Finite Group Databasebeta

← D61⋊#1346 #30604750

Subgroups — D61⋊#1346 #30604750

Order 15616.

544 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 88 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#21461522C211yesmaximal, characteristic
2D61⋊#324C211yesmaximal, characteristic
3#21460804C212yesmaximal, complemented
4#21460803C212yesmaximal, complemented
5#398×D61C211yesmaximal, characteristic
6C2×D61⋊M16—21no—
7D61⋊(C22⋊C8)—21no—
8#16840642—21no—
9#16840642C2212yes—
10#16840608C2212yes—
11#16840607—21no—
12C2×C4⋊C4×D61—21no—
13C2×C4⋊C4×D61C411yescharacteristic
14C2×C4⋊C4×D61C2211yescharacteristic
15#16839696—21no—
16#16839695—21no—
17#16839694C2211yescharacteristic
18#16839693C2211yescharacteristic
19#16839692C411yescharacteristic
20#95×D61—21no—
21#95×D61C411yescharacteristic
22C61×#398C411yescharacteristic
23C2×#11758213—41no—
24D61⋊M16—24no—
25D61⋊M16—42no—
26C2×#11758217—22no—
27C2×D61⋊C8—41no—
28C2×D61⋊C8—41no—
29#14519834—41no—
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⋊Dic61D411yescharacteristic
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196D411yescharacteristic
43C2×#11758196C2311yescharacteristic
44C4⋊C4×D61—41no—
45C4⋊C4×D61—41no—
46C4⋊C4×D61—41no—
47C4⋊C4×D61—41no—
48C4⋊C4×D61—42no—
49C4⋊C4×D61—42no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684C2×C411yescharacteristic
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C4⋊C4×C61C2×C411yescharacteristic
58#95×C61—21no—
59#95×C61C2×C411yescharacteristic
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—21no—
72C2×C4×D61—21no—
73C2×C4×D61—22no—
74C2×C4×D61—24no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—42no—
80C2×C4×D61—42no—
81C2×C4×D61—42no—
82C2×C4×D61—42no—
83C2×C4×D61—41no—
84C2×C4×D61—41no—
85C2×C4×D61—42no—
86C2×C4×D61—42no—
87C2×C4×D61D812yes—
88C2×C4×D61SD1612yes—
89#11758217—24no—
90#11758217—42no—
91C2×#92420—42no—
92C2×#92420—42no—
93#11758213—44no—
94D61⋊C8—44no—
95D61⋊C8—82no—
96C4⋊C4×C61—41no—
97C4⋊C4×C61—41no—
98C4⋊C4×C61—42no—
99C4⋊Dic61—41no—
100C4⋊Dic61—41no—
101C4⋊Dic61—41no—
102C4⋊Dic61—41no—
103#11758196—41no—
104#11758196—41no—
105#11758196—42no—
106#11758196—42no—
107#11758196—41no—
108#11758196—41no—
109C23×C61C2×C22⋊C411yescharacteristic
110C22×D61—22no—
111C22×D61—22no—
112C22×D61#9911yescharacteristic
113C22×D61#9911yescharacteristic
114C22×D61#10212yes—
115C22×D61#10412yes—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—22no—
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×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61#10212yes—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—22no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61C2×D811yescharacteristic
142C2×Dic61C2×SD1611yescharacteristic
143C4×D61—22no—
144C4×D61—22no—
145C4×D61—22no—
146C4×D61—22no—
147C4×D61—48no—
148C4×D61—42no—
149C4×D61—42no—
150C4×D61—42no—
151C4×D61—81no—
152C4×D61—82no—
153C4×D61—82no—
154#92420—44no—
155#92420—82no—
156C2×#1346—611nomaximal, Sylow
157C22×C61—21no—
158C22×C61—21no—
159C22×C61C2×#9911yescharacteristic
160C22×C61C2×#10211yescharacteristic
161C22×C61C2×#10411yescharacteristic
162C2×D61—21no—
163C2×D61—21no—
164C2×D61—24no—
165C2×D61—24no—
166C2×D61#32712yes—
167C2×D61#32712yes—
168C2×D61#35212yes—
169C2×D61#35612yes—
170C4×C61—22no—
171C4×C61—42no—
172C4×C61—41no—
173C4×C61—41no—
174C4×C61—81no—
175Dic61—21no—
176Dic61—21no—
177Dic61—42no—
178Dic61—41no—
179Dic61—41no—
180Dic61—81no—
181C2×#398—611no—
182C2×#343—611no—
183C2×#324—611no—
184#1346—612no—
185#1346—612no—
186C2×C61—21no—
187C2×C61—21no—
188C2×C61C2×#32711yescharacteristic
189C2×C61C2×#35211yescharacteristic
190C2×C61C2×#35611yescharacteristic
191D61—22no—
192D61#134614yescomplemented
193C22×M16—1221no—
