Finite Group Databasebeta

← #30620156

Subgroups — #30620156

Order 15616.

1462 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462559C212yesmaximal, complemented
2C2×#16840748C212yesmaximal, complemented
3#21461961C212yesmaximal, complemented
4#21461845C214yesmaximal, complemented
5#21461685C211yesmaximal, characteristic, complemented
6#21461655C212yesmaximal, complemented
7C4×#14519838C211yesmaximal, characteristic, complemented
8C2×#16840433C211yesmaximal, characteristic
9C2×D61⋊M16C2214yes—
10#16840796—22no—
11#16840792—24no—
12#16840790—22no—
13#16840765C2212yes—
14#16840748—28no—
15C2×#14519838C2211yescharacteristic
16C2×#14519838C2212yes—
17C2×#14519838C2211yescharacteristic
18C2×#14519837C2214yes—
19C2×#14519837C2214yes—
20#16840734C2214yes—
21C4×#11758217C2212yes—
22#16840642C2212yes—
23#16840642C2212yes—
24C22×#11758222C2212yes—
25#16840433—22no—
26#16840433—24no—
27#16840433—22no—
28C2×#14519774C411yescharacteristic
29C2×#14519773C411yescharacteristic
30C2×#14519773C2211yescharacteristic
31C2×#14519751C412yes—
32C2×#14519750C412yes—
33C2×#14519750C2212yes—
34C2×C4×Dic122C2211yescharacteristic
35C2×#14519739C411yescharacteristic
36C2×#14519739C2211yescharacteristic
37C2×C4×D4×C61C411yescharacteristic
38C2×#11758213—24no—
39D61⋊M16—28no—
40D61⋊M16—44no—
41C2×#11758217C2312yes—
42C2×#11758217C2314yes—
43C2×#11758217C2312yes—
44C2×D61⋊C8—24no—
45#14519844—22no—
46C4⋊#92420—22no—
47#14519838—24no—
48#14519838—22no—
49#14519838D414yescomplemented
50#14519837—28no—
51#14519837—44no—
52#14519834—24no—
53#14519834—24no—
54#14519832—22no—
55C4×#92420—22no—
56C2×#11758222—24no—
57C2×#11758222—24no—
58C2×#11758222—24no—
59C2×#11758222—24no—
60C2×#11758222—44no—
61C22×Dic122C2311yescharacteristic
62C22×D244C2×C412yes—
63C22×D244C2×C411yescharacteristic
64C22×D244C2×C412yes—
65C22×D244C2×C411yescharacteristic
66C22×C22⋊D61C2×C412yes—
67C22×C22⋊D61C2×C412yes—
68C22×C22⋊D61C2×C412yes—
69C22×C22⋊D61C2312yes—
70C22×C4×D61C2×C412yes—
71C22×C4×D61C2312yes—
72#14519774—22no—
73#14519774—22no—
74#14519773—22no—
75#14519773—22no—
76#14519773—22no—
77#14519773—22no—
78#14519751—24no—
79#14519751—24no—
80#14519750—24no—
81#14519750—24no—
82#14519750—24no—
83#14519750—24no—
84C4×Dic122—22no—
85C4×Dic122—22no—
86#14519739—22no—
87#14519739—21no—
88#14519739—21no—
89#14519739D412yes—
90#14519739D414yes—
91#14519739D412yes—
92C2×C4⋊Dic61C2×C411yescharacteristic
93C2×#11758196C2×C411yescharacteristic
94C2×#11758196C2311yescharacteristic
95C2×#11758198C2×C412yes—
96C2×#11758198C2×C412yes—
97C2×C4×Dic61C2×C411yescharacteristic
98C2×C4×Dic61C2311yescharacteristic
99C22×D4×C61C2×C411yescharacteristic
100C23×C4×C61C2×C412yes—
101C4×D4×C61—22no—
102C4×D4×C61—21no—
103C4×D4×C61—21no—
104C2×C4⋊C4×C61C2×C411yescharacteristic
105C2×C22⋊C4×C61C2×C412yes—
106C2×C42×C61C2×C411yescharacteristic
107C24×C61C22×C412yes—
108C23×D61C22×C412yes—
109C23×D61C22×C412yes—
110C2×D4×C61—21no—
111C2×D4×C61—21no—
112C2×D4×C61—42no—
113C22×C4×C61—22no—
114C22×C4×C61—22no—
115C22×C4×C61—24no—
116C22×C4×C61—42no—
117C22×C4×C61C22×C412yes—
118C22×C4×C61C22×C411yescharacteristic
119C22×C4×C61C22×C411yescharacteristic
120C22×C4×C61C22×C411yescharacteristic
121C2×C22⋊D61—24no—
