Finite Group Databasebeta

← #30603306

Subgroups — #30603306

Order 15616.

910 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519846C211yesmaximal, characteristic, complemented
2C2×#16840753C212yesmaximal
3C2×#16840641C212yesmaximal, complemented
4#21461511C211yesmaximal, characteristic, complemented
5#408×D61C211yesmaximal, characteristic
6C2×D61⋊M16C2212yes—
7C22×C4⋊#6923C2212yes—
8C2×#14519846—22no—
9C2×#14519846—24no—
10#16840753—24no—
11#16840753—24no—
12C2×#14519840—22no—
13C2×#14519839—22no—
14#16840641—24no—
15#16840638—22no—
16C2×#41×D61C2211yescharacteristic
17C2×M16×D61C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19#16839730C411yescharacteristic, complemented
20#16839729C411yescharacteristic, complemented
21#16839728C411yescharacteristic, complemented
22#16839727—22no—
23C22⋊C8×D61—22no—
24C61×#408C411yescharacteristic, complemented
25C23×#6923—22no—
26C2×#11758213—22no—
27D61⋊M16—22no—
28D61⋊M16—22no—
29D61⋊M16—22no—
30D61⋊M16D414yes—
31C2×#11758217—22no—
32C2×D61⋊C8—22no—
33C2×C4⋊#6923—22no—
34C2×C4⋊#6923—22no—
35C2×C4⋊#6923—22no—
36C2×C4⋊#6923—22no—
37C2×C4⋊#6923—22no—
38C2×C4⋊#6923D414yes—
39#14519846—28no—
40#14519840—28no—
41#14519839—28no—
42C2×#11758226Q811yescharacteristic
43C2×#11758222—21no—
44C2×#11758222C2×C411yescharacteristic
45C2×#11758224—21no—
46C2×#11758224Q811yescharacteristic
47#41×D61—22no—
48#41×D61—22no—
49#41×D61—22no—
50#41×D61—22no—
51C2×Q8×D61D411yescharacteristic
52C2×D4×D61—21no—
53C2×D4×D61D411yescharacteristic
54C22×C4×D61—21no—
55C22×C4×D61C2311yescharacteristic
56C2×#11758194C2×C411yescharacteristic
57C2×#11758189—21no—
58M16×D61—22no—
59M16×D61—22no—
60C22×#92418C2×C411yescharacteristic
61C2×C8×D61—22no—
62C2×C8×D61—22no—
63C2×C8×D61—21no—
64C2×C8×D61D412yes—
65C2×C8×D61D412yes—
66C22⋊#92418—22no—
67#14519689—22no—
68#14519689—22no—
69C2×#41×C61C2×C411yescharacteristic
70C2×M16×C61C2×C411yescharacteristic
71C22×C8×C61C2×C411yescharacteristic
72C22⋊C8×C61—22no—
73C23×D61—21no—
74C23×D61#4111yescharacteristic
75C22×#6923—24no—
76C22×#6923—42no—
77C22×#6923—42no—
78C22×#6923—84no—
79#41×C61—22no—
80#41×C61—22no—
81C2×Q8×C61C4⋊C411yescharacteristic
82C2×D4×C61—21no—
83C2×D4×C61C4⋊C411yescharacteristic
84C22×C4×C61—21no—
85C22×C4×C61C22×C411yescharacteristic
86C2×C22⋊D61—21no—
87C2×C22⋊D61—21no—
88C2×C22⋊D61—21no—
89C22×Dic61—21no—
90C22×Dic61#4111yescharacteristic
91#11758226—22no—
92#11758226—22no—
93Q8×D61—22no—
94Q8×D61—22no—
95#11758224—22no—
96#11758224—22no—
97#11758224—42no—
98#11758224—42no—
99D4×D61—22no—
100D4×D61—22no—
101D4×D61—42no—
102D4×D61—42no—
103#11758222—22no—
104#11758222—22no—
105#11758222—42no—
106#11758222—42no—
107C2×D244—21no—
108C2×D244C4⋊C411yescharacteristic
