Finite Group Databasebeta

← #30599228

Subgroups — #30599228

Order 15616.

680 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461673C211yesmaximal, characteristic
2C4×C22⋊#92420C211yesmaximal, characteristic
3#21460655C214yesmaximal, complemented
4C2×C4⋊C4×Dic61C211yesmaximal, characteristic
5C2×C4⋊#92420C2212yes—
6C2×C22⋊#92420—21no—
7C2×C22⋊#92420—21no—
8C2×C4×#92420C2212yes—
9#16840628—21no—
10#16840628—21no—
11C22×C4⋊Dic61C411yescharacteristic
12C22×C4×Dic61—21no—
13C22×C4×Dic61C2211yescharacteristic
14C4⋊C4×Dic61—21no—
15C4⋊C4×Dic61—21no—
16C4⋊C4×Dic61C412yes—
17C4⋊C4×Dic61C2212yes—
18C2×#14519684—21no—
19C22×C4⋊C4×C61C411yescharacteristic
20C22×#92420—22no—
21C22×#92420—22no—
22C4⋊#92420—24no—
23C22⋊#92420—24no—
24C22⋊#92420—42no—
25C4×#92420—24no—
26C23×Dic61—21no—
27C23×Dic61D411yescharacteristic
28C23×Dic61D411yescharacteristic
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61—22no—
31C2×C4⋊Dic61C814yescomplemented
32C2×C4⋊Dic61C2×C412yes—
33C2×C4×Dic61—24no—
34C2×C4×Dic61—22no—
35C2×C4×Dic61—22no—
36C2×C4×Dic61—42no—
37C2×C4×Dic61—42no—
38C2×C4×Dic61C2×C411yescharacteristic
39C2×C4×Dic61D411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61C2311yescharacteristic
42#14519684—22no—
43#14519684—22no—
44C23×C4×C61—21no—
45C23×C4×C61C2×C411yescharacteristic
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61—24no—
48C2×C4⋊C4×C61C2×C412yes—
49C24×C61C22⋊C411yescharacteristic
50C22×C4×C61—22no—
51C22×C4×C61—22no—
52C22×C4×C61—24no—
53C22×C4×C61—22no—
54C22×C4×C61—42no—
55C22×C4×C61—42no—
56C22×C4×C61C22⋊C411yescharacteristic
57C22×C4×C61C2×C812yes—
58C22×C4×C61M1612yes—
59C22×C4×C61C22×C411yescharacteristic
60C22×Dic61—22no—
61C22×Dic61—22no—
62C22×Dic61—24no—
63C22×Dic61—22no—
64C22×Dic61—22no—
65C22×Dic61—22no—
66C22×Dic61—41no—
67C22×Dic61—42no—
68C22×Dic61—42no—
69C22×Dic61C22⋊C411yescharacteristic
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61D812yes—
72C22×Dic61SD1612yes—
73C22×Dic61C2×D411yescharacteristic
74C22×Dic61C2×D411yescharacteristic
75C2×#92420—24no—
76C2×#92420—42no—
77C2×#92420—42no—
78C2×#92420—42no—
79C2×#92420—42no—
80C2×#92420—42no—
81C4⋊C4×C61—24no—
82C4⋊C4×C61—22no—
83C4⋊C4×C61M1614yes—
84C4⋊Dic61—24no—
85C4⋊Dic61—22no—
86C4⋊Dic61C2×C814yes—
87C4×Dic61—22no—
88C4×Dic61—22no—
89C4×Dic61—22no—
90C4×Dic61—44no—
91C4×Dic61—42no—
92C4×Dic61—42no—
93C4×Dic61#4114yes—
94C23×C61—21no—
95C23×C61—21no—
96C23×C61—21no—
97C23×C61—21no—
98C23×C61C22⋊C812yes—
99C23×C61#10212yes—
100C23×C61#10412yes—
101C23×C61C2×C22⋊C411yescharacteristic
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—24no—
105C2×C4×C61—24no—
106C2×C4×C61—24no—
107C2×C4×C61—48no—
108C2×C4×C61—42no—
109C2×C4×C61—42no—
110C2×C4×C61C22⋊C812yes—
111C2×C4×C61#11712yes—
112C2×C4×C61C22×C811yescharacteristic
113C2×C4×C61C2×M1612yes—
114C2×C4×C61C2×M1611yescharacteristic
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—24no—
120C2×Dic61—24no—
121C2×Dic61—21no—
122C2×Dic61—24no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—44no—
126C2×Dic61—48no—
127C2×Dic61—42no—
128C2×Dic61—42no—
129C2×Dic61#10212yes—
130C2×Dic61#12312yes—
131C2×Dic61#12312yes—
132C2×Dic61C2×D811yescharacteristic
133C2×Dic61C2×SD1611yescharacteristic
134C2×Dic61#13712yes—
135#92420—44no—
136#92420—82no—
137#8706—611nomaximal, Sylow
138C22×C61—22no—
139C22×C61—22no—
140C22×C61—22no—
141C22×C61—22no—
142C22×C61—22no—
143C22×C61—22no—
144C22×C61D4⋊C814yes—
145C22×C61#38111yescharacteristic
146C22×C61C2×C22⋊C811yescharacteristic
147C22×C61#40711yescharacteristic
148C22×C61C2×#10211yescharacteristic
149C22×C61#41911yescharacteristic
150C22×C61C2×#10411yescharacteristic
151C22×C61#42111yescharacteristic
152C4×C61—22no—
153C4×C61—44no—
154C4×C61#43112yes—
155C4×C61#43212yes—
156Dic61—22no—
157Dic61—22no—
158Dic61—41no—
159Dic61—44no—
160Dic61#48012yes—
161Dic61#48312yes—
162C2×C4×C4⋊C4—611no—
163#1797—611no—
164C4×C22⋊C8—611no—
165#1279—614no—
