Finite Group Databasebeta

← #30606496

Subgroups — #30606496

Order 15616.

382 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462787C211yesmaximal, characteristic
2#21462039C211yesmaximal, characteristic, complemented
3C2×#16840652C211yesmaximal, characteristic, complemented
4#21461597C211yesmaximal, characteristic
5#21460868C211yesmaximal, characteristic, complemented
6#21460865C211yesmaximal, characteristic, complemented
7#21447445C211yesmaximal, characteristic
8#16840821—22no—
9#16840821C412yescomplemented
10#16840820C412yescomplemented
11C2×#14519852—21no—
12C2×#14519852C2211yescharacteristic
13D61⋊M32—21no—
14D61⋊M32C2211yescharacteristic
15D61⋊#104C411yescharacteristic
16#16840752C411yescharacteristic
17#16840725C2211yescharacteristic
18C2×#14519831C2211yescharacteristic
19#16840653—21no—
20#16840652—22no—
21#16840652—21no—
22#16840637C411yescharacteristic
23#16840634C411yescharacteristic
24#131×D61C2211yescharacteristic
25C2×#14519716C2211yescharacteristic
26M32×D61C2211yescharacteristic
27#16839547C411yescharacteristic, complemented
28#16839546C411yescharacteristic, complemented
29#16839545C411yescharacteristic, complemented
30C61×#350C411yescharacteristic, complemented
31D61⋊M16C2×C411yescharacteristic
32C2×D61⋊C8C2×C411yescharacteristic
33#14519856C2×C411yescharacteristic
34C2×C4×#6923C2×C411yescharacteristic
35#14519852—21no—
36#14519852—22no—
37#14519852D411yescharacteristic
38#14519852D411yescharacteristic
39#14519852D412yes—
40#14519851—22no—
41#14519851C2×C412yes—
42D61⋊C16—21no—
43D61⋊C16—22no—
44C2×#11758187—22no—
45C2×#11758187C2×C412yes—
46#14519842—21no—
47#14519841—21no—
48#14519840—21no—
49#14519839—21no—
50#14519831—21no—
51#14519831—21no—
52#14519831—21no—
53C8×#6923—21no—
54#41×D61C2×C411yescharacteristic
55#14519785—21no—
56#14519785C2×C411yescharacteristic
57#14519784C2×C411yescharacteristic
58#14519783—21no—
59#14519783C2×C411yescharacteristic
60M16×D61—21no—
61M16×D61C2×C411yescharacteristic
62C2×C8×D61—21no—
63C2×C8×D61C2311yescharacteristic
64#14519717C2×C411yescharacteristic
65#14519716—21no—
66#14519716—21no—
67#14519716—21no—
68C2×#11758185C2×C411yescharacteristic
69C16×D61—21no—
70#131×C61C2×C411yescharacteristic
71M32×C61C2×C411yescharacteristic
72C2×C16×C61C2×C411yescharacteristic
73C22×#6923—21no—
74#41×C61C4211yescharacteristic
75#11758226M1611yescharacteristic
76Q8×D61M1611yescharacteristic
77#11758224—21no—
78#11758224M1611yescharacteristic
79D4×D61—21no—
80D4×D61M1611yescharacteristic
81#11758222—21no—
82#11758222C4211yescharacteristic
83C2×C4×D61—21no—
84C2×C4×D61C22×C411yescharacteristic
85C22⋊#6923—21no—
86#11758217—21no—
87C2×#92420—21no—
88C4⋊#6923—21no—
89C4×#6923—21no—
90C4×#6923—21no—
91C4×#6923—21no—
92#11758213—21no—
93D61⋊C8—21no—
94D61⋊C8—21no—
95D61⋊C8—21no—
96M16×C61—21no—
97M16×C61C4211yescharacteristic
98C2×C8×C61—21no—
99C2×C8×C61C22×C411yescharacteristic
