×C4×D6112yes—
598C22×C4D4×D6112yes—
599C22×C4D4×D6112yes—
600C4⋊C4—12216no—
601C4⋊C4—1228no—
602C22⋊C4—48no—
603C22⋊C4—1228no—
604C22⋊C4—1228no—
605C22⋊C4—2448no—
606C22⋊C4—2448no—
607C22⋊C4—2448no—
608C42—6116no—
609C42—12216no—
610C42—2448no—
611C23—22no—
612C23—22no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—22no—
618C23—22no—
619C23—24no—
620C23—22no—
621C23—22no—
622C23—24no—
623C23—42no—
624C23—42no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—614no—
634C23—1222no—
635C23—1222no—
636C23—1224no—
637C23—1224no—
638C23—1224no—
639C23—1224no—
640C23—1222no—
641C23—1222no—
642C23—1224no—
643C23—1222no—
644C23—1222no—
645C23—1224no—
646C23—2442no—
647C23—2442no—
648C23—2441no—
649C23—2441no—
650C23—2441no—
651C23—2441no—
652C23—2442no—
653C23—2442no—
654C23—2442no—
655C23—2442no—
656C23C42×D6114yes—
657C23C22×C4×D6111yescharacteristic
658C23C22×C4×D6112yes—
659C23C2×D4×D6111yescharacteristic
660C23C2×D4×D6111yescharacteristic
661C23#41×D6112yes—
662C23#1451982212yes—
663C23#1451982212yes—
664C23#1451982211yescharacteristic
665C23#1451982311yescharacteristic
666C23#1451982411yescharacteristic
667C23#1451982511yescharacteristic
668D4—12232no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—416no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—614no—
694C2×C4—614no—
695C2×C4—614no—
696C2×C4—618no—
697C2×C4—618no—
698C2×C4—614no—
699C2×C4—1222no—
700C2×C4—1222no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—1222no—
704C2×C4—1222no—
705C2×C4—1222no—
706C2×C4—1224no—
707C2×C4—1224no—
708C2×C4—1224no—
709C2×C4—1224no—
710C2×C4—1224no—
711C2×C4—1222no—
712C2×C4—1222no—
713C2×C4—1224no—
714C2×C4—24416no—
715C2×C4—2442no—
716C2×C4—2442no—
717C2×C4—2442no—
718C2×C4—2442no—
719C2×C4—2442no—
720C2×C4—2442no—
721C2×C4—2442no—
722C2×C4—2442no—
723C2×C4—2442no—
724C2×C4—2442no—
725C2×C4C22⋊C4×D6114yes—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—42no—
730C22—42no—
731C22—44no—
732C22—44no—
733C22—44no—
734C22—44no—
735C22—42no—
736C22—42no—
737C22—1224no—
738C22—1224no—
739C22—1224no—
740C22—2442no—
741C22—2442no—
742C22—2444no—
743C22—2444no—
744C22—2444no—
745C22—2444no—
746C22—2442no—
747C22—2442no—
748C22C2×C42×D6111yescharacteristic
749C22C2×C22⋊C4×D6111yescharacteristic
750C22#117×D6111yescharacteristic
751C22C4×D4×D6112yes—
752C22C4×D4×D6112yes—
753C22#1684023412yes—
754C22#1684023511yescharacteristic
755C22#1684023511yescharacteristic
756C22#1684023512yes—
757C22#1684024112yes—
758C22#1684024211yescharacteristic
759C22#1684024311yescharacteristic
760C22#1684024312yes—
761C22#1684032712yes—
762C22#1684032712yes—
763C22#1684032811yescharacteristic
764C22#1684033511yescharacteristic
765C22#1684034111yescharacteristic
766C22#1684034211yescharacteristic
767C22#1684036212yes—
768C22#1684036412yes—
769C22#1684038012yes—
770C22#1684038212yes—
771C4—24no—
772C4—44no—
773C4—44no—
774C4—42no—
775C4—618no—
776C4—1224no—
777C4—2444no—
778C4—2444no—
779C4—2442no—
780C2—44no—
781C2—2444no—
782C2C4×C22⋊C4×D6111yescharacteristic
783C2#2144817711yescharacteristic
784C2#2144817811yescharacteristic
785C2#2144840011yescharacteristic
786C2#2144840811yescharacteristic
787C2#2144845911yescharacteristic
788C2#2144846111yescharacteristic
789C2#2144850912yes—
790C2#2144851112yes—
791C2#2144852512yes—
792C2#2144854012yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC22×C61C22×C42
FittingC61×C22⋊#95C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC22⋊#95D61
hypocenterC61#13785
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#16839613C2semidirect
4. C2×#16839607C2semidirect
5. #21444056C2semidirect
6. #21444055C2semidirect
7. #21444047C2semidirect
8. #21444042C2semidirect
9. #21444040C2semidirect
10. #21444040C2semidirect
11. C61×C22⋊#95C2semidirect
16. C2×C4×C22⋊D61C4semidirect
27. #16839662C4semidirect
63. C2×#11758196C2×C4semidirect
69. C2×C22⋊Dic61C2×C4semidirect
77. C2×#11758198C2×C4semidirect
78. C2×#11758198C2×C4semidirect
85. C2×C4×Dic61C2×C4semidirect
106. C2×C22⋊C4×C61C2×C4semidirect
166. C2×C22⋊D61C42semidirect
213. C4×Dic61C22⋊C4semidirect
394. C22⋊#95D61semidirect
437. C61#13785semidirect
488. C2×C22⋊C4C4×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×#168396132
C2×#168396072
#214440562
#214440552
#214440472
#214440422
#214440402
C61×C22⋊#952
#1378561