Finite Group Databasebeta

← #29681413

Subgroups — #29681413

Order 15616.

1738 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519809C211yesmaximal, characteristic
2C2×#16840238C211yesmaximal, characteristic, complemented
3C2×#16839757C211yesmaximal, characteristic
4C2×#103×D61C211yesmaximal, characteristic, complemented
5#21448410C211yesmaximal, characteristic
6#21446175C211yesmaximal, characteristic, complemented
7#21446174C211yesmaximal, characteristic, complemented
8#21446173C211yesmaximal, characteristic, complemented
9#21446172C211yesmaximal, characteristic, complemented
10#21446163C211yesmaximal, characteristic, complemented
11#21446162C211yesmaximal, characteristic, complemented
12#21446157C211yesmaximal, characteristic, complemented
13#21445537C211yesmaximal, characteristic, complemented
14#21445514C211yesmaximal, 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×C8×D61C2211yescharacteristic
26#16840238—24no—
27#16840238—24no—
28C2×Q8×Dic61C2211yescharacteristic
29C2×C4×Dic122—21no—
30C2×C4×Dic122C2211yescharacteristic
31C2×#14519742—21no—
32C2×#14519742C2211yescharacteristic
33C2×#14519735—21no—
34C2×#14519735C2211yescharacteristic
35C2×#14519734—21no—
36C2×#14519734C2211yescharacteristic
37C2×C4⋊C4×D61C2211yescharacteristic
38#16839757—24no—
39C2×#14519702C2211yescharacteristic
40C2×#14519701C2211yescharacteristic
41C2×#14519701C2211yescharacteristic
42C2×#14519700C2211yescharacteristic
43#103×D61—24no—
44C2×#14519699C2211yescharacteristic
45C2×#14519697C2211yescharacteristic
46#16839669C2211yescharacteristic
47#16839664C2211yescharacteristic
48#16839663C2211yescharacteristic
49#16839640—21no—
50#16839640—21no—
51#16839621—21no—
52#16839621—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×#11758226—22no—
70C2×#11758226—22no—
71C2×#11758226C2×C414yes—
72C22×Dic122—21no—
73C22×Dic122C2311yescharacteristic
74C2×Q8×D61—22no—
75C2×Q8×D61—22no—
76C2×Q8×D61—22no—
77C2×Q8×D61C2×C414yes—
78C2×Q8×D61D414yes—
79C2×Q8×D61D414yes—
80C22×D244—21no—
81C22×D244C2311yescharacteristic
82C22×C4×D61—21no—
83C22×C4×D61—21no—
84C22×C4×D61—21no—
85C22×C4×D61C2311yescharacteristic
86#14519809—232no—
87C2×#11758202—22no—
88C2×#11758202—22no—
89C2×#11758202C2×C414yescomplemented
90C2×#11758190—22no—
91C2×#11758190—22no—
92C2×#11758190C2×C414yescomplemented
93C2×#11758201—22no—
94C2×#11758201—22no—
95C2×#11758201C2×C414yescomplemented
96C2×#11758189—22no—
97C2×#11758189—22no—
98C2×#11758189C2×C414yes—
99C22×#92418C2311yescharacteristic
100C22×#92418C2311yescharacteristic
101C2×C8×D61—22no—
102C2×C8×D61—22no—
103C2×C8×D61—22no—
104Q8×Dic61—22no—
105Q8×Dic61—22no—
106C4×Dic122—28no—
107C4×Dic122—22no—
108C4×Dic122—22no—
109#14519742—28no—
