Finite Group Databasebeta

← #30602536

Subgroups — #30602536

Order 15616.

1162 conjugacy classes of subgroups; only the 212 normal subgroups are shown.

normal subgroups only

This group has 1162 conjugacy classes of subgroups — too many to draw. Only its 212 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
1C22×#14519838C212yesmaximal
2C2×#16840643C214yesmaximal
3C2×#16840239C211yesmaximal, characteristic
4C22×#11758217C2214yes—
5C2×#14519838—24no—
6C2×#14519838—22no—
7C2×#14519838—22no—
8C2×#14519838C418yescomplemented
9#16840643—28no—
10C23×Dic122C2211yescharacteristic
11#16840239—28no—
12C2×C4×Dic122—22no—
13C2×#14519742—22no—
14C2×#14519736C411yescharacteristic
15C2×#14519733C412yes—
16C2×#14519733C2212yes—
17C2×#117×C61C411yescharacteristic
18C2×#11758217—24no—
19C2×#11758217—24no—
20C2×#11758217—24no—
21C2×#11758217—24no—
22C2×#11758217—24no—
23C2×#11758217C2×C418yes—
24C22×#92420—24no—
25#14519838—28no—
26#14519838—28no—
27C22×Dic122—24no—
28C22×Dic122—24no—
29C22×Dic122C2×C414yes—
30C22×Dic122D412yes—
31C22×Dic122D412yes—
32C22×Dic122D412yes—
33C22×Dic122Q812yes—
34C23×Dic61C2×C411yescharacteristic
35C23×Dic61C2311yescharacteristic
36C4×Dic122—216no—
37#14519742—216no—
38#14519736—24no—
39#14519733—24no—
40#14519733—24no—
41#14519733—24no—
42#14519733D418yes—
43C2×C4⋊Dic61—21no—
44C2×#11758196—22no—
45C2×#11758196—22no—
46C2×C22⋊Dic61C2×C412yes—
47C2×C4×Dic61—21no—
48C2×C4×Dic61—22no—
49C2×C4×Dic61—22no—
50C23×C4×C61C2×C411yescharacteristic
51#117×C61—24no—
52C2×C4⋊C4×C61—21no—
53C2×C22⋊C4×C61C2×C412yes—
54C2×C42×C61—21no—
55C24×C61C22×C411yescharacteristic
56C22×C4×C61—22no—
57C22×C4×C61—22no—
58C22×C4×C61—22no—
59C22×C4×C61C4212yes—
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C4⋊C412yes—
63C22×Dic61—22no—
64C22×Dic61—22no—
65C22×Dic61—22no—
66C22×Dic61C4212yes—
67C22×Dic61C22⋊C412yes—
68C22×Dic61C4⋊C412yes—
69C22×Dic61C22×C412yes—
70C22×Dic61C2×D411yescharacteristic
71C22×Dic61C2×D412yes—
72C22×Dic61C2×D414yes—
73C22×Dic61C2×Q811yescharacteristic
74C22×Dic61#4114yes—
75C2×Dic122—28no—
76C2×Dic122—28no—
77C2×Dic122—24no—
78C2×Dic122—24no—
79C2×Dic122—28no—
80C2×Dic122—28no—
81C2×Dic122—24no—
82C2×Dic122—24no—
83C2×Dic122C22⋊C414yes—
84C2×Dic122C22⋊C414yes—
85C2×Dic122C4⋊C414yes—
86C2×Dic122C4⋊C414yes—
87#11758217—28no—
88#11758217—28no—
89#11758217—44no—
90#11758217—44no—
91C2×#92420—28no—
92C2×#92420—44no—
93C2×#92420—44no—
94C4⋊C4×C61—24no—
95C22⋊C4×C61—22no—
96C22⋊C4×C61C22⋊C414yes—
97C42×C61—24no—
98C22⋊Dic61—22no—
99C22⋊Dic61C22⋊C414yes—
100C4⋊Dic61—24no—
101#11758196—28no—
102#11758196—28no—
103C4×Dic61—28no—
104C4×Dic61—24no—
105C4×Dic61—28no—
106C23×C61—42no—
107C23×C61C2×C4211yescharacteristic
108C23×C61C2×C22⋊C411yescharacteristic
109C23×C61C2×C22⋊C412yes—
110C23×C61C2×C4⋊C411yescharacteristic
111C23×C61#11712yes—
112C2×C4×C61—24no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—24no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—24no—
119C2×C4×C61—44no—
120C2×C4×C61#9512yes—
121C2×C4×C61#9512yes—
122C2×Dic61—24no—
123C2×Dic61—22no—
124C2×Dic61—24no—
125C2×Dic61—22no—
126C2×Dic61—24no—
127C2×Dic61—44no—
128C2×Dic61#9514yes—
129C2×Dic61C2×C22⋊C412yes—
130C2×Dic61C2×C4⋊C412yes—
131C2×Dic61C4×D414yes—
132C2×Dic61C4×D414yes—
133C2×Dic61#12014yes—
134C2×Dic61#12114yes—
135C2×Dic61C22⋊Q814yes—
136C2×Dic61#12314yes—
137Dic122—28no—
138Dic122—28no—
139Dic122—28no—
140Dic122—28no—
141#92420—48no—
142#10770—611nomaximal, Sylow
143C22×C61—22no—
144C22×C61—24no—
145C22×C61—41no—
146C22×C61—42no—
147C22×C61—41no—
148C22×C61C2×#9511yescharacteristic
149C22×C61C4×C22⋊C412yes—
150C22×C61#37911yescharacteristic
151C22×C61#38012yes—
152C22×C61#38111yescharacteristic
153C4×C61—22no—
154C4×C61—22no—
155C4×C61—44no—
156Dic61—24no—
