Finite Group Databasebeta

← #30606480

Subgroups — #30606480

Order 15616.

420 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462047C211yesmaximal, characteristic
2C2×#16840653C211yesmaximal, characteristic, complemented
3C2×#16840652C211yesmaximal, characteristic, complemented
4#21461555C211yesmaximal, characteristic
5#21460859C211yesmaximal, characteristic, complemented
6#21460859C211yesmaximal, characteristic, complemented
7C2×M32×D61C211yesmaximal, characteristic
8C2×#14519852C2211yescharacteristic
9C2×#14519852C2211yescharacteristic
10D61⋊(C22⋊C8)C411yescharacteristic
11C2×#14519831C2211yescharacteristic
12C2×#14519831C2211yescharacteristic
13C4×C22⋊#6923C411yescharacteristic
14#16840657C412yescomplemented
15C22⋊#11758187C412yescomplemented
16#16840653—22no—
17#16840652—22no—
18(C2×#6923)⋊C8C411yescharacteristic
19(C2×#6923)⋊C8C411yescharacteristic
20C22×C8×D61C2211yescharacteristic
21C2×#14519717C411yescharacteristic, complemented
22C2×#14519716C2211yescharacteristic
23C2×#14519716C2211yescharacteristic
24M32×D61—22no—
25M32×D61—22no—
26C2×C16×D61C411yescharacteristic, complemented
27C2×C16×D61C411yescharacteristic, complemented
28C2×M32×C61C411yescharacteristic, complemented
29C2×D61⋊C8C2×C411yescharacteristic
30C2×D61⋊C8C2×C411yescharacteristic
31C2×C22⋊#6923—21no—
32C2×C4×#6923C2×C411yescharacteristic
33C2×C4×#6923C2×C411yescharacteristic
34#14519852—21no—
35#14519852—21no—
36#14519852—21no—
37#14519852—21no—
38C2×#11758187C2×C412yes—
39C2×#11758187C2×C412yes—
40#14519834—21no—
41C22⋊#92420—21no—
42#14519831—21no—
43#14519831—21no—
44#14519831—21no—
45#14519831—21no—
46(C2×#6923)⋊C4—21no—
47C22×C4×D61C2×C411yescharacteristic
48C22×#92418C2×C411yescharacteristic
49C2×C8×D61—21no—
50C2×C8×D61—21no—
51C2×C8×D61—21no—
52C2×C8×D61—21no—
53C2×C8×D61C2×C411yescharacteristic
54C2×C8×D61C2×C411yescharacteristic
55C2×C8×D61C2×C411yescharacteristic
56C2×C8×D61C2311yescharacteristic
57#14519717—22no—
58#14519716—21no—
59#14519716—21no—
60#14519716D412yes—
61#14519716D412yes—
62C2×#11758185C2×C411yescharacteristic
63C2×#11758185C2×C411yescharacteristic
64C16×D61—22no—
65C16×D61—22no—
66C22×C8×C61C2×C411yescharacteristic
67M32×C61—22no—
68C2×C16×C61C2×C411yescharacteristic
69C2×C16×C61C2×C411yescharacteristic
70C23×D61M1611yescharacteristic
71C22×#6923—21no—
72C22×#6923—21no—
73C22×C4×C61C4211yescharacteristic
74C22×Dic61M1611yescharacteristic
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61C4211yescharacteristic
80C2×C4×D61M1611yescharacteristic
81C2×C4×D61M1611yescharacteristic
82C2×C4×D61C22×C411yescharacteristic
83C22⋊#6923—42no—
84C2×#92420—21no—
85C2×#92420—21no—
86C4×#6923—21no—
87C4×#6923—21no—
88C4×#6923—21no—
89C4×#6923—21no—
90D61⋊C8—21no—
91D61⋊C8—21no—
92D61⋊C8—21no—
93D61⋊C8—21no—
94C2×C8×C61—21no—
95C2×C8×C61—21no—
96C2×C8×C61C4211yescharacteristic
97C2×C8×C61C22×C411yescharacteristic
98C2×#92418—21no—
99C2×#92418—21no—
100C2×#92418C4211yescharacteristic
101C2×#92418C22×C411yescharacteristic
102C8×D61—21no—
103C8×D61—21no—