194C22×C4⋊C4—611no—
195C22×C4⋊C4—611no—
196C22×C4⋊C4—1221no—
197C2×C22⋊C8—1221no—
198#398—611no—
199#398—611no—
200#398—611no—
201#398—1221no—
202#398—1221no—
203#398#692311yescharacteristic
204C2×#95—611no—
205C2×#95—1221no—
206#343—612no—
207#343—1221no—
208#324—612no—
209#324—1221no—
210C61C2×#134611yescharacteristic, complemented, Sylow
211C23×C4—611no—
212C23×C4—611no—
213C23×C4—611no—
214C23×C4—1221no—
215C23×C4—1221no—
216C2×M16—1222no—
217C2×M16—1224no—
218C2×M16—2442no—
219C2×M16—2441no—
220C22×C8—2441no—
221C22×C8—2441no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—611no—
224C2×C4⋊C4—611no—
225C2×C4⋊C4—611no—
226C2×C4⋊C4—611no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4—1221no—
229C2×C4⋊C4—1221no—
230C2×C4⋊C4—1221no—
231C2×C4⋊C4—2442no—
232C2×C4⋊C4—2442no—
233C2×C4⋊C4—2441no—
234C2×C4⋊C4—2441no—
235C2×C4⋊C4—2441no—
236C2×C4⋊C4—2441no—
237C2×C4⋊C4C2×#692311yescharacteristic
238C2×C4⋊C4C2×#692311yescharacteristic
239C22⋊C8—1222no—
240C22⋊C8—2441no—
241#95—21no—
242#95—611no—
243#95—1221no—
244#95—1221no—
245#95—1221no—
246#95—1221no—
247#95C2×#692311yescharacteristic
248C24—611no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—611no—
252C22×C4—612no—
253C22×C4—612no—
254C22×C4—611no—
255C22×C4—611no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4—1222no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—1224no—
264C22×C4—1221no—
265C22×C4—1221no—
266C22×C4—2442no—
267C22×C4—2441no—
268C22×C4—2441no—
269C22×C4—2442no—
270C22×C4—2442no—
271C22×C4—2442no—
272C22×C4—2442no—
273C22×C4—2442no—
274C22×C4C22⋊#692311yescharacteristic
275C22×C4C22⋊#692311yescharacteristic
276C22×C4C22×#692311yescharacteristic
277M16—1224no—
278M16—2442no—
279M16—2444no—
280C2×C8—4882no—
281C2×C8—2442no—
282C2×C8—2444no—
283C2×C8—2442no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—42no—
287C4⋊C4—2441no—
288C4⋊C4—2441no—
289C4⋊C4—2441no—
290C4⋊C4—2441no—
291C4⋊C4—2441no—
292C4⋊C4—2441no—
293C4⋊C4—2441no—
294C4⋊C4—2441no—
295C4⋊C4—2442no—
296C4⋊C4—2442no—
297C23—611no—
298C23—611no—
299C23—612no—
300C23—612no—
301C23—1222no—
302C23—1222no—
303C23C2×C22⋊#692311yescharacteristic
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—611no—
317C2×C4—611no—
318C2×C4—1222no—
319C2×C4—1222no—
320C2×C4—1222no—
321C2×C4—1222no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—1222no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—4881no—
328C2×C4—4882no—
329C2×C4—4882no—
330C2×C4—2442no—
331C2×C4—2442no—
332C2×C4—2448no—
333C2×C4—2442no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4#1451983912yes—
342C8—4882no—
343C8—2444no—
344C22—21no—
345C22—21no—
346C22—612no—
347C22—612no—
348C22—612no—
349C22—612no—
350C22—1224no—
351C22—1224no—
352C22—1221no—
353C22—1221no—
354C22D61⋊#9911yescharacteristic
355C22C2×#1451983911yescharacteristic
356C22D61⋊#10411yescharacteristic
357C4—22no—
358C4—42no—
359C4—41no—
360C4—41no—
361C4—81no—
362C4—1221no—
363C4—1221no—
364C4—4881no—
365C4—2442no—
366C4—2441no—
367C4—2441no—
368C2—21no—
369C2—21no—
370C2—614no—
371C2—1222no—
372C2D61⋊#32711yescharacteristic
373C2D61⋊#35211yescharacteristic
374C2D61⋊#35611yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#398C4
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC2×#11758196C23
hypercenter#398#6923
hypocenterC61C2×#1346
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #398

Complements

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

NH ≅ G/Ntype
3. #21460804C2semidirect
4. #21460803C2semidirect
192. D61#1346semidirect
210. C61C2×#1346semidirect

Maximal subgroups

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

subgroupindex
#214615222
D61⋊#3242
#214608042
#214608032
#398×D612
C2×#134661