Finite Group Databasebeta

← #29584539

Subgroups — #29584539

Order 15616.

370 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21446780C211yesmaximal, characteristic
2#21446766C211yesmaximal, characteristic
3#21446578C211yesmaximal, characteristic
4#21446537C211yesmaximal, characteristic
5C2×#16839510C211yesmaximal, characteristic
6#21443703C211yesmaximal, characteristic
7C2×C61×#334C211yesmaximal, characteristic
8C2×#14519777C2211yescharacteristic
9C2×#14519711—21no—
10C2×C4⋊#92418C2211yescharacteristic
11C2×#14519706—21no—
12#16839632C2211yescharacteristic
13C4×C4⋊Dic61C2211yescharacteristic
14#16839525—21no—
15#16839525—21no—
16#16839525—21no—
17#16839525—21no—
18#16839525—21no—
19#16839516—21no—
20#16839510—22no—
21C2×C4⋊C8×C61C2211yescharacteristic
22C2×C4⋊C8×C61C2211yescharacteristic
23C2×C4×C8×C61C2211yescharacteristic
24C61×#334—22no—
25C22×Dic122—21no—
26C22×#92418—21no—
27#14519777—21no—
28#14519777—21no—
29#14519777—21no—
30#14519777Q812yes—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61D411yescharacteristic
37C2×C4⋊Dic61D411yescharacteristic
38C2×C4×Dic61—21no—
39#14519711—42no—
40C4⋊#92418—21no—
41C4⋊#92418—21no—
42#14519706—42no—
43#14519684—21no—
44C22×C8×C61—21no—
45C22×C8×C61—21no—
46C22×C8×C61D411yescharacteristic
47C22×C8×C61D411yescharacteristic
48C2×C42×C61C2311yescharacteristic
49C4⋊C8×C61—21no—
50C4⋊C8×C61—21no—
51C4⋊C8×C61—21no—
52C4⋊C8×C61D412yes—
53C4×C8×C61—21no—
54C4×C8×C61—21no—
55C22×C4×C61C2×D411yescharacteristic
56C22×C4×C61C2×D411yescharacteristic
57C22×C4×C61#4111yescharacteristic
58C22×Dic61—21no—
59C22×Dic61—21no—
60C22×Dic61—41no—
61C22×Dic61—41no—
62C2×Dic122—22no—
63C2×Dic122—41no—
64C2×Dic122—81no—
65C2×Dic122—81no—
66C2×C8×C61—21no—
67C2×C8×C61—21no—
68C2×C8×C61—21no—
69C2×C8×C61—22no—
70C2×C8×C61—21no—
71C2×C8×C61—21no—
72C2×C8×C61—41no—
73C2×C8×C61—41no—
74C2×C8×C61—41no—
75C2×C8×C61—41no—
76C2×C8×C61—41no—
77C2×C8×C61Q1612yes—
78C42×C61C2×D411yescharacteristic
79C42×C61C2×Q811yescharacteristic
80C42×C61#4111yescharacteristic
81C42×C61#4111yescharacteristic
82C4⋊Dic61—21no—
83C4⋊Dic61—22no—
84C4⋊Dic61—22no—
85C4⋊Dic61—21no—
86C4⋊Dic61—21no—
87C4⋊Dic61—41no—
88C4⋊Dic61—41no—
89C4⋊Dic61—41no—
90C4⋊Dic61—41no—
91C4⋊Dic61—41no—
92C4⋊Dic61—41no—
93C4⋊Dic61—81no—
94C4⋊Dic61SD1612yes—
95C4×Dic61—41no—
96C4×Dic61—41no—
97C2×#92418—41no—
98C2×#92418—41no—
99C2×#92418—41no—
100C23×C61#12111yescharacteristic
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61#12111yescharacteristic
104C2×C4×C61#12111yescharacteristic
105C2×C4×C61C22⋊Q811yescharacteristic
106C2×C4×C61C22⋊Q811yescharacteristic
107C2×C4×C61C22⋊Q811yescharacteristic
108C2×C4×C61#12611yescharacteristic
109C2×C4×C61C2×SD1611yescharacteristic
110C2×C4×C61C2×Q1611yescharacteristic
111C2×C4×C61#13511yescharacteristic
112C2×C4×C61#13511yescharacteristic
113C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
114C2×C4×C61#13711yescharacteristic
115C2×C4×C61#13711yescharacteristic
116C2×C4×C61#13711yescharacteristic
117C2×Dic61—22no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61—42no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—81no—
125C2×Dic61—81no—
126C2×Dic61—81no—
127C2×Dic61—81no—
128C2×Dic61—81no—
129Dic122—82no—
130Dic122—82no—
131C8×C61—22no—
132C8×C61—42no—
133C8×C61—41no—
134C8×C61—81no—
135#92418—81no—
136#10589—611nomaximal, Sylow
137C22×C61#39611yescharacteristic
138C22×C61#46211yescharacteristic
139C22×C61#46311yescharacteristic
140C22×C61#46511yescharacteristic
141C22×C61#47011yescharacteristic
142C22×C61#47111yescharacteristic
143C22×C61#47211yescharacteristic
144C4×C61—21no—
145C4×C61—21no—
146C4×C61#46111yescharacteristic
147C4×C61#46411yescharacteristic
148C4×C61#46711yescharacteristic
149C4×C61#46811yescharacteristic
150C4×C61#47511yescharacteristic
151C4×C61#47711yescharacteristic
152C4×C61#47911yescharacteristic
153C4×C61#47911yescharacteristic
154Dic61—42no—
155Dic61—82no—
156Dic61—81no—
157Dic61—161no—
158#1990—611no—
159#1987—611no—
160#1947—611no—
161#1939—611no—
162C2×#334D6111yescharacteristic
163C2×#333—611no—
164#1296—611no—
165C2×C61#167211yescharacteristic
166C2×C61#167711yescharacteristic
