Finite Group Databasebeta

← #30595367

Subgroups — #30595367

Order 15616.

516 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
1C4×#14519844C211yesmaximal, characteristic
2C4×#14519844C211yesmaximal, characteristic
3#21460638C212yesmaximal
4#21460637C212yesmaximal
5C4×#14519776C211yesmaximal, characteristic
6C2×#14519844—21no—
7C2×#14519844—21no—
8C2×C4×#92420—21no—
9C2×C4×#92420—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519776C411yescharacteristic
13C2×C4×Dic122—21no—
14#16839666—21no—
15#16839661C2211yescharacteristic
16#16839659—21no—
17#16839658C2211yescharacteristic
18#16839631C411yescharacteristic
19C4×#11758196—21no—
20C4×C4⋊Dic61C411yescharacteristic
21C42×Dic61C2211yescharacteristic
22C4×C4⋊C4×C61C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25#14519844—24no—
26#14519844—24no—
27C4×#92420—42no—
28C4×#92420—42no—
29C22×Dic122—21no—
30#14519776—22no—
31#14519776C814yescomplemented
32C4×Dic122—42no—
33C4×Dic122—42no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×C4×Dic61—21no—
42C2×C4×Dic61C2×C411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61C2311yescharacteristic
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51C2×C4⋊C4×C61C2×C411yescharacteristic
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C42×C61—21no—
54C2×C42×C61C2×C411yescharacteristic
55#95×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C22×C411yescharacteristic
61C22×Dic61—21no—
62C22×Dic61—21no—
63C22×Dic61C22⋊C411yescharacteristic
64C22×Dic61C22⋊C411yescharacteristic
65C22×Dic61C2×D411yescharacteristic
66C22×Dic61C2×D411yescharacteristic
67C2×Dic122—24no—
68C2×Dic122—42no—
69C2×Dic122—42no—
70C2×#92420—24no—
71C2×#92420—24no—
72C2×#92420—42no—
73C2×#92420—42no—
74C2×#92420—42no—
75C2×#92420—42no—
76C4⋊C4×C61—21no—
77C4⋊C4×C61—41no—
78C4⋊C4×C61C2×C812yes—
79C42×C61—22no—
80C42×C61—42no—
81C4⋊Dic61—21no—
82C4⋊Dic61—41no—
83C4⋊Dic61—41no—
84C4⋊Dic61—41no—
85C4⋊Dic61C2×C812yes—
86#11758196—24no—
87#11758196—42no—
88#11758196—42no—
89#11758196—41no—
90#11758196—41no—
91C4×Dic61—22no—
92C4×Dic61—22no—
93C4×Dic61—41no—
94C4×Dic61—42no—
95C4×Dic61C2×C812yes—
96C4×Dic61M1612yes—
97C4×Dic61D812yes—
98C4×Dic61SD1612yes—
99C4×Dic61SD1612yes—
100C4×Dic61Q1612yes—
101C23×C61C2×C22⋊C411yescharacteristic
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—22no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61#10112yes—
114C2×C4×C61#10212yes—
115C2×C4×C61#10312yes—
116C2×C4×C61C22×C811yescharacteristic
117C2×C4×C61C2×M1611yescharacteristic
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—22no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61C22⋊C812yes—
129C2×Dic61C22⋊C812yes—
130C2×Dic61#10212yes—
131C2×Dic61#10312yes—
132C2×Dic61#10412yes—
133C2×Dic61#10412yes—
134C2×Dic61C2×D811yescharacteristic
135C2×Dic61C2×SD1611yescharacteristic
136C2×Dic61C2×SD1611yescharacteristic
137C2×Dic61C2×Q1611yescharacteristic
138Dic122—48no—
139#92420—44no—
140#92420—44no—
141#7570—611nomaximal, Sylow
142C22×C61C2×C22⋊C811yescharacteristic
143C22×C61#41011yescharacteristic
144C22×C61C2×#10111yescharacteristic
145C22×C61C2×#10211yescharacteristic
146C22×C61C2×#10311yescharacteristic
147C22×C61C2×#10411yescharacteristic
148C22×C61C2×#10411yescharacteristic
149C4×C61—21no—
150C4×C61—21no—
151C4×C61—42no—
152C4×C61—41no—
153C4×C61—81no—
154C4×C61#33214yes—
155Dic61—21no—
156Dic61—21no—
157Dic61—21no—
158Dic61—21no—
159Dic61—42no—
160Dic61—81no—
161Dic61D4⋊C814yes—
162Dic61Q8⋊C814yes—
163C4×C4⋊Q8—611no—
164C4×C4⋊C8—611no—
165C4×C4⋊C8—611no—
166#1271—612no—
167#1271—612no—
168C2×C61#146111yescharacteristic
169C2×C61C2×D4⋊C811yescharacteristic
170C2×C61C2×Q8⋊C811yescharacteristic
171C2×C61#150211yescharacteristic
