Finite Group Databasebeta

← #30610283

Subgroups — #30610283

Order 15616.

1290 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462407C212yesmaximal, complemented
2#21461097C212yesmaximal, complemented
3#21461086C214yesmaximal, complemented
4#21461076C211yesmaximal, characteristic, complemented
5#21461067C212yesmaximal, complemented
6#21461056C211yesmaximal, characteristic, complemented
7C2×#16840607C212yesmaximal, complemented
8C2×#16840416C211yesmaximal, characteristic
9C2×#14519864—22no—
10#16840736—22no—
11#16840735—24no—
12#16840733C2212yes—
13#16840732C2214yes—
14D61⋊(C22⋊C8)C2212yes—
15C2×C22⋊#92420C2214yes—
16#16840607C2211yescharacteristic
17#16840607C2212yes—
18#16840607C2214yes—
19#16840607C2211yescharacteristic
20#16840607C2214yes—
21#16840606C2212yes—
22#16840606C2212yes—
23C22×#11758224C411yescharacteristic
24C22×#11758224C2211yescharacteristic
25#16840416—22no—
26#16840416—24no—
27#16840416—22no—
28C2×#14519777C411yescharacteristic
29C2×#14519761C412yes—
30C2×#14519761C2212yes—
31C2×#14519757C411yescharacteristic
32C2×#14519757C2211yescharacteristic
33C2×#14519751C412yes—
34C2×C4×D244C2211yescharacteristic
35C22×C4⋊Dic61C2212yes—
36C2×C4×D4×C61C411yescharacteristic
37#14519864—48no—
38C2×#11758213—22no—
39C2×#11758217—24no—
40C2×D61⋊C8—22no—
41C22×#92420—24no—
42#14519834—22no—
43#14519834—22no—
44C22⋊#92420—24no—
45C22⋊#92420—24no—
46C22⋊#92420C2312yes—
47C22⋊#92420C2314yes—
48C22⋊#92420C2312yes—
49C2×#11758224—22no—
50C2×#11758224—21no—
51C2×#11758224—21no—
52C2×#11758224—44no—
53C2×#11758224—44no—
54C2×#11758224D412yes—
55C2×#11758224D414yes—
56C2×#11758224D412yes—
57C22×Dic122C2×C411yescharacteristic
58C22×Dic122C2×C411yescharacteristic
59C22×D244C2×C411yescharacteristic
60C22×C22⋊D61C2×C412yes—
61C22×C22⋊D61C2×C412yes—
62C23×Dic61C2×C412yes—
63C23×Dic61C2312yes—
64C22×C4×D61C2×C411yescharacteristic
65C22×C4×D61C2311yescharacteristic
66#14519777—22no—
67#14519777—22no—
68#14519761—24no—
69#14519761—24no—
70#14519761—24no—
71#14519761—24no—
72#14519757—22no—
73#14519757—22no—
74#14519757—22no—
75#14519757—22no—
76#14519751—24no—
77#14519751—24no—
78C4×D244—22no—
79C4×D244—22no—
80C2×C4⋊Dic61—24no—
81C2×C4⋊Dic61—24no—
82C2×C4⋊Dic61C2×C412yes—
83C2×C4⋊Dic61C2×C412yes—
84C2×C4⋊Dic61C2×C412yes—
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C4⋊Dic61C2312yes—
87C2×#11758198C2×C411yescharacteristic
88C2×#11758198C2×C412yes—
89C2×#11758198C2×C412yes—
90C2×#11758198C2311yescharacteristic
91C22×D4×C61C2×C411yescharacteristic
92C23×C4×C61C2×C412yes—
93C4×D4×C61—22no—
94C4×D4×C61—21no—
95C4×D4×C61—21no—
96C2×C4⋊C4×C61C2×C411yescharacteristic
97C2×C22⋊C4×C61C2×C412yes—
98C2×C42×C61C2×C411yescharacteristic
99C24×C61C22×C412yes—
100C23×D61C22×C411yescharacteristic
101C23×D61C22×C411yescharacteristic
102C2×D4×C61—24no—
103C2×D4×C61C22⋊C412yes—
104C2×D4×C61C22⋊C411yescharacteristic
105C2×D4×C61C22⋊C411yescharacteristic
106C22×C4×C61—22no—
107C22×C4×C61—22no—
108C22×C4×C61—24no—
109C22×C4×C61—42no—
110C22×C4×C61C22×C412yes—
