Finite Group Databasebeta

← #30620158

Subgroups — #30620158

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
1D4×#11758217C212yesmaximal, complemented
2C2×#16840749C212yesmaximal, complemented
3#21461961C212yesmaximal, complemented
4#21461844C214yesmaximal, complemented
5#21461685C211yesmaximal, characteristic, complemented
6#21461656C212yesmaximal, complemented
7C4×#14519838C211yesmaximal, characteristic, complemented
8C2×#16840432C211yesmaximal, characteristic
9C22×#11758217C2214yes—
10#16840797—22no—
11#16840793—24no—
12D4×#92420—22no—
13#16840765C2212yes—
14#16840749—28no—
15C2×#14519838C2211yescharacteristic
16C2×#14519838C2212yes—
17C2×#14519838C2211yescharacteristic
18C2×#14519837C2214yes—
19C2×#14519837C2214yes—
20#16840732C2214yes—
21C4×#11758217C2212yes—
22#16840642C2212yes—
23#16840642C2212yes—
24C22×#11758224C2212yes—
25#16840432—22no—
26#16840432—24no—
27#16840432—22no—
28C2×#14519773C411yescharacteristic
29C2×#14519773C2211yescharacteristic
30C2×#14519749C412yes—
31C2×#14519749C2212yes—
32C2×#14519748C412yes—
33C2×C4×Dic122C2211yescharacteristic
34C2×C4×D244C411yescharacteristic
35C2×D4×Dic61C411yescharacteristic
36C2×D4×Dic61C2211yescharacteristic
37C2×#127×C61C411yescharacteristic
38C2×#11758217—24no—
39C2×#11758217—28no—
40C2×#11758217—44no—
41C2×#11758217C2312yes—
42C2×#11758217C2314yes—
43C2×#11758217C2312yes—
44C22×#92420—24no—
45#14519844—22no—
46C4⋊#92420—22no—
47#14519838—24no—
48#14519838—22no—
49#14519838D414yescomplemented
50#14519837—28no—
51#14519837—44no—
52C22⋊#92420—24no—
53C22⋊#92420—24no—
54#14519832—22no—
55C4×#92420—22no—
56C2×#11758224—24no—
57C2×#11758224—24no—
58C2×#11758224—24no—
59C2×#11758224—24no—
60C2×#11758224—44no—
61C22×Dic122C2311yescharacteristic
62C22×D244C2×C411yescharacteristic
63C22×C22⋊D61C2×C412yes—
64C22×C22⋊D61C2×C412yes—
65C22×C22⋊D61C2×C412yes—
66C22×C22⋊D61C2312yes—
67C23×Dic61C2×C412yes—
68C23×Dic61C2312yes—
69C22×C4×D61C2×C412yes—
70#14519773—22no—
71#14519773—22no—
72#14519773—22no—
73#14519773—22no—
74#14519749—24no—
75#14519749—24no—
76#14519749—24no—
77#14519749—24no—
78#14519748—24no—
79#14519748—24no—
80C4×Dic122—22no—
81C4×Dic122—22no—
82C4×D244—22no—
83C4×D244—21no—
84C4×D244—21no—
85D4×Dic61—22no—
86D4×Dic61—21no—
87D4×Dic61—21no—
88D4×Dic61D412yes—
89D4×Dic61D414yes—
90D4×Dic61D412yes—
91C2×C4⋊Dic61C2×C411yescharacteristic
92C2×C4⋊Dic61C2×C411yescharacteristic
93C2×#11758196C2×C411yescharacteristic
94C2×#11758196C2311yescharacteristic
95C2×C22⋊Dic61C2×C412yes—
96C2×C22⋊Dic61C2×C412yes—
97C2×#11758198C2×C412yes—
98C2×C4×Dic61C2×C411yescharacteristic
99C2×C4×Dic61C2311yescharacteristic
100C22×D4×C61C2×C412yes—
101C22×D4×C61C2×C411yescharacteristic
102C22×D4×C61C2×C412yes—
