Finite Group Databasebeta

← #29647500

Subgroups — #29647500

Order 15616.

1510 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840272C211yesmaximal, characteristic
2C2×#16839724C211yesmaximal, characteristic, complemented
3#380×D61C211yesmaximal, characteristic, complemented
4#21444392C211yesmaximal, characteristic, complemented
5#21444390C211yesmaximal, characteristic, complemented
6#21444387C211yesmaximal, characteristic, complemented
7#21444359C214yesmaximal, complemented
8#21444320C214yesmaximal, complemented
9C61×#1519C211yesmaximal, characteristic, complemented
10C22×#11758224C411yescharacteristic, complemented
11C23×C4×D61C2211yescharacteristic
12C22×#11758189—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×C4⋊C4×D61—21no—
30C2×C22⋊C4×D61—21no—
31#16839724—21no—
32#16839724—21no—
33#16839724C2212yescomplemented
34#16839724C2212yescomplemented
35C2×C22⋊#92418C2211yescharacteristic
36C2×#14519689—21no—
37#16839622C2211yescharacteristic
38#16839621C2212yescomplemented
39#16839620—21no—
40#16839619—21no—
41#95×D61C2212yescomplemented
42#16839500C2214yescomplemented
43#16839498C2214yescomplemented
44#16839496C2214yescomplemented
45C2×#121×C61C2211yescharacteristic
46C2×C22⋊C8×C61C2211yescharacteristic
47C61×#380C2211yescharacteristic
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×#11758189—22no—
75C2×#11758189—22no—
76C2×#11758189—44no—
77C22×#92418—21no—
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⋊Dic61—21no—
112C2×C4⋊Dic61C2×C411yescharacteristic, complemented
113C2×#11758196—21no—
114C2×#11758196—22no—
115C4⋊C4×D61—44no—
116C2×C22⋊Dic61—21no—
117C2×C22⋊Dic61—21no—
118C2×C22⋊Dic61—21no—
119C2×#11758198—21no—
120C2×#11758198—21no—
121C2×#11758198—22no—
122C22⋊C4×D61—44no—
123C2×C4×Dic61—21no—
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
133C22×C8×C61—21no—
134#121×C61—21no—
135#121×C61—21no—
136#121×C61C2×C412yescomplemented
137#121×C61C2312yes—
138C2×C4⋊C4×C61—21no—
139C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142C22⋊C8×C61—21no—
143C22⋊C8×C61C2312yes—
144#95×C61C2312yes—
145C24×C61—21no—
146C24×C61C2×D411yescharacteristic
147C23×D61—22no—
148C23×D61—22no—
149C23×D61—42no—
150C23×D61—42no—
151C23×D61C22⋊C411yescharacteristic
152C23×D61C22⋊C411yescharacteristic
153C23×D61C22⋊C411yescharacteristic
154C23×D61C22⋊C411yescharacteristic
155C23×D61C2×D411yescharacteristic
156C23×D61C2×D411yescharacteristic
157C2×D4×C61—22no—
158C2×D4×C61—22no—
159C2×D4×C61—21no—
160C2×D4×C61—42no—
161C2×D4×C61—42no—
162C2×D4×C61—42no—
163C2×D4×C61C22×C412yes—
164C22×C4×C61—21no—
165C22×C4×C61—22no—
166C22×C4×C61—42no—
167C22×C4×C61C22×C411yescharacteristic
168C22×C4×C61C22×C411yescharacteristic
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61C2×D411yescharacteristic
171C22×C4×C61C2×D411yescharacteristic
172C22×C4×C61C2411yescharacteristic
173C2×C22⋊D61—22no—
174C2×C22⋊D61—22no—
175C2×C22⋊D61—22no—
176C2×C22⋊D61—22no—
177C2×C22⋊D61—44no—
178C2×C22⋊D61—44no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61—22no—
182C22×Dic61—22no—
183C22×Dic61—22no—
184C22×Dic61—42no—
185C22×Dic61—44no—
186C22×Dic61C22⋊C411yescharacteristic
187C22×Dic61C22⋊C411yescharacteristic
188C22×Dic61C22⋊C411yescharacteristic
