Finite Group Databasebeta

← #29689817

Subgroups — #29689817

Order 15616.

1598 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840272C211yesmaximal, characteristic
2#21448200C211yesmaximal, characteristic, complemented
3#380×D61C211yesmaximal, characteristic, complemented
4#21446804C211yesmaximal, characteristic, complemented
5#21446803C211yesmaximal, characteristic, complemented
6#21446656C211yesmaximal, characteristic, complemented
7#21446269C214yesmaximal, complemented
8#21445805C214yesmaximal, complemented
9C61×#1964C211yesmaximal, characteristic, complemented
10C22×#11758224C411yescharacteristic, complemented
11C23×C4×D61C2211yescharacteristic
12#16840272—21no—
13#16840272—21no—
14#16840272—21no—
15#16840272—21no—
16#16840272—21no—
17#16840272—21no—
18#16840272—21no—
19#16840272—21no—
20C2×#14519759C412yescomplemented
21C2×#14519757C411yescharacteristic, complemented
22C2×#14519756C2211yescharacteristic
23C2×#14519748C411yescharacteristic, complemented
24C2×#14519745C2212yes—
25C2×D4×Dic61C2212yes—
26C2×#14519737C412yescomplemented
27C2×#14519735C411yescharacteristic, complemented
28C2×#14519734—21no—
29C2×C4⋊C4×D61—21no—
30C2×C22⋊C4×D61C2212yes—
31C2×#14519692C2214yes—
32#16839624—21no—
33#16839622C2211yescharacteristic
34#16839621—21no—
35#16839621—21no—
36#16839620C2212yes—
37#16839620C2212yes—
38#16839619—21no—
39#16839617C2212yes—
40C4×#11758198—21no—
41C4×C22⋊Dic61C2211yescharacteristic
42#95×D61—21no—
43#16839528C2214yes—
44#16839528C2214yes—
45C2×#121×C61C2211yescharacteristic
46C2×#99×C61C2214yes—
47C61×#380C2211yescharacteristic
48C4×C22⋊C4×C61C2211yescharacteristic
49C24×D61C2311yescharacteristic
50C2×#11758224—21no—
51C2×#11758224—21no—
52C2×#11758224—21no—
53C2×#11758224—21no—
54C2×#11758224—44no—
55C22×Dic122C2×C411yescharacteristic, complemented
56C22×C22⋊D61C2×C412yes—
57C22×C22⋊D61C2×C412yes—
58C23×Dic61C2×C412yescomplemented
59C23×Dic61C2311yescharacteristic
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×D61D411yescharacteristic
73C22×C4×D61D411yescharacteristic
74#14519759—22no—
75#14519759—22no—
76#14519759—22no—
77#14519759—22no—
78#14519757—21no—
79#14519757—21no—
80#14519757—21no—
81#14519757—21no—
82#14519756—21no—
83#14519756—21no—
84#14519756—21no—
85#14519756—21no—
86#14519748—21no—
87#14519748—21no—
88#14519748—21no—
89#14519748—21no—
90#14519745—22no—
91#14519745—22no—
92#14519745—22no—
93#14519745—22no—
94D4×Dic61—22no—
95D4×Dic61—22no—
96D4×Dic61—22no—
97D4×Dic61—22no—
98#14519737—22no—
99#14519737—22no—
100#14519737—22no—
101#14519737—22no—
102#14519735—21no—
103#14519735—21no—
104#14519735—21no—
105#14519735—21no—
106#14519734—44no—
