Finite Group Databasebeta

← #30603421

Subgroups — #30603421

Order 15616.

1042 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 1042 conjugacy classes of subgroups — too many to draw. Only its 156 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×#16840734C212yesmaximal
2C2×#16840642C214yesmaximal, complemented
3C2×#16839621C211yesmaximal, characteristic
4C22×#11758217C2214yes—
5#16840734—28no—
6C2×#14519834—22no—
7C2×#14519834—22no—
8#16840642—28no—
9C23×C4×D61C2211yescharacteristic
10C22×#11758196C2212yes—
11C22×#11758198C412yes—
12#16839621—22no—
13#16839621—22no—
14C2×#14519684C411yescharacteristic
15C2×#95×C61C411yescharacteristic
16C2×#11758217—24no—
17C2×#11758217—24no—
18C2×#11758217—24no—
19C2×#11758217—24no—
20C2×#11758217—24no—
21C2×#11758217D418yes—
22C22×#92420—24no—
23#14519834—28no—
24#14519834—28no—
25C24×D61C2×C411yescharacteristic
26C23×Dic61C2×C412yes—
27C23×Dic61C2311yescharacteristic
28C22×C4×D61—24no—
29C22×C4×D61—24no—
30C22×C4×D61—24no—
31C22×C4×D61D412yes—
32C22×C4×D61D412yes—
33C2×#11758196—24no—
34C2×#11758196—22no—
35C2×#11758196—22no—
36C2×#11758196—24no—
37C2×#11758198—22no—
38C2×#11758198—22no—
39C2×#11758198—44no—
40#14519684—22no—
41C23×C4×C61C2×C412yes—
42C23×C4×C61C2×C411yescharacteristic
43#95×C61—22no—
44C24×C61C22×C411yescharacteristic
45C23×D61—22no—
46C23×D61—22no—
47C23×D61—22no—
48C23×D61—24no—
49C23×D61—42no—
50C23×D61C22⋊C411yescharacteristic
51C23×D61C22⋊C411yescharacteristic
52C22×C4×C61—22no—
53C22×C4×C61—24no—
54C22×C4×C61—22no—
55C22×C4×C61—24no—
56C22×C4×C61—42no—
57C22×C4×C61—42no—
58C22×C4×C61C22⋊C412yes—
59C22×Dic61—22no—
60C22×Dic61—24no—
61C22×Dic61—42no—
62C22×Dic61—42no—
63C22×Dic61C2×D414yes—
64C22×Dic61C2×D412yes—
65C22×Dic61#4114yes—
66C22×Dic61#4114yes—
67C2×C4×D61—22no—
68C2×C4×D61—22no—
69C2×C4×D61—24no—
70C2×C4×D61—24no—
71C2×C4×D61—24no—
72C2×C4×D61—24no—
73C2×C4×D61—22no—
74C2×C4×D61—22no—
75C2×C4×D61—44no—
76C2×C4×D61—44no—
77C2×C4×D61—44no—
78C2×C4×D61—44no—
79#11758217—28no—
80#11758217—28no—
81#11758217—44no—
82#11758217—44no—
83C2×#92420—28no—
84C2×#92420—44no—
85C2×#92420—44no—
86#11758198—44no—
87#11758198—44no—
88#11758196—42no—
89#11758196—44no—
90#11758196—42no—
91C23×C61—21no—
92C23×C61—21no—
93C23×C61—22no—
94C23×C61C2×C22⋊C411yescharacteristic
95C23×C61#11712yes—
96C23×C61C4×D414yes—
97C22×D61—28no—
98C22×D61—21no—
99C22×D61—21no—
100C22×D61—22no—
101C22×D61—22no—
102C22×D61—21no—
103C22×D61—21no—
104C22×D61—22no—
105C22×D61—22no—
106C22×D61—48no—
107C22×D61—48no—
108C22×D61—44no—
109C22×D61—44no—
110C22×D61#10012yes—
111C22×D61#10112yes—
112C2×C4×C61—22no—
113C2×C4×C61—22no—
114C2×C4×C61—22no—
115C2×C4×C61—44no—
116C2×C4×C61—42no—
117C2×C4×C61—42no—
118C2×C4×C61—42no—
119C2×C4×C61—84no—
120C2×Dic61—42no—
121C2×Dic61—42no—
122C2×Dic61—42no—
123C2×Dic61—84no—
124C2×Dic61#12012yes—
125C2×Dic61#12114yes—
126C2×Dic61#12114yes—
127C2×Dic61#12314yes—
128C2×Dic61#12314yes—
129C2×Dic61#12312yes—
130C2×Dic61#12414yes—
131C2×Dic61#12614yes—
132C4×D61—44no—
133C4×D61—44no—
134C4×D61—44no—
135C4×D61—44no—
136#92420—48no—
137#11198—611nomaximal, Sylow
138C22×C61—22no—
139C22×C61—22no—
140C22×C61—24no—
141C22×C61—24no—
142C22×C61#38111yescharacteristic
143C22×C61#38612yes—
144C22×C61#38814yes—
145C22×C61C2×#10011yescharacteristic
146C22×C61C2×#10111yescharacteristic
147C22×C61#41312yes—
148C2×D61—22no—
149C2×D61—22no—
150C2×D61—24no—
151C2×D61—24no—
152C2×D61—416no—
153C2×D61—41no—
154C2×D61—41no—
155C2×D61—42no—
156C2×D61—42no—
157C2×D61—41no—
158C2×D61—41no—
159C4×C61—42no—
160C4×C61—82no—
161Dic61—82no—
162Dic61#39414yes—
163Dic61#39714yes—
164C2×#407—612no—
165C2×#380—611no—
166C2×#343—614no—
