Finite Group Databasebeta

← #29681781

Subgroups — #29681781

Order 15616.

1830 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459149C211yesmaximal, characteristic
2C2×C4×#11758222C211yesmaximal, characteristic, complemented
3C2×#16839777C211yesmaximal, characteristic, complemented
4C2×#104×D61C211yesmaximal, characteristic, complemented
5#21454262C211yesmaximal, characteristic, complemented
6#21446268C211yesmaximal, characteristic, complemented
7#21446266C211yesmaximal, characteristic, complemented
8#21446265C211yesmaximal, characteristic, complemented
9#21446264C211yesmaximal, characteristic, complemented
10#21446262C211yesmaximal, characteristic, complemented
11#21446261C211yesmaximal, characteristic, complemented
12#21446259C211yesmaximal, characteristic, complemented
13#21445527C211yesmaximal, characteristic, complemented
14#339×D61C211yesmaximal, characteristic, complemented
15C61×#1896C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C2×#41×D61C2211yescharacteristic
18C2×M16×D61C2211yescharacteristic
19C2×M16×D61C2211yescharacteristic
20#16840342C412yescomplemented
21#16840341C412yescomplemented
22#16840335C412yescomplemented
23#16840334—21no—
24#16840328C412yescomplemented
25#16840327—21no—
26#16840323—21no—
27#16840322—21no—
28#16840309—22no—
29#16840274C2211yescharacteristic
30#16840273C2211yescharacteristic
31#16840271—22no—
32#16840269C2211yescharacteristic
33C4×#11758222—24no—
34C4×#11758222—24no—
35C2×C4×Dic122—21no—
36C2×C4×D244—21no—
37C2×C4×C22⋊D61—21no—
38C2×C4×C22⋊D61—21no—
39C2×#14519736C2211yescharacteristic, complemented
40C2×#14519734C2211yescharacteristic
41C2×#14519734C2211yescharacteristic, complemented
42#117×D61C2211yescharacteristic
43C2×C42×D61C2211yescharacteristic
44C2×C42×D61C2211yescharacteristic, complemented
45#16839777—24no—
46C2×#14519705C2211yescharacteristic
47C2×#14519705C2211yescharacteristic
48C2×#14519704C2211yescharacteristic
49C2×#14519704C2211yescharacteristic
50C2×#14519703C2211yescharacteristic
51C2×#14519703C2211yescharacteristic
52#104×D61—24no—
53#16839727—22no—
54#16839727—22no—
55#16839726C2211yescharacteristic, complemented
56#16839725C2211yescharacteristic, complemented
57#16839725C2211yescharacteristic, complemented
58#16839523C2211yescharacteristic, complemented
59#16839523C2211yescharacteristic, complemented
60#16839522C2211yescharacteristic, complemented
61#16839522C2211yescharacteristic, complemented
62#16839521C2211yescharacteristic, complemented
63#16839521C2211yescharacteristic, complemented
64C61×#525C2211yescharacteristic
65C22×C42×C61C2211yescharacteristic, complemented
66C2×#104×C61C2211yescharacteristic
67C2×#104×C61C2211yescharacteristic
68C61×#407C2211yescharacteristic, complemented
69C61×#339C2211yescharacteristic, complemented
70C61×#339C2211yescharacteristic, complemented
71C2×#11758226C2×C411yescharacteristic, complemented
72C2×#11758222—22no—
73C2×#11758222—22no—
74C2×#11758222—21no—
75C2×#11758222—22no—
