Finite Group Databasebeta

← D61⋊#1339 #30604707

Subgroups — D61⋊#1339 #30604707

Order 15616.

496 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 78 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
1D61⋊#349C211yesmaximal, characteristic, complemented
2#21461491C211yesmaximal, characteristic, complemented
3#21460790C212yesmaximal, complemented
4#21460789C212yesmaximal, complemented
5#469×D61C211yesmaximal, characteristic
6C2×#14519856—21no—
7D61⋊M32—21no—
8#16840659C2212yescomplemented
9#16840658—21no—
10#16840630—21no—
11#16840630C2212yescomplemented
12C2×D8×D61C411yescharacteristic, complemented
13C2×M16×D61C2211yescharacteristic
14#121×D61—21no—
15#16840016C2211yescharacteristic
16#16840015C411yescharacteristic, complemented
17#16840014—21no—
18#16840013—21no—
19#16840012C2211yescharacteristic
20#106×D61C411yescharacteristic, complemented
21#102×D61—21no—
22C61×#469C411yescharacteristic, complemented
23#14519856—22no—
24#14519856—22no—
25#14519856—41no—
26#14519856—41no—
27C2×C4⋊#6923—41no—
28C2×C22⋊#6923—41no—
29C2×C4×#6923—22no—
30#14519852—41no—
31#14519851—22no—
32D61⋊C16—41no—
33C2×D4×D61—21no—
34C2×D4×D61—41no—
35C22×C4×D61D411yescharacteristic
36C2×D488C2×C411yescharacteristic, complemented
37C2×#11758199—21no—
38D8×D61—41no—
39D8×D61—41no—
40C2×#11758194D411yescharacteristic
41C2×#11758189D411yescharacteristic
42C2×#11758189C2311yescharacteristic
43M16×D61—41no—
44M16×D61—41no—
45C2×C8×D61C2×C411yescharacteristic
46C2×C8×D61D411yescharacteristic
47#14519752—21no—
48#14519751—21no—
49#14519750—41no—
50#14519749—41no—
51#14519748—21no—
52C4⋊C4×D61—21no—
53C22⋊C4×D61—41no—
54#14519709C2×C411yescharacteristic, complemented
55#14519708—21no—
56#14519699—21no—
57#14519698—21no—
58#14519697—21no—
59C2×D8×C61C2×C411yescharacteristic, complemented
60C2×M16×C61C2×C411yescharacteristic
61#121×C61—21no—
62#106×C61C2×C411yescharacteristic, complemented
63#102×C61—21no—
64C23×D61—41no—
65C23×D61D811yescharacteristic
66C22×#6923—42no—
67C2×D4×C61—21no—
68C2×D4×C61—41no—
69C22×C4×C61C22⋊C411yescharacteristic
70C2×C22⋊D61—41no—
71C2×C22⋊D61—41no—
72C2×C22⋊D61—41no—
73C22×Dic61SD1611yescharacteristic
74D4×D61—41no—
75D4×D61—41no—
76D4×D61—41no—
77D4×D61—41no—
78D4×D61—84no—
79C2×D244—21no—
80C2×D244—41no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—41no—
86C2×C4×D61C22⋊C411yescharacteristic
87C2×C4×D61D811yescharacteristic
88C2×C4×D61SD1611yescharacteristic
89C2×C4×D61C2×D411yescharacteristic
90C22⋊#6923—42no—
91C22⋊#6923—42no—
92C4⋊#6923—42no—
93C4⋊#6923—42no—
94C4×#6923—24no—
95C4×#6923—42no—
96D8×C61—41no—
97M16×C61—41no—
98C2×C8×C61C22⋊C411yescharacteristic
99C2×C8×C61C22×C411yescharacteristic
100C4⋊C4×C61—21no—
101C22⋊C4×C61—41no—
102C22⋊Dic61—41no—
103#11758199—42no—
104#11758198—41no—
105#11758198—41no—
106C4⋊Dic61—21no—
107#11758196—41no—
108#11758194—41no—
109C2×#92418C22⋊C411yescharacteristic
110C2×#92418C2×D411yescharacteristic
111D488—41no—
112#11758189—41no—
113#11758189—41no—
114C8×D61—21no—
115C8×D61—21no—
116C8×D61—21no—
117C8×D61—21no—
118#11758187—42no—
119C23×C61—41no—
120C23×C61#10211yescharacteristic
121C22×D61—21no—
122C22×D61—21no—