109C2×C4×D61—21no—
110C2×C4×D61—21no—
111C2×C4×D61—21no—
112C2×C4×D61—41no—
113C2×C4×D61—41no—
114C2×C4×D61—41no—
115C2×C4×D61—41no—
116C2×C4×D61C2×D412yes—
117C2×C4×D61C2×D411yescharacteristic
118C2×C4×D61C2×D412yes—
119C2×C4×D61C2×D411yescharacteristic
120C2×C4×D61C2×D411yescharacteristic
121C2×C4×D61C2×Q811yescharacteristic
122C2×C4×D61#4112yes—
123C2×C4×D61#4112yes—
124C2×Dic122—21no—
125C2×Dic122C4⋊C411yescharacteristic
126#11758217—24no—
127#11758217—42no—
128C2×#92420—42no—
129C4⋊#6923—24no—
130C4⋊#6923—24no—
131C4⋊#6923—42no—
132C4⋊#6923—42no—
133#11758213—24no—
134#11758213—42no—
135D61⋊C8—24no—
136D61⋊C8—42no—
137M16×C61—22no—
138C2×C8×C61—22no—
139C2×C8×C61—21no—
140C2×C8×C61C22⋊C412yes—
141#11758194—22no—
142C2×#92418—22no—
143C2×#92418—21no—
144C2×#92418C22⋊C412yes—
145#11758189—42no—
146C8×D61—22no—
147C8×D61—24no—
148C8×D61—22no—
149C8×D61—41no—
150C8×D61—41no—
151C23×C61—21no—
152C23×C61#11711yescharacteristic
153C22×D61—22no—
154C22×D61—22no—
155C22×D61—21no—
156C22×D61—41no—
157C22×D61—41no—
158C22×D61—42no—
159C22×D61—42no—
160C22×D61#12112yes—
161C22×D61#12111yescharacteristic
162C22×D61C22⋊Q811yescharacteristic
163C22×D61#12612yes—
164C2×#6923—44no—
165C2×#6923—84no—
166C2×#6923—84no—
167C2×#6923—84no—
168Q8×C61—22no—
169D4×C61—22no—
170D4×C61—42no—
171C2×C4×C61—21no—
172C2×C4×C61—41no—
173C2×C4×C61—41no—
174C2×C4×C61C2×C22⋊C411yescharacteristic
175C2×C4×C61C2×C4⋊C411yescharacteristic
176C2×C4×C61C4×D412yes—
177C2×C4×C61C4×D412yes—
178C22⋊D61—42no—
179C22⋊D61—42no—
180C22⋊D61—42no—
181C2×Dic61—21no—
182C2×Dic61—41no—
183C2×Dic61—41no—
184C2×Dic61#12111yescharacteristic
185C2×Dic61C22⋊Q811yescharacteristic
186C2×Dic61#12312yes—
187C2×Dic61#12412yes—
188D244—22no—
189D244—42no—
190C4×D61—41no—
191C4×D61—41no—
192C4×D61—41no—
193C4×D61—41no—
194C4×D61—41no—
195C4×D61—41no—
196C4×D61#12011yescharacteristic
197C4×D61#12012yes—
198C4×D61#12112yes—
199C4×D61#12112yes—
200C4×D61C22⋊Q812yes—
201C4×D61C22⋊Q812yes—
202C4×D61#12312yes—
203C4×D61#12311yescharacteristic
204C4×D61#12411yescharacteristic
205C4×D61#12711yescharacteristic
206Dic122—22no—
207Dic122—42no—
208#92420—44no—
209C8×C61—22no—
210C8×C61—41no—
211#92418—22no—
212#92418—41no—
213#11107—611nomaximal, Sylow
214C22×C61—22no—
215C22×C61—42no—
216C22×C61—41no—
217C22×C61#38011yescharacteristic
218C22×C61#38812yes—
219C2×D61—22no—
220C2×D61—24no—
221C2×D61—22no—
222C2×D61—22no—
223C2×D61—42no—
224C2×D61—41no—
225C2×D61—82no—
226C2×D61—81no—
227C2×D61—81no—
228C2×D61#39211yescharacteristic
229C2×D61#39612yes—
230C2×D61#39711yescharacteristic
231C2×D61#47212yes—
232C2×D61#47312yes—
233#6923—84no—
234C4×C61—41no—
235C4×C61#38512yes—
236C4×C61#38611yescharacteristic
