Finite Group Databasebeta

← #29646003

Subgroups — #29646003

Order 15616.

1446 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840275C211yesmaximal, characteristic
2#407×D61C211yesmaximal, characteristic, complemented
3C2×C22⋊C8×D61C211yesmaximal, characteristic, complemented
4#21444183C211yesmaximal, characteristic, complemented
5#21444180C211yesmaximal, characteristic, complemented
6#21444178C211yesmaximal, characteristic, complemented
7#21444166C214yesmaximal, complemented
8#21444136C214yesmaximal, complemented
9C61×#1472C211yesmaximal, characteristic, complemented
10C22×#11758226C411yescharacteristic
11C23×C4×D61C2211yescharacteristic
12C2×M16×D61—21no—
13C22×C8×D61—21no—
14#16840275—21no—
15#16840275—21no—
16#16840275—21no—
17#16840275—21no—
18#16840275—21no—
19#16840275—21no—
20#16840275—21no—
21#16840275—21no—
22C2×#14519762C2212yes—
23C2×#14519753C411yescharacteristic
24C2×#14519752C411yescharacteristic
25C2×#14519751C2211yescharacteristic
26C2×#14519747C412yes—
27C2×#14519739C2212yes—
28C2×#14519737C412yes—
29C2×#14519735C411yescharacteristic
30#16839726C2211yescharacteristic
31#16839725—21no—
32#16839724—21no—
33#16839724C2212yes—
34C2×C22⋊#92418C2211yescharacteristic
35C2×#14519689—21no—
36C22⋊C8×D61—21no—
37C22⋊C8×D61—21no—
38C22⋊C8×D61—21no—
39C22⋊C8×D61C2212yes—
40C22⋊C8×D61C2212yes—
41C22⋊C8×D61C2212yes—
42#16839488C2214yescomplemented
43#16839485C2214yescomplemented
44#16839485C2214yescomplemented
45C2×C22⋊Q8×C61C2211yescharacteristic
46C61×#407C2211yescharacteristic
47C2×C22⋊C8×C61C2211yescharacteristic
48C61×#324C2214yescomplemented
49C24×D61C2×C411yescharacteristic
50C2×#11758226—21no—
51C2×#11758226—21no—
52C2×#11758226—21no—
53C2×#11758226—21no—
54C2×#11758226—44no—
55C22×D244C2×C412yes—
56C22×D244C2×C412yes—
57C22×D244C2×C411yescharacteristic
58C22×C22⋊D61C2×C412yes—
59C23×Dic61C2×C411yescharacteristic
60C22×C4×D61—44no—
61C22×C4×D61C2×C411yescharacteristic
62C22×C4×D61C2×C412yes—
63C22×C4×D61C2×C411yescharacteristic
64C22×C4×D61D411yescharacteristic
65C22×C4×D61D411yescharacteristic
66C22×C4×D61D411yescharacteristic
67C22×C4×D61D411yescharacteristic
68C22×C4×D61D411yescharacteristic
69C22×C4×D61D411yescharacteristic
70C22×C4×D61D411yescharacteristic
71C22×C4×D61D411yescharacteristic
72C22×C4×D61C2311yescharacteristic
73C22×C4×D61C2311yescharacteristic
74C2×#11758194—21no—
75C2×#11758189—22no—
76M16×D61—44no—
77C22×#92418—21no—
78C2×C8×D61—22no—
79C2×C8×D61—22no—
80C2×C8×D61—22no—
81C2×C8×D61—44no—
82#14519762—22no—
83#14519762—22no—
84#14519762—22no—
85#14519762—22no—
86#14519753—21no—
87#14519753—21no—
88#14519753—21no—
89#14519753—21no—
90#14519752—21no—
91#14519752—21no—
92#14519752—21no—
93#14519752—21no—
94#14519751—21no—
95#14519751—21no—
96#14519751—21no—
97#14519751—21no—
98#14519747—22no—
99#14519747—22no—
100#14519747—22no—