76C2×#11758222—22no—
77C2×#11758222C2×C412yes—
78C2×#11758222C2×C412yes—
79C2×#11758222D412yes—
80C2×#11758222D412yes—
81C2×#11758222C2311yescharacteristic
82C2×#11758224—21no—
83C2×#11758224C2×C411yescharacteristic, complemented
84#41×D61—22no—
85#41×D61—22no—
86#41×D61—22no—
87#41×D61—22no—
88C22×Dic122D411yescharacteristic
89C2×Q8×D61C2×C411yescharacteristic, complemented
90C22×D244D411yescharacteristic
91C22×C22⋊D61D411yescharacteristic
92C22×C22⋊D61D411yescharacteristic
93C2×D4×D61—21no—
94C2×D4×D61C2×C411yescharacteristic, complemented
95C22×C4×D61—21no—
96C22×C4×D61—21no—
97C22×C4×D61—21no—
98C22×C4×D61C2311yescharacteristic
99C22×C4×D61C2311yescharacteristic
100C2×#11758194C2311yescharacteristic
101C2×#11758194C2311yescharacteristic
102C2×#11758189—21no—
103C2×#11758189—21no—
104M16×D61—22no—
105M16×D61—22no—
106M16×D61—22no—
107M16×D61—22no—
108C2×C8×D61—21no—
109C2×C8×D61—21no—
110#14519776—22no—
111#14519773—22no—
112#14519763—22no—
113#14519763—22no—
114#14519762—22no—
115#14519761—21no—
116#14519760—21no—
117#14519759—22no—
118#14519758—21no—
119#14519757C2×C412yescomplemented
120#14519756C2×C412yescomplemented
121#14519755—22no—
122#14519754—22no—
123#14519753C2×C412yescomplemented
124#14519752—22no—
125#14519752C2×C412yescomplemented
126#14519751C2×C412yescomplemented
127#14519750—22no—
128#14519750—22no—
129#14519750—22no—
130#14519749—22no—
131#14519748—22no—
132#14519748C2×C412yescomplemented
133#14519747—21no—
134#14519747—22no—
135#14519746—21no—
136#14519745—21no—
137#14519745—22no—
138C4×Dic122—28no—
139C4×D244—28no—
140C4×D244—22no—
141C4×C22⋊D61—28no—
142C4×C22⋊D61—28no—
143C4×C22⋊D61—22no—
144C4×C22⋊D61—22no—
145#14519736—22no—
146#14519736—22no—
147#14519736C2311yescharacteristic
148#14519735C2×C412yescomplemented
149#14519734—21no—
150#14519734—22no—
151#14519734—22no—
152#14519734—22no—
153#14519734D414yescomplemented
154#14519733—21no—
155C2×C4⋊Dic61—21no—
156C2×#11758196—21no—
157C2×#11758196—21no—
158C4⋊C4×D61C2×C412yescomplemented
159C2×C22⋊Dic61—21no—
160C2×#11758198—21no—
161C2×#11758198—21no—
162C22⋊C4×D61—21no—
163C2×C4×Dic61—21no—
164C2×C4×Dic61—21no—
165C2×C4×Dic61C2311yescharacteristic
166C2×C4×Dic61C2311yescharacteristic
167C42×D61—22no—
168C42×D61—21no—
169C42×D61—22no—
170C42×D61—22no—
171C42×D61D414yescomplemented
172#14519705—22no—
173#14519705—22no—
174#14519704—22no—
175#14519704—22no—
176#14519703—22no—
177#14519703—22no—
178C22⋊#92418—22no—
179#14519689—22no—
180#14519689—22no—
181C2×#41×C61C2311yescharacteristic
182C23×C4×C61—21no—
183C23×C4×C61C2311yescharacteristic
184C2×M16×C61C2311yescharacteristic
185C2×M16×C61C2311yescharacteristic
186#123×C61—21no—
187C22⋊Q8×C61C2×C412yescomplemented
188#121×C61C2×C412yescomplemented
189#120×C61—21no—
190C4×D4×C61—22no—
191#117×C61C2311yescharacteristic
192C2×C42×C61—21no—
193C2×C42×C61—22no—
194C2×C42×C61—22no—
195C2×C42×C61C2311yescharacteristic
196C2×C42×C61C2311yescharacteristic
197#104×C61—22no—
