Finite Group Databasebeta

← #30624098

Subgroups — #30624098

Order 15616.

706 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840821C212yesmaximal
2#21462156C212yesmaximal, complemented
3#21462155C214yesmaximal, complemented
4#21462152C212yesmaximal, complemented
5#21462151C211yesmaximal, characteristic, complemented
6D61⋊(C4⋊C16)C212yesmaximal, complemented
7C2×C4⋊#11758187C211yesmaximal, characteristic, complemented
8C4×#14519785C211yesmaximal, characteristic
9#16840821—28no—
10C2×#14519852C2214yes—
11C2×#14519851C2212yes—
12C2×D61⋊C16C2214yes—
13C22×#11758187C2212yes—
14#16840683C2214yes—
15#16840683C2214yes—
16C4⋊#11758187C2211yescharacteristic
17C4⋊#11758187C2211yescharacteristic
18C4⋊#11758187C2212yes—
19C4⋊#11758187C2212yes—
20C4⋊#11758187C2212yes—
21C2×#14519785C411yescharacteristic
22C2×#14519785C2211yescharacteristic
23C4×#11758222C411yescharacteristic
24#16839720C411yescharacteristic
25#16839720C2211yescharacteristic
26#16839719C412yes—
27#16839719C2212yes—
28C4×#11758189C412yes—
29C2×C4×#92418C2211yescharacteristic
30C4×C8×D61C2212yes—
31C4×M16×C61C411yescharacteristic
32#14519852—28no—
33#14519851—24no—
34D61⋊C16—28no—
35C2×#11758187—24no—
36C2×#11758187C2312yes—
37C2×#11758187C2312yes—
38C2×#11758187C2314yes—
39C2×#11758222C2×C411yescharacteristic
40#14519785—24no—
41#14519785D414yes—
42#14519785Q814yes—
43C2×#11758189C2×C412yes—
44C2×#11758189C2×C412yes—
45C22×#92418C2×C411yescharacteristic
46C22×#92418C2311yescharacteristic
47C2×C8×D61C2×C412yes—
48C2×C8×D61C2312yes—
49C4×Dic122C811yescharacteristic
50C4×Dic122C811yescharacteristic
51C4×D244C811yescharacteristic
52C4×D244C811yescharacteristic
53C4×C22⋊D61C812yes—
54C4×C22⋊D61C812yes—
55#14519736C2×C411yescharacteristic
56#14519734C2×C412yes—
57C42×D61C2×C412yes—
58#14519687C2×C412yes—
59#14519687C2×C412yes—
60C4×#92418C2×C411yescharacteristic
61C4×#92418C2×C411yescharacteristic
62C4×#92418C2311yescharacteristic
63C4×#92418C2311yescharacteristic
64C8×Dic61C2×C412yes—
65C8×Dic61C2312yes—
66C2×M16×C61C2×C411yescharacteristic
67C2×M16×C61C2×C411yescharacteristic
68C2×C42×C61C2×C411yescharacteristic
69#97×C61C2×C412yes—
70C4×C8×C61C2×C412yes—
71C22×C4×C61C2×C811yescharacteristic
72C22×C4×C61C2×C811yescharacteristic
73C22×C4×C61C22×C411yescharacteristic
74C2×C22⋊D61C2×C812yes—
75#11758222C4⋊C414yes—
76#11758222M1614yes—
77C2×D244C2×C811yescharacteristic
78C2×C4×D61C2×C812yes—
79C2×C4×D61C2×C812yes—
80C2×C4×D61C22×C412yes—
81C2×Dic122C2×C811yescharacteristic
82M16×C61—22no—
83M16×C61C4⋊C414yes—
84C2×C8×C61C22×C412yes—
85C2×C8×C61C22×C412yes—
86C42×C61C2×C811yescharacteristic
87C42×C61C2×C811yescharacteristic
88C42×C61C22×C411yescharacteristic
89C42×C61C22×C411yescharacteristic
90C22⋊Dic61C2×C812yes—
91#11758198C2×C812yes—
92#11758198C2×C812yes—
93C4⋊Dic61C2×C811yescharacteristic
94C4⋊Dic61C2×C811yescharacteristic