101#14519747—22no—
102#14519739—22no—
103#14519739—22no—
104#14519739—22no—
105#14519739—22no—
106#14519737—22no—
107#14519737—22no—
108#14519737—22no—
109#14519737—22no—
110#14519735—21no—
111#14519735—21no—
112#14519735—21no—
113#14519735—21no—
114C2×C4⋊Dic61C2×C411yescharacteristic
115C2×#11758196C2×C412yes—
116C2×#11758198C2×C412yes—
117C2×#11758198C2×C412yes—
118C2×#11758198C2×C412yes—
119C2×#11758198C2312yes—
120C2×C4×Dic61C2×C412yes—
121C22⋊#92418—21no—
122C22⋊#92418—21no—
123C22⋊#92418C2312yes—
124C22⋊#92418C2312yes—
125#14519689—22no—
126#14519689—22no—
127#14519689—22no—
128#14519689—22no—
129C22×Q8×C61C2×C411yescharacteristic
130C23×C4×C61C2311yescharacteristic
131C2×M16×C61—21no—
132C22×C8×C61—21no—
133C22⋊Q8×C61—21no—
134C22⋊Q8×C61—21no—
135C22⋊Q8×C61—21no—
136C22⋊Q8×C61—21no—
137C2×C4⋊C4×C61C2×C411yescharacteristic
138C2×C4⋊C4×C61C2312yes—
139C2×C22⋊C4×C61C2×C412yes—
140C22⋊C8×C61—21no—
141C22⋊C8×C61—21no—
142C22⋊C8×C61C2312yes—
143C22⋊C8×C61C2312yes—
144C24×C61C22×C411yescharacteristic
145C23×D61—24no—
146C23×D61—42no—
147C23×D61—42no—
148C23×D61C22⋊C411yescharacteristic
149C23×D61C22⋊C411yescharacteristic
150C23×D61C22⋊C411yescharacteristic
151C23×D61C22⋊C411yescharacteristic
152C23×D61C22×C411yescharacteristic
153C23×D61C22×C412yes—
154C23×D61C22×C411yescharacteristic
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—42no—
158C22×C4×C61—42no—
159C22×C4×C61C22×C412yes—
160C22×C4×C61C22×C411yescharacteristic
161C22×C4×C61C22×C412yes—
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2411yescharacteristic
167C2×C22⋊D61—22no—
168C2×C22⋊D61—22no—
169C2×C22⋊D61—44no—
170C22×Dic61—42no—
171C22×Dic61C22⋊C411yescharacteristic
172C22×Dic61C22⋊C411yescharacteristic
173C22×Dic61C22⋊C411yescharacteristic
174C22×Dic61C22⋊C411yescharacteristic
175C22×Dic61C22×C411yescharacteristic
176C22×Dic61C22×C412yes—
177C22×Dic61C22×C411yescharacteristic
178#11758226—44no—
179#11758226—44no—
180#11758226—44no—
181#11758226—44no—
182C2×D244—22no—
183C2×D244—22no—
184C2×D244—22no—
185C2×D244—22no—
186C2×D244—28no—
187C2×D244—21no—
188C2×D244—21no—
189C2×D244—42no—
190C2×D244—44no—
191C2×C4×D61—24no—
192C2×C4×D61—24no—
193C2×C4×D61—24no—
194C2×C4×D61—22no—
195C2×C4×D61—22no—
196C2×C4×D61—42no—
197C2×C4×D61—42no—
198C2×C4×D61—42no—
199C2×C4×D61—42no—
200C2×C4×D61—42no—
201C2×C4×D61—42no—
202C2×C4×D61—42no—
203C2×C4×D61—42no—
204C2×C4×D61—42no—
205C2×C4×D61—44no—
206C2×C4×D61C22⋊C411yescharacteristic
207C2×C4×D61C22⋊C411yescharacteristic
208C2×C4×D61C22⋊C411yescharacteristic
209C2×C4×D61C22⋊C411yescharacteristic
210C2×C4×D61C22⋊C411yescharacteristic
211C2×C4×D61C22⋊C411yescharacteristic
212C2×C4×D61C22⋊C411yescharacteristic
213C2×C4×D61C22⋊C411yescharacteristic
214C2×C4×D61C2×D411yescharacteristic
215C2×C4×D61C2×D411yescharacteristic
216C2×C4×D61C2×D411yescharacteristic
