Finite Group Databasebeta

← #30595439

Subgroups — #30595439

Order 15616.

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

normal subgroups only

This group has 478 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#21461735C211yesmaximal, characteristic
2#21461534C211yesmaximal, characteristic
3#21460640C212yesmaximal
4#21460639C212yesmaximal
5C4×#14519775C211yesmaximal, characteristic
6C2×#14519844—21no—
7C2×C4×#92420—21no—
8#16840628—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519775C411yescharacteristic
13C2×C4×Dic122C411yescharacteristic
14#16839669C2211yescharacteristic
15#16839667C2211yescharacteristic
16#16839657—21no—
17#16839657—21no—
18#16839631C411yescharacteristic
19C4×#11758196—21no—
20C4×#11758196—21no—
21C42×Dic61C2211yescharacteristic
22C2×C4×Q8×C61C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25#14519844—42no—
26C4×#92420—24no—
27C22×Dic122C2×C411yescharacteristic
28#14519775—22no—
29#14519775C814yescomplemented
30C4×Dic122—42no—
31C2×C4⋊Dic61C2×C411yescharacteristic
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×C4×Dic61—21no—
38C2×C4×Dic61C2×C411yescharacteristic
39C2×C4×Dic61D411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61C2311yescharacteristic
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48C22×Q8×C61C2×C411yescharacteristic
49C4×Q8×C61—42no—
50C2×C4⋊C4×C61—21no—
51C2×C4⋊C4×C61C2×C411yescharacteristic
52C2×C42×C61—21no—
53C2×C42×C61C2×C411yescharacteristic
54C2×Q8×C61—21no—
55C2×Q8×C61—41no—
56C2×Q8×C61—41no—
57C2×Q8×C61C2×C812yes—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22×C411yescharacteristic
63C22×Dic61—21no—
64C22×Dic61—21no—
65C22×Dic61C22⋊C411yescharacteristic
66C22×Dic61C22⋊C411yescharacteristic
67C22×Dic61C2×D411yescharacteristic
68C22×Dic61C2×D411yescharacteristic
69C2×Dic122—21no—
70C2×Dic122—41no—
71C2×Dic122—41no—
72C2×Dic122C2×C812yes—
73C2×#92420—24no—
74C2×#92420—42no—
75C2×#92420—42no—
76C2×#92420—42no—
77C2×#92420—42no—
78C2×#92420—42no—
79C4⋊C4×C61—41no—
80C4⋊C4×C61—42no—
81C42×C61—22no—
82C42×C61—42no—
83C4⋊Dic61—41no—
84#11758196—24no—
85#11758196—24no—
86#11758196—42no—
87#11758196—42no—
88#11758196—42no—
89C4×Dic61—22no—
90C4×Dic61—22no—
91C4×Dic61—41no—
92C4×Dic61—41no—
93C4×Dic61—42no—
94C4×Dic61C2×C812yes—
95C4×Dic61M1612yes—
96C4×Dic61SD1612yes—
97C4×Dic61Q1612yes—
98C23×C61C2×C22⋊C411yescharacteristic
99Q8×C61—42no—
100Q8×C61—42no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—22no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61#10012yes—
114C2×C4×C61#10312yes—
115C2×C4×C61C22×C811yescharacteristic
116C2×C4×C61C2×M1611yescharacteristic
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—22no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61C22⋊C812yes—
130C2×Dic61C22⋊C812yes—
131C2×Dic61#10312yes—
132C2×Dic61#10412yes—
133C2×Dic61C2×SD1611yescharacteristic
134C2×Dic61C2×Q1611yescharacteristic
135C2×Dic61#13712yes—
136Dic122—42no—
137Dic122—42no—
138#92420—44no—
139#92420—82no—
140#7590—611nomaximal, Sylow
141C22×C61C2×C22⋊C811yescharacteristic
142C22×C61#41011yescharacteristic
143C22×C61C2×#10011yescharacteristic
144C22×C61C2×#10311yescharacteristic
145C22×C61#41911yescharacteristic
146C22×C61C2×#10411yescharacteristic
147C22×C61#42111yescharacteristic
148C4×C61—22no—
149C4×C61—21no—
150C4×C61—21no—
151C4×C61—22no—
152C4×C61—42no—
153C4×C61—81no—
154Dic61—22no—
155Dic61—22no—
156Dic61—21no—
157Dic61—21no—
158Dic61—42no—
159Dic61—81no—
160Dic61Q8⋊C814yes—
161C4×C4⋊Q8—611no—
162#1831—611no—
163#1744—611no—
164#1272—612no—
165#1272—612no—
166C2×C61#146011yescharacteristic
167C2×C61C2×Q8⋊C811yescharacteristic
168C2×C61#147911yescharacteristic
