Finite Group Databasebeta

← #29681388

Subgroups — #29681388

Order 15616.

1830 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519809C211yesmaximal, characteristic
2C2×C4×#11758226C211yesmaximal, characteristic
3C2×#16839762C211yesmaximal, characteristic
4C2×#16839769C211yesmaximal, characteristic, complemented
5#391×D61C211yesmaximal, characteristic, complemented
6#21446162C211yesmaximal, characteristic, complemented
7#21446160C211yesmaximal, characteristic, complemented
8#21446158C211yesmaximal, characteristic, complemented
9#21446156C211yesmaximal, characteristic, complemented
10#21446154C211yesmaximal, characteristic, complemented
11#21446152C211yesmaximal, characteristic, complemented
12#21446150C211yesmaximal, characteristic, complemented
13#21445537C211yesmaximal, characteristic, complemented
14#21445511C211yesmaximal, characteristic, complemented
15C61×#1878C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×Q8×D61C2211yescharacteristic
18C2×#14519809—24no—
19C2×#14519809—24no—
20C2×#14519809C418yescomplemented
21C22×#11758202C2211yescharacteristic
22C22×#11758190C2211yescharacteristic
23C22×#11758201C2211yescharacteristic
24C22×#11758189C2211yescharacteristic
25C22×#11758189C2211yescharacteristic
26C4×#11758226—24no—
27C4×#11758226—24no—
28C2×Q8×Dic61C2211yescharacteristic
29C2×C4×D244—21no—
30C2×C4×D244C2211yescharacteristic
31C2×#14519739—21no—
32C2×#14519739C2211yescharacteristic
33C2×#14519735—21no—
34C2×#14519735C2211yescharacteristic
35C2×C4⋊C4×D61C2211yescharacteristic
36C2×C42×D61—21no—
37C2×C42×D61C2211yescharacteristic
38#16839769—24no—
39#16839762—24no—
40C2×#14519702C2211yescharacteristic
41C2×#14519701C2211yescharacteristic
42C2×#14519701C2211yescharacteristic
43C2×#14519700C2211yescharacteristic
44C2×#14519699C2211yescharacteristic
45C2×#14519697C2211yescharacteristic
46#16839669C2211yescharacteristic
47#16839668C2211yescharacteristic
48#16839667C2211yescharacteristic
49#16839666—21no—
50#16839666—21no—
51#95×D61—21no—
52#95×D61—21no—
53#16839525C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839524C2211yescharacteristic
56#16839517C2211yescharacteristic
57#16839516C2211yescharacteristic
58#16839516C2211yescharacteristic
59C22×Q16×C61C2211yescharacteristic
60C2×C4×Q8×C61C2211yescharacteristic
61C2×#103×C61C2211yescharacteristic
62C2×#103×C61C2211yescharacteristic
63C61×#391C2211yescharacteristic
64C61×#340C2211yescharacteristic
65C61×#336C2211yescharacteristic
66C2×#11758226—22no—
67C2×#11758226—22no—
68C2×#11758226—22no—
69C2×#11758226C2×C414yes—
70C2×#11758226D414yes—
71C2×#11758226D414yes—
72C22×Dic122—21no—
73C22×Dic122C2311yescharacteristic
74C2×Q8×D61—22no—
75C2×Q8×D61—22no—
76C2×Q8×D61—22no—
