Finite Group Databasebeta

← #30620153

Subgroups — #30620153

Order 15616.

1410 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462559C212yesmaximal, complemented
2C2×#16840748C212yesmaximal, complemented
3#21461962C212yesmaximal, complemented
4#21461847C214yesmaximal, complemented
5#21461683C211yesmaximal, characteristic, complemented
6#21461655C212yesmaximal, complemented
7C4×#14519837C211yesmaximal, characteristic, complemented
8C2×#16840413C211yesmaximal, characteristic
9C2×D61⋊M16C2214yes—
10#16840796—22no—
11#16840792—24no—
12#16840790—22no—
13#16840765C2212yes—
14#16840748—28no—
15C2×#14519838C2214yes—
16C2×#14519838C2214yes—
17C2×#14519837C2211yescharacteristic
18C2×#14519837C2212yes—
19C2×#14519837C2211yescharacteristic
20#16840734C2214yes—
21C4×#11758217C2212yes—
22#16840642C2212yes—
23#16840642C2212yes—
24C22×#11758222C2212yes—
25#16840413—22no—
26#16840413—24no—
27#16840413—22no—
28C2×#14519776C2211yescharacteristic
29C2×#14519762C412yes—
30C2×#14519760C412yes—
31C2×#14519755C2212yes—
32C2×#14519752C411yescharacteristic
33C2×#14519751C411yescharacteristic
34C2×#14519739C2211yescharacteristic
35C2×C4×C22⋊D61C2211yescharacteristic
36C2×C4⋊C4×D61C411yescharacteristic
37C22×C4⋊C4×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—28no—
48#14519838—44no—
49#14519837—24no—
50#14519837—22no—
51#14519837D414yescomplemented
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×Dic122C2312yes—
62C22×D244C2×C412yes—
63C22×D244C2×C411yescharacteristic
64C22×C22⋊D61C2×C412yes—
65C22×C22⋊D61C2311yescharacteristic
66C22×C4×D61C2×C412yes—
67C22×C4×D61C2×C411yescharacteristic
68C22×C4×D61C2312yes—
69#14519776—22no—
70#14519776—22no—
71#14519762—24no—
72#14519762—24no—
73#14519760—24no—
74#14519760—24no—
75#14519755—24no—
76#14519755—24no—
77#14519752—22no—
78#14519752—22no—
79#14519751—22no—
80#14519751—22no—
81#14519739D412yes—
82#14519739D414yes—
83#14519739D412yes—
84C4×C22⋊D61—22no—
85C4×C22⋊D61—22no—
86C2×C4⋊Dic61C2×C411yescharacteristic
87C2×#11758196C2×C412yes—
88C2×#11758196C2×C412yes—
89C2×#11758196C2311yescharacteristic
90C4⋊C4×D61—22no—
91C4⋊C4×D61—21no—
92C4⋊C4×D61—21no—
93C2×C22⋊Dic61C2×C411yescharacteristic
94C2×#11758198C2×C411yescharacteristic
95C2×#11758198C2×C412yes—
96C2×#11758198C2×C412yes—
97C2×#11758198C2×C412yes—
98C2×C4×Dic61C2311yescharacteristic
99C23×C4×C61C2×C412yes—
100C23×C4×C61C2×C411yescharacteristic
101C2×C4⋊C4×C61—22no—
102C2×C4⋊C4×C61—21no—
103C2×C4⋊C4×C61—21no—
104C2×C4⋊C4×C61C2×C411yescharacteristic
105C2×C4⋊C4×C61C2×C412yes—
106C2×C4⋊C4×C61C2×C411yescharacteristic
107C24×C61C22×C411yescharacteristic
108C23×D61C22×C412yes—
109C23×D61C22×C411yescharacteristic
110C22×C4×C61—24no—
111C22×C4×C61—22no—
112C22×C4×C61—22no—
113C22×C4×C61—21no—
114C22×C4×C61—21no—
115C22×C4×C61—42no—
116C22×C4×C61—42no—
117C22×C4×C61C22×C412yes—
118C22×C4×C61C22×C412yes—
119C22×C4×C61C22×C411yescharacteristic
120C22×C4×C61C22×C411yescharacteristic
121C2×C22⋊D61—24no—
122C2×C22⋊D61—24no—
123C2×C22⋊D61—22no—
124C2×C22⋊D61—22no—
125C2×C22⋊D61—42no—
126C2×C22⋊D61C2×D412yes—
