Finite Group Databasebeta

← #29583630

Subgroups — #29583630

Order 15616.

408 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839973C211yesmaximal, characteristic
2#21445812C211yesmaximal, characteristic
3#21444492C211yesmaximal, characteristic
4#21444490C211yesmaximal, characteristic
5#21444213C211yesmaximal, characteristic
6#21443716C211yesmaximal, characteristic
7C61×#1570C211yesmaximal, characteristic
8C22×Dic244—21no—
9C2×#14519777C2211yescharacteristic
10C2×C4×Dic122C2211yescharacteristic
11#16839973—22no—
12#16839973—22no—
13#16839815C2211yescharacteristic
14#16839786C2211yescharacteristic
15C2×#14519702—21no—
16C2×#14519695—21no—
17#16839530—21no—
18#16839509—22no—
19#16839507—22no—
20#16839492—22no—
21C61×#431C2211yescharacteristic
22C61×#423C2211yescharacteristic
23C2×C4⋊C8×C61C2211yescharacteristic
24C61×#334—22no—
25C22×Dic122—21no—
26C22×Dic122D411yescharacteristic
27C2×Dic244—24no—
28C2×Dic244—42no—
29C2×Dic244—42no—
30C2×#11758194—21no—
31#14519777—21no—
32#14519777—21no—
33#14519777—21no—
34#14519777D412yes—
35C4×Dic122—21no—
36C4×Dic122—21no—
37C4×Dic122—21no—
38C4×Dic122—21no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61D411yescharacteristic
42C2×#11758196—21no—
43C2×C4×Dic61—21no—
44C4⋊#92418—21no—
45C4⋊#92418—21no—
46C4⋊#92418—21no—
47#14519702—24no—
48#14519695—42no—
49C22⋊#92418—21no—
50C4×#92418—21no—
51C2×M16×C61—21no—
52C22×C8×C61—21no—
53C2×C42×C61C2311yescharacteristic
54C4⋊C8×C61—21no—
55C4⋊C8×C61—21no—
56C4⋊C8×C61—21no—
57C4⋊C8×C61D412yes—
58C4⋊C8×C61D412yes—
59C22⋊C8×C61—21no—
60C4×C8×C61—21no—
61C22×C4×C61C2×D411yescharacteristic
62C22×C4×C61#4111yescharacteristic
63C22×C4×C61#4111yescharacteristic
64C22×Dic61—21no—
65C22×Dic61—21no—
66C22×Dic61—41no—
67C2×Dic122—21no—
68C2×Dic122—21no—
69C2×Dic122—21no—
70C2×Dic122—21no—
71C2×Dic122—21no—
72C2×Dic122—22no—
73C2×Dic122—41no—
74C2×Dic122—41no—
75C2×Dic122—41no—
76C2×Dic122—41no—
77C2×Dic122—41no—
78C2×Dic122SD1612yes—
79M16×C61—41no—
80M16×C61—41no—
81C2×C8×C61—22no—
82C2×C8×C61—22no—
83C2×C8×C61—41no—
84C2×C8×C61—41no—
85C2×C8×C61—41no—
86C42×C61C2×D411yescharacteristic
87C42×C61C2×D411yescharacteristic
88C42×C61C2×D411yescharacteristic
89C42×C61#4111yescharacteristic
90C4⋊Dic61—21no—
91C4⋊Dic61—22no—
92C4⋊Dic61—21no—
93C4⋊Dic61—22no—
94C4⋊Dic61—41no—
95C4⋊Dic61—41no—
96#11758196—41no—
97#11758196—41no—
98C4×Dic61—41no—
99C4×Dic61—41no—
100#11758194—41no—
101#11758194—41no—
102C2×#92418—41no—
103C2×#92418—41no—
104Dic244—48no—
105C23×C61#12311yescharacteristic
106C2×C4×C61—22no—
107C2×C4×C61—41no—
108C2×C4×C61#12011yescharacteristic
109C2×C4×C61#12111yescharacteristic
110C2×C4×C61#12111yescharacteristic
111C2×C4×C61#12111yescharacteristic
112C2×C4×C61#12311yescharacteristic
113C2×C4×C61#12411yescharacteristic
114C2×C4×C61C2×SD1611yescharacteristic
115C2×C4×C61#13511yescharacteristic
116C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
117C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
118C2×Dic61—22no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61—42no—
123C2×Dic61—81no—
124C2×Dic61—81no—
125C2×Dic61—81no—
126Dic122—22no—
127Dic122—22no—
128Dic122—41no—
129Dic122—41no—
130Dic122—42no—
131Dic122—42no—
132Dic122—81no—
133Dic122—81no—
134C8×C61—42no—
135C8×C61—42no—
136C8×C61—81no—
137#92418—81no—
138#92418—81no—
139#10447—611nomaximal, Sylow
140C22×C61—21no—
141C22×C61—21no—
142C22×C61#39411yescharacteristic
143C22×C61#48111yescharacteristic
144C22×C61#48211yescharacteristic
145C4×C61—21no—
146C4×C61—21no—
147C4×C61—21no—
148C4×C61#44911yescharacteristic
149C4×C61#45011yescharacteristic
150C4×C61#46511yescharacteristic
151C4×C61#46911yescharacteristic
152C4×C61#47312yes—
153Dic61—42no—
154Dic61—81no—
155Dic61—82no—
156C2×#462—611no—
157#1801—611no—
158#1570D6111yescharacteristic
159#1546—611no—
160#1546—611no—
