Finite Group Databasebeta

← #30606489

Subgroups — #30606489

Order 15616.

382 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
1#21462062C211yesmaximal, characteristic
2#21462038C211yesmaximal, characteristic, complemented
3C2×#16840653C211yesmaximal, characteristic, complemented
4#21461597C211yesmaximal, characteristic
5#21460871C211yesmaximal, characteristic, complemented
6#21460865C211yesmaximal, characteristic, complemented
7#21458920C211yesmaximal, characteristic
8C2×#14519852C2211yescharacteristic
9D61⋊M32C2211yescharacteristic
10D61⋊#104C411yescharacteristic
11#16840752C411yescharacteristic
12#16840725C2211yescharacteristic
13C2×#14519831C2211yescharacteristic
14#16840661C412yescomplemented
15#16840660C412yescomplemented
16#16840653—21no—
17#16840653—21no—
18#16840653—21no—
19#16840652—21no—
20#16840637C411yescharacteristic
21#16840634C411yescharacteristic
22#131×D61C2211yescharacteristic
23#16840180—21no—
24#16840180C411yescharacteristic, complemented
25#16840179C411yescharacteristic, complemented
26#16840178—21no—
27#16840178C411yescharacteristic, complemented
28C2×#14519716—21no—
29C2×#14519716C2211yescharacteristic
30M32×D61—21no—
31M32×D61C2211yescharacteristic
32C61×#504C411yescharacteristic, complemented
33D61⋊M16C2×C411yescharacteristic
34C2×D61⋊C8C2×C411yescharacteristic
35#14519856C2×C411yescharacteristic
36C2×C4×#6923C2×C411yescharacteristic
37#14519852—21no—
38#14519852—21no—
39#14519852—21no—
40#14519851C2×C412yes—
41D61⋊C16—21no—
42C2×#11758187C2×C412yes—
43#14519842—21no—
44#14519841—21no—
45#14519840—21no—
46#14519839—21no—
47#14519831—21no—
48#14519831—21no—
49#14519831—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—
66#14519716D411yescharacteristic
67#14519716D411yescharacteristic
68#14519716D411yescharacteristic
69#14519716D411yescharacteristic
70C2×#11758185—21no—
71C2×#11758185C2×C411yescharacteristic
72C16×D61—21no—
73C16×D61—21no—
74C16×D61—21no—
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#11758226M1611yescharacteristic
83Q8×D61M1611yescharacteristic
84#11758224—21no—
85#11758224M1611yescharacteristic
86D4×D61—21no—
87D4×D61M1611yescharacteristic
88#11758222—21no—
89#11758222C4211yescharacteristic
90C2×C4×D61—21no—
91C2×C4×D61C22×C411yescharacteristic
92C22⋊#6923—21no—
93#11758217—21no—
94C2×#92420—21no—
95C4⋊#6923—21no—
96C4×#6923—21no—
97C4×#6923—21no—
98C4×#6923—21no—
99#11758213—21no—
100D61⋊C8—21no—
101D61⋊C8—21no—
102D61⋊C8—21no—
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—41no—
132C2×#6923—41no—
133C2×#6923—81no—
134Q8×C61#9711yescharacteristic
135D4×C61—21no—
136D4×C61#9711yescharacteristic
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—
145D244#9711yescharacteristic
146C4×D61—21no—
147C4×D61—21no—
148C4×D61—21no—
149C4×D61C4×D411yescharacteristic
150C4×D61C4×D411yescharacteristic
151C4×D61C2×M1611yescharacteristic
152C4×D61C2×M1611yescharacteristic
153Dic122—21no—
154Dic122#9711yescharacteristic
155#92420—41no—
156#92420—41no—
157C8×C61—21no—
158C8×C61C2×C22⋊C411yescharacteristic
159C8×C61#11711yescharacteristic
160#92418—21no—
161#92418C4×D411yescharacteristic
162#92418C4×D411yescharacteristic
163#12618—611nomaximal, Sylow
164C22×C61—21no—
165C22×C61#40511yescharacteristic
166C2×D61—21no—
167C2×D61—41no—
168C2×D61—81no—
169C2×D61#43511yescharacteristic
