Finite Group Databasebeta

← #30603107

Subgroups — #30603107

Order 15616.

978 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519838C212yesmaximal
2C2×C4×#11758217C211yesmaximal, characteristic
3C2×#16840642C212yesmaximal
4#21461482C211yesmaximal, characteristic
5C2×#16839666C211yesmaximal, characteristic
6C22×#11758217C2212yes—
7C22×#11758217C2212yes—
8C2×#14519838—24no—
9C2×#14519838—24no—
10C2×#14519838C418yescomplemented
11C4×#11758217—24no—
12C2×#14519832—21no—
13C2×C4×#92420—21no—
14#16840642—24no—
15#16840628—21no—
16#16840628—21no—
17C23×Dic122C2211yescharacteristic
18C22×#11758196C2211yescharacteristic
19C22×C4×Dic61C2211yescharacteristic
20#16839666—21no—
21#16839666—21no—
22#16839666—21no—
23#16839666—21no—
24C2×#14519684C411yescharacteristic
25C2×#14519684C411yescharacteristic
26C2×#14519684C411yescharacteristic
27C2×#95×C61C411yescharacteristic
28C2×#11758217—22no—
29C2×#11758217—22no—
30C2×#11758217—22no—
31C2×#11758217—22no—
32C2×#11758217—22no—
33C2×#11758217—22no—
34C2×#11758217—22no—
35C2×#11758217—22no—
36C2×#11758217C2×C414yes—
37C2×#11758217C2×C414yes—
38C2×#11758217D414yes—
39C2×#11758217D414yes—
40C22×#92420—22no—
41C22×#92420—22no—
42#14519838—216no—
43#14519832—24no—
44C4×#92420—24no—
45C22×Dic122—22no—
46C22×Dic122—22no—
47C22×Dic122—21no—
48C22×Dic122—21no—
49C22×Dic122—22no—
50C22×Dic122—22no—
51C22×Dic122—22no—
52C22×Dic122C2×C414yes—
53C23×Dic61C2×C411yescharacteristic
54C23×Dic61C2×C411yescharacteristic
55C23×Dic61C2×C411yescharacteristic
56C23×Dic61C2311yescharacteristic
57C2×#11758196—22no—
58C2×#11758196—21no—
59C2×#11758196—21no—
60C2×#11758196—22no—
61C2×C4×Dic61—22no—
62C2×C4×Dic61—22no—
63C2×C4×Dic61D411yescharacteristic
64C2×C4×Dic61D411yescharacteristic
65C2×C4×Dic61D411yescharacteristic
66C2×C4×Dic61D411yescharacteristic
67#14519684—21no—
68#14519684—21no—
69#14519684—21no—
70#14519684—21no—
71#14519684—21no—
72#14519684—21no—
73C23×C4×C61C2×C411yescharacteristic
74C23×C4×C61C2×C411yescharacteristic
75C23×C4×C61C2×C411yescharacteristic
76#95×C61—21no—
77#95×C61—21no—
78C24×C61C22×C411yescharacteristic
79C22×C4×C61—21no—
80C22×C4×C61—21no—
81C22×C4×C61—22no—
82C22×C4×C61—22no—
83C22×C4×C61—22no—
84C22×C4×C61—22no—
85C22×C4×C61—21no—
86C22×C4×C61—22no—
87C22×C4×C61—41no—
88C22×C4×C61—41no—
89C22×C4×C61—41no—
90C22×C4×C61C4212yes—
91C22×C4×C61C22⋊C411yescharacteristic
92C22×C4×C61C22⋊C411yescharacteristic
93C22×Dic61—21no—
94C22×Dic61—21no—
95C22×Dic61—22no—
96C22×Dic61—22no—
97C22×Dic61—22no—
98C22×Dic61—22no—
99C22×Dic61—21no—
100C22×Dic61—22no—
101C22×Dic61—41no—
102C22×Dic61—41no—
103C22×Dic61—41no—
104C22×Dic61C4212yes—
105C22×Dic61C22⋊C411yescharacteristic
106C22×Dic61C22⋊C411yescharacteristic
107C22×Dic61C22×C412yes—
