Finite Group Databasebeta

← #30603461

Subgroups — #30603461

Order 15616.

686 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462463C211yesmaximal, characteristic
2#21461519C211yesmaximal, characteristic
3#21461506C212yesmaximal
4C2×#16840629C212yesmaximal
5#21448444C211yesmaximal, characteristic
6C2×D61⋊M16C2212yes—
7C2×#14519856C2212yes—
8#16840769—24no—
9#16840765—22no—
10#16840640—22no—
11#16840635—24no—
12#16840629—24no—
13C2×#14519735C2211yescharacteristic
14C2×#14519734C2211yescharacteristic
15C2×C4⋊C4×D61C2211yescharacteristic
16#16839659—22no—
17#16839636—22no—
18#16839632C411yescharacteristic, complemented
19#16839631C411yescharacteristic, complemented
20#16839627C411yescharacteristic, complemented
21C61×#382C411yescharacteristic, complemented
22C2×#11758213—22no—
23D61⋊M16—22no—
24D61⋊M16—22no—
25D61⋊M16—22no—
26D61⋊M16—22no—
27C2×#11758217—22no—
28C2×D61⋊C8D414yes—
29#14519856—22no—
30#14519856—22no—
31#14519856—22no—
32#14519856Q814yes—
33C2×C4⋊#6923—22no—
34C2×C22⋊#6923—22no—
35C2×C4×#6923—22no—
36#14519844—24no—
37C4⋊#92420—24no—
38C22×C4×D61—21no—
39C22×C4×D61C2311yescharacteristic
40#14519735—22no—
41#14519735—22no—
42#14519734—21no—
43#14519734—21no—
44#14519734D412yes—
45#14519734Q812yes—
46C2×C4⋊Dic61—22no—
47C2×C4⋊Dic61C2×C411yescharacteristic
48C2×C4⋊Dic61C2×C411yescharacteristic
49C2×#11758196—21no—
50C2×#11758196—21no—
51C2×#11758196—22no—
52C4⋊C4×D61—22no—
53C4⋊C4×D61—22no—
54C2×#11758198—21no—
55C2×#11758198D412yes—
56C2×C4×Dic61C2×C411yescharacteristic
57C2×C4×Dic61D412yes—
58#14519684—22no—
59C2×C4⋊C4×C61C2×C411yescharacteristic
60C2×C4⋊C4×C61C2×C411yescharacteristic
61C2×C42×C61C2×C411yescharacteristic
62#95×C61—22no—
63C23×D61C2×D411yescharacteristic
64C22×#6923—42no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61C22⋊C412yes—
68C22×C4×C61C22×C411yescharacteristic
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61C22⋊C412yes—
72C22×Dic61C2×D411yescharacteristic
73C2×C4×D61—42no—
74C2×C4×D61—82no—
75C2×C4×D61C2×D411yescharacteristic
76C2×C4×D61C2×D412yes—
77C2×C4×D61C2×Q812yes—
78C2×C4×D61C2×Q811yescharacteristic
79C2×C4×D61#4112yes—
80C2×C4×D61#4111yescharacteristic
81C2×C4×D61#4112yes—
82C2×C4×D61#4111yescharacteristic
83C22⋊#6923—24no—
84C22⋊#6923—42no—
85#11758217—42no—
86#11758217—42no—
87C2×#92420—24no—
88C4⋊#6923—24no—
89C4⋊#6923—42no—
90C4×#6923—24no—
91C4×#6923—42no—
92#11758213—42no—
93#11758213—42no—
94D61⋊C8—24no—
95D61⋊C8—24no—
96C4⋊C4×C61—22no—
97C4⋊C4×C61—22no—
98C42×C61—21no—
99C42×C61C4⋊C412yes—
100#11758198—22no—
101#11758198—24no—
102#11758198—22no—
103C4⋊Dic61—22no—
104C4⋊Dic61—22no—
105C4⋊Dic61—82no—
106#11758196—22no—
107#11758196—22no—
108#11758196—41no—
109#11758196—41no—
110#11758196—82no—
111C4×Dic61—21no—
112C4×Dic61—22no—
113C4×Dic61—22no—
114C4×Dic61C4⋊C412yes—
115C23×C61C2×C22⋊C411yescharacteristic
116C22×D61—41no—
117C22×D61—41no—