77C2×Q8×D61—22no—
78C2×Q8×D61—22no—
79C2×Q8×D61C2×C414yescomplemented
80C22×D244—21no—
81C22×D244C2311yescharacteristic
82C22×C4×D61—21no—
83C22×C4×D61—21no—
84C22×C4×D61—21no—
85C22×C4×D61—21no—
86C22×C4×D61—21no—
87C22×C4×D61D411yescharacteristic
88C22×C4×D61D411yescharacteristic
89C22×C4×D61C2311yescharacteristic
90#14519809—232no—
91C2×#11758202—22no—
92C2×#11758202—22no—
93C2×#11758202C2×C414yescomplemented
94C2×#11758190—22no—
95C2×#11758190—22no—
96C2×#11758190C2×C414yescomplemented
97C2×#11758201—22no—
98C2×#11758201—22no—
99C2×#11758201C2×C414yescomplemented
100C2×#11758189—22no—
101C2×#11758189—22no—
102C2×#11758189—22no—
103C2×#11758189—22no—
104C2×#11758189—22no—
105C2×#11758189C2×C414yescomplemented
106C22×#92418C2311yescharacteristic
107C22×#92418C2311yescharacteristic
108Q8×Dic61—22no—
109Q8×Dic61—22no—
110C4×D244—28no—
111C4×D244—22no—
112C4×D244—22no—
113#14519739—28no—
114#14519739—22no—
115#14519739—22no—
116#14519735—28no—
117#14519735—22no—
118#14519735D414yes—
119C2×C4⋊Dic61—21no—
120C2×C4⋊Dic61C2311yescharacteristic
121C2×C4⋊Dic61C2311yescharacteristic
122C2×#11758196—21no—
123C4⋊C4×D61—22no—
124C4⋊C4×D61—22no—
125C2×#11758198—21no—
126C2×#11758198—21no—
127C2×#11758198—21no—
128C2×C4×Dic61—21no—
129C2×C4×Dic61—21no—
130C2×C4×Dic61D411yescharacteristic
131C2×C4×Dic61D411yescharacteristic
132C2×C4×Dic61C2311yescharacteristic
133C42×D61—28no—
134C42×D61—22no—
135C42×D61—22no—
136#14519702—22no—
137#14519701—22no—
138#14519701—22no—
139#14519700—22no—
140#14519699—22no—
141#14519697—22no—
142#14519684—21no—
143#14519684—21no—
144#14519684—21no—
145#14519684—21no—
146#14519684—21no—
147#14519684—21no—
148C22×Q8×C61C2311yescharacteristic
149C22×Q8×C61C2311yescharacteristic
150C2×Q16×C61—22no—
151C2×Q16×C61—22no—
152C2×Q16×C61C2×C414yescomplemented
153C22×C8×C61C2311yescharacteristic
154C22×C8×C61C2311yescharacteristic
155C4×Q8×C61—22no—
156C4×Q8×C61—22no—
157C2×C4⋊C4×C61—21no—
158C2×C4⋊C4×C61C2311yescharacteristic
159C2×C4⋊C4×C61C2311yescharacteristic
160C2×C42×C61—21no—
161C2×C42×C61C2311yescharacteristic
162#103×C61—22no—
163#103×C61—22no—
164#95×C61—21no—
165#95×C61—21no—
166C23×D61—21no—
167C23×D61C2×D411yescharacteristic
168C2×Q8×C61—21no—
169C2×Q8×C61—21no—
170C2×Q8×C61—21no—
171C2×Q8×C61—21no—
172C2×Q8×C61—21no—
173C2×Q8×C61—21no—
174C2×Q8×C61—21no—
175C2×Q8×C61—21no—
176C2×Q8×C61C22×C412yes—
177C2×Q8×C61C22×C412yes—
178C2×Q8×C61C2×D412yes—
179C2×Q8×C61C2×D412yes—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2411yescharacteristic
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61C2×D411yescharacteristic
191C22×Dic61C2×D411yescharacteristic
192C22×Dic61C2×D411yescharacteristic
193#11758226—28no—
