Finite Group Databasebeta

← #29601307

Subgroups — #29601307

Order 15616.

2686 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D61C211yesmaximal, characteristic
2C2×#16839638C212yesmaximal
3C2×#16839609C211yesmaximal, characteristic, complemented
4C2×#95×D61C211yesmaximal, characteristic, complemented
5#21444056C212yesmaximal, complemented
6#21444050C212yesmaximal, complemented
7#21444043C211yesmaximal, characteristic, complemented
8#21444043C211yesmaximal, characteristic, complemented
9#21444042C211yesmaximal, characteristic, complemented
10#21444040C212yesmaximal, complemented
11C61×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×C22⋊D61C2211yescharacteristic
13C23×C4×D61C2212yes—
14C23×C4×D61C2211yescharacteristic
15C2×C4×C22⋊D61—24no—
16C2×C4×C22⋊D61—24no—
17C2×C4×C22⋊D61C418yescomplemented
18C22×#11758196C2211yescharacteristic
19C22×C22⋊Dic61C2211yescharacteristic
20C22×C22⋊Dic61C2212yes—
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2212yes—
23C22×C4×Dic61C2211yescharacteristic
24C22×C4×Dic61C2212yes—
25#16839638C4116yescomplemented
26#16839609—24no—
27C2×#14519684C2211yescharacteristic
28C2×#14519684C2211yescharacteristic
29C2×#14519684C2212yes—
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35#95×D61—24no—
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×Dic61C2311yescharacteristic
49C23×Dic61C2312yes—
50C23×Dic61C2311yescharacteristic
51C23×Dic61C2311yescharacteristic
52C22×C4×D61—24no—
53C22×C4×D61—24no—
54C22×C4×D61—42no—
55C22×C4×D61—42no—
56C22×C4×D61—42no—
57C22×C4×D61—42no—
58C22×C4×D61—42no—
59C22×C4×D61—42no—
60C22×C4×D61C2×C414yes—
61C22×C4×D61C2×C418yescomplemented
62C22×C4×D61D414yes—
63C22×C4×D61D414yes—
64C4×C22⋊D61—232no—
65C2×#11758196—22no—
66C2×#11758196—22no—
67C2×#11758196C2×C414yescomplemented
68C2×C22⋊Dic61—22no—
69C2×C22⋊Dic61—22no—
70C2×C22⋊Dic61—42no—
71C2×C22⋊Dic61—42no—
72C2×C22⋊Dic61C2×C414yescomplemented
73C2×C22⋊Dic61C2×C418yescomplemented
74C2×#11758198—22no—
75C2×#11758198—22no—
76C2×#11758198—24no—
77C2×#11758198—24no—
78C2×#11758198C2×C414yes—
79C2×#11758198C2×C418yescomplemented
80C2×C4×Dic61—22no—
81C2×C4×Dic61—22no—
82C2×C4×Dic61—24no—
83C2×C4×Dic61—42no—
84C2×C4×Dic61—42no—
85C2×C4×Dic61C2×C414yescomplemented
86#14519684—22no—
87#14519684—22no—
88#14519684—24no—
89#14519684—42no—
90#14519684—42no—
91#14519684—42no—
92#14519684C2×C418yescomplemented
93#14519684C2×C418yescomplemented
94C25×C61C2311yescharacteristic
95C23×C4×C61—22no—
96C23×C4×C61—22no—
97C23×C4×C61—42no—
98C23×C4×C61—42no—
99C23×C4×C61C2×C414yescomplemented
100C23×C4×C61C2312yes—
101C23×C4×C61C2311yescharacteristic
102C23×C4×C61C2312yes—
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—22no—
123C23×D61—22no—
124C23×D61—21no—
125C23×D61—21no—
126C23×D61—21no—
127C23×D61—21no—
128C23×D61C22×C412yes—
129C23×D61C22×C414yes—
130C23×D61C2×D412yes—
131C23×D61C2×D412yes—
132C23×D61#4114yes—
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—22no—
170C22×Dic61—22no—
171C22×Dic61—22no—
172C22×Dic61—22no—
173C22×Dic61—22no—
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—22no—
177C22×Dic61—22no—
178C22×Dic61—22no—