95#11758196C2×C812yes—
96#11758196C2×C812yes—
97C4×Dic61C2×C812yes—
98C4×Dic61C2×C812yes—
99C4×Dic61C22×C412yes—
100C2×#92418—22no—
101C2×#92418C22×C411yescharacteristic
102C2×#92418C22×C411yescharacteristic
103C2×#92418C22×C411yescharacteristic
104C2×#92418C2×D412yes—
105C2×#92418C2×Q812yes—
106C2×#92418C2411yescharacteristic
107#11758189—24no—
108#11758189C4⋊C418yes—
109C8×D61—24no—
110C8×D61C2×D414yes—
111C8×D61C2×Q814yes—
112#11758187—22no—
113#11758187—22no—
114#11758187—24no—
115C23×C61C22×C811yescharacteristic
116C22×D61C22×C812yes—
117C2×C4×C61—22no—
118C2×C4×C61—41no—
119C2×C4×C61C2×C4⋊C412yes—
120C2×C4×C61C22×C811yescharacteristic
121C2×C4×C61C22×C811yescharacteristic
122C2×C4×C61C22×C811yescharacteristic
123C2×C4×C61C22×C811yescharacteristic
124C2×C4×C61C22×C811yescharacteristic
125C2×C4×C61C2×M1612yes—
126C2×C4×C61C23×C411yescharacteristic
127C22⋊D61C4⋊C818yes—
128C2×Dic61C22×C812yes—
129C2×Dic61C22×C812yes—
130C2×Dic61C22×C812yes—
131D244C4⋊C814yes—
132C4×D61—24no—
133C4×D61—42no—
134C4×D61C2×C4⋊C414yes—
135C4×D61C2×M1614yes—
136Dic122C4⋊C814yes—
137C8×C61—22no—
138C8×C61C2×C4⋊C414yes—
139#92418—21no—
140#92418—21no—
141#92418C2×C4⋊C412yes—
142#92418C22×D411yescharacteristic
143#92418C22×Q811yescharacteristic
144#33398—611nomaximal, Sylow
145C22×C61—21no—
146C22×C61—21no—
147C22×C61C2×C4⋊C812yes—
148C22×C61C23×C811yescharacteristic
149C2×D61—22no—
150C2×D61—22no—
151C2×D61C2×C4⋊C814yes—
152C4×C61—21no—
153C4×C61—21no—
154C4×C61—21no—
155C4×C61C2×C4⋊C812yes—
156C4×C61#50412yescomplemented
157C4×C61C22×C4⋊C411yescharacteristic
158C4×C61C22×M1611yescharacteristic
159Dic61—22no—
160Dic61—22no—
161Dic61C2×C4⋊C814yes—
162C2×#504—612no—
163C4×#131—611no—
164#2151—614no—
165#2151—612no—
166#2150—611no—
167#2150—612no—
168C2×C4⋊C16—611no—
169C2×C4⋊C16—612no—
170C2×C61—22no—
171C2×C61C22×C4⋊C811yescharacteristic
172C2×C61C2×#50411yescharacteristic
173C2×C61#340711yescharacteristic
174D61—24no—
175C2×#131—611no—
176C2×#131—611no—
177C4×#41—611no—
178#504—1228no—
179C2×M32—612no—
180C2×M32—614no—
181C22×C16—612no—
182C22×C16—614no—
183#405—611no—
184#405—611no—
185#405—612no—
186#405—612no—
187C4×M16—612no—
188C4×M16#692311yescharacteristic
189C2×C4×C8—611no—
190C2×C4×C8—612no—
191C4⋊C16—611no—
192C4⋊C16—611no—
193C4⋊C16—612no—
194C4⋊C16—612no—
195C4⋊C16—614no—
196C4⋊C16—612no—
197C4⋊C16—614no—
198C61#3339811yescharacteristic, complemented, Sylow
199C2×#41—611no—
200#131—614no—
201#131—614no—
202#131—1224no—
203C2×M16—612no—
204C2×M16—612no—
205C2×M16C2×#692311yescharacteristic
206C2×M16C2×#692311yescharacteristic
207C22×C8—611no—
208C22×C8—612no—
209C22×C8—611no—
210C22×C8—612no—
211C4×Q8—611no—
212C4×Q8—611no—
213C4×D4—612no—
214C4×D4—612no—
215C4×D4—611no—
216C4×D4—611no—
217#117—611no—
218#117—612no—
219C2×C42—612no—
220C2×C42C2×#692311yescharacteristic
221M32—1224no—
222M32—1228no—
