Finite Group Databasebeta

← #30595865

Subgroups — #30595865

Order 15616.

500 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 92 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#21461676C211yesmaximal, characteristic
2#21461483C211yesmaximal, characteristic
3#21460637C212yesmaximal, complemented
4#21460637C212yesmaximal, complemented
5#21454130C211yesmaximal, characteristic
6C22×#11758213—21no—
7C2×#14519844—21no—
8C2×#14519834—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519769C411yescharacteristic
13C2×C42×D61C2211yescharacteristic
14#16839661C2211yescharacteristic
15#16839661C2211yescharacteristic
16#16839647—21no—
17#16839647—21no—
18#16839636—21no—
19#16839636—21no—
20#16839619C411yescharacteristic
21#16839619C411yescharacteristic
22C61×#382C411yescharacteristic
23C2×#11758213—24no—
24C2×#11758213—42no—
25C2×#11758213—42no—
26C22×#92420—22no—
27C22×#92420—22no—
28#14519844—42no—
29#14519834—42no—
30C22×C4×D61C2×C411yescharacteristic
31C22×C4×D61D411yescharacteristic
32C22×C4×D61D411yescharacteristic
33#14519769—42no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61C2311yescharacteristic
45C42×D61—42no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50C2×C4⋊C4×C61C2×C411yescharacteristic
51C2×C4⋊C4×C61C2×C411yescharacteristic
52C2×C42×C61C2×C411yescharacteristic
53#95×C61—21no—
54#95×C61—21no—
55C23×D61C22⋊C411yescharacteristic
56C22×C4×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C22×C411yescharacteristic
61C22×Dic61—21no—
62C22×Dic61—21no—
63C22×Dic61C22⋊C411yescharacteristic
64C22×Dic61C2×D411yescharacteristic
65C22×Dic61C2×D411yescharacteristic
66C2×C4×D61—22no—
67C2×C4×D61—22no—
68C2×C4×D61—21no—
69C2×C4×D61—21no—
70C2×C4×D61—22no—
71C2×C4×D61—22no—
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61—41no—
75C2×C4×D61—41no—
76C2×C4×D61—41no—
77C2×#92420—24no—
78C2×#92420—42no—
79C2×#92420—42no—
80C2×#92420—42no—
81C2×#92420—42no—
82C2×#92420—42no—
83#11758213—48no—
84C4⋊C4×C61—22no—
85C4⋊C4×C61—22no—
86C42×C61—22no—
87#11758198—42no—
88#11758198—42no—
89C4⋊Dic61—41no—
90C4⋊Dic61—41no—
91C4⋊Dic61—41no—
92C4⋊Dic61—41no—
93C4⋊Dic61—41no—
94C4⋊Dic61—41no—
95#11758196—42no—
96#11758196—42no—
97C4×Dic61—22no—
98C4×Dic61—41no—
99C4×Dic61—41no—
100C23×C61C2×C22⋊C411yescharacteristic
101C22×D61—21no—
102C22×D61—21no—
103C22×D61—21no—
104C22×D61—21no—
105C22×D61—21no—
106C22×D61—21no—
107C22×D61#10412yes—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61#9912yes—
122C2×C4×C61#13112yes—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61#10112yes—
136C2×Dic61AGL(1,ℤ/8)11yescharacteristic
137C2×Dic61AGL(1,ℤ/8)11yescharacteristic
138C2×Dic61#13711yescharacteristic
139C2×Dic61#13711yescharacteristic
140C4×D61—24no—
141C4×D61—24no—
142C4×D61—44no—
143C4×D61—42no—
144C4×D61—42no—
145#92420—44no—
146#92420—82no—
147#7711—611nomaximal, Sylow
148C22×C61#40811yescharacteristic
149C22×C61C2×#9911yescharacteristic
150C22×C61C2×#10111yescharacteristic
151C22×C61#41711yescharacteristic
152C22×C61#41711yescharacteristic
153C22×C61C2×#10411yescharacteristic
154C22×C61#42111yescharacteristic
155C2×D61—22no—
156C2×D61—22no—
157C2×D61—22no—
158C2×D61—41no—
159C2×D61—41no—
160C2×D61—41no—
161C2×D61—41no—
162C4×C61—22no—
163C4×C61—22no—
164C4×C61—41no—
165C4×C61—81no—
166C4×C61—81no—
167Dic61—22no—
168Dic61—21no—
169Dic61—21no—
170Dic61—21no—
171Dic61—21no—
172Dic61—81no—
173Dic61—81no—
174#2851—611no—
175#1797—611no—
176#1728—611no—
177#1271—612no—
178#1271—612no—
179C2×C61#147211yescharacteristic
180C2×C61#148311yescharacteristic
181C2×C61#149511yescharacteristic