104C8×D61—21no—
105C8×D61—21no—
106C8×D61—21no—
107C8×D61—21no—
108C8×D61C2×D411yescharacteristic
109C8×D61C2×D411yescharacteristic
110C8×D61#4111yescharacteristic
111C8×D61#4111yescharacteristic
112#11758187—22no—
113#11758187—22no—
114C16×C61—21no—
115C16×C61C22⋊C412yescomplemented
116#11758185—21no—
117#11758185C22⋊C412yescomplemented
118C23×C61#9711yescharacteristic
119C22×D61—22no—
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—41no—
123C22×D61#9711yescharacteristic
124C22×D61C2×M1611yescharacteristic
125C2×#6923—41no—
126C2×#6923—41no—
127C2×#6923—41no—
128C2×#6923—41no—
129C2×#6923—41no—
130C2×#6923—41no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61#9711yescharacteristic
134C2×C4×C61C2×C4211yescharacteristic
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61#9711yescharacteristic
138C2×Dic61C2×M1611yescharacteristic
139C4×D61—21no—
140C4×D61—21no—
141C4×D61—21no—
142C4×D61—21no—
143C4×D61—21no—
144C4×D61—21no—
145C4×D61C4×D411yescharacteristic
146C4×D61C4×D411yescharacteristic
147C4×D61#13111yescharacteristic
148C4×D61#13111yescharacteristic
149#92420—41no—
150#92420—41no—
151C8×C61—21no—
152C8×C61C2×C22⋊C411yescharacteristic
153C8×C61#11711yescharacteristic
154#92418—21no—
155#92418C4×D411yescharacteristic
156#92418C4×D411yescharacteristic
157#12616—611nomaximal, Sylow
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61C2×#9711yescharacteristic
162C2×D61—21no—
163C2×D61—21no—
164C2×D61—21no—
165C2×D61—21no—
166C2×D61—42no—
167C2×D61—42no—
168C2×D61#34712yescomplemented
169C2×D61#43511yescharacteristic
170C2×D61#43511yescharacteristic
171#6923—81no—
172#6923—81no—
173C4×C61—21no—
174C4×C61C4×C22⋊C411yescharacteristic
175C4×C61#40511yescharacteristic
176Dic61—21no—
177Dic61#43511yescharacteristic
178Dic61#43511yescharacteristic
179C22×M32—611no—
180#2112—611no—
181C2×#347—611no—
182C2×#347—611no—
183#1752—611no—
184#1375—611no—
185#1375—611no—
186C2×C61—41no—
187C2×C61#175211yescharacteristic
188C2×C61C2×#34711yescharacteristic
189C2×C61#211011yescharacteristic
190D61—21no—
191D61—21no—
192D61—22no—
193C23×C8—611no—
194C2×M32—611no—
195C2×M32—611no—
196C2×M32—611no—
197C2×M32—611no—
198C2×M32—611no—
199C2×M32—1222no—
200C2×M32—1222no—
201C2×M32#692311yescharacteristic, complemented
202C22×C16—611no—
203C22×C16—611no—
204C2×C22⋊C8—611no—
205C2×#97—611no—
206C2×#97—611no—
207C4×C22⋊C4—611no—
208C22⋊C16—612no—
209C22⋊C16—612no—
210#347—1222no—
211#347—1222no—
212#336—611no—
213#336—611no—
214C61#1261611yescharacteristic, complemented, Sylow
215C23×C4—611no—
216C22×C8—611no—
217C22×C8—611no—
218C22×C8—611no—
219C22×C8—611no—
220C22×C8—611no—
221C22×C8—611no—
222C22×C8—611no—
223C22×C8—1221no—
224C22×C8—1221no—
225C22×C8—1221no—
226C22×C8—1221no—
227C22×C8C2×#692311yescharacteristic
228C2×C22⋊C4—1221no—
229C2×C42—611no—
230C2×C42—611no—
231M32—22no—
232M32—612no—
233M32—612no—
234M32—1221no—
235M32—1221no—
236M32—1222no—
237M32—1221no—
238M32—1221no—
239M32—1221no—
240M32—1221no—
241C2×C16—611no—
242C2×C16—612no—