122C2×C22⋊D61—24no—
123C2×C22⋊D61—24no—
124C2×C22⋊D61—24no—
125C2×C22⋊D61—22no—
126C2×C22⋊D61—24no—
127C2×C22⋊D61—22no—
128C2×C22⋊D61—24no—
129C2×C22⋊D61—42no—
130C2×C22⋊D61—82no—
131C2×C22⋊D61—82no—
132C22×Dic61C22×C411yescharacteristic
133C22×Dic61C22×C411yescharacteristic
134C22×Dic61C22×C411yescharacteristic
135C22×Dic61C2411yescharacteristic
136#11758222—48no—
137#11758222—48no—
138#11758222—48no—
139#11758222—48no—
140C2×D244—24no—
141C2×D244—21no—
142C2×D244—21no—
143C2×D244—24no—
144C2×D244—24no—
145C2×D244—42no—
146C2×D244—42no—
147C2×D244—42no—
148C2×D244—82no—
149C2×D244C22⋊C412yes—
150C2×D244C22⋊C412yes—
151C2×C4×D61—22no—
152C2×C4×D61—22no—
153C2×C4×D61—24no—
154C2×C4×D61—22no—
155C2×C4×D61—22no—
156C2×C4×D61—24no—
157C2×C4×D61—42no—
158C2×C4×D61C2×D414yes—
159C2×C4×D61C2×D414yes—
160C2×Dic122—22no—
161C2×Dic122—22no—
162C2×Dic122C2×D412yes—
163C2×Dic122#4112yes—
164#11758217—22no—
165#11758217—24no—
166#11758217—22no—
167#11758217—22no—
168#11758217—24no—
169#11758217C2×D414yes—
170C2×#92420—22no—
171C2×#92420—22no—
172C2×#92420—24no—
173#11758213—48no—
174D61⋊C8—48no—
175C4⋊C4×C61C22⋊C412yes—
176C4⋊C4×C61C22⋊C411yescharacteristic
177C4⋊C4×C61C22⋊C411yescharacteristic
178C22⋊C4×C61—22no—
179C22⋊C4×C61—22no—
180C42×C61—21no—
181C42×C61—21no—
182#11758198—22no—
183#11758198—22no—
184#11758198C22⋊C414yes—
185#11758198C22⋊C414yes—
186C4⋊Dic61—22no—
187#11758196—22no—
188#11758196—22no—
189C4×Dic61—21no—
190C4×Dic61—21no—
191C4×Dic61C2×D412yes—
192C4×Dic61C2×D412yes—
193C23×C61—22no—
194C23×C61—22no—
195C23×C61—22no—
196C23×C61—42no—
197C23×C61—42no—
198C23×C61C23×C411yescharacteristic
199C22×D61—22no—
200C22×D61—22no—
201C22×D61—22no—
202C22×D61—22no—
203C22×D61—22no—
204C22×D61—42no—
205C22×D61—42no—
206C22×D61—42no—
207C22×D61—42no—
208C22×D61C2×C22⋊C414yes—
209D4×C61—42no—
210D4×C61—42no—
211C2×C4×C61—21no—
212C2×C4×C61—22no—
213C2×C4×C61—21no—
214C2×C4×C61—22no—
215C2×C4×C61—22no—
216C2×C4×C61—21no—
217C2×C4×C61—44no—
218C2×C4×C61—44no—
219C2×C4×C61—41no—
220C2×C4×C61C2×C22⋊C411yescharacteristic
221C2×C4×C61C2×C22⋊C412yes—
222C2×C4×C61C2×C22⋊C412yes—
223C2×C4×C61C2×C22⋊C411yescharacteristic
224C2×C4×C61C4×D412yes—
225C22⋊D61—48no—
226C22⋊D61—44no—
227C22⋊D61—44no—
228C22⋊D61—84no—
229C22⋊D61—84no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—41no—
234C2×Dic61—41no—
235C2×Dic61C2×C22⋊C412yes—
236C2×Dic61C4×D412yes—
237C2×Dic61C22×D411yescharacteristic
238C2×Dic61C22×D412yes—
239C2×Dic61C2×#4111yescharacteristic
240C2×Dic61H(5,𝔽2)12yes—
241D244—24no—
242D244—42no—
243D244—48no—
244D244—42no—
245D244—42no—
246D244—84no—
247C4×D61—24no—
248C4×D61—24no—
249C4×D61—24no—
250C4×D61—24no—
251C4×D61—44no—
252C4×D61—44no—
253Dic122—24no—
254Dic122—24no—
255#92420—24no—
256#92420—44no—
257#92420—42no—
258#22412—611nomaximal, Sylow
259C22×C61—21no—
260C22×C61—21no—
261C22×C61—42no—
262C22×C61—42no—
263C22×C61—42no—
264C22×C61—82no—
265C22×C61—82no—
266C22×C61C22×C22⋊C411yescharacteristic
267C22×C61C2×C4×D411yescharacteristic
268C22×C61#51811yescharacteristic
269C2×D61—24no—
270C2×D61—24no—
271C2×D61—24no—
272C2×D61—42no—
273C2×D61—42no—
274C2×D61—42no—
275C2×D61—82no—
276C2×D61—82no—
277C2×D61—82no—
278C2×D61—82no—
