Finite Group Databasebeta

← #30599245

Subgroups — #30599245

Order 15616.

496 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 114 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#21461674C211yesmaximal, characteristic
2C4×#14519834C211yesmaximal, characteristic
3#21460655C212yesmaximal, complemented
4#21460655C212yesmaximal, complemented
5#21448212C211yesmaximal, characteristic
6C2×C4⋊#92420C2212yes—
7C2×#14519834—21no—
8C2×#14519834—21no—
9C2×C4×#92420C2212yes—
10#16840628—21no—
11#16840628—21no—
12C2×C42×D61C2211yescharacteristic
13#16839629—21no—
14#16839628C411yescharacteristic
15#16839624—21no—
16#16839619C411yescharacteristic
17#16839619C411yescharacteristic
18C4⋊C4×Dic61C2211yescharacteristic
19C4⋊C4×Dic61C2211yescharacteristic
20#16839609—21no—
21#16839607—21no—
22C61×#382C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C4⋊#92420—24no—
26#14519834—24no—
27#14519834—42no—
28C4×#92420—24no—
29C22×C4×D61C2×C411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C22×C4×D61D411yescharacteristic
32C2×C4⋊Dic61C2×C411yescharacteristic
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×#11758198—21no—
35C2×#11758198—21no—
36C2×C4×Dic61—21no—
37C2×C4×Dic61—21no—
38C2×C4×Dic61D411yescharacteristic
39C2×C4×Dic61D411yescharacteristic
40C2×C4×Dic61C2311yescharacteristic
41C42×D61—24no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48C2×C4⋊C4×C61C2×C411yescharacteristic
49C2×C4⋊C4×C61C2×C411yescharacteristic
50C2×C42×C61C2×C411yescharacteristic
51#95×C61—21no—
52#95×C61—21no—
53C23×D61C22⋊C411yescharacteristic
54C22×C4×C61—21no—
55C22×C4×C61—21no—
56C22×C4×C61C22⋊C411yescharacteristic
57C22×C4×C61C22⋊C411yescharacteristic
58C22×C4×C61C22×C411yescharacteristic
59C22×Dic61—21no—
60C22×Dic61—21no—
61C22×Dic61C22⋊C411yescharacteristic
62C22×Dic61C2×D411yescharacteristic
63C22×Dic61C2×D411yescharacteristic
64C2×C4×D61—22no—
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—21no—
72C2×C4×D61—21no—
73C2×C4×D61—41no—
74C2×#92420—24no—
75C2×#92420—42no—
76C2×#92420—42no—
77C2×#92420—42no—
78C2×#92420—42no—
79C2×#92420—42no—
80C4⋊C4×C61—22no—
81C4⋊C4×C61—22no—
82C42×C61—22no—
83#11758198—42no—
84#11758198—42no—
85C4⋊Dic61—22no—
86C4⋊Dic61—22no—
87C4×Dic61—22no—
88C4×Dic61—22no—
89C4×Dic61—42no—
90C4×Dic61—41no—
91C4×Dic61—41no—
92C4×Dic61#4114yes—
93C23×C61C2×C22⋊C411yescharacteristic
94C22×D61—21no—
95C22×D61—21no—
96C22×D61—21no—
97C22×D61—21no—
98C22×D61—21no—
99C22×D61—21no—
100C22×D61#10412yes—
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—41no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61#11712yes—
114C2×C4×C61#13112yes—
115C2×C4×C61#13112yes—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61#12312yes—
128C2×Dic61#12312yes—
129C2×Dic61#13512yes—
130C2×Dic61AGL(1,ℤ/8)11yescharacteristic
131C2×Dic61#13711yescharacteristic
132C4×D61—44no—
133C4×D61—44no—
134C4×D61—42no—
135C4×D61—42no—
136#92420—44no—
137#92420—82no—
138#8711—611nomaximal, Sylow
139C22×C61#38111yescharacteristic
140C22×C61#40811yescharacteristic
141C22×C61#40811yescharacteristic
142C22×C61#41611yescharacteristic
143C22×C61#41711yescharacteristic
144C22×C61C2×#10411yescharacteristic
145C22×C61#42111yescharacteristic
146C2×D61—22no—
147C2×D61—22no—
148C2×D61—22no—
149C2×D61—41no—
150C2×D61—41no—
151C2×D61—41no—
152C2×D61—41no—
153C4×C61—41no—
154C4×C61—41no—
155C4×C61—81no—
156C4×C61—81no—
157C4×C61#43314yes—
158Dic61—22no—
159Dic61—41no—
160Dic61—81no—
161Dic61—81no—
162Dic61#48212yes—
163Dic61#48512yes—
164#2283—611no—
165#1797—611no—
166C4×C22⋊C8—611no—
167#1279—612no—
168#1279—612no—
169C2×C61#148211yescharacteristic
