Finite Group Databasebeta

← #30608417

Subgroups — #30608417

Order 15616.

326 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 60 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
1#21462112C211yesmaximal, characteristic
2#21462092C211yesmaximal, characteristic
3#21460965C212yesmaximal, complemented
4#21460964C212yesmaximal, complemented
5#21456144C211yesmaximal, characteristic
6#16840748—21no—
7#16840741—21no—
8#16840673—21no—
9#16840671C2212yes—
10#16840669C2212yes—
11#16840667—21no—
12#16840312C2211yescharacteristic
13#16840119C411yescharacteristic, complemented
14#16840119C411yescharacteristic, complemented
15#16840119C2211yescharacteristic
16#16840119C2211yescharacteristic
17#16840114—21no—
18#16840110—21no—
19#16839756—21no—
20#16839756—21no—
21C2×C4×#92418C411yescharacteristic, complemented
22C61×#533C411yescharacteristic, complemented
23D61⋊M16—41no—
24#14519856—41no—
25#14519838—22no—
26#14519837—41no—
27#14519836—22no—
28#14519835—41no—
29C2×#11758222D411yescharacteristic
30C2×#11758222D411yescharacteristic
31C22×#92418—21no—
32#14519777D411yescharacteristic
33#14519774D411yescharacteristic
34#14519765C2×C411yescharacteristic
35#14519765C2311yescharacteristic
36#14519751—41no—
37C4×D244—41no—
38#14519700—21no—
39#14519700—21no—
40#14519700—21no—
41#14519700—21no—
42#14519697—21no—
43#14519697—21no—
44#14519697—21no—
45#14519697—21no—
46C4×#92418—21no—
47C4×#92418C2×C411yescharacteristic
48C4×#92418C2×C411yescharacteristic
49C4⋊Q8×C61—21no—
50#125×C61C2×C411yescharacteristic
51#125×C61C2×C411yescharacteristic
52C22⋊Q8×C61—41no—
53C4×Q8×C61—41no—
54#117×C61—21no—
55C2×C42×C61C2×C411yescharacteristic
56C2×Q8×C61—41no—
57C22×C4×C61—21no—
58C22×C4×C61C22⋊C411yescharacteristic
59C2×C22⋊D61—21no—
60C2×C22⋊D61—21no—
61#11758222—41no—
62#11758222—41no—
63#11758222—41no—
64#11758222—41no—
65C2×D244—41no—
66C2×D244C22⋊C411yescharacteristic
67C2×D244C2×D411yescharacteristic
68C2×C4×D61—21no—
69C2×C4×D61—21no—
70C2×Dic122C22⋊C411yescharacteristic
71C2×Dic122C2×D411yescharacteristic
72C22⋊#6923—42no—
73#11758217—42no—
74C4⋊#6923—81no—
75C4×#6923—81no—
76#11758213—81no—
77D61⋊C8—81no—
78C4⋊C4×C61—21no—
79C4⋊C4×C61—21no—
80C4⋊C4×C61—41no—
81C4⋊C4×C61—41no—
82C4⋊C4×C61—41no—
83C22⋊C4×C61—41no—
84C42×C61—21no—
85C42×C61—41no—
86C42×C61C22⋊C411yescharacteristic
87C42×C61C22×C411yescharacteristic
88#11758198—41no—
89#11758198—41no—
90C4⋊Dic61—41no—
91C2×#92418—21no—
92C2×#92418—21no—
93C2×#92418—41no—
94C2×#92418—41no—
95C23×C61#9911yescharacteristic
96C22×D61—21no—
97C22×D61—21no—
98C2×#6923—82no—
99Q8×C61—82no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—42no—
105C2×C4×C61—41no—
106C2×C4×C61—41no—
107C2×C4×C61#9911yescharacteristic
108C2×C4×C61C2×C22⋊C411yescharacteristic
109C22⋊D61—81no—
110C22⋊D61—81no—
111C2×Dic61—21no—
112C2×Dic61—21no—
113D244—41no—
114D244—41no—
115D244—82no—
116C4×D61—41no—
117C4×D61—41no—
118C4×D61—41no—
119C4×D61—41no—
120Dic122—41no—
121Dic122—41no—
122#92420—82no—
123#92418—41no—
124#92418—41no—
125#13602—611nomaximal, Sylow
126C22×C61—21no—
127C22×C61—41no—
128C22×C61C2×#9911yescharacteristic
129C2×D61—41no—
130C2×D61—41no—
131C2×D61—81no—
132C2×D61—81no—
133#6923—162no—
134C4×C61—22no—
135C4×C61—21no—
136C4×C61—41no—
137C4×C61—81no—
138C4×C61—81no—
139C4×C61#35411yescharacteristic
140C4×C61#35411yescharacteristic