217C2×C4×D61C2×D411yescharacteristic
218C2×C4×D61C2×D411yescharacteristic
219C2×C4×D61C2×D411yescharacteristic
220C2×C4×D61C2×D411yescharacteristic
221C2×C4×D61C2×D411yescharacteristic
222M16×C61—42no—
223C2×C8×C61—22no—
224C2×C8×C61—22no—
225C2×C8×C61—42no—
226C4⋊C4×C61—21no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—22no—
229C4⋊C4×C61—22no—
230C22⋊C4×C61—22no—
231C22⋊C4×C61—22no—
232#11758198—22no—
233#11758198—22no—
234#11758198—22no—
235#11758198—22no—
236#11758198—22no—
237#11758198—22no—
238#11758198—22no—
239#11758198—22no—
240C4⋊Dic61—21no—
241C4⋊Dic61—21no—
242#11758196—22no—
243#11758196—22no—
244C4×Dic61—22no—
245C4×Dic61—22no—
246#11758194—42no—
247C2×#92418—22no—
248C2×#92418—22no—
249C2×#92418—42no—
250#11758189—44no—
251C8×D61—44no—
252C8×D61—44no—
253C8×D61—44no—
254C23×C61—22no—
255C23×C61—22no—
256C23×C61—41no—
257C23×C61C2×C22⋊C411yescharacteristic
258C23×C61C2×C22⋊C411yescharacteristic
259C23×C61C23×C411yescharacteristic
260C22×D61—22no—
261C22×D61—22no—
262C22×D61—22no—
263C22×D61—22no—
264C22×D61—22no—
265C22×D61—22no—
266C22×D61—22no—
267C22×D61—22no—
268C22×D61—22no—
269C22×D61—22no—
270C22×D61—22no—
271C22×D61—24no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61—416no—
280C22×D61—42no—
281C22×D61—42no—
282C22×D61C2×C22⋊C411yescharacteristic
283C22×D61C2×C22⋊C411yescharacteristic
284C22×D61C2×C22⋊C411yescharacteristic
285C22×D61C2×C22⋊C411yescharacteristic
286C22×D61#13114yes—
287Q8×C61—42no—
288Q8×C61—42no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—24no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—42no—
299C2×C4×C61C2×C22⋊C411yescharacteristic
300C2×C4×C61C2×C22⋊C411yescharacteristic
301C2×C4×C61C22×D411yescharacteristic
302C2×C4×C61C22×D411yescharacteristic
303C22⋊D61—44no—
304C22⋊D61—44no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—42no—
313C2×Dic61C2×C22⋊C411yescharacteristic
314C2×Dic61C2×C22⋊C411yescharacteristic
315C2×Dic61C2×C22⋊C411yescharacteristic
316C2×Dic61C2×C22⋊C411yescharacteristic
317D244—42no—
318D244—44no—
319D244—44no—
320D244—44no—
321D244—44no—
322D244—42no—
323C4×D61—22no—
324C4×D61—22no—
325C4×D61—22no—
326C4×D61—22no—
327C4×D61—22no—
328C4×D61—22no—
329C4×D61—22no—
330C4×D61—22no—
331C4×D61—22no—
332C4×D61—41no—
333C4×D61—41no—
334C4×D61—41no—
335C4×D61—41no—
336C4×D61—41no—
337C4×D61—41no—
338C4×D61—44no—
339C4×D61—44no—
340C4×D61#9914yes—
341C8×C61—42no—
342C8×C61—42no—
343#92418—42no—
344#92418—42no—
345#17381—611nomaximal, Sylow
346C22×C61—21no—
347C22×C61—21no—
348C22×C61—21no—
349C22×C61—21no—
350C22×C61—21no—
351C22×C61—21no—
352C22×C61—21no—
353C22×C61—44no—
354C22×C61#41312yes—
355C22×C61C22×C22⋊C411yescharacteristic
356C22×C61C2×#13112yes—
357C2×D61—28no—
358C2×D61—21no—
359C2×D61—21no—
360C2×D61—21no—
361C2×D61—21no—
362C2×D61—21no—
363C2×D61—21no—
364C2×D61—21no—
365C2×D61—21no—