189C22×Dic61C22⋊C411yescharacteristic
190C22×Dic61C2×D411yescharacteristic
191C22×Dic61C2×D411yescharacteristic
192#11758224—44no—
193#11758224—44no—
194#11758224—44no—
195#11758224—44no—
196C2×C4×D61—24no—
197C2×C4×D61—24no—
198C2×C4×D61—24no—
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—42no—
208C2×C4×D61—44no—
209C2×C4×D61—44no—
210C2×C4×D61—44no—
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×D61C22×C411yescharacteristic
222C2×C4×D61C22×C411yescharacteristic
223C2×C4×D61C2×D411yescharacteristic
224C2×C4×D61C2×D411yescharacteristic
225C2×C4×D61C2×D411yescharacteristic
226C2×C4×D61C2×D411yescharacteristic
227C2×Dic122—21no—
228C2×Dic122—42no—
229C2×Dic122C22×C412yes—
230C2×C8×C61—22no—
231C2×C8×C61—42no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—42no—
234C4⋊C4×C61C22×C412yes—
235C22⋊C4×C61—22no—
236C22⋊C4×C61—22no—
237C22⋊C4×C61—42no—
238C22⋊Dic61—22no—
239C22⋊Dic61—22no—
240C22⋊Dic61—22no—
241C22⋊Dic61—22no—
242C22⋊Dic61—42no—
243#11758198—22no—
244#11758198—22no—
245#11758198—22no—
246#11758198—22no—
247#11758198—44no—
248C4⋊Dic61—21no—
249C4⋊Dic61—22no—
250C4⋊Dic61—22no—
251C4⋊Dic61—42no—
252C4⋊Dic61C22×C412yes—
253#11758196—22no—
254#11758196—22no—
255#11758196—44no—
256C4×Dic61—22no—
257C4×Dic61—22no—
258C2×#92418—22no—
259C2×#92418—42no—
260#11758189—44no—
261#11758189—44no—
262C23×C61—22no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—42no—
266C23×C61—42no—
267C23×C61—42no—
268C23×C61C2×C22⋊C411yescharacteristic
269C23×C61C2×C22⋊C411yescharacteristic
270C23×C61AGL(1,ℤ/8)12yes—
271C23×C61#13712yes—
272C23×C61C22×D411yescharacteristic
273C22×D61—21no—
274C22×D61—21no—
275C22×D61—22no—
276C22×D61—22no—
277C22×D61—21no—
278C22×D61—21no—
279C22×D61—22no—
280C22×D61—22no—
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—22no—
284C22×D61—22no—
285C22×D61—22no—
286C22×D61—22no—
287C22×D61—41no—
288C22×D61—41no—
289C22×D61—41no—
290C22×D61—41no—
291C22×D61—41no—
292C22×D61—41no—
293C22×D61—48no—
294C22×D61—48no—
295C22×D61C2×C22⋊C411yescharacteristic
296C22×D61C2×C22⋊C411yescharacteristic
297C22×D61C2×C22⋊C411yescharacteristic
298C22×D61C2×C22⋊C411yescharacteristic
299D4×C61—42no—
300D4×C61—42no—
301D4×C61—42no—
302D4×C61—44no—
303D4×C61—42no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—42no—
312C2×C4×C61—42no—
313C2×C4×C61—42no—
314C2×C4×C61—42no—
315C2×C4×C61C2×C22⋊C411yescharacteristic
316C2×C4×C61C2×C22⋊C411yescharacteristic
317C2×C4×C61C23×C411yescharacteristic
318C2×C4×C61C22×D411yescharacteristic
319C22⋊D61—44no—
320C22⋊D61—44no—
321C22⋊D61—44no—
322C22⋊D61—44no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—44no—
332C2×Dic61—42no—
333C2×Dic61—42no—
334C2×Dic61—44no—
335C2×Dic61—42no—
336C2×Dic61—42no—
337C2×Dic61—42no—
338C2×Dic61C2×C22⋊C411yescharacteristic
339C2×Dic61C2×C22⋊C411yescharacteristic
340C2×Dic61C2×C22⋊C411yescharacteristic
341C2×Dic61C2×C22⋊C411yescharacteristic
342C4×D61—22no—
343C4×D61—22no—
344C4×D61—22no—
345C4×D61—22no—
346C4×D61—22no—
347C4×D61—22no—
348C4×D61—22no—
349C4×D61—22no—
350C4×D61—22no—
351C4×D61—41no—
352C4×D61—41no—
353C4×D61—41no—
354C4×D61—41no—
355C4×D61—41no—
356C4×D61—41no—
357C4×D61—88no—
358C4×D61#9914yes—
359Dic122—42no—
360Dic122—42no—
361C8×C61—42no—
