Finite Group Databasebeta

← D61⋊#1271 #30595329

Subgroups — D61⋊#1271 #30595329

Order 15616.

714 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461480C211yesmaximal, characteristic
2#21461480C211yesmaximal, characteristic
3#21460638C212yesmaximal, complemented
4#21460637C212yesmaximal, complemented
5#389×D61C211yesmaximal, characteristic
6C22×D61⋊C8—21no—
7C22×D61⋊C8—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
23C2×D61⋊C8—24no—
24C2×D61⋊C8—24no—
25C2×D61⋊C8—42no—
26C2×D61⋊C8—42no—
27C2×D61⋊C8—42no—
28C2×D61⋊C8—42no—
29C22×#92420—22no—
30C22×#92420—22no—
31C22×C4×D61—21no—
32C22×C4×D61—21no—
33C22×C4×D61C2×C411yescharacteristic
34C22×C4×D61D411yescharacteristic
35C22×C4×D61D411yescharacteristic
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×C4⋊Dic61C2×C411yescharacteristic
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196—21no—
43C4⋊C4×D61—22no—
44C4⋊C4×D61—42no—
45C4⋊C4×D61—42no—
46C4⋊C4×D61—42no—
47C4⋊C4×D61C814yescomplemented
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61C2311yescharacteristic
51C42×D61—42no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C4⋊C4×C61C2×C411yescharacteristic
58C2×C42×C61C2×C411yescharacteristic
59#95×C61—21no—
60C23×D61C22⋊C411yescharacteristic
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22×C411yescharacteristic
66C22×Dic61—21no—
67C22×Dic61—21no—
68C22×Dic61C22⋊C411yescharacteristic
69C22×Dic61C2×D411yescharacteristic
70C22×Dic61C2×D411yescharacteristic
71C2×C4×D61—22no—
72C2×C4×D61—22no—
73C2×C4×D61—22no—
74C2×C4×D61—22no—
75C2×C4×D61—22no—
76C2×C4×D61—22no—
77C2×C4×D61—24no—
78C2×C4×D61—42no—
79C2×C4×D61—42no—
80C2×C4×D61—42no—
81C2×C4×D61—42no—
82C2×C4×D61—42no—
83C2×C4×D61C2×C812yes—
84C2×C4×D61M1612yes—
85C2×C4×D61D812yes—
86C2×C4×D61SD1612yes—
87C2×C4×D61SD1612yes—
88C2×C4×D61Q1612yes—
89C2×#92420—24no—
90C2×#92420—24no—
91C2×#92420—42no—
92C2×#92420—42no—
93C2×#92420—42no—
94C2×#92420—42no—
95D61⋊C8—48no—
96D61⋊C8—48no—
97C4⋊C4×C61—21no—
98C4⋊C4×C61—41no—
99C4⋊C4×C61—42no—
100C4⋊C4×C61C2×C812yescomplemented
101C42×C61—41no—
102C4⋊Dic61—21no—
103C4⋊Dic61—41no—
104C4⋊Dic61—41no—
105C4⋊Dic61—41no—
106C4⋊Dic61C2×C812yescomplemented
107#11758196—24no—
108#11758196—42no—
109#11758196—42no—
110#11758196—41no—
111#11758196—41no—
112C4×Dic61—41no—
113C4×Dic61—41no—
114C4×Dic61—41no—
115C23×C61C2×C22⋊C411yescharacteristic
116C22×D61C22⋊C812yes—
117C22×D61#9912yes—
118C22×D61#10112yes—
119C22×D61#10212yes—
120C22×D61#10312yes—
121C22×D61#10412yes—
122C22×D61#10412yes—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—22no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61#10212yes—
136C2×C4×C61#10312yes—
137C2×C4×C61C22×C811yescharacteristic
138C2×C4×C61C2×M1611yescharacteristic