366C2×D61—21no—
367C2×D61—44no—
368C2×D61—44no—
369C2×D61—44no—
370C2×D61—44no—
371C2×D61—44no—
372C2×D61—42no—
373C2×D61—42no—
374C2×D61—42no—
375C2×D61—84no—
376C2×D61#40812yes—
377C2×D61#40812yes—
378C2×D61C2×#9912yes—
379C4×C61—21no—
380C4×C61—21no—
381C4×C61—21no—
382C4×C61—42no—
383C4×C61—42no—
384C4×C61C2×#9912yes—
385Dic61—21no—
386Dic61—21no—
387Dic61—21no—
388Dic61—42no—
389Dic61C2×#9912yes—
390C2×#525—611no—
391C2×#407—611no—
392C22×C22⋊C8—611no—
393#1472—611no—
394#1472D6111yescharacteristic, complemented
395#1471—611no—
396#1471—611no—
397#1468—614no—
398#1459—614no—
399C2×C61—22no—
400C2×C61—22no—
401C2×C61—41no—
402C2×C61C2×#40811yescharacteristic
403C2×C61C22×#9911yescharacteristic
404C2×C61C2×#41311yescharacteristic
405D61—22no—
406D61—22no—
407D61—22no—
408D61—41no—
409D61—82no—
410C22×#41—611no—
411C24×C4—611no—
412C22×M16—1221no—
413C23×C8—1221no—
414#525—1221no—
415#525—1221no—
416#525—1221no—
417#525—1221no—
418#525—1221no—
419#525—1221no—
420#525—1221no—
421#525—1221no—
422C2×#123—612no—
423C2×C22⋊Q8—611no—
424C2×C22⋊Q8C2×D6111yescharacteristic
425C2×#121—611no—
426C2×#121—611no—
427C2×#120—612no—
428C2×C4×D4—612no—
429C2×C4×D4—612no—
430C2×#117—611no—
431#407—611no—
432#407—612no—
433#407—1221no—
434#407—1221no—
435#407C2×D6111yescharacteristic
436C2×C22⋊C8—611no—
437C2×C22⋊C8—612no—
438C2×C22⋊C8—612no—
439C2×C22⋊C8—612no—
440C2×C22⋊C8—1221no—
441C2×C22⋊C8—1221no—
442C2×C22⋊C8—1221no—
443C2×C22⋊C8—1221no—
444C2×C22⋊C8C2×D6111yescharacteristic
445#324—614no—
446#324C2×D6114yescomplemented
447#323—614no—
448#323—614no—
449C61#1738111yescharacteristic, complemented, Sylow
450C25—611no—
451C2×#41—1221no—
452C2×#41—1221no—
453C2×#41—1221no—
454C2×#41—1221no—
455C2×#41—2444no—
456C22×Q8C4×D6111yescharacteristic
457C22×D4—612no—
458C22×D4—612no—
459C22×D4—612no—
460C22×D4—611no—
461C23×C4—611no—
462C23×C4—611no—
463C23×C4—611no—
464C23×C4—611no—
465C23×C4—611no—
466C23×C4—611no—
467C23×C4—611no—
468C23×C4—611no—
469C23×C4—611no—
470C23×C4—611no—
471C23×C4—611no—
472C23×C4—611no—
473C23×C4—611no—
474C23×C4—612no—
475C23×C4—2444no—
476C23×C4C22×D6111yescharacteristic
477C2×M16—21no—
478C2×M16—1222no—
479C2×M16—1221no—
480C2×M16—2444no—
481C22×C8—21no—
482C22×C8—1222no—
483C22×C8—1222no—
484C22×C8—1222no—
485C22×C8—1221no—
486C22×C8—2444no—
487#123—1222no—
488#123—1222no—
489#123—1222no—
490#123—1222no—
491C22⋊Q8—21no—
492C22⋊Q8—21no—
493C22⋊Q8—21no—
494C22⋊Q8—21no—
495C22⋊Q8—1221no—
496C22⋊Q8—1221no—
497C22⋊Q8—1221no—
498C22⋊Q8—1221no—
499#121—1221no—
500#121—1221no—
501#121—1221no—
502#121—1221no—
503#121—1221no—
504#121—1221no—
505#121—1221no—
506#121—1221no—
507#120—1222no—
508#120—1222no—
509#120—1222no—
510#120—1222no—
511C4×D4—1222no—
512C4×D4—1222no—
513C4×D4—1222no—
514C4×D4—1222no—
515C4×D4—1222no—
516C4×D4—1222no—
517C4×D4—1222no—
518C4×D4—1222no—
