Finite Group Databasebeta

← #29719018

Subgroups — #29719018

Order 15616.

966 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839919C211yesmaximal, characteristic
2C2×#103×D61C211yesmaximal, characteristic
3#21450301C211yesmaximal, characteristic
4#21448653C211yesmaximal, characteristic
5#21447240C211yesmaximal, characteristic, complemented
6#21447141C211yesmaximal, characteristic, complemented
7#21447140C211yesmaximal, characteristic, complemented
8#21446241C211yesmaximal, characteristic
9#21446161C211yesmaximal, characteristic, complemented
10#21446159C211yesmaximal, characteristic, complemented
11#21445998C211yesmaximal, characteristic
12#21445904C211yesmaximal, characteristic
13#21445833C211yesmaximal, characteristic, complemented
14#21445831C211yesmaximal, characteristic, complemented
15C61×#2074C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C22×Dic244C2211yescharacteristic
18C22×#11758202C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20C2×#14519757C2211yescharacteristic
21C2×C4×Dic122C2211yescharacteristic
22C2×#14519742C2211yescharacteristic
23C2×C4⋊C4×D61C2211yescharacteristic
24#16839919—24no—
25C2×C4⋊#92418C2211yescharacteristic
26C2×#14519706C2211yescharacteristic
27C2×#14519702C2211yescharacteristic
28C2×#14519702C2211yescharacteristic
29C2×#14519701C2211yescharacteristic
30C2×#14519700C2211yescharacteristic
31C2×#14519700C2211yescharacteristic
32C2×#14519700C2211yescharacteristic
33#103×D61—24no—
34C2×#14519689C2211yescharacteristic
35#16839704—21no—
36#16839704—21no—
37#16839669C2211yescharacteristic
38#16839668C2211yescharacteristic
39#16839667C2211yescharacteristic
40#16839666—21no—
41#16839666—21no—
42#16839627C2211yescharacteristic
43#16839624—21no—
44#16839624—21no—
45#16839621—21no—
46#16839619C2211yescharacteristic
47C4×#11758198C2211yescharacteristic
48#16839609—21no—
49#16839525C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839516C2211yescharacteristic
54C2×#103×C61C2211yescharacteristic
55C2×#103×C61C2211yescharacteristic
56C61×#391C2211yescharacteristic
57C61×#382C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C22×Dic122—21no—
62C22×Dic122C2311yescharacteristic
63C22×Dic122C2311yescharacteristic
64C2×Q8×D61—22no—
65C2×Q8×D61—22no—
66C2×Q8×D61—22no—
67C2×Q8×D61—41no—
68C2×Q8×D61—41no—
69C2×Q8×D61D414yes—
70C22×C4×D61—21no—
71C22×C4×D61—21no—
72C22×C4×D61C2311yescharacteristic
73C2×Dic244—22no—
74C2×Dic244—22no—
75C2×Dic244—22no—
76C2×#11758202—22no—
77C2×#11758202—41no—
78C2×#11758202—41no—
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81C2×C8×D61—22no—
82C2×C8×D61—41no—
83C2×C8×D61—41no—
84#14519757—22no—
85#14519757—22no—
86C4×Dic122—22no—
87C4×Dic122—41no—
88#14519742—22no—
89#14519742—41no—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×#11758196—21no—
94C2×#11758196—21no—
95C2×#11758196—21no—
96C4⋊C4×D61—22no—
