Finite Group Databasebeta

← #29647172

Subgroups — #29647172

Order 15616.

1574 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840272C211yesmaximal, characteristic
2#407×D61C211yesmaximal, characteristic, complemented
3C4×C22⋊C4×D61C211yesmaximal, characteristic, complemented
4#21444340C211yesmaximal, characteristic, complemented
5#21444338C211yesmaximal, characteristic, complemented
6#21444335C211yesmaximal, characteristic, complemented
7#21444320C214yesmaximal, complemented
8#21444307C214yesmaximal, complemented
9C61×#1507C211yesmaximal, characteristic, complemented
10C22×#11758224C411yescharacteristic, complemented
11C23×C4×D61C2211yescharacteristic
12C2×M16×D61—21no—
13#16840272—21no—
14#16840272—21no—
15#16840272—21no—
16#16840272—21no—
17#16840272C412yescomplemented
18#16840272C412yescomplemented
19#16840272C2212yes—
20#16840272C2212yes—
21C2×#14519759—21no—
22C2×#14519757C411yescharacteristic, complemented
23C2×#14519756C2211yescharacteristic
24C2×#14519748C411yescharacteristic, complemented
25C2×#14519745—21no—
26C2×D4×Dic61—21no—
27C2×#14519737—21no—
28C2×#14519735C411yescharacteristic, complemented
29C2×C22⋊C4×D61—21no—
30C2×C42×D61—21no—
31#16839726C2211yescharacteristic
32#16839725—21no—
33#16839724—21no—
34#16839724C2212yescomplemented
35C22⋊C8×D61—21no—
36C22⋊C8×D61C2212yescomplemented
37C22⋊C4×Dic61—21no—
38C4×#11758198—21no—
39C4×C22⋊Dic61C2211yescharacteristic
40#16839609C2212yescomplemented
41#95×D61C2212yescomplemented
42#16839500C2214yescomplemented
43#16839498C2214yescomplemented
44#16839496C2214yescomplemented
45C2×#121×C61C2211yescharacteristic
46C61×#407C2211yescharacteristic
47C4×C22⋊C4×C61C2211yescharacteristic
48C61×#327C2214yescomplemented
49C24×D61D411yescharacteristic
50C2×#11758224—21no—
51C2×#11758224—21no—
52C2×#11758224—44no—
53C2×#11758224C2×C412yes—
54C2×#11758224C2×C412yescomplemented
55C22×Dic122C2×C411yescharacteristic, complemented
56C22×C22⋊D61—21no—
57C22×C22⋊D61—21no—
58C23×Dic61—21no—
59C23×Dic61D411yescharacteristic
60C22×C4×D61—22no—
61C22×C4×D61—44no—
62C22×C4×D61C2×C411yescharacteristic
63C22×C4×D61C2×C411yescharacteristic
64C22×C4×D61C2×C411yescharacteristic
65C22×C4×D61C2×C411yescharacteristic
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—
77C2×C8×D61—22no—
78#14519759—22no—
79#14519759—22no—
80#14519759—22no—
81#14519759—22no—
82#14519757—21no—
83#14519757—21no—
84#14519757C2×C412yes—
85#14519757C2×C412yescomplemented
86#14519756—21no—
87#14519756—21no—
88#14519756C2×C412yescomplemented
89#14519756C2312yes—
90#14519748—21no—
91#14519748—21no—
92#14519748C2×C412yes—
93#14519748C2×C412yescomplemented
94#14519745—22no—
95#14519745—22no—
96#14519745—22no—
97#14519745—22no—
98D4×Dic61—22no—
99D4×Dic61—22no—
100D4×Dic61—22no—
101D4×Dic61—22no—
102#14519737—22no—
103#14519737—22no—
104#14519737—22no—
105#14519737—22no—
106#14519735—21no—
107#14519735—21no—
108#14519735C2×C412yes—
109#14519735C2×C412yescomplemented
110C2×C4⋊Dic61—21no—