198#104×C61—22no—
199C22⋊C8×C61—22no—
200C24×C61C2×D411yescharacteristic
201C23×D61—21no—
202C23×D61C2×D411yescharacteristic
203C23×D61C2×D411yescharacteristic
204#41×C61—21no—
205#41×C61—21no—
206#41×C61—21no—
207#41×C61—21no—
208C2×Q8×C61C22×C411yescharacteristic
209C2×D4×C61—21no—
210C2×D4×C61—22no—
211C2×D4×C61C22×C411yescharacteristic
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—24no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—44no—
221C22×C4×C61C22×C412yes—
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D412yes—
224C22×C4×C61C2411yescharacteristic
225C2×C22⋊D61—22no—
226C2×C22⋊D61—22no—
227C2×C22⋊D61—21no—
228C2×C22⋊D61—21no—
229C2×C22⋊D61—22no—
230C2×C22⋊D61—22no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—22no—
233C2×C22⋊D61—22no—
234C2×C22⋊D61C22⋊C412yes—
235C2×C22⋊D61C22⋊C412yes—
236C2×C22⋊D61C22⋊C412yes—
237C2×C22⋊D61C22⋊C412yes—
238C22×Dic61—21no—
239C22×Dic61—21no—
240C22×Dic61—21no—
241C22×Dic61C2×D411yescharacteristic
242C22×Dic61C2×D411yescharacteristic
243#11758226—22no—
244#11758226—22no—
245Q8×D61—22no—
246Q8×D61—22no—
247#11758224—22no—
248#11758224—22no—
249#11758224—42no—
250#11758224—42no—
251D4×D61—22no—
252D4×D61—22no—
253D4×D61—42no—
254D4×D61—42no—
255#11758222—24no—
256#11758222—24no—
257#11758222—24no—
258#11758222—24no—
259#11758222—24no—
260#11758222—24no—
261#11758222—24no—
262#11758222—24no—
263#11758222—21no—
264#11758222—21no—
265#11758222—21no—
266#11758222—21no—
267#11758222—42no—
268#11758222—42no—
269C2×D244—22no—
270C2×D244—22no—
271C2×D244—21no—
272C2×D244—22no—
273C2×D244C22⋊C412yes—
274C2×D244C22⋊C412yes—
275C2×D244C22×C411yescharacteristic
276C2×C4×D61—21no—
277C2×C4×D61—21no—
278C2×C4×D61—21no—
279C2×C4×D61—21no—
280C2×C4×D61—24no—
281C2×C4×D61—21no—
282C2×C4×D61—24no—
283C2×C4×D61—21no—
284C2×C4×D61—21no—
285C2×C4×D61—22no—
286C2×C4×D61—44no—
287C2×C4×D61—44no—
288C2×C4×D61—42no—
289C2×C4×D61—42no—
290C2×C4×D61C22×C412yes—
291C2×C4×D61C22×C411yescharacteristic
292C2×C4×D61C22×C411yescharacteristic
293C2×C4×D61C2×D412yes—
294C2×C4×D61C2×D412yes—
295C2×C4×D61C2×D412yes—
296C2×C4×D61C2×D411yescharacteristic
297C2×C4×D61C2×D411yescharacteristic
298C2×C4×D61#4112yes—
299C2×C4×D61#4112yes—
300C2×Dic122—22no—
301C2×Dic122—22no—
302C2×Dic122—21no—
303C2×Dic122C22⋊C412yes—
304C2×Dic122C22⋊C412yes—
305C2×Dic122C22×C411yescharacteristic
306M16×C61—21no—
307M16×C61—21no—
308M16×C61—21no—
309M16×C61—21no—
310C2×C8×C61—21no—
311C2×C8×C61—21no—
312C4⋊C4×C61—22no—
313C4⋊C4×C61C22×C412yes—
314C22⋊C4×C61—22no—
315C22⋊C4×C61—21no—
316C22⋊C4×C61—22no—
317C42×C61—24no—
318C42×C61—21no—
319C42×C61—21no—
320C42×C61—21no—
321C42×C61C2×D412yes—
322C42×C61C2×D412yes—
323C22⋊Dic61—24no—
324C22⋊Dic61—22no—
325C22⋊Dic61—21no—
326C22⋊Dic61—22no—
327#11758198—24no—
328#11758198—22no—
329#11758198—22no—
330#11758198—22no—
331#11758198—24no—
332#11758198—22no—
333#11758198—22no—
334C4⋊Dic61—24no—
335C4⋊Dic61—22no—
336C4⋊Dic61C22×C412yes—