110#14519742—22no—
111#14519742—22no—
112#14519735—28no—
113#14519735—22no—
114#14519735D414yes—
115#14519734—28no—
116#14519734—22no—
117#14519734—22no—
118C2×C4⋊Dic61—21no—
119C2×C4⋊Dic61C2311yescharacteristic
120C2×C4⋊Dic61C2311yescharacteristic
121C2×#11758196—21no—
122C2×#11758196—21no—
123C2×#11758196—21no—
124C2×#11758196D411yescharacteristic
125C2×#11758196D411yescharacteristic
126C4⋊C4×D61—22no—
127C4⋊C4×D61—22no—
128C2×#11758198—21no—
129C2×#11758198—21no—
130C2×#11758198—21no—
131C2×#11758198—21no—
132C2×#11758198—21no—
133C2×#11758198D411yescharacteristic
134C2×#11758198D411yescharacteristic
135C2×C4×Dic61—21no—
136C2×C4×Dic61—21no—
137C2×C4×Dic61—21no—
138C2×C4×Dic61—21no—
139C2×C4×Dic61C2311yescharacteristic
140#14519702—22no—
141#14519701—22no—
142#14519701—22no—
143#14519700—22no—
144#14519699—22no—
145#14519697—22no—
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—44no—
196#11758226—44no—
197Q8×D61—28no—
198Q8×D61—28no—
199Q8×D61—28no—
200Q8×D61C22⋊C4116yescomplemented
201C2×D244—21no—
202C2×D244—21no—
203C2×D244—21no—
204C2×D244—21no—
205C2×D244—24no—
206C2×D244—21no—
207C2×D244—42no—
208C2×D244—42no—
209C2×D244C22×C412yes—
210C2×C4×D61—24no—
211C2×C4×D61—24no—
212C2×C4×D61—24no—
213C2×C4×D61—24no—
214C2×C4×D61—42no—
215C2×C4×D61—42no—
216C2×C4×D61—42no—
217C2×C4×D61—81no—
218C2×C4×D61—81no—
219C2×C4×D61C22×C412yes—
220C2×C4×D61C2×D412yes—
221C2×C4×D61C2×D412yes—
222C2×C4×D61C2×D412yes—
223C2×C4×D61#4112yes—
224C2×C4×D61#4112yes—
225C2×Dic122—21no—
226C2×Dic122—21no—
227C2×Dic122—21no—
228C2×Dic122—24no—
229C2×Dic122—24no—
230C2×Dic122—24no—
231C2×Dic122C22×C412yes—
232C2×Dic122C2×D412yes—
233C2×Dic122C2×D412yes—
234Q16×C61—28no—
235C2×C8×C61—21no—
236C2×C8×C61—21no—
237C2×C8×C61—21no—
238C2×C8×C61—21no—
239C2×C8×C61—21no—
240C2×C8×C61C22×C412yes—
241C4⋊C4×C61—24no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61C2×D412yes—
246C42×C61—24no—
247C42×C61—21no—
248C42×C61—21no—
249#11758202—28no—
250#11758201—28no—
251#11758198—24no—
252#11758198—22no—
253#11758198—22no—
254#11758198—81no—
255#11758198—81no—
256#11758198—81no—
257#11758198—81no—
258C4⋊Dic61—24no—
259C4⋊Dic61—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61C2×D412yes—
263#11758196—24no—
264#11758196—24no—
265#11758196—22no—
266#11758196—22no—
267#11758196—42no—
268C4×Dic61—24no—
269C4×Dic61—24no—
270C4×Dic61—24no—
271C4×Dic61—21no—
272C4×Dic61—21no—
273C4×Dic61—24no—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418C22×C412yes—
280#11758190—28no—
281#11758189—28no—
282C8×D61—44no—
283C23×C61C22×D411yescharacteristic
284C22×D61—21no—
285C22×D61—21no—
286C22×D61—21no—
287C22×D61—21no—
288C22×D61—22no—
289C22×D61—41no—
290C22×D61—41no—