519#117—1221no—
520#117—1221no—
521#117—1221no—
522#117—1221no—
523C2×C4⋊C4—611no—
524C2×C4⋊C4—612no—
525C2×C4⋊C4C4×D6111yescharacteristic
526C2×C4⋊C4C22×D6112yes—
527C2×C22⋊C4—612no—
528C2×C22⋊C4—612no—
529C2×C22⋊C4—612no—
530C2×C22⋊C4—612no—
531C2×C22⋊C4C4×D6112yes—
532C2×C42—612no—
533C22⋊C8—21no—
534C22⋊C8—21no—
535C22⋊C8—612no—
536C22⋊C8—612no—
537C22⋊C8—1222no—
538C22⋊C8—1222no—
539C22⋊C8—1222no—
540C22⋊C8—1222no—
541C22⋊C8—1221no—
542C22⋊C8—1221no—
543C22⋊C8C22×D6112yes—
544C22⋊C8C22×D6112yes—
545C24—611no—
546C24—611no—
547C24—611no—
548C24—611no—
549C24—611no—
550C24—611no—
551C24—612no—
552C24—1224no—
553C24—2442no—
554C24—2442no—
555C24C2×C4×D6111yescharacteristic
556#41—2444no—
557#41—2444no—
558#41—2444no—
559#41—2444no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—42no—
563C2×D4—1222no—
564C2×D4—1222no—
565C2×D4—1222no—
566C2×D4—1222no—
567C2×D4—1228no—
568C2×D4—1222no—
569C2×D4—1222no—
570C2×D4—1221no—
571C2×D4—1221no—
572C2×D4—2442no—
573C2×D4—2444no—
574C2×D4—2444no—
575C22×C4—42no—
576C22×C4—611no—
577C22×C4—611no—
578C22×C4—611no—
579C22×C4—611no—
580C22×C4—611no—
581C22×C4—611no—
582C22×C4—611no—
583C22×C4—611no—
584C22×C4—611no—
585C22×C4—611no—
586C22×C4—611no—
587C22×C4—611no—
588C22×C4—611no—
589C22×C4—611no—
590C22×C4—611no—
591C22×C4—611no—
592C22×C4—611no—
593C22×C4—611no—
594C22×C4—611no—
595C22×C4—611no—
596C22×C4—611no—
597C22×C4—611no—
598C22×C4—612no—
599C22×C4—1224no—
600C22×C4—1224no—
601C22×C4—1224no—
602C22×C4—1222no—
603C22×C4—1222no—
604C22×C4—2442no—
605C22×C4—2442no—
606C22×C4—2442no—
607C22×C4—2442no—
608C22×C4—2442no—
609C22×C4—2442no—
610C22×C4—2442no—
611C22×C4—2442no—
612C22×C4—2442no—
613C22×C4—2444no—
614C22×C4—2442no—
615C22×C4C2×C4×D6112yes—
616C22×C4C2×C4×D6111yescharacteristic
617C22×C4C2×C4×D6112yes—
618C22×C4D4×D6111yescharacteristic
619C22×C4D4×D6111yescharacteristic
620C22×C4D4×D6111yescharacteristic
621C22×C4D4×D6111yescharacteristic
622C22×C4C23×D6111yescharacteristic
623M16—42no—
624M16—2444no—
625M16—2442no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—42no—
629C2×C8—1222no—
630C2×C8—1222no—
631C2×C8—2444no—
632C2×C8—2444no—
633C2×C8—2444no—
634C2×C8—2442no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—1222no—
640C4⋊C4—1222no—
641C4⋊C4—1221no—
642C4⋊C4—1221no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—1222no—
646C22⋊C4—1222no—
647C22⋊C4—1222no—
648C22⋊C4—1222no—
649C22⋊C4—1222no—
650C22⋊C4—1222no—
651C22⋊C4—1222no—
652C22⋊C4—1222no—
653C42—1222no—
654C42—1222no—
655C23—22no—
656C23—22no—
657C23—41no—
658C23—611no—
659C23—611no—
660C23—611no—
661C23—614no—
662C23—611no—
663C23—1222no—
664C23—1222no—
665C23—1222no—
666C23—1222no—
667C23—1222no—
668C23—1222no—
669C23—1222no—
670C23—1222no—
671C23—1222no—
672C23—1222no—
673C23—1224no—
674C23—1222no—
675C23—2441no—
676C23—2441no—
677C23—2441no—
