Finite Group Databasebeta

← #30595712

Subgroups — #30595712

Order 15616.

568 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 126 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
2#21461480C211yesmaximal, characteristic
3#21460638C214yesmaximal, complemented
4#21454166C211yesmaximal, characteristic
5C22×D61⋊C8—21no—
6C2×C4⋊#92420—21no—
7C2×#14519834—21no—
8#16840628—21no—
9#16840628C2212yes—
10#16840628C2212yes—
11C2×#14519753—21no—
12C2×C42×D61C2211yescharacteristic
13#16839669—21no—
14#16839658—21no—
15#16839658C2212yes—
16#16839632C411yescharacteristic
17#16839619—21no—
18#16839619C412yes—
19C2×C4⋊Q8×C61C411yescharacteristic
20C2×D61⋊C8—24no—
21C2×D61⋊C8—42no—
22C2×D61⋊C8—42no—
23C22×#92420—22no—
24C22×#92420—22no—
25C4⋊#92420—42no—
26#14519834—42no—
27C22×C4×D61C2×C411yescharacteristic
28C22×C4×D61D411yescharacteristic
29C22×C4×D61D411yescharacteristic
30#14519753—42no—
31#14519753—42no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61C2×C412yes—
35C2×#11758196—22no—
36C2×#11758198—22no—
37C2×C4×Dic61D411yescharacteristic
38C2×C4×Dic61D411yescharacteristic
39C2×C4×Dic61C2311yescharacteristic
40C42×D61—42no—
41#14519684—22no—
42#14519684—22no—
43C22×Q8×C61—21no—
44C4⋊Q8×C61—42no—
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61C2×C412yes—
47C2×C42×C61C2×C411yescharacteristic
48C23×D61C22⋊C411yescharacteristic
49C2×Q8×C61—42no—
50C2×Q8×C61—42no—
51C2×Q8×C61—42no—
52C22×C4×C61—22no—
53C22×C4×C61C22⋊C411yescharacteristic
54C22×C4×C61C22⋊C411yescharacteristic
55C22×C4×C61C22×C411yescharacteristic
56C22×Dic61—22no—
57C22×Dic61C22⋊C411yescharacteristic
58C22×Dic61C2×D411yescharacteristic
59C22×Dic61C2×D411yescharacteristic
60C2×C4×D61—22no—
61C2×C4×D61—22no—
62C2×C4×D61—22no—
63C2×C4×D61—22no—
64C2×C4×D61—41no—
65C2×C4×D61—41no—
66C2×C4×D61—41no—
67C2×C4×D61D812yes—
68C2×C4×D61SD1612yes—
69C2×C4×D61SD1612yes—
70C2×C4×D61Q1612yes—
71C2×#92420—24no—
72C2×#92420—42no—
73C2×#92420—42no—
74C2×#92420—42no—
75C2×#92420—42no—
76C2×#92420—42no—
77D61⋊C8—48no—
78C4⋊C4×C61—42no—
79C4⋊C4×C61—42no—
80C42×C61—22no—
81#11758198—44no—
82C4⋊Dic61—24no—
83C4⋊Dic61—42no—
84C4⋊Dic61—42no—
85#11758196—42no—
86#11758196—42no—
87C4×Dic61—22no—
88C4×Dic61—41no—
89C4×Dic61—41no—
90C23×C61C2×C22⋊C411yescharacteristic
91C22×D61—21no—
92C22×D61—21no—
93C22×D61—21no—
94C22×D61—21no—
95C22×D61#10112yes—
96C22×D61#10212yes—
97C22×D61#10312yes—
98Q8×C61—84no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—42no—
104C2×C4×C61—42no—
105C2×C4×C61—42no—
106C2×C4×C61#9912yes—
107C2×C4×C61#10212yes—
108C2×C4×C61#10312yes—
109C2×C4×C61#10412yes—
110C2×C4×C61#13112yes—
111C2×Dic61—21no—
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—42no—
119C2×Dic61—42no—
120C2×Dic61—42no—
121C2×Dic61C2×D811yescharacteristic
122C2×Dic61C2×SD1611yescharacteristic
123C2×Dic61C2×SD1611yescharacteristic
124C2×Dic61C2×Q1611yescharacteristic
125C4×D61—24no—
126C4×D61—24no—
127C4×D61—42no—
128C4×D61—42no—
129C4×D61—44no—
130#92420—44no—
131#92420—82no—
132#7668—611nomaximal, Sylow
133C22×C61#40811yescharacteristic
134C22×C61C2×#9911yescharacteristic
135C22×C61C2×#10111yescharacteristic
136C22×C61C2×#10211yescharacteristic
137C22×C61C2×#10311yescharacteristic
138C22×C61C2×#10411yescharacteristic
139C22×C61#42111yescharacteristic
140C2×D61—22no—
141C2×D61—22no—
142C2×D61—22no—
143C2×D61—22no—
144C2×D61—22no—
145C2×D61—22no—
146C2×D61#33214yes—
147C4×C61—22no—
148C4×C61—22no—
149C4×C61—82no—
150C4×C61#32714yes—
151Dic61—21no—
152Dic61—21no—
153Dic61—21no—
154Dic61—21no—
155Dic61—41no—
156Dic61—82no—
157#2857—611no—
158#1797—611no—
159C2×#336—611no—
160#1271—614no—
161C2×C61#147211yescharacteristic