291C22×D61—41no—
292C22×D61—41no—
293C22×D61—41no—
294C22×D61—41no—
295C22×D61C4×D412yes—
296C22×D61#12012yes—
297C22×D61#12112yes—
298Q8×C61—22no—
299Q8×C61—22no—
300Q8×C61—22no—
301Q8×C61—22no—
302Q8×C61—22no—
303Q8×C61—41no—
304Q8×C61—41no—
305Q8×C61C2×C22⋊C414yes—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—21no—
311C2×C4×C61—22no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61C23×C411yescharacteristic
325C2×C4×C61C22×D411yescharacteristic
326C2×C4×C61C22×D411yescharacteristic
327C2×C4×C61C22×D411yescharacteristic
328C2×C4×C61C2×#4111yescharacteristic
329C2×C4×C61C2×#4111yescharacteristic
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—21no—
334C2×Dic61—21no—
335C2×Dic61—22no—
336C2×Dic61—21no—
337C2×Dic61—21no—
338C2×Dic61—21no—
339C2×Dic61—21no—
340C2×Dic61—41no—
341C2×Dic61—41no—
342C2×Dic61—41no—
343C2×Dic61—41no—
344C2×Dic61—41no—
345C2×Dic61C4×D412yes—
346C2×Dic61#12012yes—
347C2×Dic61#12112yes—
348D244—22no—
349D244—22no—
350D244—48no—
351D244—41no—
352D244—41no—
353C4×D61—216no—
354C4×D61—48no—
355C4×D61—84no—
356C4×D61C2×C22⋊C414yes—
357C4×D61C4×D414yes—
358C4×D61#12114yes—
359C4×D61#12314yes—
360Dic122—22no—
361Dic122—22no—
362Dic122—22no—
363Dic122—216no—
364Dic122C2×C22⋊C414yes—
365C8×C61—22no—
366C8×C61—41no—
367#92418—22no—
368#92418—41no—
369#20930—611nomaximal, Sylow
370C22×C61C2×C4×D411yescharacteristic
371C22×C61C2×#12011yescharacteristic
372C22×C61C2×#12111yescharacteristic
373C22×C61#57711yescharacteristic
374C22×C61#57711yescharacteristic
375C22×C61#57811yescharacteristic
376C22×C61#57811yescharacteristic
377C2×D61—22no—
378C2×D61—22no—
379C2×D61—22no—
380C2×D61—22no—
381C2×D61—22no—
382C2×D61—22no—
383C2×D61—42no—
384C2×D61—42no—
385C2×D61—42no—
386C2×D61—81no—
387C2×D61—81no—
388C2×D61—81no—
389C2×D61—81no—
390C2×D61#38614yes—
391C4×C61—24no—
392C4×C61—41no—
393C4×C61—41no—
394C4×C61—42no—
395C4×C61—42no—
396C4×C61—81no—
397C4×C61C22×C22⋊C411yescharacteristic
398C4×C61C2×C4×D411yescharacteristic
399C4×C61C2×#12111yescharacteristic
400C4×C61C2×#12311yescharacteristic
401Dic61—24no—
402Dic61—41no—
403Dic61—41no—
404Dic61—42no—
405Dic61—81no—
406Dic61#38614yes—
407C22×#137—611no—
408C2×#519—611no—
409C2×#416—611no—
410C22×#103—611no—
411#2311—611no—
412#1880—611no—
413#1880—611no—
414#1880—611no—
415#1880—611no—
416#1878—611no—
417#1878—611no—
418#1878—611no—
419#1878D6111yescharacteristic, complemented
420#1736—611no—
421#1729—611no—
422C2×C61C2×#38611yescharacteristic
423C2×C61#294711yescharacteristic
424C2×C61#294711yescharacteristic
425C2×C61#301311yescharacteristic
426C2×C61#301311yescharacteristic
427C2×C61#304311yescharacteristic
428C2×C61#304411yescharacteristic
429D61—24no—
