Finite Group Databasebeta

← #29578860

Subgroups — #29578860

Order 15616.

640 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21445799C211yesmaximal, characteristic
2#21445581C211yesmaximal, characteristic
3C2×#16839488C214yesmaximal
4C2×C61×#389C211yesmaximal, characteristic
5C2×C4⋊#92418—21no—
6C2×C22⋊#92418C2212yes—
7C2×C22⋊#92418C2212yes—
8C2×#14519688—21no—
9#16839517—21no—
10#16839517—21no—
11#16839488—28no—
12C22×C4⋊C4×C61C411yescharacteristic
13C22×C4⋊C4×C61C411yescharacteristic
14C22×C4⋊C4×C61C2212yes—
15C22×C42×C61C2211yescharacteristic
16C61×#389—21no—
17C61×#389—21no—
18C61×#389—21no—
19C61×#389—21no—
20C2×#95×C61C412yes—
21C22×#92418—22no—
22C22×#92418—22no—
23C4⋊#92418—42no—
24C22⋊#92418—22no—
25C22⋊#92418—24no—
26C22⋊#92418D414yes—
27#14519688—42no—
28C23×C4×C61C2×C411yescharacteristic
29C23×C4×C61C2×C412yes—
30C23×C4×C61C2×C411yescharacteristic
31C23×C4×C61C2×C412yes—
32C23×C4×C61C2311yescharacteristic
33C2×C4⋊C4×C61—21no—
34C2×C4⋊C4×C61—21no—
35C2×C4⋊C4×C61—24no—
36C2×C4⋊C4×C61—21no—
37C2×C4⋊C4×C61—21no—
38C2×C4⋊C4×C61—24no—
39C2×C4⋊C4×C61—22no—
40C2×C4⋊C4×C61—22no—
41C2×C4⋊C4×C61—24no—
42C2×C4⋊C4×C61—42no—
43C2×C42×C61—42no—
44C2×C42×C61D411yescharacteristic
45C2×C42×C61D411yescharacteristic
46C2×C42×C61D411yescharacteristic
47C2×C42×C61D411yescharacteristic
48#95×C61—22no—
49#95×C61—22no—
50C24×C61C22×C411yescharacteristic
51C22×C4×C61—22no—
52C22×C4×C61—22no—
53C22×C4×C61—22no—
54C22×C4×C61—22no—
55C22×C4×C61—24no—
56C22×C4×C61—22no—
57C22×C4×C61—22no—
58C22×C4×C61—24no—
59C22×C4×C61—22no—
60C22×C4×C61—22no—
61C22×C4×C61—24no—
62C22×C4×C61—41no—
63C22×C4×C61—41no—
64C22×C4×C61—41no—
65C22×C4×C61—42no—
66C22×C4×C61—42no—
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61M1614yes—
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×D412yes—
75C22×C4×C61#4112yes—
76C4⋊C4×C61—24no—
77C4⋊C4×C61—24no—
78C4⋊C4×C61—42no—
79C4⋊C4×C61—42no—
80C4⋊C4×C61—44no—
81C4⋊C4×C61—42no—
82C4⋊C4×C61—42no—
83C42×C61—22no—
84C42×C61—22no—
85C42×C61—41no—
86C42×C61—41no—
87C2×#92418—24no—
88C2×#92418—42no—
89C2×#92418—42no—
90C2×#92418—42no—
91C2×#92418—42no—
92C2×#92418—42no—
93C23×C61—21no—
94C23×C61—21no—
95C23×C61—21no—
96C23×C61—21no—
97C23×C61C2×C22⋊C411yescharacteristic
98C23×C61C4×D412yes—
99C23×C61C2×M1612yes—
100C23×C61#13112yes—
101C2×C4×C61—28no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—24no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—28no—
117C2×C4×C61—42no—
118C2×C4×C61—42no—
119C2×C4×C61—44no—
120C2×C4×C61—42no—
121C2×C4×C61—42no—
122C2×C4×C61—44no—
123C2×C4×C61—42no—
124C2×C4×C61—42no—
125C2×C4×C61—42no—
126C2×C4×C61—84no—
127C2×C4×C61#9912yes—
128C2×C4×C61#10112yes—
129C2×C4×C61#10112yes—
130C2×C4×C61#12112yes—
131C2×C4×C61#12411yescharacteristic
132C2×C4×C61#12711yescharacteristic
133#92418—44no—
134#92418—82no—
135#9654—611nomaximal, Sylow
136C22×C61—22no—
137C22×C61—22no—
138C22×C61—22no—
139C22×C61—22no—
140C22×C61—22no—
141C22×C61—22no—
142C22×C61#39011yescharacteristic
143C22×C61#40711yescharacteristic
144C22×C61#40811yescharacteristic
145C22×C61C2×#9911yescharacteristic
146C22×C61#41011yescharacteristic
147C22×C61C2×#10111yescharacteristic
148C22×C61C2×#10111yescharacteristic
149C22×C61#43514yes—
150C4×C61—22no—
151C4×C61—21no—
152C4×C61—21no—
153C4×C61—22no—
154C4×C61—22no—
155C4×C61—22no—
156C4×C61—44no—
157C4×C61—41no—
158C4×C61—82no—
159C2×#389D6111yescharacteristic
160#1797—611no—
161#1749—611no—
162C2×#324—614no—
163C2×C61—24no—
164C2×C61#146311yescharacteristic
165C2×C61#146711yescharacteristic
166C2×C61#147011yescharacteristic
167C2×C61#147211yescharacteristic
168C2×C61#195511yescharacteristic
169C2×C61#196411yescharacteristic
170C2×C61#196611yescharacteristic