107C2×C4⋊Dic61—21no—
108C2×C4⋊Dic61C2×C411yescharacteristic, complemented
109C2×C4⋊Dic61C2×C412yescomplemented
110C2×#11758196—22no—
111C2×#11758196—22no—
112C2×#11758196C2×C412yescomplemented
113C4⋊C4×D61—44no—
114C2×C22⋊Dic61C2×C412yescomplemented
115C2×C22⋊Dic61C2312yes—
116C2×C22⋊Dic61C2312yes—
117C2×C22⋊Dic61C2312yes—
118C2×#11758198—22no—
119C2×#11758198—22no—
120C2×#11758198—22no—
121C2×#11758198C2×C412yes—
122C2×#11758198C2×C412yes—
123C22⋊C4×D61—44no—
124C2×C4×Dic61—21no—
125C2×C4×Dic61C2×C412yescomplemented
126#14519692—44no—
127#14519684—21no—
128#14519684—21no—
129#14519684—22no—
130#14519684—22no—
131C22×D4×C61C2×C411yescharacteristic, complemented
132C22×D4×C61C2312yes—
133C23×C4×C61C2311yescharacteristic
134#121×C61—21no—
135#121×C61—21no—
136#121×C61—21no—
137#121×C61—21no—
138C2×C4⋊C4×C61—21no—
139C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
140C2×C22⋊C4×C61C2×C412yescomplemented
141C2×C22⋊C4×C61C2312yes—
142C2×C22⋊C4×C61C2312yes—
143C2×C42×C61—21no—
144#99×C61—44no—
145#95×C61—21no—
146#95×C61—21no—
147C24×C61C22×C412yes—
148C24×C61C2411yescharacteristic
149C23×D61—22no—
150C23×D61—22no—
151C23×D61—42no—
152C23×D61—42no—
153C23×D61C22×C411yescharacteristic
154C23×D61C22×C411yescharacteristic
155C23×D61C2×D411yescharacteristic
156C23×D61C2×D411yescharacteristic
157C23×D61C2×D411yescharacteristic
158C23×D61C2×D411yescharacteristic
159C2×D4×C61—22no—
160C2×D4×C61—22no—
161C2×D4×C61—24no—
162C2×D4×C61—24no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—42no—
166C22×C4×C61—22no—
167C22×C4×C61—22no—
168C22×C4×C61—42no—
169C22×C4×C61C22×C412yes—
170C22×C4×C61C22×C411yescharacteristic
171C22×C4×C61C22×C411yescharacteristic
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61C2×D411yescharacteristic
175C22×C4×C61C2×D411yescharacteristic
176C2×C22⋊D61—22no—
177C2×C22⋊D61—22no—
178C2×C22⋊D61—22no—
179C2×C22⋊D61—22no—
180C2×C22⋊D61—44no—
181C2×C22⋊D61—44no—
182C22×Dic61—22no—
183C22×Dic61—22no—
184C22×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—42no—
187C22×Dic61—44no—
188C22×Dic61C22×C411yescharacteristic
189C22×Dic61C22×C412yes—
190C22×Dic61C22×C412yes—
191C22×Dic61C22×C411yescharacteristic
192C22×Dic61C2×D411yescharacteristic
193C22×Dic61C2×D411yescharacteristic
194C22×Dic61C2×D411yescharacteristic
195C22×Dic61C2×D411yescharacteristic
196#11758224—44no—
197#11758224—44no—
198#11758224—44no—
199#11758224—44no—
200C2×C4×D61—24no—
201C2×C4×D61—24no—
202C2×C4×D61—24no—
203C2×C4×D61—42no—
204C2×C4×D61—42no—
205C2×C4×D61—42no—
206C2×C4×D61—42no—
207C2×C4×D61—42no—
208C2×C4×D61—42no—
209C2×C4×D61—42no—
210C2×C4×D61—42no—
211C2×C4×D61—42no—
212C2×C4×D61—44no—