127C2×C22⋊D61#4112yes—
128C22×Dic61C22×C412yes—
129C22×Dic61C22×C411yescharacteristic
130C22×Dic61C22×C411yescharacteristic
131C22×Dic61C2411yescharacteristic
132#11758222—48no—
133#11758222—48no—
134#11758222—48no—
135#11758222—48no—
136C2×D244—24no—
137C2×D244—24no—
138C2×D244—42no—
139C2×D244—42no—
140C2×D244C22⋊C412yes—
141C2×D244C22⋊C412yes—
142C2×C4×D61—22no—
143C2×C4×D61—22no—
144C2×C4×D61—24no—
145C2×C4×D61—24no—
146C2×C4×D61—22no—
147C2×C4×D61—22no—
148C2×C4×D61—21no—
149C2×C4×D61—21no—
150C2×C4×D61—42no—
151C2×C4×D61—42no—
152C2×C4×D61C2×D414yes—
153C2×C4×D61C2×D414yes—
154C2×Dic122—22no—
155C2×Dic122—24no—
156C2×Dic122—22no—
157C2×Dic122—24no—
158#11758217—22no—
159#11758217—24no—
160#11758217—22no—
161#11758217—22no—
162#11758217—24no—
163#11758217C2×D414yes—
164C2×#92420—22no—
165C2×#92420—22no—
166C2×#92420—24no—
167#11758213—48no—
168D61⋊C8—48no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—22no—
172C4⋊C4×C61—22no—
173C4⋊C4×C61C22⋊C412yes—
174C4⋊C4×C61C22⋊C411yescharacteristic
175C4⋊C4×C61C22⋊C411yescharacteristic
176C22⋊Dic61—22no—
177#11758198—24no—
178#11758198—24no—
179#11758198—22no—
180#11758198C22⋊C414yes—
181#11758198C22⋊C414yes—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184#11758196—22no—
185#11758196—22no—
186#11758196—24no—
187#11758196—22no—
188C4×Dic61C2×D412yes—
189C4×Dic61C2×D412yes—
190C23×C61—21no—
191C23×C61—21no—
192C23×C61—41no—
193C23×C61—41no—
194C23×C61C4×D412yes—
195C23×C61C23×C411yescharacteristic
196C22×D61—21no—
197C22×D61—21no—
198C22×D61—22no—
199C22×D61—22no—
200C22×D61—42no—
201C22×D61—42no—
202C22×D61—41no—
203C22×D61—41no—
204C22×D61C2×C22⋊C414yes—
205C22×D61C4×D412yes—
206C2×C4×C61—22no—
207C2×C4×C61—22no—
208C2×C4×C61—22no—
209C2×C4×C61—21no—
210C2×C4×C61—22no—
211C2×C4×C61—22no—
212C2×C4×C61—22no—
213C2×C4×C61—44no—
214C2×C4×C61—44no—
215C2×C4×C61—42no—
216C2×C4×C61—42no—
217C2×C4×C61—41no—
218C2×C4×C61C2×C22⋊C411yescharacteristic
219C2×C4×C61C2×C22⋊C412yes—
220C2×C4×C61C2×C22⋊C412yes—
221C2×C4×C61C2×C22⋊C411yescharacteristic
222C22⋊D61—24no—
223C22⋊D61—24no—
224C22⋊D61—48no—
225C2×Dic61—21no—
226C2×Dic61—22no—
227C2×Dic61—22no—
228C2×Dic61—22no—
229C2×Dic61—41no—
230C2×Dic61—41no—
231C2×Dic61C2×C22⋊C412yes—
232C2×Dic61C22×D411yescharacteristic
233C2×Dic61C22×D412yes—
234C2×Dic61C2×#4111yescharacteristic
235C2×Dic61H(5,𝔽2)12yes—
236D244—24no—
237D244—42no—
238D244—48no—
239C4×D61—24no—
240C4×D61—24no—
241C4×D61—24no—
242C4×D61—24no—
243C4×D61—44no—
244C4×D61—44no—
245C4×D61—42no—
246C4×D61—42no—
247Dic122—44no—
248Dic122—44no—
249#92420—24no—
250#92420—44no—
251#92420—42no—
252#22411—611nomaximal, Sylow
253C22×C61—21no—
254C22×C61—21no—
255C22×C61—22no—
256C22×C61—42no—
257C22×C61—42no—
258C22×C61—41no—
259C22×C61—41no—
260C22×C61C22×C22⋊C411yescharacteristic
261C22×C61C2×C4×D411yescharacteristic
262C22×C61#51811yescharacteristic
263C2×D61—24no—
264C2×D61—22no—
265C2×D61—24no—
266C2×D61—24no—
267C2×D61—42no—
268C2×D61—41no—
269C2×D61—41no—
270C2×D61—42no—
271C2×D61—82no—
272C2×D61—82no—
273C4×C61—22no—
274C4×C61—22no—
275C4×C61—21no—