108C22×Dic61C2×D412yes—
109C22×Dic61C2×D412yes—
110C22×Dic61C2×D411yescharacteristic
111C22×Dic61C2×D411yescharacteristic
112C22×Dic61#4112yes—
113C22×Dic61#4112yes—
114C22×Dic61#4112yes—
115C2×Dic122—24no—
116C2×Dic122—24no—
117C2×Dic122—24no—
118C2×Dic122—24no—
119C2×Dic122—24no—
120C2×Dic122—24no—
121C2×Dic122—41no—
122C2×Dic122—42no—
123C2×Dic122—42no—
124C2×Dic122—42no—
125C2×Dic122—42no—
126C2×Dic122—41no—
127C2×Dic122—41no—
128C2×Dic122—42no—
129C2×Dic122—42no—
130C2×Dic122—41no—
131#11758217—24no—
132#11758217—24no—
133#11758217—24no—
134#11758217—24no—
135#11758217—24no—
136#11758217—42no—
137#11758217—42no—
138#11758217C22⋊C418yes—
139C2×#92420—24no—
140C2×#92420—24no—
141C2×#92420—24no—
142C2×#92420—24no—
143C2×#92420—42no—
144C2×#92420—42no—
145#11758196—42no—
146#11758196—41no—
147#11758196—41no—
148C4×Dic61—21no—
149C4×Dic61—21no—
150C4×Dic61—22no—
151C4×Dic61—22no—
152C4×Dic61—21no—
153C4×Dic61—21no—
154C23×C61—21no—
155C23×C61—21no—
156C23×C61—21no—
157C23×C61—21no—
158C23×C61C2×C4211yescharacteristic
159C23×C61C2×C22⋊C411yescharacteristic
160C23×C61#11711yescharacteristic
161C23×C61C4×D412yes—
162C23×C61C4×D412yes—
163C2×C4×C61—21no—
164C2×C4×C61—21no—
165C2×C4×C61—22no—
166C2×C4×C61—24no—
167C2×C4×C61—21no—
168C2×C4×C61—21no—
169C2×C4×C61—21no—
170C2×C4×C61—44no—
171C2×C4×C61—41no—
172C2×C4×C61—42no—
173C2×C4×C61—41no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61—82no—
178C2×C4×C61#10112yescomplemented
179C2×Dic61—21no—
180C2×Dic61—21no—
181C2×Dic61—22no—
182C2×Dic61—24no—
183C2×Dic61—21no—
184C2×Dic61—21no—
185C2×Dic61—21no—
186C2×Dic61—44no—
187C2×Dic61—41no—
188C2×Dic61—42no—
189C2×Dic61—41no—
190C2×Dic61—41no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61—82no—
194C2×Dic61#10112yescomplemented
195C2×Dic61C2×C22⋊C412yes—
196C2×Dic61#11712yes—
197C2×Dic61C4×D412yes—
198C2×Dic61C4×D412yes—
199C2×Dic61C4×D412yes—
200C2×Dic61C4×D412yes—
201C2×Dic61#12011yescharacteristic
202C2×Dic61#12112yes—
203C2×Dic61#12112yes—
204C2×Dic61#12112yes—
205C2×Dic61#12312yes—
206C2×Dic61#12311yescharacteristic
207C2×Dic61#12411yescharacteristic
208C2×Dic61#12412yes—
209C2×Dic61#12612yes—
210C2×Dic61#12711yescharacteristic
211Dic122—44no—
212Dic122—44no—
213Dic122—44no—
214Dic122—44no—
215#92420—28no—
216#92420—44no—
217#10963—611nomaximal, Sylow
218C22×C61—22no—
219C22×C61—22no—
220C22×C61—22no—
221C22×C61—22no—
222C22×C61—21no—
223C22×C61—21no—
224C22×C61—21no—
225C22×C61—21no—
226C22×C61C4×C22⋊C411yescharacteristic
227C22×C61C4×C22⋊C412yes—
228C22×C61#38611yescharacteristic
229C22×C61#38812yes—
230C22×C61#39011yescharacteristic
231C22×C61C2×#10111yescharacteristic
232C22×C61C2×#10111yescharacteristic
233C22×C61#41311yescharacteristic
234C22×C61#41311yescharacteristic