213C2×C4×D61—44no—
214C2×C4×D61—44no—
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×D61C22⋊C411yescharacteristic
224C2×C4×D61C22⋊C411yescharacteristic
225C2×C4×D61C22⋊C411yescharacteristic
226C2×C4×D61C22⋊C411yescharacteristic
227C2×C4×D61C22⋊C411yescharacteristic
228C2×C4×D61C22⋊C411yescharacteristic
229C2×C4×D61C22⋊C411yescharacteristic
230C2×C4×D61C22⋊C411yescharacteristic
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122—42no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61—42no—
237C22⋊C4×C61—22no—
238C22⋊C4×C61—22no—
239C22⋊C4×C61—22no—
240C22⋊C4×C61—24no—
241C22⋊C4×C61—22no—
242C42×C61—42no—
243C22⋊Dic61—22no—
244C22⋊Dic61—22no—
245C22⋊Dic61—22no—
246C22⋊Dic61—22no—
247C22⋊Dic61—22no—
248C22⋊Dic61—24no—
249C22⋊Dic61—22no—
250#11758198—22no—
251#11758198—22no—
252#11758198—22no—
253#11758198—22no—
254#11758198—44no—
255#11758198—44no—
256#11758198—44no—
257C4⋊Dic61—21no—
258C4⋊Dic61—21no—
259C4⋊Dic61—22no—
260C4⋊Dic61—22no—
261C4⋊Dic61—42no—
262#11758196—22no—
263#11758196—22no—
264#11758196—44no—
265#11758196—44no—
266C4×Dic61—22no—
267C4×Dic61—22no—
268C4×Dic61—42no—
269C23×C61—22no—
270C23×C61—24no—
271C23×C61—41no—
272C23×C61—41no—
273C23×C61—42no—
274C23×C61—42no—
275C23×C61C23×C411yescharacteristic
276C23×C61C22×D411yescharacteristic
277C23×C61C22×D411yescharacteristic
278C23×C61H(5,𝔽2)12yes—
279C23×C612−1+412yes—
280C22×D61—21no—
281C22×D61—21no—
282C22×D61—22no—
283C22×D61—22no—
284C22×D61—22no—
285C22×D61—22no—
286C22×D61—21no—
287C22×D61—21no—
288C22×D61—22no—
289C22×D61—22no—
290C22×D61—22no—
291C22×D61—22no—
292C22×D61—22no—
293C22×D61—22no—
294C22×D61—41no—
295C22×D61—41no—
296C22×D61—41no—
297C22×D61—41no—
298C22×D61—41no—
299C22×D61—41no—
300C22×D61—48no—
301C22×D61—48no—
302C22×D61C2×C22⋊C411yescharacteristic
303C22×D61C2×C22⋊C411yescharacteristic
304C22×D61C2×C22⋊C411yescharacteristic
305C22×D61C2×C22⋊C411yescharacteristic
306D4×C61—42no—
307D4×C61—42no—
308D4×C61—42no—
309D4×C61—44no—
310D4×C61—42no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—24no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—42no—
320C2×C4×C61—42no—
321C2×C4×C61—42no—
322C2×C4×C61—42no—
323C2×C4×C61—42no—
324C2×C4×C61—42no—
325C2×C4×C61C2×C22⋊C411yescharacteristic
326C2×C4×C61C2×C22⋊C411yescharacteristic
327C2×C4×C61C2×C22⋊C411yescharacteristic
328C2×C4×C61C2×C22⋊C411yescharacteristic
329C22⋊D61—44no—
330C22⋊D61—44no—
331C22⋊D61—44no—
332C22⋊D61—44no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341C2×Dic61—44no—
342C2×Dic61—44no—
343C2×Dic61—42no—
344C2×Dic61—42no—
345C2×Dic61—42no—
346C2×Dic61—42no—
347C2×Dic61—42no—
348C2×Dic61—42no—
349C2×Dic61—42no—
