Finite Group Databasebeta

← #30615190

Subgroups — #30615190

Order 15616.

1694 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462495C212yesmaximal, complemented
2#21461718C212yesmaximal, complemented
3#21461684C214yesmaximal, complemented
4#21461651C212yesmaximal
5#21461569C214yesmaximal, complemented
6C22×#14519737C211yesmaximal, characteristic
7#16840783—22no—
8#16840782—22no—
9#16840779—22no—
10#16840778—22no—
11#16840765C2214yescomplemented
12C2×#14519837C2218yes—
13#16840732C2214yes—
14C4×#11758217C2214yescomplemented
15#16840642C2218yescomplemented
16C23×C22⋊D61C2211yescharacteristic
17C24×Dic61C411yescharacteristic
18C23×C4×D61C411yescharacteristic
19C2×#14519737—22no—
20C2×#14519737—22no—
21C2×#14519737—22no—
22C2×#14519737—22no—
23C2×#14519737C412yes—
24C2×#14519737C412yes—
25C2×#14519737C2212yes—
26C2×#14519737C2212yes—
27C22×#11758196C2211yescharacteristic
28C22×#11758198C411yescharacteristic
29C22×C4×Dic61C2211yescharacteristic
30C22×C22⋊C4×C61C411yescharacteristic
31C2×#11758217C2318yes—
32#14519844—24no—
33C4⋊#92420—24no—
34#14519837—216no—
35C22⋊#92420—24no—
36C22⋊#92420—24no—
37#14519832—24no—
38C4×#92420—24no—
39C24×D61C2×C411yescharacteristic
40C22×C22⋊D61—28no—
41C22×C22⋊D61—22no—
42C22×C22⋊D61—22no—
43C22×C22⋊D61C2×C412yes—
44C22×C22⋊D61C2312yes—
45C23×Dic61—21no—
46C23×Dic61—21no—
47C23×Dic61—21no—
48C23×Dic61—21no—
49C23×Dic61—44no—
50C23×Dic61C2×C411yescharacteristic
51C23×Dic61C2×C411yescharacteristic
52C23×Dic61C2×C412yes—
53C23×Dic61C2×C412yes—
54C23×Dic61C2311yescharacteristic
55C22×C4×D61—21no—
56C22×C4×D61—21no—
57C22×C4×D61—21no—
58C22×C4×D61—21no—
59C22×C4×D61—44no—
60C22×C4×D61C2×C412yes—
61C22×C4×D61C2×C412yes—
62#14519737—24no—
63#14519737—24no—
64#14519737—24no—
65#14519737—24no—
66#14519737—24no—
67#14519737—24no—
68#14519737—24no—
69#14519737—24no—
70C2×#11758196—22no—
71C2×#11758196—22no—
72C2×#11758196C2×C412yes—
73C2×#11758196C2312yes—
74C2×#11758198—22no—
75C2×#11758198—22no—
76C2×#11758198C2×C412yes—
77C2×#11758198C2×C412yes—
78C2×C4×Dic61C2×C411yescharacteristic
79C2×C4×Dic61C2×C411yescharacteristic
80C2×C4×Dic61D412yes—
81C2×C4×Dic61D412yes—
82C2×C4×Dic61D412yes—
83C2×C4×Dic61D412yes—
84C2×C4×Dic61C2311yescharacteristic
85C2×C4×Dic61C2311yescharacteristic
86C25×C61C2×C411yescharacteristic
87C23×C4×C61C2×C411yescharacteristic
88C23×C4×C61C2×C411yescharacteristic
89C2×C22⋊C4×C61—22no—
90C2×C22⋊C4×C61—22no—
91C2×C22⋊C4×C61C2×C412yes—
92C2×C22⋊C4×C61C2×C412yes—
93C24×C61—21no—
94C24×C61—21no—
95C24×C61—24no—
96C24×C61—42no—
97C24×C61—42no—
98C24×C61C22×C411yescharacteristic
99C24×C61C22×C412yes—
100C23×D61—21no—
101C23×D61—21no—
102C23×D61—24no—
103C23×D61—42no—
104C23×D61—42no—
105C23×D61C22×C412yes—
106C22×C4×C61—21no—
107C22×C4×C61—21no—
108C22×C4×C61—42no—
109C22×C4×C61—42no—
110C22×C4×C61C22⋊C412yes—
111C22×C4×C61C22⋊C412yes—
112C22×C4×C61C22×C412yes—
113C22×C4×C61C22×C411yescharacteristic
114C22×C4×C61C22×C411yescharacteristic
115C2×C22⋊D61—216no—
116C2×C22⋊D61—216no—
117C2×C22⋊D61—24no—
118C2×C22⋊D61—24no—
119C2×C22⋊D61—24no—
120C2×C22⋊D61—24no—
121C2×C22⋊D61—24no—