279C4×C61—22no—
280C4×C61—22no—
281C4×C61—22no—
282C4×C61—21no—
283C4×C61—41no—
284C4×C61#41312yescomplemented
285Dic61—22no—
286Dic61—22no—
287Dic61—41no—
288Dic61D4212yes—
289Dic61#54612yes—
290C2×#550—611no—
291D4×M16—612no—
292C2×#413—612no—
293#1965—612no—
294#1900—614no—
295#1801—611no—
296#1785—612no—
297C4×#101—611no—
298C2×C61—21no—
299C2×C61—21no—
300C2×C61—82no—
301C2×C61D4×C22⋊C411yescharacteristic
302C2×C61C2×#41311yescharacteristic
303C2×C61#288811yescharacteristic
304D61—44no—
305D61—82no—
306C22×#41—612no—
307C22×M16—614no—
308#550—1222no—
309#550—1224no—
310#550—1222no—
311C2×#127—611no—
312C2×#127—611no—
313C2×#127—611no—
314C2×#121—612no—
315C2×#121—612no—
316C2×#121—612no—
317C2×C4×Q8—611no—
318C2×C4×D4—611no—
319C2×C4×D4—611no—
320C2×C4×D4#692311yescharacteristic
321#436—1222no—
322#435—1224no—
323C8×D4—1222no—
324#423—612no—
325#413—1228no—
326C2×#101—611no—
327C2×#101—612no—
328C2×#101—611no—
329C2×#100—614no—
330C2×#100—614no—
331#407—614no—
332C4×M16—612no—
333#343—612no—
334#343—612no—
335C61#2241211yescharacteristic, complemented, Sylow
336C2×#41—1224no—
337C2×#41—1224no—
338C2×#41—1224no—
339C2×#41—1224no—
340C2×#41—2444no—
341C22×Q8—611no—
342C22×D4—612no—
343C22×D4—612no—
344C22×D4—612no—
345C22×D4—612no—
346C22×D4—611no—
347C22×D4—612no—
348C22×D4—612no—
349C22×D4—611no—
350C22×D4C2×#692311yescharacteristic
351C23×C4—612no—
352C23×C4—612no—
353C23×C4C2×#692312yes—
354C2×M16—612no—
355C2×M16—614no—
356C2×M16—612no—
357C2×M16—1224no—
358C2×M16—1228no—
359C2×M16—2444no—
360C22×C8—1224no—
361#127—1222no—
362#127—1222no—
363#127—1222no—
364#127—1222no—
365#127—1222no—
366#127—1222no—
367#121—1224no—
368#121—1224no—
369#121—1224no—
370#121—1224no—
371#121—1224no—
372#121—1224no—
373C4×Q8—1222no—
374C4×Q8—1222no—
375C4×D4—22no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—612no—
379C4×D4—614no—
380C4×D4—612no—
381C4×D4—1222no—
382C4×D4—1221no—
383C4×D4—1221no—
384C2×C4⋊C4—611no—
385C2×C4⋊C4—611no—
386C2×C4⋊C4—611no—
387C2×C4⋊C4C2×#692311yescharacteristic
388C2×C22⋊C4—612no—
389C2×C22⋊C4—612no—
390C2×C22⋊C4C2×#692312yes—
391C2×C42—611no—
392C2×C42—611no—
393C2×C42C2×#692311yescharacteristic
394C4⋊C8—1222no—
395C4⋊C8—1222no—
396#101—614no—
397#101—1222no—
398#101—1224no—
399#100—1228no—
400#100—2444no—
401C22⋊C8—1224no—
402C22⋊C8—1224no—
403#97—1222no—
404C4×C8—1222no—
405C24—612no—
406C24—612no—
407C24C22×#692312yes—
408#41—2448no—
409#41—2448no—
410#41—2448no—
411#41—2448no—
412C2×Q8—612no—
413C2×Q8—612no—
414C2×Q8—1222no—
415C2×Q8—1222no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—42no—
419C2×D4—612no—
420C2×D4—612no—
421C2×D4—1224no—
422C2×D4—1224no—
423C2×D4—1224no—
424C2×D4—1222no—
425C2×D4—1224no—
426C2×D4—1224no—
427C2×D4—1222no—
428C2×D4—1224no—
429C2×D4—1224no—
430C2×D4—1224no—
431C2×D4—1221no—
432C2×D4—1221no—
433C2×D4—1224no—
434C2×D4—4882no—
435C2×D4—4882no—
436C2×D4—4882no—
437C2×D4—2442no—
438C2×D4—2442no—
439C2×D4—2442no—
440C2×D4—2442no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—24no—
444C22×C4—42no—
445C22×C4—611no—
446C22×C4—611no—
447C22×C4—611no—
448C22×C4—614no—
449C22×C4—614no—
450C22×C4—611no—
451C22×C4—1222no—
452C22×C4—1224no—
453C22×C4—1222no—
454C22×C4—1224no—
