Finite Group Databasebeta

← #30601664

Subgroups — #30601664

Order 15616.

640 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 640 conjugacy classes of subgroups — too many to draw. Only its 122 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#21461675C211yesmaximal, characteristic
2#21461545C211yesmaximal, characteristic
3C2×#16840608C214yesmaximal
4C2×#16839658C211yesmaximal, characteristic
5C2×#14519844—21no—
6C2×C22⋊#92420C2212yes—
7C2×C22⋊#92420C2212yes—
8C2×#14519832—21no—
9#16840628—21no—
10#16840628—21no—
11#16840608—28no—
12C22×C4⋊Dic61C411yescharacteristic
13C22×#11758196C2212yes—
14C22×C4×Dic61C2211yescharacteristic
15#16839658—21no—
16#16839658—21no—
17#16839658—21no—
18#16839658—21no—
19C2×#14519684C412yes—
20C22×C4⋊C4×C61C411yescharacteristic
21C22×#92420—22no—
22C22×#92420—22no—
23#14519844—42no—
24C22⋊#92420—22no—
25C22⋊#92420—24no—
26C22⋊#92420D414yes—
27#14519832—42no—
28C23×Dic61C2×C412yes—
29C23×Dic61C2×C411yescharacteristic
30C23×Dic61C2311yescharacteristic
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61—24no—
34C2×#11758196—24no—
35C2×#11758196—22no—
36C2×#11758196—22no—
37C2×#11758196—24no—
38C2×C4×Dic61—42no—
39C2×C4×Dic61D411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43#14519684—22no—
44#14519684—22no—
45C23×C4×C61C2×C412yes—
46C23×C4×C61C2×C411yescharacteristic
47C2×C4⋊C4×C61—21no—
48C2×C4⋊C4×C61—21no—
49C2×C4⋊C4×C61—42no—
50C24×C61C22×C411yescharacteristic
51C22×C4×C61—22no—
52C22×C4×C61—22no—
53C22×C4×C61—22no—
54C22×C4×C61—22no—
55C22×C4×C61—24no—
56C22×C4×C61—42no—
57C22×C4×C61—42no—
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22⋊C411yescharacteristic
60C22×Dic61—22no—
61C22×Dic61—24no—
62C22×Dic61—22no—
63C22×Dic61—22no—
64C22×Dic61—24no—
65C22×Dic61—22no—
66C22×Dic61—41no—
67C22×Dic61—41no—
68C22×Dic61—41no—
69C22×Dic61C22⋊C411yescharacteristic
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61M1614yes—
72C22×Dic61C2×D411yescharacteristic
73C22×Dic61C2×D411yescharacteristic
74C22×Dic61C2×D412yes—
75C22×Dic61#4112yes—
76C2×#92420—24no—
77C2×#92420—42no—
78C2×#92420—42no—
79C2×#92420—42no—
80C2×#92420—42no—
81C2×#92420—42no—
82C4⋊C4×C61—42no—
83C4⋊C4×C61—42no—
84C4⋊Dic61—24no—
85C4⋊Dic61—24no—
86#11758196—44no—
87#11758196—42no—
88#11758196—42no—
89C4×Dic61—22no—
90C4×Dic61—22no—
91C4×Dic61—41no—
92C4×Dic61—41no—
93C23×C61—21no—
94C23×C61—21no—
95C23×C61—21no—
96C23×C61—21no—
97C23×C61C2×C22⋊C411yescharacteristic
98C23×C61C4×D412yes—
99C23×C61C2×M1612yes—
100C23×C61#13112yes—
101C2×C4×C61—28no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—42no—
107C2×C4×C61—42no—
108C2×C4×C61—42no—
109C2×C4×C61—84no—
110C2×C4×C61#9912yes—
111C2×C4×C61#10112yes—
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—24no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—28no—
123C2×Dic61—42no—
124C2×Dic61—42no—
125C2×Dic61—44no—
126C2×Dic61—42no—
127C2×Dic61—42no—
128C2×Dic61—44no—
129C2×Dic61#10112yes—
130C2×Dic61#12112yes—
131C2×Dic61#12411yescharacteristic
132C2×Dic61#12711yescharacteristic
133#92420—44no—
134#92420—82no—
135#9654—611nomaximal, Sylow
136C22×C61—22no—
137C22×C61—22no—
138C22×C61—22no—
139C22×C61—22no—
140C22×C61—22no—
141C22×C61—22no—
142C22×C61#39011yescharacteristic
143C22×C61#40711yescharacteristic
144C22×C61#40811yescharacteristic
145C22×C61C2×#9911yescharacteristic
146C22×C61#41011yescharacteristic
147C22×C61C2×#10111yescharacteristic
148C22×C61C2×#10111yescharacteristic
149C22×C61#43514yes—
150C4×C61—22no—
151C4×C61—22no—
152C4×C61—82no—
153Dic61—22no—
154Dic61—21no—
155Dic61—21no—
156Dic61—22no—
157Dic61—44no—
158Dic61—41no—
159C2×#389—611no—
160#1797—611no—
161#1749—611no—
162C2×#324—614no—
163C2×C61—24no—
164C2×C61#146311yescharacteristic