111C2×C4⋊Dic61C2×C411yescharacteristic, complemented
112C2×#11758196—21no—
113C2×C22⋊Dic61—21no—
114C2×C22⋊Dic61—21no—
115C2×C22⋊Dic61—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—22no—
119C22⋊C4×D61—28no—
120C2×C4×Dic61—21no—
121C2×C4×Dic61—21no—
122C2×C4×Dic61—22no—
123C42×D61—44no—
124C22⋊#92418—21no—
125C22⋊#92418C2312yes—
126#14519689—22no—
127#14519689—22no—
128#14519684—22no—
129#14519684C2312yes—
130C22×D4×C61—21no—
131C22×D4×C61C2×C411yescharacteristic, complemented
132C23×C4×C61C2311yescharacteristic
133C2×M16×C61—21no—
134#121×C61—21no—
135#121×C61—21no—
136#121×C61C2×C412yescomplemented
137#121×C61C2312yes—
138C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C2×C42×C61—21no—
142C22⋊C8×C61—21no—
143C22⋊C8×C61C2312yes—
144#95×C61C2312yes—
145C24×C61—21no—
146C24×C61C2×D411yescharacteristic
147C23×D61—24no—
148C23×D61—42no—
149C23×D61—42no—
150C23×D61C22⋊C411yescharacteristic
151C23×D61C22⋊C411yescharacteristic
152C23×D61C22⋊C411yescharacteristic
153C23×D61C22⋊C411yescharacteristic
154C23×D61C2×D411yescharacteristic
155C23×D61C2×D411yescharacteristic
156C2×D4×C61—22no—
157C2×D4×C61—22no—
158C2×D4×C61—21no—
159C2×D4×C61—42no—
160C2×D4×C61—44no—
161C2×D4×C61C22×C412yes—
162C22×C4×C61—21no—
163C22×C4×C61—22no—
164C22×C4×C61—42no—
165C22×C4×C61C22×C411yescharacteristic
166C22×C4×C61C22×C411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61C2411yescharacteristic
171C2×C22⋊D61—22no—
172C2×C22⋊D61—22no—
173C2×C22⋊D61—22no—
174C2×C22⋊D61—22no—
175C2×C22⋊D61—44no—
176C2×C22⋊D61—44no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—22no—
180C22×Dic61—22no—
181C22×Dic61—22no—
182C22×Dic61—42no—
183C22×Dic61—44no—
184C22×Dic61C22⋊C411yescharacteristic
185C22×Dic61C22⋊C411yescharacteristic
186C22×Dic61C22⋊C411yescharacteristic
187C22×Dic61C22⋊C411yescharacteristic
188C22×Dic61C2×D411yescharacteristic
189C22×Dic61C2×D411yescharacteristic
190#11758224—44no—
191#11758224—44no—
192#11758224—44no—
193#11758224—44no—
194C2×C4×D61—24no—
195C2×C4×D61—24no—
196C2×C4×D61—24no—
197C2×C4×D61—28no—
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—42no—
206C2×C4×D61—42no—
207C2×C4×D61—44no—
208C2×C4×D61—44no—
209C2×C4×D61C22⋊C411yescharacteristic
210C2×C4×D61C22⋊C411yescharacteristic
211C2×C4×D61C22⋊C411yescharacteristic
212C2×C4×D61C22⋊C411yescharacteristic
213C2×C4×D61C22⋊C411yescharacteristic
214C2×C4×D61C22⋊C411yescharacteristic
215C2×C4×D61C22⋊C411yescharacteristic
216C2×C4×D61C22⋊C411yescharacteristic
217C2×C4×D61C22×C411yescharacteristic
218C2×C4×D61C22×C411yescharacteristic
219C2×C4×D61C22×C411yescharacteristic
220C2×C4×D61C22×C411yescharacteristic
221C2×C4×D61C2×D411yescharacteristic
222C2×C4×D61C2×D411yescharacteristic
223C2×C4×D61C2×D411yescharacteristic
224C2×C4×D61C2×D411yescharacteristic
225C2×Dic122—21no—
226C2×Dic122—42no—
227C2×Dic122C22×C412yes—
228M16×C61—42no—
229C2×C8×C61—22no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61C22×C412yes—
232C22⋊C4×C61—24no—
233C22⋊C4×C61—22no—