179C22×Dic61—22no—
180C22×Dic61—22no—
181C22×Dic61—22no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61—22no—
190C22×Dic61C22×C414yes—
191C22×Dic61C22×C414yes—
192C22×Dic61C22×C412yes—
193C22×Dic61C22×C414yes—
194C22×Dic61C22×C412yes—
195C22×Dic61C22×C412yes—
196C22×Dic61C2×D412yes—
197C22×Dic61C2×D412yes—
198C2×C4×D61—216no—
199C2×C4×D61—44no—
200C2×C4×D61—44no—
201C2×C4×D61—48no—
202C2×C4×D61—48no—
203C2×C4×D61—48no—
204C2×C4×D61—48no—
205C2×C4×D61—48no—
206C2×C4×D61—48no—
207C2×C4×D61—48no—
208C2×C4×D61—48no—
209C2×C4×D61C22⋊C4116yescomplemented
210C22⋊C4×C61—48no—
211C22⋊Dic61—28no—
212C22⋊Dic61—48no—
213#11758198—28no—
214#11758198—216no—
215#11758196—28no—
216C4×Dic61—28no—
217C4×Dic61—48no—
218C23×C61—22no—
219C23×C61—22no—
220C23×C61—24no—
221C23×C61—24no—
222C23×C61—24no—
223C23×C61—24no—
224C23×C61—22no—
225C23×C61—22no—
226C23×C61—22no—
227C23×C61—22no—
228C23×C61—24no—
229C23×C61—24no—
230C23×C61—42no—
231C23×C61—42no—
232C23×C61—41no—
233C23×C61—41no—
234C23×C61—41no—
235C23×C61—41no—
236C23×C61—42no—
237C23×C61—42no—
238C23×C61—42no—
239C23×C61—42no—
240C23×C61C2×C4214yes—
241C23×C61C23×C411yescharacteristic
242C23×C61C23×C412yes—
243C23×C61C22×D411yescharacteristic
244C23×C61C22×D411yescharacteristic
245C23×C61C2×#4112yes—
246C23×C61H(5,𝔽2)12yes—
247C23×C61H(5,𝔽2)12yes—
248C23×C61H(5,𝔽2)11yescharacteristic
249C23×C61H(5,𝔽2)11yescharacteristic
250C23×C612−1+411yescharacteristic
251C23×C612−1+411yescharacteristic
252C22×D61—22no—
253C22×D61—22no—
254C22×D61—24no—
255C22×D61—24no—
256C22×D61—22no—
257C22×D61—22no—
258C22×D61—24no—
259C22×D61—24no—
260C22×D61—24no—
261C22×D61—24no—
262C22×D61—22no—
263C22×D61—22no—
264C22×D61—22no—
265C22×D61—22no—
266C22×D61—24no—
267C22×D61—24no—
268C22×D61—24no—
269C22×D61—24no—
270C22×D61C2×C4214yes—
271C22×D61C2×C22⋊C414yes—
272C22×D61#11714yes—
273C22×D61C4×D418yes—
274C22×D61C4×D418yes—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—24no—
278C2×C4×C61—24no—
279C2×C4×C61—22no—
280C2×C4×C61—24no—
281C2×C4×C61—24no—
282C2×C4×C61—24no—
283C2×C4×C61—24no—
284C2×C4×C61—24no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—24no—
288C2×C4×C61—416no—
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×C61—42no—
296C2×C4×C61—42no—
297C2×C4×C61—42no—
298C2×C4×C61—42no—
299C2×C4×C61C2×C22⋊C414yes—
300C22⋊D61—232no—
301C2×Dic61—22no—
302C2×Dic61—22no—
303C2×Dic61—24no—
304C2×Dic61—24no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—24no—
308C2×Dic61—24no—
309C2×Dic61—22no—
310C2×Dic61—24no—
311C2×Dic61—24no—
312C2×Dic61—24no—
313C2×Dic61—24no—
314C2×Dic61—24no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—24no—
318C2×Dic61—42no—
319C2×Dic61—42no—
320C2×Dic61—42no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—42no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61—42no—
330C2×Dic61C2×C4214yes—
331C2×Dic61C2×C22⋊C414yes—
332C4×D61—416no—
333C4×D61—432no—
334#13784—611nomaximal, Sylow
335C22×C61—24no—
336C22×C61—24no—
337C22×C61—24no—
338C22×C61—42no—
339C22×C61—42no—
340C22×C61—42no—
341C22×C61—42no—
342C22×C61—44no—
343C22×C61—44no—
344C22×C61—44no—
345C22×C61—44no—
