Finite Group Databasebeta

← #30610285

Subgroups — #30610285

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#21462408C212yesmaximal, complemented
2#21461099C212yesmaximal, complemented
3#21461087C214yesmaximal, complemented
4#21461076C211yesmaximal, characteristic, complemented
5#21461068C212yesmaximal, complemented
6#21461056C211yesmaximal, characteristic, complemented
7D61⋊#324C212yesmaximal, complemented
8C2×#16840415C211yesmaximal, characteristic
9C2×#14519865—22no—
10#16840737—24no—
11#16840737—22no—
12#16840733C2214yes—
13#16840733C2212yes—
14D61⋊(C22⋊C8)C2214yes—
15D61⋊(C22⋊C8)C2212yes—
16#16840608C2214yes—
17#16840608C2214yes—
18#16840607C2211yescharacteristic
19#16840607C2212yes—
20#16840607C2211yescharacteristic
21#16840606C2212yes—
22#16840606C2212yes—
23C22×#11758226C411yescharacteristic
24C22×#11758226C2211yescharacteristic
25#16840415—22no—
26#16840415—24no—
27#16840415—22no—
28C2×#14519762C412yes—
29C2×#14519762C2212yes—
30C2×#14519753C411yescharacteristic
31C2×#14519753C2211yescharacteristic
32C2×#14519752C412yes—
33C2×C4×D244C411yescharacteristic
34C2×C4×D244C2211yescharacteristic
35C2×C4⋊C4×D61C2212yes—
36C2×C4⋊Q8×C61C411yescharacteristic
37#14519865—48no—
38C2×#11758213—24no—
39C2×#11758213—22no—
40C2×D61⋊C8—24no—
41C2×D61⋊C8—22no—
42#14519834—24no—
43#14519834—22no—
44#14519834—24no—
45#14519834—22no—
46C22⋊#92420C2312yes—
47C22⋊#92420C2314yes—
48C22⋊#92420C2312yes—
49C2×#11758226—21no—
50C2×#11758226—22no—
51C2×#11758226—21no—
52C2×#11758226—44no—
53C2×#11758226—44no—
54C2×#11758226D412yes—
55C2×#11758226D414yes—
56C2×#11758226D412yes—
57C22×D244C2×C411yescharacteristic
58C22×D244C2×C411yescharacteristic
59C22×D244C2×C412yes—
60C22×D244C2×C412yes—
61C22×C4×D61C2×C412yes—
62C22×C4×D61C2×C412yes—
63C22×C4×D61C2×C411yescharacteristic
64C22×C4×D61C2312yes—
65C22×C4×D61C2311yescharacteristic
66#14519762—24no—
67#14519762—24no—
68#14519762—24no—
69#14519762—24no—
70#14519753—22no—
71#14519753—22no—
72#14519753—22no—
73#14519753—22no—
74#14519752—24no—
75#14519752—24no—
76C4×D244—22no—
77C4×D244—21no—
78C4×D244—21no—
79C4×D244—22no—
80C4×D244—22no—
81C2×C4⋊Dic61C2×C411yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×#11758196C2×C412yes—
84C2×#11758196C2312yes—
85C4⋊C4×D61—24no—
86C4⋊C4×D61—24no—
87C2×#11758198C2×C412yes—
88C2×#11758198C2×C411yescharacteristic
89C2×#11758198C2×C412yes—
90C2×#11758198C2×C412yes—
91C2×#11758198C2311yescharacteristic
92C22×Q8×C61C2×C411yescharacteristic
93C22×Q8×C61C2×C411yescharacteristic
94C4⋊Q8×C61—22no—
95C4⋊Q8×C61—22no—
96C2×C4⋊C4×C61C2×C412yes—
97C2×C4⋊C4×C61C2×C412yes—
98C2×C42×C61C2×C411yescharacteristic
99C23×D61C22×C412yes—
100C23×D61C22×C411yescharacteristic
101C23×D61C22×C411yescharacteristic
102C2×Q8×C61—21no—
103C2×Q8×C61—21no—
104C2×Q8×C61—42no—
105C2×Q8×C61—42no—
106C2×Q8×C61C22⋊C412yes—