455C22×C4—1222no—
456C22×C4—1222no—
457C22×C4—2442no—
458C22×C4C22×#692311yescharacteristic
459C22×C4C22×#692312yes—
460C22×C4C22×#692311yescharacteristic
461C22×C4C22×#692311yescharacteristic
462M16—614no—
463M16—1222no—
464M16—1224no—
465M16—1222no—
466M16—1224no—
467M16—1222no—
468M16—2448no—
469C2×C8—1222no—
470C2×C8—1222no—
471C2×C8—1224no—
472C2×C8—2448no—
473C4⋊C4—1222no—
474C4⋊C4—1222no—
475C4⋊C4—1222no—
476C4⋊C4C22⋊#692312yes—
477C4⋊C4C22⋊#692311yescharacteristic
478C4⋊C4C22⋊#692311yescharacteristic
479C22⋊C4—22no—
480C22⋊C4—22no—
481C22⋊C4—614no—
482C22⋊C4—614no—
483C22⋊C4—1222no—
484C22⋊C4—1222no—
485C42—21no—
486C42—21no—
487C42—612no—
488C42—612no—
489C42—1221no—
490C42—1221no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—42no—
495C23—42no—
496C23—614no—
497C23—1222no—
498C23—1222no—
499C23—1222no—
500C23—1222no—
501C23—1222no—
502C23—2442no—
503C23—2442no—
504C23—2442no—
505C23—2442no—
506C23C23×#692311yescharacteristic
507Q8—1224no—
508Q8—1224no—
509D4—42no—
510D4—42no—
511D4—1224no—
512D4—4884no—
513D4—4884no—
514D4—4884no—
515D4—2442no—
516D4—2448no—
517D4—2442no—
518D4—2444no—
519D4—2444no—
520D4—2448no—
521D4—2442no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—21no—
528C2×C4—44no—
529C2×C4—44no—
530C2×C4—41no—
531C2×C4—612no—
532C2×C4—611no—
533C2×C4—611no—
534C2×C4—612no—
535C2×C4—612no—
536C2×C4—612no—
537C2×C4—1224no—
538C2×C4—1224no—
539C2×C4—1224no—
540C2×C4—1224no—
541C2×C4—1221no—
542C2×C4—1221no—
543C2×C4—1221no—
544C2×C4—2444no—
545C2×C4—2444no—
546C2×C4—2441no—
547C2×C4—2441no—
548C2×C4C2×C22⋊#692311yescharacteristic
549C2×C4C2×C22⋊#692312yes—
550C2×C4C2×C22⋊#692312yes—
551C2×C4C2×C22⋊#692311yescharacteristic
552C2×C4D4×#692312yes—
553C8—1224no—
554C8—2444no—
555C8—2442no—
556C22—21no—
557C22—21no—
558C22—42no—
559C22—42no—
560C22—42no—
561C22—82no—
562C22—82no—
563C22—1224no—
564C22—1224no—
565C22—1224no—
566C22—4882no—
567C22—4882no—
568C22—4882no—
569C22—4882no—
570C22—2442no—
571C22—2442no—
572C22—2442no—
573C22C22×C22⋊#692311yescharacteristic
574C22C2×D4×#692311yescharacteristic
575C22#1684082911yescharacteristic
576C4—22no—
577C4—22no—
578C4—22no—
579C4—21no—
580C4—41no—
581C4—612no—
582C4—612no—
583C4—1222no—
584C4—1222no—
585C4—2441no—
586C4#1684074812yescomplemented
587C2—21no—
588C2—21no—
589C2—82no—
590C2—4882no—
591C2—2444no—
592C2D4×C22⋊#692311yescharacteristic
593C2C2×#1684074811yescharacteristic
594C2#2146243011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×C4×D4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840433C2
cosocleC22×Dic61C24
hypercenterC2×C4×D4#6923
hypocenterC61#22412
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4⋊C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #21462559C2semidirect
2. C2×#16840748C2semidirect
3. #21461961C2semidirect
4. #21461845C2semidirect
5. #21461685C2semidirect
6. #21461655C2semidirect
7. C4×#14519838C2semidirect
49. #14519838D4semidirect
284. C4×C61#413semidirect
335. C61#22412semidirect
586. C4#16840748semidirect

Maximal subgroups

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

subgroupindex
#214625592
C2×#168407482
#214619612
#214618452
#214616852
#214616552
C4×#145198382
C2×#168404332
#2241261