350C2×Dic61—42no—
351C2×Dic61C2×C22⋊C411yescharacteristic
352C2×Dic61C2×C22⋊C411yescharacteristic
353C2×Dic61C2×C22⋊C411yescharacteristic
354C2×Dic61C2×C22⋊C411yescharacteristic
355C4×D61—22no—
356C4×D61—22no—
357C4×D61—22no—
358C4×D61—22no—
359C4×D61—22no—
360C4×D61—22no—
361C4×D61—22no—
362C4×D61—22no—
363C4×D61—22no—
364C4×D61—41no—
365C4×D61—41no—
366C4×D61—41no—
367C4×D61—41no—
368C4×D61—41no—
369C4×D61—41no—
370C4×D61—88no—
371C4×D61#9914yescomplemented
372Dic122—42no—
373Dic122—42no—
374#21874—611nomaximal, Sylow
375C22×C61—21no—
376C22×C61—21no—
377C22×C61—21no—
378C22×C61—21no—
379C22×C61—21no—
380C22×C61—21no—
381C22×C61—42no—
382C22×C61—42no—
383C22×C61—42no—
384C22×C61—42no—
385C22×C61—42no—
386C22×C61—84no—
387C22×C61C22×C22⋊C411yescharacteristic
388C22×C61#52012yes—
389C22×C61#53511yescharacteristic
390C22×C61#53611yescharacteristic
391C22×C61#53712yes—
392C2×D61—24no—
393C2×D61—24no—
394C2×D61—21no—
395C2×D61—21no—
396C2×D61—21no—
397C2×D61—21no—
398C2×D61—21no—
399C2×D61—21no—
400C2×D61—21no—
401C2×D61—21no—
402C2×D61—21no—
403C2×D61—21no—
404C2×D61—44no—
405C2×D61—44no—
406C2×D61—44no—
407C2×D61—44no—
408C2×D61—42no—
409C2×D61—42no—
410C2×D61C2×#9912yes—
411C2×D61#41012yes—
412C4×C61—21no—
413C4×C61—21no—
414C4×C61—21no—
415C4×C61—42no—
416C4×C61—82no—
417C4×C61—82no—
418C4×C61C2×#9912yes—
419Dic61—21no—
420Dic61—21no—
421Dic61—21no—
422Dic61—42no—
423Dic61—42no—
424Dic61—82no—
425Dic61—82no—
426Dic61C2×#9912yes—
427C2×#525—611no—
428#2280—611no—
429C2×#380—611no—
430#1996—611no—
431#1996—611no—
432#1964—611no—
433#1964D6111yescharacteristic, complemented
434#1898—614no—
435#1799—614no—
436C2×C61—21no—
437C2×C61—22no—
438C2×C61—21no—
439C2×C61—22no—
440C2×C61—82no—
441C2×C61#231111yescharacteristic
442C2×C61C22×#9911yescharacteristic
443C2×C61C2×#41011yescharacteristic
444D61—22no—
445D61—22no—
446D61—41no—
447D61—41no—
448C22×#41—611no—
449C24×C4—611no—
450#525—1221no—
451#525—1221no—
452#525—1221no—
453#525—1221no—
454#525—1221no—
455#525—1221no—
456#525—1221no—
457#525—1221no—
458C2×#123—612no—
459C2×C22⋊Q8—611no—
460C2×C22⋊Q8—611no—
461C2×#121—611no—
462C2×#121C2×D6111yescharacteristic
463C2×#120—612no—
464C2×C4×D4—612no—
465C2×C4×D4—612no—
466C2×#117—611no—
467C2×#117—1221no—
468C22×C4⋊C4—1221no—
469C22×C22⋊C4—612no—
470C2×#99—614no—
471C2×#99C2×D6114yes—
472#381—1221no—
473#380—611no—
474#380—612no—
475#380—612no—
476#380—1221no—
477#380—1221no—
478#380—1221no—
479#380C2×D6111yescharacteristic
480#379—612no—
481C4×C22⋊C4—611no—
482C4×C22⋊C4—1221no—
483C4×C22⋊C4C2×D6111yescharacteristic
484C2×#95—1221no—
485#342—614no—
486#342—614no—
487C61#2187411yescharacteristic, complemented, Sylow