122C2×C22⋊D61#4118yes—
123C22×Dic61—24no—
124C22×Dic61—24no—
125C22×Dic61—21no—
126C22×Dic61—21no—
127C22×Dic61—22no—
128C22×Dic61—22no—
129C22×Dic61—22no—
130C22×Dic61—22no—
131C22×Dic61—44no—
132C22×Dic61—44no—
133C22×Dic61—44no—
134C22×Dic61—44no—
135C22×Dic61—44no—
136C22×Dic61—44no—
137C22×Dic61—42no—
138C22×Dic61C22⋊C411yescharacteristic
139C22×Dic61C22⋊C411yescharacteristic
140C22×Dic61C22⋊C411yescharacteristic
141C22×Dic61C22⋊C411yescharacteristic
142C22×Dic61C22×C411yescharacteristic
143C22×Dic61C22×C411yescharacteristic
144C22×Dic61C22×C411yescharacteristic
145C22×Dic61C22×C412yes—
146C22×Dic61C2×D412yes—
147C22×Dic61C2×D412yes—
148C22×Dic61C2411yescharacteristic
149C2×C4×D61—22no—
150C2×C4×D61—22no—
151C2×C4×D61—22no—
152C2×C4×D61—22no—
153C2×C4×D61—44no—
154C2×C4×D61—44no—
155C2×C4×D61—44no—
156C2×C4×D61—44no—
157C2×C4×D61—44no—
158C2×C4×D61—44no—
159#11758217—216no—
160C2×#92420—28no—
161C22⋊C4×C61—24no—
162C22⋊C4×C61—24no—
163#11758198—24no—
164#11758198—24no—
165#11758196—24no—
166#11758196—24no—
167C4×Dic61C22⋊C412yes—
168C4×Dic61C22⋊C412yes—
169C4×Dic61C22⋊C412yes—
170C4×Dic61C22⋊C412yes—
171C4×Dic61C2×D412yes—
172C4×Dic61C2×D412yes—
173C4×Dic61C2×D412yes—
174C4×Dic61C2×D412yes—
175C23×C61—22no—
176C23×C61—22no—
177C23×C61—22no—
178C23×C61—24no—
179C23×C61—24no—
180C23×C61—22no—
181C23×C61—22no—
182C23×C61—42no—
183C23×C61—416no—
184C23×C61—42no—
185C23×C61—42no—
186C23×C61—42no—
187C23×C61—42no—
188C23×C61—42no—
189C23×C61C2×C22⋊C411yescharacteristic
190C23×C61C2×C22⋊C411yescharacteristic
191C23×C61#11714yes—
192C23×C61C23×C411yescharacteristic
193C22×D61—24no—
194C22×D61—24no—
195C22×D61—22no—
196C22×D61—22no—
197C22×D61—42no—
198C22×D61—416no—
199C22×D61—42no—
200C22×D61—42no—
201C22×D61—42no—
202C22×D61—42no—
203C22×D61—42no—
204C22×D61#11714yes—
205C2×C4×C61—24no—
206C2×C4×C61—22no—
207C2×C4×C61—42no—
208C2×C4×C61—41no—
209C2×C4×C61—41no—
210C2×C4×C61—42no—
211C2×C4×C61—42no—
212C2×C4×C61—42no—
213C2×C4×C61C2×C22⋊C412yes—
214C2×C4×C61C2×C22⋊C412yes—
215C22⋊D61—216no—
216C22⋊D61—216no—
217C2×Dic61—22no—
218C2×Dic61—22no—
219C2×Dic61—24no—
220C2×Dic61—24no—
221C2×Dic61—22no—
222C2×Dic61—22no—
223C2×Dic61—22no—
224C2×Dic61—22no—
225C2×Dic61—22no—
226C2×Dic61—44no—
227C2×Dic61—44no—
228C2×Dic61—42no—
229C2×Dic61—42no—
230C2×Dic61—44no—
231C2×Dic61—44no—
232C2×Dic61—42no—
233C2×Dic61#10014yescomplemented
234C2×Dic61C2×C22⋊C412yes—
235C2×Dic61C2×C22⋊C411yescharacteristic
236C2×Dic61C2×C22⋊C411yescharacteristic
237C2×Dic61C2×C22⋊C411yescharacteristic
238C2×Dic61C2×C22⋊C411yescharacteristic
239C2×Dic61C22×D412yes—
240C2×Dic61C2×#4114yes—
241C4×D61—44no—
242C4×D61—44no—
243C4×D61—44no—
244C4×D61—44no—
245#92420—48no—
246#20726—611nomaximal, Sylow
247C22×C61—28no—
248C22×C61—21no—
249C22×C61—21no—
250C22×C61—21no—
251C22×C61—21no—
252C22×C61—21no—
253C22×C61—21no—
254C22×C61—24no—
255C22×C61—44no—
256C22×C61—44no—
257C22×C61—48no—
258C22×C61—48no—
259C22×C61—42no—
260C22×C61—42no—
261C22×C61C2×#10012yes—
262C22×C61#41312yes—
263C22×C61C22×C22⋊C411yescharacteristic
264C22×C61C2×#11712yes—
265C2×D61—24no—
