Finite Group Databasebeta

← #30615206

Subgroups — #30615206

Order 15616.

1242 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462501C212yesmaximal, complemented
2#21461719C212yesmaximal, complemented
3#21461685C212yesmaximal, complemented
4#21461684C212yesmaximal, complemented
5#21461655C212yesmaximal
6C4×#14519838C212yesmaximal, complemented
7#21461569C212yesmaximal, complemented
8C2×#16840242C211yesmaximal, characteristic
9#16840787—28no—
10#16840765C2214yes—
11C2×#14519838C2214yes—
12C2×#14519837C2214yes—
13#16840734C2214yes—
14C4×#11758217C2214yes—
15#16840642C2214yes—
16#16840642C2214yes—
17C22×#11758222C2211yescharacteristic
18#16840242—28no—
19C2×C4×Dic122C2211yescharacteristic
20C2×C4×Dic122C2211yescharacteristic
21C2×C4×D244C411yescharacteristic
22C2×C4×D244C411yescharacteristic
23C2×#14519737C411yescharacteristic
24C2×#14519737C411yescharacteristic
25C2×#14519737C2211yescharacteristic
26C2×#14519737C2211yescharacteristic
27C2×#14519735C411yescharacteristic
28C2×#14519735C2211yescharacteristic
29C22×C4⋊Dic61C411yescharacteristic
30C2×C4⋊C4×D61C411yescharacteristic
31C2×C4⋊C4×D61C2211yescharacteristic
32C2×#117×C61C411yescharacteristic
33C2×#11758217C2318yes—
34#14519844—24no—
35C4⋊#92420—24no—
36#14519838—28no—
37#14519837—28no—
38#14519834—28no—
39#14519832—24no—
40C4×#92420—24no—
41C2×#11758222—24no—
42C2×#11758222—24no—
43C2×#11758222—24no—
44C22×Dic122C2311yescharacteristic
45C22×D244C2×C411yescharacteristic
46C22×C22⋊D61C2×C411yescharacteristic
47C22×C22⋊D61C2311yescharacteristic
48C23×Dic61C2×C411yescharacteristic
49C23×Dic61C2×C411yescharacteristic
50C22×C4×D61C2×C411yescharacteristic
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61C2×C411yescharacteristic
54C22×C4×D61C2×C411yescharacteristic
55C22×C4×D61C2311yescharacteristic
56C4×Dic122—24no—
57C4×Dic122—24no—
58C4×D244—24no—
59C4×D244—24no—
60#14519737—24no—
61#14519737—24no—
62#14519737—24no—
63#14519737—24no—
64#14519735—24no—
65#14519735D418yes—
66C2×C4⋊Dic61—24no—
67C2×C4⋊Dic61C2×C411yescharacteristic
68C2×C4⋊Dic61C2×C411yescharacteristic
69C2×C4⋊Dic61C2×C411yescharacteristic
70C2×C4⋊Dic61C2×C411yescharacteristic
71C2×#11758196C2×C411yescharacteristic
72C2×#11758196C2×C411yescharacteristic
73C2×#11758196C2311yescharacteristic
74C2×#11758196C2311yescharacteristic
75C4⋊C4×D61—24no—
76C4⋊C4×D61—24no—
77C2×#11758198C2×C411yescharacteristic
78C2×#11758198C2×C411yescharacteristic
79C2×#11758198C2×C411yescharacteristic
80C2×#11758198C2×C411yescharacteristic
81C2×C4×Dic61C2×C411yescharacteristic
82C2×C4×Dic61C2×C411yescharacteristic
83C2×C4×Dic61C2311yescharacteristic
84C2×C4×Dic61C2311yescharacteristic
85C23×C4×C61C2×C411yescharacteristic
86#117×C61—24no—
87C2×C4⋊C4×C61C2×C411yescharacteristic
88C2×C4⋊C4×C61C2×C411yescharacteristic
89C2×C22⋊C4×C61C2×C411yescharacteristic
90C2×C22⋊C4×C61C2×C411yescharacteristic
91C2×C42×C61C2×C411yescharacteristic
92C2×C42×C61C2×C411yescharacteristic
93C24×C61C22×C411yescharacteristic
94C23×D61C22×C411yescharacteristic
