Finite Group Databasebeta

← #30595464

Subgroups — #30595464

Order 15616.

654 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 654 conjugacy classes of subgroups — too many to draw. Only its 124 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#21461673C212yesmaximal, complemented
2#21460640C212yesmaximal, complemented
3#21460636C212yesmaximal, complemented
4#21448307C211yesmaximal, characteristic
5C2×C4⋊#92420—22no—
6C2×C22⋊#92420—22no—
7#16840628C2214yes—
8C22×#11758222C411yescharacteristic
9C22×C4×Dic61C2211yescharacteristic
10#16839667C411yescharacteristic
11#16839667C2211yescharacteristic
12#16839663C411yescharacteristic
13#16839663C2211yescharacteristic
14#16839639—22no—
15C4×#11758198—22no—
16C2×#117×C61C411yescharacteristic
17C22×#92420—24no—
18C4⋊#92420—44no—
19C22⋊#92420—44no—
20C2×#11758222—22no—
21C2×#11758222—42no—
22C2×#11758222—42no—
23C2×#11758222C814yescomplemented
24C22×Dic122C2×C411yescharacteristic
25C22×D244C2×C411yescharacteristic
26C22×C22⋊D61—21no—
27C23×Dic61D412yes—
28C22×C4×D61—21no—
29C2×#11758198—22no—
30C2×#11758198—22no—
31C2×C4×Dic61—42no—
32C2×C4×Dic61C2×C411yescharacteristic
33C2×C4×Dic61D412yes—
34C2×C4×Dic61C2311yescharacteristic
35#14519684—22no—
36#14519684—22no—
37C23×C4×C61C2×C411yescharacteristic
38#117×C61—42no—
39C2×C4⋊C4×C61C2×C411yescharacteristic
40C2×C4⋊C4×C61C2×C411yescharacteristic
41C2×C22⋊C4×C61—21no—
42C2×C42×C61—21no—
43C24×C61C22⋊C411yescharacteristic
44C23×D61—21no—
45C22×C4×C61—22no—
46C22×C4×C61—22no—
47C22×C4×C61—21no—
48C22×C4×C61—21no—
49C22×C4×C61C22⋊C411yescharacteristic
50C22×C4×C61C2×C812yes—
51C22×C4×C61M1612yes—
52C22×C4×C61C22×C411yescharacteristic
53C2×C22⋊D61—24no—
54C2×C22⋊D61—42no—
55C2×C22⋊D61—42no—
56C22×Dic61—21no—
57C22×Dic61—22no—
58C22×Dic61—22no—
59C22×Dic61—42no—
60C22×Dic61—42no—
61C22×Dic61C22⋊C412yes—
62C22×Dic61C2×D412yes—
63#11758222—48no—
64#11758222—48no—
65C2×D244—21no—
66C2×D244—41no—
67C2×D244—41no—
68C2×D244C2×C812yes—
69C2×C4×D61—24no—
70C2×C4×D61—42no—
71C2×C4×D61—42no—
72C2×Dic122—21no—
73C2×Dic122—41no—
74C2×Dic122—41no—
75C2×Dic122C2×C812yes—
76C2×#92420—44no—
77C2×#92420—44no—
78C2×#92420—44no—
79C4⋊C4×C61—41no—
80C4⋊C4×C61—41no—
81C22⋊C4×C61—42no—
82C42×C61—42no—
83#11758198—44no—
84#11758198—42no—
85#11758198—42no—
86C4×Dic61—24no—
87C4×Dic61—41no—
88C4×Dic61—41no—
89C23×C61—21no—
90C23×C61—21no—
91C23×C61—22no—
92C23×C61—22no—
93C23×C61C22⋊C812yes—
94C23×C61C2×C22⋊C411yescharacteristic
95C22×D61—22no—
96C22×D61—41no—
97C22×D61—41no—
98C22×D61—42no—
99C22×D61—42no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—24no—
103C2×C4×C61—24no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61—42no—
107C2×C4×C61—42no—
108C2×C4×C61C22⋊C812yes—
109C2×C4×C61#9912yes—
110C2×C4×C61#10012yes—
111C2×C4×C61C22×C811yescharacteristic
112C2×C4×C61C2×M1611yescharacteristic
113C22⋊D61—48no—
114C2×Dic61—22no—
115C2×Dic61—22no—
116C2×Dic61—22no—
117C2×Dic61—22no—
118C2×Dic61—22no—
119C2×Dic61—22no—
120C2×Dic61—44no—
121C2×Dic61—44no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61AGL(1,ℤ/8)12yes—
125C2×Dic61#13712yes—
126D244—42no—
127D244—42no—
128C4×D61—48no—
129Dic122—42no—
130Dic122—42no—
131#92420—84no—
132#7597—611nomaximal, Sylow
133C22×C61—22no—
134C22×C61—24no—
135C22×C61—41no—
136C22×C61—41no—
137C22×C61—42no—
138C22×C61C2×C22⋊C811yescharacteristic
139C22×C61C2×#9911yescharacteristic
140C22×C61C2×#10011yescharacteristic
141C22×C61#41712yes—
142C22×C61#42112yes—
143C2×D61—42no—
144C2×D61—44no—
145C2×D61—81no—
146C2×D61—81no—
147C2×D61—82no—
148C4×C61—21no—
149C4×C61—21no—
150C4×C61—81no—
151C4×C61—81no—
152C4×C61#32314yes—
153Dic61—22no—
154Dic61—22no—
155Dic61—42no—
156Dic61—42no—
157#2297—611no—
158#1797—612no—