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—22no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61C22⋊C812yes—
152C2×Dic61C2×D811yescharacteristic
153C2×Dic61C2×SD1611yescharacteristic
154C2×Dic61C2×SD1611yescharacteristic
155C2×Dic61C2×Q1611yescharacteristic
156C4×D61—24no—
157C4×D61—24no—
158C4×D61—24no—
159C4×D61—24no—
160C4×D61—24no—
161C4×D61—24no—
162C4×D61—48no—
163C4×D61—84no—
164#92420—44no—
165#92420—44no—
166C2×#1271—611nomaximal, Sylow
167C22×C61C2×C22⋊C811yescharacteristic
168C22×C61C2×#9911yescharacteristic
169C22×C61C2×#10111yescharacteristic
170C22×C61C2×#10211yescharacteristic
171C22×C61C2×#10311yescharacteristic
172C22×C61C2×#10411yescharacteristic
173C22×C61C2×#10411yescharacteristic
174C2×D61#32414yes—
175C2×D61D4⋊C814yes—
176C2×D61Q8⋊C814yes—
177C2×D61#32714yes—
178C2×D61#32814yes—
179C2×D61#33014yes—
180C2×D61#33214yes—
181C4×C61—21no—
182C4×C61—21no—
183C4×C61—22no—
184C4×C61—22no—
185C4×C61—42no—
186C4×C61—81no—
187Dic61—22no—
188Dic61—21no—
189Dic61—21no—
190Dic61—21no—
191Dic61—21no—
192Dic61—42no—
193Dic61—81no—
194C2×#389—611no—
195C2×#336—611no—
196C2×#336—611no—
197#1271—612no—
198#1271—612no—
199C2×C61C2×#32411yescharacteristic
200C2×C61C2×D4⋊C811yescharacteristic
201C2×C61C2×Q8⋊C811yescharacteristic
202C2×C61C2×#32711yescharacteristic
203C2×C61C2×#32811yescharacteristic
204C2×C61C2×#33011yescharacteristic
205C2×C61C2×#33211yescharacteristic
206D61#127118yescomplemented
207C23×C8—1221no—
208C23×C8—1221no—
209C22×C4⋊C4—611no—
210C22×C4⋊C4—611no—
211C22×C4⋊C4—1221no—
212C22×C42—611no—
213#389—611no—
214#389—611no—
215#389—611no—
216#389—1221no—
217#389—1221no—
218#389#692311yescharacteristic
219C2×#95—1221no—
220#336—612no—
221#336—612no—
222#336—1221no—
223#336—1221no—
224C61C2×#127111yescharacteristic, complemented, Sylow
225C23×C4—611no—
226C23×C4—611no—
227C23×C4—611no—
228C23×C4—1221no—
229C23×C4—1221no—
230C22×C8—1222no—
231C22×C8—1222no—
232C22×C8—1224no—
233C22×C8—1224no—
234C22×C8—2442no—
235C22×C8—2442no—
236C22×C8—2442no—
237C22×C8—2442no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—611no—
240C2×C4⋊C4—614no—
241C2×C4⋊C4—611no—
242C2×C4⋊C4—1222no—
243C2×C4⋊C4—1221no—
244C2×C4⋊C4—1221no—
245C2×C4⋊C4—1221no—
246C2×C4⋊C4—1221no—
247C2×C4⋊C4—1221no—
248C2×C4⋊C4—2442no—
249C2×C4⋊C4—2442no—
250C2×C4⋊C4—2442no—
251C2×C4⋊C4C2×#692311yescharacteristic
252C2×C4⋊C4C2×#692311yescharacteristic
253C2×C42—611no—
254C2×C42—611no—
255C2×C42—611no—
256C2×C42—2442no—
257C2×C42C2×#692311yescharacteristic
258#95—21no—
259#95—1221no—
260#95—1221no—
261#95—1221no—
262C24—611no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—611no—
268C22×C4—612no—
269C22×C4—612no—
270C22×C4—612no—
271C22×C4—612no—
