Finite Group Databasebeta

← #30606468

Subgroups — #30606468

Order 15616.

418 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#350C211yesmaximal, characteristic
2#21462027C211yesmaximal, characteristic, complemented
3C2×#16840649C211yesmaximal, characteristic, complemented
4#21461593C211yesmaximal, characteristic
5#21460875C211yesmaximal, characteristic, complemented
6#21460862C211yesmaximal, characteristic, complemented
7#504×D61C211yesmaximal, characteristic
8D61⋊M32C2211yescharacteristic
9C2×D61⋊C16C2211yescharacteristic
10D61⋊#104C411yescharacteristic
11#16840752C411yescharacteristic
12#16840725C2211yescharacteristic
13C2×C8×#6923C2211yescharacteristic
14#16840661C412yescomplemented
15#16840660C412yescomplemented
16#16840649—21no—
17#16840649—21no—
18#16840649—21no—
19C16×#6923—21no—
20#16840637C411yescharacteristic
21#16840634C411yescharacteristic
22#131×D61C2211yescharacteristic
23#16840180—21no—
24#16840180C411yescharacteristic, complemented
25#16840179C411yescharacteristic, complemented
26#16840178—21no—
27#16840178C411yescharacteristic, complemented
28M32×D61—21no—
29M32×D61C2211yescharacteristic
30C2×C16×D61—21no—
31C2×C16×D61C2211yescharacteristic
32C61×#504C411yescharacteristic, complemented
33D61⋊M16C2×C411yescharacteristic
34C2×D61⋊C8C2×C411yescharacteristic
35#14519856C2×C411yescharacteristic
36C2×C4×#6923C2×C411yescharacteristic
37#14519852—21no—
38#14519851C2×C412yes—
39D61⋊C16—21no—
40D61⋊C16—21no—
41D61⋊C16—21no—
42C2×#11758187C2×C412yes—
43#14519842C812yes—
44#14519841C812yes—
45#14519840C812yes—
46#14519839C812yes—
47#14519831—21no—
48C8×#6923—21no—
49C8×#6923—21no—
50C8×#6923—21no—
51#41×D61C2×C411yescharacteristic
52#14519785—21no—
53#14519785C2×C411yescharacteristic
54#14519784C2×C411yescharacteristic
55#14519783—21no—
56#14519783C2×C411yescharacteristic
57M16×D61—21no—
58M16×D61C2×C411yescharacteristic
59C2×C8×D61—21no—
60C2×C8×D61C2311yescharacteristic
61#14519717—21no—
62#14519717C2×C411yescharacteristic
63#14519716—21no—
64#14519716—21no—
65#14519716—21no—
66C2×#11758185—21no—
67C2×#11758185C2×C411yescharacteristic
68C16×D61—21no—
69C16×D61—21no—
70C16×D61—21no—
71C16×D61D411yescharacteristic
72C16×D61D411yescharacteristic
73C16×D61D411yescharacteristic
74C16×D61D411yescharacteristic
75#131×C61C2×C411yescharacteristic
76M32×C61—21no—
77M32×C61C2×C411yescharacteristic
78C2×C16×C61—21no—
79C2×C16×C61C2×C411yescharacteristic
80C22×#6923—21no—
81#41×C61C4211yescharacteristic
82#11758226C2×C811yescharacteristic
83Q8×D61C2×C811yescharacteristic
84#11758224—21no—
85#11758224C2×C811yescharacteristic
86D4×D61—21no—
87D4×D61C2×C811yescharacteristic
88#11758222—21no—
89#11758222C4211yescharacteristic
90C2×C4×D61—21no—
91C2×C4×D61C22×C411yescharacteristic
92C22⋊#6923—21no—
93#11758217—21no—
94C2×#92420—21no—
95C4⋊#6923C2×C812yes—
96C4×#6923—21no—
97C4×#6923—21no—
98C4×#6923C2×C812yes—
99#11758213C2×C812yes—
100D61⋊C8—21no—
101D61⋊C8—21no—
102D61⋊C8C2×C812yes—
103M16×C61—21no—
104M16×C61C4211yescharacteristic
105C2×C8×C61—21no—