123C22×D61—42no—
124C22×D61—41no—
125C22×D61—82no—
126C22×D61—82no—
127C22×D61—81no—
128C22×D61—81no—
129C22×D61#10211yescharacteristic
130C22×D61C2×D811yescharacteristic
131C2×#6923—44no—
132C2×#6923—84no—
133D4×C61—41no—
134D4×C61—41no—
135D4×C61—82no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—41no—
139C2×C4×C61#10211yescharacteristic
140C2×C4×C61C2×C22⋊C411yescharacteristic
141C22⋊D61—82no—
142C22⋊D61—82no—
143C22⋊D61—81no—
144C22⋊D61—81no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—41no—
148C2×Dic61#10211yescharacteristic
149C2×Dic61C2×SD1611yescharacteristic
150D244—41no—
151D244—41no—
152D244—82no—
153C4×D61—21no—
154C4×D61—21no—
155C4×D61—21no—
156C4×D61—21no—
157C4×D61—21no—
158C4×D61—21no—
159C4×D61—82no—
160C4×D61#9911yescharacteristic
161C4×D61#9911yescharacteristic
162C4×D61#10411yescharacteristic
163C4×D61#10411yescharacteristic
164C8×C61—21no—
165C8×C61—21no—
166#92418—21no—
167#92418—21no—
168C2×#1339—611nomaximal, Sylow
169C22×C61—21no—
170C22×C61—41no—
171C22×C61—81no—
172C22×C61—81no—
173C22×C61—81no—
174C22×C61C2×#10211yescharacteristic
175C2×D61—22no—
176C2×D61—21no—
177C2×D61—42no—
178C2×D61—41no—
179C2×D61—81no—
180C2×D61—81no—
181C2×D61—81no—
182C2×D61—81no—
183C2×D61—162no—
184C2×D61—162no—
185C2×D61#32711yescharacteristic
186C2×D61#32711yescharacteristic
187#6923—84no—
188C4×C61—21no—
189C4×C61—81no—
190C4×C61C2×#9911yescharacteristic
191C4×C61C2×#10411yescharacteristic
192Dic61—21no—
193Dic61—81no—
194Dic61#32711yescharacteristic
195Dic61#32711yescharacteristic
196C2×#469—611no—
197C2×#349—611no—
198C2×H(3,ℤ/4)—611no—
199#1339—612no—
200#1339—612no—
201C2×C61—21no—
202C2×C61—41no—
203C2×C61—161no—
204C2×C61C2×#32711yescharacteristic
205D61—21no—
206D61—41no—
207D61—161no—
208D61#133912yescomplemented
209C22×D8—611no—
210C22×M16—611no—
211C2×#121—1221no—
212C2×#117—1221no—
213C2×M32—1221no—
214#469—611no—
215#469—611no—
216#469—611no—
217#469—1221no—
218#469—1221no—
219#469#692311yescharacteristic, complemented
220C2×#106—611no—
221C2×#102—1221no—
222#349—612no—
223#349—1221no—
224H(3,ℤ/4)—612no—
225H(3,ℤ/4)—1221no—
226C61C2×#133911yescharacteristic, complemented, Sylow
227C22×D4—1221no—
228C22×D4—2441no—
229C23×C4—611no—
230C2×D8—611no—
231C2×D8—1221no—
232C2×D8—2441no—
233C2×D8—2441no—
234C2×D8C2×#692311yescharacteristic, complemented
235C2×M16—611no—
236C2×M16—611no—
237C2×M16—611no—
238C2×M16—2441no—
239C2×M16—2441no—
240C2×M16C2×#692311yescharacteristic
241C22×C8—611no—
242C22×C8—611no—
243#121—21no—
244#121—1221no—
245#121—1221no—
246#121—1221no—
247#121—2441no—
248#121—2441no—
249#117—1222no—
250#117—1222no—
251#117—2441no—
252#117—2441no—
253C2×C4⋊C4—1221no—
254C2×C4⋊C4—2441no—
255C2×C22⋊C4—2441no—
256C2×C22⋊C4—2441no—
257C2×C42—1222no—
258M32—1222no—
259M32—2441no—
260C2×C16—2441no—
261#106—611no—
262#106—1221no—
263#106C2×#692311yescharacteristic, complemented
264#102—21no—
265#102—1221no—
266#102—1221no—
267#102—1221no—
268C24—611no—
269C24—2441no—
270C2×D4—21no—
271C2×D4—41no—
272C2×D4—1221no—
273C2×D4—4884no—
274C2×D4—2441no—
275C2×D4—2441no—
276C2×D4—2441no—
277C2×D4—2441no—
278C2×D4—2441no—
279C2×D4—2441no—
280C2×D4—2441no—
