Finite Group Databasebeta

← #29710941

Subgroups — #29710941

Order 15616.

766 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519777C211yesmaximal, characteristic
2#21447296C212yesmaximal
3#21447290C212yesmaximal
4#21447152C212yesmaximal
5#21447144C212yesmaximal
6#21445717C214yesmaximal
7#21445568C211yesmaximal, characteristic
8C4×C4⋊Q8×C61C211yesmaximal, characteristic
9C2×#14519777C2211yescharacteristic
10C2×C4×Dic122—21no—
11C2×#14519710C2214yes—
12C2×#14519708C2214yes—
13C2×#14519688C2212yes—
14#16839668—21no—
15#16839660—21no—
16#16839660C2212yes—
17#16839632C2211yescharacteristic
18C4×C4⋊Dic61—21no—
19C4×C4⋊Dic61C2212yes—
20#16839524C2214yes—
21#16839524C2214yes—
22#16839517C2212yes—
23#16839517C2212yes—
24C2×C4⋊Q8×C61C2211yescharacteristic
25C2×C4×Q8×C61—21no—
26C61×#391—21no—
27C61×#389—21no—
28C61×#389C2212yes—
29C61×#384C2211yescharacteristic
30C4×C4⋊C4×C61—21no—
31C4×C4⋊C4×C61C2212yes—
32C43×C61C2211yescharacteristic
33C22×Dic122—21no—
34C22×#92418C2314yes—
35#14519777—24no—
36C4×Dic122—44no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61C2312yes—
41C2×C4⋊Dic61C2312yes—
42C2×#11758196—22no—
43C2×C4×Dic61—22no—
44#14519710—28no—
45#14519708—28no—
46#14519688Q818yescomplemented
47#14519684—22no—
48#14519684—22no—
49C22×Q8×C61—21no—
50C4⋊Q8×C61—24no—
51C4×Q8×C61—44no—
52C2×C4⋊C4×C61—21no—
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61—21no—
55C2×C4⋊C4×C61—22no—
56C2×C4⋊C4×C61C2312yes—
57C2×C4⋊C4×C61C2312yes—
58C2×C42×C61—22no—
59C2×C42×C61D411yescharacteristic
60C2×C42×C61D411yescharacteristic
61C2×C42×C61D411yescharacteristic
62C2×C42×C61D411yescharacteristic
63C2×C42×C61C2311yescharacteristic
64C2×C42×C61C2311yescharacteristic
65C2×C42×C61C2311yescharacteristic
66#95×C61—22no—
67#95×C61—22no—
68C2×Q8×C61—24no—
69C2×Q8×C61—42no—
70C2×Q8×C61—42no—
71C22×C4×C61—22no—
72C22×C4×C61—22no—
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2411yescharacteristic
80C22×Dic61—22no—
81C22×Dic61—22no—
82C2×Dic122—24no—
83C2×Dic122—42no—
84C2×Dic122—42no—
85C4⋊C4×C61—24no—
86C4⋊C4×C61—22no—
87C4⋊C4×C61—24no—
88C4⋊C4×C61—42no—
89C4⋊C4×C61—44no—
90C4⋊C4×C61—42no—
91C4⋊C4×C61#4114yes—
92C42×C61—22no—
93C42×C61—22no—
94C42×C61—22no—
95C42×C61—22no—
96C42×C61—22no—
97C42×C61—22no—
98C42×C61—44no—
99C42×C61C2×Q814yes—
100C4⋊Dic61—24no—
101C4⋊Dic61—22no—
102C4⋊Dic61—24no—
103C4⋊Dic61—42no—
104C4⋊Dic61—42no—
105C4⋊Dic61#4114yes—
106#11758196—44no—
107C4×Dic61—44no—
108C2×#92418—24no—
109C2×#92418—24no—
110C2×#92418C2×Q818yes—
111C23×C61C22×D411yescharacteristic
112Q8×C61—48no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—24no—
126C2×C4×C61—42no—
127C2×C4×C61—42no—
128C2×C4×C61—42no—
129C2×C4×C61—42no—
130C2×C4×C61—42no—
131C2×C4×C61C4⋊Q812yes—
132C2×C4×C61C4⋊Q812yes—
133C2×C4×C61AGL(1,ℤ/8)12yes—
134C2×C4×C61AGL(1,ℤ/8)12yes—
135C2×C4×C61#13712yes—
136C2×C4×C61#13712yes—
137C2×C4×C61C22×Q812yes—
138C2×C4×C61C2×#4112yes—
139C2×C4×C61C2×#4112yes—
140C2×Dic61—24no—
141C2×Dic61—42no—
142C2×Dic61—42no—
143C2×Dic61—42no—
144C2×Dic61—42no—
145C2×Dic61—42no—
146Dic122—48no—
147#92418—28no—
148#23839—611nomaximal, Sylow
149C22×C61#52511yescharacteristic
150C22×C61#52511yescharacteristic
151C22×C61C2×C4⋊Q811yescharacteristic
152C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
153C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
154C22×C61C2×#13711yescharacteristic
155C22×C61C2×#13711yescharacteristic
156C4×C61—22no—
157C4×C61—22no—
158C4×C61—22no—
159C4×C61—22no—
160C4×C61—22no—
161C4×C61—22no—
162C4×C61—44no—
163C4×C61—82no—
164C4×C61#53314yes—
165Dic61—44no—
166Dic61—82no—
167C4×C4⋊Q8—611no—
168C4×C4⋊Q8D6111yescharacteristic
169#2084—612no—
170#2083—612no—
171#2058—612no—
172#2057—612no—
173#1776—614no—
174#1745—611no—
175C2×C61#239911yescharacteristic
176C2×C61#310911yescharacteristic
177C2×C61#311011yescharacteristic
178C2×C61#311211yescharacteristic