237C4×C61#39011yescharacteristic
238Dic61—41no—
239Dic61#39311yescharacteristic
240Dic61#39412yes—
241Dic61#39911yescharacteristic
242C22×#107—611no—
243C2×#417—612no—
244C2×#408—611no—
245C2×#343—612no—
246C2×#341—611no—
247C2×C61—22no—
248C2×C61—81no—
249C2×C61#143911yescharacteristic
250C2×C61#181612yes—
251D61—22no—
252D61—81no—
253D61#201811yescharacteristic
254D61#202011yescharacteristic
255D61#207812yes—
256C22×#41—611no—
257C22×M16—612no—
258C22×M16—611no—
259C23×C8—611no—
260C22×C4⋊C4—612no—
261C2×#107—1224no—
262C2×#107—1222no—
263#417—1224no—
264#417—1224no—
265C2×#103—1222no—
266C2×#102—1222no—
267#408—611no—
268#408—611no—
269#408—611no—
270#408—1222no—
271#408#692311yescharacteristic, complemented
272C2×C22⋊C8—1222no—
273#343—1224no—
274#341—1222no—
275C61#1110711yescharacteristic, complemented, Sylow
276C2×#41—611no—
277C2×#41—611no—
278C2×#41—611no—
279C2×#41—1221no—
280C2×#41—1221no—
281C2×#41—1222no—
282C2×#41—1222no—
283C2×#41—1222no—
284C2×#41—1222no—
285C2×#41C2×#692311yescharacteristic
286C22×Q8—611no—
287C22×D4—611no—
288C22×D4—1221no—
289C23×C4—611no—
290C23×C4—1221no—
291C23×C4—1222no—
292C2×M16—614no—
293C2×M16—611no—
294C2×M16—1221no—
295C2×M16—1222no—
296C2×M16—1222no—
297C2×M16—1222no—
298C2×M16—1222no—
299C2×M16—1222no—
300C2×M16—1222no—
301C2×M16—1222no—
302C2×M16C2×#692311yescharacteristic
303C22×C8—611no—
304C22×C8—612no—
305C22×C8—612no—
306C22×C8—1222no—
307C22×C8—1222no—
308C22×C8—1221no—
309C22×C8—1222no—
310C22×C8C2×#692311yescharacteristic
311C2×C4⋊C4—614no—
312C2×C4⋊C4—1222no—
313C2×C4⋊C4—1222no—
314C2×C4⋊C4—1222no—
315C2×C4⋊C4—1222no—
316C2×C4⋊C4—1222no—
317#107—1228no—
318#103—1228no—
319#102—1228no—
320C22⋊C8—22no—
321C22⋊C8—1222no—
322C22⋊C8—1222no—
323C22⋊C8—1222no—
324C24—611no—
325C24—1221no—
326#41—22no—
327#41—22no—
328#41—1222no—
329#41—1222no—
330#41—1222no—
331#41—1222no—
332#41—1222no—
333#41—1222no—
334#41—2442no—
335#41—2442no—
336#41—2442no—
337#41—2442no—
338C2×Q8—611no—
339C2×Q8—1221no—
340C2×Q8—1222no—
341C2×Q8—1222no—
342C2×Q8C4⋊#692311yescharacteristic
343C2×D4—21no—
344C2×D4—611no—
345C2×D4—1221no—
346C2×D4—1222no—
347C2×D4—1222no—
348C2×D4—1221no—
349C2×D4—1221no—
350C2×D4—1221no—
351C2×D4—2442no—
352C2×D4—2442no—
353C2×D4C4⋊#692311yescharacteristic
354C22×C4—21no—
355C22×C4—611no—
356C22×C4—611no—
357C22×C4—611no—
358C22×C4—611no—
359C22×C4—611no—
360C22×C4—612no—
361C22×C4—612no—
362C22×C4—612no—
363C22×C4—612no—
364C22×C4—1221no—
365C22×C4—1221no—
366C22×C4—1221no—
367C22×C4—1221no—
368C22×C4—1224no—
369C22×C4—4884no—
370C22×C4—2441no—
371C22×C4—2441no—
372C22×C4—2441no—
373C22×C4—2441no—
374C22×C4—2442no—
375C22×C4—2442no—
376C22×C4C22×#692311yescharacteristic
377M16—22no—
378M16—1224no—
