Finite Group Databasebeta

← D61⋊#1336 #30604439

Subgroups — D61⋊#1336 #30604439

Order 15616.

398 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 98 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⋊#364C211yesmaximal, characteristic, complemented
2#21461013C211yesmaximal, characteristic, complemented
3#21460784C212yesmaximal, complemented
4#21460783C212yesmaximal, complemented
5#443×D61C211yesmaximal, characteristic
6D61⋊M32—21no—
7C4×D61⋊C8—21no—
8#16840685—21no—
9#16840684C2212yescomplemented
10#16840603—21no—
11#16840603C2212yescomplemented
12#135×D61C411yescharacteristic
13#131×D61—21no—
14#16839880C411yescharacteristic
15#16839879C2211yescharacteristic
16#16839878C2211yescharacteristic
17#16839877—21no—
18#16839876—21no—
19#108×D61C411yescharacteristic
20#104×D61—21no—
21C4×C8×D61C2211yescharacteristic
22C61×#443C411yescharacteristic
23C2×D61⋊C8—22no—
24#14519852—41no—
25#14519851—22no—
26D61⋊C16—41no—
27C4×#92420—22no—
28C4×#92420—22no—
29#41×D61—21no—
30#14519800C811yescharacteristic, complemented
31#14519799C2×C411yescharacteristic
32#14519798—21no—
33#14519797—21no—
34#14519796C811yescharacteristic, complemented
35Q16×D61C811yescharacteristic, complemented
36SD16×D61—21no—
37D8×D61C811yescharacteristic, complemented
38#14519785—21no—
39#14519785—41no—
40#14519784—21no—
41#14519783—21no—
42#14519783—41no—
43M16×D61—21no—
44M16×D61—41no—
45C2×C8×D61—41no—
46C2×C8×D61C2×C411yescharacteristic
47C2×C8×D61D411yescharacteristic
48C42×D61D411yescharacteristic
49#14519713C2×C411yescharacteristic
50#14519712—21no—
51#14519705—21no—
52#14519704—21no—
53#14519703—21no—
54C4×#92418D411yescharacteristic
55C8×Dic61D411yescharacteristic
56C8×Dic61C2311yescharacteristic
57#135×C61C2×C411yescharacteristic
58#131×C61—21no—
59#108×C61C2×C411yescharacteristic
60#104×C61—21no—
61C4×C8×C61C2×C411yescharacteristic
62#41×C61—21no—
63#11758226—21no—
64Q8×D61—21no—
65#11758224—21no—
66#11758224—41no—
67D4×D61—21no—
68D4×D61—41no—
69#11758222—21no—
70#11758222—41no—
71C2×C4×D61—21no—
72C2×C4×D61—41no—
73C2×C4×D61C22⋊C411yescharacteristic
74C2×#92420—24no—
75D61⋊C8—44no—
76Q16×C61C2×C811yescharacteristic, complemented
77SD16×C61—21no—
78D8×C61C2×C811yescharacteristic, complemented
79M16×C61—21no—
80M16×C61—41no—
81C2×C8×C61—41no—
82C2×C8×C61C22⋊C411yescharacteristic
83C2×C8×C61C22×C411yescharacteristic
84C42×C61C22⋊C411yescharacteristic
85#11758202—21no—
86#11758201—21no—
87#11758200—21no—
88#11758199—21no—
89C4×Dic61—21no—
90C4×Dic61C2×D411yescharacteristic
91#11758194—21no—
92#11758194—41no—
93C2×#92418—41no—
94C2×#92418C22⋊C411yescharacteristic
95C2×#92418C2×D411yescharacteristic
96Dic244C2×C811yescharacteristic, complemented
97D488C2×C811yescharacteristic, complemented
98#11758190—21no—
99#11758189—41no—
100#11758189—41no—
101#11758189—41no—
102C8×D61—41no—
103C8×D61—41no—
104C8×D61—41no—