106C2×C8×C61C22×C411yescharacteristic
107#11758194—21no—
108#11758194C4211yescharacteristic
109C2×#92418—21no—
110C2×#92418C22×C411yescharacteristic
111#11758189—21no—
112#11758189—21no—
113#11758189—21no—
114C8×D61—21no—
115C8×D61—21no—
116C8×D61—21no—
117C8×D61C2×D411yescharacteristic
118C8×D61C2×D411yescharacteristic
119C8×D61#4111yescharacteristic
120C8×D61#4111yescharacteristic
121#11758187—22no—
122#11758187—22no—
123C16×C61—21no—
124C16×C61C22⋊C411yescharacteristic
125C16×C61C22⋊C411yescharacteristic
126#11758185—21no—
127#11758185C22⋊C411yescharacteristic
128#11758185C22⋊C411yescharacteristic
129C22×D61—21no—
130C22×D61#13111yescharacteristic
131C2×#6923—22no—
132C2×#6923—22no—
133C2×#6923—42no—
134Q8×C61C4×C811yescharacteristic
135D4×C61—21no—
136D4×C61C4×C811yescharacteristic
137C2×C4×C61—21no—
138C2×C4×C61C2×C4211yescharacteristic
139C22⋊D61—21no—
140C22⋊D61—21no—
141C22⋊D61—21no—
142C2×Dic61—21no—
143C2×Dic61#13111yescharacteristic
144D244—21no—
145D244C4×C811yescharacteristic
146C4×D61—21no—
147C4×D61—21no—
148C4×D61—21no—
149C4×D61C4×D411yescharacteristic
150C4×D61C4×D411yescharacteristic
151C4×D61C22×C811yescharacteristic
152C4×D61C22×C811yescharacteristic
153Dic122—21no—
154Dic122C4×C811yescharacteristic
155#92420—22no—
156#92420—22no—
157C8×C61—21no—
158C8×C61C2×C22⋊C411yescharacteristic
159C8×C61#11711yescharacteristic
160#92418—21no—
161#92418C4×D411yescharacteristic
162#92418C4×D411yescharacteristic
163#12615—611nomaximal, Sylow
164C22×C61—21no—
165C22×C61#40511yescharacteristic
166C2×D61—22no—
167C2×D61—21no—
168C2×D61—42no—
169C2×D61C8×D411yescharacteristic
170C2×D61C8×D411yescharacteristic
171#6923—42no—
172#6923—42no—
173C4×C61—21no—
174C4×C61C4×C22⋊C411yescharacteristic
175C4×C61C2×C4×C811yescharacteristic
176Dic61—21no—
177Dic61C8×D411yescharacteristic
178Dic61C8×D411yescharacteristic
179C2×#504—611no—
180C2×#350—611no—
181#2108—611no—
182C2×#346—611no—
183#1764—611no—
184#1379—611no—
185#1376—611no—
186C2×C61—21no—
187C2×C61—41no—
188C2×C61C8×C22⋊C411yescharacteristic
189D61—21no—
190D61—41no—
191D61#217112yes—
192C2×#131—611no—
193#504—611no—
194#504—611no—
195#504—611no—
196#504—1221no—
197#504—1221no—
198#504#692311yescharacteristic, complemented
199C2×M32—611no—
200C2×M32—611no—
201C2×M32—1221no—
202C22×C16—611no—
203C22×C16—611no—
204C22×C16—1221no—
205C2×#104—611no—
206#416—611no—
207#405—611no—
208C2×C4×C8—611no—
209#350—612no—
210#350—612no—
211#346—1221no—
212#346—1221no—
213#346—1221no—
214C4×C16—1221no—
215#341—611no—
216#339—611no—
217C61#1261511yescharacteristic, complemented, Sylow
218C2×#41—611no—
219#131—611no—
220#131—611no—
221#131—611no—
222#131—1221no—
223#131—1221no—
224#131C2×#692311yescharacteristic
225C2×M16—611no—
226C2×M16—611no—
227C2×M16—1221no—
228C22×C8—611no—
229C22×C8—611no—
230C22×C8—1221no—
231#117—611no—
232C2×C42—611no—
233M32—21no—
234M32—612no—
235M32—611no—
236M32—1221no—
237M32—1221no—
238M32—1221no—
239M32—1221no—
240M32—1221no—
241M32C2×#692311yescharacteristic
242C2×C16—21no—
243C2×C16—611no—
244C2×C16—611no—