235C4×C61—22no—
236C4×C61—41no—
237C4×C61—42no—
238C4×C61—81no—
239Dic61—22no—
240Dic61—41no—
241Dic61—42no—
242Dic61—81no—
243Dic61#38612yes—
244Dic61#38812yes—
245Dic61#38812yes—
246Dic61#39012yes—
247C22×#101—612no—
248C2×C4×M16—611no—
249C2×#391—611no—
250C2×#343—612no—
251#1728—611no—
252C2×C61—22no—
253C2×C61—22no—
254C2×C61#143711yescharacteristic
255C2×C61C4×#10111yescharacteristic
256C2×C61C4×#10111yescharacteristic
257C2×C61#190111yescharacteristic
258C2×C61#190111yescharacteristic
259C2×C61#196611yescharacteristic
260C2×C61#196711yescharacteristic
261C23×Q8—611no—
262C22×M16—612no—
263C22×M16—612no—
264C22×C4⋊C4—611no—
265C22×C42—611no—
266C2×#101—618no—
267C2×#101—1224no—
268C2×#101—1224no—
269C4×M16—1224no—
270C2×#97—1221no—
271C2×C4×C8—1221no—
272#391—1221no—
273#391—1221no—
274#391—1221no—
275#391—1221no—
276C2×#95—611no—
277C2×#95—611no—
278C2×#95—611no—
279C2×#95#692311yescharacteristic
280#343—1224no—
281#336—1221no—
282#336—1221no—
283C61#1096311yescharacteristic, complemented, Sylow
284C22×Q8—614no—
285C22×Q8—1222no—
286C22×Q8—1222no—
287C22×Q8—1222no—
288C22×Q8—1221no—
289C22×Q8—1221no—
290C22×Q8—1222no—
291C22×Q8—1222no—
292C23×C4—611no—
293C23×C4—611no—
294C23×C4—611no—
295C23×C4—611no—
296C23×C4C2×#692311yescharacteristic
297C23×C4C2×#692311yescharacteristic
298C23×C4C2×#692311yescharacteristic
299C2×M16—614no—
300C2×M16—614no—
301C2×M16—614no—
302C2×M16—614no—
303C2×M16—1222no—
304C2×M16—1222no—
305C2×M16—1222no—
306C2×M16—1222no—
307C2×M16—1222no—
308C2×M16—1222no—
309C2×M16—1222no—
310C2×M16—1222no—
311C22×C8—1222no—
312C22×C8—1222no—
313C2×C4⋊C4—1222no—
314C2×C4⋊C4—1221no—
315C2×C4⋊C4—1221no—
316C2×C4⋊C4—1222no—
317C2×C42—611no—
318C2×C42—611no—
319C2×C42—611no—
320C2×C42—611no—
321C2×C42—1222no—
322C2×C42—1222no—
323#101—12216no—
324#97—1224no—
325C4×C8—1224no—
326#95—21no—
327#95—21no—
328#95—1221no—
329#95—1221no—
330#95—1221no—
331#95—1221no—
332#95—1221no—
333#95—1221no—
334C24C22×#692311yescharacteristic
335C2×Q8—1224no—
336C2×Q8—1224no—
337C2×Q8—1224no—
338C2×Q8—1224no—
339C2×Q8—1224no—
340C2×Q8—1224no—
341C2×Q8—2441no—
342C2×Q8—2442no—
343C2×Q8—2441no—
344C2×Q8—2442no—
345C2×Q8—2442no—
346C2×Q8—2442no—
347C2×Q8—2442no—
348C2×Q8—2442no—
349C2×Q8—2441no—
350C2×Q8—2441no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—612no—
363C22×C4—611no—
364C22×C4—611no—
365C22×C4—612no—
366C22×C4—612no—
367C22×C4—612no—
368C22×C4—612no—
369C22×C4—612no—
370C22×C4—611no—
371C22×C4—612no—
372C22×C4—611no—
373C22×C4—1222no—
374C22×C4—1221no—
375C22×C4—1221no—
376C22×C4—1222no—
377C22×C4—1222no—
378C22×C4—1222no—
379C22×C4—1222no—
380C22×C4—1221no—
381C22×C4—2441no—
382C22×C4—2441no—
383C22×C4—2441no—
384C22×C4C4×#692312yes—
385C22×C4C22⋊#692311yescharacteristic