159#1272—612no—
160#1270—612no—
161C2×C61—42no—
162C2×C61C2×#32311yescharacteristic
163C2×C61#147712yes—
164C2×C61#151312yes—
165C2×C61#153611yescharacteristic
166C2×C61#156011yescharacteristic
167D61—82no—
168C22×#41—611no—
169C2×#117#692311yescharacteristic
170C22×C42—611no—
171C2×C4⋊C8—1222no—
172C2×C22⋊C8—1222no—
173#391—611no—
174#391—611no—
175#390—611no—
176#390—611no—
177#386—1222no—
178C4×C22⋊C4—1222no—
179#336—614no—
180C61#759711yescharacteristic, complemented, Sylow
181C2×#41—614no—
182C2×#41—1222no—
183C2×#41—2442no—
184C2×#41—2442no—
185C22×Q8—611no—
186C22×D4—611no—
187C22×D4—1221no—
188C23×C4—612no—
189C23×C4—1221no—
190C23×C4C2×#692311yescharacteristic
191C22×C8—1224no—
192#117—42no—
193C2×C4⋊C4C2×#692311yescharacteristic
194C2×C4⋊C4C2×#692311yescharacteristic
195C2×C22⋊C4—21no—
196C2×C22⋊C4—1222no—
197C2×C22⋊C4—1222no—
198C2×C42—21no—
199C2×C42—612no—
200C2×C42—611no—
201C2×C42—611no—
202C2×C42—2442no—
203C4⋊C8—2444no—
204C22⋊C8—2444no—
205#95—1222no—
206#95—1222no—
207C24—1221no—
208C24C22⋊#692311yescharacteristic
209#41—2448no—
210#41—2448no—
211C2×Q8—612no—
212C2×Q8—1221no—
213C2×Q8—2441no—
214C2×Q8—2441no—
215C2×D4—612no—
216C2×D4—1224no—
217C2×D4—1221no—
218C2×D4—2441no—
219C2×D4—2441no—
220C2×D4—2442no—
221C2×D4—2442no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—612no—
227C22×C4—612no—
228C22×C4—1222no—
229C22×C4—1222no—
230C22×C4—1221no—
231C22×C4—1224no—
232C22×C4—2442no—
233C22×C4—2442no—
234C22×C4—2442no—
235C22×C4—2442no—
236C22×C4D61⋊C812yes—
237C22×C4#1175821312yes—
238C22×C4C22⋊#692311yescharacteristic
239C22×C4C22×#692311yescharacteristic
240C2×C8—2444no—
241C2×C8—2444no—
242C2×C8—2444no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C22⋊C4—42no—
246C22⋊C4—2442no—
247C22⋊C4—2442no—
248C22⋊C4—2444no—
249C42—42no—
250C42—1224no—
251C42—2441no—
252C42—2441no—
253C23—21no—
254C23—21no—
255C23—22no—
256C23—22no—
257C23—1222no—
258C23—2441no—
259C23—2441no—
260C23—2442no—
261C23—2442no—
262C23#1451983412yes—
263C23C2×C22⋊#692311yescharacteristic
264Q8—2442no—
265Q8—2442no—
266D4—2442no—
267D4—2442no—
268D4—2448no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—24no—
272C2×C4—24no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—612no—
278C2×C4—612no—
279C2×C4—1222no—
280C2×C4—1222no—
281C2×C4—1222no—
282C2×C4—1222no—
283C2×C4—1222no—
284C2×C4—1222no—
285C2×C4—2444no—
286C2×C4—2444no—
287C2×C4—2441no—
288C2×C4—2441no—
289C2×C4—2448no—
290C2×C4#1451983412yes—
291C2×C4#1451983612yes—
292C2×C4#1451983712yes—
293C2×C4C2×D61⋊C811yescharacteristic
294C2×C4C2×#1175821311yescharacteristic
295C8—4884no—
296C22—22no—
297C22—24no—
298C22—41no—
299C22—41no—
300C22—42no—
301C22—4881no—
302C22—4881no—
303C22—4882no—
304C22—2442no—
305C22—2444no—
306C22C2×#1451983411yescharacteristic
307C22C2×#1451983611yescharacteristic
308C22C2×#1451983711yescharacteristic
309C22#1684075312yes—
310C22#1684075912yes—
311C4—21no—
312C4—21no—
313C4—81no—
314C4—81no—
315C4—1222no—
316C4—1222no—
317C4—2442no—
318C4—2442no—
319C4#1684060614yes—
320C2—42no—
321C2—4882no—
322C2C2×#1684060611yescharacteristic
323C2#2146111612yes—
324C2#2146123612yes—
325C2#2146130711yescharacteristic
326C2#2146135611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC2×#117×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC22×#11758222C4
cosocleC2×C4×Dic61C23
hypercenterC2×#117#6923
hypocenterC61#7597
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. #21461673C2semidirect
2. #21460640C2semidirect
3. #21460636C2semidirect
23. C2×#11758222C8semidirect
180. C61#7597semidirect

Maximal subgroups

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

subgroupindex
#214616732
#214606402
#214606362
#214483072
#759761