167C2×C61#169611yescharacteristic
168C2×C61#170311yescharacteristic
169C2×C61#206311yescharacteristic
170C2×C61#206611yescharacteristic
171C2×C61#206811yescharacteristic
172C2×C4⋊Q8—611no—
173C2×#107—1221no—
174C2×C4⋊C8—611no—
175C2×C4⋊C8—1221no—
176C2×C4⋊C8C2×D6111yescharacteristic
177C2×C4⋊C8C2×D6111yescharacteristic
178C2×C4×C8C2×D6111yescharacteristic
179#384—611no—
180C4×C4⋊C4—611no—
181#340—1221no—
182#340—1221no—
183#340—1221no—
184#340—1221no—
185#340—1221no—
186#336—1221no—
187#334—22no—
188#333—1222no—
189C61#1058911yescharacteristic, complemented, Sylow
190C22×Q8—1221no—
191C22×C8—21no—
192C22×C8—21no—
193C22×C8—1221no—
194C22×C8D24411yescharacteristic
195C22×C8D24411yescharacteristic
196C4⋊Q8—612no—
197C4⋊Q8—1221no—
198C4⋊Q8—1221no—
199C4⋊Q8—1221no—
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×C42—1221no—
208C2×C42C22×D6111yescharacteristic
209#107—2442no—
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—1221no—
214C4⋊C8—1221no—
215C4⋊C8—2442no—
216C4⋊C8C22⋊D6112yes—
217C4×C8—21no—
218C4×C8—21no—
219#95—1221no—
220C2×Q8—1222no—
221C2×Q8—4881no—
222C2×Q8—4881no—
223C2×Q8—2441no—
224C22×C4—1221no—
225C22×C4—1221no—
226C22×C4—2441no—
227C22×C4—2441no—
228C22×C4C2×D24411yescharacteristic
229C22×C4D4×D6111yescharacteristic
230C22×C4#1175822611yescharacteristic
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—22no—
235C2×C8—21no—
236C2×C8—21no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—2441no—
243C2×C8—2441no—
244C2×C8—2441no—
245C2×C8Dic24412yes—
246C4⋊C4—612no—
247C4⋊C4—1221no—
248C4⋊C4—1222no—
249C4⋊C4—1222no—
250C4⋊C4—1221no—
251C4⋊C4—1221no—
252C4⋊C4—4881no—
253C4⋊C4—2441no—
254C4⋊C4—2441no—
255C4⋊C4—2441no—
256C4⋊C4—2441no—
257C4⋊C4—2441no—
258C4⋊C4—2441no—
259C42—2441no—
260C42—2441no—
261C42#1175822211yescharacteristic
262C42#1175822411yescharacteristic
263C42Q8×D6111yescharacteristic
264C42C2×C22⋊D6111yescharacteristic
265C23#1451975211yescharacteristic
266Q8—4882no—
267Q8—4882no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—1222no—
271C2×C4—4881no—
272C2×C4—4881no—
273C2×C4—4881no—
274C2×C4—4881no—
275C2×C4—4881no—
276C2×C4—2442no—
277C2×C4—2441no—
278C2×C4—2441no—
279C2×C4—2441no—
280C2×C4—2441no—
281C2×C4—2441no—
282C2×C4#1451974911yescharacteristic
283C2×C4#1451975111yescharacteristic
284C2×C4#1451975311yescharacteristic
285C2×C4#1451975511yescharacteristic
286C2×C4#1451975711yescharacteristic
287C2×C4#1451977211yescharacteristic
288C2×C4SD16×D6111yescharacteristic
289C2×C4C2×Dic24411yescharacteristic
290C2×C4#1451979811yescharacteristic
291C2×C4#1451979911yescharacteristic
292C2×C4#1451980511yescharacteristic
293C2×C4#1451980611yescharacteristic
294C2×C4#1451980611yescharacteristic
295C2×C4#1451981011yescharacteristic
296C8—22no—
297C8—42no—
298C8—41no—
299C8—81no—
300C8—4881no—
301C22#1683968411yescharacteristic
302C22#1683997311yescharacteristic
303C22#1683997811yescharacteristic
304C22#1683999211yescharacteristic
305C22#1684002111yescharacteristic
306C22#1684002611yescharacteristic
307C22#1684003311yescharacteristic
308C4—21no—
309C4—21no—
310C4—9761no—
311C4—4882no—
312C4—4881no—
313C4—2442no—
314C4#1683996511yescharacteristic
315C4#1683998211yescharacteristic
316C4#1684000311yescharacteristic
317C4#1684000811yescharacteristic
318C4#1684004611yescharacteristic
319C4#1684005811yescharacteristic
320C4#1684007011yescharacteristic
321C4#1684007211yescharacteristic
322C2#2144520211yescharacteristic
323C2#2144522911yescharacteristic
324C2#2144534811yescharacteristic
325C2#2144539511yescharacteristic
326C2#2144717411yescharacteristic
327C2#2144719511yescharacteristic
328C2#2144721311yescharacteristic
subgroupG/H
centerC23#14519752
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC2×C61×#334C2
socle, prime radicalC23×C61#121
hypercenterC2×#334D61
hypocenterC61#10589
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#334

Complements

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

NH ≅ G/Ntype
189. C61#10589semidirect

Maximal subgroups

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

subgroupindex
#214467802
#214467662
#214465782
#214465372
C2×#168395102
#214437032
C2×C61×#3342
#1058961