276C4×C61—42no—
277C4×C61—41no—
278C4×C61#41312yescomplemented
279Dic61—22no—
280Dic61—42no—
281Dic61—41no—
282Dic61D4212yes—
283Dic61#54612yes—
284C2×#547—611no—
285D4×M16—612no—
286C2×#413—612no—
287#1966—612no—
288#1901—614no—
289#1800—611no—
290#1785—612no—
291C4×#100—611no—
292C2×C61—21no—
293C2×C61—21no—
294C2×C61—42no—
295C2×C61D4×C22⋊C411yescharacteristic
296C2×C61C2×#41311yescharacteristic
297C2×C61#288911yescharacteristic
298D61—44no—
299D61—42no—
300C22×#41—612no—
301C22×M16—614no—
302#547—1222no—
303#547—1224no—
304#547—1222no—
305C2×C4⋊Q8—611no—
306C2×#123—612no—
307C2×#123—612no—
308C2×C22⋊Q8—612no—
309C2×#121—611no—
310C2×#121—611no—
311C2×C4×D4—611no—
312C2×C4×D4—611no—
313C22×C4⋊C4—611no—
314C22×C4⋊C4#692311yescharacteristic
315#436—1222no—
316#435—1224no—
317C8×D4—1222no—
318#423—612no—
319#413—1228no—
320C2×#101—614no—
321C2×#101—614no—
322C2×#100—611no—
323C2×#100—612no—
324C2×#100—611no—
325#407—614no—
326C4×M16—612no—
327#343—612no—
328#343—612no—
329C61#2241111yescharacteristic, complemented, Sylow
330C2×#41—1224no—
331C2×#41—1224no—
332C2×#41—1224no—
333C2×#41—1224no—
334C2×#41—2444no—
335C22×Q8—612no—
336C22×D4—611no—
337C22×D4—612no—
338C22×D4—611no—
339C22×D4—612no—
340C23×C4—612no—
341C23×C4—612no—
342C23×C4—611no—
343C23×C4C2×#692312yes—
344C23×C4C2×#692311yescharacteristic
345C2×M16—612no—
346C2×M16—614no—
347C2×M16—612no—
348C2×M16—1224no—
349C2×M16—1228no—
350C2×M16—2444no—
351C22×C8—1224no—
352C4⋊Q8—1222no—
353C4⋊Q8—1222no—
354#123—1224no—
355#123—1224no—
356#123—1224no—
357#123—1224no—
358C22⋊Q8—1224no—
359C22⋊Q8—1224no—
360#121—1222no—
361#121—1222no—
362#121—1222no—
363#121—1222no—
364C4×D4—612no—
365C4×D4—614no—
366C4×D4—612no—
367C4×D4—1222no—
368C4×D4—1222no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—611no—
373C2×C4⋊C4—612no—
374C2×C4⋊C4—611no—
375C2×C4⋊C4—612no—
376C2×C4⋊C4—1222no—
377C2×C4⋊C4—1221no—
378C2×C4⋊C4—1221no—
379C2×C4⋊C4C2×#692311yescharacteristic
380C2×C4⋊C4C2×#692312yes—
381C2×C4⋊C4C2×#692311yescharacteristic
382C2×C22⋊C4—612no—
383C2×C22⋊C4—611no—
384C2×C22⋊C4—611no—
385C2×C22⋊C4—612no—
386C2×C22⋊C4—612no—
387C2×C42—611no—
388C4⋊C8—1222no—
389C4⋊C8—1222no—
390#101—1228no—
391#101—2444no—
392#100—614no—
393#100—1222no—
394#100—1224no—
395C22⋊C8—1224no—
396C22⋊C8—1224no—
397#97—1222no—
398C4×C8—1222no—
399C24—612no—
400C24—611no—
401C24C22×#692311yescharacteristic
402#41—2448no—
403#41—2448no—
404#41—2448no—
405#41—2448no—
406C2×Q8—1222no—
407C2×Q8—1224no—
408C2×Q8—1224no—
409C2×Q8—1222no—
410C2×D4—612no—
411C2×D4—612no—
412C2×D4—612no—
413C2×D4—612no—
414C2×D4—1224no—
415C2×D4—1224no—
416C2×D4—1222no—
417C2×D4—1222no—
418C2×D4—1224no—
419C2×D4—1224no—
420C2×D4—2442no—
421C2×D4—2442no—
422C2×D4—2442no—
423C22×C4—24no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4—611no—
431C22×C4—611no—
432C22×C4—614no—
433C22×C4—614no—
434C22×C4—612no—
435C22×C4—611no—
436C22×C4—1222no—
437C22×C4—1224no—
438C22×C4—1222no—
439C22×C4—1224no—
440C22×C4—1221no—
441C22×C4—1221no—
442C22×C4—1222no—
443C22×C4—1222no—
444C22×C4—2442no—