194#11758226—28no—
195#11758226—28no—
196#11758226C22⋊C4116yes—
197Q8×D61—28no—
198Q8×D61—28no—
199Q8×D61—44no—
200Q8×D61—44no—
201C2×D244—24no—
202C2×D244—24no—
203C2×D244—24no—
204C2×D244—21no—
205C2×D244—21no—
206C2×D244—21no—
207C2×D244C22×C412yes—
208C2×D244C2×D412yes—
209C2×D244C2×D412yes—
210C2×C4×D61—24no—
211C2×C4×D61—24no—
212C2×C4×D61—24no—
213C2×C4×D61—24no—
214C2×C4×D61—24no—
215C2×C4×D61—24no—
216C2×C4×D61—22no—
217C2×C4×D61—22no—
218C2×C4×D61—22no—
219C2×C4×D61—22no—
220C2×C4×D61—41no—
221C2×C4×D61—41no—
222C2×C4×D61—42no—
223C2×C4×D61—42no—
224C2×C4×D61—42no—
225C2×C4×D61—42no—
226C2×C4×D61—42no—
227C2×C4×D61—42no—
228C2×C4×D61—42no—
229C2×C4×D61—42no—
230C2×C4×D61—42no—
231C2×C4×D61C22×C412yes—
232C2×C4×D61C2×D412yes—
233C2×C4×D61C2×D412yes—
234C2×C4×D61C2×D412yes—
235C2×C4×D61#4112yes—
236C2×C4×D61#4112yes—
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122—21no—
240C2×Dic122—21no—
241C2×Dic122—21no—
242C2×Dic122—24no—
243C2×Dic122—42no—
244C2×Dic122—42no—
245C2×Dic122C22×C412yes—
246Q16×C61—28no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61—21no—
250C2×C8×C61—21no—
251C2×C8×C61—21no—
252C2×C8×C61C22×C412yes—
253C4⋊C4×C61—24no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61C2×D412yes—
258C42×C61—24no—
259C42×C61—21no—
260C42×C61—21no—
261#11758202—28no—
262#11758201—28no—
263#11758198—24no—
264#11758198—24no—
265#11758198—24no—
266C4⋊Dic61—24no—
267C4⋊Dic61—21no—
268C4⋊Dic61—21no—
269C4⋊Dic61—21no—
270C4⋊Dic61C2×D412yes—
271#11758196—42no—
272C4×Dic61—24no—
273C4×Dic61—21no—
274C4×Dic61—21no—
275C4×Dic61—22no—
276C4×Dic61—24no—
277C4×Dic61—22no—
278C2×#92418—21no—
279C2×#92418—21no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418C22×C412yes—
284#11758190—28no—
285#11758189—28no—
286#11758189—44no—
287C23×C61C22×D411yescharacteristic
288C22×D61—21no—
289C22×D61—21no—
290C22×D61—21no—
291C22×D61—21no—
292C22×D61—22no—
293C22×D61—22no—
294C22×D61—22no—
295C22×D61—41no—
296C22×D61—41no—
297C22×D61—41no—
298C22×D61—41no—
299C22×D61C4×D412yes—
300C22×D61#12012yes—
301C22×D61#12112yes—
302Q8×C61—22no—
303Q8×C61—22no—
304Q8×C61—22no—
305Q8×C61—22no—
306Q8×C61—22no—
307Q8×C61—41no—
308Q8×C61—41no—
309Q8×C61C2×C22⋊C414yes—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—21no—
313C2×C4×C61—22no—
314C2×C4×C61—21no—
315C2×C4×C61—22no—
316C2×C4×C61—21no—
317C2×C4×C61—22no—
318C2×C4×C61—21no—
319C2×C4×C61—21no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61#13712yescomplemented
328C2×C4×C61C23×C411yescharacteristic
329C2×C4×C61C22×D411yescharacteristic
330C2×C4×C61C22×D411yescharacteristic
331C2×C4×C61C22×D411yescharacteristic
332C2×C4×C61C2×#4111yescharacteristic