266C2×D61—44no—
267C2×D61—48no—
268C2×D61—48no—
269C2×D61—42no—
270C2×D61—42no—
271C2×D61—44no—
272C4×C61—22no—
273C4×C61—22no—
274C4×C61—42no—
275Dic61—21no—
276Dic61—21no—
277Dic61—22no—
278Dic61—42no—
279Dic61C2×#10012yes—
280Dic61C2×#10012yes—
281Dic61#52514yes—
282C22×C4×D4—611no—
283#2920—612no—
284#1821—612no—
285#1800—614no—
286#1783—612no—
287C4×#100—614no—
288C2×C61—22no—
289C2×C61—22no—
290C2×C61—22no—
291C2×C61—44no—
292C2×C61#228011yescharacteristic
293C2×C61C22×#10011yescharacteristic
294C2×C61C2×#41311yescharacteristic
295D61—44no—
296C23×D4—611no—
297C24×C4—611no—
298C24×C4—611no—
299C2×C4×D4—612no—
300C2×C4×D4—612no—
301C2×C4×D4—612no—
302C2×C4×D4—612no—
303C2×C4×D4—1222no—
304C2×C4×D4—1222no—
305C2×C4×D4—1222no—
306C2×C4×D4—1222no—
307C22×C4⋊C4—611no—
308C22×C22⋊C4—611no—
309C22×C22⋊C4#692311yescharacteristic
310C22×C42—611no—
311#432—1222no—
312#432—1222no—
313#431—1222no—
314#431—1222no—
315#423—614no—
316C2×#100—618no—
317#407—614no—
318C4×M16—614no—
319#343—618no—
320C61#2072611yescharacteristic, complemented, Sylow
321C25—611no—
322C25C2×#692311yescharacteristic
323C22×D4—612no—
324C22×D4—612no—
325C22×D4—1222no—
326C22×D4—1222no—
327C22×D4—1228no—
328C23×C4—611no—
329C23×C4—611no—
330C23×C4—611no—
331C23×C4—612no—
332C23×C4—612no—
333C23×C4—612no—
334C23×C4—612no—
335C23×C4—1221no—
336C23×C4—1221no—
337C23×C4—1221no—
338C23×C4—1221no—
339C23×C4—1221no—
340C23×C4—1221no—
341C23×C4—1221no—
342C23×C4—1221no—
343C23×C4—2444no—
344C23×C4—2444no—
345C23×C4C2×#692311yescharacteristic
346C23×C4C2×#692311yescharacteristic
347C2×M16—618no—
348C4×D4—1224no—
349C4×D4—1224no—
350C4×D4—1224no—
351C4×D4—1224no—
352C4×D4—1224no—
353C4×D4—1224no—
354C4×D4—1224no—
355C4×D4—1224no—
356C2×C4⋊C4—612no—
357C2×C4⋊C4—612no—
358C2×C4⋊C4—1222no—
359C2×C4⋊C4—1222no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—612no—
363C2×C22⋊C4—612no—
364C2×C22⋊C4—1222no—
365C2×C22⋊C4—1222no—
366C2×C22⋊C4C2×#692312yes—
367C2×C22⋊C4C2×#692312yes—
368C2×C42—612no—
369C2×C42—612no—
370C2×C42—612no—
371C2×C42—612no—
372C2×C42—611no—
373C2×C42—611no—
374C2×C42—611no—
375C2×C42—611no—
376C4⋊C8—1224no—
377C4⋊C8—1224no—
378#100—12216no—
379C22⋊C8—1224no—
380C22⋊C8—1224no—
381#97—1224no—
382C4×C8—1224no—
383C24—21no—
384C24—21no—
385C24—24no—
386C24—42no—
387C24—42no—
388C24—612no—
389C24—1224no—
390C24—1221no—
391C24—1221no—
392C24—2442no—
393C24—2442no—
394C24C22×#692311yescharacteristic
395C24C22×#692312yes—
396C2×D4—618no—
397C2×D4—1224no—
398C2×D4—1224no—
399C2×D4—1224no—
400C2×D4—1224no—
401C2×D4—12216no—
402C2×D4—12216no—
403C2×D4—1224no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—42no—
407C22×C4—42no—
408C22×C4—611no—
409C22×C4—611no—
410C22×C4—612no—
411C22×C4—612no—
412C22×C4—611no—
413C22×C4—611no—
414C22×C4—611no—
415C22×C4—611no—
416C22×C4—611no—
417C22×C4—611no—
418C22×C4—612no—
419C22×C4—1222no—
420C22×C4—1222no—
421C22×C4—1222no—
422C22×C4—1222no—
423C22×C4—1224no—
424C22×C4—1224no—
425C22×C4—1222no—
426C22×C4—1222no—
427C22×C4—1222no—
428C22×C4—1222no—
429C22×C4—1221no—
430C22×C4—1221no—
431C22×C4—2444no—