337#11758196—24no—
338#11758196—22no—
339#11758196—22no—
340#11758196—22no—
341#11758196—24no—
342C4×Dic61—24no—
343C4×Dic61—21no—
344C4×Dic61—21no—
345C4×Dic61—21no—
346C4×Dic61—22no—
347C4×Dic61—24no—
348C4×Dic61C2×D412yes—
349C4×Dic61C2×D412yes—
350#11758194—21no—
351#11758194—21no—
352#11758194—21no—
353#11758194—21no—
354C2×#92418—21no—
355C2×#92418—21no—
356#11758189—42no—
357#11758189—42no—
358C8×D61—42no—
359C8×D61—42no—
360C23×C61—21no—
361C23×C61—21no—
362C23×C61—21no—
363C23×C61—42no—
364C23×C61C2×C22⋊C412yes—
365C23×C61C22×D411yescharacteristic
366C22×D61—21no—
367C22×D61—21no—
368C22×D61—21no—
369C22×D61—42no—
370C22×D61—42no—
371C22×D61—42no—
372C22×D61—82no—
373C22×D61C2×C22⋊C412yes—
374C22×D61C2×C22⋊C411yescharacteristic
375C22×D61C2×C22⋊C411yescharacteristic
376C22×D61#12012yes—
377C22×D61#12312yes—
378Q8×C61—21no—
379Q8×C61—21no—
380D4×C61—21no—
381D4×C61—21no—
382D4×C61—41no—
383D4×C61—41no—
384D4×C61—82no—
385C2×C4×C61—24no—
386C2×C4×C61—22no—
387C2×C4×C61—21no—
388C2×C4×C61—21no—
389C2×C4×C61—22no—
390C2×C4×C61—22no—
391C2×C4×C61—22no—
392C2×C4×C61—22no—
393C2×C4×C61—22no—
394C2×C4×C61—21no—
395C2×C4×C61—22no—
396C2×C4×C61—48no—
397C2×C4×C61—42no—
398C2×C4×C61—41no—
399C2×C4×C61—41no—
400C2×C4×C61C2×C22⋊C412yes—
401C2×C4×C61C23×C411yescharacteristic
402C2×C4×C61C22×D411yescharacteristic
403C2×C4×C61C22×D411yescharacteristic
404C2×C4×C61C22×D411yescharacteristic
405C2×C4×C61C2×#4111yescharacteristic
406C2×C4×C61C2×#4111yescharacteristic
407C22⋊D61—24no—
408C22⋊D61—24no—
409C22⋊D61—24no—
410C22⋊D61—24no—
411C22⋊D61—41no—
412C22⋊D61—41no—
413C22⋊D61—42no—
414C22⋊D61—42no—
415C22⋊D61—82no—
416C22⋊D61—82no—
417C2×Dic61—21no—
418C2×Dic61—21no—
419C2×Dic61—22no—
420C2×Dic61—21no—
421C2×Dic61—22no—
422C2×Dic61—22no—
423C2×Dic61—42no—
424C2×Dic61—42no—
425C2×Dic61—42no—
426C2×Dic61C2×C22⋊C412yes—
427C2×Dic61C2×C22⋊C411yescharacteristic
428C2×Dic61C2×C22⋊C411yescharacteristic
429C2×Dic61#12012yes—
430C2×Dic61#12312yes—
431D244—24no—
432D244—24no—
433D244—21no—
434D244—21no—
435D244—42no—
436D244—82no—
437C4×D61—22no—
438C4×D61—22no—
439C4×D61—22no—
440C4×D61—22no—
441C4×D61—48no—
442C4×D61—48no—
443C4×D61—42no—
444C4×D61—41no—
445C4×D61—41no—
446C4×D61—42no—
447C4×D61—82no—
448C4×D61C4×D412yes—
449C4×D61C4×D412yes—
450C4×D61C4×D412yes—
451C4×D61C4×D412yes—
452C4×D61#12112yes—
453C4×D61#12112yes—
454C4×D61#12112yes—
455C4×D61#12112yes—
456Dic122—24no—
457Dic122—24no—
458Dic122—21no—
459Dic122—21no—
460Dic122—42no—
461C8×C61—41no—
462C8×C61—41no—
463#92418—41no—
464#92418—41no—
465#20980—611nomaximal, Sylow
466C22×C61—22no—
467C22×C61—22no—
468C22×C61—22no—
469C22×C61—22no—
470C22×C61—42no—
471C22×C61—42no—
472C22×C61—42no—
473C22×C61—41no—
474C22×C61C22×C22⋊C411yescharacteristic
475C22×C61C2×#12011yescharacteristic
476C22×C61C2×#12311yescharacteristic
477C2×D61—22no—
478C2×D61—22no—
479C2×D61—22no—
480C2×D61—22no—
481C2×D61—22no—
482C2×D61—42no—
483C2×D61—42no—
484C2×D61—42no—