430D61—82no—
431C22×#41—611no—
432C23×Q8—611no—
433C2×#137—618no—
434C2×#137—1224no—
435C2×#137—1224no—
436C22×Q16—611no—
437C22×Q16C2×D6111yescharacteristic
438C22×SD16—611no—
439C22×SD16—611no—
440C22×M16—611no—
441C23×C8—611no—
442#519—1224no—
443#519—1224no—
444C2×C4×Q8—611no—
445C2×C4×Q8—611no—
446C2×C4×Q8—611no—
447C2×C4×Q8—1221no—
448C2×C4×Q8—1221no—
449C2×C4×Q8C2×D6111yescharacteristic
450C2×#117—611no—
451C2×#117—611no—
452C2×#117—1221no—
453C2×#117—1221no—
454C22×C4⋊C4—611no—
455#416—1224no—
456C2×#103—611no—
457C2×#103—611no—
458C2×#103—611no—
459C2×#103—611no—
460C2×#103—1224no—
461C2×#103C2×D6111yescharacteristic
462C2×#103C2×D6111yescharacteristic
463C2×#102—611no—
464C2×#102—611no—
465#391—611no—
466#391C2×D6111yescharacteristic
467#390—611no—
468#390—611no—
469#386—1221no—
470#386—1221no—
471#380—1221no—
472#380—1221no—
473#340—611no—
474#340—611no—
475#340—611no—
476#340C2×D6111yescharacteristic
477#336—611no—
478#336—611no—
479#336—611no—
480#336C2×D6111yescharacteristic
481C61#2093011yescharacteristic, complemented, Sylow
482C2×#41—614no—
483C2×#41—1222no—
484C2×#41—1222no—
485C2×#41—1222no—
486C2×#41—1222no—
487C2×#41—1222no—
488C22×Q8—614no—
489C22×Q8—614no—
490C22×Q8—614no—
491C22×Q8—611no—
492C22×Q8—1221no—
493C22×Q8—1222no—
494C22×Q8—1222no—
495C22×Q8—1222no—
496C22×Q8C22×D6111yescharacteristic
497C22×Q8C22×D6111yescharacteristic
498C22×D4—611no—
499C22×D4—1221no—
500C23×C4—611no—
501C23×C4—1221no—
502C23×C4—1221no—
503C23×C4—1221no—
504#137—12232no—
505C2×Q16—22no—
506C2×Q16—22no—
507C2×Q16—614no—
508C2×Q16—1222no—
509C2×Q16—1222no—
510C2×Q16C4×D6114yescomplemented
511C2×SD16—614no—
512C2×SD16—614no—
513C2×SD16—1222no—
514C2×SD16—1222no—
515C2×SD16—1222no—
516C2×SD16—1222no—
517C2×M16—614no—
518C2×M16—1222no—
519C2×M16—1222no—
520C22×C8—611no—
521C22×C8—611no—
522C22×C8—1222no—
523C22×C8—1222no—
524C22×C8—1222no—
525C22×C8C22×D6111yescharacteristic
526C22×C8C22×D6111yescharacteristic
527C4×Q8—22no—
528C4×Q8—22no—
529C4×Q8—1222no—
530C4×Q8—1222no—
531C4×Q8—1228no—
532C4×Q8—1222no—
533C4×Q8—1228no—
534C4×Q8—1222no—
535C4×Q8—1222no—
536C4×Q8—1222no—
537#117—614no—
538#117—1222no—
539#117—1222no—
540#117—1228no—
541#117—1222no—
542#117—1228no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—611no—
545C2×C4⋊C4—611no—
546C2×C4⋊C4—611no—
547C2×C4⋊C4—611no—
548C2×C4⋊C4—1222no—
549C2×C4⋊C4—1222no—
550C2×C4⋊C4—1221no—
551C2×C4⋊C4—1221no—
552C2×C4⋊C4—1221no—
553C2×C4⋊C4—1221no—
554C2×C4⋊C4C22×D6111yescharacteristic
555C2×C4⋊C4C22×D6111yescharacteristic
556C2×C22⋊C4—611no—
557C2×C22⋊C4—611no—
558C2×C22⋊C4—1221no—
559C2×C22⋊C4—1221no—
560C2×C22⋊C4—1221no—
561C2×C22⋊C4—1221no—
562C2×C22⋊C4—1221no—
563C2×C42—21no—