103C22×D4×C61C2×C411yescharacteristic
104#127×C61—22no—
105#127×C61—22no—
106C2×C42×C61C2×C411yescharacteristic
107C24×C61C22×C412yes—
108C24×C61C22×C412yes—
109C23×D61C22×C412yes—
110C2×D4×C61—24no—
111C2×D4×C61—24no—
112C2×D4×C61—21no—
113C2×D4×C61—21no—
114C2×D4×C61—24no—
115C2×D4×C61—42no—
116C2×D4×C61—42no—
117C2×D4×C61—42no—
118C2×D4×C61—82no—
119C2×D4×C61C22⋊C412yes—
120C2×D4×C61C22⋊C412yes—
121C22×C4×C61C22×C411yescharacteristic
122C22×C4×C61C22×C411yescharacteristic
123C22×C4×C61C22×C411yescharacteristic
124C2×C22⋊D61—24no—
125C2×C22⋊D61—24no—
126C2×C22⋊D61—24no—
127C2×C22⋊D61—24no—
128C2×C22⋊D61—22no—
129C2×C22⋊D61—24no—
130C2×C22⋊D61—22no—
131C2×C22⋊D61—24no—
132C2×C22⋊D61—42no—
133C2×C22⋊D61—82no—
134C2×C22⋊D61—82no—
135C22×Dic61—22no—
136C22×Dic61—22no—
137C22×Dic61—24no—
138C22×Dic61—22no—
139C22×Dic61—22no—
140C22×Dic61—24no—
141C22×Dic61—42no—
142C22×Dic61C22×C412yes—
143C22×Dic61C22×C411yescharacteristic
144C22×Dic61C22×C411yescharacteristic
145C22×Dic61C22×C411yescharacteristic
146C22×Dic61C2×D414yes—
147C22×Dic61C2×D414yes—
148C22×Dic61C2411yescharacteristic
149#11758224—48no—
150#11758224—48no—
151#11758224—48no—
152#11758224—48no—
153C2×D244—21no—
154C2×D244—21no—
155C2×D244—42no—
156C2×C4×D61—24no—
157C2×C4×D61—22no—
158C2×C4×D61—22no—
159C2×C4×D61—42no—
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#11758217—48no—
170#11758217C2×D414yes—
171C2×#92420—22no—
172C2×#92420—22no—
173C2×#92420—24no—
174C2×#92420—48no—
175C42×C61—21no—
176C42×C61—21no—
177C22⋊Dic61—22no—
178C22⋊Dic61—22no—
179C22⋊Dic61C22⋊C414yes—
180C22⋊Dic61C22⋊C414yes—
181#11758198—22no—
182#11758198—22no—
183C4⋊Dic61—22no—
184C4⋊Dic61C22⋊C412yes—
185C4⋊Dic61C22⋊C411yescharacteristic
186C4⋊Dic61C22⋊C411yescharacteristic
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—22no—
197C23×C61—22no—
198C23×C61—42no—
199C23×C61—42no—
200C23×C61—42no—
201C23×C61—42no—
202C23×C61C2×C22⋊C414yes—
203C23×C61C23×C411yescharacteristic
204C22×D61—22no—
205C22×D61—22no—
206C22×D61—22no—
207C22×D61—42no—
208C22×D61—42no—
209D4×C61—24no—
210D4×C61—42no—
211D4×C61—48no—
212D4×C61—42no—
213D4×C61—42no—
214D4×C61—84no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—22no—
218C2×C4×C61—21no—
219C2×C4×C61—41no—
220C2×C4×C61C2×C22⋊C411yescharacteristic
221C2×C4×C61C2×C22⋊C411yescharacteristic
222C2×C4×C61C4×D412yes—
223C22⋊D61—48no—
224C22⋊D61—44no—
225C22⋊D61—44no—
226C22⋊D61—84no—
227C22⋊D61—84no—
228C2×Dic61—21no—
229C2×Dic61—22no—
230C2×Dic61—21no—
231C2×Dic61—22no—
232C2×Dic61—24no—
233C2×Dic61—24no—
234C2×Dic61—24no—
235C2×Dic61—24no—
236C2×Dic61—21no—
237C2×Dic61—41no—
238C2×Dic61—44no—
239C2×Dic61—44no—
240C2×Dic61—41no—
241C2×Dic61C2×C22⋊C412yes—
242C2×Dic61C2×C22⋊C412yes—