678C23—2441no—
679C23—2441no—
680C23—2441no—
681C23—2441no—
682C23—2442no—
683C23—2442no—
684C23—24416no—
685C23C22⋊C4×D6111yescharacteristic
686C23C22⋊C4×D6111yescharacteristic
687C23C22×C4×D6111yescharacteristic
688Q8—42no—
689Q8—42no—
690D4—2442no—
691D4—2444no—
692D4—2444no—
693D4—2444no—
694D4—2444no—
695D4—2444no—
696D4—2444no—
697D4—2442no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—42no—
708C2×C4—611no—
709C2×C4—614no—
710C2×C4—611no—
711C2×C4—611no—
712C2×C4—611no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—1222no—
716C2×C4—1222no—
717C2×C4—1222no—
718C2×C4—1222no—
719C2×C4—1222no—
720C2×C4—1222no—
721C2×C4—1222no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—1222no—
725C2×C4—1222no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4—2441no—
731C2×C4—2441no—
732C2×C4—2444no—
733C2×C4—2444no—
734C2×C4—2441no—
735C2×C4—2441no—
736C2×C4—2441no—
737C2×C4—2442no—
738C2×C4C22⋊C4×D6111yescharacteristic
739C2×C4C22⋊C4×D6111yescharacteristic
740C2×C4C2×D4×D6111yescharacteristic
741C2×C4C2×D4×D6111yescharacteristic
742C8—42no—
743C8—42no—
744C8—2442no—
745C8—2442no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—44no—
754C22—612no—
755C22—612no—
756C22—612no—
757C22—1228no—
758C22—1221no—
759C22—1221no—
760C22—1221no—
761C22—1221no—
762C22—1221no—
763C22—1221no—
764C22—1221no—
765C22—1221no—
766C22—1221no—
767C22—4884no—
768C22—2444no—
769C22—2444no—
770C22—2444no—
771C22—2444no—
772C22—2444no—
773C22—2442no—
774C22—2442no—
775C22—2442no—
776C22#1683974512yes—
777C22C2×C22⋊C4×D6111yescharacteristic
778C22#131×D6112yes—
779C4—21no—
780C4—21no—
781C4—21no—
782C4—42no—
783C4—42no—
784C4—612no—
785C4—1221no—
786C4—1221no—
787C4—1221no—
788C4—2442no—
789C4#99×D6112yes—
790C2—22no—
791C2—22no—
792C2—41no—
793C2—1222no—
794C2—1222no—
795C2—1222no—
796C2—4882no—
797C2—2441no—
798C2#408×D6111yescharacteristic
799C2C2×#99×D6111yescharacteristic
800C2C2×#1683974511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1472C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840275C2
cosocleC22×C4×C61C24
hypercenter#1472D61
hypocenterC61#17381
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1472

Complements

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

NH ≅ G/Ntype
2. #407×D61C2semidirect
3. C2×C22⋊C8×D61C2semidirect
4. #21444183C2semidirect
5. #21444180C2semidirect
6. #21444178C2semidirect
7. #21444166C2semidirect
8. #21444136C2semidirect
9. C61×#1472C2semidirect
42. #16839488C22semidirect
43. #16839485C22semidirect
44. #16839485C22semidirect
48. C61×#324C22semidirect
394. #1472D61semidirect
446. #324C2×D61semidirect
449. C61#17381semidirect

Maximal subgroups

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

subgroupindex
C2×#168402752
#407×D612
C2×C22⋊C8×D612
#214441832
#214441802
#214441782
#214441662
#214441362
C61×#14722
#1738161