170C2×C61#148311yescharacteristic
171C2×C61#149411yescharacteristic
172C2×C61#149511yescharacteristic
173C2×C61#181811yescharacteristic
174C2×C61#182511yescharacteristic
175C2×C61#182611yescharacteristic
176D61—42no—
177C22×C42—611no—
178C2×C4⋊C8—612no—
179C2×C22⋊C8—1221no—
180C2×C22⋊C8—1221no—
181C2×C4×C8—612no—
182#383—1221no—
183#382—611no—
184#382#692311yescharacteristic
185#381—1221no—
186#380—611no—
187#380—611no—
188C4×C4⋊C4—611no—
189C4×C4⋊C4—611no—
190C4×C22⋊C4—1221no—
191#376—1221no—
192#336—1221no—
193#336—1221no—
194C61#871111yescharacteristic, complemented, Sylow
195C23×C4—611no—
196C23×C4—611no—
197C23×C4—611no—
198C22×C8—1222no—
199C22×C8—1222no—
200C2×C4⋊C4—611no—
201C2×C4⋊C4—611no—
202C2×C4⋊C4C2×#692311yescharacteristic
203C2×C4⋊C4C2×#692311yescharacteristic
204C2×C22⋊C4—1221no—
205C2×C22⋊C4—1221no—
206C2×C42—611no—
207C2×C42—611no—
208C2×C42—611no—
209C2×C42—1224no—
210C2×C42—1221no—
211C2×C42—1221no—
212C2×C42C2×#692311yescharacteristic
213C4⋊C8—1224no—
214C22⋊C8—1224no—
215C22⋊C8—2442no—
216C4×C8—1224no—
217#95—21no—
218#95—21no—
219#95—1221no—
220#95—1221no—
221#95—1221no—
222#95—1221no—
223#95—1221no—
224#95—1221no—
225C24—611no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—611no—
229C22×C4—611no—
230C22×C4—611no—
231C22×C4—1221no—
232C22×C4—1222no—
233C22×C4—1222no—
234C22×C4—1222no—
235C22×C4—1221no—
236C22×C4—1222no—
237C22×C4—1222no—
238C22×C4—1222no—
239C22×C4—1222no—
240C22×C4—1221no—
241C22×C4—1221no—
242C22×C4—2441no—
243C22×C4C22⋊#692311yescharacteristic
244C22×C4C22⋊#692311yescharacteristic
245C22×C4C22×#692311yescharacteristic
246C2×C8—1224no—
247C2×C8—2442no—
248C2×C8—2442no—
249C2×C8—2442no—
250C2×C8—2442no—
251C2×C8—2442no—
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4—1222no—
255C4⋊C4—1222no—
256C22⋊C4—2442no—
257C22⋊C4—2442no—
258C42—22no—
259C42—614no—
260C42—1222no—
261C42—1222no—
262C42—2442no—
263C42—2441no—
264C42—2441no—
265C23—612no—
266C23—1221no—
267C23—1221no—
268C23—1221no—
269C23—1221no—
270C23—1221no—
271C23—1221no—
272C23C2×C22⋊#692311yescharacteristic
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
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—2442no—
296C2×C4—2442no—
297C2×C4—2444no—
298C2×C4—2441no—
299C2×C4—2441no—
300C2×C4—2441no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4—2444no—
305C2×C4#1451985612yes—
306C2×C4#1451986412yes—
307C2×C4#1451986512yes—
308C8—4882no—
309C8—2444no—
310C22—1222no—
311C22—1222no—
312C22—1222no—
313C22—2441no—
314C22—2441no—
315C22—2441no—
316C22—2441no—
317C22#1684070511yescharacteristic
318C22#1684073611yescharacteristic
319C22#1684073711yescharacteristic
320C22#1684075211yescharacteristic
321C22#1684075311yescharacteristic
322C22D61⋊#10411yescharacteristic
323C22#1684075911yescharacteristic
324C4—41no—
325C4—41no—
326C4—81no—
327C4—81no—
328C4—612no—
329C4—612no—
330C4—1222no—
331C4—4881no—
332C4—4881no—
333C4—2441no—
334C4#1684078714yes—
335C2—2442no—
336C2#2146113111yescharacteristic
337C2#2146113511yescharacteristic
338C2#2146117311yescharacteristic
339C2#2146117711yescharacteristic
340C2#2146171311yescharacteristic
341C2#2146172411yescharacteristic
342C2#2146172711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#382C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#382#6923
hypocenterC61#8711
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
3. #21460655C2semidirect
4. #21460655C2semidirect
194. C61#8711semidirect

Maximal subgroups

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

subgroupindex
#214616742
C4×#145198342
#214606552
#214482122
#871161