165C2×C61#146711yescharacteristic
166C2×C61#147011yescharacteristic
167C2×C61#147211yescharacteristic
168C2×C61#195511yescharacteristic
169C2×C61#196411yescharacteristic
170C2×C61#196611yescharacteristic
171C22×C4⋊C4—612no—
172C22×C4⋊C4—611no—
173C22×C4⋊C4#692311yescharacteristic
174C22×C42—611no—
175C2×C4⋊C8—1221no—
176C2×C22⋊C8—612no—
177C2×C22⋊C8—612no—
178C2×#97—1221no—
179#389—1221no—
180#389—1221no—
181#389—1221no—
182#389—1221no—
183C2×#95—612no—
184#336—1221no—
185#336—1221no—
186#324—1228no—
187C61#965411yescharacteristic, complemented, Sylow
188C23×C4—611no—
189C23×C4—612no—
190C23×C4—611no—
191C23×C4C2×#692312yes—
192C23×C4C2×#692311yescharacteristic
193C22×C8—1222no—
194C22×C8—1222no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—42no—
198C2×C4⋊C4—1224no—
199C2×C4⋊C4—1221no—
200C2×C4⋊C4—1221no—
201C2×C4⋊C4—1224no—
202C2×C4⋊C4—1222no—
203C2×C4⋊C4—1222no—
204C2×C4⋊C4—1224no—
205C2×C42—611no—
206C2×C42—611no—
207C2×C42—611no—
208C2×C42—611no—
209C2×C42—2442no—
210C4⋊C8—2442no—
211C22⋊C8—614no—
212C22⋊C8—1222no—
213C22⋊C8—1224no—
214#97—2442no—
215#95—1222no—
216#95—1222no—
217C24C22×#692311yescharacteristic
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—24no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—611no—
226C22×C4—611no—
227C22×C4—611no—
228C22×C4—612no—
229C22×C4—612no—
230C22×C4—611no—
231C22×C4—614no—
232C22×C4—1222no—
233C22×C4—1222no—
234C22×C4—1224no—
235C22×C4—1222no—
236C22×C4—1222no—
237C22×C4—1224no—
238C22×C4—2441no—
239C22×C4—2441no—
240C22×C4—2441no—
241C22×C4C22⋊#692311yescharacteristic
242C22×C4C22⋊#692311yescharacteristic
243C2×C8—1224no—
244C2×C8—2442no—
245C2×C8—2442no—
246C2×C8—2442no—
247C2×C8—2442no—
248C2×C8—2442no—
249C4⋊C4—42no—
250C4⋊C4—42no—
251C4⋊C4—1224no—
252C4⋊C4—1224no—
253C4⋊C4—2444no—
254C4⋊C4—2442no—
255C4⋊C4—2442no—
256C42—1222no—
257C42—1222no—
258C42—2441no—
259C42—2441no—
260C23—21no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23C2×C22⋊#692311yescharacteristic
265C23D4×#692312yes—
266C23D61⋊M1612yes—
267C23#1451986512yes—
268C2×C4—28no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—84no—
277C2×C4—612no—
278C2×C4—611no—
279C2×C4—611no—
280C2×C4—612no—
281C2×C4—1221no—
282C2×C4—1221no—
283C2×C4—1221no—
284C2×C4—1221no—
285C2×C4—1221no—
286C2×C4—1221no—
287C2×C4—1224no—
288C2×C4—1221no—
289C2×C4—1221no—
290C2×C4—1221no—
291C2×C4—1228no—
292C2×C4—2442no—
293C2×C4—2442no—
294C2×C4—2444no—
295C2×C4—2442no—
296C2×C4—2442no—
297C2×C4—2444no—
298C2×C4#1451983512yes—
299C2×C4#1451983812yes—
300C8—4882no—
301C8—2444no—
302C22—22no—
303C22—22no—
304C22—22no—
305C22—22no—
306C22—22no—
307C22—22no—
308C22#1684071411yescharacteristic
309C22#1684073411yescharacteristic
310C22#1684073711yescharacteristic
311C22C2×#1451983511yescharacteristic
312C22#1684074211yescharacteristic
313C22C2×#1451983811yescharacteristic
314C22D61⋊#10111yescharacteristic
315C22#1684079214yes—
316C4—22no—
317C4—22no—
318C4—82no—
319C4—1222no—
320C4—1221no—
321C4—1222no—
322C4—1221no—
323C4—2441no—
324C4—2444no—
325C2—24no—
326C2#2146106911yescharacteristic
327C2#2146108311yescharacteristic
328C2#2146109311yescharacteristic
329C2#2146109911yescharacteristic
330C2#2146194511yescharacteristic
331C2#2146195811yescharacteristic
332C2#2146196211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutator, prime radicalC24×C61C22×C4
FrattiniC24C22×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
cosocleC23×Dic61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#9654
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
187. C61#9654semidirect

Maximal subgroups

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

subgroupindex
#214616752
#214615452
C2×#168406082
C2×#168396582
#965461