162C2×C61#148011yescharacteristic
163C2×C61#149311yescharacteristic
164C2×C61C2×#32711yescharacteristic
165C2×C61#152011yescharacteristic
166C2×C61#153111yescharacteristic
167C2×C61C2×#33211yescharacteristic
168D61—24no—
169C23×C8—1221no—
170C2×C4⋊Q8#692311yescharacteristic
171C2×C22⋊Q8—1221no—
172C22×C42—611no—
173C2×C4⋊C8—1221no—
174C2×C22⋊C8—1221no—
175#391—1221no—
176#389—612no—
177#389—1221no—
178#384—611no—
179#380—612no—
180#380—1221no—
181#336—612no—
182#336—612no—
183#336—1221no—
184C61#766811yescharacteristic, complemented, Sylow
185C22×Q8—21no—
186C23×C4—611no—
187C23×C4—611no—
188C23×C4—611no—
189C22×C8—1222no—
190C22×C8—1224no—
191C22×C8—1222no—
192C22×C8—2442no—
193C22×C8—2442no—
194C4⋊Q8—42no—
195C22⋊Q8—2442no—
196C22⋊Q8—2442no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—612no—
199C2×C4⋊C4—1222no—
200C2×C4⋊C4—1221no—
201C2×C4⋊C4—1221no—
202C2×C4⋊C4C2×#692312yes—
203C2×C22⋊C4—1222no—
204C2×C42—611no—
205C2×C42—611no—
206C2×C42—611no—
207C2×C42—2442no—
208C2×C42C2×#692311yescharacteristic
209C4⋊C8—2442no—
210C22⋊C8—2442no—
211#95—1222no—
212#95—1222no—
213C24—611no—
214C2×Q8—42no—
215C2×Q8—42no—
216C2×Q8—42no—
217C22×C4—22no—
218C22×C4—611no—
219C22×C4—611no—
220C22×C4—612no—
221C22×C4—612no—
222C22×C4—612no—
223C22×C4—612no—
224C22×C4—611no—
225C22×C4—1222no—
226C22×C4—1222no—
227C22×C4—1222no—
228C22×C4—1222no—
229C22×C4—1222no—
230C22×C4—2441no—
231C22×C4—2441no—
232C22×C4—2441no—
233C22×C4C22⋊#692311yescharacteristic
234C22×C4C22⋊#692311yescharacteristic
235C22×C4C22×#692311yescharacteristic
236C2×C8—1224no—
237C2×C8—2442no—
238C2×C8—2442no—
239C2×C8—2442no—
240C2×C8—2442no—
241C2×C8—2448no—
242C2×C8—2442no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C4⋊C4—1224no—
246C4⋊C4—2442no—
247C4⋊C4—2442no—
248C4⋊C4—2442no—
249C4⋊C4—2442no—
250C22⋊C4—2444no—
251C42—22no—
252C42—1222no—
253C42—2441no—
254C42—2441no—
255C23—612no—
256C23—612no—
257C23—612no—
258C23—1221no—
259C23—1221no—
260C23—1221no—
261C23—1221no—
262C23C2×C22⋊#692311yescharacteristic
263Q8—84no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—611no—
272C2×C4—611no—
273C2×C4—611no—
274C2×C4—611no—
275C2×C4—1221no—
276C2×C4—1221no—
277C2×C4—1221no—
278C2×C4—1221no—
279C2×C4—1224no—
280C2×C4—1224no—
281C2×C4—1221no—
282C2×C4—1221no—
283C2×C4—1221no—
284C2×C4—2442no—
285C2×C4—2442no—
286C2×C4—2444no—
287C2×C4—2442no—
288C2×C4—2442no—
289C2×C4—2442no—
290C2×C4#1451983512yes—
291C2×C4#1451983912yes—
292C2×C4#1451984012yes—
293C2×C4#1451984112yes—
294C2×C4#1451986512yes—
295C8—4882no—
296C8—2444no—
297C22—614no—
298C22—1222no—
299C22—1222no—
300C22—1222no—
301C22—1222no—
302C22—1222no—
303C22—1222no—
304C22#1684073711yescharacteristic
305C22C2×#1451983511yescharacteristic
306C22D61⋊#10111yescharacteristic
307C22C2×#1451983911yescharacteristic
308C22C2×#1451984011yescharacteristic
309C22C2×#1451984111yescharacteristic
310C22#1684076111yescharacteristic
311C4—22no—
312C4—22no—
313C4—82no—
314C4—1221no—
315C4—1221no—
316C4—1221no—
317C4—1221no—
318C4—4882no—
319C4—2441no—
320C4#1684061314yes—
321C2—1224no—
322C2#2146109911yescharacteristic
323C2#2146112611yescharacteristic
324C2#2146116911yescharacteristic
325C2C2×#1684061311yescharacteristic
326C2#2146125911yescharacteristic
327C2#2146129211yescharacteristic
328C2D61⋊#33211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4⋊Q8×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×C4⋊Q8#6923
hypocenterC61#7668
LCSG ▷ C22×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
3. #21460638C2semidirect
184. C61#7668semidirect

Maximal subgroups

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

subgroupindex
#214616742
#214614802
#214606382
#214541662
#766861