167C2×C61—24no—
168C2×C61#144011yescharacteristic
169C2×C61#182111yescharacteristic
170C2×C61#182211yescharacteristic
171C2×C61#190012yes—
172C2×C61#190112yes—
173D61—42no—
174D61—42no—
175C24×C4—611no—
176C22×M16—614no—
177C22×C4⋊C4—612no—
178C22×C22⋊C4—612no—
179#407—1228no—
180C2×C22⋊C8—1222no—
181C2×C22⋊C8—1222no—
182#380—1222no—
183#380—1222no—
184C2×#95—611no—
185C2×#95#692311yescharacteristic
186#343—1228no—
187C61#1119811yescharacteristic, complemented, Sylow
188C25—611no—
189C23×C4—611no—
190C23×C4—612no—
191C23×C4—612no—
192C23×C4—612no—
193C23×C4—1224no—
194C23×C4—1224no—
195C23×C4—1224no—
196C23×C4C2×#692312yes—
197C23×C4C2×#692311yescharacteristic
198C2×M16—618no—
199C2×M16—1224no—
200C2×M16—1224no—
201C2×M16—1224no—
202C2×M16—1224no—
203C2×M16—1224no—
204C22×C8—1224no—
205C2×C4⋊C4—1224no—
206C2×C4⋊C4—1222no—
207C2×C4⋊C4—1222no—
208C2×C4⋊C4—1224no—
209C2×C22⋊C4—1222no—
210C2×C22⋊C4—1222no—
211C2×C22⋊C4—2444no—
212C22⋊C8—1228no—
213C22⋊C8—1228no—
214#95—22no—
215#95—1222no—
216C24—611no—
217C24—611no—
218C24—1222no—
219C24—1222no—
220C24—1222no—
221C24—1224no—
222C24—2442no—
223C24C22×#692311yescharacteristic
224C22×C4—22no—
225C22×C4—24no—
226C22×C4—22no—
227C22×C4—24no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—612no—
231C22×C4—614no—
232C22×C4—614no—
233C22×C4—614no—
234C22×C4—1222no—
235C22×C4—1222no—
236C22×C4—1224no—
237C22×C4—1224no—
238C22×C4—1224no—
239C22×C4—1224no—
240C22×C4—1222no—
241C22×C4—1222no—
242C22×C4—1224no—
243C22×C4—1222no—
244C22×C4—2444no—
245C22×C4—2444no—
246C22×C4—2444no—
247C22×C4—2444no—
248C22×C4—2442no—
249C22×C4—2442no—
250C22×C4C22⋊#692312yes—
251M16—1228no—
252M16—1228no—
253M16—2444no—
254M16—2444no—
255C2×C8—1228no—
256C2×C8—2444no—
257C2×C8—2444no—
258C4⋊C4—2442no—
259C4⋊C4—2444no—
260C4⋊C4—2442no—
261C22⋊C4—2444no—
262C22⋊C4—2444no—
263C23—21no—
264C23—21no—
265C23—22no—
266C23—612no—
267C23—612no—
268C23—1228no—
269C23—1221no—
270C23—1221no—
271C23—1222no—
272C23—1222no—
273C23—1221no—
274C23—1221no—
275C23—1222no—
276C23—1222no—
277C23—2448no—
278C23—2448no—
279C23—2444no—
280C23—2444no—
281C23C2×C22⋊#692311yescharacteristic
282C23#1451985612yes—
283C23D4×#692314yes—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—44no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—84no—
292C2×C4—614no—
293C2×C4—612no—
294C2×C4—614no—
295C2×C4—612no—
296C2×C4—614no—
297C2×C4—614no—
298C2×C4—614no—
299C2×C4—614no—
300C2×C4—4884no—
301C2×C4—2444no—
302C2×C4—2444no—
303C2×C4—2444no—
304C2×C4—2444no—
305C2×C4—2442no—
306C2×C4—2442no—
307C2×C4—2442no—
308C8—2448no—
309C22—24no—
310C22—24no—
311C22—22no—
312C22—22no—
313C22—1224no—
314C22—1224no—
315C22—1222no—
316C22—1222no—
317C22—24416no—
318C22—2441no—
319C22—2441no—
320C22—2442no—
321C22—2442no—
322C22—2441no—
323C22—2441no—
324C22#1684070511yescharacteristic
325C22#1684071012yes—
326C22#1684071214yes—
327C22D61⋊#10011yescharacteristic
328C22D61⋊#10111yescharacteristic
329C22#1684074812yes—
330C4—42no—
331C4—82no—
332C4—614no—
333C4—614no—
334C4—4882no—
335C2—24no—
336C2—2442no—
337C2—2442no—
338C2#2146100311yescharacteristic
339C2#2146171911yescharacteristic
340C2#2146172011yescharacteristic
341C2#2146184512yes—
342C2#2146184712yes—
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC2×#95×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×D61C2×C4
cosocleC23×Dic61C23
hypercenterC2×#95#6923
hypocenterC61#11198
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
2. C2×#16840642C2semidirect
187. C61#11198semidirect

Maximal subgroups

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

subgroupindex
C2×#168407342
C2×#168406422
C2×#168396212
#1119861