111C22×C4×C61C22×C411yescharacteristic
112C22×C4×C61C22×C411yescharacteristic
113C22×C4×C61C22×C411yescharacteristic
114C2×C22⋊D61—22no—
115C2×C22⋊D61—22no—
116C2×C22⋊D61—44no—
117C2×C22⋊D61—44no—
118C2×C22⋊D61C22⋊C414yes—
119C2×C22⋊D61C22⋊C414yes—
120C22×Dic61—22no—
121C22×Dic61—22no—
122C22×Dic61—44no—
123C22×Dic61—44no—
124C22×Dic61C22×C411yescharacteristic
125C22×Dic61C22×C412yes—
126C22×Dic61C22×C412yes—
127C22×Dic61C2×D414yes—
128C22×Dic61C2×D414yes—
129C22×Dic61C2411yescharacteristic
130#11758224—28no—
131#11758224—44no—
132#11758224—48no—
133#11758224—48no—
134#11758224—44no—
135#11758224—44no—
136C2×D244—22no—
137C2×D244—22no—
138C2×D244—41no—
139C2×C4×D61—21no—
140C2×C4×D61—21no—
141C2×C4×D61—42no—
142C2×C4×D61—42no—
143C2×C4×D61C2×D412yes—
144C2×C4×D61C2×D412yes—
145C2×Dic122—21no—
146C2×Dic122—21no—
147C2×Dic122—42no—
148C2×Dic122—42no—
149C2×Dic122C22⋊C412yes—
150C2×Dic122C22⋊C412yes—
151#11758217—48no—
152C2×#92420—22no—
153C2×#92420—24no—
154C2×#92420—22no—
155C2×#92420—48no—
156#11758213—44no—
157D61⋊C8—44no—
158C4⋊C4×C61—21no—
159C4⋊C4×C61—21no—
160C22⋊C4×C61—22no—
161C22⋊C4×C61—22no—
162C42×C61—21no—
163C42×C61—21no—
164#11758198—22no—
165#11758198—24no—
166#11758198—24no—
167#11758198—22no—
168C4⋊Dic61—24no—
169C4⋊Dic61—24no—
170C4⋊Dic61—24no—
171C4⋊Dic61—22no—
172C4⋊Dic61—24no—
173C23×C61—22no—
174C23×C61—22no—
175C23×C61—24no—
176C23×C61—42no—
177C23×C61C2×C22⋊C412yes—
178C23×C61C2×C22⋊C412yes—
179C23×C61C23×C411yescharacteristic
180C22×D61—21no—
181C22×D61—21no—
182C22×D61—21no—
183C22×D61—21no—
184C22×D61—21no—
185C22×D61—41no—
186C22×D61—41no—
187C22×D61—41no—
188C22×D61—41no—
189C22×D61C2×C22⋊C412yes—
190D4×C61—24no—
191D4×C61—22no—
192D4×C61#9914yes—
193C2×C4×C61—21no—
194C2×C4×C61—21no—
195C2×C4×C61—22no—
196C2×C4×C61—21no—
197C2×C4×C61—22no—
198C2×C4×C61—22no—
199C2×C4×C61—22no—
200C2×C4×C61—44no—
201C2×C4×C61—44no—
202C2×C4×C61—41no—
203C2×C4×C61C2×C22⋊C411yescharacteristic
204C2×C4×C61C2×C22⋊C411yescharacteristic
205C2×C4×C61#13112yescomplemented
206C22⋊D61—28no—
207C22⋊D61—44no—
208C22⋊D61—44no—
209C22⋊D61—44no—
210C2×Dic61—28no—
211C2×Dic61—22no—
212C2×Dic61—21no—
213C2×Dic61—42no—
214C2×Dic61—41no—
215C2×Dic61—44no—
216C2×Dic61—44no—
217C2×Dic61—44no—
218C2×Dic61—42no—
219C2×Dic61—41no—
220C2×Dic61C2×C22⋊C414yes—
221C2×Dic61C22×D412yes—
222D244—44no—
223C4×D61—24no—
224C4×D61—42no—
225C4×D61—42no—
226C4×D61—42no—
227Dic122—24no—
228Dic122—42no—
229Dic122—42no—
230Dic122—42no—
231#92420—42no—
232#92420—42no—
233#92420—44no—
234#17416—611nomaximal, Sylow
235C22×C61—22no—
236C22×C61—21no—
237C22×C61—21no—
238C22×C61—22no—
239C22×C61—22no—
240C22×C61—22no—
241C22×C61—22no—
242C22×C61—44no—
243C22×C61—44no—
244C22×C61C2×#9914yes—
245C22×C61C22×C22⋊C411yescharacteristic
246C22×C61C2×#13111yescharacteristic
247C22×C61#56811yescharacteristic
248C2×D61—22no—
249C2×D61—22no—
250C2×D61—22no—
251C2×D61—41no—
252C2×D61—41no—
253C2×D61—41no—
254C2×D61—81no—
255C2×D61—81no—
256C2×D61—81no—
257C2×D61—81no—
258C4×C61—22no—
259C4×C61—21no—
260C4×C61—42no—
