Finite Group Databasebeta

← #30602133

Subgroups — #30602133

Order 15616.

460 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461605C211yesmaximal, characteristic
2C4×C4⋊#92420C211yesmaximal, characteristic
3#21460655C212yesmaximal
4#21460655C212yesmaximal
5#21448378C211yesmaximal, characteristic
6C2×C4⋊#92420—21no—
7C2×C4⋊#92420C2212yes—
8C2×#14519832—21no—
9C2×C4×#92420C2212yes—
10#16840628—21no—
11#16840628—21no—
12C2×#14519768C411yescharacteristic
13#16839660C411yescharacteristic
14#16839647—21no—
15#16839643—21no—
16#16839627C411yescharacteristic
17C4⋊C4×Dic61—21no—
18C4⋊C4×Dic61C2211yescharacteristic
19C4⋊C4×Dic61C2211yescharacteristic
20#16839613—21no—
21C42×Dic61C2211yescharacteristic
22C61×#389C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C4⋊#92420—24no—
26C4⋊#92420—22no—
27C4⋊#92420Q814yes—
28#14519832—42no—
29C4×#92420—24no—
30#14519768—22no—
31#14519768—22no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×C4×Dic61—21no—
38C2×C4×Dic61—21no—
39C2×C4×Dic61C2×C411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61C2311yescharacteristic
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50C2×C4⋊C4×C61—21no—
51C2×C4⋊C4×C61C2×C411yescharacteristic
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C42×C61C2×C411yescharacteristic
54#95×C61—21no—
55C22×C4×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61C22⋊C411yescharacteristic
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22×C411yescharacteristic
60C22×Dic61—21no—
61C22×Dic61—21no—
62C22×Dic61C22⋊C411yescharacteristic
63C22×Dic61C22⋊C411yescharacteristic
64C22×Dic61C2×D411yescharacteristic
65C22×Dic61C2×D411yescharacteristic
66C2×#92420—24no—
67C2×#92420—24no—
68C2×#92420—42no—
69C2×#92420—42no—
70C2×#92420—42no—
71C2×#92420—42no—
72C4⋊C4×C61—21no—
73C4⋊C4×C61—22no—
74C4⋊C4×C61—42no—
75C4⋊C4×C61M1612yes—
76C42×C61—22no—
77C4⋊Dic61—24no—
78C4⋊Dic61—21no—
79C4⋊Dic61—22no—
80C4⋊Dic61M1612yes—
81#11758196—24no—
82#11758196—42no—
83C4×Dic61—22no—
84C4×Dic61—21no—
85C4×Dic61—21no—
86C4×Dic61—22no—
87C4×Dic61—21no—
88C4×Dic61—21no—
89C4×Dic61—41no—
90C4×Dic61—42no—
91C4×Dic61—41no—
92C4×Dic61—41no—
93C4×Dic61C2×Q812yes—
94C4×Dic61#4112yes—
95C23×C61C2×C22⋊C411yescharacteristic
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—22no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—41no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61—41no—
107C2×C4×C61#10412yes—
108C2×C4×C61C4×Q812yes—
109C2×C4×C61C2×M1611yescharacteristic
110C2×C4×C61C2×M1611yescharacteristic
111C2×C4×C61#13112yes—
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—22no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61C22⋊Q812yes—
127C2×Dic61#12411yescharacteristic
128C2×Dic61C4⋊Q811yescharacteristic
129C2×Dic61#13512yes—
130C2×Dic61AGL(1,ℤ/8)11yescharacteristic
131C2×Dic61#13711yescharacteristic
132#92420—44no—
133#92420—44no—
134#9867—611nomaximal, Sylow
135C22×C61#39111yescharacteristic
136C22×C61#40711yescharacteristic
137C22×C61#40811yescharacteristic
138C22×C61#41611yescharacteristic
139C22×C61#41711yescharacteristic
140C22×C61C2×#10411yescharacteristic
141C22×C61#42111yescharacteristic
142C4×C61—22no—
143C4×C61—42no—
144C4×C61—41no—
145C4×C61—81no—
146C4×C61#44612yes—
147C4×C61#44612yes—
148Dic61—21no—
149Dic61—21no—
150Dic61—41no—
151Dic61—42no—
152Dic61—41no—
153Dic61—81no—
154Dic61#47812yes—
155Dic61#47912yes—
156C4×#125—611no—
157#1767—611no—
158C4×C4⋊C8—611no—
159#1279—612no—
160#1279—612no—
161C2×C61#148811yescharacteristic
162C2×C61#148911yescharacteristic