564C2×C42—611no—
565C2×C42—1221no—
566C2×C42—1221no—
567C2×C42—1221no—
568C2×C42—1221no—
569C2×C42C22×D6111yescharacteristic
570#103—22no—
571#103—22no—
572#103—1222no—
573#103—1222no—
574#103—1222no—
575#103—1222no—
576#102—1222no—
577#102—1222no—
578#95—21no—
579#95—21no—
580#95—1221no—
581#95—1221no—
582C24—611no—
583C24—1221no—
584#41—1228no—
585#41—1228no—
586#41—2444no—
587#41—2444no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—6116no—
597C2×Q8—612no—
598C2×Q8—612no—
599C2×Q8—612no—
600C2×Q8—1224no—
601C2×Q8—1224no—
602C2×Q8—1224no—
603C2×Q8—1228no—
604C2×Q8—1228no—
605C2×Q8—1228no—
606C2×Q8—1221no—
607C2×Q8—1221no—
608C2×Q8—1221no—
609C2×Q8C2×C4×D6112yes—
610C2×Q8C2×C4×D6112yes—
611C2×Q8D4×D6112yes—
612C2×Q8D4×D6112yes—
613C2×D4—612no—
614C2×D4—1224no—
615C2×D4—1221no—
616C2×D4—1221no—
617C2×D4—1221no—
618C2×D4—1221no—
619C2×D4—1221no—
620C2×D4—2442no—
621C2×D4—2442no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—611no—
627C22×C4—612no—
628C22×C4—612no—
629C22×C4—612no—
630C22×C4—612no—
631C22×C4—612no—
632C22×C4—612no—
633C22×C4—611no—
634C22×C4—611no—
635C22×C4—1224no—
636C22×C4—1224no—
637C22×C4—1224no—
638C22×C4—1224no—
639C22×C4—1221no—
640C22×C4—1221no—
641C22×C4—1221no—
642C22×C4—4881no—
643C22×C4—4881no—
644C22×C4—2442no—
645C22×C4—2442no—
646C22×C4—2442no—
647C22×C4D4×D6111yescharacteristic
648C22×C4D4×D6111yescharacteristic
649C22×C4C23×D6111yescharacteristic
650Q16—28no—
651Q16—1228no—
652SD16—1228no—
653SD16—1228no—
654M16—1228no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—612no—
661C2×C8—1221no—
662C2×C8—1221no—
663C2×C8—1221no—
664C2×C8—1221no—
665C2×C8—1221no—
666C2×C8—2444no—
667C2×C8C2×C4×D6112yes—
668C4⋊C4—24no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—612no—
673C4⋊C4—1222no—
674C4⋊C4—1222no—
675C4⋊C4—1224no—
676C4⋊C4—1224no—
677C4⋊C4—1224no—
678C4⋊C4—1221no—
679C4⋊C4—1221no—
680C4⋊C4—1221no—
681C4⋊C4—2442no—
682C4⋊C4D4×D6112yes—
683C22⋊C4—1222no—
684C22⋊C4—1222no—
685C22⋊C4—1224no—
686C22⋊C4—4881no—
687C22⋊C4—4881no—
688C22⋊C4—4881no—
689C22⋊C4—4881no—
690C42—24no—
691C42—21no—
692C42—21no—
693C42—1224no—
694C42—1224no—
695C42—1224no—
696C42—1224no—
697C42—1221no—
698C42—1221no—
699C23—612no—
700C23—612no—
701C23—612no—
702C23—1221no—
703C23—1221no—
704C23—1221no—
705C23—1221no—
706C23—1222no—
707C23—2441no—
708C23—2441no—
709C23—2441no—
710C23—2441no—
711C23—2441no—
712C23—2441no—
713C23C2×D4×D6111yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—22no—
717Q8—22no—
718Q8—22no—
719Q8—41no—
720Q8—41no—
721Q8—614no—
722Q8—12216no—
723Q8—1222no—
724Q8—1222no—
725Q8—1222no—
726Q8C22⋊C4×D6114yes—
727D4—1222no—
728D4—1222no—
729D4—2448no—
730D4—2441no—