95C23×D61C22×C411yescharacteristic
96C22×C4×C61—22no—
97C22×C4×C61—22no—
98C22×C4×C61—22no—
99C22×C4×C61C22×C411yescharacteristic
100C22×C4×C61C22×C411yescharacteristic
101C22×C4×C61C22×C411yescharacteristic
102C22×C4×C61C22×C411yescharacteristic
103C22×C4×C61C22×C411yescharacteristic
104C22×C4×C61C22×C411yescharacteristic
105C2×C22⋊D61—22no—
106C2×C22⋊D61—22no—
107C2×C22⋊D61—22no—
108C2×C22⋊D61—22no—
109C2×C22⋊D61—22no—
110C2×C22⋊D61#4114yes—
111C22×Dic61—22no—
112C22×Dic61—22no—
113C22×Dic61—81no—
114C22×Dic61—81no—
115C22×Dic61C22×C411yescharacteristic
116C22×Dic61C22×C411yescharacteristic
117C22×Dic61C22×C411yescharacteristic
118C22×Dic61C22×C411yescharacteristic
119C22×Dic61C22×C411yescharacteristic
120C22×Dic61C2411yescharacteristic
121#11758222—232no—
122C2×D244—22no—
123C2×D244—22no—
124C2×D244—22no—
125C2×C4×D61—22no—
126C2×C4×D61—22no—
127C2×C4×D61—22no—
128C2×C4×D61—22no—
129C2×C4×D61—22no—
130C2×C4×D61—22no—
131C2×C4×D61—22no—
132C2×C4×D61—22no—
133C2×C4×D61—22no—
134C2×C4×D61—81no—
135C2×C4×D61—81no—
136C2×C4×D61—81no—
137C2×C4×D61—81no—
138C2×C4×D61C2×D414yes—
139C2×Dic122—22no—
140C2×Dic122—22no—
141C2×Dic122#4114yes—
142#11758217—28no—
143#11758217—28no—
144C2×#92420—28no—
145C4⋊C4×C61—22no—
146C4⋊C4×C61C22⋊C414yes—
147C22⋊C4×C61—22no—
148C22⋊C4×C61—22no—
149C42×C61—22no—
150C42×C61—22no—
151#11758198—22no—
152#11758198—22no—
153#11758198C22⋊C414yes—
154#11758198C22⋊C414yes—
155C4⋊Dic61—22no—
156C4⋊Dic61—22no—
157C4⋊Dic61—22no—
158C4⋊Dic61C22⋊C414yes—
159#11758196—22no—
160#11758196—22no—
161#11758196—22no—
162#11758196—22no—
163C4×Dic61—22no—
164C4×Dic61—22no—
165C4×Dic61C2×D414yes—
166C4×Dic61C2×D414yes—
167C23×C61—21no—
168C23×C61—21no—
169C23×C61—41no—
170C23×C61—41no—
171C23×C61#11712yes—
172C23×C61C23×C411yescharacteristic
173C22×D61—21no—
174C22×D61—21no—
175C22×D61—21no—
176C22×D61—21no—
177C22×D61—41no—
178C22×D61—41no—
179C22×D61—41no—
180C22×D61—41no—
181C22×D61C2×C22⋊C412yes—
182C22×D61#11712yes—
183C2×C4×C61—28no—
184C2×C4×C61—21no—
185C2×C4×C61—21no—
186C2×C4×C61—21no—
187C2×C4×C61—21no—
188C2×C4×C61—21no—
189C2×C4×C61—21no—
190C2×C4×C61—41no—
191C2×C4×C61—41no—
192C2×C4×C61—41no—
193C2×C4×C61—41no—
194C2×C4×C61C2×C22⋊C412yes—
195C2×C4×C61C2×C22⋊C412yes—
196C2×C4×C61C2×C22⋊C412yes—
197C2×C4×C61#11712yes—
198C22⋊D61—28no—
199C22⋊D61—28no—
200C2×Dic61—21no—
201C2×Dic61—21no—
202C2×Dic61—21no—
203C2×Dic61—21no—
204C2×Dic61—41no—
205C2×Dic61—41no—
206C2×Dic61—41no—
207C2×Dic61—41no—
208C2×Dic61—82no—
209C2×Dic61—82no—
210C2×Dic61C2×C22⋊C412yes—
211C2×Dic61C2×C22⋊C412yes—
212C2×Dic61#11712yes—
213C2×Dic61C22×D412yes—
214C2×Dic61C2×#4112yes—
215C2×Dic61C2×#4112yes—
216D244—28no—
217C4×D61—28no—
218C4×D61—28no—
219C4×D61—82no—
220C4×D61—82no—
221C4×D61—82no—
222C4×D61—82no—
223Dic122—28no—
224#92420—48no—
225#20731—611nomaximal, Sylow
226C22×C61—21no—
227C22×C61—21no—
228C22×C61—22no—
229C22×C61—42no—
230C22×C61—42no—
231C22×C61—41no—
232C22×C61—41no—
233C22×C61C22×C22⋊C411yescharacteristic
234C22×C61C2×#11711yescharacteristic