488C25—611no—
489C2×#41—1221no—
490C2×#41—1221no—
491C2×#41—1221no—
492C2×#41—1221no—
493C2×#41—2444no—
494C22×Q8—611no—
495C22×D4—612no—
496C22×D4—612no—
497C22×D4C4×D6111yescharacteristic, complemented
498C22×D4C22×D6112yes—
499C23×C4—611no—
500C23×C4—611no—
501C23×C4—611no—
502C23×C4—611no—
503C23×C4—611no—
504C23×C4—611no—
505C23×C4—611no—
506C23×C4—611no—
507C23×C4—611no—
508C23×C4—611no—
509C23×C4—611no—
510C23×C4—611no—
511C23×C4—611no—
512C23×C4—612no—
513C23×C4—1222no—
514C23×C4—2444no—
515C23×C4C22×D6111yescharacteristic
516#123—1222no—
517#123—1222no—
518#123—1222no—
519#123—1222no—
520C22⋊Q8—1221no—
521C22⋊Q8—1221no—
522C22⋊Q8—1221no—
523C22⋊Q8—1221no—
524C22⋊Q8—1221no—
525C22⋊Q8—1221no—
526C22⋊Q8—1221no—
527C22⋊Q8—1221no—
528#121—21no—
529#121—21no—
530#121—21no—
531#121—21no—
532#121—1221no—
533#121—1221no—
534#121—1221no—
535#121—1221no—
536#120—1222no—
537#120—1222no—
538#120—1222no—
539#120—1222no—
540C4×D4—1222no—
541C4×D4—1222no—
542C4×D4—1222no—
543C4×D4—1222no—
544C4×D4—1222no—
545C4×D4—1222no—
546C4×D4—1222no—
547C4×D4—1222no—
548#117—1221no—
549#117—1221no—
550#117—1221no—
551#117—1221no—
552#117—2444no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—611no—
555C2×C4⋊C4—612no—
556C2×C4⋊C4—612no—
557C2×C4⋊C4—1222no—
558C2×C4⋊C4—1222no—
559C2×C4⋊C4—1221no—
560C2×C4⋊C4—2444no—
561C2×C4⋊C4C4×D6111yescharacteristic, complemented
562C2×C22⋊C4—612no—
563C2×C22⋊C4—612no—
564C2×C22⋊C4—612no—
565C2×C22⋊C4—612no—
566C2×C22⋊C4—612no—
567C2×C22⋊C4—612no—
568C2×C22⋊C4—1222no—
569C2×C22⋊C4—1222no—
570C2×C22⋊C4—1222no—
571C2×C22⋊C4—2444no—
572C2×C22⋊C4C4×D6112yescomplemented
573C2×C22⋊C4C22×D6112yes—
574C2×C22⋊C4C22×D6112yes—
575C2×C42—21no—
576C2×C42—612no—
577C2×C42—1221no—
578#99—44no—
579#99—2444no—
580#95—21no—
581#95—21no—
582#95—1222no—
583#95—1222no—
584#95—1221no—
585#95—1221no—
586C24—611no—
587C24—611no—
588C24—611no—
589C24—611no—
590C24—611no—
591C24—611no—
592C24—1222no—
593C24—1222no—
594C24—2442no—
595C24—2442no—
596C24C2×C4×D6112yes—
597C24C23×D6111yescharacteristic
598#41—2444no—
599#41—2444no—
600#41—2444no—
601#41—2444no—
602C2×Q8—1221no—
603C2×Q8—1221no—
604C2×Q8—2442no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—24no—
608C2×D4—24no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—42no—
612C2×D4—1222no—
613C2×D4—1222no—
614C2×D4—1222no—
615C2×D4—1222no—
616C2×D4—2444no—
617C2×D4—2444no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—42no—
621C22×C4—611no—
622C22×C4—611no—
623C22×C4—611no—
624C22×C4—611no—
625C22×C4—611no—
626C22×C4—611no—
627C22×C4—611no—
628C22×C4—611no—
629C22×C4—611no—
630C22×C4—611no—
631C22×C4—611no—
632C22×C4—611no—