485C2×D61—42no—
486C2×D61—42no—
487C2×D61—41no—
488C2×D61—84no—
489C2×D61#38612yes—
490C2×D61#38612yes—
491C4×C61—24no—
492C4×C61—22no—
493C4×C61—42no—
494C4×C61—42no—
495C4×C61—41no—
496C4×C61C2×C4×D411yescharacteristic
497C4×C61C2×C4×D411yescharacteristic
498C4×C61C2×#12111yescharacteristic
499C4×C61C2×#12111yescharacteristic
500Dic61—22no—
501Dic61—42no—
502Dic61—42no—
503Dic61—42no—
504Dic61—41no—
505Dic61#38612yes—
506Dic61#38612yes—
507#3449—611no—
508C2×C4×#41—611no—
509C2×#421—611no—
510C22×#104—611no—
511#2879—611no—
512#1897—611no—
513#1897—611no—
514#1897—611no—
515#1897—611no—
516#1896—611no—
517#1896—611no—
518#1896—611no—
519#1896D6111yescharacteristic, complemented
520#1733—611no—
521C2×#339—611no—
522C2×C61—21no—
523C2×C61—21no—
524C2×C61—42no—
525C2×C61—81no—
526C2×C61C2×#38611yescharacteristic
527C2×C61#290112yes—
528D61—22no—
529D61—22no—
530D61—42no—
531D61—81no—
532C22×#41—611no—
533C22×#41—611no—
534C22×M16—611no—
535C22×M16—611no—
536#537—612no—
537#537—612no—
538#536—612no—
539#536—1221no—
540#535—612no—
541#535—1221no—
542#534—1221no—
543#534—1221no—
544#532—1222no—
545#525—611no—
546#525—611no—
547#525—611no—
548#525—1222no—
549#525C2×D6111yescharacteristic
550C4×#41—1224no—
551C4×#41—1224no—
552C2×C4×Q8—1221no—
553C2×C4×D4—1221no—
554C2×C4×D4—1221no—
555C2×C4×D4—1221no—
556C2×#117—611no—
557C2×#117—611no—
558C2×#117—611no—
559C2×#117—611no—
560C22×C42—611no—
561C22×C42—611no—
562C22×C42C2×D6111yescharacteristic, complemented
563#421—1224no—
564C2×#104—611no—
565C2×#104—611no—
566C2×#104—611no—
567C2×#104—611no—
568C2×#104—611no—
569C2×#104—611no—
570C2×#104—1224no—
571C2×#104C2×D6111yescharacteristic
572C2×#104C2×D6111yescharacteristic
573#408—1222no—
574#408—1222no—
575#407—611no—
576#407—611no—
577#407—611no—
578#407C2×D6111yescharacteristic, complemented
579#339—611no—
580#339—611no—
581#339—611no—
582#339—611no—
583#339—611no—
584#339—611no—
585#339C2×D6111yescharacteristic, complemented
586#339C2×D6111yescharacteristic, complemented
587C61#2098011yescharacteristic, complemented, Sylow
588C2×#41—612no—
589C2×#41—612no—
590C2×#41—612no—
591C2×#41—612no—
592C2×#41—611no—
593C2×#41—611no—
594C2×#41—611no—
595C2×#41—1222no—
596C2×#41—1222no—
597C2×#41—1222no—
598C2×#41—1222no—
599C2×#41—1221no—
600C2×#41—1221no—
601C2×#41—1222no—
602C2×#41—1222no—
603C2×#41—1222no—
604C2×#41—1222no—
605C2×#41C22×D6111yescharacteristic
606C22×Q8—611no—
607C22×Q8—611no—
608C22×D4—611no—
609C22×D4—611no—
610C22×D4—611no—
611C22×D4—611no—
612C22×D4—1221no—
613C23×C4—21no—
614C23×C4—611no—
615C23×C4—611no—
616C23×C4—1221no—
617C23×C4—1221no—
618C23×C4—1221no—
619C23×C4C22×D6111yescharacteristic
620C2×M16—611no—
621C2×M16—611no—
622C2×M16—1221no—
623C2×M16—1221no—
624C2×M16—1222no—
625C2×M16—1222no—
626C2×M16—1222no—
627C2×M16—1222no—
628C2×M16C22×D6111yescharacteristic
629C2×M16C22×D6111yescharacteristic
630C22×C8—1221no—
631C22×C8—1221no—
632C4⋊Q8—1222no—
633#127—1222no—
634#124—1222no—