105C8×D61C2×C811yescharacteristic
106C8×D61C2×C811yescharacteristic
107C8×D61M1611yescharacteristic
108C8×D61M1611yescharacteristic
109C8×D61D811yescharacteristic
110C8×D61D811yescharacteristic
111C8×D61SD1611yescharacteristic
112C8×D61SD1611yescharacteristic
113#11758187—42no—
114C22×D61—41no—
115C22×D61#10411yescharacteristic
116Q8×C61—21no—
117D4×C61—21no—
118D4×C61—41no—
119C2×C4×C61—21no—
120C2×C4×C61—41no—
121C2×C4×C61C2×C22⋊C411yescharacteristic
122C22⋊D61—41no—
123C22⋊D61—41no—
124C22⋊D61—41no—
125C2×Dic61—21no—
126C2×Dic61—41no—
127C2×Dic61#10411yescharacteristic
128D244—21no—
129D244—41no—
130C4×D61—24no—
131C4×D61—41no—
132C4×D61—41no—
133C4×D61—41no—
134C4×D61C22⋊C811yescharacteristic
135C4×D61C22⋊C811yescharacteristic
136C4×D61#10211yescharacteristic
137C4×D61#10211yescharacteristic
138Dic122—21no—
139Dic122—41no—
140#92420—44no—
141C8×C61—41no—
142C8×C61#10211yescharacteristic
143C8×C61#10211yescharacteristic
144C8×C61C22×C811yescharacteristic
145C8×C61C2×M1611yescharacteristic
146#92418—41no—
147#92418C22⋊C811yescharacteristic
148#92418C22⋊C811yescharacteristic
149#92418C2×D811yescharacteristic
150#92418C2×SD1611yescharacteristic
151C2×#1336—611nomaximal, Sylow
152C22×C61—41no—
153C22×C61C2×#10411yescharacteristic
154C2×D61—22no—
155C2×D61—41no—
156C2×D61—82no—
157C2×D61D4⋊C811yescharacteristic
158C2×D61D4⋊C811yescharacteristic
159C4×C61—22no—
160C4×C61—41no—
161C4×C61C2×C22⋊C811yescharacteristic
162C4×C61C2×#10211yescharacteristic
163Dic61—22no—
164Dic61—41no—
165Dic61D4⋊C811yescharacteristic
166Dic61D4⋊C811yescharacteristic
167C2×#443—611no—
168C2×#364—611no—
169C2×#322—611no—
170#1336—612no—
171#1336—612no—
172C2×C61—21no—
173C2×C61—81no—
174C2×C61C2×D4⋊C811yescharacteristic
175D61—21no—
176D61—81no—
177D61#133612yescomplemented
178C2×#135—611no—
179C2×#131—1221no—
180C2×M32—1221no—
181#443—611no—
182#443—611no—
183#443—611no—
184#443—1221no—
185#443—1221no—
186#443#692311yescharacteristic
187C2×#108—611no—
188C2×#104—1221no—
189C2×C4×C8—611no—
190C2×C4×C8—1221no—
191#364—612no—
192#364—1221no—
193#322—612no—
194#322—1221no—
195C61C2×#133611yescharacteristic, complemented, Sylow
196C2×#41—1221no—
197#135—611no—
198#135—611no—
199#135—611no—
200#135—1221no—
201#135—1221no—
202#135C2×#692311yescharacteristic
203C2×Q16—611no—
204C2×SD16—1221no—
205C2×D8—611no—
206#131—21no—
207#131—1221no—
208#131—1221no—
209#131—1221no—
210#131—2441no—
211#131—2441no—
212C2×M16—1221no—
213C2×M16—2441no—
214C22×C8—611no—
215C22×C8—611no—
216C22×C8—1222no—
217C22×C8—2441no—
218C2×C42—611no—
219M32—1222no—
220M32—2441no—
221C2×C16—2441no—
222#108—611no—
223#108—1221no—
224#108C2×#692311yescharacteristic
225#104—21no—
226#104—1221no—
227#104—1221no—
228#104—1221no—
229C4×C8—611no—
230C4×C8—611no—
231C4×C8—611no—
232C4×C8—1222no—
233C4×C8—1222no—
234C4×C8C2×#692311yescharacteristic
235#41—21no—
236#41—1221no—