171C22×C4⋊C4Dic6111yescharacteristic
172C22×C4⋊C4Dic6111yescharacteristic
173C22×C4⋊C4C2×D6112yes—
174C22×C42C2×D6111yescharacteristic
175C2×C4⋊C8—1221no—
176C2×C22⋊C8—612no—
177C2×C22⋊C8—612no—
178C2×#97—1221no—
179#389—21no—
180#389—21no—
181#389—21no—
182#389—21no—
183C2×#95Dic6112yes—
184#336—1221no—
185#336—1221no—
186#324—1228no—
187C61#965411yescharacteristic, complemented, Sylow
188C23×C4C2×Dic6112yes—
189C23×C4C2×Dic6111yescharacteristic
190C23×C4C2×Dic6111yescharacteristic
191C23×C4C2×Dic6112yes—
192C23×C4C22×D6111yescharacteristic
193C22×C8—1222no—
194C22×C8—1222no—
195C2×C4⋊C4—24no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—24no—
201C2×C4⋊C4—24no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4—22no—
204C2×C4⋊C4—42no—
205C2×C42—42no—
206C2×C42C22⋊D6111yescharacteristic
207C2×C42C22⋊D6111yescharacteristic
208C2×C42C22⋊D6111yescharacteristic
209C2×C42C22⋊D6111yescharacteristic
210C4⋊C8—2442no—
211C22⋊C8—614no—
212C22⋊C8—1222no—
213C22⋊C8—1224no—
214#97—2442no—
215#95—22no—
216#95—22no—
217C24C22×Dic6111yescharacteristic
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—24no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—24no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—24no—
229C22×C4—41no—
230C22×C4—41no—
231C22×C4—41no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4#1175819414yes—
235C22×C4C22⋊Dic6111yescharacteristic
236C22×C4C22⋊Dic6111yescharacteristic
237C22×C4C22⋊Dic6111yescharacteristic
238C22×C4C22⋊Dic6111yescharacteristic
239C22×C4D4×D6112yes—
240C22×C4#1175822412yes—
241C22×C4C2×C22⋊D6111yescharacteristic
242C22×C4C2×C22⋊D6111yescharacteristic
243C2×C8—1224no—
244C2×C8—2442no—
245C2×C8—2442no—
246C2×C8—2442no—
247C2×C8—2442no—
248C2×C8—2442no—
249C4⋊C4—24no—
250C4⋊C4—24no—
251C4⋊C4—42no—
252C4⋊C4—42no—
253C4⋊C4—44no—
254C4⋊C4—42no—
255C4⋊C4—42no—
256C42—22no—
257C42—22no—
258C42—41no—
259C42—41no—
260C23—21no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23C2×C22⋊Dic6111yescharacteristic
265C23D4×Dic6112yes—
266C23C2×#1175819412yes—
267C23#1451978412yes—
268C2×C4—28no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—24no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—28no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—44no—
287C2×C4—42no—
288C2×C4—44no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—84no—
294C2×C4#1451969212yes—
295C2×C4#1451969612yes—
296C2×C4#1451969612yes—
297C2×C4#1451974812yes—
298C2×C4#1451976411yescharacteristic
299C2×C4#1451977311yescharacteristic
300C8—4882no—
301C8—2444no—
302C22—22no—
303C22—22no—
304C22—22no—
305C22—22no—
306C22—22no—
307C22—22no—
308C22#1683966511yescharacteristic
309C22#1683972611yescharacteristic
310C22#1683972911yescharacteristic
311C22C2×#1451969211yescharacteristic
312C22#1683973611yescharacteristic
313C22C2×#1451969611yescharacteristic
314C22C2×#1451969611yescharacteristic
315C22#1683983414yes—
316C4—21no—
317C4—22no—
318C4—21no—
319C4—22no—
320C4—22no—
321C4—22no—
322C4—41no—
323C4—44no—
324C4—82no—
325C2—24no—
326C2#2144414911yescharacteristic
327C2#2144416311yescharacteristic
328C2#2144417511yescharacteristic
329C2#2144418311yescharacteristic
330C2#2144661811yescharacteristic
331C2#2144665611yescharacteristic
332C2#2144666411yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic61
commutator, prime radicalC24×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#389C2
socleC23×C61C2×C22⋊C4
cosocleC23×C4×C61C23
hypercenterC2×#389D61
hypocenterC61#9654
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
187. C61#9654semidirect

Maximal subgroups

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

subgroupindex
#214457992
#214455812
C2×#168394882
C2×C61×#3892
#965461