635#124—1222no—
636#123—21no—
637#123—1221no—
638#123—1222no—
639#123—1222no—
640#123—1221no—
641#123—1221no—
642C22⋊Q8—612no—
643C22⋊Q8—612no—
644C22⋊Q8—612no—
645C22⋊Q8—1222no—
646C22⋊Q8—1222no—
647C22⋊Q8C4×D6112yescomplemented
648#121—612no—
649#121—612no—
650#121—612no—
651#121—1222no—
652#121—1222no—
653#121—1222no—
654#121—1222no—
655#121—1222no—
656#121—1222no—
657#121C4×D6112yescomplemented
658#120—21no—
659#120—1222no—
660#120—1221no—
661#120—1222no—
662#120—1221no—
663#120—1221no—
664C4×Q8—1228no—
665C4×D4—22no—
666C4×D4—1222no—
667C4×D4—1228no—
668C4×D4—1222no—
669C4×D4—1228no—
670C4×D4—1228no—
671C4×D4—1222no—
672#117—614no—
673#117—611no—
674#117—612no—
675#117—1222no—
676#117—1222no—
677#117—1221no—
678#117—1222no—
679#117—1222no—
680#117—1221no—
681#117—1222no—
682#117C22×D6111yescharacteristic
683C2×C4⋊C4—612no—
684C2×C4⋊C4—1221no—
685C2×C4⋊C4—1221no—
686C2×C4⋊C4—1221no—
687C2×C22⋊C4—1221no—
688C2×C22⋊C4—1221no—
689C2×C22⋊C4—1221no—
690C2×C22⋊C4—1221no—
691C2×C42—21no—
692C2×C42—22no—
693C2×C42—22no—
694C2×C42—611no—
695C2×C42—611no—
696C2×C42—614no—
697C2×C42—1222no—
698C2×C42—1221no—
699C2×C42—1222no—
700C2×C42—1221no—
701C2×C42—1221no—
702C2×C42—1222no—
703C2×C42C22×D6111yescharacteristic
704C2×C42C22×D6111yescharacteristic
705#104—22no—
706#104—22no—
707#104—1222no—
708#104—1222no—
709#104—1222no—
710#104—1222no—
711#104—1222no—
712#104—1222no—
713C22⋊C8—22no—
714C22⋊C8—1222no—
715C22⋊C8—1222no—
716C22⋊C8—1222no—
717C24—611no—
718C24—611no—
719C24—1221no—
720C24D4×D6111yescharacteristic
721#41—21no—
722#41—21no—
723#41—21no—
724#41—21no—
725#41—1224no—
726#41—1224no—
727#41—1224no—
728#41—1224no—
729#41—1224no—
730#41—1224no—
731#41—1224no—
732#41—1224no—
733#41—1222no—
734#41—1222no—
735#41—1222no—
736#41—1222no—
737#41—1221no—
738#41—1221no—
739#41—1221no—
740#41—1221no—
741#41—2442no—
742#41—2442no—
743#41—2442no—
744#41—2442no—
745C2×Q8—612no—
746C2×Q8—612no—
747C2×Q8—611no—
748C2×Q8—1222no—
749C2×Q8—1222no—
750C2×Q8—1221no—
751C2×Q8—1222no—
752C2×Q8—1222no—
753C2×Q8C2×C4×D6111yescharacteristic
754C2×D4—21no—
755C2×D4—22no—
756C2×D4—612no—
757C2×D4—612no—
758C2×D4—612no—
759C2×D4—612no—
760C2×D4—611no—
761C2×D4—612no—
762C2×D4—612no—
763C2×D4—1222no—
764C2×D4—1222no—
765C2×D4—1222no—
766C2×D4—1221no—
767C2×D4—1222no—
768C2×D4—1222no—
769C2×D4—1222no—
770C2×D4—1222no—
771C2×D4—1221no—
772C2×D4—1222no—
773C2×D4—1222no—
774C2×D4—1222no—
775C2×D4—1222no—
776C2×D4—1221no—
777C2×D4—1221no—
778C2×D4—2442no—
779C2×D4—2442no—
780C2×D4C2×C4×D6111yescharacteristic
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—24no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—44no—
790C22×C4—611no—
791C22×C4—611no—
792C22×C4—611no—
793C22×C4—612no—
794C22×C4—612no—
795C22×C4—611no—
796C22×C4—611no—
797C22×C4—612no—
798C22×C4—612no—
799C22×C4—611no—
800C22×C4—612no—
801C22×C4—612no—
802C22×C4—1221no—
803C22×C4—1222no—
804C22×C4—1224no—
805C22×C4—1221no—
806C22×C4—1224no—
807C22×C4—1221no—