166C2×C61—24no—
167C2×C61C2×D4⋊C811yescharacteristic
168C2×C61#147911yescharacteristic
169C2×C61#148611yescharacteristic
170C2×C61#149111yescharacteristic
171C2×C61#181711yescharacteristic
172C2×C61#182311yescharacteristic
173C2×C61#182611yescharacteristic
174C22×C4⋊C4—611no—
175C22×C4⋊C4#692311yescharacteristic
176C22×C42—611no—
177C22×C42—1221no—
178C2×C4⋊C8—612no—
179C2×C22⋊C8—1221no—
180C2×C22⋊C8—1221no—
181C2×C4×C8—612no—
182C4×C4⋊C4—612no—
183C4×C4⋊C4—612no—
184C4×C4⋊C4—1221no—
185C4×C4⋊C4—1221no—
186C2×#95—1221no—
187#336—1221no—
188#336—1221no—
189C61#870611yescharacteristic, complemented, Sylow
190C23×C4—21no—
191C23×C4—611no—
192C23×C4—611no—
193C23×C4—1221no—
194C23×C4C2×#692311yescharacteristic
195C22×C8—1222no—
196C22×C8—1222no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—24no—
199C2×C4⋊C4—614no—
200C2×C4⋊C4—612no—
201C2×C4⋊C4—1222no—
202C2×C4⋊C4—1221no—
203C2×C4⋊C4C2×#692312yes—
204C2×C42—611no—
205C2×C42—611no—
206C2×C42—611no—
207C2×C42—611no—
208C2×C42—1224no—
209C2×C42—1222no—
210C2×C42—1222no—
211C2×C42—2442no—
212C2×C42—2442no—
213C4⋊C8—1224no—
214C22⋊C8—1224no—
215C22⋊C8—2442no—
216C4×C8—1224no—
217#95—1222no—
218#95—1222no—
219C24C22⋊#692311yescharacteristic
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—24no—
223C22×C4—22no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4—611no—
227C22×C4—612no—
228C22×C4—612no—
229C22×C4—611no—
230C22×C4—611no—
231C22×C4—611no—
232C22×C4—1222no—
233C22×C4—1222no—
234C22×C4—1222no—
235C22×C4—1224no—
236C22×C4—1222no—
237C22×C4—1222no—
238C22×C4—2441no—
239C22×C4—2442no—
240C22×C4—2442no—
241C22×C4D61⋊C812yes—
242C22×C4#1175821312yes—
243C22×C4C22⋊#692311yescharacteristic
244C22×C4C22×#692311yescharacteristic
245C2×C8—1224no—
246C2×C8—2442no—
247C2×C8—2442no—
248C2×C8—2442no—
249C2×C8—2442no—
250C2×C8—2442no—
251C4⋊C4—24no—
252C4⋊C4—22no—
253C4⋊C4—614no—
254C4⋊C4—1224no—
255C4⋊C4—1222no—
256C4⋊C4#1175821714yes—
257C42—614no—
258C42—1222no—
259C42—1222no—
260C42—1222no—
261C42—2442no—
262C42—2442no—
263C42—2444no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23#1451983412yes—
269C23#1451983912yes—
270C23#1451984212yes—
271C23C2×C22⋊#692311yescharacteristic
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—24no—
275C2×C4—24no—
276C2×C4—24no—
277C2×C4—48no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—612no—
281C2×C4—611no—
282C2×C4—611no—
283C2×C4—612no—
284C2×C4—612no—
285C2×C4—612no—
286C2×C4—1224no—
287C2×C4—1224no—
288C2×C4—1221no—
289C2×C4—1221no—
290C2×C4—1221no—
291C2×C4—1221no—
292C2×C4—1221no—
293C2×C4—1224no—
294C2×C4—1221no—
295C2×C4—1221no—
296C2×C4—2444no—
297C2×C4—2442no—
298C2×C4—2442no—
299C2×C4—2448no—
300C2×C4#1451983412yes—
301C2×C4#1451985612yes—
302C2×C4C2×D61⋊C811yescharacteristic
303C2×C4C2×#1175821712yes—
304C2×C4C2×#1175821311yescharacteristic
305C8—4882no—
306C8—2444no—
307C22—22no—
308C22—22no—
309C22—22no—
310C22—22no—
311C22—22no—
312C22—22no—
313C22#1684061014yes—
314C22#1684070511yescharacteristic
315C22C2×#1451983411yescharacteristic
316C22#1684073211yescharacteristic
317C22C2×#1451983911yescharacteristic
318C22#1684075511yescharacteristic
319C22C2×#1451984211yescharacteristic
320C22#1684076011yescharacteristic
321C4—22no—
322C4—44no—
323C4—612no—
324C4—612no—
325C4—1222no—
326C4—1222no—
327C4—2444no—
328C4—2441no—
329C4#1684077912yes—
330C4#1684078312yes—
331C2—24no—
332C2C2×#1684061011yescharacteristic
333C2#2146112311yescharacteristic
334C2#2146114411yescharacteristic
335C2#2146116111yescharacteristic
336C2#2146171011yescharacteristic
337C2#2146172211yescharacteristic
338C2#2146172611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#8706
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #21460655C2semidirect
31. C2×C4⋊Dic61C8semidirect
189. C61#8706semidirect

Maximal subgroups

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

subgroupindex
#214616732
C4×C22⋊#924202
#214606552
C2×C4⋊C4×Dic612
#870661