170C2×D61#43511yescharacteristic
171#6923—81no—
172#6923—81no—
173C4×C61—21no—
174C4×C61C4×C22⋊C411yescharacteristic
175C4×C61C2×#9711yescharacteristic
176Dic61—21no—
177Dic61#43511yescharacteristic
178Dic61#43511yescharacteristic
179#3407—611no—
180#2117—611no—
181#2110—611no—
182C2×#347—611no—
183#1765—611no—
184#1378—611no—
185#1377—611no—
186C2×C61—21no—
187C2×C61—41no—
188C2×C61#175211yescharacteristic
189D61—21no—
190D61—21no—
191D61—41no—
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—611no—
202C2×M32—611no—
203C2×M32—1221no—
204C2×M32—1221no—
205C2×#104—611no—
206#416—611no—
207#405—611no—
208C2×#97—611no—
209#350—612no—
210#350—612no—
211#347—1221no—
212#347—1221no—
213#347—1221no—
214#347—1221no—
215#341—611no—
216#339—611no—
217C61#1261811yescharacteristic, 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—611no—
235M32—611no—
236M32—611no—
237M32—611no—
238M32—612no—
239M32—611no—
240M32—1221no—
241M32—1221no—
242M32—1221no—
243M32—1221no—
244M32—1221no—
245M32—1221no—
246M32—1221no—
247M32C2×#692311yescharacteristic
248C2×C16—21no—
249C2×C16—611no—
250C2×C16—612no—
251C2×C16—1221no—
252C2×C16—1221no—
253C2×C16—1221no—
254C2×C16—1221no—
255C2×C16—1221no—
256C2×C16C2×#692311yescharacteristic
257#104—1221no—
258#104—1221no—
259#103—1221no—
260#102—1221no—
261#97—1221no—
262#97—1221no—
263#97—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—611no—
279M16—1221no—
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—1221no—
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—1221no—
302C22⋊C4—1221no—
303C42—1221no—
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—
318Q8#1451983111yescharacteristic
319D4—21no—
320D4—611no—
321D4—1221no—
322D4—1221no—
323D4—1221no—
324D4—1221no—
325D4#1451983111yescharacteristic
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—4881no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4C2×C4×#692311yescharacteristic
340C8—21no—
341C8—611no—
342C8—611no—
343C8—1221no—
344C8—2441no—
345C8—2441no—
346C8C2×C22⋊#692311yescharacteristic
347C8#1451985611yescharacteristic
348C22—21no—
349C22—611no—
350C22—611no—
351C22—1221no—
352C22—4881no—
353C22—2441no—
354C22#1684072511yescharacteristic
355C4—21no—
356C4—611no—
357C4—611no—
358C4—1221no—
359C4—4881no—
360C4—4881no—
361C4C4×C22⋊#692311yescharacteristic
362C4C2×#1451983111yescharacteristic
363C2—21no—
364C2—41no—
365C2—1221no—
366C2—1221no—
367C2—2441no—
368C2#2146155511yescharacteristic
subgroupG/H
centerC4C4×C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC2×C8C22×#6923
FittingC61×#504C4
socleC2×C61#1752
prime radical#41×D61C2×C4
cosocleC2×C8×D61C23
hypercenter#504#6923
hypocenterC61#12618
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C16 ◁ #504

Complements

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

NH ≅ G/Ntype
2. #21462038C2semidirect
3. C2×#16840653C2semidirect
5. #21460871C2semidirect
6. #21460865C2semidirect
14. #16840661C4semidirect
15. #16840660C4semidirect
24. #16840180C4semidirect
25. #16840179C4semidirect
27. #16840178C4semidirect
32. C61×#504C4semidirect
198. #504#6923semidirect
217. C61#12618semidirect

Maximal subgroups

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

subgroupindex
#214620622
#214620382
C2×#168406532
#214615972
#214608712
#214608652
#214589202
#1261861