346C22×C61C22×C4211yescharacteristic
347C22×C61C22×C22⋊C411yescharacteristic
348C22×C61C2×#11711yescharacteristic
349C22×C61C2×C4×D412yes—
350C22×C61C2×C4×D412yes—
351C22×C61#51812yes—
352C22×C61#51811yescharacteristic
353C22×C61#51811yescharacteristic
354C22×C61#51812yes—
355C22×C61#52012yes—
356C22×C61#52011yescharacteristic
357C22×C61#52011yescharacteristic
358C22×C61#52012yes—
359C22×C61#53412yes—
360C22×C61#53412yes—
361C22×C61#53511yescharacteristic
362C22×C61#53611yescharacteristic
363C22×C61#53711yescharacteristic
364C22×C61#53711yescharacteristic
365C22×C61#53812yes—
366C22×C61#53812yes—
367C22×C61#53912yes—
368C22×C61#53912yes—
369C2×D61—24no—
370C2×D61—24no—
371C2×D61—24no—
372C2×D61—24no—
373C2×D61—28no—
374C2×D61—28no—
375C2×D61—28no—
376C2×D61—28no—
377C2×D61—24no—
378C2×D61—24no—
379C2×D61C4×C22⋊C418yes—
380C4×C61—24no—
381C4×C61—42no—
382C4×C61—44no—
383C4×C61—44no—
384Dic61—24no—
385Dic61—24no—
386Dic61—42no—
387Dic61—44no—
388Dic61—44no—
389C22×C4×D4—611no—
390C2×#386—612no—
391C2×C4×C22⋊C4—611no—
392C22×#95—611no—
393#1437—612no—
394#1436—612no—
395#1434—611no—
396#1434—611no—
397C22⋊#95—612no—
398C22⋊#95—611no—
399C22⋊#95D6111yescharacteristic, complemented
400C2×C61—44no—
401C2×C61C2×C4×C22⋊C411yescharacteristic
402C2×C61#227511yescharacteristic
403C2×C61#227511yescharacteristic
404C2×C61#230811yescharacteristic
405C2×C61#231111yescharacteristic
406C2×C61#231811yescharacteristic
407C2×C61#231811yescharacteristic
408C2×C61#232112yes—
409C2×C61#232212yes—
410C2×C61#232512yes—
411C2×C61#232512yes—
412D61—28no—
413C23×D4—611no—
414C24×C4—611no—
415C24×C4—612no—
416C24×C4C2×D6111yescharacteristic
417C2×C4×D4—618no—
418C2×C4×D4—1224no—
419C2×C4×D4—1224no—
420C22×C4⋊C4—611no—
421C22×C22⋊C4—611no—
422C22×C22⋊C4—611no—
423C22×C22⋊C4—612no—
424C22×C22⋊C4—612no—
425C22×C22⋊C4C2×D6112yes—
426C22×C42—611no—
427C22×C42—612no—
428#386—6116no—
429C4×C22⋊C4—1224no—
430C2×#95—612no—
431C2×#95—612no—
432C2×#95—611no—
433C2×#95—611no—
434C2×#95—612no—
435C2×#95—612no—
436C2×#95—612no—
437C2×#95—612no—
438C2×#95—1224no—
439C2×#95C2×D6111yescharacteristic
440C2×#95C2×D6111yescharacteristic
441C2×#95C2×D6112yes—
442C61#1378411yescharacteristic, complemented, Sylow
443C25—611no—
444C25C22×D6111yescharacteristic
445C22×D4—614no—
446C22×D4—618no—
447C22×D4—1222no—
448C22×D4—1222no—
449C22×D4—1224no—
450C23×C4—22no—
451C23×C4—22no—
452C23×C4—42no—
453C23×C4—42no—
454C23×C4—611no—
455C23×C4—611no—
456C23×C4—614no—
457C23×C4—614no—
458C23×C4—614no—
459C23×C4—612no—
460C23×C4—611no—
461C23×C4—612no—
462C23×C4—618no—
463C23×C4—1224no—
464C23×C4—1224no—
465C23×C4—2442no—
466C23×C4—2442no—
467C23×C4—2442no—
468C23×C4—2442no—
469C23×C4—2442no—
470C23×C4—2442no—
471C23×C4C4×D6114yescomplemented
472C23×C4C22×D6112yes—
473C23×C4C22×D6111yescharacteristic
474C23×C4C22×D6112yes—
475C23×C4C22×D6111yescharacteristic
476C4×D4—12232no—
477C2×C4⋊C4—614no—
478C2×C4⋊C4—1222no—
479C2×C4⋊C4—1222no—
480C2×C22⋊C4—42no—
481C2×C22⋊C4—42no—
482C2×C22⋊C4—614no—
483C2×C22⋊C4—614no—
484C2×C22⋊C4—618no—
485C2×C22⋊C4—618no—
486C2×C22⋊C4—1222no—
487C2×C22⋊C4—1222no—
488C2×C22⋊C4—1224no—
