Finite Group Databasebeta

← #30602152

Subgroups — #30602152

Order 15616.

490 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#21461736C211yesmaximal, characteristic
2#21461533C211yesmaximal, characteristic
3#21460655C212yesmaximal
4#21460655C212yesmaximal
5#21448390C211yesmaximal, characteristic
6C2×C4⋊#92420C2212yes—
7C2×C4×#92420C2212yes—
8#16840628—21no—
9#16840628—21no—
10#16840628—21no—
11#16840628—21no—
12C2×#14519776C411yescharacteristic
13C2×#14519742—21no—
14#16839666—21no—
15#16839660C411yescharacteristic
16#16839657—21no—
17#16839631C411yescharacteristic
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×#92420Q814yescomplemented
28C22×Dic122—21no—
29#14519776—22no—
30#14519776C814yescomplemented
31#14519742—44no—
32C2×C4⋊Dic61C2×C411yescharacteristic
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×C4×Dic61—21no—
39C2×C4×Dic61—21no—
40C2×C4×Dic61C2×C411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61C2311yescharacteristic
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49C2×C4⋊C4×C61—21no—
50C2×C4⋊C4×C61C2×C411yescharacteristic
51C2×C4⋊C4×C61C2×C411yescharacteristic
52C2×C42×C61C2×C411yescharacteristic
53#95×C61—21no—
54C22×C4×C61—21no—
55C22×C4×C61—21no—
56C22×C4×C61C22⋊C411yescharacteristic
57C22×C4×C61C22⋊C411yescharacteristic
58C22×C4×C61C22×C411yescharacteristic
59C22×Dic61—21no—
60C22×Dic61—21no—
61C22×Dic61C22⋊C411yescharacteristic
62C22×Dic61C22⋊C411yescharacteristic
63C22×Dic61C2×D411yescharacteristic
64C22×Dic61C2×D411yescharacteristic
65C2×Dic122—24no—
66C2×Dic122—42no—
67C2×Dic122—42no—
68C2×#92420—24no—
69C2×#92420—42no—
70C2×#92420—42no—
71C2×#92420—42no—
72C2×#92420—42no—
73C2×#92420—42no—
74C4⋊C4×C61—21no—
75C4⋊C4×C61—22no—
76C4⋊C4×C61—42no—
77C4⋊C4×C61C2×C812yes—
78C42×C61—22no—
79C4⋊Dic61—21no—
80C4⋊Dic61—22no—
81C4⋊Dic61C2×C812yes—
82#11758196—24no—
83#11758196—42no—
84#11758196—42no—
85#11758196—42no—
86C4×Dic61—22no—
87C4×Dic61—22no—
88C4×Dic61—41no—
89C4×Dic61—41no—
90C4×Dic61—42no—
91C4×Dic61—42no—
92C4×Dic61C2×C812yes—
93C4×Dic61M1612yes—
94C4×Dic61C2×Q812yes—
95C4×Dic61#4112yes—
96C23×C61C2×C22⋊C411yescharacteristic
97C2×C4×C61—22no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61C4×Q812yes—
110C2×C4×C61C22×C811yescharacteristic
111C2×C4×C61C2×M1611yescharacteristic
112C2×C4×C61#13112yes—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—22no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61C22⋊C812yes—
126C2×Dic61C22⋊C812yes—
127C2×Dic61C22⋊Q812yes—
128C2×Dic61#12411yescharacteristic
129C2×Dic61C4⋊Q811yescharacteristic
130C2×Dic61AGL(1,ℤ/8)12yes—
131C2×Dic61#13712yes—
132Dic122—48no—
133#92420—44no—
134#92420—82no—
135#9873—611nomaximal, Sylow
136C22×C61#39111yescharacteristic
137C22×C61C2×C22⋊C811yescharacteristic
138C22×C61#40811yescharacteristic
139C22×C61#41811yescharacteristic
140C22×C61#41911yescharacteristic
141C22×C61#42111yescharacteristic
142C22×C61#42111yescharacteristic
143C4×C61—42no—
144C4×C61—41no—
145C4×C61—41no—
146C4×C61—81no—
147C4×C61C8×Q812yes—
148C4×C61#44612yes—
149Dic61—22no—
150Dic61—22no—
151Dic61—22no—
152Dic61—42no—
153Dic61—81no—
154Dic61#48912yes—
155Dic61#50112yes—
156C4×C4⋊Q8—611no—
157#1831—611no—
158#1744—611no—
159#1279—612no—
160#1279—612no—
161C2×C61#147811yescharacteristic
162C2×C61#147911yescharacteristic
163C2×C61#149611yescharacteristic
164C2×C61#149711yescharacteristic
165C2×C61#198411yescharacteristic
166C2×C61#199311yescharacteristic