362#92418—42no—
363#17592—611nomaximal, Sylow
364C22×C61—21no—
365C22×C61—21no—
366C22×C61—21no—
367C22×C61—21no—
368C22×C61—21no—
369C22×C61—21no—
370C22×C61—42no—
371C22×C61—42no—
372C22×C61—42no—
373C22×C61—42no—
374C22×C61—42no—
375C22×C61—84no—
376C22×C61#41712yes—
377C22×C61#41712yes—
378C22×C61C22×C22⋊C411yescharacteristic
379C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
380C22×C61C2×#13711yescharacteristic
381C2×D61—24no—
382C2×D61—24no—
383C2×D61—21no—
384C2×D61—21no—
385C2×D61—21no—
386C2×D61—21no—
387C2×D61—21no—
388C2×D61—21no—
389C2×D61—21no—
390C2×D61—21no—
391C2×D61—21no—
392C2×D61—21no—
393C2×D61—44no—
394C2×D61—44no—
395C2×D61—44no—
396C2×D61—44no—
397C2×D61—42no—
398C2×D61—42no—
399C2×D61C2×#9912yes—
400C2×D61#42112yes—
401C4×C61—21no—
402C4×C61—21no—
403C4×C61—21no—
404C4×C61—42no—
405C4×C61—82no—
406C4×C61C2×#9912yes—
407Dic61—21no—
408Dic61—21no—
409Dic61—21no—
410Dic61—42no—
411Dic61—42no—
412Dic61—82no—
413Dic61C2×#9912yes—
414C2×#525—611no—
415C2×#407—611no—
416C2×#380—611no—
417#1520—611no—
418#1520—611no—
419#1519—611no—
420#1519D6111yescharacteristic, complemented
421#1513—614no—
422#1504—614no—
423C2×C61—21no—
424C2×C61—21no—
425C2×C61—22no—
426C2×C61—22no—
427C2×C61—82no—
428C2×C61C22×#9911yescharacteristic
429C2×C61C2×#41711yescharacteristic
430C2×C61C2×#42111yescharacteristic
431D61—22no—
432D61—22no—
433D61—41no—
434D61—41no—
435C22×#41—611no—
436C24×C4—611no—
437C22×M16—1221no—
438#525—612no—
439#525—612no—
440#525—612no—
441#525—612no—
442#525—1221no—
443#525—1221no—
444#525—1221no—
445#525—1221no—
446C2×#123—1221no—
447C2×C22⋊Q8—611no—
448C2×C22⋊Q8—611no—
449C2×#121—611no—
450C2×#121C2×D6111yescharacteristic
451C2×#120—1221no—
452C2×C4×D4—1221no—
453C2×C4×D4—1221no—
454C2×#117—611no—
455C22×C4⋊C4—1221no—
456C22×C22⋊C4—1221no—
457#407—612no—
458#407—612no—
459#407—1221no—
460#407—1221no—
461C2×C22⋊C8—611no—
462C2×C22⋊C8—1221no—
463C2×C22⋊C8C2×D6111yescharacteristic
464#380—611no—
465#380—612no—
466#380—1221no—
467#380—1221no—
468#380C2×D6111yescharacteristic
469C2×#95—612no—
470#328—614no—
471#328—614no—
472#327—614no—
473#327C2×D6114yescomplemented
474C61#1759211yescharacteristic, complemented, Sylow
475C25—611no—
476C2×#41—612no—
477C2×#41—612no—
478C2×#41—1221no—
479C2×#41—1221no—
480C2×#41—2444no—
481C22×Q8—611no—
482C22×D4—21no—
483C22×D4—1221no—
484C22×D4—1221no—
485C22×D4C4×D6111yescharacteristic, complemented
486C23×C4—611no—
487C23×C4—611no—
488C23×C4—611no—
489C23×C4—611no—
490C23×C4—611no—
491C23×C4—611no—
492C23×C4—611no—
493C23×C4—611no—
494C23×C4—611no—
495C23×C4—611no—
496C23×C4—611no—
497C23×C4—611no—
498C23×C4—611no—
499C23×C4—1222no—
500C23×C4—1221no—
501C23×C4—2444no—
502C23×C4C22×D6111yescharacteristic
503C2×M16—1222no—
504C2×M16—1222no—
505C2×M16—2444no—
506C22×C8—21no—
507C22×C8—1221no—
508#123—1222no—
509#123—1222no—
510#123—1222no—
511#123—1222no—
512C22⋊Q8—612no—
513C22⋊Q8—612no—
514C22⋊Q8—612no—
515C22⋊Q8—612no—
516C22⋊Q8—1221no—
517C22⋊Q8—1221no—
518C22⋊Q8—1221no—
519C22⋊Q8—1221no—
520#121—21no—
521#121—21no—
522#121—612no—
523#121—612no—
524#121—1221no—
525#121—1221no—
526#121C4×D6112yescomplemented
527#121C22×D6112yes—
528#120—1222no—
529#120—1222no—
530#120—1222no—
531#120—1222no—