107C2×Q8×C61C22⋊C412yes—
108C22×C4×C61C22×C411yescharacteristic
109C22×C4×C61C22×C411yescharacteristic
110C22×C4×C61C22×C412yes—
111C22×C4×C61C22×C411yescharacteristic
112C22×C4×C61C22×C412yes—
113C22×Dic61C22×C412yes—
114C22×Dic61C22×C411yescharacteristic
115C22×Dic61C2411yescharacteristic
116#11758226—28no—
117#11758226—48no—
118#11758226—44no—
119#11758226—48no—
120#11758226—44no—
121#11758226—44no—
122C2×D244—24no—
123C2×D244—22no—
124C2×D244—22no—
125C2×D244—22no—
126C2×D244—22no—
127C2×D244—44no—
128C2×D244—41no—
129C2×D244—44no—
130C2×D244C22⋊C412yes—
131C2×D244C22⋊C411yescharacteristic
132C2×D244C22⋊C414yes—
133C2×D244C22⋊C414yes—
134C2×D244C22⋊C411yescharacteristic
135C2×C4×D61—22no—
136C2×C4×D61—22no—
137C2×C4×D61—22no—
138C2×C4×D61—22no—
139C2×C4×D61—21no—
140C2×C4×D61—21no—
141C2×C4×D61—24no—
142C2×C4×D61—42no—
143C2×C4×D61—44no—
144C2×C4×D61—42no—
145C2×C4×D61—42no—
146C2×C4×D61—44no—
147C2×C4×D61C2×D414yes—
148C2×C4×D61C2×D412yes—
149C2×C4×D61C2×D414yes—
150C2×C4×D61C2×D412yes—
151C2×#92420—22no—
152C2×#92420—24no—
153C2×#92420—22no—
154#11758213—48no—
155#11758213—44no—
156D61⋊C8—48no—
157D61⋊C8—44no—
158C4⋊C4×C61—24no—
159C4⋊C4×C61—24no—
160C42×C61—21no—
161C42×C61—21no—
162#11758198—22no—
163#11758198—22no—
164#11758198—22no—
165#11758198—24no—
166#11758198—24no—
167#11758198—22no—
168C4⋊Dic61—21no—
169C4⋊Dic61—21no—
170C4⋊Dic61—22no—
171#11758196—24no—
172#11758196—24no—
173C23×C61C23×C411yescharacteristic
174C22×D61—22no—
175C22×D61—22no—
176C22×D61—21no—
177C22×D61—21no—
178C22×D61—24no—
179C22×D61—21no—
180C22×D61—21no—
181C22×D61—21no—
182C22×D61—42no—
183C22×D61—41no—
184C22×D61—41no—
185C22×D61—41no—
186C22×D61—41no—
187C22×D61C2×C22⋊C412yes—
188C22×D61C2×C22⋊C412yes—
189C22×D61C2×C22⋊C412yes—
190Q8×C61—24no—
191Q8×C61—42no—
192Q8×C61—42no—
193Q8×C61—42no—
194C2×C4×C61—21no—
195C2×C4×C61—21no—
196C2×C4×C61—22no—
197C2×C4×C61—22no—
198C2×C4×C61—21no—
199C2×C4×C61—42no—
200C2×C4×C61—42no—
201C2×C4×C61—41no—
202C2×C4×C61C2×C22⋊C414yes—
203C2×C4×C61C2×C22⋊C411yescharacteristic
204C2×C4×C61C2×C22⋊C411yescharacteristic
205C2×C4×C61#13112yescomplemented
206C2×Dic61—22no—
207C2×Dic61—21no—
208C2×Dic61—22no—
209C2×Dic61—22no—
210C2×Dic61—41no—
211C2×Dic61—41no—
212C2×Dic61C22×D412yes—
213D244—24no—
214D244—28no—
215D244—22no—
216D244—44no—
217D244—44no—
218D244—44no—
219D244—44no—
220D244#9914yes—
221C4×D61—28no—
222C4×D61—24no—
223C4×D61—44no—
224C4×D61—42no—
225C4×D61—44no—
226C4×D61—44no—
227C4×D61—42no—
228C4×D61—44no—
229C4×D61—44no—
230C4×D61—42no—
231#92420—42no—
232#92420—44no—
233#92420—42no—
234#17416—611nomaximal, Sylow
235C22×C61—21no—
236C22×C61—21no—
237C22×C61C22×C22⋊C411yescharacteristic
238C22×C61C2×#13111yescharacteristic
239C22×C61#56811yescharacteristic
240C2×D61—22no—
241C2×D61—22no—
242C2×D61—22no—
243C2×D61—22no—
244C2×D61—22no—