808C22×C4—1221no—
809C22×C4—1221no—
810C22×C4—1221no—
811C22×C4—1221no—
812C22×C4—1221no—
813C22×C4—1221no—
814C22×C4—1221no—
815C22×C4—2444no—
816C22×C4—2444no—
817C22×C4—2442no—
818C22×C4—2442no—
819C22×C4C2×C4×D6112yes—
820C22×C4D4×D6112yes—
821C22×C4D4×D6111yescharacteristic
822C22×C4C23×D6111yescharacteristic
823M16—21no—
824M16—21no—
825M16—21no—
826M16—21no—
827M16—1221no—
828M16—1221no—
829M16—1221no—
830M16—1221no—
831M16—2442no—
832M16—2442no—
833C2×C8—21no—
834C2×C8—21no—
835C2×C8—1221no—
836C2×C8—1221no—
837C2×C8—2442no—
838C2×C8—2442no—
839C4⋊C4—22no—
840C4⋊C4—612no—
841C4⋊C4—1222no—
842C4⋊C4—1224no—
843C4⋊C4—1222no—
844C4⋊C4—1222no—
845C4⋊C4—1224no—
846C4⋊C4—1224no—
847C4⋊C4—1222no—
848C4⋊C4C2×C4×D6112yes—
849C22⋊C4—21no—
850C22⋊C4—22no—
851C22⋊C4—22no—
852C22⋊C4—1222no—
853C22⋊C4—1224no—
854C22⋊C4—1222no—
855C22⋊C4—1222no—
856C22⋊C4—1222no—
857C22⋊C4—1224no—
858C22⋊C4—1222no—
859C22⋊C4—1224no—
860C22⋊C4—1221no—
861C22⋊C4—1222no—
862C22⋊C4—1222no—
863C42—24no—
864C42—21no—
865C42—21no—
866C42—21no—
867C42—612no—
868C42—612no—
869C42—1224no—
870C42—1222no—
871C42—1224no—
872C42—1221no—
873C42—1221no—
874C42—1221no—
875C42D4×D6112yes—
876C42D4×D6112yes—
877C23—21no—
878C23—21no—
879C23—21no—
880C23—42no—
881C23—611no—
882C23—611no—
883C23—612no—
884C23—612no—
885C23—612no—
886C23—1221no—
887C23—1221no—
888C23—1221no—
889C23—4882no—
890C23—2442no—
891C23—2442no—
892C23—2442no—
893C23C22⋊C4×D6112yes—
894C23C2×D4×D6111yescharacteristic
895Q8—21no—
896Q8—21no—
897Q8—1224no—
898Q8—1224no—
899Q8—1221no—
900Q8—1221no—
901Q8—2442no—
902D4—21no—
903D4—21no—
904D4—41no—
905D4—41no—
906D4—82no—
907D4—1224no—
908D4—1224no—
909D4—1224no—
910D4—1224no—
911D4—1224no—
912D4—1224no—
913D4—1221no—
914D4—1221no—
915D4—4882no—
916D4—4882no—
917D4—4882no—
918D4—2442no—
919D4—2442no—
920D4—2442no—
921D4—2441no—
922D4—2441no—
923C2×C4—24no—
924C2×C4—21no—
925C2×C4—22no—
926C2×C4—21no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—21no—
933C2×C4—22no—
934C2×C4—48no—
935C2×C4—42no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—611no—
939C2×C4—611no—
940C2×C4—612no—
941C2×C4—612no—
942C2×C4—612no—
943C2×C4—612no—
944C2×C4—612no—
945C2×C4—612no—
946C2×C4—612no—
947C2×C4—612no—
948C2×C4—612no—
949C2×C4—612no—
950C2×C4—612no—
951C2×C4—1221no—
952C2×C4—1221no—
953C2×C4—1222no—
954C2×C4—1222no—
955C2×C4—1222no—
956C2×C4—1222no—
957C2×C4—1222no—
958C2×C4—1221no—
959C2×C4—1222no—
960C2×C4—1222no—
961C2×C4—4882no—
962C2×C4—2448no—
963C2×C4—2448no—
964C2×C4—2442no—
965C2×C4—2442no—
966C2×C4—2442no—
967C2×C4—2442no—
968C2×C4—2442no—
969C2×C4—2441no—
970C2×C4—2441no—
971C2×C4C22⋊C4×D6112yes—
972C2×C4C22×C4×D6111yescharacteristic
973C2×C4C2×D4×D6111yescharacteristic
974C2×C4C2×D4×D6111yescharacteristic
975C2×C4C2×D4×D6111yescharacteristic
976C2×C4#41×D6111yescharacteristic
977C2×C4#41×D6111yescharacteristic
978C8—41no—
979C8—41no—
980C8—2441no—
981C8—2441no—
982C22—22no—
983C22—22no—
984C22—22no—