179C2×C61#311311yescharacteristic
180C2×C61#316511yescharacteristic
181C2×C61#316511yescharacteristic
182C2×C4⋊Q8—611no—
183C2×C4⋊Q8C2×D6111yescharacteristic
184C2×C4×Q8—21no—
185C2×C4×Q8—1221no—
186C2×#107—614no—
187C2×#106—614no—
188C2×#97—612no—
189#391—21no—
190#391—1221no—
191#389—21no—
192#389—612no—
193#389—1221no—
194#389C2×D6112yes—
195#384—611no—
196#384C2×D6111yescharacteristic
197C4×C4⋊C4—21no—
198C4×C4⋊C4—612no—
199C4×C4⋊C4—1221no—
200C4×C4⋊C4C2×D6112yes—
201C43C2×D6111yescharacteristic
202#340—614no—
203#340—614no—
204#336—612no—
205#336—612no—
206C61#2383911yescharacteristic, complemented, Sylow
207C22×Q8—21no—
208C22×Q8—1221no—
209C22×C8—614no—
210C4⋊Q8—24no—
211C4⋊Q8—1224no—
212C4×Q8—44no—
213C4×Q8—2444no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—22no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—612no—
219C2×C4⋊C4—612no—
220C2×C4⋊C4—1221no—
221C2×C4⋊C4—1221no—
222C2×C4⋊C4—1222no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4C22×D6112yes—
225C2×C4⋊C4C22×D6112yes—
226C2×C42—22no—
227C2×C42—1222no—
228C2×C42C22⋊D6111yescharacteristic
229C2×C42C22⋊D6111yescharacteristic
230C2×C42C22⋊D6111yescharacteristic
231C2×C42C22⋊D6111yescharacteristic
232C2×C42C22×D6111yescharacteristic
233C2×C42C22×D6111yescharacteristic
234C2×C42C22×D6111yescharacteristic
235#107—1228no—
236#106—1228no—
237#97—618no—
238#95—22no—
239#95—22no—
240#95—1222no—
241#95—1222no—
242C2×Q8—24no—
243C2×Q8—42no—
244C2×Q8—42no—
245C2×Q8—1224no—
246C2×Q8—2442no—
247C2×Q8—2442no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—1222no—
251C22×C4—1222no—
252C22×C4C2×C22⋊D6111yescharacteristic
253C22×C4C2×C22⋊D6111yescharacteristic
254C22×C4C2×C22⋊D6111yescharacteristic
255C22×C4C2×C22⋊D6111yescharacteristic
256C22×C4C2×C22⋊D6111yescharacteristic
257C22×C4C2×C22⋊D6111yescharacteristic
258C22×C4C23×D6111yescharacteristic
259C2×C8—618no—
260C2×C8—1224no—
261C2×C8—1224no—
262C4⋊C4—24no—
263C4⋊C4—22no—
264C4⋊C4—24no—
265C4⋊C4—42no—
266C4⋊C4—44no—
267C4⋊C4—42no—
268C4⋊C4—614no—
269C4⋊C4—1224no—
270C4⋊C4—1222no—
271C4⋊C4—1224no—
272C4⋊C4—2442no—
273C4⋊C4—2444no—
274C4⋊C4—2442no—
275C4⋊C4#1175822214yes—
276C42—22no—
277C42—22no—
278C42—22no—
279C42—22no—
280C42—22no—
281C42—22no—
282C42—44no—
283C42—2444no—
284C42Q8×D6114yes—
285C23C22×C22⋊D6111yescharacteristic
286Q8—48no—
287Q8—2448no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—24no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—1224no—
307C2×C4—2442no—
308C2×C4—2442no—
309C2×C4—2442no—
310C2×C4—2442no—
311C2×C4—2442no—
312C2×C4#1451977512yes—
313C2×C4#1451977512yes—
314C2×C4#1451980212yes—
315C2×C4#1451980312yes—
316C2×C4#1451980712yes—
317C2×C4#1451980812yes—
318C2×C4C2×Q8×D6112yes—
319C2×C4#41×D6112yes—
320C2×C4C2×#1175822212yes—
321C8—1228no—
322C22#1684026911yescharacteristic
323C22#1684027311yescharacteristic
324C22C2×#1451977511yescharacteristic
325C22C2×#1451980211yescharacteristic
326C22C2×#1451980311yescharacteristic
327C22C2×#1451980711yescharacteristic
328C22C2×#1451980811yescharacteristic
329C4—22no—
330C4—22no—
331C4—22no—
332C4—22no—
333C4—22no—
334C4—22no—
335C4—44no—
336C4—82no—
337C4—4882no—
338C4—2444no—
339C4#1684031614yes—
340C2#2144911011yescharacteristic
341C2#2145591011yescharacteristic
342C2#2145591411yescharacteristic
343C2#2145593711yescharacteristic
344C2#2145594911yescharacteristic
345C2#2145636111yescharacteristic
346C2#2145636611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC4×C4⋊Q8×C61C2
socle, prime radicalC23×C61C22×D4
hypercenterC4×C4⋊Q8D61
hypocenterC61#23839
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C43 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
46. #14519688Q8semidirect
206. C61#23839semidirect

Maximal subgroups

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

subgroupindex
C4×#145197772
#214472962
#214472902
#214471522
#214471442
#214457172
#214455682
C4×C4⋊Q8×C612
#2383961