172C2×C61#150311yescharacteristic
173C2×C61#152611yescharacteristic
174C2×C61C2×#33211yescharacteristic
175C2×C4⋊Q8—611no—
176C2×C4×Q8—1221no—
177C2×C4⋊C8—1221no—
178C2×C4⋊C8—1221no—
179C2×C4×C8—1221no—
180C2×C4×C8—1221no—
181#391—1221no—
182#389—611no—
183#389—611no—
184#389—1221no—
185#384—611no—
186C4×C4⋊C4—611no—
187C4×C4⋊C4—1221no—
188C4×C4⋊C4#692311yescharacteristic
189C43—611no—
190#336—612no—
191#336—612no—
192C61#757011yescharacteristic, complemented, Sylow
193C22×Q8—1221no—
194C22×C8—1222no—
195C22×C8—1222no—
196C4⋊Q8—614no—
197C4⋊Q8—1222no—
198C4×Q8—2442no—
199C4×Q8—2442no—
200C2×C4⋊C4—611no—
201C2×C4⋊C4—611no—
202C2×C4⋊C4—1221no—
203C2×C4⋊C4—1221no—
204C2×C4⋊C4—1221no—
205C2×C4⋊C4—1221no—
206C2×C4⋊C4—1221no—
207C2×C4⋊C4C2×#692311yescharacteristic
208C2×C4⋊C4C2×#692311yescharacteristic
209C2×C42—21no—
210C2×C42—611no—
211C2×C42—611no—
212C2×C42—611no—
213C2×C42—611no—
214C2×C42—611no—
215C2×C42—611no—
216C2×C42—1221no—
217C2×C42C2×#692311yescharacteristic
218C4⋊C8—1224no—
219C4⋊C8—1224no—
220C4×C8—2442no—
221C4×C8—2442no—
222#95—21no—
223#95—1221no—
224#95—1221no—
225#95—1221no—
226C2×Q8—1224no—
227C2×Q8—2442no—
228C2×Q8—2442no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—611no—
232C22×C4—611no—
233C22×C4—611no—
234C22×C4—611no—
235C22×C4—1221no—
236C22×C4—1221no—
237C22×C4C22⋊#692311yescharacteristic
238C22×C4C22⋊#692311yescharacteristic
239C22×C4C22×#692311yescharacteristic
240C2×C8—1224no—
241C2×C8—1224no—
242C2×C8—2442no—
243C2×C8—2442no—
244C2×C8—2442no—
245C2×C8—2442no—
246C4⋊C4—21no—
247C4⋊C4—41no—
248C4⋊C4—612no—
249C4⋊C4—1224no—
250C4⋊C4—1221no—
251C4⋊C4—2441no—
252C4⋊C4—2442no—
253C4⋊C4—2442no—
254C4⋊C4—2441no—
255C4⋊C4—2441no—
256C4⋊C4—2441no—
257C4⋊C4—2441no—
258C4⋊C4D61⋊C812yes—
259C42—22no—
260C42—42no—
261C42—612no—
262C42—612no—
263C42—612no—
264C42—612no—
265C42—612no—
266C42—612no—
267C42—1222no—
268C42—1222no—
269C42—2441no—
270C42—2442no—
271C23C2×C22⋊#692311yescharacteristic
272Q8—2448no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—22no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—612no—
285C2×C4—612no—
286C2×C4—612no—
287C2×C4—612no—
288C2×C4—612no—
289C2×C4—612no—
290C2×C4—611no—
291C2×C4—611no—
292C2×C4—611no—
293C2×C4—611no—
294C2×C4—1221no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—1221no—
298C2×C4—1222no—
299C2×C4—2441no—
300C2×C4—2441no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4#1451983812yes—
305C2×C4#1451983912yes—
306C2×C4#1451984012yes—
307C2×C4C2×D61⋊C811yescharacteristic
308C2×C4D61⋊M1611yescharacteristic
309C8—2444no—
310C8—2444no—
311C22D61⋊(C22⋊C8)11yescharacteristic
312C22#1684074111yescharacteristic
313C22C2×#1451983811yescharacteristic
314C22C2×#1451983911yescharacteristic
315C22C2×#1451984011yescharacteristic
316C22D61⋊#10411yescharacteristic
317C22D61⋊#10411yescharacteristic
318C4—21no—
319C4—21no—
320C4—41no—
321C4—42no—
322C4—81no—
323C4—614no—
324C4—614no—
325C4—1221no—
326C4—1221no—
327C4—1221no—
328C4—1221no—
329C4—4881no—
330C4—2442no—
331C4#1684062114yes—
332C2#2146106111yescharacteristic
333C2D61⋊(D4⋊C8)11yescharacteristic
334C2D61⋊(Q8⋊C8)11yescharacteristic
335C2#2146119811yescharacteristic
336C2#2146120111yescharacteristic
337C2#2146127611yescharacteristic
338C2C2×#1684062111yescharacteristic
subgroupG/H
centerC22×C4C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC4×C4⋊C4×C61C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC4×C4⋊C4#6923
hypocenterC61#7570
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
31. #14519776C8semidirect
192. C61#7570semidirect

Maximal subgroups

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

subgroupindex
C4×#145198442
#214606382
#214606372
C4×#145197762
#757061