Finite Group Databasebeta

← #30595668

Subgroups — #30595668

Order 15616.

518 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 102 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#21461711C211yesmaximal, characteristic
2#21461480C211yesmaximal, characteristic
3#21460640C212yesmaximal, complemented
4#21460638C212yesmaximal, complemented
5#21454157C211yesmaximal, characteristic
6C22×D61⋊C8—21no—
7C2×#14519834—21no—
8#16840628—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519757C411yescharacteristic
13C2×C42×D61C2211yescharacteristic
14#16839668C411yescharacteristic
15#16839667C2211yescharacteristic
16#16839658C2211yescharacteristic
17#16839649—21no—
18#16839648—21no—
19#16839633—21no—
20#16839624—21no—
21#16839619C411yescharacteristic
22C61×#389C411yescharacteristic
23C2×D61⋊C8—24no—
24C2×D61⋊C8—42no—
25C2×D61⋊C8—42no—
26C22×#92420—22no—
27C22×#92420—22no—
28#14519834—42no—
29C22×Dic122C2×C411yescharacteristic
30C22×C4×D61C2×C411yescharacteristic
31C22×C4×D61D411yescharacteristic
32C22×C4×D61D411yescharacteristic
33#14519757—42no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×#11758196—21no—
37C2×#11758198—21no—
38C2×#11758198—21no—
39C2×C4×Dic61D411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61C2311yescharacteristic
42C42×D61—42no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49C2×C4⋊C4×C61—21no—
50C2×C4⋊C4×C61C2×C411yescharacteristic
51C2×C4⋊C4×C61C2×C411yescharacteristic
52C2×C42×C61C2×C411yescharacteristic
53#95×C61—21no—
54C23×D61C22⋊C411yescharacteristic
55C22×C4×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61C22⋊C411yescharacteristic
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22×C411yescharacteristic
60C22×Dic61—21no—
61C22×Dic61—21no—
62C22×Dic61C22⋊C411yescharacteristic
63C22×Dic61C2×D411yescharacteristic
64C22×Dic61C2×D411yescharacteristic
65C2×C4×D61—22no—
66C2×C4×D61—22no—
67C2×C4×D61—22no—
68C2×C4×D61—22no—
69C2×C4×D61—22no—
70C2×C4×D61—22no—
71C2×C4×D61—41no—
72C2×C4×D61—41no—
73C2×C4×D61SD1612yes—
74C2×C4×D61Q1612yes—
75C2×Dic122—22no—
76C2×Dic122—41no—
77C2×Dic122—41no—
78C2×#92420—24no—
79C2×#92420—42no—
80C2×#92420—42no—
81C2×#92420—42no—
82C2×#92420—42no—
83C2×#92420—42no—
84D61⋊C8—48no—
85C4⋊C4×C61—42no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—41no—
88C42×C61—41no—
89#11758198—42no—
90#11758198—42no—
91C4⋊Dic61—22no—
92C4⋊Dic61—42no—
93#11758196—42no—
94C4×Dic61—41no—
95C4×Dic61—41no—
96C4×Dic61—41no—
97C23×C61C2×C22⋊C411yescharacteristic
98C22×D61—21no—
99C22×D61—21no—
100C22×D61—21no—
101C22×D61—21no—
102C22×D61#9912yes—
103C22×D61#10312yes—
104C22×D61#10412yes—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61#10312yes—
119C2×C4×C61#13112yes—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61C2×SD1611yescharacteristic
134C2×Dic61C2×Q1611yescharacteristic
135C2×Dic61#13512yes—
136C4×D61—24no—
137C4×D61—24no—
138C4×D61—44no—
139C4×D61—44no—
140Dic122—82no—
141#92420—44no—
142#92420—82no—
143#7655—611nomaximal, Sylow
144C22×C61#40811yescharacteristic
145C22×C61C2×#9911yescharacteristic
146C22×C61#41311yescharacteristic
147C22×C61C2×#10311yescharacteristic
148C22×C61#41611yescharacteristic
149C22×C61C2×#10411yescharacteristic
150C22×C61#42111yescharacteristic
151C2×D61—22no—
152C2×D61—22no—
153C2×D61—22no—
154C2×D61—22no—
155C2×D61—22no—
156C2×D61—22no—
157C2×D61#32814yes—
158C4×C61—22no—
159C4×C61—22no—
160C4×C61—41no—
161C4×C61—81no—
162C4×C61—81no—
163Dic61—21no—
164Dic61—21no—
165Dic61—22no—
166Dic61—41no—
167Dic61—81no—
168Dic61—81no—
169#2855—611no—
170#1817—611no—
171C2×#336—611no—
172#1272—612no—
173#1271—612no—
174C2×C61#146811yescharacteristic