97C4⋊C4×D61—22no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198D411yescharacteristic
101C2×#11758198D411yescharacteristic
102C2×C4×Dic61—21no—
103C2×C4×Dic61—21no—
104C2×C4×Dic61C2311yescharacteristic
105C4⋊#92418—41no—
106#14519706—41no—
107#14519702—22no—
108#14519702—41no—
109#14519701—22no—
110#14519700—22no—
111#14519700—22no—
112#14519700—41no—
113#14519689—22no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119#14519684—21no—
120#14519684—21no—
121#14519684—21no—
122#14519684—21no—
123#14519684D411yescharacteristic
124#14519684D411yescharacteristic
125C22×Q8×C61C2311yescharacteristic
126C22×C8×C61C2311yescharacteristic
127C22×C8×C61C2311yescharacteristic
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C4⋊C4×C61C2311yescharacteristic
131C2×C42×C61C2311yescharacteristic
132#103×C61—22no—
133#103×C61—22no—
134#95×C61—21no—
135#95×C61—21no—
136#95×C61—21no—
137#95×C61—21no—
138C23×D61C2×D411yescharacteristic
139C2×Q8×C61—21no—
140C2×Q8×C61—21no—
141C2×Q8×C61—21no—
142C2×Q8×C61—21no—
143C2×Q8×C61—21no—
144C2×Q8×C61C2×D412yes—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2411yescharacteristic
152C22×Dic61—21no—
153C22×Dic61—21no—
154C22×Dic61—21no—
155C22×Dic61—21no—
156C22×Dic61C2×D411yescharacteristic
157C22×Dic61C2×D411yescharacteristic
158C22×Dic61C2×D411yescharacteristic
159Q8×D61—28no—
160Q8×D61—44no—
161Q8×D61—44no—
162Q8×D61—44no—
163C2×C4×D61—21no—
164C2×C4×D61—21no—
165C2×C4×D61—21no—
166C2×C4×D61—21no—
167C2×C4×D61—24no—
168C2×C4×D61—42no—
169C2×C4×D61—42no—
170C2×C4×D61—42no—
171C2×C4×D61—42no—
172C2×C4×D61—42no—
173C2×C4×D61C2×D412yes—
174C2×C4×D61#4112yes—
175C2×Dic122—21no—
176C2×Dic122—21no—
177C2×Dic122—21no—
178C2×Dic122—24no—
179C2×Dic122—21no—
180C2×Dic122—21no—
181C2×Dic122—21no—
182C2×Dic122—21no—
183C2×Dic122—21no—
184C2×Dic122—21no—
185C2×Dic122—42no—
186C2×Dic122—42no—
187C2×Dic122C2×D412yes—
188C2×Dic122#4112yes—
189C2×Dic122#4112yes—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C42×C61—21no—
203C42×C61—21no—
204#11758202—44no—
205#11758198—22no—
206#11758198—22no—
207#11758198—42no—
208#11758198—42no—
209C4⋊Dic61—21no—
210C4⋊Dic61—21no—
211C4⋊Dic61—21no—
212C4⋊Dic61—21no—
213C4⋊Dic61—42no—
214#11758196—42no—
215#11758196—42no—
216#11758196—42no—
217C4×Dic61—21no—
218C4×Dic61—21no—
219C4×Dic61—42no—
220C4×Dic61—42no—
221C2×#92418—21no—
222C2×#92418—21no—
223C2×#92418—21no—
224C2×#92418—21no—
225C2×#92418—21no—
226C2×#92418—21no—
227Dic244—44no—
228C8×D61—44no—
229C23×C61C22×D411yescharacteristic
230C22×D61—21no—
231C22×D61—21no—
232C22×D61—21no—
233C22×D61—21no—
234C22×D61#12112yes—
235C22×D61#13512yes—
236C22×D61#13712yes—
237Q8×C61—22no—
238Q8×C61—22no—
239Q8×C61—41no—
240Q8×C61—41no—
241C2×C4×C61—22no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61C22×D411yescharacteristic
260C2×C4×C61C2×#4111yescharacteristic
261C2×C4×C61C2×#4111yescharacteristic
262C2×C4×C61C2×#4111yescharacteristic