118C22×D61#12112yes—
119C22×D61#12111yescharacteristic
120C22×D61C22⋊Q812yes—
121C22×D61C22⋊Q811yescharacteristic
122C2×#6923—44no—
123C2×#6923—82no—
124C2×#6923—82no—
125C2×C4×C61—22no—
126C2×C4×C61—22no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—42no—
130C2×C4×C61—42no—
131C2×C4×C61—41no—
132C2×C4×C61C2×C4⋊C411yescharacteristic
133C2×C4×C61#11711yescharacteristic
134C2×C4×C61C4×D412yes—
135C2×C4×C61C4×Q812yes—
136C2×Dic61—22no—
137C2×Dic61—22no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—42no—
141C2×Dic61—42no—
142C2×Dic61—41no—
143C2×Dic61#12011yescharacteristic
144C2×Dic61#12111yescharacteristic
145C2×Dic61C22⋊Q811yescharacteristic
146C2×Dic61#12311yescharacteristic
147C2×Dic61#12411yescharacteristic
148C2×Dic61C4⋊Q811yescharacteristic
149C4×D61—84no—
150C4×D61#12112yes—
151C4×D61C22⋊Q812yes—
152C4×D61C22⋊Q812yes—
153C4×D61#12312yes—
154C4×D61#12512yes—
155C4×D61#12512yes—
156C4×D61#12612yes—
157C4×D61C4⋊Q812yes—
158#92420—44no—
159#11225—611nomaximal, Sylow
160C22×C61—21no—
161C22×C61—21no—
162C22×C61#38011yescharacteristic
163C22×C61#38611yescharacteristic
164C22×C61#39111yescharacteristic
165C2×D61—22no—
166C2×D61—22no—
167C2×D61—41no—
168C2×D61—42no—
169C2×D61—41no—
170C2×D61#39612yes—
171C2×D61#39812yes—
172#6923—84no—
173C4×C61—42no—
174C4×C61—42no—
175C4×C61—81no—
176C4×C61#38712yes—
177C4×C61#38912yes—
178Dic61—42no—
179Dic61—42no—
180Dic61—81no—
181Dic61#39411yescharacteristic
182Dic61#39511yescharacteristic
183Dic61#39811yescharacteristic
184Dic61#40011yescharacteristic
185#2905—611no—
186#2317—611no—
187#1740—611no—
188#1736—612no—
189C2×H(3,ℤ/4)—612no—
190C2×C61—21no—
191C2×C61—21no—
192C2×C61#144111yescharacteristic
193C2×C61#190911yescharacteristic
194C2×C61#191011yescharacteristic
195D61—22no—
196D61—22no—
197C22×M16—612no—
198C2×#117—611no—
199C2×#117—611no—
200C2×#117—612no—
201C22×C4⋊C4—611no—
202#424—1224no—
203#423—1222no—
204#389—1222no—
205#385—1222no—
206#384—611no—
207#384—611no—
208#382—611no—
209#382#692311yescharacteristic, complemented
210#342—1222no—
211#340—1224no—
212H(3,ℤ/4)—1224no—
213C61#1122511yescharacteristic, complemented, Sylow
214C23×C4—611no—
215C23×C4—1221no—
216C2×M16—1222no—
217C2×M16—1222no—
218C2×M16—1222no—
219C2×M16—1222no—
220C2×M16—1222no—
221C2×M16—1222no—
222C22×C8—614no—
223#117—612no—
224#117—612no—
225#117—614no—
226#117—1221no—
227#117—1221no—
228#117—1222no—
229#117—1222no—
230#117—1222no—
231#117—1222no—
232#117—1222no—
233C2×C4⋊C4—611no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4—1222no—
236C2×C4⋊C4—1222no—
237C2×C4⋊C4—1221no—
238C2×C4⋊C4—1222no—
239C2×C4⋊C4—1222no—
240C2×C4⋊C4—1222no—
241C2×C4⋊C4—1221no—
242C2×C4⋊C4C2×#692311yescharacteristic
243C2×C4⋊C4C2×#692311yescharacteristic
244C2×C22⋊C4—612no—
245C2×C22⋊C4—1221no—
246C2×C22⋊C4—1222no—
247C2×C42—611no—
248C2×C42—612no—
249C2×C42—1222no—
250C2×C42C2×#692311yescharacteristic