100#11758194—21no—
101#11758194C4211yescharacteristic
102C2×#92418—21no—
103C2×#92418C22×C411yescharacteristic
104#11758189—21no—
105#11758189—21no—
106#11758189—21no—
107C8×D61—21no—
108C8×D61—21no—
109C8×D61—21no—
110C8×D61C2×D411yescharacteristic
111C8×D61C2×D411yescharacteristic
112C8×D61#4111yescharacteristic
113C8×D61#4111yescharacteristic
114#11758187—22no—
115#11758187C22⋊C412yes—
116#11758187C22⋊C412yes—
117C16×C61—21no—
118C16×C61—21no—
119#11758185—21no—
120#11758185—21no—
121C22×D61—21no—
122C22×D61#13111yescharacteristic
123C2×#6923—41no—
124C2×#6923—41no—
125C2×#6923—81no—
126Q8×C61#9711yescharacteristic
127D4×C61—21no—
128D4×C61#9711yescharacteristic
129C2×C4×C61—21no—
130C2×C4×C61C2×C4211yescharacteristic
131C22⋊D61—21no—
132C22⋊D61—21no—
133C22⋊D61—21no—
134C2×Dic61—21no—
135C2×Dic61#13111yescharacteristic
136D244—21no—
137D244#9711yescharacteristic
138C4×D61—21no—
139C4×D61—21no—
140C4×D61—21no—
141C4×D61C4×D411yescharacteristic
142C4×D61C4×D411yescharacteristic
143C4×D61C2×M1611yescharacteristic
144C4×D61C2×M1611yescharacteristic
145Dic122—21no—
146Dic122#9711yescharacteristic
147#92420—41no—
148#92420—41no—
149C8×C61—21no—
150C8×C61C4×D411yescharacteristic
151C8×C61C4×D411yescharacteristic
152#92418—21no—
153#92418C2×C22⋊C411yescharacteristic
154#92418#11711yescharacteristic
155#12618—611nomaximal, Sylow
156C22×C61—21no—
157C22×C61#40511yescharacteristic
158C2×D61—21no—
159C2×D61—41no—
160C2×D61—81no—
161C2×D61#43511yescharacteristic
162C2×D61#43511yescharacteristic
163#6923—81no—
164#6923—81no—
165C4×C61—21no—
166C4×C61C4×C22⋊C411yescharacteristic
167C4×C61C2×#9711yescharacteristic
168Dic61—21no—
169Dic61#43511yescharacteristic
170Dic61#43511yescharacteristic
171#3407—611no—
172#2117—611no—
173#2110—611no—
174C2×#347—611no—
175#1765—611no—
176#1378—611no—
177#1377—611no—
178C2×C61—21no—
179C2×C61—41no—
180C2×C61#175211yescharacteristic
181D61—21no—
182D61—21no—
183D61—41no—
184C2×#131—611no—
185#504—612no—
186#504—612no—
187#504—1222no—
188C2×M32—611no—
189C2×M32—611no—
190C2×M32—611no—
191C2×M32—611no—
192C2×M32—1221no—
193C2×M32—1221no—
194C2×#104—611no—
195#416—611no—
196#405—611no—
197C2×#97—611no—
198#350—611no—
199#350—611no—
200#350—611no—
201#350#692311yescharacteristic, complemented
202#347—1222no—
203#347—1221no—
204#347—1221no—
205#341—611no—
206#339—611no—
207C61#1261811yescharacteristic, complemented, Sylow
208C2×#41—611no—
209#131—611no—
210#131—611no—
211#131—611no—
212#131—1221no—
213#131—1221no—
214#131C2×#692311yescharacteristic
215C2×M16—611no—
216C2×M16—611no—
217C2×M16—1221no—
218C22×C8—611no—
219C22×C8—611no—
220C22×C8—1221no—
221#117—611no—
222C2×C42—611no—
223M32—611no—
224M32—611no—
225M32—612no—
226M32—612no—
227M32—611no—
228M32—1221no—
229M32—1221no—
230M32—1221no—
231M32—1222no—
232M32—1222no—
233M32—1221no—
234M32C2×#692311yescharacteristic
235C2×C16—612no—