281C2×D4—2441no—
282C22×C4—611no—
283C22×C4—611no—
284C22×C4—611no—
285C22×C4—611no—
286C22×C4—611no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4—1221no—
291C22×C4—2441no—
292C22×C4—2442no—
293C22×C4C22⋊#692311yescharacteristic
294D8—41no—
295D8—2441no—
296D8—2442no—
297M16—41no—
298M16—2441no—
299M16—2441no—
300M16—2441no—
301C2×C8—611no—
302C2×C8—611no—
303C2×C8—1221no—
304C2×C8—1221no—
305C2×C8—1221no—
306C2×C8—1221no—
307C2×C8C22⋊#692311yescharacteristic
308C2×C8C22×#692311yescharacteristic
309C4⋊C4—21no—
310C4⋊C4—1221no—
311C4⋊C4—2441no—
312C4⋊C4—2442no—
313C4⋊C4—2442no—
314C22⋊C4—41no—
315C22⋊C4—2441no—
316C22⋊C4—2441no—
317C22⋊C4—2442no—
318C22⋊C4—2442no—
319C22⋊C4—2441no—
320C42—1224no—
321C42—2442no—
322C16—2442no—
323C23—41no—
324C23—611no—
325C23—611no—
326C23—1221no—
327C23—1221no—
328C23—4881no—
329C23—4881no—
330C23—4882no—
331C23—4882no—
332C23—2442no—
333C23—2441no—
334C23#1451983911yescharacteristic
335D4—41no—
336D4—41no—
337D4—82no—
338D4—4882no—
339D4—4881no—
340D4—4881no—
341D4—4882no—
342D4—4882no—
343D4—2441no—
344D4—2441no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—41no—
348C2×C4—611no—
349C2×C4—611no—
350C2×C4—611no—
351C2×C4—611no—
352C2×C4—611no—
353C2×C4—611no—
354C2×C4—1221no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—1221no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—1221no—
361C2×C4—1221no—
362C2×C4—4882no—
363C2×C4—4884no—
364C2×C4—2444no—
365C2×C4—2441no—
366C2×C4#1451983911yescharacteristic
367C2×C4C2×C22⋊#692311yescharacteristic
368C8—21no—
369C8—21no—
370C8—1221no—
371C8—1221no—
372C22—21no—
373C22—41no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—611no—
378C22—611no—
379C22—1222no—
380C22—1221no—
381C22—9762no—
382C22—9762no—
383C22—4881no—
384C22—4881no—
385C22—4881no—
386C22—4881no—
387C22—2441no—
388C22—2442no—
389C22C2×#1451983911yescharacteristic
390C4—21no—
391C4—81no—
392C4—611no—
393C4—611no—
394C4—1221no—
395C4—4881no—
396C4—4884no—
397C4D61⋊#9911yescharacteristic
398C4D61⋊#10411yescharacteristic
399C2—21no—
400C2—41no—
401C2—161no—
402C2—612no—
403C2—1221no—
404C2—9761no—
405C2—2441no—
406C2D61⋊#32711yescharacteristic
subgroupG/H
centerC2D61⋊#327
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#469C4
socleC2×C61C2×#327
prime radical#469×D61C2
cosocleC2×#11758189C23
hypercenter#469#6923
hypocenterC61C2×#1339
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #469

Complements

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

NH ≅ G/Ntype
1. D61⋊#349C2semidirect
2. #21461491C2semidirect
3. #21460790C2semidirect
4. #21460789C2semidirect
8. #16840659C22semidirect
11. #16840630C22semidirect
12. C2×D8×D61C4semidirect
16. #16840015C4semidirect
20. #106×D61C4semidirect
22. C61×#469C4semidirect
36. C2×D488C2×C4semidirect
54. #14519709C2×C4semidirect
59. C2×D8×C61C2×C4semidirect
62. #106×C61C2×C4semidirect
208. D61#1339semidirect
219. #469#6923semidirect
226. C61C2×#1339semidirect
234. C2×D8C2×#6923semidirect
263. #106C2×#6923semidirect

Maximal subgroups

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

subgroupindex
D61⋊#3492
#214614912
#214607902
#214607892
#469×D612
C2×#133961