175C2×C61#148111yescharacteristic
176C2×C61#149411yescharacteristic
177C2×C61C2×#32811yescharacteristic
178C2×C61#151611yescharacteristic
179C2×C61#153211yescharacteristic
180C2×C61#154211yescharacteristic
181D61—24no—
182C23×C8—1221no—
183C2×C22⋊Q8—611no—
184C22×C42—611no—
185C2×C22⋊C8—1221no—
186#391—611no—
187#391—611no—
188#389—611no—
189#389#692311yescharacteristic
190#387—1221no—
191#387—1221no—
192#385—1221no—
193#381—1221no—
194#380—611no—
195#336—612no—
196#336—612no—
197#336—1221no—
198#336—1221no—
199C61#765511yescharacteristic, complemented, Sylow
200C22×Q8—611no—
201C23×C4—611no—
202C23×C4—611no—
203C23×C4—611no—
204C22×C8—1222no—
205C22×C8—1224no—
206C22×C8—1222no—
207C22×C8—2442no—
208C22×C8—2442no—
209C22⋊Q8—2442no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—611no—
212C2×C4⋊C4—1221no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4C2×#692311yescharacteristic
215C2×C4⋊C4C2×#692311yescharacteristic
216C2×C22⋊C4—1221no—
217C2×C22⋊C4—1221no—
218C2×C42—611no—
219C2×C42—611no—
220C2×C42—611no—
221C2×C42—2442no—
222C2×C42C2×#692311yescharacteristic
223C22⋊C8—2442no—
224#95—21no—
225#95—1221no—
226#95—1221no—
227#95—1221no—
228#95—1221no—
229#95—1221no—
230#95—1221no—
231C24—611no—
232C2×Q8—1222no—
233C2×Q8—2441no—
234C2×Q8—2441no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—611no—
238C22×C4—611no—
239C22×C4—612no—
240C22×C4—612no—
241C22×C4—611no—
242C22×C4—1222no—
243C22×C4—1222no—
244C22×C4—1222no—
245C22×C4—1222no—
246C22×C4—1222no—
247C22×C4—1222no—
248C22×C4—1221no—
249C22×C4—1221no—
250C22×C4—2441no—
251C22×C4—2441no—
252C22×C4C22⋊#692311yescharacteristic
253C22×C4C22⋊#692311yescharacteristic
254C22×C4C22×#692311yescharacteristic
255C2×C8—1224no—
256C2×C8—2442no—
257C2×C8—2442no—
258C2×C8—2442no—
259C2×C8—2442no—
260C2×C8—2448no—
261C2×C8—2442no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—42no—
265C4⋊C4—1222no—
266C4⋊C4—2442no—
267C4⋊C4—2442no—
268C22⋊C4—2442no—
269C22⋊C4—2442no—
270C42—41no—
271C42—2441no—
272C42—2441no—
273C42—2441no—
274C23—612no—
275C23—612no—
276C23—612no—
277C23—1221no—
278C23—1221no—
279C23—1221no—
280C23—1221no—
281C23C2×C22⋊#692311yescharacteristic
282Q8—4882no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—611no—
297C2×C4—611no—
298C2×C4—612no—
299C2×C4—1224no—
300C2×C4—1224no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—2444no—
309C2×C4—2444no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4#1451984012yes—
317C2×C4#1451986512yes—
318C8—4882no—
319C8—2444no—
320C22—614no—
321C22—1222no—
322C22—1222no—
323C22—1222no—
324C22—1222no—
325C22—1222no—
326C22—1222no—
327C22#1684073711yescharacteristic
328C22D61⋊#9911yescharacteristic
329C22#1684074811yescharacteristic
330C22C2×#1451984011yescharacteristic
331C22#1684075211yescharacteristic
332C22D61⋊#10411yescharacteristic
333C22#1684076011yescharacteristic
334C4—22no—
335C4—22no—
336C4—41no—
337C4—81no—
338C4—81no—
339C4—1221no—
340C4—1221no—
341C4—1222no—
342C4—4881no—
343C4—4881no—
344C4—2441no—
345C2—1224no—
346C2#2146108711yescharacteristic
347C2#2146112911yescharacteristic
348C2#2146117311yescharacteristic
349C2D61⋊#32811yescharacteristic
350C2#2146124411yescharacteristic
351C2#2146129411yescharacteristic
352C2#2146132011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#389C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#389#6923
hypocenterC61#7655
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
3. #21460640C2semidirect
4. #21460638C2semidirect
199. C61#7655semidirect

Maximal subgroups

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

subgroupindex
#214617112
#214614802
#214606402
#214606382
#214541572
#765561