263C2×C4×C61H(5,𝔽2)11yescharacteristic
264C2×C4×C61H(5,𝔽2)11yescharacteristic
265C2×Dic61—22no—
266C2×Dic61—22no—
267C2×Dic61—22no—
268C2×Dic61—21no—
269C2×Dic61—21no—
270C2×Dic61—21no—
271C2×Dic61—21no—
272C2×Dic61—21no—
273C2×Dic61—21no—
274C2×Dic61—21no—
275C2×Dic61—21no—
276C2×Dic61—41no—
277C2×Dic61—41no—
278C2×Dic61—41no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61—41no—
282C2×Dic61—41no—
283C2×Dic61—41no—
284C2×Dic61—41no—
285C2×Dic61#12112yes—
286C4×D61—22no—
287C4×D61—22no—
288C4×D61—22no—
289C4×D61—22no—
290C4×D61—48no—
291C4×D61—84no—
292Dic122—22no—
293Dic122—22no—
294Dic122—22no—
295Dic122—48no—
296Dic122—41no—
297Dic122—41no—
298Dic122—41no—
299Dic122—41no—
300Dic122#12314yes—
301C8×C61—41no—
302C8×C61—41no—
303#92418—41no—
304#92418—41no—
305#24529—611nomaximal, Sylow
306C22×C61C2×#12111yescharacteristic
307C22×C61#54611yescharacteristic
308C22×C61#54611yescharacteristic
309C22×C61C2×#13511yescharacteristic
310C22×C61C2×#13711yescharacteristic
311C22×C61#57811yescharacteristic
312C22×C61#57811yescharacteristic
313C2×D61—22no—
314C2×D61—22no—
315C2×D61—22no—
316C2×D61—22no—
317C2×D61—22no—
318C2×D61—22no—
319C2×D61#46414yes—
320C4×C61—42no—
321C4×C61—41no—
322C4×C61—41no—
323C4×C61—81no—
324C4×C61—81no—
325C4×C61—81no—
326C4×C61C2×#12311yescharacteristic
327C4×C61#53411yescharacteristic
328C4×C61#55111yescharacteristic
329C4×C61#55111yescharacteristic
330Dic61—24no—
331Dic61—22no—
332Dic61—41no—
333Dic61—41no—
334Dic61—81no—
335Dic61—81no—
336Dic61—81no—
337C2×#451—611no—
338C22×#103—611no—
339#2503—611no—
340Q8×C22⋊C4—611no—
341#2074—611no—
342#2074D6111yescharacteristic, complemented
343#2056—611no—
344#2056—611no—
345#1892—611no—
346#1878—611no—
347#1878—611no—
348#1850—611no—
349#1823—611no—
350#1805—611no—
351#1805—611no—
352C2×C61#241211yescharacteristic
353C2×C61C2×#46411yescharacteristic
354C2×C61#304411yescharacteristic
355C2×C61#330011yescharacteristic
356C2×C61#330011yescharacteristic
357C2×C61#331211yescharacteristic
358C2×C61#331211yescharacteristic
359D61—24no—
360C23×Q8—611no—
361C22×Q16—611no—
362C22×Q16—611no—
363C23×C8—611no—
364C2×C22⋊Q8—611no—
365C2×C4×Q8—611no—
366C2×C4×Q8—611no—
367C22×C4⋊C4—611no—
368#451—1224no—
369C2×C4⋊C8—611no—
370C2×C4⋊C8—611no—
371C2×#103—611no—
372C2×#103—611no—
373C2×#103—611no—
374C2×#103—611no—
375C2×#103—611no—
376C2×#103—611no—
377C2×#103—1224no—
378C2×#103C2×D6111yescharacteristic
379C2×#103C2×D6111yescharacteristic
380C2×C22⋊C8—611no—
381#400—1221no—
382#400—1221no—
383#391—611no—
384#391—611no—
385#391—611no—
386#391—1221no—
387#391—1221no—
388#391C2×D6111yescharacteristic
389#382—611no—
390#382C2×D6111yescharacteristic
391#381—1221no—
392#381—1221no—
393#380—611no—
394#380—1221no—
395C4×C22⋊C4—611no—
396C4×C22⋊C4—1221no—
397#340—611no—
398#340—611no—
399#340—611no—
400#340—611no—
401#340C2×D6111yescharacteristic
402#340C2×D6111yescharacteristic