182C2×C61#150411yescharacteristic
183C2×C61#151311yescharacteristic
184C2×C61#152811yescharacteristic
185C2×C61#156111yescharacteristic
186D61—42no—
187C22×M16—1221no—
188C2×#125—611no—
189C22×C42—611no—
190C2×C4⋊C8—1221no—
191C2×C22⋊C8—1221no—
192#389—611no—
193#389—611no—
194#387—1221no—
195#387—1221no—
196#385—1221no—
197#385—1221no—
198#382#692311yescharacteristic
199#380—611no—
200#380—611no—
201#336—612no—
202#336—612no—
203#336—1221no—
204C61#771111yescharacteristic, complemented, Sylow
205C23×C4—611no—
206C23×C4—611no—
207C23×C4—611no—
208C2×M16—1224no—
209C2×M16—2442no—
210C2×M16—2442no—
211C22×C8—1222no—
212C22×C8—1222no—
213#125—2442no—
214C2×C4⋊C4—611no—
215C2×C4⋊C4—611no—
216C2×C4⋊C4—1221no—
217C2×C4⋊C4—1221no—
218C2×C4⋊C4—1221no—
219C2×C4⋊C4—1221no—
220C2×C4⋊C4C2×#692311yescharacteristic
221C2×C4⋊C4C2×#692311yescharacteristic
222C2×C22⋊C4—1221no—
223C2×C22⋊C4—1221no—
224C2×C42—611no—
225C2×C42—611no—
226C2×C42—611no—
227C2×C42—2442no—
228C2×C42C2×#692311yescharacteristic
229C4⋊C8—2442no—
230C22⋊C8—2442no—
231#95—21no—
232#95—21no—
233#95—1221no—
234#95—1221no—
235#95—1221no—
236#95—1221no—
237C24—611no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—611no—
241C22×C4—611no—
242C22×C4—611no—
243C22×C4—1221no—
244C22×C4—1221no—
245C22×C4—1221no—
246C22×C4—1222no—
247C22×C4—1221no—
248C22×C4—1222no—
249C22×C4—1222no—
250C22×C4—1222no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—2441no—
254C22×C4—2441no—
255C22×C4—2441no—
256C22×C4C22⋊#692311yescharacteristic
257C22×C4C22⋊#692311yescharacteristic
258C22×C4C22×#692311yescharacteristic
259M16—2448no—
260C2×C8—1224no—
261C2×C8—2442no—
262C2×C8—2442no—
263C2×C8—2442no—
264C2×C8—2442no—
265C2×C8—2442no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—2441no—
269C4⋊C4—2441no—
270C4⋊C4—2442no—
271C4⋊C4—2441no—
272C4⋊C4—2441no—
273C4⋊C4—2441no—
274C4⋊C4—2441no—
275C4⋊C4—2442no—
276C22⋊C4—2442no—
277C22⋊C4—2442no—
278C42—22no—
279C42—1222no—
280C42—2441no—
281C42—2441no—
282C23—612no—
283C23—1221no—
284C23—1221no—
285C23—1221no—
286C23—1221no—
287C23—1221no—
288C23—1221no—
289C23C2×C22⋊#692311yescharacteristic
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—612no—
304C2×C4—611no—
305C2×C4—611no—
306C2×C4—611no—
307C2×C4—611no—
308C2×C4—1224no—
309C2×C4—1224no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—2444no—
317C2×C4—2442no—
318C2×C4—2442no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4#1451983612yes—
326C2×C4#1451986412yes—
327C8—4882no—
328C8—2444no—
329C22—1222no—
330C22—1222no—
331C22—1222no—
332C22—2441no—
333C22—2441no—
334C22—2441no—
335C22—2441no—
336C22#1684073611yescharacteristic
337C22C2×#1451983611yescharacteristic
338C22D61⋊#10111yescharacteristic
339C22#1684075311yescharacteristic
340C22#1684075311yescharacteristic
341C22D61⋊#10411yescharacteristic
342C22#1684075911yescharacteristic
343C4—22no—
344C4—22no—
345C4—41no—
346C4—81no—
347C4—81no—
348C4—1222no—
349C4—1221no—
350C4—1221no—
351C4—1221no—
352C4—1221no—
353C4—4881no—
354C4—4881no—
355C2—2442no—
356C2#2146109711yescharacteristic
357C2#2146113511yescharacteristic
358C2#2146117511yescharacteristic
359C2#2146120711yescharacteristic
360C2#2146123611yescharacteristic
361C2#2146128211yescharacteristic
362C2#2146135911yescharacteristic
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#7711
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
3. #21460637C2semidirect
4. #21460637C2semidirect
204. C61#7711semidirect

Maximal subgroups

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

subgroupindex
#214616762
#214614832
#214606372
#214541302
#771161