243C2×Dic61C2×C22⋊C412yes—
244C2×Dic61C4×D412yes—
245C2×Dic61C22×D411yescharacteristic
246C2×Dic61C22×D412yes—
247C2×Dic61C2×#4111yescharacteristic
248C2×Dic61H(5,𝔽2)12yes—
249D244—42no—
250D244—42no—
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—24no—
262C22×C61—24no—
263C22×C61—24no—
264C22×C61—42no—
265C22×C61—42no—
266C22×C61—42no—
267C22×C61—82no—
268C22×C61—82no—
269C22×C61—82no—
270C22×C61—82no—
271C22×C61C22×C22⋊C411yescharacteristic
272C22×C61C2×C4×D411yescharacteristic
273C22×C61#51811yescharacteristic
274C2×D61—42no—
275C2×D61—42no—
276C2×D61—42no—
277C2×D61—82no—
278C2×D61—82no—
279C4×C61—22no—
280C4×C61—21no—
281C4×C61—41no—
282C4×C61#41312yescomplemented
283Dic61—22no—
284Dic61—22no—
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—44no—
301C2×C61—82no—
302C2×C61D4×C22⋊C411yescharacteristic
303C2×C61C2×#41311yescharacteristic
304C2×C61#288811yescharacteristic
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#692311yescharacteristic
314C2×#121—612no—
315C2×#121—612no—
316C2×#121—612no—
317C2×C4×Q8—611no—
318C2×C4×D4—611no—
319C2×C4×D4—611no—
320C2×C4×D4—611no—
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×D4C2×#692312yes—
348C22×D4C2×#692311yescharacteristic
349C22×D4C2×#692312yes—
350C22×D4C2×#692311yescharacteristic
351C23×C4—612no—
352C23×C4—612no—
353C23×C4—612no—
354C2×M16—612no—
355C2×M16—614no—
356C2×M16—612no—
357C2×M16—1224no—
358C2×M16—1228no—
359C2×M16—2444no—
360C22×C8—1224no—
361#127—22no—
362#127—22no—
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—612no—
376C4×D4—614no—
377C4×D4—612no—
378C4×D4—1222no—
379C4×D4—1221no—
380C4×D4—1221no—
381C4×D4—1222no—
382C4×D4—1221no—
383C4×D4—1221no—
384C2×C4⋊C4—611no—
385C2×C4⋊C4—611no—
386C2×C4⋊C4—611no—
387C2×C4⋊C4—611no—
388C2×C22⋊C4—612no—
389C2×C22⋊C4—612no—
390C2×C22⋊C4—612no—
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—
406C24C22×#692312yes—
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—24no—
417C2×D4—24no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—24no—
421C2×D4—42no—
422C2×D4—42no—
423C2×D4—42no—
424C2×D4—82no—
425C2×D4—1224no—
426C2×D4—1222no—
427C2×D4—1224no—
428C2×D4—1224no—
429C2×D4—1222no—
430C2×D4—1224no—
431C2×D4—1224no—
432C2×D4—1224no—
433C2×D4—1221no—
434C2×D4—1221no—
435C2×D4—4882no—
436C2×D4—4882no—
437C2×D4—2442no—
438C2×D4—2442no—
439C2×D4C22⋊#692312yes—
440C2×D4C22⋊#692312yes—
441C22×C4—611no—
442C22×C4—614no—
443C22×C4—614no—
444C22×C4—611no—
445C22×C4—612no—
446C22×C4—611no—
447C22×C4—611no—
448C22×C4—1222no—
449C22×C4—1222no—
450C22×C4—1222no—
451C22×C4—1224no—
452C22×C4—1222no—
453C22×C4—1222no—
454C22×C4—1222no—
455C22×C4—1224no—
456C22×C4—1224no—
457C22×C4—2442no—
458C22×C4—2442no—