251C4⋊C8—1224no—
252C4⋊C8—1224no—
253#95—22no—
254#95—1222no—
255C24—611no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—611no—
259C22×C4—611no—
260C22×C4—611no—
261C22×C4—611no—
262C22×C4—611no—
263C22×C4—612no—
264C22×C4—612no—
265C22×C4—612no—
266C22×C4—612no—
267C22×C4—612no—
268C22×C4—1221no—
269C22×C4—1221no—
270C22×C4—4882no—
271C22×C4—2442no—
272C22×C4—2442no—
273C22×C4C22⋊#692312yes—
274C22×C4C22×#692311yescharacteristic
275M16—2442no—
276M16—2442no—
277M16—2442no—
278M16—2442no—
279C2×C8—1224no—
280C2×C8—1224no—
281C2×C8—1224no—
282C4⋊C4—22no—
283C4⋊C4—22no—
284C4⋊C4—1222no—
285C4⋊C4—1222no—
286C4⋊C4—1224no—
287C4⋊C4—1222no—
288C4⋊C4—1222no—
289C4⋊C4—4882no—
290C4⋊C4—4882no—
291C4⋊C4—2441no—
292C4⋊C4—2441no—
293C4⋊C4—2442no—
294C22⋊C4—1224no—
295C22⋊C4—1222no—
296C22⋊C4—1222no—
297C22⋊C4—1224no—
298C22⋊C4—2442no—
299C42—21no—
300C42—612no—
301C42—1222no—
302C42—1222no—
303C42—1224no—
304C42—1221no—
305C42—2442no—
306C42C4⋊#692312yes—
307C23—612no—
308C23—611no—
309C23—611no—
310C23—612no—
311C23—2441no—
312C23—2441no—
313C23C2×C22⋊#692311yescharacteristic
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—41no—
321C2×C4—611no—
322C2×C4—611no—
323C2×C4—611no—
324C2×C4—611no—
325C2×C4—611no—
326C2×C4—611no—
327C2×C4—612no—
328C2×C4—612no—
329C2×C4—612no—
330C2×C4—612no—
331C2×C4—612no—
332C2×C4—612no—
333C2×C4—612no—
334C2×C4—612no—
335C2×C4—1222no—
336C2×C4—1222no—
337C2×C4—4884no—
338C2×C4—4882no—
339C2×C4—4882no—
340C2×C4—2442no—
341C2×C4—2444no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4—2442no—
346C2×C4C2×C4⋊#692311yescharacteristic
347C2×C4#1451985611yescharacteristic
348C2×C4D4×#692312yes—
349C2×C4Q8×#692312yes—
350C8—2444no—
351C22—21no—
352C22—21no—
353C22—612no—
354C22—612no—
355C22—1222no—
356C22—1222no—
357C22—2441no—
358C22—2441no—
359C22—2442no—
360C22#1684070411yescharacteristic
361C22#1684071011yescharacteristic
362C22(C2×#6923)⋊Q811yescharacteristic
363C4—42no—
364C4—42no—
365C4—81no—
366C4—611no—
367C4—611no—
368C4—611no—
369C4—611no—
370C4—4884no—
371C4—4881no—
372C4—2442no—
373C4—2442no—
374C4#1684071112yes—
375C4#1684071312yes—
376C2—21no—
377C2—21no—
378C2—1222no—
379C2—1222no—
380C2#2146100411yescharacteristic
381C2#2146186011yescharacteristic
382C2#2146186311yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#382C4
socleC22×C61#386
prime radicalC23×D61C2×D4
cosocleC22×C4×D61C23
hypercenter#382#6923
hypocenterC61#11225
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #382

Complements

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

NH ≅ G/Ntype
18. #16839632C4semidirect
19. #16839631C4semidirect
20. #16839627C4semidirect
21. C61×#382C4semidirect
209. #382#6923semidirect
213. C61#11225semidirect

Maximal subgroups

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

subgroupindex
#214624632
#214615192
#214615062
C2×#168406292
#214484442
#1122561