Finite Group Databasebeta

← #29578615

Subgroups — #29578615

Order 15616.

368 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21445672C211yesmaximal, characteristic
2C4×C4⋊#92418C211yesmaximal, characteristic
3C2×#16839514C211yesmaximal, characteristic
4C2×#16839512C211yesmaximal, characteristic
5#21443653C211yesmaximal, characteristic
6#21443653C211yesmaximal, characteristic
7C61×#1831C211yesmaximal, characteristic
8C2×C4⋊#92418C411yescharacteristic
9C2×C4⋊#92418C411yescharacteristic
10C2×C4⋊#92418C2211yescharacteristic
11C2×C4⋊#92418C2211yescharacteristic
12C2×#14519688—21no—
13C2×C4×#92418C2211yescharacteristic
14C2×C4×#92418C2211yescharacteristic
15#16839517—21no—
16#16839517C411yescharacteristic
17#16839517C411yescharacteristic
18#16839514—22no—
19#16839512—22no—
20C2×C4⋊C8×C61C2211yescharacteristic
21C2×C4⋊C8×C61C2211yescharacteristic
22C43×C61C2211yescharacteristic
23C61×#336—21no—
24C61×#336—21no—
25C22×#92418—21no—
26C22×#92418—21no—
27C22×#92418C2×C411yescharacteristic
28C22×#92418C2×C411yescharacteristic
29C22×#92418C2×C411yescharacteristic
30C22×#92418C2×C411yescharacteristic
31C4⋊#92418—21no—
32C4⋊#92418—21no—
33C4⋊#92418—22no—
34C4⋊#92418—22no—
35C4⋊#92418D412yes—
36C4⋊#92418Q812yes—
37#14519688—42no—
38C4×#92418—21no—
39C4×#92418—21no—
40C4×#92418—21no—
41C4×#92418—21no—
42C22×C8×C61—21no—
43C22×C8×C61—21no—
44C2×C42×C61C2×C411yescharacteristic
45C2×C42×C61C2×C411yescharacteristic
46C2×C42×C61D411yescharacteristic
47C2×C42×C61D411yescharacteristic
48C2×C42×C61Q811yescharacteristic
49C2×C42×C61Q811yescharacteristic
50C2×C42×C61C2311yescharacteristic
51C4⋊C8×C61—21no—
52C4⋊C8×C61—21no—
53C4⋊C8×C61—21no—
54C4⋊C8×C61—21no—
55C22×C4×C61C4⋊C411yescharacteristic
56C22×C4×C61C4⋊C411yescharacteristic
57C22×C4×C61C4⋊C411yescharacteristic
58C22×C4×C61C4⋊C411yescharacteristic
59C22×C4×C61C22×C411yescharacteristic
60C22×C4×C61C2×D411yescharacteristic
61C22×C4×C61C2×Q811yescharacteristic
62C2×C8×C61—41no—
63C2×C8×C61—41no—
64C2×C8×C61—41no—
65C2×C8×C61—41no—
66C2×C8×C61—41no—
67C2×C8×C61—41no—
68C42×C61—22no—
69C42×C61—21no—
70C42×C61—21no—
71C42×C61—21no—
72C42×C61—21no—
73C42×C61—21no—
74C42×C61—21no—
75C42×C61—21no—
76C42×C61—21no—
77C42×C61—41no—
78C42×C61C2×D411yescharacteristic
79C42×C61C2×Q811yescharacteristic
80C42×C61#4111yescharacteristic
81C42×C61#4111yescharacteristic
82C2×#92418—21no—
83C2×#92418—21no—
84C2×#92418—21no—
85C2×#92418—21no—
86C2×#92418—21no—
87C2×#92418—21no—
88C2×#92418—22no—
89C2×#92418—22no—
90C2×#92418—21no—
91C2×#92418—21no—
92C2×#92418—21no—
93C2×#92418—21no—
94C2×#92418—41no—
95C2×#92418—41no—
96C2×#92418—41no—
97C2×#92418—41no—
98C2×#92418M1612yes—
99C2×#92418M1612yes—
100C23×C61C2×C4⋊C411yescharacteristic
101C2×C4×C61—21no—
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—21no—
113C2×C4×C61—21no—
114C2×C4×C61#10812yes—