234C22⋊C4×C61—22no—
235C42×C61—42no—
236C22⋊Dic61—24no—
237C22⋊Dic61—22no—
238C22⋊Dic61—22no—
239C22⋊Dic61—22no—
240C22⋊Dic61—22no—
241#11758198—28no—
242#11758198—22no—
243#11758198—22no—
244#11758198—22no—
245#11758198—22no—
246C4⋊Dic61—21no—
247C4⋊Dic61—22no—
248C4⋊Dic61—22no—
249C4⋊Dic61C22×C412yes—
250#11758196—22no—
251#11758196—22no—
252C4×Dic61—22no—
253C4×Dic61—22no—
254C4×Dic61—44no—
255C4×Dic61—42no—
256#11758194—42no—
257C2×#92418—22no—
258#11758189—44no—
259C8×D61—44no—
260C23×C61—22no—
261C23×C61—22no—
262C23×C61—22no—
263C23×C61—41no—
264C23×C61—42no—
265C23×C61—42no—
266C23×C61—42no—
267C23×C61C2×C22⋊C411yescharacteristic
268C23×C61C2×C22⋊C411yescharacteristic
269C23×C61C22×D411yescharacteristic
270C22×D61—22no—
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—22no—
274C22×D61—22no—
275C22×D61—22no—
276C22×D61—22no—
277C22×D61—22no—
278C22×D61—22no—
279C22×D61—22no—
280C22×D61—41no—
281C22×D61—41no—
282C22×D61—41no—
283C22×D61—41no—
284C22×D61—41no—
285C22×D61—41no—
286C22×D61—41no—
287C22×D61—416no—
288C22×D61#10414yes—
289C22×D61C2×C22⋊C411yescharacteristic
290C22×D61C2×C22⋊C411yescharacteristic
291C22×D61C2×C22⋊C411yescharacteristic
292C22×D61C2×C22⋊C411yescharacteristic
293D4×C61—42no—
294D4×C61—44no—
295D4×C61—44no—
296D4×C61—42no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—24no—
301C2×C4×C61—22no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—42no—
306C2×C4×C61—42no—
307C2×C4×C61—42no—
308C2×C4×C61C2×C22⋊C411yescharacteristic
309C2×C4×C61C2×C22⋊C411yescharacteristic
310C2×C4×C61C23×C411yescharacteristic
311C2×C4×C61C22×D411yescharacteristic
312C22⋊D61—44no—
313C22⋊D61—44no—
314C22⋊D61—44no—
315C22⋊D61—44no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—24no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—44no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61—42no—
330C2×Dic61—44no—
331C2×Dic61C2×C22⋊C411yescharacteristic
332C2×Dic61C2×C22⋊C411yescharacteristic
333C2×Dic61C2×C22⋊C411yescharacteristic
334C2×Dic61C2×C22⋊C411yescharacteristic
335C4×D61—22no—
336C4×D61—22no—
337C4×D61—22no—
338C4×D61—22no—
339C4×D61—22no—
340C4×D61—22no—
341C4×D61—22no—
342C4×D61—22no—
343C4×D61—22no—
344C4×D61—41no—
345C4×D61—41no—
346C4×D61—41no—
347C4×D61—41no—
348C4×D61—41no—
349C4×D61—41no—
350C4×D61—416no—
351C4×D61#9914yes—
352Dic122—42no—
353Dic122—42no—
354C8×C61—42no—
355#92418—42no—
356#17542—611nomaximal, Sylow
357C22×C61—21no—
358C22×C61—21no—
359C22×C61—21no—
360C22×C61—21no—
361C22×C61—21no—
362C22×C61—21no—
363C22×C61—21no—
364C22×C61—44no—
365C22×C61—42no—
366C22×C61—42no—
367C22×C61—42no—
368C22×C61—84no—
369C22×C61C2×#10412yes—
370C22×C61C22×C22⋊C411yescharacteristic
371C22×C61#57512yes—
372C2×D61—28no—
373C2×D61—21no—
374C2×D61—21no—
375C2×D61—21no—
376C2×D61—21no—
377C2×D61—21no—
378C2×D61—21no—
379C2×D61—21no—
380C2×D61—21no—
381C2×D61—21no—
382C2×D61—44no—
383C2×D61—44no—
384C2×D61—44no—
385C2×D61—44no—
386C2×D61—44no—
387C2×D61C2×#9912yes—
388C2×D61C2×#10412yes—