333C2×C4×C61C2×#4111yescharacteristic
334C2×Dic61—21no—
335C2×Dic61—21no—
336C2×Dic61—22no—
337C2×Dic61—21no—
338C2×Dic61—22no—
339C2×Dic61—21no—
340C2×Dic61—21no—
341C2×Dic61—41no—
342C2×Dic61—41no—
343C2×Dic61—41no—
344C2×Dic61—41no—
345C2×Dic61—41no—
346C2×Dic61—41no—
347C2×Dic61—41no—
348C2×Dic61C4×D412yes—
349C2×Dic61#12012yes—
350C2×Dic61#12112yes—
351C2×Dic61#13712yescomplemented
352D244—216no—
353D244—22no—
354D244—22no—
355D244—22no—
356D244C2×C22⋊C414yes—
357C4×D61—216no—
358C4×D61—44no—
359C4×D61—48no—
360C4×D61—44no—
361C4×D61—48no—
362C4×D61—48no—
363C4×D61—84no—
364C4×D61C2×C22⋊C414yes—
365C4×D61C4×D414yes—
366C4×D61#12114yes—
367C4×D61#12314yes—
368Dic122—22no—
369Dic122—22no—
370Dic122—41no—
371Dic122—41no—
372Dic122—48no—
373C8×C61—22no—
374C8×C61—41no—
375#92418—22no—
376#92418—41no—
377#20927—611nomaximal, Sylow
378C22×C61C2×C4×D411yescharacteristic
379C22×C61C2×#12011yescharacteristic
380C22×C61C2×#12111yescharacteristic
381C22×C61C2×#13711yescharacteristic
382C22×C61C2×#13711yescharacteristic
383C22×C61#57511yescharacteristic
384C22×C61#57511yescharacteristic
385C2×D61—22no—
386C2×D61—22no—
387C2×D61—22no—
388C2×D61—22no—
389C2×D61—22no—
390C2×D61—22no—
391C2×D61—24no—
392C2×D61—42no—
393C2×D61—42no—
394C2×D61—42no—
395C2×D61—42no—
396C2×D61—42no—
397C2×D61—42no—
398C2×D61#38614yes—
399C4×C61—22no—
400C4×C61—24no—
401C4×C61—41no—
402C4×C61—42no—
403C4×C61—42no—
404C4×C61—81no—
405C4×C61C22×C22⋊C411yescharacteristic
406C4×C61C2×C4×D411yescharacteristic
407C4×C61C2×#12111yescharacteristic
408C4×C61C2×#12311yescharacteristic
409Dic61—22no—
410Dic61—41no—
411Dic61—42no—
412Dic61—42no—
413Dic61—81no—
414Dic61#38614yes—
415C22×#137—611no—
416C2×C4×#41—611no—
417C2×#417—611no—
418C2×#419—611no—
419C2×#391—611no—
420#1878—611no—
421#1878—611no—
422#1878—611no—
423#1878D6111yescharacteristic, complemented
424#1877—611no—
425#1877—611no—
426#1877—611no—
427#1877—611no—
428#1736—611no—
429#1728—611no—
430C2×C61C2×#38611yescharacteristic
431C2×C61C4×#13711yescharacteristic
432C2×C61C4×#13711yescharacteristic
433C2×C61#300711yescharacteristic
434C2×C61#300711yescharacteristic
435C2×C61#303911yescharacteristic
436C2×C61#304011yescharacteristic
437D61—24no—
438D61—44no—
439C22×#41—611no—
440C23×Q8—611no—
441C2×#137—618no—
442C2×#137—1224no—
443C2×#137—1224no—
444C22×Q16—611no—
445C22×Q16C2×D6111yescharacteristic
446C22×SD16—611no—
447C22×SD16—611no—
448C22×M16—611no—
449C22×M16—611no—
450C4×#41—1224no—
451C4×#41—1224no—
452C2×C4×Q8—611no—
453C2×C4×Q8C2×D6111yescharacteristic
454C2×C4×D4—611no—
455C2×C4×D4—611no—
456C2×C4×D4—1221no—
457C2×C4×D4—1221no—
458C2×#117—611no—
459C2×#117—1221no—
460C22×C4⋊C4—611no—
461C22×C42—611no—
462C22×C42—1221no—