445C22×C4—2442no—
446C22×C4C22×#692312yes—
447C22×C4C22×#692311yescharacteristic
448C22×C4C22×#692312yes—
449C22×C4C22×#692311yescharacteristic
450M16—614no—
451M16—1222no—
452M16—1224no—
453M16—1222no—
454M16—1222no—
455M16—1224no—
456M16—2448no—
457C2×C8—1222no—
458C2×C8—1222no—
459C2×C8—1224no—
460C2×C8—2448no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—1222no—
466C4⋊C4—1224no—
467C4⋊C4—1222no—
468C4⋊C4—1222no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4C22⋊#692312yes—
472C4⋊C4C22⋊#692311yescharacteristic
473C4⋊C4C22⋊#692311yescharacteristic
474C22⋊C4—614no—
475C22⋊C4—614no—
476C22⋊C4—1222no—
477C22⋊C4—1224no—
478C22⋊C4—1224no—
479C22⋊C4—1222no—
480C42—612no—
481C42—612no—
482C23—21no—
483C23—21no—
484C23—41no—
485C23—41no—
486C23—614no—
487C23—612no—
488C23—1222no—
489C23—1222no—
490C23—1221no—
491C23—1221no—
492C23—2442no—
493C23—2442no—
494C23—2441no—
495C23—2441no—
496C23D4×#692312yes—
497C23C23×#692311yescharacteristic
498Q8—2444no—
499Q8—2444no—
500D4—1224no—
501D4—1224no—
502D4—1224no—
503D4—2442no—
504D4—2448no—
505D4—2448no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—44no—
514C2×C4—44no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—41no—
518C2×C4—612no—
519C2×C4—611no—
520C2×C4—611no—
521C2×C4—612no—
522C2×C4—612no—
523C2×C4—1224no—
524C2×C4—1224no—
525C2×C4—1224no—
526C2×C4—1224no—
527C2×C4—1221no—
528C2×C4—1222no—
529C2×C4—1222no—
530C2×C4—1222no—
531C2×C4—2444no—
532C2×C4—2444no—
533C2×C4—2442no—
534C2×C4—2441no—
535C2×C4—2442no—
536C2×C4—2441no—
537C2×C4C2×C22⋊#692311yescharacteristic
538C2×C4C2×C22⋊#692312yes—
539C2×C4C2×C22⋊#692312yes—
540C2×C4C2×C22⋊#692311yescharacteristic
541C8—1224no—
542C8—2444no—
543C8—2442no—
544C22—21no—
545C22—21no—
546C22—22no—
547C22—42no—
548C22—42no—
549C22—41no—
550C22—41no—
551C22—1224no—
552C22—1222no—
553C22—1224no—
554C22—1224no—
555C22—4882no—
556C22—4882no—
557C22—2442no—
558C22—2442no—
559C22—2441no—
560C22—2441no—
561C22C22×C22⋊#692311yescharacteristic
562C22C2×D4×#692311yescharacteristic
563C22#1684082911yescharacteristic
564C4—22no—
565C4—22no—
566C4—21no—
567C4—42no—
568C4—41no—
569C4—612no—
570C4—612no—
571C4—1222no—
572C4—2442no—
573C4—2441no—
574C4#1684074812yescomplemented
575C2—21no—
576C2—21no—
577C2—42no—
578C2—2444no—
579C2—2442no—
580C2D4×C22⋊#692311yescharacteristic
581C2C2×#1684074811yescharacteristic
582C2#2146243211yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC22×C4⋊C4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840413C2
cosocleC22×Dic61C24
hypercenterC22×C4⋊C4#6923
hypocenterC61#22411
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4⋊C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #21462559C2semidirect
2. C2×#16840748C2semidirect
3. #21461962C2semidirect
4. #21461847C2semidirect
5. #21461683C2semidirect
6. #21461655C2semidirect
7. C4×#14519837C2semidirect
51. #14519837D4semidirect
278. C4×C61#413semidirect
329. C61#22411semidirect
574. 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
#214619622
#214618472
#214616832
#214616552
C4×#145198372
C2×#168404132
#2241161