223C2×C16—612no—
224C2×C16—612no—
225C2×C16—614no—
226C2×C16—1224no—
227C2×C16—1228no—
228#97—612no—
229#97—612no—
230#97C2×#692312yes—
231C4×C8—612no—
232C4×C8—612no—
233C4×C8—611no—
234C4×C8—611no—
235C4×C8—611no—
236C4×C8—611no—
237C4×C8C2×#692312yes—
238#41—614no—
239#41—614no—
240C2×Q8—611no—
241C2×D4—612no—
242C2×D4—611no—
243C22×C4—612no—
244C22×C4—612no—
245C22×C4—612no—
246C22×C4D61⋊C811yescharacteristic
247C22×C4D61⋊C811yescharacteristic
248C22×C4C22×#692311yescharacteristic
249M16—22no—
250M16—618no—
251M16—1224no—
252M16C4⋊#692314yes—
253C2×C8—612no—
254C2×C8—612no—
255C2×C8—611no—
256C2×C8—611no—
257C2×C8—614no—
258C2×C8—614no—
259C2×C8—611no—
260C2×C8—611no—
261C2×C8—1224no—
262C2×C8—1222no—
263C2×C8C22×#692312yes—
264C2×C8C22×#692312yes—
265C4⋊C4—612no—
266C4⋊C4—612no—
267C4⋊C4—611no—
268C4⋊C4—611no—
269C22⋊C4—612no—
270C22⋊C4—612no—
271C22⋊C4—612no—
272C42—612no—
273C42—612no—
274C42—612no—
275C42D61⋊C811yescharacteristic
276C42D61⋊C811yescharacteristic
277C42C22×#692311yescharacteristic
278C42C22×#692311yescharacteristic
279C16—1222no—
280C16—1222no—
281C16—1224no—
282C23—612no—
283C23C2×D61⋊C811yescharacteristic
284Q8—614no—
285D4—618no—
286D4—614no—
287C2×C4—22no—
288C2×C4—41no—
289C2×C4—612no—
290C2×C4—614no—
291C2×C4—614no—
292C2×C4—612no—
293C2×C4—612no—
294C2×C4—1224no—
295C2×C4—2442no—
296C2×C4C2×C4⋊#692312yes—
297C2×C4C2×D61⋊C811yescharacteristic
298C2×C4C2×D61⋊C811yescharacteristic
299C2×C4C2×D61⋊C811yescharacteristic
300C2×C4C2×D61⋊C811yescharacteristic
301C2×C4C2×D61⋊C811yescharacteristic
302C2×C4D61⋊M1612yes—
303C2×C4C23×#692311yescharacteristic
304C8—22no—
305C8—612no—
306C8—611no—
307C8—611no—
308C8—1221no—
309C8—1221no—
310C8C2×C4⋊#692314yes—
311C22—21no—
312C22—21no—
313C22—614no—
314C22—1222no—
315C22—1222no—
316C22D61⋊(C4⋊C8)12yes—
317C22C22×D61⋊C811yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—614no—
322C4—1222no—
323C4—1222no—
324C4D61⋊(C4⋊C8)12yes—
325C4#1684082112yescomplemented
326C4C22×C4⋊#692311yescharacteristic
327C4C2×D61⋊M1611yescharacteristic
328C2—22no—
329C2—1224no—
330C2C2×D61⋊(C4⋊C8)11yescharacteristic
331C2C2×#1684082111yescharacteristic
332C2#2146278811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×#6923
commutator, socleC22×C61C23×C8
FittingC4×M16×C61C4
prime radicalC2×#11758222C2×C4
cosocleC2×#92418C24
hypercenterC4×M16#6923
hypocenterC61#33398
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
2. #21462156C2semidirect
3. #21462155C2semidirect
4. #21462152C2semidirect
5. #21462151C2semidirect
6. D61⋊(C4⋊C16)C2semidirect
7. C2×C4⋊#11758187C2semidirect
156. C4×C61#504semidirect
198. C61#33398semidirect
325. C4#16840821semidirect

Maximal subgroups

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

subgroupindex
C2×#168408212
#214621562
#214621552
#214621522
#214621512
D61⋊(C4⋊C16)2
C2×C4⋊#117581872
C4×#145197852
#3339861