163C2×C61#149411yescharacteristic
164C2×C61#149511yescharacteristic
165C2×C61#198511yescharacteristic
166C2×C61#198611yescharacteristic
167C2×C61#198911yescharacteristic
168C2×#125—611no—
169C2×C4⋊C8—612no—
170C2×C4⋊C8—1221no—
171C2×#97—1221no—
172C2×C4×C8—612no—
173#389—611no—
174#389#692311yescharacteristic
175#387—1221no—
176#387—1221no—
177#382—611no—
178C4×C4⋊C4—611no—
179C4×C4⋊C4—611no—
180C4×C4⋊C4—1221no—
181C4×C4⋊C4—1221no—
182C43—611no—
183#336—1221no—
184#336—1221no—
185C61#986711yescharacteristic, complemented, Sylow
186C22×C8—1222no—
187C22×C8—1222no—
188#125—1222no—
189#125—1222no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—611no—
192C2×C4⋊C4—611no—
193C2×C4⋊C4—1221no—
194C2×C4⋊C4—1221no—
195C2×C4⋊C4—1221no—
196C2×C4⋊C4C2×#692311yescharacteristic
197C2×C4⋊C4C2×#692311yescharacteristic
198C2×C42—611no—
199C2×C42—611no—
200C2×C42—611no—
201C2×C42—611no—
202C2×C42—611no—
203C2×C42—611no—
204C2×C42—1221no—
205C2×C42—1221no—
206C2×C42C2×#692311yescharacteristic
207C4⋊C8—614no—
208C4⋊C8—1222no—
209C4⋊C8—1224no—
210#97—2442no—
211C4×C8—1224no—
212#95—21no—
213#95—1221no—
214#95—1221no—
215#95—1221no—
216#95—1221no—
217#95—1221no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—611no—
221C22×C4—611no—
222C22×C4—611no—
223C22×C4—611no—
224C22×C4—1221no—
225C22×C4—1221no—
226C22×C4C22⋊#692311yescharacteristic
227C22×C4C22⋊#692311yescharacteristic
228C22×C4C22×#692311yescharacteristic
229C2×C8—1224no—
230C2×C8—1224no—
231C2×C8—2442no—
232C2×C8—2442no—
233C2×C8—2442no—
234C2×C8—2442no—
235C4⋊C4—21no—
236C4⋊C4—22no—
237C4⋊C4—42no—
238C4⋊C4—612no—
239C4⋊C4—1224no—
240C4⋊C4—1224no—
241C4⋊C4—1221no—
242C4⋊C4—1222no—
243C4⋊C4—2442no—
244C4⋊C4#1175821312yes—
245C42—22no—
246C42—612no—
247C42—612no—
248C42—1221no—
249C42—1222no—
250C42—1221no—
251C42—1222no—
252C42—1221no—
253C42—1221no—
254C42—2441no—
255C42—2441no—
256C42—2441no—
257C42—2442no—
258C23C2×C22⋊#692311yescharacteristic
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—612no—
271C2×C4—612no—
272C2×C4—611no—
273C2×C4—611no—
274C2×C4—611no—
275C2×C4—611no—
276C2×C4—1221no—
277C2×C4—1221no—
278C2×C4—1221no—
279C2×C4—1221no—
280C2×C4—1222no—
281C2×C4—1221no—
282C2×C4—1221no—
283C2×C4—1221no—
284C2×C4—1221no—
285C2×C4—2441no—
286C2×C4—2441no—
287C2×C4—2441no—
288C2×C4—2441no—
289C2×C4—2441no—
290C2×C4#1451984112yes—
291C2×C4Q8×#692312yes—
292C2×C4D61⋊M1611yescharacteristic
293C2×C4C2×#1175821311yescharacteristic
294C2×C4#1451986412yes—
295C8—2444no—
296C8—2444no—
297C22(C2×#6923)⋊Q811yescharacteristic
298C22#1684073311yescharacteristic
299C22#1684073511yescharacteristic
300C22#1684075211yescharacteristic
301C22#1684075311yescharacteristic
302C22C2×#1451984111yescharacteristic
303C22#1684076111yescharacteristic
304C4—22no—
305C4—42no—
306C4—41no—
307C4—81no—
308C4—612no—
309C4—612no—
310C4—1221no—
311C4—1221no—
312C4—4881no—
313C4—2441no—
314C4—2442no—
315C4—2441no—
316C4#1684081212yes—
317C4#1684081412yes—
318C2#2146115311yescharacteristic
319C2#2146115511yescharacteristic
320C2#2146117011yescharacteristic
321C2#2146117611yescharacteristic
322C2#2146199211yescharacteristic
323C2#2146199511yescharacteristic
324C2#2146199911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#389C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#389#6923
hypocenterC61#9867
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
185. C61#9867semidirect

Maximal subgroups

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

subgroupindex
#214616052
C4×C4⋊#924202
#214606552
#214483782
#986761