243C2×C16—612no—
244C2×C16—611no—
245C2×C16—1222no—
246C2×C16—1222no—
247C2×C16C2×#692311yescharacteristic
248C2×C16C2×#692311yescharacteristic
249C22⋊C8—1221no—
250C22⋊C8—1221no—
251#97—1221no—
252#97—1221no—
253#97—1221no—
254#97—1221no—
255#95—1221no—
256C24—611no—
257C22×C4—611no—
258C22×C4—611no—
259C22×C4—611no—
260C22×C4—611no—
261C22×C4—611no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4—1221no—
265C22×C4—1221no—
266C22×C4—1221no—
267C22×C4—1221no—
268C22×C4C4×#692311yescharacteristic
269C2×C8—21no—
270C2×C8—21no—
271C2×C8—611no—
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×C8—1221no—
286C2×C8—1221no—
287C2×C8—1221no—
288C2×C8—1221no—
289C2×C8—1221no—
290C2×C8—1221no—
291C2×C8C4×#692311yescharacteristic
292C2×C8C22×#692311yescharacteristic
293C22⋊C4—2442no—
294C42—1221no—
295C42—1221no—
296C42—1221no—
297C42—1221no—
298C16—21no—
299C16—612no—
300C16—1222no—
301C16—1222no—
302C16—1221no—
303C16C22⋊#692312yescomplemented
304C23—611no—
305C23—611no—
306C23—1222no—
307C23—1221no—
308C23—1221no—
309C23—2441no—
310C23#1451983111yescharacteristic
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—611no—
314C2×C4—611no—
315C2×C4—611no—
316C2×C4—611no—
317C2×C4—611no—
318C2×C4—611no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4—2441no—
333C2×C4#1451983111yescharacteristic
334C2×C4C2×C4×#692311yescharacteristic
335C8—21no—
336C8—611no—
337C8—611no—
338C8—1221no—
339C8—2441no—
340C8—2441no—
341C8C2×C22⋊#692311yescharacteristic
342C8#1451985611yescharacteristic
343C22—21no—
344C22—21no—
345C22—21no—
346C22—612no—
347C22—611no—
348C22—611no—
349C22—1221no—
350C22—1221no—
351C22—1221no—
352C22—1221no—
353C22—2442no—
354C22—2442no—
355C22C2×#1451983111yescharacteristic
356C4—21no—
357C4—611no—
358C4—611no—
359C4—1221no—
360C4—4881no—
361C4—4881no—
362C4C4×C22⋊#692311yescharacteristic
363C4#1684072511yescharacteristic
364C2—41no—
365C2—1221no—
366C2—1221no—
367C2—1222no—
368C2#2146155511yescharacteristic
369C2#2146203411yescharacteristic
370C2#2146203911yescharacteristic
subgroupG/H
centerC2×C4C2×C4×#6923
commutatorC2×C4×C61C2×C42
FrattiniC2×C8C22×#6923
FittingC2×M32×C61C4
socleC22×C61C2×#97
prime radicalC23×D61M16
cosocleC2×C8×D61C23
hypercenterC2×M32#6923
hypocenterC61#12616
LCSG ▷ C2×C4×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×M32

Complements

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

NH ≅ G/Ntype
2. C2×#16840653C2semidirect
3. C2×#16840652C2semidirect
5. #21460859C2semidirect
6. #21460859C2semidirect
14. #16840657C4semidirect
15. C22⋊#11758187C4semidirect
21. C2×#14519717C4semidirect
26. C2×C16×D61C4semidirect
27. C2×C16×D61C4semidirect
28. C2×M32×C61C4semidirect
115. C16×C61C22⋊C4semidirect
117. #11758185C22⋊C4semidirect
168. C2×D61#347semidirect
201. C2×M32#6923semidirect
214. C61#12616semidirect
303. C16C22⋊#6923semidirect

Maximal subgroups

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

subgroupindex
#214620472
C2×#168406532
C2×#168406522
#214615552
#214608592
C2×M32×D612
#1261661