167C2×C61#199511yescharacteristic
168C2×C4⋊Q8—611no—
169C2×C4×Q8—1221no—
170C2×C4⋊C8—612no—
171C2×C4×C8—612no—
172#391—1221no—
173#389—611no—
174#389—1221no—
175#389#692311yescharacteristic
176#384—611no—
177C4×C4⋊C4—611no—
178C4×C4⋊C4—611no—
179C4×C4⋊C4—1221no—
180C43—611no—
181#336—1221no—
182#336—1221no—
183#336—1221no—
184#336—1221no—
185C61#987311yescharacteristic, complemented, Sylow
186C22×Q8—1221no—
187C22×C8—1222no—
188C22×C8—1222no—
189C4⋊Q8—614no—
190C4⋊Q8—1222no—
191C4×Q8—2444no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—611no—
194C2×C4⋊C4—611no—
195C2×C4⋊C4—1221no—
196C2×C4⋊C4—1221no—
197C2×C4⋊C4—1221no—
198C2×C4⋊C4—1221no—
199C2×C4⋊C4C2×#692311yescharacteristic
200C2×C4⋊C4C2×#692311yescharacteristic
201C2×C42—611no—
202C2×C42—611no—
203C2×C42—611no—
204C2×C42—611no—
205C2×C42—611no—
206C2×C42—611no—
207C2×C42—1221no—
208C2×C42—1221no—
209C2×C42C2×#692311yescharacteristic
210C4⋊C8—1224no—
211C4×C8—614no—
212C4×C8—1222no—
213#95—21no—
214#95—1221no—
215#95—1221no—
216#95—1221no—
217C2×Q8—1224no—
218C2×Q8—2442no—
219C2×Q8—2442no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—611no—
223C22×C4—611no—
224C22×C4—611no—
225C22×C4—611no—
226C22×C4—1221no—
227C22×C4—1221no—
228C22×C4C22⋊#692311yescharacteristic
229C22×C4C22⋊#692311yescharacteristic
230C22×C4C22×#692311yescharacteristic
231C2×C8—1224no—
232C2×C8—2442no—
233C2×C8—2442no—
234C2×C8—2442no—
235C2×C8—2442no—
236C2×C8—2442no—
237C4⋊C4—21no—
238C4⋊C4—22no—
239C4⋊C4—42no—
240C4⋊C4—612no—
241C4⋊C4—1224no—
242C4⋊C4—1221no—
243C4⋊C4—1222no—
244C4⋊C4—2442no—
245C4⋊C4—2442no—
246C4⋊C4—2442no—
247C4⋊C4D61⋊C812yes—
248C42—22no—
249C42—612no—
250C42—612no—
251C42—612no—
252C42—612no—
253C42—1222no—
254C42—1222no—
255C42—2441no—
256C42—2441no—
257C42—2442no—
258C42—2442no—
259C23C2×C22⋊#692311yescharacteristic
260Q8—2448no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—611no—
274C2×C4—611no—
275C2×C4—612no—
276C2×C4—612no—
277C2×C4—612no—
278C2×C4—612no—
279C2×C4—612no—
280C2×C4—1221no—
281C2×C4—1221no—
282C2×C4—1221no—
283C2×C4—1221no—
284C2×C4—1221no—
285C2×C4—1221no—
286C2×C4—1222no—
287C2×C4—2441no—
288C2×C4—2441no—
289C2×C4—2441no—
290C2×C4—2441no—
291C2×C4—2441no—
292C2×C4Q8×#692312yes—
293C2×C4C2×D61⋊C811yescharacteristic
294C2×C4D61⋊M1611yescharacteristic
295C2×C4#1451986412yes—
296C8—4882no—
297C8—2444no—
298C22(C2×#6923)⋊Q811yescharacteristic
299C22D61⋊(C22⋊C8)11yescharacteristic
300C22#1684073511yescharacteristic
301C22#1684075411yescharacteristic
302C22#1684075511yescharacteristic
303C22#1684075911yescharacteristic
304C22#1684075911yescharacteristic
305C4—42no—
306C4—41no—
307C4—41no—
308C4—81no—
309C4—612no—
310C4—612no—
311C4—1222no—
312C4—1222no—
313C4—1222no—
314C4—4881no—
315C4—2442no—
316C4#1684081112yes—
317C4#1684081412yes—
318C2#2146111911yescharacteristic
319C2#2146112211yescharacteristic
320C2#2146117811yescharacteristic
321C2#2146118111yescharacteristic
322C2#2146199011yescharacteristic
323C2#2146200311yescharacteristic
324C2#2146200611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#389C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#389#6923
hypocenterC61#9873
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
27. C4×#92420Q8semidirect
30. #14519776C8semidirect
185. C61#9873semidirect

Maximal subgroups

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

subgroupindex
#214617362
#214615332
#214606552
#214483902
#987361