386C22×C4C22⋊#692311yescharacteristic
387M16—618no—
388M16—1224no—
389M16—1224no—
390M16—1224no—
391M16—1224no—
392M16—1224no—
393M16—2442no—
394M16—2442no—
395C2×C8—1224no—
396C2×C8—1224no—
397C2×C8—1224no—
398C2×C8—1224no—
399C2×C8—2442no—
400C2×C8—2442no—
401C4⋊C4—2442no—
402C4⋊C4—2441no—
403C4⋊C4—2441no—
404C42—1221no—
405C42—1221no—
406C42—1222no—
407C42—1221no—
408C42—1222no—
409C42—1221no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23C2×C4×#692311yescharacteristic
415C23C2×C22⋊#692311yescharacteristic
416C23#1451985611yescharacteristic
417C23D4×#692312yes—
418C23D4×#692312yes—
419Q8—2444no—
420Q8—2444no—
421Q8—2444no—
422Q8—2444no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—22no—
429C2×C4—24no—
430C2×C4—44no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—82no—
438C2×C4—611no—
439C2×C4—612no—
440C2×C4—611no—
441C2×C4—612no—
442C2×C4—612no—
443C2×C4—612no—
444C2×C4—612no—
445C2×C4—612no—
446C2×C4—611no—
447C2×C4—611no—
448C2×C4—612no—
449C2×C4—612no—
450C2×C4—612no—
451C2×C4—612no—
452C2×C4—612no—
453C2×C4—612no—
454C2×C4—612no—
455C2×C4—1221no—
456C2×C4—1221no—
457C2×C4—1221no—
458C2×C4—1221no—
459C2×C4—1221no—
460C2×C4—1222no—
461C2×C4—1224no—
462C2×C4—4882no—
463C2×C4—2444no—
464C2×C4—2441no—
465C2×C4—2441no—
466C2×C4—2441no—
467C2×C4—2441no—
468C2×C4—2442no—
469C2×C4—2441no—
470C2×C4#1451983812yescomplemented
471C8—1228no—
472C8—2444no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—22no—
478C22—22no—
479C22—22no—
480C22—22no—
481C22C4×C22⋊#692311yescharacteristic
482C22C22⋊C4×#692312yes—
483C22#1684071011yescharacteristic
484C22#1684071212yes—
485C22#1684071411yescharacteristic
486C22C2×#1451983811yescharacteristic
487C22D61⋊#10111yescharacteristic
488C22#1684074811yescharacteristic
489C22#1684074911yescharacteristic
490C4—22no—
491C4—42no—
492C4—41no—
493C4—81no—
494C4—612no—
495C4—612no—
496C4—612no—
497C4—612no—
498C4—1222no—
499C4—4881no—
500C4—2442no—
501C4—2441no—
502C2—22no—
503C2—22no—
504C2#2146100011yescharacteristic
505C2C4×#1451983811yescharacteristic
506C2#2146157211yescharacteristic
507C2#2146184611yescharacteristic
508C2#2146184711yescharacteristic
509C2#2146196211yescharacteristic
510C2#2146196311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC2×#95×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22×C4
cosocleC23×Dic61C23
hypercenterC2×#95#6923
hypocenterC61#10963
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
10. C2×#14519838C4semidirect
178. C2×C4×C61#101semidirect
194. C2×Dic61#101semidirect
283. C61#10963semidirect
470. C2×C4#14519838semidirect

Maximal subgroups

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

subgroupindex
C22×#145198382
C2×C4×#117582172
C2×#168406422
#214614822
C2×#168396662
#1096361