Finite Group Databasebeta

← #30595449

Subgroups — #30595449

Order 15616.

566 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 110 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#21461711C211yesmaximal, characteristic
3#21460638C212yesmaximal, complemented
4#21460637C212yesmaximal, complemented
5#389×D61C211yesmaximal, characteristic
6C2×#14519834—21no—
7C2×#14519834—21no—
8#16840628—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×C4⋊C4×D61—21no—
13C2×C4⋊C4×D61C411yescharacteristic
14C2×C4⋊C4×D61C411yescharacteristic
15C2×C42×D61C2211yescharacteristic
16#16839661C2211yescharacteristic
17#16839660C411yescharacteristic
18#16839659—21no—
19#16839658C2211yescharacteristic
20#16839657—21no—
21#95×D61—21no—
22C61×#389C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25#14519834—42no—
26#14519834—42no—
27C22×C4×D61—21no—
28C22×C4×D61—21no—
29C22×C4×D61C2×C411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C22×C4×D61D411yescharacteristic
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C4⋊C4×D61—22no—
40C4⋊C4×D61—42no—
41C4⋊C4×D61—44no—
42C4⋊C4×D61C814yescomplemented
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61C2311yescharacteristic
46C42×D61—42no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50C2×C4⋊C4×C61—21no—
51C2×C4⋊C4×C61C2×C411yescharacteristic
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C42×C61C2×C411yescharacteristic
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—24no—
69C2×C4×D61—22no—
70C2×C4×D61—22no—
71C2×C4×D61—22no—
72C2×C4×D61—22no—
73C2×C4×D61—41no—
74C2×C4×D61—41no—
75C2×C4×D61—42no—
76C2×C4×D61—42no—
77C2×C4×D61—42no—
78C2×C4×D61—42no—
79C2×C4×D61—42no—
80C2×C4×D61C2×C812yes—
81C2×C4×D61M1612yes—
82C2×#92420—42no—
83C2×#92420—42no—
84C2×#92420—42no—
85C2×#92420—42no—
86C2×#92420—42no—
87C2×#92420—42no—
88C4⋊C4×C61—21no—
89C4⋊C4×C61—42no—
90C4⋊C4×C61—41no—
91C4⋊C4×C61C2×C812yes—
92C42×C61—41no—
93C4⋊Dic61—21no—
94C4⋊Dic61—42no—
95C4⋊Dic61—41no—
96C4⋊Dic61C2×C812yes—
97#11758196—24no—
98#11758196—42no—
99#11758196—42no—
100#11758196—42no—
101C4×Dic61—41no—
102C4×Dic61—41no—
103C4×Dic61—41no—
104C23×C61C2×C22⋊C411yescharacteristic
105C22×D61—21no—
106C22×D61—21no—
107C22×D61—21no—
108C22×D61—21no—
109C22×D61C22⋊C812yes—
110C22×D61#9912yes—
111C22×D61#10112yes—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—22no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61C22×C811yescharacteristic
127C2×C4×C61C2×M1611yescharacteristic
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—22no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61C22⋊C812yes—
141C2×Dic61AGL(1,ℤ/8)12yes—
142C2×Dic61#13712yes—
143C4×D61—24no—
144C4×D61—24no—
145C4×D61—44no—
146C4×D61—44no—
147C4×D61—48no—
148C4×D61—84no—
149#92420—82no—
150#92420—82no—
151#7593—611nomaximal, Sylow
152C22×C61C2×C22⋊C811yescharacteristic
153C22×C61C2×#9911yescharacteristic
154C22×C61C2×#10111yescharacteristic
155C22×C61#41811yescharacteristic
156C22×C61#41911yescharacteristic
157C22×C61#42111yescharacteristic
158C22×C61#42111yescharacteristic
159C2×D61—22no—
160C2×D61—22no—
161C2×D61—22no—
162C2×D61—22no—
163C2×D61—22no—
164C2×D61—22no—
165C2×D61#32414yes—
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—42no—
169C4×C61—41no—
170C4×C61—41no—
171C4×C61—81no—
172Dic61—22no—
173Dic61—22no—
174Dic61—22no—
175Dic61—42no—
176Dic61—81no—
177C2×#389—611no—
178#1817—611no—
179#1817—611no—
180#1271—612no—
181#1271—612no—
182C2×C61C2×#32411yescharacteristic
183C2×C61#147811yescharacteristic
184C2×C61#147911yescharacteristic
185C2×C61#151011yescharacteristic
186C2×C61#151111yescharacteristic
187C2×C61#153411yescharacteristic
188C2×C61#155611yescharacteristic
189D61—24no—