157Dic61—44no—
158Dic61#38514yes—
159Dic61#38614yes—
160C2×#519—611no—
161C22×#101—612no—
162C2×#344—614no—
163C2×C61—21no—
164C2×C61—21no—
165C2×C61—22no—
166C2×C61—22no—
167C2×C61C22⋊#9511yescharacteristic
168C2×C61#183012yes—
169C23×Q8—611no—
170C22×M16—614no—
171#519—1228no—
172C2×C4×Q8—1222no—
173C2×C4×Q8—1222no—
174C2×#117—611no—
175C2×#117—612no—
176C2×#117—612no—
177C2×#117#692311yescharacteristic
178C2×#101—618no—
179C2×#101—1224no—
180C2×#101—1222no—
181C2×#101—1222no—
182#344—1228no—
183C61#1077011yescharacteristic, complemented, Sylow
184C22×Q8—614no—
185C22×Q8—612no—
186C22×Q8—612no—
187C22×Q8—612no—
188C22×Q8—612no—
189C22×Q8—1224no—
190C22×Q8—1224no—
191C23×C4—611no—
192C23×C4—611no—
193C23×C4C2×#692311yescharacteristic
194C2×M16—618no—
195C2×M16—1224no—
196C2×M16—1224no—
197C2×M16—1224no—
198C2×M16—1224no—
199C2×M16—1224no—
200C22×C8—1224no—
201C4×Q8—12216no—
202C4×Q8—12216no—
203#117—24no—
204#117—618no—
205#117—1224no—
206#117—1224no—
207#117—1224no—
208#117—1224no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—1222no—
211C2×C4⋊C4—1222no—
212C2×C4⋊C4—1221no—
213C2×C22⋊C4—612no—
214C2×C22⋊C4C2×#692312yes—
215C2×C42—21no—
216C2×C42—1222no—
217C2×C42—1222no—
218C2×C42—1221no—
219#101—1228no—
220#101—1228no—
221C24C22×#692311yescharacteristic
222C2×Q8—614no—
223C2×Q8—614no—
224C2×Q8—614no—
225C2×Q8—614no—
226C2×Q8—1224no—
227C2×Q8—1224no—
228C2×Q8—1228no—
229C2×Q8—1228no—
230C2×Q8—1224no—
231C2×Q8—1224no—
232C2×Q8—1228no—
233C2×Q8—1228no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—612no—
238C22×C4—612no—
239C22×C4—614no—
240C22×C4—611no—
241C22×C4—611no—
242C22×C4—614no—
243C22×C4—612no—
244C22×C4—612no—
245C22×C4—612no—
246C22×C4—1222no—
247C22×C4—1222no—
248C22×C4—1222no—
249C22×C4C4×#692312yes—
250C22×C4C4⋊#692312yes—
251C22×C4C22⋊#692311yescharacteristic
252C22×C4C22⋊#692311yescharacteristic
253M16—1228no—
254M16—1228no—
255M16—2444no—
256M16—2444no—
257C2×C8—1228no—
258C2×C8—2444no—
259C2×C8—2444no—
260C4⋊C4—24no—
261C4⋊C4—1228no—
262C4⋊C4—1228no—
263C4⋊C4—1224no—
264C22⋊C4—22no—
265C22⋊C4—614no—
266C22⋊C4—1222no—
267C22⋊C4C22⋊#692314yes—
268C42—24no—
269C42—1228no—
270C42—1224no—
271C42—1228no—
272C23—42no—
273C23C2×C4×#692311yescharacteristic
274C23C2×C22⋊#692311yescharacteristic
275C23C2×C22⋊#692312yes—
276C23C2×C4⋊#692311yescharacteristic
277C23#1451985612yes—
278Q8—1228no—
279Q8—1228no—
280Q8—1228no—
281Q8—1228no—
282C2×C4—24no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—24no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—24no—
289C2×C4—44no—
290C2×C4—614no—
291C2×C4—614no—
292C2×C4—614no—
293C2×C4—612no—
294C2×C4—612no—
295C2×C4—614no—
296C2×C4—614no—
297C2×C4—614no—
298C2×C4—614no—
299C2×C4—1224no—
300C2×C4—1222no—
301C2×C4—1224no—
302C2×C4—1222no—
303C2×C4—1224no—
304C2×C4—2444no—
305C2×C4(C2×#6923)⋊C412yes—
306C2×C4(C2×#6923)⋊C412yes—
307C8—2448no—
308C22—22no—
309C22—24no—
310C22—41no—
311C22—42no—
312C22—41no—
313C22C2×(C2×#6923)⋊C411yescharacteristic
314C22C4×C22⋊#692312yes—
315C22#1684070311yescharacteristic
316C22#1684070412yes—
317C22#1684070511yescharacteristic
318C4—22no—
319C4—22no—
320C4—44no—
321C4—614no—
322C4—614no—
323C4—1224no—
324C4—2444no—
325C2—21no—
326C2—22no—
327C2—21no—
328C2—22no—
329C2#2146099311yescharacteristic
330C2#2146173312yes—
subgroupG/H
centerC22#16840705
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC2×#117×C61C4
socleC22×C61#381
prime radicalC24×C61C22×C4
cosocleC23×Dic61C23
hypercenterC2×#117#6923
hypocenterC61#10770
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
8. C2×#14519838C4semidirect
183. C61#10770semidirect

Maximal subgroups

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

subgroupindex
C22×#145198382
C2×#168406432
C2×#168402392
#1077061