169C2×C61#150611yescharacteristic
170C2×C61#151811yescharacteristic
171C2×C61#153011yescharacteristic
172C2×C61#154811yescharacteristic
173C2×C4⋊Q8—611no—
174C2×C4×Q8—611no—
175C2×C4×Q8#692311yescharacteristic
176C2×C4⋊C8—1221no—
177C2×C4×C8—1221no—
178#391—611no—
179#391—611no—
180#389—1221no—
181#389—1221no—
182#384—611no—
183C4×C4⋊C4—1221no—
184C4×C4⋊C4—1221no—
185C43—611no—
186#336—612no—
187#336—612no—
188#336—1221no—
189#336—1221no—
190C61#759011yescharacteristic, complemented, Sylow
191C22×Q8—611no—
192C22×Q8C2×#692311yescharacteristic
193C22×C8—1222no—
194C22×C8—1222no—
195C4⋊Q8—614no—
196C4⋊Q8—1222no—
197C4×Q8—42no—
198C4×Q8—2442no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—611no—
201C2×C4⋊C4—1221no—
202C2×C4⋊C4—1221no—
203C2×C4⋊C4—1221no—
204C2×C4⋊C4—1221no—
205C2×C4⋊C4—1221no—
206C2×C4⋊C4C2×#692311yescharacteristic
207C2×C42—21no—
208C2×C42—611no—
209C2×C42—611no—
210C2×C42—611no—
211C2×C42—611no—
212C2×C42—611no—
213C2×C42—611no—
214C2×C42—1221no—
215C2×C42C2×#692311yescharacteristic
216C4⋊C8—2442no—
217C4×C8—1224no—
218#95—1221no—
219#95—1221no—
220#95—1221no—
221#95—1221no—
222C2×Q8—21no—
223C2×Q8—41no—
224C2×Q8—41no—
225C2×Q8—612no—
226C2×Q8—1221no—
227C2×Q8—2441no—
228C2×Q8—2441no—
229C2×Q8D61⋊C812yes—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—611no—
233C22×C4—611no—
234C22×C4—611no—
235C22×C4—611no—
236C22×C4—1221no—
237C22×C4—1221no—
238C22×C4C22⋊#692311yescharacteristic
239C22×C4C22⋊#692311yescharacteristic
240C22×C4C22×#692311yescharacteristic
241C2×C8—1224no—
242C2×C8—2442no—
243C2×C8—2442no—
244C2×C8—2442no—
245C2×C8—2442no—
246C2×C8—2442no—
247C4⋊C4—41no—
248C4⋊C4—42no—
249C4⋊C4—1224no—
250C4⋊C4—1224no—
251C4⋊C4—2441no—
252C4⋊C4—2442no—
253C4⋊C4—2442no—
254C4⋊C4—2442no—
255C42—22no—
256C42—42no—
257C42—612no—
258C42—612no—
259C42—612no—
260C42—612no—
261C42—1222no—
262C42—1222no—
263C42—2441no—
264C42—2441no—
265C42—2442no—
266C23C2×C22⋊#692311yescharacteristic
267Q8—42no—
268Q8—42no—
269Q8—2442no—
270Q8—2442no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—22no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—612no—
284C2×C4—612no—
285C2×C4—612no—
286C2×C4—612no—
287C2×C4—611no—
288C2×C4—611no—
289C2×C4—612no—
290C2×C4—1221no—
291C2×C4—1221no—
292C2×C4—1221no—
293C2×C4—1221no—
294C2×C4—1221no—
295C2×C4—1221no—
296C2×C4—1222no—
297C2×C4—2441no—
298C2×C4—2441no—
299C2×C4—2441no—
300C2×C4—2441no—
301C2×C4—2441no—
302C2×C4#1451983712yes—
303C2×C4#1451984012yes—
304C2×C4C2×D61⋊C811yescharacteristic
305C2×C4D61⋊M1611yescharacteristic
306C8—4882no—
307C8—2444no—
308C22D61⋊(C22⋊C8)11yescharacteristic
309C22#1684074111yescharacteristic
310C22C2×#1451983711yescharacteristic
311C22C2×#1451984011yescharacteristic
312C22#1684075511yescharacteristic
313C22D61⋊#10411yescharacteristic
314C22#1684075911yescharacteristic
315C4—22no—
316C4—21no—
317C4—21no—
318C4—22no—
319C4—42no—
320C4—81no—
321C4—614no—
322C4—1221no—
323C4—1221no—
324C4—1222no—
325C4—1222no—
326C4—4881no—
327C4—2442no—
328C2#2146105811yescharacteristic
329C2D61⋊(Q8⋊C8)11yescharacteristic
330C2#2146112211yescharacteristic
331C2#2146121211yescharacteristic
332C2#2146125211yescharacteristic
333C2#2146128811yescharacteristic
334C2#2146133211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC2×C4×Q8×C61C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×C4×Q8#6923
hypocenterC61#7590
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
29. #14519775C8semidirect
190. C61#7590semidirect

Maximal subgroups

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

subgroupindex
#214617352
#214615342
#214606402
#214606392
C4×#145197752
#759061