236C2×C16—611no—
237C2×C16—1221no—
238C2×C16—1222no—
239C2×C16—1222no—
240C2×C16—1221no—
241C2×C16C2×#692311yescharacteristic
242#104—1221no—
243#104—1221no—
244#103—1221no—
245#102—1221no—
246#97—1221no—
247#97—1221no—
248#97—1221no—
249C4×C8—1221no—
250#41—611no—
251#41—611no—
252#41—611no—
253#41—1221no—
254#41—1221no—
255#41C4×#692311yescharacteristic
256C2×Q8—611no—
257C2×D4—611no—
258C2×D4—1221no—
259C22×C4—611no—
260C22×C4—1221no—
261C22×C4—1221no—
262M16—21no—
263M16—611no—
264M16—1221no—
265M16—1221no—
266M16—1221no—
267M16—1221no—
268M16—1221no—
269M16—1221no—
270M16C4×#692311yescharacteristic
271C2×C8—21no—
272C2×C8—611no—
273C2×C8—611no—
274C2×C8—611no—
275C2×C8—611no—
276C2×C8—611no—
277C2×C8—1221no—
278C2×C8—1221no—
279C2×C8—1221no—
280C2×C8—1221no—
281C2×C8—1221no—
282C2×C8—1221no—
283C2×C8—1221no—
284C2×C8—1221no—
285C2×C8C22×#692311yescharacteristic
286C4⋊C4—1221no—
287C22⋊C4—1221no—
288C42—1221no—
289C42—1221no—
290C42—1221no—
291C16—21no—
292C16—21no—
293C16—612no—
294C16—612no—
295C16—1222no—
296C16—1221no—
297C16—1221no—
298C23—611no—
299C23—1221no—
300Q8—611no—
301Q8—1221no—
302Q8#1451983111yescharacteristic
303D4—21no—
304D4—611no—
305D4—1221no—
306D4—1221no—
307D4—1221no—
308D4—1221no—
309D4#1451983111yescharacteristic
310C2×C4—21no—
311C2×C4—611no—
312C2×C4—611no—
313C2×C4—611no—
314C2×C4—611no—
315C2×C4—611no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—4881no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4C2×C4×#692311yescharacteristic
324C8—21no—
325C8—611no—
326C8—611no—
327C8—1221no—
328C8—2441no—
329C8—2441no—
330C8D4×#692311yescharacteristic
331C8D4×#692311yescharacteristic
332C22—21no—
333C22—611no—
334C22—611no—
335C22—1221no—
336C22—4881no—
337C22—2441no—
338C22#1684072811yescharacteristic
339C4—21no—
340C4—611no—
341C4—611no—
342C4—1221no—
343C4—4881no—
344C4—4881no—
345C4C22⋊C4×#692311yescharacteristic
346C4C2×#1451983111yescharacteristic
347C2—21no—
348C2—41no—
349C2—1221no—
350C2—1221no—
351C2—2441no—
352C2#2146155811yescharacteristic
subgroupG/H
centerC4C22⋊C4×#6923
commutatorC2×C4×C61C2×C42
FrattiniC2×C8C22×#6923
FittingC61×#350C4
socleC2×C61#1752
prime radical#41×D61C2×C4
cosocleC2×C8×D61C23
hypercenter#350#6923
hypocenterC61#12618
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C8 ◁ #350

Complements

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

NH ≅ G/Ntype
2. #21462039C2semidirect
3. C2×#16840652C2semidirect
5. #21460868C2semidirect
6. #21460865C2semidirect
9. #16840821C4semidirect
10. #16840820C4semidirect
27. #16839547C4semidirect
28. #16839546C4semidirect
29. #16839545C4semidirect
30. C61×#350C4semidirect
201. #350#6923semidirect
207. C61#12618semidirect

Maximal subgroups

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

subgroupindex
#214627872
#214620392
C2×#168406522
#214615972
#214608682
#214608652
#214474452
#1261861