532C4×D4—1222no—
533C4×D4—1222no—
534C4×D4—1222no—
535C4×D4—1222no—
536C4×D4—1222no—
537C4×D4—1222no—
538C4×D4—1222no—
539C4×D4—1222no—
540#117—612no—
541#117—612no—
542#117—1221no—
543#117—1221no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—611no—
546C2×C4⋊C4—1221no—
547C2×C4⋊C4—1221no—
548C2×C4⋊C4—1222no—
549C2×C4⋊C4—1221no—
550C2×C4⋊C4—2444no—
551C2×C4⋊C4C4×D6111yescharacteristic, complemented
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—1221no—
555C2×C22⋊C4—1221no—
556C2×C22⋊C4—1221no—
557C2×C22⋊C4—1221no—
558C2×C22⋊C4—1222no—
559C2×C22⋊C4—1221no—
560C2×C22⋊C4—2444no—
561C2×C42—1221no—
562C22⋊C8—21no—
563C22⋊C8—612no—
564C22⋊C8—1222no—
565C22⋊C8—1222no—
566C22⋊C8—1221no—
567C22⋊C8C22×D6112yes—
568#95—612no—
569#95—1222no—
570#95C22×D6112yes—
571C24—21no—
572C24—611no—
573C24—611no—
574C24—611no—
575C24—611no—
576C24—611no—
577C24—611no—
578C24—1222no—
579C24—1222no—
580C24—2442no—
581C24—2442no—
582C24D4×D6111yescharacteristic
583#41—2444no—
584#41—2444no—
585#41—2444no—
586#41—2444no—
587C2×Q8—612no—
588C2×Q8—1221no—
589C2×Q8—2442no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—21no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—1222no—
597C2×D4—1222no—
598C2×D4—1222no—
599C2×D4—1222no—
600C2×D4—2444no—
601C2×D4—2444no—
602C2×D4C2×C4×D6112yes—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—42no—
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—611no—
615C22×C4—611no—
616C22×C4—611no—
617C22×C4—611no—
618C22×C4—611no—
619C22×C4—611no—
620C22×C4—611no—
621C22×C4—611no—
622C22×C4—611no—
623C22×C4—611no—
624C22×C4—611no—
625C22×C4—611no—
626C22×C4—611no—
627C22×C4—611no—
628C22×C4—1224no—
629C22×C4—1224no—
630C22×C4—1224no—
631C22×C4—1222no—
632C22×C4—1222no—
633C22×C4—1221no—
634C22×C4—1221no—
635C22×C4—1222no—
636C22×C4—2442no—
637C22×C4—2442no—
638C22×C4—2442no—
639C22×C4—2442no—
640C22×C4—2442no—
641C22×C4—2442no—
642C22×C4—2442no—
643C22×C4—2442no—
644C22×C4—2442no—
645C22×C4—2444no—
646C22×C4—2444no—
647C22×C4—2444no—
648C22×C4—2442no—
649C22×C4—2444no—
650C22×C4C2×C4×D6111yescharacteristic
651C22×C4C2×C4×D6111yescharacteristic
652C22×C4D4×D6111yescharacteristic
653C22×C4D4×D6111yescharacteristic
654C22×C4D4×D6111yescharacteristic
655C22×C4C23×D6111yescharacteristic
656M16—2444no—
657M16—2444no—
658C2×C8—22no—
659C2×C8—42no—
660C2×C8—1222no—
661C2×C8—2442no—
662C4⋊C4—21no—
663C4⋊C4—42no—
664C4⋊C4—612no—
665C4⋊C4—1222no—
666C4⋊C4—1222no—
667C4⋊C4—1222no—
668C4⋊C4—1221no—
669C4⋊C4—1222no—
670C4⋊C4—2442no—
671C4⋊C4—2444no—
672C4⋊C4C2×C4×D6112yes—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—42no—
676C22⋊C4—1222no—
677C22⋊C4—1222no—
678C22⋊C4—1222no—
679C22⋊C4—1222no—
680C22⋊C4—1222no—
681C22⋊C4—1222no—
682C22⋊C4—1222no—
683C22⋊C4—1222no—
684C22⋊C4—2444no—
685C22⋊C4—2442no—
686C42—1222no—
687C42—1222no—
688C23—22no—
689C23—41no—
690C23—41no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—611no—
695C23—611no—
696C23—611no—
697C23—611no—
698C23—1222no—
699C23—1222no—
700C23—1222no—
701C23—1222no—
702C23—1222no—
703C23—1222no—
704C23—1221no—
705C23—1221no—
706C23—1222no—
707C23—1222no—
708C23—1222no—
709C23—1222no—
710C23—1221no—
711C23—1221no—
712C23—2441no—
713C23—2441no—
714C23—2441no—
715C23—2441no—