261C4×C61—41no—
262C4×C61C2×#9912yes—
263Dic61—22no—
264Dic61—24no—
265Dic61—42no—
266Dic61—41no—
267C2×#547—611no—
268#2880—612no—
269#1472—612no—
270#1468—614no—
271#1465—611no—
272#1463—612no—
273#1459—611no—
274C2×#324—612no—
275C2×C61—21no—
276C2×C61—21no—
277C2×C61—24no—
278C2×C61—42no—
279C2×C61#288011yescharacteristic
280C2×C61C22×#9911yescharacteristic
281C2×C61#288911yescharacteristic
282D61—42no—
283D61—81no—
284C22×#41—611no—
285C22×#41—611no—
286C2×#131—1222no—
287#547—1222no—
288#547—1224no—
289#547—1222no—
290C2×C4⋊Q8—611no—
291C2×#123—612no—
292C2×#123—612no—
293C2×C22⋊Q8—611no—
294C2×C22⋊Q8—611no—
295C2×#121—612no—
296C2×C4×D4—611no—
297C2×C4×D4#692311yescharacteristic
298C22×C4⋊C4—612no—
299#408—1224no—
300#408—1222no—
301#407—614no—
302#407—612no—
303C2×C22⋊C8—614no—
304C2×C22⋊C8—612no—
305#324—611no—
306#324—612no—
307#324—614no—
308#324—611no—
309#324—614no—
310#323—612no—
311#323—612no—
312C61#1741611yescharacteristic, complemented, Sylow
313C2×#41—612no—
314C2×#41—614no—
315C2×#41—612no—
316C2×#41—1221no—
317C2×#41—1222no—
318C2×#41—1221no—
319C2×#41—2444no—
320C2×#41—2444no—
321C22×Q8—611no—
322C22×Q8—611no—
323C22×D4—612no—
324C22×D4—612no—
325C22×D4—611no—
326C22×D4C2×#692311yescharacteristic
327C23×C4—612no—
328C23×C4—611no—
329C23×C4—612no—
330C23×C4—611no—
331C23×C4C2×#692312yes—
332#131—2448no—
333C2×M16—1224no—
334C2×M16—1222no—
335C22×C8—1224no—
336C22×C8—1222no—
337C4⋊Q8—1222no—
338C4⋊Q8—1222no—
339#123—1224no—
340#123—1224no—
341#123—1224no—
342#123—1224no—
343C22⋊Q8—1222no—
344C22⋊Q8—1222no—
345C22⋊Q8—1222no—
346C22⋊Q8—1222no—
347#121—1224no—
348#121—1224no—
349C4×D4—22no—
350C4×D4—21no—
351C4×D4—21no—
352C4×D4—1222no—
353C4×D4—1222no—
354C2×C4⋊C4—611no—
355C2×C4⋊C4—612no—
356C2×C4⋊C4—612no—
357C2×C4⋊C4—612no—
358C2×C4⋊C4—612no—
359C2×C4⋊C4—1224no—
360C2×C4⋊C4—1224no—
361C2×C4⋊C4C2×#692311yescharacteristic
362C2×C22⋊C4—611no—
363C2×C22⋊C4—611no—
364C2×C22⋊C4—612no—
365C2×C22⋊C4—612no—
366C2×C22⋊C4C2×#692312yes—
367C2×C42C2×#692311yescharacteristic
368C22⋊C8—612no—
369C22⋊C8—614no—
370C22⋊C8—612no—
371C22⋊C8—1224no—
372C22⋊C8—1224no—
373C22⋊C8—1222no—
374C22⋊C8—1222no—
375C24—611no—
376C24—611no—
377C24C22×#692312yes—
378#41—1228no—
379#41—2448no—
380#41—2444no—
381#41—2448no—
382#41—2444no—
383#41—2444no—
384C2×Q8—612no—
385C2×Q8—612no—
386C2×Q8—1221no—
387C2×Q8—1221no—
388C2×Q8—2442no—
389C2×Q8—2442no—
390C2×D4—24no—
391C2×D4—614no—
392C2×D4—614no—
393C2×D4—1222no—
394C2×D4—1222no—
395C2×D4—1222no—
396C2×D4—1222no—
397C2×D4—2441no—
398C2×D4—2444no—
399C2×D4—2444no—
400C2×D4C22⋊#692312yes—
401C2×D4C22⋊#692311yescharacteristic
402C2×D4C22⋊#692311yescharacteristic
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—24no—
406C22×C4—42no—
407C22×C4—614no—
408C22×C4—614no—
409C22×C4—611no—
410C22×C4—612no—
411C22×C4—612no—
412C22×C4—612no—
413C22×C4—611no—
414C22×C4—612no—
415C22×C4—1222no—
416C22×C4—1222no—
417C22×C4—1221no—
418C22×C4—1221no—
419C22×C4—2442no—
420C22×C4—2442no—
421C22×C4—2444no—
422C22×C4—2444no—