161#1479—611no—
162#1301—611no—
163C2×C61—21no—
164C2×C61—21no—
165C2×C61#203411yescharacteristic
166C2×C61#204711yescharacteristic
167C2×C61#204911yescharacteristic
168C22×Q16—1221no—
169C2×C4⋊Q8—611no—
170C2×C4×Q8—611no—
171#462—1222no—
172#462—1222no—
173#431—611no—
174#431C2×D6111yescharacteristic
175#423—611no—
176#423C2×D6111yescharacteristic
177C2×C4⋊C8C2×D6111yescharacteristic
178C2×#103—1221no—
179C2×#101—1221no—
180#343—1221no—
181#334—22no—
182#332—1222no—
183#332—1222no—
184Q8⋊C8—1222no—
185C61#1044711yescharacteristic, complemented, Sylow
186C22×Q8—611no—
187C22×Q8—1221no—
188C2×Q16—1224no—
189C2×Q16—2442no—
190C2×Q16—2442no—
191C2×M16—21no—
192C2×M16—1221no—
193C22×C8—21no—
194C4⋊Q8—612no—
195C4⋊Q8—1221no—
196C4⋊Q8—1221no—
197C4⋊Q8—1221no—
198C4×Q8—1221no—
199C4×Q8—1221no—
200C4×Q8—1221no—
201C4×Q8—1221no—
202C2×C4⋊C4—611no—
203C2×C4⋊C4—1221no—
204C2×C4⋊C4—1221no—
205C2×C4⋊C4—1221no—
206C2×C42—1221no—
207C2×C42C22×D6111yescharacteristic
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8—1221no—
212C4⋊C8—1221no—
213C4⋊C8—1221no—
214C4⋊C8D24412yes—
215C4⋊C8C22⋊D6112yes—
216#103—1224no—
217#101—2442no—
218C22⋊C8—21no—
219C22⋊C8—1221no—
220C4×C8—21no—
221C4×C8—1221no—
222C2×Q8—612no—
223C2×Q8—1221no—
224C2×Q8—1221no—
225C2×Q8—1222no—
226C2×Q8—1221no—
227C2×Q8—1221no—
228C2×Q8—1221no—
229C2×Q8—2441no—
230C2×Q8—2441no—
231C2×Q8—2441no—
232C2×Q8—2441no—
233C2×Q8—2441no—
234C22×C4—1221no—
235C22×C4—1221no—
236C22×C4—2441no—
237C22×C4#1175822211yescharacteristic
238C22×C4D4×D6111yescharacteristic
239C22×C4#1175822611yescharacteristic
240Q16—2448no—
241M16—41no—
242M16—41no—
243M16—2441no—
244M16—2441no—
245C2×C8—22no—
246C2×C8—22no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—2441no—
251C2×C8—2441no—
252C4⋊C4—1221no—
253C4⋊C4—1221no—
254C4⋊C4—1222no—
255C4⋊C4—1222no—
256C4⋊C4—2441no—
257C4⋊C4—2441no—
258C4⋊C4—2441no—
259C4⋊C4—2441no—
260C42—2441no—
261C42—2441no—
262C42C2×D24411yescharacteristic
263C42D4×D6111yescharacteristic
264C42#1175822611yescharacteristic
265C42C2×C22⋊D6111yescharacteristic
266C23#1451976211yescharacteristic
267Q8—1222no—
268Q8—1222no—
269Q8—4881no—
270Q8—4881no—
271Q8—2442no—
272Q8—2442no—
273Q8—2441no—
274Q8—2441no—
275C2×C4—22no—
276C2×C4—41no—
277C2×C4—1222no—
278C2×C4—4881no—
279C2×C4—4881no—
280C2×C4—4881no—
281C2×C4—2441no—
282C2×C4—2442no—
283C2×C4—2441no—
284C2×C4—2441no—
285C2×C4#1451974511yescharacteristic
286C2×C4#1451975111yescharacteristic
287C2×C4#1451975211yescharacteristic
288C2×C4#1451975211yescharacteristic
289C2×C4#1451976211yescharacteristic
290C2×C4#1451976611yescharacteristic
291C2×C4SD16×D6111yescharacteristic
292C2×C4#1451979811yescharacteristic
293C2×C4#1451980411yescharacteristic
294C2×C4#1451980411yescharacteristic
295C8—42no—
296C8—42no—
297C8—81no—
298C8—4881no—
299C8—4881no—
300C22—21no—
301C22—21no—
302C22#1683967911yescharacteristic
303C22#1684008211yescharacteristic
304C22#1684008811yescharacteristic
305C4—21no—
306C4—21no—
307C4—21no—
308C4—4882no—
309C4—4881no—
310C4—2442no—
311C4#1683990611yescharacteristic
312C4#1683991111yescharacteristic
313C4#1683999211yescharacteristic
314C4#1684001611yescharacteristic
315C4#1684003712yes—
316C2—21no—
317C2—21no—
318C2#2144701011yescharacteristic
319C2#2144708711yescharacteristic
320C2#2144710111yescharacteristic
subgroupG/H
centerC22#16839679
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1570C2
socleC22×C61#394
prime radicalC23×C61#123
hypercenter#1570D61
hypocenterC61#10447
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1570

Complements

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

NH ≅ G/Ntype
185. C61#10447semidirect

Maximal subgroups

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

subgroupindex
C2×#168399732
#214458122
#214444922
#214444902
#214442132
#214437162
C61×#15702
#1044761