141Dic61—41no—
142Dic61—41no—
143#3131—611no—
144#2132—611no—
145#2126—611no—
146#1414—612no—
147#1414—612no—
148C2×C61—21no—
149C2×C61—41no—
150C2×C61C2×#35411yescharacteristic
151D61—81no—
152D61—81no—
153#533#692311yescharacteristic, complemented
154#532—611no—
155#488—611no—
156#488—611no—
157#488—611no—
158#488—611no—
159#487—1221no—
160#486—1221no—
161#416—1221no—
162#416—1221no—
163#413—1221no—
164#410—1221no—
165C2×C4×C8—611no—
166#356—1221no—
167#355—612no—
168#354—612no—
169#353—1221no—
170C61#1360211yescharacteristic, complemented, Sylow
171C2×#41—611no—
172C2×#41—611no—
173C2×M16—2441no—
174C22×C8—1221no—
175C4⋊Q8—21no—
176C4⋊Q8—611no—
177#127—611no—
178#125C2×#692311yescharacteristic
179#125C2×#692311yescharacteristic
180#124—611no—
181#124—611no—
182C22⋊Q8—41no—
183#121—2441no—
184C4×Q8—41no—
185C4×D4—2441no—
186#117—21no—
187#117—2441no—
188C2×C42C2×#692311yescharacteristic
189#103—1221no—
190#103—1221no—
191#103—1221no—
192#103—1221no—
193#102—1221no—
194#102—1221no—
195#102—1221no—
196#102—1221no—
197#101—1222no—
198#100—2441no—
199#99—1222no—
200#99—2441no—
201C4×C8—611no—
202C4×C8—611no—
203C4×C8—1221no—
204#41—2441no—
205#41—2441no—
206#41—2441no—
207#41—2441no—
208C2×Q8—41no—
209C2×Q8—611no—
210C2×Q8—611no—
211C2×D4—611no—
212C2×D4—611no—
213C2×D4—1221no—
214C2×D4—1221no—
215C2×D4—2441no—
216C22×C4—21no—
217C22×C4—1221no—
218C22×C4—1221no—
219C22×C4C22⋊#692311yescharacteristic
220M16—4881no—
221M16—2442no—
222C2×C8—1221no—
223C2×C8—1221no—
224C2×C8—4881no—
225C2×C8—2441no—
226C2×C8—2441no—
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—4881no—
233C4⋊C4—2441no—
234C22⋊C4—41no—
235C22⋊C4—2441no—
236C22⋊C4—2441no—
237C22⋊C4—2442no—
238C42—21no—
239C42—41no—
240C42—4881no—
241C42C22⋊#692311yescharacteristic
242C42C22×#692311yescharacteristic
243C23—1221no—
244C23—1221no—
245C23#1451983511yescharacteristic
246Q8—82no—
247Q8—2441no—
248Q8—2441no—
249D4—4882no—
250D4—4881no—
251D4—4881no—
252D4—2441no—
253D4—2441no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—42no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—1221no—
262C2×C4—1221no—
263C2×C4—4882no—
264C2×C4—2441no—
265C2×C4—2441no—
266C2×C4—2441no—
267C2×C4—2441no—
268C2×C4#1451983511yescharacteristic
269C2×C4C2×C22⋊#692311yescharacteristic
270C8—4882no—
271C8—2441no—
272C8—2441no—
273C22—21no—
274C22—41no—
275C22—4881no—
276C22—4881no—
277C22—2441no—
278C22—2441no—
279C22C2×#1451983511yescharacteristic
280C4—22no—
281C4—21no—
282C4—41no—
283C4—81no—
284C4—81no—
285C4—9762no—
286C4—2441no—
287C4—2441no—
288C4#1684066811yescharacteristic
289C4#1684066811yescharacteristic
290C2—21no—
291C2—41no—
292C2—4881no—
293C2—4881no—
294C2C2×#1684066811yescharacteristic
subgroupG/H
centerC4#16840668
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#533C4
socleC2×C61C2×#354
prime radical#16840312C22
cosocle#14519765C23
hypercenter#533#6923
hypocenterC61#13602
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
3. #21460965C2semidirect
4. #21460964C2semidirect
13. #16840119C4semidirect
14. #16840119C4semidirect
21. C2×C4×#92418C4semidirect
22. C61×#533C4semidirect
153. #533#6923semidirect
170. C61#13602semidirect

Maximal subgroups

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

subgroupindex
#214621122
#214620922
#214609652
#214609642
#214561442
#1360261