985C22—22no—
986C22—42no—
987C22—42no—
988C22—42no—
989C22—41no—
990C22—612no—
991C22—612no—
992C22—1222no—
993C22—1222no—
994C22—1222no—
995C22—1222no—
996C22—1222no—
997C22—4884no—
998C22—2442no—
999C22—2442no—
1000C22—2442no—
1001C22—2442no—
1002C22—2442no—
1003C22—2441no—
1004C22C2×C22⋊C4×D6111yescharacteristic
1005C22#120×D6111yescharacteristic
1006C22#123×D6111yescharacteristic
1007C4—24no—
1008C4—22no—
1009C4—42no—
1010C4—42no—
1011C4—41no—
1012C4—612no—
1013C4—612no—
1014C4—1222no—
1015C4—2442no—
1016C4—2442no—
1017C4—2442no—
1018C4—2441no—
1019C4C4×D4×D6111yescharacteristic
1020C4C4×D4×D6111yescharacteristic
1021C4#121×D6111yescharacteristic
1022C4#121×D6111yescharacteristic
1023C2—21no—
1024C2—21no—
1025C2—42no—
1026C2—81no—
1027C2—1222no—
1028C2—1222no—
1029C2—4881no—
1030C2—2442no—
1031C2#386×D6111yescharacteristic
1032C2#2145436312yes—
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1896C2
socleC22×C61C22×C22⋊C4
prime radical#21459149C2
cosocleC22×C4×C61C24
hypercenter#1896D61
hypocenterC61#20980
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1896

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11758222C2semidirect
3. C2×#16839777C2semidirect
4. C2×#104×D61C2semidirect
5. #21454262C2semidirect
6. #21446268C2semidirect
7. #21446266C2semidirect
8. #21446265C2semidirect
9. #21446264C2semidirect
10. #21446262C2semidirect
11. #21446261C2semidirect
12. #21446259C2semidirect
13. #21445527C2semidirect
14. #339×D61C2semidirect
15. C61×#1896C2semidirect
20. #16840342C4semidirect
21. #16840341C4semidirect
22. #16840335C4semidirect
24. #16840328C4semidirect
39. C2×#14519736C22semidirect
41. C2×#14519734C22semidirect
44. C2×C42×D61C22semidirect
55. #16839726C22semidirect
56. #16839725C22semidirect
57. #16839725C22semidirect
58. #16839523C22semidirect
59. #16839523C22semidirect
60. #16839522C22semidirect
61. #16839522C22semidirect
62. #16839521C22semidirect
63. #16839521C22semidirect
65. C22×C42×C61C22semidirect
68. C61×#407C22semidirect
69. C61×#339C22semidirect
70. C61×#339C22semidirect
71. C2×#11758226C2×C4semidirect
83. C2×#11758224C2×C4semidirect
89. C2×Q8×D61C2×C4semidirect
94. C2×D4×D61C2×C4semidirect
119. #14519757C2×C4semidirect
120. #14519756C2×C4semidirect
123. #14519753C2×C4semidirect
125. #14519752C2×C4semidirect
126. #14519751C2×C4semidirect
132. #14519748C2×C4semidirect
148. #14519735C2×C4semidirect
153. #14519734D4semidirect
158. C4⋊C4×D61C2×C4semidirect
171. C42×D61D4semidirect
187. C22⋊Q8×C61C2×C4semidirect
188. #121×C61C2×C4semidirect
519. #1896D61semidirect
562. C22×C42C2×D61semidirect
578. #407C2×D61semidirect
585. #339C2×D61semidirect
586. #339C2×D61semidirect
587. C61#20980semidirect
647. C22⋊Q8C4×D61semidirect
657. #121C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214591492
C2×C4×#117582222
C2×#168397772
C2×#104×D612
#214542622
#214462682
#214462662
#214462652
#214462642
#214462622
#214462612
#214462592
#214455272
#339×D612
C61×#18962
#2098061