403#336—611no—
404#336C2×D6111yescharacteristic
405C61#2452911yescharacteristic, complemented, Sylow
406C22×Q8—614no—
407C22×Q8—611no—
408C22×Q8—611no—
409C22×Q8—1221no—
410C22×Q8—1222no—
411C22×Q8—1222no—
412C22×Q8—1222no—
413C22×Q8—2441no—
414C22×Q8—2441no—
415C22×Q8C22×D6111yescharacteristic
416C23×C4—611no—
417C23×C4—1221no—
418C23×C4—1221no—
419C2×Q16—1222no—
420C2×Q16—1222no—
421C2×Q16—1222no—
422C2×Q16—1222no—
423C2×Q16—2441no—
424C2×Q16—2441no—
425C22×C8—611no—
426C22×C8—611no—
427C22×C8—1222no—
428C22×C8—2441no—
429C22×C8—2441no—
430C22×C8C22×D6111yescharacteristic
431C22×C8C22×D6111yescharacteristic
432C22⋊Q8—1222no—
433C22⋊Q8—1222no—
434C4×Q8—1222no—
435C4×Q8—1222no—
436C4×Q8—2441no—
437C4×Q8—2441no—
438C2×C4⋊C4—611no—
439C2×C4⋊C4—611no—
440C2×C4⋊C4—1222no—
441C2×C4⋊C4—1222no—
442C2×C4⋊C4—1221no—
443C2×C4⋊C4—1221no—
444C2×C4⋊C4—1221no—
445C2×C4⋊C4—1221no—
446C2×C4⋊C4C22×D6111yescharacteristic
447C2×C4⋊C4C22×D6111yescharacteristic
448C2×C4⋊C4C22×D6111yescharacteristic
449C2×C22⋊C4—611no—
450C2×C22⋊C4—611no—
451C2×C22⋊C4—1221no—
452C2×C22⋊C4—1221no—
453C2×C42—611no—
454C2×C42—1221no—
455C2×C42—1221no—
456C2×C42C22×D6111yescharacteristic
457C4⋊C8—2441no—
458C4⋊C8—2441no—
459#103—22no—
460#103—22no—
461#103—1222no—
462#103—1222no—
463#103—1222no—
464#103—1222no—
465#103—2441no—
466#103—2441no—
467C22⋊C8—1222no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—611no—
473#95—611no—
474#95—1221no—
475#95—1221no—
476#95—1221no—
477#95—1221no—
478#95—1221no—
479#95—1221no—
480#95—1221no—
481#95—1221no—
482#95—1221no—
483C24—611no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—612no—
490C2×Q8—612no—
491C2×Q8—612no—
492C2×Q8—1224no—
493C2×Q8—1221no—
494C2×Q8—1221no—
495C2×Q8—1221no—
496C2×Q8—1228no—
497C2×Q8—1221no—
498C2×Q8—1221no—
499C2×Q8—1221no—
500C2×Q8—1221no—
501C2×Q8—1221no—
502C2×Q8—1221no—
503C2×Q8—2442no—
504C2×Q8—2442no—
505C2×Q8—2444no—
506C2×Q8—2444no—
507C2×Q8—2444no—
508C2×Q8D4×D6112yes—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—611no—
514C22×C4—612no—
515C22×C4—612no—
516C22×C4—611no—
517C22×C4—611no—
518C22×C4—1224no—
519C22×C4—1221no—
520C22×C4—1221no—
521C22×C4—1221no—
522C22×C4—1221no—
523C22×C4—1221no—
524C22×C4—1221no—
525C22×C4—1221no—
526C22×C4—1221no—
527C22×C4—2442no—
528C22×C4—2442no—
529C22×C4—2442no—
530C22×C4—2442no—
531C22×C4—2442no—
532C22×C4D4×D6111yescharacteristic
533C22×C4D4×D6111yescharacteristic
534C22×C4C23×D6111yescharacteristic
535Q16—2444no—
536Q16—2444no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—1221no—
544C2×C8—1221no—
545C2×C8—1221no—
546C2×C8—1221no—
547C2×C8—1221no—
548C2×C8—1221no—
549C2×C8—2444no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—1221no—
557C4⋊C4—1221no—
558C4⋊C4—1221no—
559C4⋊C4—1221no—
560C4⋊C4—2442no—
561C4⋊C4—2442no—
562C4⋊C4—2442no—
563C4⋊C4—2442no—
564C22⋊C4—1222no—
565C22⋊C4—1222no—
566C22⋊C4—2442no—