190C22×C4⋊C4—611no—
191C22×C4⋊C4—611no—
192C22×C4⋊C4—1221no—
193C22×C42—611no—
194C2×C22⋊C8—1221no—
195C2×C22⋊C8—1221no—
196#389—611no—
197#389—611no—
198#389—611no—
199#389—1221no—
200#389—1221no—
201#389#692311yescharacteristic
202C2×#95—1221no—
203#336—612no—
204#336—612no—
205#336—1221no—
206#336—1221no—
207C61#759311yescharacteristic, complemented, Sylow
208C23×C4—611no—
209C23×C4—611no—
210C23×C4—611no—
211C23×C4—1221no—
212C23×C4—1221no—
213C22×C8—1222no—
214C22×C8—1222no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—611no—
217C2×C4⋊C4—614no—
218C2×C4⋊C4—611no—
219C2×C4⋊C4—1222no—
220C2×C4⋊C4—1221no—
221C2×C4⋊C4—1221no—
222C2×C4⋊C4—1221no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4—1221no—
225C2×C4⋊C4—2442no—
226C2×C4⋊C4—2444no—
227C2×C4⋊C4C2×#692311yescharacteristic
228C2×C4⋊C4C2×#692311yescharacteristic
229C2×C42—611no—
230C2×C42—611no—
231C2×C42—611no—
232C2×C42—2442no—
233C2×C42C2×#692311yescharacteristic
234C22⋊C8—2442no—
235C22⋊C8—2442no—
236#95—21no—
237#95—1221no—
238#95—1221no—
239#95—1221no—
240C24—611no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—611no—
244C22×C4—611no—
245C22×C4—611no—
246C22×C4—612no—
247C22×C4—612no—
248C22×C4—1222no—
249C22×C4—1222no—
250C22×C4—1222no—
251C22×C4—1222no—
252C22×C4—1222no—
253C22×C4—1222no—
254C22×C4—1224no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—2441no—
258C22×C4—2441no—
259C22×C4—2442no—
260C22×C4—2442no—
261C22×C4—2442no—
262C22×C4—2442no—
263C22×C4—2442no—
264C22×C4C22⋊#692311yescharacteristic
265C22×C4C22⋊#692311yescharacteristic
266C22×C4C22×#692311yescharacteristic
267C2×C8—2442no—
268C2×C8—2442no—
269C2×C8—2442no—
270C2×C8—2442no—
271C2×C8—2442no—
272C2×C8—2442no—
273C4⋊C4—21no—
274C4⋊C4—41no—
275C4⋊C4—42no—
276C4⋊C4—612no—
277C4⋊C4—1224no—
278C4⋊C4—1221no—
279C4⋊C4—2441no—
280C4⋊C4—2442no—
281C4⋊C4—2442no—
282C4⋊C4—2442no—
283C4⋊C4—2442no—
284C4⋊C4D61⋊C812yes—
285C42—41no—
286C42—2441no—
287C42—2441no—
288C42—2441no—
289C23—612no—
290C23—612no—
291C23—612no—
292C23—1221no—
293C23—1221no—
294C23—1221no—
295C23—1221no—
296C23C2×C22⋊#692311yescharacteristic
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—612no—
312C2×C4—612no—
313C2×C4—612no—
314C2×C4—1224no—
315C2×C4—1224no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1222no—
323C2×C4—4884no—
324C2×C4—2444no—
325C2×C4—2444no—
326C2×C4—2448no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4C2×D61⋊C811yescharacteristic
333C2×C4D61⋊M1611yescharacteristic
334C8—4882no—
335C8—4882no—
336C22—614no—
337C22—1222no—
338C22—1222no—
339C22—1222no—
340C22—1222no—
341C22—1222no—
342C22—1222no—
343C22D61⋊(C22⋊C8)11yescharacteristic
344C22D61⋊#9911yescharacteristic
345C22D61⋊#10111yescharacteristic
346C22#1684075411yescharacteristic
347C22#1684075511yescharacteristic
348C22#1684075911yescharacteristic
349C22#1684075911yescharacteristic
350C4—21no—
351C4—21no—
352C4—42no—
353C4—41no—
354C4—41no—
355C4—81no—
356C4—1222no—
357C4—1222no—
358C4—1222no—
359C4—4881no—
360C4—2442no—
361C2—1224no—
362C2D61⋊#32411yescharacteristic
363C2#2146111911yescharacteristic
364C2#2146112211yescharacteristic
365C2#2146122511yescharacteristic
366C2#2146122811yescharacteristic
367C2#2146130211yescharacteristic
368C2#2146134911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#389C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#389#6923
hypocenterC61#7593
LCSG ▷ C2×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. #21460638C2semidirect
4. #21460637C2semidirect
42. C4⋊C4×D61C8semidirect
207. C61#7593semidirect

Maximal subgroups

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

subgroupindex
#214617112
#214606382
#214606372
#389×D612
#759361