459C22×C4C22×#692311yescharacteristic
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—612no—
474C4⋊C4—611no—
475C4⋊C4—611no—
476C4⋊C4—1222no—
477C4⋊C4—1222no—
478C4⋊C4—1222no—
479C22⋊C4—614no—
480C22⋊C4—614no—
481C22⋊C4—1222no—
482C22⋊C4—1222no—
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—22no—
495C23—22no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—1222no—
501C23—1222no—
502C23—1222no—
503C23—2442no—
504C23—2442no—
505C23C2×C22⋊#692314yes—
506C23C23×#692311yescharacteristic
507Q8—1224no—
508Q8—1224no—
509D4—24no—
510D4—42no—
511D4—48no—
512D4—42no—
513D4—42no—
514D4—84no—
515D4—4884no—
516D4—4884no—
517D4—2442no—
518D4—2444no—
519D4—2444no—
520D4—2448no—
521D4—2442no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—612no—
528C2×C4—611no—
529C2×C4—611no—
530C2×C4—612no—
531C2×C4—612no—
532C2×C4—612no—
533C2×C4—612no—
534C2×C4—612no—
535C2×C4—1224no—
536C2×C4—1224no—
537C2×C4—1224no—
538C2×C4—1224no—
539C2×C4—1221no—
540C2×C4—1222no—
541C2×C4—1222no—
542C2×C4—1221no—
543C2×C4—1221no—
544C2×C4—2444no—
545C2×C4—2444no—
546C2×C4—2441no—
547C2×C4—2444no—
548C2×C4—2444no—
549C2×C4—2441no—
550C2×C4C2×C22⋊#692311yescharacteristic
551C2×C4C2×C22⋊#692311yescharacteristic
552C2×C4D4×#692312yes—
553C8—1224no—
554C8—2444no—
555C8—2442no—
556C22—21no—
557C22—21no—
558C22—24no—
559C22—24no—
560C22—24no—
561C22—42no—
562C22—42no—
563C22—42no—
564C22—82no—
565C22—82no—
566C22—82no—
567C22—82no—
568C22—4882no—
569C22—4882no—
570C22—2442no—
571C22—2442no—
572C22—2442no—
573C22C22×C22⋊#692311yescharacteristic
574C22C2×D4×#692311yescharacteristic
575C22#1684082911yescharacteristic
576C4—22no—
577C4—21no—
578C4—41no—
579C4—612no—
580C4—612no—
581C4—1222no—
582C4—1222no—
583C4—1222no—
584C4—1222no—
585C4—2441no—
586C4#1684074912yescomplemented
587C2—21no—
588C2—21no—
589C2—44no—
590C2—82no—
591C2—4882no—
592C2D4×C22⋊#692311yescharacteristic
593C2C2×#1684074911yescharacteristic
594C2#2146242911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#127×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840432C2
cosocleC22×Dic61C24
hypercenterC2×#127#6923
hypocenterC61#22412
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×D4 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. D4×#11758217C2semidirect
2. C2×#16840749C2semidirect
3. #21461961C2semidirect
4. #21461844C2semidirect
5. #21461685C2semidirect
6. #21461656C2semidirect
7. C4×#14519838C2semidirect
49. #14519838D4semidirect
282. C4×C61#413semidirect
335. C61#22412semidirect
586. C4#16840749semidirect

Maximal subgroups

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

subgroupindex
D4×#117582172
C2×#168407492
#214619612
#214618442
#214616852
#214616562
C4×#145198382
C2×#168404322
#2241261