245C2×C16—611no—
246C2×C16—611no—
247C2×C16—611no—
248C2×C16—612no—
249C2×C16—1221no—
250C2×C16—1221no—
251C2×C16—1221no—
252C2×C16—1221no—
253C2×C16—1221no—
254C2×C16—1221no—
255C2×C16—1221no—
256C2×C16C2×#692311yescharacteristic
257#104—612no—
258#104—612no—
259#103—612no—
260#102—612no—
261#97—1221no—
262C4×C8—1221no—
263C4×C8—1221no—
264C4×C8—1221no—
265#41—611no—
266#41—611no—
267#41—611no—
268#41—1221no—
269#41—1221no—
270#41C4×#692311yescharacteristic
271C2×Q8—611no—
272C2×D4—611no—
273C2×D4—1221no—
274C22×C4—611no—
275C22×C4—1221no—
276C22×C4—1221no—
277M16—21no—
278M16—612no—
279M16—611no—
280M16—1221no—
281M16—1221no—
282M16—1221no—
283M16—1221no—
284M16—1221no—
285M16C4×#692311yescharacteristic
286C2×C8—21no—
287C2×C8—611no—
288C2×C8—611no—
289C2×C8—611no—
290C2×C8—611no—
291C2×C8—611no—
292C2×C8—612no—
293C2×C8—1221no—
294C2×C8—1221no—
295C2×C8—1221no—
296C2×C8—1221no—
297C2×C8—1221no—
298C2×C8—1221no—
299C2×C8—1221no—
300C2×C8C22×#692311yescharacteristic
301C4⋊C4—612no—
302C22⋊C4—1221no—
303C42—612no—
304C42—1221no—
305C42—1221no—
306C16—21no—
307C16—611no—
308C16—611no—
309C16—1222no—
310C16—1222no—
311C16—1221no—
312C16C22⋊#692311yescharacteristic
313C16C22⋊#692311yescharacteristic
314C23—611no—
315C23—1221no—
316Q8—611no—
317Q8—1221no—
318Q8C8×#692311yescharacteristic
319D4—21no—
320D4—611no—
321D4—1221no—
322D4—1221no—
323D4—1221no—
324D4—1221no—
325D4C8×#692311yescharacteristic
326C2×C4—21no—
327C2×C4—611no—
328C2×C4—611no—
329C2×C4—611no—
330C2×C4—611no—
331C2×C4—611no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—1222no—
337C2×C4—1222no—
338C2×C4—2442no—
339C2×C4C2×C4×#692311yescharacteristic
340C8—21no—
341C8—611no—
342C8—611no—
343C8—1222no—
344C8—1222no—
345C8—1221no—
346C8C2×C22⋊#692311yescharacteristic
347C8#1451985611yescharacteristic
348C22—21no—
349C22—611no—
350C22—611no—
351C22—1222no—
352C22—1221no—
353C22—2442no—
354C22#1684072511yescharacteristic
355C4—21no—
356C4—611no—
357C4—611no—
358C4—1221no—
359C4—2442no—
360C4—2442no—
361C4C4×C22⋊#692311yescharacteristic
362C4C2×C8×#692311yescharacteristic
363C2—21no—
364C2—41no—
365C2—612no—
366C2—1221no—
367C2—2441no—
368C2C8×C22⋊#692311yescharacteristic
subgroupG/H
centerC8C2×C22⋊#6923
commutatorC4×C61C2×C4×C8
FrattiniC2×C8C22×#6923
FittingC61×#504C4
socleC2×C61C8×C22⋊C4
prime radical#41×D61C2×C4
cosocleC2×C8×D61C23
hypercenter#504#6923
hypocenterC61#12615
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C8 ◁ C2×C16 ◁ #504

Complements

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

NH ≅ G/Ntype
2. #21462027C2semidirect
3. C2×#16840649C2semidirect
5. #21460875C2semidirect
6. #21460862C2semidirect
14. #16840661C4semidirect
15. #16840660C4semidirect
24. #16840180C4semidirect
25. #16840179C4semidirect
27. #16840178C4semidirect
32. C61×#504C4semidirect
198. #504#6923semidirect
217. C61#12615semidirect

Maximal subgroups

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

subgroupindex
D61⋊#3502
#214620272
C2×#168406492
#214615932
#214608752
#214608622
#504×D612
#1261561