489C2×C22⋊C4—1224no—
490C2×C22⋊C4—1222no—
491C2×C22⋊C4—1222no—
492C2×C22⋊C4—2442no—
493C2×C22⋊C4—2442no—
494C2×C22⋊C4C4×D6118yescomplemented
495C2×C42—614no—
496C2×C42—1222no—
497C2×C42—1222no—
498C2×C42—1224no—
499C2×C42—2442no—
500C2×C42—2442no—
501#95—22no—
502#95—22no—
503#95—42no—
504#95—618no—
505#95—618no—
506#95—1224no—
507#95—1222no—
508#95—1222no—
509#95—2442no—
510#95—2442no—
511#95—2442no—
512C24—21no—
513C24—21no—
514C24—22no—
515C24—21no—
516C24—22no—
517C24—22no—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—612no—
522C24—614no—
523C24—612no—
524C24—612no—
525C24—614no—
526C24—1222no—
527C24—1222no—
528C24—1221no—
529C24—1221no—
530C24—1221no—
531C24—1221no—
532C24C2×C4×D6114yes—
533C24C2×C4×D6112yes—
534C24C23×D6111yescharacteristic
535C2×D4—6116no—
536C2×D4—1228no—
537C2×D4—1228no—
538C2×D4—12216no—
539C2×D4—12216no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—28no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—48no—
562C22×C4—48no—
563C22×C4—614no—
564C22×C4—612no—
565C22×C4—612no—
566C22×C4—612no—
567C22×C4—612no—
568C22×C4—6116no—
569C22×C4—614no—
570C22×C4—614no—
571C22×C4—612no—
572C22×C4—12216no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—1222no—
576C22×C4—1222no—
577C22×C4—1222no—
578C22×C4—1222no—
579C22×C4—1222no—
580C22×C4—1221no—
581C22×C4—1221no—
582C22×C4—1222no—
583C22×C4—1222no—
584C22×C4—1221no—
585C22×C4—1222no—
586C22×C4—1222no—
587C22×C4—1222no—
588C22×C4—1222no—
589C22×C4—1222no—
590C22×C4—1221no—
591C22×C4—1222no—
592C22×C4—1222no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1222no—
596C22×C4—2444no—
597C22×C4—2444no—
598C22×C4—2448no—
599C22×C4—2448no—
600C22×C4—2448no—
601C22×C4—2448no—
602C22×C4—2448no—
603C22×C4—2448no—
604C22×C4—2448no—
605C22×C4—2448no—
606C22×C4C2×C4×D6114yes—
607C22×C4C2×C4×D6114yes—
608C22×C4C2×C4×D6112yes—
609C22×C4C2×C4×D6112yes—
610C22×C4D4×D6112yes—
611C22×C4D4×D6112yes—
612C4⋊C4—1228no—
613C22⋊C4—48no—
614C22⋊C4—1228no—
615C22⋊C4—12216no—
616C22⋊C4—1228no—
617C22⋊C4—2448no—
618C42—1228no—
619C42—2448no—
620C23—22no—
621C23—22no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—22no—
627C23—22no—
628C23—24no—
629C23—22no—
630C23—22no—
631C23—24no—
632C23—42no—
633C23—42no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—614no—
643C23—614no—
644C23—614no—
645C23—618no—
646C23—618no—
647C23—1224no—
648C23—1222no—
649C23—1222no—
650C23—1224no—
651C23—1224no—
652C23—1222no—
653C23—1222no—
654C23—1224no—
655C23—1224no—
656C23—1224no—
657C23—1222no—
658C23—1222no—
659C23—1222no—
660C23—1222no—
661C23—1224no—
662C23—1224no—
663C23—1224no—
664C23—1224no—
665C23C42×D6114yes—
666C23C22×C4×D6111yescharacteristic
667C23C22×C4×D6112yes—
668C23C2×D4×D6111yescharacteristic
669C23C2×D4×D6111yescharacteristic
670C23#41×D6112yes—
671C23#1451982212yes—
672C23#1451982212yes—
673C23#1451982211yescharacteristic
674C23#1451982311yescharacteristic
675C23#1451982411yescharacteristic
676C23#1451982511yescharacteristic
677D4—12232no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—416no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—614no—
703C2×C4—614no—
704C2×C4—1222no—