379M16—1224no—
380M16—1222no—
381M16—2442no—
382M16—2442no—
383M16—2442no—
384C2×C8—22no—
385C2×C8—21no—
386C2×C8—612no—
387C2×C8—1222no—
388C2×C8—1224no—
389C2×C8—1222no—
390C2×C8—1222no—
391C2×C8—1224no—
392C2×C8—1221no—
393C2×C8—2441no—
394C2×C8—2441no—
395C2×C8—2442no—
396C2×C8—2442no—
397C2×C8C22⋊#692312yes—
398C4⋊C4—1224no—
399C4⋊C4—1224no—
400C4⋊C4—2442no—
401C4⋊C4—2442no—
402C23—21no—
403C23—611no—
404C23—611no—
405C23—612no—
406C23—612no—
407C23—1222no—
408C23—1222no—
409C23—1221no—
410C23—2441no—
411C23—2441no—
412C23—2442no—
413C23—2442no—
414C23#1451985611yescharacteristic
415Q8—22no—
416Q8—1222no—
417Q8—2442no—
418D4—22no—
419D4—42no—
420D4—1222no—
421D4—2442no—
422D4—2442no—
423D4—2442no—
424D4—2442no—
425C2×C4—21no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—611no—
429C2×C4—611no—
430C2×C4—612no—
431C2×C4—612no—
432C2×C4—612no—
433C2×C4—612no—
434C2×C4—612no—
435C2×C4—612no—
436C2×C4—611no—
437C2×C4—612no—
438C2×C4—611no—
439C2×C4—612no—
440C2×C4—611no—
441C2×C4—611no—
442C2×C4—1221no—
443C2×C4—4884no—
444C2×C4—4884no—
445C2×C4—4884no—
446C2×C4—2441no—
447C2×C4—2441no—
448C2×C4—2441no—
449C2×C4—2441no—
450C2×C4—2441no—
451C2×C4—2441no—
452C2×C4—2444no—
453C2×C4—2441no—
454C2×C4—2441no—
455C2×C4C2×C22⋊#692311yescharacteristic
456C2×C4C2×C4⋊#692311yescharacteristic
457C2×C4D4×#692312yes—
458C2×C4D4×#692312yes—
459C8—22no—
460C8—41no—
461C8—1222no—
462C8—2444no—
463C8—2441no—
464C22—22no—
465C22—41no—
466C22—42no—
467C22—611no—
468C22—611no—
469C22—612no—
470C22—612no—
471C22—612no—
472C22—1222no—
473C22—1224no—
474C22—1222no—
475C22—1222no—
476C22—4881no—
477C22—4882no—
478C22—4881no—
479C22—2441no—
480C22—2442no—
481C22#1684070411yescharacteristic
482C22#1684071212yes—
483C4—41no—
484C4—611no—
485C4—612no—
486C4—611no—
487C4—4884no—
488C4—2441no—
489C4#1684070912yes—
490C4#1684071011yescharacteristic
491C4#1684071411yescharacteristic
492C2—22no—
493C2—81no—
494C2—611no—
495C2—612no—
496C2—611no—
497C2—1222no—
498C2—4881no—
499C2#2146100211yescharacteristic
500C2#2146170812yes—
subgroupG/H
centerC22#16840704
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#408C4
socleC22×C61#380
prime radicalC2×#41×D61C22
cosocleC22×C4×D61C23
hypercenter#408#6923
hypocenterC61#11107
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
1. C22×#14519846C2semidirect
3. C2×#16840641C2semidirect
4. #21461511C2semidirect
19. #16839730C4semidirect
20. #16839729C4semidirect
21. #16839728C4semidirect
24. C61×#408C4semidirect
271. #408#6923semidirect
275. C61#11107semidirect

Maximal subgroups

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

subgroupindex
C22×#145198462
C2×#168407532
C2×#168406412
#214615112
#408×D612
#1110761