731D4—2441no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—612no—
751C2×C4—612no—
752C2×C4—612no—
753C2×C4—614no—
754C2×C4—614no—
755C2×C4—614no—
756C2×C4—614no—
757C2×C4—12216no—
758C2×C4—1222no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1221no—
763C2×C4—1221no—
764C2×C4—1221no—
765C2×C4—1221no—
766C2×C4—1221no—
767C2×C4—1221no—
768C2×C4—4884no—
769C2×C4—2448no—
770C2×C4—2441no—
771C2×C4—2441no—
772C2×C4—2441no—
773C2×C4—2441no—
774C2×C4—2441no—
775C2×C4C22×C4×D6111yescharacteristic
776C2×C4C2×D4×D6111yescharacteristic
777C2×C4C2×D4×D6111yescharacteristic
778C2×C4C2×D4×D6111yescharacteristic
779C2×C4#41×D6111yescharacteristic
780C2×C4#41×D6111yescharacteristic
781C8—22no—
782C8—41no—
783C8—1222no—
784C8—2441no—
785C22—614no—
786C22—1222no—
787C22—1222no—
788C22—1222no—
789C22—1222no—
790C22—1222no—
791C22—1222no—
792C22—4881no—
793C22—4881no—
794C22—4881no—
795C22—4881no—
796C22—2442no—
797C22—2442no—
798C22—2442no—
799C22C4×D4×D6111yescharacteristic
800C22#120×D6111yescharacteristic
801C22#121×D6111yescharacteristic
802C22#1684056911yescharacteristic
803C22#1684057111yescharacteristic
804C22#1684057511yescharacteristic
805C22#1684057811yescharacteristic
806C4—24no—
807C4—41no—
808C4—41no—
809C4—42no—
810C4—42no—
811C4—81no—
812C4—614no—
813C4—1224no—
814C4—4881no—
815C4—2441no—
816C4—2442no—
817C4—2441no—
818C4C2×C22⋊C4×D6111yescharacteristic
819C4C4×D4×D6111yescharacteristic
820C4#121×D6111yescharacteristic
821C4#123×D6111yescharacteristic
822C2—1224no—
823C2—4882no—
824C2#386×D6111yescharacteristic
825C2#2145465711yescharacteristic
826C2#2145466111yescharacteristic
827C2#2145513511yescharacteristic
828C2#2145513811yescharacteristic
829C2#2145533811yescharacteristic
830C2#2145534411yescharacteristic
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#20930
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
2. C2×#16840238C2semidirect
4. C2×#103×D61C2semidirect
6. #21446175C2semidirect
7. #21446174C2semidirect
8. #21446173C2semidirect
9. #21446172C2semidirect
10. #21446163C2semidirect
11. #21446162C2semidirect
12. #21446157C2semidirect
13. #21445537C2semidirect
14. #21445514C2semidirect
15. C61×#1878C2semidirect
20. C2×#14519809C4semidirect
89. C2×#11758202C2×C4semidirect
92. C2×#11758190C2×C4semidirect
95. C2×#11758201C2×C4semidirect
152. C2×Q16×C61C2×C4semidirect
200. Q8×D61C22⋊C4semidirect
419. #1878D61semidirect
481. C61#20930semidirect
510. C2×Q16C4×D61semidirect

Maximal subgroups

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

subgroupindex
C22×#145198092
C2×#168402382
C2×#168397572
C2×#103×D612
#214484102
#214461752
#214461742
#214461732
#214461722
#214461632
#214461622
#214461572
#214455372
#214455142
C61×#18782
#2093061