432C22×C4—2444no—
433C22×C4—2444no—
434C22×C4—2444no—
435C22×C4—2444no—
436C22×C4—2444no—
437C22×C4—2444no—
438C22×C4—2444no—
439C22×C4—2444no—
440C22×C4—2444no—
441C22×C4—2444no—
442C22×C4—2444no—
443C22×C4—2442no—
444C22×C4C22⋊#692312yes—
445C22×C4C22⋊#692312yes—
446C22×C4C22×#692312yes—
447C22×C4C22×#692311yescharacteristic
448C22×C4C22×#692311yescharacteristic
449M16—12216no—
450C2×C8—1228no—
451C4⋊C4—1224no—
452C4⋊C4—1224no—
453C22⋊C4—24no—
454C22⋊C4—24no—
455C22⋊C4—1224no—
456C22⋊C4—1224no—
457C42—612no—
458C42—612no—
459C42—612no—
460C42—612no—
461C42—612no—
462C42—612no—
463C42—612no—
464C42—612no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—24no—
469C23—24no—
470C23—22no—
471C23—22no—
472C23—42no—
473C23—42no—
474C23—42no—
475C23—416no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23—614no—
480C23—1224no—
481C23—1224no—
482C23—1222no—
483C23—1222no—
484C23—2442no—
485C23—2442no—
486C23—2442no—
487C23—24416no—
488C23—2442no—
489C23—2442no—
490C23—2442no—
491C23C2×C22⋊#692311yescharacteristic
492C23C2×C22⋊#692311yescharacteristic
493C23#1451985614yes—
494C23C23×#692311yescharacteristic
495D4—12216no—
496D4—12216no—
497C2×C4—24no—
498C2×C4—22no—
499C2×C4—42no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—614no—
506C2×C4—611no—
507C2×C4—611no—
508C2×C4—612no—
509C2×C4—614no—
510C2×C4—612no—
511C2×C4—611no—
512C2×C4—611no—
513C2×C4—1222no—
514C2×C4—1222no—
515C2×C4—1222no—
516C2×C4—1222no—
517C2×C4—1224no—
518C2×C4—1224no—
519C2×C4—1222no—
520C2×C4—1222no—
521C2×C4—1222no—
522C2×C4—2444no—
523C2×C4—2444no—
524C2×C4—2444no—
525C2×C4—2444no—
526C2×C4—2444no—
527C2×C4—2444no—
528C2×C4—2444no—
529C2×C4—2444no—
530C2×C4—2442no—
531C2×C4—2442no—
532C2×C4—2442no—
533C2×C4C2×C22⋊#692312yes—
534C2×C4C2×C22⋊#692312yes—
535C8—2448no—
536C22—28no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—24no—
544C22—44no—
545C22—48no—
546C22—48no—
547C22—44no—
548C22—42no—
549C22—42no—
550C22—1224no—
551C22—2444no—
552C22—2448no—
553C22—2448no—
554C22—2444no—
555C22—2442no—
556C22—2442no—
557C22D61⋊#10012yes—
558C22#1684074912yes—
559C22C22×C22⋊#692311yescharacteristic
560C22C2×#1451985612yes—
561C4—22no—
562C4—22no—
563C4—42no—
564C4—612no—
565C4—612no—
566C4—614no—
567C4—1221no—
568C4—1221no—
569C4—1222no—
570C4—2442no—
571C2—22no—
572C2—22no—
573C2—22no—
574C2—44no—
575C2—2444no—
576C2#2146226311yescharacteristic
577C2C2×D61⋊#10011yescharacteristic
578C2C2×#1684074911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC22×C22⋊C4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC23×C22⋊D61C22
cosocleC22×Dic61C24
hypercenterC22×C22⋊C4#6923
hypocenterC61#20726
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #21462495C2semidirect
2. #21461718C2semidirect
3. #21461684C2semidirect
5. #21461569C2semidirect
11. #16840765C22semidirect
14. C4×#11758217C22semidirect
15. #16840642C22semidirect
233. C2×Dic61#100semidirect
320. C61#20726semidirect

Maximal subgroups

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

subgroupindex
#214624952
#214617182
#214616842
#214616512
#214615692
C22×#145197372
#2072661