463#419—1224no—
464#417—1224no—
465C2×#103—611no—
466C2×#103—611no—
467C2×#103—611no—
468C2×#103—611no—
469C2×#103C2×D6111yescharacteristic
470C2×#103C2×D6111yescharacteristic
471C2×#102—611no—
472C2×#102—611no—
473#391—611no—
474#391—611no—
475#391—611no—
476#391—1221no—
477#391—1221no—
478#391C2×D6111yescharacteristic
479C2×#95—1221no—
480C2×#95—1221no—
481#340—611no—
482#340—611no—
483#340—611no—
484#340C2×D6111yescharacteristic
485#336—611no—
486#336—611no—
487#336—611no—
488#336C2×D6111yescharacteristic
489C61#2092711yescharacteristic, complemented, Sylow
490C2×#41—614no—
491C2×#41—614no—
492C2×#41—614no—
493C2×#41—1222no—
494C2×#41—1222no—
495C2×#41—1222no—
496C22×Q8—614no—
497C22×Q8—611no—
498C22×Q8—1221no—
499C22×Q8—1222no—
500C22×Q8—1222no—
501C22×Q8—1222no—
502C22×Q8—1222no—
503C22×Q8—1222no—
504C22×Q8C22×D6111yescharacteristic
505C22×Q8C22×D6111yescharacteristic
506C22×D4—611no—
507C22×D4—1221no—
508C23×C4—611no—
509C23×C4—611no—
510C23×C4—611no—
511C23×C4—1221no—
512C23×C4—1221no—
513C23×C4—1221no—
514C23×C4—1221no—
515C23×C4—1221no—
516#137—12232no—
517C2×Q16—22no—
518C2×Q16—22no—
519C2×Q16—614no—
520C2×Q16—1222no—
521C2×Q16—1222no—
522C2×Q16C4×D6114yescomplemented
523C2×SD16—614no—
524C2×SD16—614no—
525C2×SD16—1222no—
526C2×SD16—1222no—
527C2×SD16—1222no—
528C2×SD16—1222no—
529C2×M16—614no—
530C2×M16—1222no—
531C2×M16—1222no—
532C2×M16—1222no—
533C2×M16—1222no—
534C2×M16—1222no—
535C22×C8—611no—
536C22×C8—611no—
537C22×C8C22×D6111yescharacteristic
538C22×C8C22×D6111yescharacteristic
539C4×Q8—22no—
540C4×Q8—22no—
541C4×Q8—1222no—
542C4×Q8—1222no—
543C4×D4—1222no—
544C4×D4—1222no—
545C4×D4—1228no—
546C4×D4—1222no—
547C4×D4—1228no—
548C4×D4—1222no—
549#117—614no—
550#117—1222no—
551#117—1228no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—611no—
554C2×C4⋊C4—611no—
555C2×C4⋊C4—1222no—
556C2×C4⋊C4—1222no—
557C2×C4⋊C4—1221no—
558C2×C4⋊C4—1221no—
559C2×C4⋊C4C22×D6111yescharacteristic
560C2×C4⋊C4C22×D6111yescharacteristic
561C2×C22⋊C4—1221no—
562C2×C22⋊C4—1221no—
563C2×C22⋊C4—1221no—
564C2×C42—21no—
565C2×C42—611no—
566C2×C42—611no—
567C2×C42—611no—
568C2×C42—1222no—
569C2×C42—1222no—
570C2×C42—1228no—
571C2×C42—1221no—
572C2×C42—1221no—
573C2×C42C22×D6111yescharacteristic
574#103—22no—
575#103—22no—
576#103—1222no—
577#103—1222no—
578#103—1222no—
579#103—1222no—
580#102—1222no—
581#102—1222no—
582#95—21no—
583#95—21no—
584#95—1221no—
585#95—1221no—
586#95—1221no—
587#95—1221no—
588#95—1221no—
589#95—1221no—
590C24—611no—
591C24—1221no—
592#41—6116no—
593#41—1228no—
594#41—1228no—
595#41—1228no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—612no—
605C2×Q8—1224no—
606C2×Q8—1228no—
607C2×Q8—1228no—
608C2×Q8—1221no—