389C2×D61C2×#10412yes—
390C4×C61—21no—
391C4×C61—21no—
392C4×C61—21no—
393C4×C61—44no—
394C4×C61—42no—
395C4×C61C2×#9912yes—
396Dic61—21no—
397Dic61—21no—
398Dic61—21no—
399Dic61—44no—
400Dic61—42no—
401Dic61—42no—
402Dic61C2×#9912yes—
403C2×#525—611no—
404C2×#407—611no—
405C2×C4×C22⋊C4—611no—
406#1508—611no—
407#1508—611no—
408#1507—611no—
409#1507D6111yescharacteristic, complemented
410#1504—614no—
411#1501—614no—
412C2×C61—22no—
413C2×C61—22no—
414C2×C61—41no—
415C2×C61—82no—
416C2×C61C22×#9911yescharacteristic
417C2×C61#289611yescharacteristic
418C2×C61C22×#10411yescharacteristic
419D61—22no—
420D61—22no—
421D61—22no—
422D61—41no—
423C22×#41—611no—
424C24×C4—611no—
425C22×M16—1221no—
426#525—612no—
427#525—612no—
428#525—612no—
429#525—612no—
430#525—1221no—
431#525—1221no—
432#525—1221no—
433#525—1221no—
434C2×#123—1221no—
435C2×C22⋊Q8—611no—
436C2×C22⋊Q8—611no—
437C2×#121—611no—
438C2×#121C2×D6111yescharacteristic
439C2×#120—1221no—
440C2×C4×D4—1221no—
441C2×C4×D4—1221no—
442C2×#117—611no—
443C22×C22⋊C4—1221no—
444C22×C42—1221no—
445#407—611no—
446#407—612no—
447#407—1221no—
448#407—1221no—
449#407C2×D6111yescharacteristic
450C2×C22⋊C8—612no—
451C2×C22⋊C8—1221no—
452C4×C22⋊C4—611no—
453C4×C22⋊C4—612no—
454C4×C22⋊C4—1221no—
455C4×C22⋊C4—1221no—
456C4×C22⋊C4C2×D6111yescharacteristic
457C2×#95—612no—
458#328—614no—
459#328—614no—
460#327—614no—
461#327C2×D6114yescomplemented
462C61#1754211yescharacteristic, complemented, Sylow
463C25—611no—
464C2×#41—612no—
465C2×#41—612no—
466C2×#41—1221no—
467C2×#41—1221no—
468C2×#41—2444no—
469C22×Q8—611no—
470C22×D4—21no—
471C22×D4—1221no—
472C22×D4—1221no—
473C22×D4C4×D6111yescharacteristic, complemented
474C23×C4—611no—
475C23×C4—611no—
476C23×C4—611no—
477C23×C4—611no—
478C23×C4—611no—
479C23×C4—611no—
480C23×C4—611no—
481C23×C4—611no—
482C23×C4—611no—
483C23×C4—611no—
484C23×C4—611no—
485C23×C4—611no—
486C23×C4—611no—
487C23×C4—1222no—
488C23×C4—1221no—
489C23×C4—2444no—
490C23×C4C22×D6111yescharacteristic
491C2×M16—21no—
492C2×M16—1222no—
493C2×M16—1221no—
494C2×M16—2444no—
495C22×C8—1222no—
496#123—1222no—
497#123—1222no—
498#123—1222no—
499#123—1222no—
500C22⋊Q8—612no—
501C22⋊Q8—612no—
502C22⋊Q8—612no—
503C22⋊Q8—612no—
504C22⋊Q8—1221no—
505C22⋊Q8—1221no—
506C22⋊Q8—1221no—
507C22⋊Q8—1221no—
508#121—21no—
509#121—21no—
510#121—612no—
511#121—612no—
512#121—1221no—
513#121—1221no—
514#121C4×D6112yescomplemented
515#121C22×D6112yes—
516#120—1222no—
517#120—1222no—
518#120—1222no—
519#120—1222no—
520C4×D4—1222no—
521C4×D4—1222no—
522C4×D4—1222no—
523C4×D4—1222no—
524C4×D4—1222no—
525C4×D4—1222no—
526C4×D4—1222no—
527C4×D4—1222no—
528#117—612no—
529#117—612no—
530#117—1221no—
531#117—1221no—
532C2×C4⋊C4—611no—
533C2×C4⋊C4—1221no—
534C2×C4⋊C4—1221no—
535C2×C4⋊C4C4×D6111yescharacteristic, complemented
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—1228no—
539C2×C22⋊C4—1222no—
540C2×C22⋊C4—1221no—
541C2×C22⋊C4—1221no—
542C2×C22⋊C4—1221no—
543C2×C22⋊C4—1221no—