245C2×D61—22no—
246C2×D61—22no—
247C2×D61—22no—
248C2×D61—44no—
249C2×D61—44no—
250C2×D61—41no—
251C2×D61—41no—
252C2×D61—41no—
253C2×D61—81no—
254C2×D61—81no—
255C2×D61—81no—
256C2×D61—81no—
257C2×D61C2×#9914yes—
258C4×C61—22no—
259C4×C61—24no—
260C4×C61—21no—
261C4×C61—42no—
262C4×C61—41no—
263C4×C61C2×#9912yes—
264Dic61—22no—
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#288011yescharacteristic
278C2×C61C22×#9911yescharacteristic
279C2×C61#288911yescharacteristic
280D61—24no—
281D61—42no—
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#692311yescharacteristic
291C2×#123—612no—
292C2×#123—612no—
293C2×C22⋊Q8—611no—
294C2×C22⋊Q8—611no—
295C2×#121—612no—
296C2×C4×D4—611no—
297C2×C4×D4—611no—
298C22×C4⋊C4—612no—
299#408—1222no—
300#408—1224no—
301#407—614no—
302#407—612no—
303C2×C22⋊C8—614no—
304C2×C22⋊C8—612no—
305#324—611no—
306#324—612no—
307#324—611no—
308#324—614no—
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×Q8C2×#692311yescharacteristic
322C22×Q8C2×#692311yescharacteristic
323C22×D4—611no—
324C22×D4—612no—
325C22×D4—611no—
326C22×D4—612no—
327C23×C4—612no—
328C23×C4—611no—
329C23×C4—612no—
330C23×C4—612no—
331C23×C4—611no—
332#131—2448no—
333C2×M16—1224no—
334C2×M16—1222no—
335C22×C8—1224no—
336C22×C8—1222no—
337C4⋊Q8—22no—
338C4⋊Q8—22no—
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—1222no—
350C4×D4—1222no—
351C4×D4—1221no—
352C4×D4—1222no—
353C4×D4—1221no—
354C2×C4⋊C4—611no—
355C2×C4⋊C4—612no—
356C2×C4⋊C4—612no—
357C2×C4⋊C4—611no—
358C2×C4⋊C4—1224no—
359C2×C4⋊C4—1224no—
360C2×C4⋊C4C2×#692312yes—
361C2×C4⋊C4C2×#692312yes—
362C2×C22⋊C4—611no—
363C2×C22⋊C4—612no—
364C2×C22⋊C4—611no—
365C2×C22⋊C4—612no—
366C2×C22⋊C4—612no—
367C2×C42C2×#692311yescharacteristic
368C22⋊C8—612no—
369C22⋊C8—612no—
370C22⋊C8—614no—
371C22⋊C8—1224no—
372C22⋊C8—1222no—
373C22⋊C8—1224no—
374C22⋊C8—1222no—
375C24—612no—
376C24—611no—
377C24—611no—
378#41—1228no—
379#41—2448no—
380#41—2444no—
381#41—2444no—
382#41—2448no—
383#41—2444no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—42no—
387C2×Q8—42no—
388C2×Q8C22⋊#692312yes—
389C2×Q8C22⋊#692312yes—
390C2×D4—611no—
391C2×D4—612no—
392C2×D4—611no—
393C2×D4—614no—
394C2×D4—614no—
395C2×D4—1224no—
396C2×D4—1222no—
397C2×D4—1222no—
398C2×D4—1222no—
399C2×D4—1222no—
400C2×D4—2441no—
401C2×D4—2444no—
402C2×D4—2444no—
403C22×C4—611no—
404C22×C4—614no—
405C22×C4—612no—
406C22×C4—614no—
407C22×C4—612no—
408C22×C4—612no—
409C22×C4—611no—
410C22×C4—1222no—
411C22×C4—1222no—
412C22×C4—1222no—
413C22×C4—1222no—
414C22×C4—1221no—
415C22×C4—1221no—
416C22×C4—1224no—
417C22×C4—2442no—
418C22×C4—2442no—
419C22×C4—2442no—
420C22×C4—2444no—
421C22×C4—2444no—
422C22×C4C22×#692311yescharacteristic
423C22×C4C22×#692311yescharacteristic
424C22×C4C22×#692311yescharacteristic
425C22×C4C22×#692312yes—
426C22×C4C22×#692312yes—
427M16—2448no—