705C2×C4—1222no—
706C2×C4—1224no—
707C2×C4—1224no—
708C2×C4—1222no—
709C2×C4—1222no—
710C2×C4—1224no—
711C2×C4—1224no—
712C2×C4—1222no—
713C2×C4—1224no—
714C2×C4—1224no—
715C2×C4—1224no—
716C2×C4—1224no—
717C2×C4—1224no—
718C2×C4—1222no—
719C2×C4—1224no—
720C2×C4—1222no—
721C2×C4—24416no—
722C2×C4—24432no—
723C2×C4—2442no—
724C2×C4—2442no—
725C2×C4—2441no—
726C2×C4—2442no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2442no—
730C2×C4—2441no—
731C2×C4—2442no—
732C2×C4—2442no—
733C2×C4—2442no—
734C2×C4—2442no—
735C2×C4C22⋊C4×D6114yes—
736C22—24no—
737C22—24no—
738C22—24no—
739C22—42no—
740C22—42no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—44no—
745C22—42no—
746C22—42no—
747C22—618no—
748C22—1224no—
749C22—1224no—
750C22—1228no—
751C22—1228no—
752C22—1228no—
753C22—1228no—
754C22—1224no—
755C22—1224no—
756C22—1224no—
757C22—1224no—
758C22C2×C42×D6111yescharacteristic
759C22C2×C22⋊C4×D6111yescharacteristic
760C22#117×D6111yescharacteristic
761C22C4×D4×D6112yes—
762C22C4×D4×D6112yes—
763C22#1684023412yes—
764C22#1684023511yescharacteristic
765C22#1684023511yescharacteristic
766C22#1684023512yes—
767C22#1684024112yes—
768C22#1684024211yescharacteristic
769C22#1684024311yescharacteristic
770C22#1684024312yes—
771C22#1684032212yes—
772C22#1684032212yes—
773C22#1684032811yescharacteristic
774C22#1684033511yescharacteristic
775C22#1684034111yescharacteristic
776C22#1684034211yescharacteristic
777C22#1684034412yes—
778C22#1684034812yes—
779C22#1684035512yes—
780C22#1684035812yes—
781C4—24no—
782C4—44no—
783C4—44no—
784C4—42no—
785C4—1224no—
786C4—1224no—
787C4—2444no—
788C4—2444no—
789C4—2442no—
790C2—44no—
791C2—1228no—
792C2C4×C22⋊C4×D6111yescharacteristic
793C2#2144817711yescharacteristic
794C2#2144817811yescharacteristic
795C2#2144839511yescharacteristic
796C2#2144840811yescharacteristic
797C2#2144844811yescharacteristic
798C2#2144845411yescharacteristic
799C2#2144847512yes—
800C2#2144848612yes—
801C2#2144851612yes—
802C2#2144852112yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC22×C61C22×C42
FittingC61×C22⋊#95C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC22⋊#95D61
hypocenterC61#13784
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#16839609C2semidirect
4. C2×#95×D61C2semidirect
5. #21444056C2semidirect
6. #21444050C2semidirect
7. #21444043C2semidirect
8. #21444043C2semidirect
9. #21444042C2semidirect
10. #21444040C2semidirect
11. C61×C22⋊#95C2semidirect
17. C2×C4×C22⋊D61C4semidirect
25. #16839638C4semidirect
61. C22×C4×D61C2×C4semidirect
67. C2×#11758196C2×C4semidirect
72. C2×C22⋊Dic61C2×C4semidirect
73. C2×C22⋊Dic61C2×C4semidirect
79. C2×#11758198C2×C4semidirect
85. C2×C4×Dic61C2×C4semidirect
92. #14519684C2×C4semidirect
93. #14519684C2×C4semidirect
99. C23×C4×C61C2×C4semidirect
106. C2×C22⋊C4×C61C2×C4semidirect
166. C2×C22⋊D61C42semidirect
209. C2×C4×D61C22⋊C4semidirect
399. C22⋊#95D61semidirect
442. C61#13784semidirect
471. C23×C4C4×D61semidirect
494. 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×#168396382
C2×#168396092
C2×#95×D612
#214440562
#214440502
#214440432
#214440422
#214440402
C61×C22⋊#952
#1378461