544C2×C22⋊C4—1221no—
545C2×C42—21no—
546C2×C42—1221no—
547C2×C42—1222no—
548C2×C42—1221no—
549C2×C42—2444no—
550C22⋊C8—21no—
551C22⋊C8—612no—
552C22⋊C8—1222no—
553C22⋊C8—1222no—
554C22⋊C8—1221no—
555C22⋊C8C22×D6112yes—
556#95—612no—
557#95—1222no—
558#95C22×D6112yes—
559C24—21no—
560C24—611no—
561C24—611no—
562C24—611no—
563C24—611no—
564C24—611no—
565C24—611no—
566C24—1224no—
567C24—2442no—
568C24—2442no—
569C24D4×D6111yescharacteristic
570#41—2444no—
571#41—2444no—
572#41—2444no—
573#41—2444no—
574C2×Q8—612no—
575C2×Q8—1221no—
576C2×Q8—2442no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—21no—
580C2×D4—42no—
581C2×D4—44no—
582C2×D4—1222no—
583C2×D4—1222no—
584C2×D4—1222no—
585C2×D4—1222no—
586C2×D4—2444no—
587C2×D4—2444no—
588C2×D4C2×C4×D6112yes—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—42no—
592C22×C4—611no—
593C22×C4—611no—
594C22×C4—611no—
595C22×C4—611no—
596C22×C4—611no—
597C22×C4—611no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—611no—
605C22×C4—611no—
606C22×C4—611no—
607C22×C4—611no—
608C22×C4—611no—
609C22×C4—611no—
610C22×C4—611no—
611C22×C4—611no—
612C22×C4—611no—
613C22×C4—611no—
614C22×C4—1224no—
615C22×C4—1224no—
616C22×C4—1224no—
617C22×C4—1228no—
618C22×C4—1222no—
619C22×C4—1222no—
620C22×C4—1222no—
621C22×C4—1221no—
622C22×C4—1221no—
623C22×C4—2442no—
624C22×C4—2442no—
625C22×C4—2442no—
626C22×C4—2442no—
627C22×C4—2442no—
628C22×C4—2442no—
629C22×C4—2442no—
630C22×C4—2442no—
631C22×C4—2442no—
632C22×C4—2444no—
633C22×C4—2444no—
634C22×C4—2442no—
635C22×C4—2444no—
636C22×C4C2×C4×D6111yescharacteristic
637C22×C4C2×C4×D6111yescharacteristic
638C22×C4D4×D6111yescharacteristic
639C22×C4D4×D6111yescharacteristic
640C22×C4D4×D6111yescharacteristic
641C22×C4C23×D6111yescharacteristic
642M16—42no—
643M16—2444no—
644M16—2442no—
645C2×C8—22no—
646C2×C8—1222no—
647C2×C8—2444no—
648C4⋊C4—21no—
649C4⋊C4—612no—
650C4⋊C4—1222no—
651C4⋊C4—1222no—
652C4⋊C4—1222no—
653C4⋊C4—1221no—
654C4⋊C4—1222no—
655C4⋊C4C2×C4×D6112yes—
656C22⋊C4—24no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—1222no—
660C22⋊C4—1222no—
661C22⋊C4—1222no—
662C22⋊C4—1222no—
663C22⋊C4—1228no—
664C22⋊C4—1222no—
665C22⋊C4—1222no—
666C22⋊C4—1224no—
667C22⋊C4—1222no—
668C22⋊C4—1222no—
669C42—42no—
670C42—1222no—
671C42—1222no—
672C42—2442no—
673C42—2444no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—41no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—611no—
682C23—611no—
683C23—611no—
684C23—614no—
685C23—611no—
686C23—1222no—
687C23—1222no—
688C23—1222no—
689C23—1222no—
690C23—1222no—
691C23—1222no—
692C23—1222no—
693C23—1222no—
694C23—1222no—
695C23—1222no—
696C23—2441no—
697C23—2441no—
698C23—2441no—
699C23—2441no—
700C23—2441no—
701C23—2441no—
702C23—2441no—
703C23—24416no—
704C23C22⋊C4×D6111yescharacteristic
705C23C22⋊C4×D6111yescharacteristic
706C23C2×D4×D6111yescharacteristic
707Q8—2442no—
708Q8—2442no—
709D4—42no—
710D4—44no—
711D4—44no—
712D4—42no—
713D4—2444no—
714D4—2444no—
715D4—2444no—