428M16—2444no—
429C2×C8—1222no—
430C2×C8—1222no—
431C2×C8—1224no—
432C2×C8—2448no—
433C2×C8—2444no—
434C4⋊C4—24no—
435C4⋊C4—24no—
436C4⋊C4—1222no—
437C4⋊C4—1224no—
438C4⋊C4—1224no—
439C4⋊C4—1221no—
440C4⋊C4—1221no—
441C22⋊C4—1222no—
442C22⋊C4—1222no—
443C22⋊C4—1222no—
444C22⋊C4—1222no—
445C22⋊C4—1224no—
446C22⋊C4—1224no—
447C42—21no—
448C42—21no—
449C23—612no—
450C23—612no—
451C23—612no—
452C23—1224no—
453C23—1221no—
454C23—1221no—
455C23—1222no—
456C23—1222no—
457C23—1221no—
458C23—1221no—
459C23—1221no—
460C23—2441no—
461C23—2441no—
462C23—2442no—
463C23—2441no—
464C23—2441no—
465C23C23×#692311yescharacteristic
466Q8—24no—
467Q8—42no—
468Q8—42no—
469Q8—42no—
470D4—614no—
471D4—1224no—
472D4—1228no—
473D4—1222no—
474D4—2444no—
475D4—2444no—
476D4—2444no—
477D4—2444no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—22no—
481C2×C4—21no—
482C2×C4—22no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—612no—
487C2×C4—1228no—
488C2×C4—1224no—
489C2×C4—1222no—
490C2×C4—1221no—
491C2×C4—1222no—
492C2×C4—1222no—
493C2×C4—2442no—
494C2×C4—2444no—
495C2×C4—2444no—
496C2×C4—2444no—
497C2×C4—2442no—
498C2×C4—2444no—
499C2×C4—2444no—
500C2×C4—2441no—
501C2×C4—2442no—
502C2×C4—2441no—
503C2×C4C2×C22⋊#692311yescharacteristic
504C2×C4C2×C22⋊#692314yes—
505C2×C4C2×C22⋊#692311yescharacteristic
506C2×C4#1451986512yescomplemented
507C8—2442no—
508C8—2444no—
509C8—2442no—
510C22—21no—
511C22—21no—
512C22—614no—
513C22—1222no—
514C22—1222no—
515C22—1222no—
516C22—1222no—
517C22—1222no—
518C22—1222no—
519C22—1222no—
520C22—1222no—
521C22—4881no—
522C22—4881no—
523C22—4881no—
524C22—4881no—
525C22—2444no—
526C22—2444no—
527C22—2441no—
528C22—2441no—
529C22—2441no—
530C22C22×C22⋊#692311yescharacteristic
531C22C2×#1451986511yescharacteristic
532C22#1684084211yescharacteristic
533C4—22no—
534C4—21no—
535C4—24no—
536C4—42no—
537C4—41no—
538C4—1222no—
539C4—2442no—
540C4—2441no—
541C4D61⋊#9912yes—
542C2—21no—
543C2—21no—
544C2—1224no—
545C2—4881no—
546C2—2442no—
547C2—2442no—
548C2#2146240811yescharacteristic
549C2C2×D61⋊#9911yescharacteristic
550C2#2146243211yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×C4⋊Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840415C2
cosocleC22×Dic61C24
hypercenterC2×C4⋊Q8#6923
hypocenterC61#17416
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×Q8 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #21462408C2semidirect
2. #21461099C2semidirect
3. #21461087C2semidirect
4. #21461076C2semidirect
5. #21461068C2semidirect
6. #21461056C2semidirect
7. D61⋊#324C2semidirect
205. C2×C4×C61#131semidirect
312. C61#17416semidirect
506. C2×C4#14519865semidirect

Maximal subgroups

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

subgroupindex
#214624082
#214610992
#214610872
#214610762
#214610682
#214610562
D61⋊#3242
C2×#168404152
#1741661