609C2×Q8—1221no—
610C2×Q8—1221no—
611C2×Q8—1221no—
612C2×Q8—1221no—
613C2×Q8—2442no—
614C2×Q8—2442no—
615C2×Q8—2444no—
616C2×Q8—2444no—
617C2×Q8C2×C4×D6112yes—
618C2×Q8C2×C4×D6112yes—
619C2×Q8D4×D6112yes—
620C2×Q8D4×D6112yes—
621C2×D4—612no—
622C2×D4—612no—
623C2×D4—612no—
624C2×D4—1224no—
625C2×D4—1224no—
626C2×D4—1224no—
627C2×D4—1221no—
628C2×D4—1221no—
629C2×D4—1221no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—611no—
635C22×C4—612no—
636C22×C4—612no—
637C22×C4—612no—
638C22×C4—612no—
639C22×C4—612no—
640C22×C4—612no—
641C22×C4—611no—
642C22×C4—611no—
643C22×C4—1224no—
644C22×C4—1224no—
645C22×C4—1224no—
646C22×C4—1222no—
647C22×C4—1222no—
648C22×C4—1222no—
649C22×C4—1224no—
650C22×C4—1224no—
651C22×C4—1224no—
652C22×C4—1221no—
653C22×C4—1221no—
654C22×C4—1222no—
655C22×C4—1221no—
656C22×C4—2441no—
657C22×C4—2441no—
658C22×C4—2442no—
659C22×C4—2442no—
660C22×C4—2442no—
661C22×C4—2442no—
662C22×C4—2442no—
663C22×C4—2442no—
664C22×C4—2442no—
665C22×C4—2442no—
666C22×C4—2442no—
667C22×C4D4×D6111yescharacteristic
668C22×C4D4×D6111yescharacteristic
669C22×C4C23×D6111yescharacteristic
670Q16—28no—
671Q16—1228no—
672SD16—1228no—
673SD16—1228no—
674M16—1228no—
675M16—2444no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—612no—
682C2×C8—1221no—
683C2×C8—1221no—
684C2×C8—1221no—
685C2×C8—1221no—
686C2×C8—1221no—
687C2×C8C2×C4×D6112yes—
688C4⋊C4—24no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—612no—
693C4⋊C4—1224no—
694C4⋊C4—1221no—
695C4⋊C4—1221no—
696C4⋊C4—1221no—
697C4⋊C4—2442no—
698C4⋊C4D4×D6112yes—
699C22⋊C4—1224no—
700C22⋊C4—1224no—
701C22⋊C4—1224no—
702C42—24no—
703C42—21no—
704C42—21no—
705C42—1222no—
706C42—1222no—
707C42—1224no—
708C42—1224no—
709C42—1221no—
710C42—1221no—
711C23—612no—
712C23—612no—
713C23—612no—
714C23—1221no—
715C23—1221no—
716C23—1221no—
717C23—1221no—
718C23—1222no—
719C23—1222no—
720C23—1222no—
721C23—2441no—
722C23—2441no—
723C23—2441no—
724C23—2441no—
725C23C2×D4×D6111yescharacteristic
726Q8—22no—
727Q8—22no—
728Q8—22no—
729Q8—22no—
730Q8—22no—
731Q8—41no—
732Q8—41no—
733Q8—1222no—
734Q8—1222no—
735Q8—2448no—
736Q8—2441no—
737Q8—2441no—
738Q8C22⋊C4×D6114yes—
739D4—614no—
740D4—12216no—
741D4—1222no—
742D4—1222no—
743D4—1222no—
744C2×C4—22no—
745C2×C4—21no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—612no—
762C2×C4—612no—
763C2×C4—612no—
764C2×C4—614no—
765C2×C4—614no—
766C2×C4—614no—
767C2×C4—614no—
768C2×C4—612no—
769C2×C4—12216no—
770C2×C4—1221no—
771C2×C4—1221no—
772C2×C4—1222no—
773C2×C4—1222no—
774C2×C4—1221no—
775C2×C4—1221no—
776C2×C4—1221no—
777C2×C4—4884no—
778C2×C4—2444no—
779C2×C4—2448no—
780C2×C4—2444no—
781C2×C4—2448no—
782C2×C4—2448no—
783C2×C4—2441no—