235C22×C61C2×#11711yescharacteristic
236C2×D61—22no—
237C2×D61—22no—
238C2×D61—22no—
239C2×D61—22no—
240C2×D61—42no—
241C2×D61—42no—
242C2×D61—42no—
243C2×D61—41no—
244C2×D61—41no—
245C2×D61—42no—
246C4×C61—22no—
247C4×C61—22no—
248C4×C61—22no—
249C4×C61—22no—
250C4×C61—41no—
251C4×C61—41no—
252Dic61—22no—
253Dic61—22no—
254Dic61—22no—
255Dic61—41no—
256Dic61—41no—
257Dic61#52514yes—
258C2×#520—611no—
259#2921—612no—
260#1821—612no—
261#1801—612no—
262#1800—612no—
263#1785—612no—
264C4×#101—612no—
265C4×#100—612no—
266C2×C61—21no—
267C2×C61—21no—
268C2×C61—42no—
269C2×C61#228011yescharacteristic
270C2×C61#288811yescharacteristic
271C2×C61#288911yescharacteristic
272D61—42no—
273D61—42no—
274C22×#41—611no—
275#520—1228no—
276C2×C4×Q8—611no—
277C2×C4×Q8—611no—
278C2×C4×D4—611no—
279C2×C4×D4—611no—
280C2×C4×D4—611no—
281C2×C4×D4—611no—
282C2×C4×D4—611no—
283C2×C4×D4—611no—
284C2×#117—611no—
285C2×#117—611no—
286C2×#117#692311yescharacteristic
287C22×C4⋊C4—611no—
288C22×C4⋊C4—611no—
289C22×C4⋊C4—611no—
290#433—1228no—
291#423—614no—
292C2×#101—614no—
293C2×#100—614no—
294#407—614no—
295C4×M16—614no—
296#343—614no—
297#343—614no—
298C61#2073111yescharacteristic, complemented, Sylow
299C2×#41—1224no—
300C2×#41—1224no—
301C2×#41—1224no—
302C22×Q8—611no—
303C22×D4—611no—
304C22×D4—611no—
305C22×D4—611no—
306C23×C4—611no—
307C23×C4—611no—
308C23×C4—611no—
309C23×C4—611no—
310C23×C4—611no—
311C23×C4—611no—
312C23×C4—611no—
313C23×C4—611no—
314C23×C4C2×#692311yescharacteristic
315C2×M16—618no—
316C4×Q8—1224no—
317C4×Q8—1224no—
318C4×D4—1224no—
319C4×D4—1224no—
320C4×D4—1224no—
321C4×D4—1224no—
322C4×D4—1224no—
323C4×D4—1224no—
324#117—24no—
325#117—618no—
326#117—1224no—
327C2×C4⋊C4—611no—
328C2×C4⋊C4—611no—
329C2×C4⋊C4—611no—
330C2×C4⋊C4—611no—
331C2×C4⋊C4—611no—
332C2×C4⋊C4—611no—
333C2×C4⋊C4—611no—
334C2×C4⋊C4—611no—
335C2×C4⋊C4—1224no—
336C2×C4⋊C4—1224no—
337C2×C4⋊C4—1224no—
338C2×C4⋊C4C2×#692311yescharacteristic
339C2×C4⋊C4C2×#692311yescharacteristic
340C2×C22⋊C4—611no—
341C2×C22⋊C4—611no—
342C2×C22⋊C4—611no—
343C2×C22⋊C4—611no—
344C2×C22⋊C4C2×#692311yescharacteristic
345C2×C22⋊C4C2×#692311yescharacteristic
346C2×C42—611no—
347C2×C42—611no—
348C2×C42—611no—
349C2×C42—611no—
350C2×C42C2×#692311yescharacteristic
351C2×C42C2×#692311yescharacteristic
352C4⋊C8—1224no—
353C4⋊C8—1224no—
354#101—1228no—
355#100—1228no—
356C22⋊C8—1228no—
357#97—1224no—
358C4×C8—1224no—
359C24—611no—
360C24—611no—
361C24C22×#692311yescharacteristic
362#41—12232no—
363C2×Q8—614no—
364C2×Q8—1222no—
365C2×Q8—1222no—
366C2×D4—614no—
367C2×D4—1222no—
368C2×D4—1222no—
369C2×D4—1222no—
370C2×D4—1222no—
371C2×D4—1222no—
372C2×D4—1222no—
373C2×D4—1222no—
374C2×D4—1222no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—611no—
379C22×C4—611no—
380C22×C4—611no—
381C22×C4—611no—
382C22×C4—614no—
383C22×C4—611no—
384C22×C4—611no—
385C22×C4—1222no—
386C22×C4—1222no—
387C22×C4—1222no—
388C22×C4—1222no—
389C22×C4—1222no—
390C22×C4—1222no—
391C22×C4—1222no—
392C22×C4—1222no—