716D4—2444no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—611no—
729C2×C4—614no—
730C2×C4—611no—
731C2×C4—611no—
732C2×C4—611no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—1222no—
744C2×C4—1222no—
745C2×C4—1224no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—24416no—
755C2×C4—2444no—
756C2×C4—2441no—
757C2×C4—2441no—
758C2×C4—2441no—
759C2×C4—2444no—
760C2×C4—2442no—
761C2×C4—2442no—
762C2×C4—2442no—
763C2×C4—2442no—
764C2×C4C22⋊C4×D6111yescharacteristic
765C2×C4C22⋊C4×D6111yescharacteristic
766C2×C4C22×C4×D6111yescharacteristic
767C2×C4C2×D4×D6111yescharacteristic
768C8—42no—
769C8—2442no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—44no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—84no—
782C22—612no—
783C22—612no—
784C22—612no—
785C22—1228no—
786C22—1221no—
787C22—1221no—
788C22—1221no—
789C22—1221no—
790C22—1221no—
791C22—1221no—
792C22—1221no—
793C22—1221no—
794C22—1221no—
795C22—2444no—
796C22—2444no—
797C22—2444no—
798C22—2444no—
799C22—2444no—
800C22#104×D6112yes—
801C22C2×C22⋊C4×D6111yescharacteristic
802C22#1684055812yes—
803C4—21no—
804C4—21no—
805C4—21no—
806C4—44no—
807C4—42no—
808C4—612no—
809C4—1221no—
810C4—1221no—
811C4—1221no—
812C4—2444no—
813C4—2442no—
814C4—2442no—
815C4#99×D6112yes—
816C2—22no—
817C2—22no—
818C2—41no—
819C2—82no—
820C2—1222no—
821C2—1222no—
822C2—1222no—
823C2—2441no—
824C2C2×#99×D6111yescharacteristic
825C2#2145433311yescharacteristic
826C2C2×#104×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1507C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840272C2
cosocleC22×C4×C61C24
hypercenter#1507D61
hypocenterC61#17542
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1507

Complements

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

NH ≅ G/Ntype
2. #407×D61C2semidirect
3. C4×C22⋊C4×D61C2semidirect
4. #21444340C2semidirect
5. #21444338C2semidirect
6. #21444335C2semidirect
7. #21444320C2semidirect
8. #21444307C2semidirect
9. C61×#1507C2semidirect
10. C22×#11758224C4semidirect
17. #16840272C4semidirect
18. #16840272C4semidirect
22. C2×#14519757C4semidirect
24. C2×#14519748C4semidirect
28. C2×#14519735C4semidirect
34. #16839724C22semidirect
36. C22⋊C8×D61C22semidirect
40. #16839609C22semidirect
41. #95×D61C22semidirect
42. #16839500C22semidirect
43. #16839498C22semidirect
44. #16839496C22semidirect
48. C61×#327C22semidirect
54. C2×#11758224C2×C4semidirect
55. C22×Dic122C2×C4semidirect
85. #14519757C2×C4semidirect
88. #14519756C2×C4semidirect
93. #14519748C2×C4semidirect
109. #14519735C2×C4semidirect
111. C2×C4⋊Dic61C2×C4semidirect
131. C22×D4×C61C2×C4semidirect
136. #121×C61C2×C4semidirect
138. C2×C4⋊C4×C61C2×C4semidirect
409. #1507D61semidirect
461. #327C2×D61semidirect
462. C61#17542semidirect
473. C22×D4C4×D61semidirect
514. #121C4×D61semidirect
535. C2×C4⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402722
#407×D612
C4×C22⋊C4×D612
#214443402
#214443382
#214443352
#214443202
#214443072
C61×#15072
#1754261