716C23—2441no—
717C23—2441no—
718C23—2448no—
719C23—2448no—
720C23C22⋊C4×D6111yescharacteristic
721C23C22⋊C4×D6111yescharacteristic
722C23#1451980112yes—
723C23#1451980612yes—
724C23C2×D4×D6111yescharacteristic
725Q8—2442no—
726Q8—2442no—
727D4—42no—
728D4—44no—
729D4—42no—
730D4—42no—
731D4—42no—
732D4—2444no—
733D4—2444no—
734D4—2444no—
735D4—2444no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—611no—
748C2×C4—614no—
749C2×C4—611no—
750C2×C4—611no—
751C2×C4—611no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—1222no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—1222no—
766C2×C4—4888no—
767C2×C4—2441no—
768C2×C4—2441no—
769C2×C4—2441no—
770C2×C4—2441no—
771C2×C4—2441no—
772C2×C4—2441no—
773C2×C4—2444no—
774C2×C4—2441no—
775C2×C4—2441no—
776C2×C4—2441no—
777C2×C4—2444no—
778C2×C4—2442no—
779C2×C4—2442no—
780C2×C4—2442no—
781C2×C4—2442no—
782C2×C4—2442no—
783C2×C4C22⋊C4×D6111yescharacteristic
784C2×C4C22⋊C4×D6111yescharacteristic
785C2×C4C22×C4×D6111yescharacteristic
786C2×C4C2×D4×D6111yescharacteristic
787C8—42no—
788C8—2442no—
789C22—21no—
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—84no—
801C22—612no—
802C22—612no—
803C22—1224no—
804C22—1224no—
805C22—1221no—
806C22—1221no—
807C22—1221no—
808C22—1221no—
809C22—1221no—
810C22—1221no—
811C22—1221no—
812C22—1221no—
813C22—1221no—
814C22—1221no—
815C22—2444no—
816C22—2444no—
817C22—2444no—
818C22—2444no—
819C22—2442no—
820C22—2442no—
821C22#1683976012yes—
822C22#1683976012yes—
823C22C2×C22⋊C4×D6111yescharacteristic
824C22C2×#1451980111yescharacteristic
825C22C2×#1451980611yescharacteristic
826C4—21no—
827C4—21no—
828C4—21no—
829C4—42no—
830C4—82no—
831C4—612no—
832C4—1221no—
833C4—1221no—
834C4—1221no—
835C4—4882no—
836C4—2442no—
837C4—2442no—
838C4#99×D6112yes—
839C2—21no—
840C2—22no—
841C2—21no—
842C2—22no—
843C2—82no—
844C2—1222no—
845C2—1222no—
846C2—2441no—
847C2—2441no—
848C2C2×#99×D6111yescharacteristic
849C2C2×#1683976011yescharacteristic
850C2#421×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1519C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840272C2
cosocleC22×C4×C61C24
hypercenter#1519D61
hypocenterC61#17592
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1519

Complements

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

NH ≅ G/Ntype
2. C2×#16839724C2semidirect
3. #380×D61C2semidirect
4. #21444392C2semidirect
5. #21444390C2semidirect
6. #21444387C2semidirect
7. #21444359C2semidirect
8. #21444320C2semidirect
9. C61×#1519C2semidirect
10. C22×#11758224C4semidirect
17. #16840272C4semidirect
18. #16840272C4semidirect
22. C2×#14519757C4semidirect
24. C2×#14519748C4semidirect
28. C2×#14519735C4semidirect
33. #16839724C22semidirect
34. #16839724C22semidirect
38. #16839621C22semidirect
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
112. C2×C4⋊Dic61C2×C4semidirect
131. C22×D4×C61C2×C4semidirect
136. #121×C61C2×C4semidirect
139. C2×C4⋊C4×C61C2×C4semidirect
420. #1519D61semidirect
473. #327C2×D61semidirect
474. C61#17592semidirect
485. C22×D4C4×D61semidirect
526. #121C4×D61semidirect
551. 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
C2×#168397242
#380×D612
#214443922
#214443902
#214443872
#214443592
#214443202
C61×#15192
#1759261