633C22×C4—611no—
634C22×C4—611no—
635C22×C4—611no—
636C22×C4—611no—
637C22×C4—611no—
638C22×C4—611no—
639C22×C4—611no—
640C22×C4—611no—
641C22×C4—611no—
642C22×C4—611no—
643C22×C4—612no—
644C22×C4—612no—
645C22×C4—1224no—
646C22×C4—1224no—
647C22×C4—1224no—
648C22×C4—1222no—
649C22×C4—1222no—
650C22×C4—1222no—
651C22×C4—1222no—
652C22×C4—2442no—
653C22×C4—2442no—
654C22×C4—2442no—
655C22×C4—2442no—
656C22×C4—2442no—
657C22×C4—2442no—
658C22×C4—2442no—
659C22×C4—2442no—
660C22×C4—2442no—
661C22×C4—2444no—
662C22×C4—2444no—
663C22×C4—2444no—
664C22×C4—2442no—
665C22×C4—2444no—
666C22×C4C2×C4×D6112yes—
667C22×C4C2×C4×D6111yescharacteristic
668C22×C4C2×C4×D6111yescharacteristic
669C22×C4D4×D6111yescharacteristic
670C22×C4D4×D6111yescharacteristic
671C22×C4D4×D6111yescharacteristic
672C22×C4D4×D6111yescharacteristic
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—42no—
676C4⋊C4—1222no—
677C4⋊C4—1222no—
678C4⋊C4—1222no—
679C4⋊C4—1222no—
680C4⋊C4—1221no—
681C4⋊C4—1221no—
682C4⋊C4—2442no—
683C4⋊C4—2444no—
684C4⋊C4—2444no—
685C22⋊C4—22no—
686C22⋊C4—22no—
687C22⋊C4—22no—
688C22⋊C4—24no—
689C22⋊C4—22no—
690C22⋊C4—1222no—
691C22⋊C4—1222no—
692C22⋊C4—1222no—
693C22⋊C4—1222no—
694C22⋊C4—1222no—
695C22⋊C4—1222no—
696C22⋊C4—1222no—
697C22⋊C4—1222no—
698C22⋊C4—1222no—
699C22⋊C4—1224no—
700C22⋊C4—1222no—
701C22⋊C4—2444no—
702C22⋊C4—2444no—
703C22⋊C4—2444no—
704C42—42no—
705C42—1222no—
706C42—1222no—
707C42—2442no—
708C23—22no—
709C23—24no—
710C23—41no—
711C23—41no—
712C23—42no—
713C23—42no—
714C23—611no—
715C23—611no—
716C23—611no—
717C23—611no—
718C23—1222no—
719C23—1222no—
720C23—1222no—
721C23—1222no—
722C23—1222no—
723C23—1222no—
724C23—1221no—
725C23—1221no—
726C23—1222no—
727C23—1222no—
728C23—1221no—
729C23—1221no—
730C23—1222no—
731C23—1222no—
732C23—2441no—
733C23—2441no—
734C23—2441no—
735C23—2441no—
736C23—2441no—
737C23—2441no—
738C23—2448no—
739C23—2448no—
740C23C22×C4×D6111yescharacteristic
741C23C2×D4×D6111yescharacteristic
742C23C2×D4×D6111yescharacteristic
743C23#1451982212yes—
744C23#1451982412yes—
745Q8—2442no—
746Q8—2442no—
747D4—42no—
748D4—42no—
749D4—42no—
750D4—44no—
751D4—42no—
752D4—2444no—
753D4—2444no—
754D4—2444no—
755D4—2444no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—611no—
771C2×C4—614no—
772C2×C4—611no—
773C2×C4—611no—
774C2×C4—611no—
775C2×C4—1222no—
776C2×C4—1222no—
777C2×C4—1222no—
778C2×C4—1222no—
779C2×C4—1222no—
780C2×C4—1222no—
781C2×C4—1222no—
782C2×C4—1222no—
783C2×C4—1222no—
784C2×C4—1222no—
785C2×C4—1222no—
786C2×C4—1222no—
787C2×C4—1222no—
788C2×C4—1222no—
789C2×C4—4888no—
790C2×C4—2441no—
791C2×C4—2441no—
792C2×C4—2441no—
793C2×C4—2441no—