567C22⋊C4—2442no—
568C42—21no—
569C42—21no—
570C42—1221no—
571C42—1221no—
572C42—2442no—
573C42—2442no—
574C23—612no—
575C23—612no—
576C23—612no—
577C23—1221no—
578C23—1221no—
579C23—1221no—
580C23—1221no—
581C23C2×D4×D6111yescharacteristic
582Q8—22no—
583Q8—22no—
584Q8—41no—
585Q8—41no—
586Q8—614no—
587Q8—1222no—
588Q8—1222no—
589Q8—1222no—
590Q8—2448no—
591Q8—2441no—
592Q8—2441no—
593Q8—2441no—
594Q8—2441no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—612no—
614C2×C4—1222no—
615C2×C4—1222no—
616C2×C4—1221no—
617C2×C4—1222no—
618C2×C4—1221no—
619C2×C4—1222no—
620C2×C4—1222no—
621C2×C4—1222no—
622C2×C4—1222no—
623C2×C4—1221no—
624C2×C4—1221no—
625C2×C4—1221no—
626C2×C4—1221no—
627C2×C4—1221no—
628C2×C4—1221no—
629C2×C4—4884no—
630C2×C4—2448no—
631C2×C4—2441no—
632C2×C4—2441no—
633C2×C4—2441no—
634C2×C4—2441no—
635C2×C4—2441no—
636C2×C4—2441no—
637C2×C4—2441no—
638C2×C4—2441no—
639C2×C4—2441no—
640C2×C4C2×D4×D6111yescharacteristic
641C2×C4#41×D6111yescharacteristic
642C2×C4#41×D6111yescharacteristic
643C2×C4#41×D6111yescharacteristic
644C2×C4#1451982311yescharacteristic
645C2×C4#1451982311yescharacteristic
646C8—41no—
647C8—41no—
648C8—2441no—
649C8—2441no—
650C22—614no—
651C22—1222no—
652C22—1222no—
653C22—1222no—
654C22—1222no—
655C22—1222no—
656C22—1222no—
657C22#121×D6111yescharacteristic
658C22#1684040411yescharacteristic
659C22#1684040511yescharacteristic
660C22#135×D6111yescharacteristic
661C22#137×D6111yescharacteristic
662C22#1684057611yescharacteristic
663C22#1684057811yescharacteristic
664C4—41no—
665C4—41no—
666C4—42no—
667C4—81no—
668C4—81no—
669C4—81no—
670C4—1222no—
671C4—1224no—
672C4—4881no—
673C4—4881no—
674C4—4881no—
675C4—2441no—
676C4—2441no—
677C4#123×D6111yescharacteristic
678C4#1684032311yescharacteristic
679C4#1684043711yescharacteristic
680C4#1684043711yescharacteristic
681C2—1224no—
682C2#2144920811yescharacteristic
683C2#464×D6111yescharacteristic
684C2#2145534711yescharacteristic
685C2#2145770511yescharacteristic
686C2#2145770911yescharacteristic
687C2#2145786911yescharacteristic
688C2#2145787311yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2074C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
hypercenter#2074D61
hypocenterC61#24529
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2074

Complements

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

NH ≅ G/Ntype
5. #21447240C2semidirect
6. #21447141C2semidirect
7. #21447140C2semidirect
9. #21446161C2semidirect
10. #21446159C2semidirect
13. #21445833C2semidirect
14. #21445831C2semidirect
15. C61×#2074C2semidirect
342. #2074D61semidirect
405. C61#24529semidirect

Maximal subgroups

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

subgroupindex
C2×#168399192
C2×#103×D612
#214503012
#214486532
#214472402
#214471412
#214471402
#214462412
#214461612
#214461592
#214459982
#214459042
#214458332
#214458312
C61×#20742
#2452961