393C22×C4—1222no—
394C22×C4—1222no—
395C22×C4—1222no—
396C22×C4—4881no—
397C22×C4—4881no—
398C22×C4—4881no—
399C22×C4—4881no—
400C22×C4—4881no—
401C22×C4—4881no—
402C22×C4C22×#692311yescharacteristic
403C22×C4C22×#692311yescharacteristic
404C22×C4C22×#692311yescharacteristic
405C22×C4C22×#692311yescharacteristic
406C22×C4C22×#692311yescharacteristic
407C22×C4C22×#692311yescharacteristic
408M16—1228no—
409M16—1228no—
410C2×C8—1228no—
411C4⋊C4—22no—
412C4⋊C4—614no—
413C4⋊C4—1222no—
414C4⋊C4—1222no—
415C4⋊C4—1222no—
416C4⋊C4—1222no—
417C4⋊C4—1222no—
418C4⋊C4—1222no—
419C4⋊C4—1222no—
420C4⋊C4C22⋊#692314yes—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C22⋊C4—614no—
424C22⋊C4—614no—
425C22⋊C4—1222no—
426C22⋊C4—1222no—
427C42—22no—
428C42—22no—
429C42—614no—
430C42—614no—
431C42—1222no—
432C42—1222no—
433C23—21no—
434C23—21no—
435C23—41no—
436C23—41no—
437C23—612no—
438C23—612no—
439C23—1221no—
440C23—1221no—
441C23—1221no—
442C23—1221no—
443C23—2441no—
444C23—2441no—
445C23—2441no—
446C23—2441no—
447C23#1451985612yes—
448C23C23×#692311yescharacteristic
449Q8—1228no—
450D4—1228no—
451D4—1228no—
452D4—1228no—
453C2×C4—28no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—612no—
465C2×C4—612no—
466C2×C4—612no—
467C2×C4—612no—
468C2×C4—612no—
469C2×C4—612no—
470C2×C4—1228no—
471C2×C4—1228no—
472C2×C4—1221no—
473C2×C4—1221no—
474C2×C4—1221no—
475C2×C4—1221no—
476C2×C4—4882no—
477C2×C4—4882no—
478C2×C4—4882no—
479C2×C4—4882no—
480C2×C4—4882no—
481C2×C4—4882no—
482C2×C4—2441no—
483C2×C4—2441no—
484C2×C4—2441no—
485C2×C4—2441no—
486C2×C4C2×C22⋊#692312yes—
487C2×C4C2×C22⋊#692312yes—
488C2×C4C2×C22⋊#692312yes—
489C2×C4#1451985612yes—
490C8—2448no—
491C22—21no—
492C22—21no—
493C22—22no—
494C22—42no—
495C22—42no—
496C22—41no—
497C22—41no—
498C22—1222no—
499C22—1222no—
500C22—1222no—
501C22—1222no—
502C22—2442no—
503C22—2442no—
504C22—2442no—
505C22—2442no—
506C22—2441no—
507C22—2441no—
508C22C22×C22⋊#692311yescharacteristic
509C22C2×#1451985611yescharacteristic
510C22C2×#1451985611yescharacteristic
511C4—22no—
512C4—22no—
513C4—22no—
514C4—22no—
515C4—41no—
516C4—41no—
517C4—614no—
518C4—1222no—
519C4—1222no—
520C4—1222no—
521C4—2441no—
522C4—2441no—
523C2—21no—
524C2—21no—
525C2—42no—
526C2—2442no—
527C2—2442no—
528C2#2146226311yescharacteristic
529C2#2146243011yescharacteristic
530C2#2146243111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#117×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC22×#11758222C22
cosocleC22×Dic61C24
hypercenterC2×#117#6923
hypocenterC61#20731
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4⋊C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. #21462501C2semidirect
2. #21461719C2semidirect
3. #21461685C2semidirect
4. #21461684C2semidirect
6. C4×#14519838C2semidirect
7. #21461569C2semidirect
298. C61#20731semidirect

Maximal subgroups

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

subgroupindex
#214625012
#214617192
#214616852
#214616842
#214616552
C4×#145198382
#214615692
C2×#168402422
#2073161