794C2×C4—2441no—
795C2×C4—2441no—
796C2×C4—2444no—
797C2×C4—2441no—
798C2×C4—2441no—
799C2×C4—2441no—
800C2×C4—2444no—
801C2×C4—2442no—
802C2×C4—2442no—
803C2×C4—2442no—
804C2×C4—2442no—
805C2×C4—2442no—
806C2×C4—2442no—
807C2×C4—2442no—
808C2×C4—2442no—
809C2×C4C22⋊C4×D6111yescharacteristic
810C2×C4C22⋊C4×D6111yescharacteristic
811C2×C4C22⋊C4×D6111yescharacteristic
812C2×C4C22⋊C4×D6111yescharacteristic
813C22—21no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—84no—
825C22—612no—
826C22—612no—
827C22—1224no—
828C22—1224no—
829C22—1221no—
830C22—1221no—
831C22—1221no—
832C22—1221no—
833C22—1221no—
834C22—1221no—
835C22—1221no—
836C22—1221no—
837C22—1221no—
838C22—1221no—
839C22—2444no—
840C22—2444no—
841C22—2444no—
842C22—2444no—
843C22—2442no—
844C22—2442no—
845C22C2×C22⋊C4×D6111yescharacteristic
846C22#1684024112yes—
847C22#1684032511yescharacteristic
848C22#1684033211yescharacteristic
849C22#1684034112yes—
850C4—21no—
851C4—21no—
852C4—21no—
853C4—42no—
854C4—82no—
855C4—82no—
856C4—612no—
857C4—1221no—
858C4—1221no—
859C4—1221no—
860C4—4882no—
861C4—4882no—
862C4—2442no—
863C4—2442no—
864C4#99×D6112yes—
865C2—21no—
866C2—22no—
867C2—22no—
868C2—21no—
869C2—82no—
870C2—1222no—
871C2—1222no—
872C2—2441no—
873C2—2441no—
874C2#2144840911yescharacteristic
875C2C2×#99×D6111yescharacteristic
876C2#410×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1964C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840272C2
cosocleC24×C61C24
hypercenter#1964D61
hypocenterC61#21874
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1964

Complements

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

NH ≅ G/Ntype
2. #21448200C2semidirect
3. #380×D61C2semidirect
4. #21446804C2semidirect
5. #21446803C2semidirect
6. #21446656C2semidirect
7. #21446269C2semidirect
8. #21445805C2semidirect
9. C61×#1964C2semidirect
10. C22×#11758224C4semidirect
20. C2×#14519759C4semidirect
21. C2×#14519757C4semidirect
23. C2×#14519748C4semidirect
26. C2×#14519737C4semidirect
27. C2×#14519735C4semidirect
55. C22×Dic122C2×C4semidirect
58. C23×Dic61C2×C4semidirect
108. C2×C4⋊Dic61C2×C4semidirect
109. C2×C4⋊Dic61C2×C4semidirect
112. C2×#11758196C2×C4semidirect
114. C2×C22⋊Dic61C2×C4semidirect
125. C2×C4×Dic61C2×C4semidirect
131. C22×D4×C61C2×C4semidirect
139. C2×C4⋊C4×C61C2×C4semidirect
140. C2×C22⋊C4×C61C2×C4semidirect
371. C4×D61#99semidirect
433. #1964D61semidirect
487. C61#21874semidirect
497. C22×D4C4×D61semidirect
561. C2×C4⋊C4C4×D61semidirect
572. C2×C22⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402722
#214482002
#380×D612
#214468042
#214468032
#214466562
#214462692
#214458052
C61×#19642
#2187461