784C2×C4—2441no—
785C2×C4—2441no—
786C2×C4—2441no—
787C2×C4—2441no—
788C2×C4—2441no—
789C2×C4—2441no—
790C2×C4#1451980912yescomplemented
791C2×C4C22×C4×D6111yescharacteristic
792C2×C4C2×D4×D6111yescharacteristic
793C2×C4C2×D4×D6111yescharacteristic
794C2×C4C2×D4×D6111yescharacteristic
795C2×C4#41×D6111yescharacteristic
796C2×C4#41×D6111yescharacteristic
797C8—22no—
798C8—41no—
799C8—1222no—
800C8—2441no—
801C22—614no—
802C22—1222no—
803C22—1222no—
804C22—1222no—
805C22—1222no—
806C22—1222no—
807C22—1222no—
808C22—1224no—
809C22—2442no—
810C22—2442no—
811C22—2442no—
812C22—2442no—
813C22—2442no—
814C22—2442no—
815C22C4×D4×D6111yescharacteristic
816C22#120×D6111yescharacteristic
817C22#121×D6111yescharacteristic
818C22#137×D6111yescharacteristic
819C22C2×#1451980911yescharacteristic
820C22#1684055911yescharacteristic
821C22#1684056111yescharacteristic
822C4—24no—
823C4—22no—
824C4—42no—
825C4—41no—
826C4—42no—
827C4—81no—
828C4—614no—
829C4—1222no—
830C4—4881no—
831C4—2442no—
832C4—2441no—
833C4—2442no—
834C4C2×C22⋊C4×D6111yescharacteristic
835C4C4×D4×D6111yescharacteristic
836C4#121×D6111yescharacteristic
837C4#123×D6111yescharacteristic
838C2—1224no—
839C2—2444no—
840C2#386×D6111yescharacteristic
841C2#2145463511yescharacteristic
842C2C4×#1451980911yescharacteristic
843C2#2145507611yescharacteristic
844C2#2145507811yescharacteristic
845C2#2145530311yescharacteristic
846C2#2145531011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1878C2
socleC23×C61C22×D4
prime radicalC22×#11758226C22
cosocleC22×C4×C61C24
hypercenter#1878D61
hypocenterC61#20927
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1878

Complements

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

NH ≅ G/Ntype
4. C2×#16839769C2semidirect
5. #391×D61C2semidirect
6. #21446162C2semidirect
7. #21446160C2semidirect
8. #21446158C2semidirect
9. #21446156C2semidirect
10. #21446154C2semidirect
11. #21446152C2semidirect
12. #21446150C2semidirect
13. #21445537C2semidirect
14. #21445511C2semidirect
15. C61×#1878C2semidirect
20. C2×#14519809C4semidirect
79. C2×Q8×D61C2×C4semidirect
93. C2×#11758202C2×C4semidirect
96. C2×#11758190C2×C4semidirect
99. C2×#11758201C2×C4semidirect
105. C2×#11758189C2×C4semidirect
152. C2×Q16×C61C2×C4semidirect
327. C2×C4×C61#137semidirect
351. C2×Dic61#137semidirect
423. #1878D61semidirect
489. C61#20927semidirect
522. C2×Q16C4×D61semidirect
790. C2×C4#14519809semidirect

Maximal subgroups

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

subgroupindex
C22×#145198092
C2×C4×#117582262
C2×#168397622
C2×#168397692
#391×D612
#214461622
#214461602
#214461582
#214461562
#214461542
#214461522
#214461502
#214455372
#214455112
C61×#18782
#2092761