423C22×C4C22×#692312yes—
424C22×C4C22×#692311yescharacteristic
425C22×C4C22×#692311yescharacteristic
426C22×C4C22×#692311yescharacteristic
427M16—2444no—
428M16—2448no—
429C2×C8—1222no—
430C2×C8—1224no—
431C2×C8—1222no—
432C2×C8—2444no—
433C2×C8—2448no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—1222no—
437C4⋊C4—1224no—
438C4⋊C4—1224no—
439C4⋊C4—1224no—
440C4⋊C4—1224no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—1222no—
444C22⋊C4—1224no—
445C22⋊C4—1222no—
446C22⋊C4—1224no—
447C42—21no—
448C42—21no—
449C23—24no—
450C23—22no—
451C23—22no—
452C23—42no—
453C23—612no—
454C23—1221no—
455C23—1221no—
456C23—1221no—
457C23—1221no—
458C23—1221no—
459C23—2441no—
460C23—2441no—
461C23—2441no—
462C23—2441no—
463C23C2×C22⋊#692312yes—
464C23C2×C22⋊#692312yes—
465C23C23×#692311yescharacteristic
466Q8—1224no—
467Q8—2442no—
468Q8—2442no—
469Q8—2442no—
470D4—24no—
471D4—22no—
472D4—1228no—
473D4—2444no—
474D4—2444no—
475D4—2444no—
476D4—2444no—
477D4#1451983614yes—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—22no—
481C2×C4—21no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—44no—
486C2×C4—44no—
487C2×C4—41no—
488C2×C4—614no—
489C2×C4—612no—
490C2×C4—1228no—
491C2×C4—1224no—
492C2×C4—1221no—
493C2×C4—1222no—
494C2×C4—2442no—
495C2×C4—2442no—
496C2×C4—2441no—
497C2×C4—2442no—
498C2×C4—2444no—
499C2×C4—2444no—
500C2×C4—2444no—
501C2×C4—2442no—
502C2×C4—2441no—
503C2×C4—2442no—
504C2×C4C2×C22⋊#692311yescharacteristic
505C2×C4C2×C22⋊#692311yescharacteristic
506C2×C4#1451986412yescomplemented
507C8—2442no—
508C8—2442no—
509C8—2444no—
510C22—22no—
511C22—21no—
512C22—21no—
513C22—22no—
514C22—22no—
515C22—22no—
516C22—22no—
517C22—44no—
518C22—44no—
519C22—1222no—
520C22—1222no—
521C22—1222no—
522C22—4881no—
523C22—4881no—
524C22—4881no—
525C22—4881no—
526C22—2441no—
527C22—2441no—
528C22—2441no—
529C22C2×#1451983614yes—
530C22C22×C22⋊#692311yescharacteristic
531C22C2×#1451986411yescharacteristic
532C22#1684084011yescharacteristic
533C4—22no—
534C4—21no—
535C4—42no—
536C4—41no—
537C4—1222no—
538C4—1224no—
539C4—2441no—
540C4—2442no—
541C4C2×#1451983612yes—
542C2—21no—
543C2—21no—
544C2—24no—
545C2—42no—
546C2—4881no—
547C2—2442no—
548C2#2146240711yescharacteristic
549C2C22×#1451983611yescharacteristic
550C2#2146243111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×C4×D4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840416C2
cosocleC22×Dic61C24
hypercenterC2×C4×D4#6923
hypocenterC61#17416
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×D4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #21462407C2semidirect
2. #21461097C2semidirect
3. #21461086C2semidirect
4. #21461076C2semidirect
5. #21461067C2semidirect
6. #21461056C2semidirect
7. C2×#16840607C2semidirect
205. C2×C4×C61#131semidirect
312. C61#17416semidirect
506. C2×C4#14519864semidirect

Maximal subgroups

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

subgroupindex
#214624072
#214610972
#214610862
#214610762
#214610672
#214610562
C2×#168406072
C2×#168404162
#1741661