237#41—1221no—
238#41—1221no—
239#41—2441no—
240#41—2441no—
241C2×Q8—1221no—
242C2×D4—1221no—
243C2×D4—2441no—
244C22×C4—611no—
245C22×C4—1221no—
246C22×C4—2441no—
247Q16—611no—
248Q16—1221no—
249Q16D61⋊C811yescharacteristic, complemented
250SD16—21no—
251SD16—1221no—
252SD16—1221no—
253SD16—1221no—
254D8—611no—
255D8—1221no—
256D8D61⋊C811yescharacteristic, complemented
257M16—21no—
258M16—41no—
259M16—1221no—
260M16—2441no—
261M16—2441no—
262M16—2441no—
263M16—2441no—
264C2×C8—41no—
265C2×C8—611no—
266C2×C8—611no—
267C2×C8—611no—
268C2×C8—611no—
269C2×C8—611no—
270C2×C8—611no—
271C2×C8—611no—
272C2×C8—611no—
273C2×C8—611no—
274C2×C8—611no—
275C2×C8—1224no—
276C2×C8—2441no—
277C2×C8—2441no—
278C2×C8—2441no—
279C2×C8—2444no—
280C2×C8—2441no—
281C2×C8C22⋊#692311yescharacteristic
282C2×C8C22×#692311yescharacteristic
283C42—611no—
284C42—1221no—
285C42C22⋊#692311yescharacteristic
286C16—2442no—
287C23—611no—
288C23—2441no—
289Q8—21no—
290Q8—1221no—
291Q8—2441no—
292D4—21no—
293D4—41no—
294D4—1221no—
295D4—2441no—
296D4—2441no—
297D4—2441no—
298D4—2441no—
299C2×C4—21no—
300C2×C4—41no—
301C2×C4—611no—
302C2×C4—611no—
303C2×C4—611no—
304C2×C4—611no—
305C2×C4—611no—
306C2×C4—1224no—
307C2×C4—1221no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4C2×C22⋊#692311yescharacteristic
313C8—41no—
314C8—611no—
315C8—611no—
316C8—611no—
317C8—611no—
318C8—2444no—
319C8—2441no—
320C8#1451983911yescharacteristic
321C8#1451983911yescharacteristic
322C8C2×D61⋊C811yescharacteristic
323C8D61⋊M1611yescharacteristic
324C22—41no—
325C22—611no—
326C22—611no—
327C22—1222no—
328C22—4882no—
329C22—2441no—
330C22D61⋊#10411yescharacteristic
331C4—22no—
332C4—41no—
333C4—611no—
334C4—611no—
335C4—1222no—
336C4—2441no—
337C4D61⋊(C22⋊C8)11yescharacteristic
338C4C2×#1451983911yescharacteristic
339C2—21no—
340C2—81no—
341C2—612no—
342C2—1221no—
343C2—4881no—
344C2D61⋊(D4⋊C8)11yescharacteristic
subgroupG/H
centerC4C2×#14519839
commutatorC8×C61C22×C8
FrattiniC2×C8C22×#6923
FittingC61×#443C4
socleC2×C61C2×D4⋊C8
prime radical#135×D61C4
cosocleC8×Dic61C23
hypercenter#443#6923
hypocenterC61C2×#1336
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C8 ◁ C4×C8 ◁ #443

Complements

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

NH ≅ G/Ntype
1. D61⋊#364C2semidirect
2. #21461013C2semidirect
3. #21460784C2semidirect
4. #21460783C2semidirect
9. #16840684C22semidirect
11. #16840603C22semidirect
30. #14519800C8semidirect
34. #14519796C8semidirect
35. Q16×D61C8semidirect
37. D8×D61C8semidirect
76. Q16×C61C2×C8semidirect
78. D8×C61C2×C8semidirect
96. Dic244C2×C8semidirect
97. D488C2×C8semidirect
177. D61#1336semidirect
195. C61C2×#1336semidirect
249. Q16D61⋊C8semidirect
256. D8D61⋊C8semidirect

Maximal subgroups

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

subgroupindex
D61⋊#3642
#214610132
#214607842
#214607832
#443×D612
C2×#133661