115C2×C4×C61C4×D411yescharacteristic
116C2×C4×C61C4×Q811yescharacteristic
117C2×C4×C61#12111yescharacteristic
118C2×C4×C61C22⋊Q811yescharacteristic
119C2×C4×C61#12511yescharacteristic
120C2×C4×C61C4⋊Q811yescharacteristic
121C2×C4×C61C2×M1611yescharacteristic
122C2×C4×C61C2×M1611yescharacteristic
123C2×C4×C61#13111yescharacteristic
124C2×C4×C61#13111yescharacteristic
125C2×C4×C61#13511yescharacteristic
126C2×C4×C61#13511yescharacteristic
127C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C61#13711yescharacteristic
129C8×C61—81no—
130C8×C61—81no—
131#92418—22no—
132#92418—22no—
133#92418—41no—
134#92418—41no—
135#92418—42no—
136#92418—42no—
137#9606—611nomaximal, Sylow
138C22×C61#38911yescharacteristic
139C22×C61#42311yescharacteristic
140C22×C61#42411yescharacteristic
141C22×C61#42711yescharacteristic
142C22×C61#42811yescharacteristic
143C22×C61C2×#10811yescharacteristic
144C22×C61#43011yescharacteristic
145C4×C61—22no—
146C4×C61—21no—
147C4×C61—21no—
148C4×C61—41no—
149C4×C61—41no—
150C4×C61—41no—
151C4×C61#43511yescharacteristic
152C4×C61#43511yescharacteristic
153C4×C61#44611yescharacteristic
154C4×C61#44611yescharacteristic
155C4×C61#46311yescharacteristic
156C4×C61#46411yescharacteristic
157C4×C61#47811yescharacteristic
158C4×C61#47911yescharacteristic
159#1831D6111yescharacteristic
160#1767—611no—
161C4×C4⋊C8—611no—
162C2×#335—611no—
163C2×#334—611no—
164#1277—611no—
165#1277—611no—
166C2×C61#156811yescharacteristic
167C2×C61#156911yescharacteristic
168C2×C61#157211yescharacteristic
169C2×C61#157411yescharacteristic
170C2×C61#194011yescharacteristic
171C2×C61#194911yescharacteristic
172C2×C61#195011yescharacteristic
173C2×C4⋊C8—611no—
174C2×C4⋊C8—611no—
175C2×C4⋊C8—611no—
176C2×C4⋊C8—611no—
177C2×C4⋊C8C2×D6111yescharacteristic
178C2×C4⋊C8C2×D6111yescharacteristic
179C2×#97—1221no—
180C2×C4×C8—611no—
181C2×C4×C8—611no—
182C43C2×D6111yescharacteristic
183#336—21no—
184#336—21no—
185#336—611no—
186#336—611no—
187#336—1221no—
188#335—1222no—
189#334—1222no—
190C61#960611yescharacteristic, complemented, Sylow
191C22×C8—21no—
192C22×C8—21no—
193C22×C8—611no—
194C22×C8—611no—
195C22×C8—611no—
196C22×C8—611no—
197C22×C8—1221no—
198C22×C8—1221no—
199C2×C42Dic12211yescharacteristic
200C2×C42Dic12211yescharacteristic
201C2×C42C4×D6111yescharacteristic
202C2×C42C4×D6111yescharacteristic
203C2×C42C22⋊D6111yescharacteristic
204C2×C42C22⋊D6111yescharacteristic
205C2×C42C22×D6111yescharacteristic
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—612no—
211C4⋊C8—612no—
212C4⋊C8—1222no—
213C4⋊C8—1222no—
214C4⋊C8—1221no—
215C4⋊C8—1221no—
216#97—2442no—
217C4×C8—1221no—
218C4×C8—1221no—
219C4×C8—1221no—
220C4×C8—1221no—
221C22×C4#1175819611yescharacteristic
222C22×C4#1175819611yescharacteristic
223C22×C4#1175819611yescharacteristic
224C22×C4#1175819611yescharacteristic