272C22×C4—612no—
273C22×C4—612no—
274C22×C4—1222no—
275C22×C4—1222no—
276C22×C4—1222no—
277C22×C4—1222no—
278C22×C4—1222no—
279C22×C4—1222no—
280C22×C4—1224no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—2442no—
284C22×C4—2442no—
285C22×C4—2442no—
286C22×C4—2442no—
287C22×C4—2442no—
288C22×C4C22⋊#692311yescharacteristic
289C22×C4C22⋊#692311yescharacteristic
290C22×C4C22×#692311yescharacteristic
291C2×C8—1224no—
292C2×C8—1224no—
293C2×C8—2442no—
294C2×C8—2442no—
295C2×C8—2448no—
296C2×C8—2448no—
297C2×C8—2442no—
298C2×C8—2442no—
299C4⋊C4—21no—
300C4⋊C4—41no—
301C4⋊C4—42no—
302C4⋊C4—612no—
303C4⋊C4—1224no—
304C4⋊C4—1221no—
305C4⋊C4—2441no—
306C4⋊C4—2441no—
307C4⋊C4—2441no—
308C4⋊C4—2441no—
309C4⋊C4—2441no—
310C4⋊C4—2442no—
311C4⋊C4—2442no—
312C4⋊C4D61⋊C812yescomplemented
313C42—41no—
314C42—2441no—
315C42—2441no—
316C42—2441no—
317C23—612no—
318C23—612no—
319C23—612no—
320C23—612no—
321C23—612no—
322C23—612no—
323C23—612no—
324C23C2×C22⋊#692311yescharacteristic
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—612no—
338C2×C4—611no—
339C2×C4—611no—
340C2×C4—611no—
341C2×C4—611no—
342C2×C4—1224no—
343C2×C4—1224no—
344C2×C4—1224no—
345C2×C4—1224no—
346C2×C4—1224no—
347C2×C4—1224no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1222no—
355C2×C4—4884no—
356C2×C4—2448no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4#1451983912yes—
363C2×C4#1451984012yes—
364C2×C4C2×D61⋊C811yescharacteristic
365C2×C4D61⋊M1611yescharacteristic
366C8—2444no—
367C8—2444no—
368C22—614no—
369C22—614no—
370C22—614no—
371C22—614no—
372C22—614no—
373C22—614no—
374C22—614no—
375C22D61⋊(C22⋊C8)11yescharacteristic
376C22D61⋊#9911yescharacteristic
377C22D61⋊#10111yescharacteristic
378C22C2×#1451983911yescharacteristic
379C22C2×#1451984011yescharacteristic
380C22D61⋊#10411yescharacteristic
381C22D61⋊#10411yescharacteristic
382C4—21no—
383C4—21no—
384C4—22no—
385C4—22no—
386C4—42no—
387C4—81no—
388C4—1222no—
389C4—1221no—
390C4—1221no—
391C4—1221no—
392C4—1221no—
393C4—4881no—
394C4—2442no—
395C2—618no—
396C2D61⋊#32411yescharacteristic
397C2D61⋊(D4⋊C8)11yescharacteristic
398C2D61⋊(Q8⋊C8)11yescharacteristic
399C2D61⋊#32711yescharacteristic
400C2D61⋊#32811yescharacteristic
401C2D61⋊#33011yescharacteristic
402C2D61⋊#33211yescharacteristic
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
hypocenterC61C2×#1271
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
47. C4⋊C4×D61C8semidirect
100. C4⋊C4×C61C2×C8semidirect
106. C4⋊Dic61C2×C8semidirect
206. D61#1271semidirect
224. C61C2×#1271semidirect
312. C4⋊C4D61⋊C8semidirect

Maximal subgroups

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

subgroupindex
#214614802
#214606382
#214606372
#389×D612
C2×#127161