225C22×C4C2×Dic12211yescharacteristic
226C22×C4C2×C4×D6111yescharacteristic
227C22×C4C2×C22⋊D6111yescharacteristic
228C2×C8—41no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—612no—
235C2×C8—612no—
236C2×C8—1221no—
237C2×C8—1221no—
238C2×C8—1221no—
239C2×C8—1221no—
240C2×C8—1221no—
241C2×C8—1221no—
242C2×C8—1222no—
243C2×C8—1222no—
244C2×C8—1221no—
245C2×C8—1221no—
246C2×C8—1221no—
247C2×C8—1221no—
248C2×C8—2441no—
249C2×C8—2441no—
250C2×C8—2441no—
251C2×C8—2441no—
252C42—22no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42—21no—
257C42—21no—
258C42—21no—
259C42—21no—
260C42—21no—
261C42—41no—
262C42D4×D6111yescharacteristic
263C42#1175822411yescharacteristic
264C42Q8×D6111yescharacteristic
265C42#1175822611yescharacteristic
266C23C2×#1175819611yescharacteristic
267C2×C4—21no—
268C2×C4—21no—
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—21no—
280C2×C4#1451971212yes—
281C2×C4#1451973911yescharacteristic
282C2×C4#1451974211yescharacteristic
283C2×C4#1451974811yescharacteristic
284C2×C4#1451975311yescharacteristic
285C2×C4#1451976811yescharacteristic
286C2×C4#1451977611yescharacteristic
287C2×C4M16×D6111yescharacteristic
288C2×C4M16×D6111yescharacteristic
289C2×C4#1451978311yescharacteristic
290C2×C4#1451978311yescharacteristic
291C2×C4#1451979711yescharacteristic
292C2×C4#1451979711yescharacteristic
293C2×C4#1451980211yescharacteristic
294C2×C4#1451980711yescharacteristic
295C8—81no—
296C8—81no—
297C8—1222no—
298C8—1222no—
299C8—2442no—
300C8—2442no—
301C8—2441no—
302C8—2441no—
303C22#1683965811yescharacteristic
304C22#1683978511yescharacteristic
305C22#1683978811yescharacteristic
306C22#1683979811yescharacteristic
307C22#1683980511yescharacteristic
308C22C2×#1451971211yescharacteristic
309C22#1683981011yescharacteristic
310C4—21no—
311C4—21no—
312C4—22no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4#1683983211yescharacteristic
317C4#1683983211yescharacteristic
318C4#1683989111yescharacteristic
319C4#1683989111yescharacteristic
320C4#1683997411yescharacteristic
321C4#1683998111yescharacteristic
322C4#1684005911yescharacteristic
323C4#1684006611yescharacteristic
324C2#2144458011yescharacteristic
325C2#2144458711yescharacteristic
326C2#2144459711yescharacteristic
327C2#2144460711yescharacteristic
328C2#2144654011yescharacteristic
329C2#2144658511yescharacteristic
330C2#2144659211yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1831C2
socle, prime radicalC23×C61C2×C4⋊C4
cosocleC2×C42×C61C23
hypercenter#1831D61
hypocenterC61#9606
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C43 ◁ #1831

Complements

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

NH ≅ G/Ntype
190. C61#9606semidirect

Maximal subgroups

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

subgroupindex
#214456722
C4×C4⋊#924182
C2×#168395142
C2×#168395122
#214436532
C61×#18312
#960661