Finite Group Databasebeta

← #30605451

Subgroups — #30605451

Order 15616.

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

normal subgroups only

This group has 400 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⋊(C22⋊C16)C211yesmaximal, characteristic, complemented
2#21461698C211yesmaximal, characteristic, complemented
3#21460812C212yesmaximal, complemented
4#21460810C212yesmaximal, complemented
5#21455401C211yesmaximal, characteristic
6C2×D61⋊C16—21no—
7C2×#14519847—21no—
8#16840733—21no—
9#16840657C2212yes—
10C22⋊#11758187—21no—
11#16840638C2212yes—
12C2×#14519799C411yescharacteristic
13C22×C8×D61C2211yescharacteristic
14#16840274—21no—
15#16840004C411yescharacteristic
16#16840004C2211yescharacteristic
17#16839999C411yescharacteristic
18#16839999C2211yescharacteristic
19#16839992—21no—
20#16839992—21no—
21#16839756—21no—
22C61×#427C411yescharacteristic
23C2×#11758213—22no—
24D61⋊C16—42no—
25C2×#11758187—22no—
26#14519847—42no—
27#14519834—41no—
28C22⋊#92420—41no—
29C2×#11758222—21no—
30C22×C4×D61D411yescharacteristic
31#14519799—42no—
32C2×Dic244C2×C411yescharacteristic
33C2×#11758190—21no—
34C2×D488C2×C411yescharacteristic
35C22×#92418D411yescharacteristic
36C2×C8×D61—42no—
37C2×C8×D61C2×C411yescharacteristic
38C2×C8×D61D411yescharacteristic
39C2×C8×D61D411yescharacteristic
40C2×C8×D61C2311yescharacteristic
41#14519761—41no—
42#14519757—21no—
43#14519757—21no—
44#14519752—21no—
45#14519752—21no—
46#14519747—41no—
47C4×D244—41no—
48C4×D244—41no—
49#14519700—21no—
50#14519700—21no—
51#14519697—21no—
52#14519697—21no—
53C22×C8×C61C2×C411yescharacteristic
54#117×C61—21no—
55#107×C61C2×C411yescharacteristic
56#107×C61C2×C411yescharacteristic
57#106×C61—21no—
58C23×D61SD1611yescharacteristic
59C22×C4×C61C22⋊C411yescharacteristic
60C2×C22⋊D61—41no—
61C22×Dic61D811yescharacteristic
62#11758222—42no—
63#11758222—42no—
64C2×D244—21no—
65C2×D244—41no—
66C2×D244—41no—
67C2×C4×D61—41no—
68C2×C4×D61—41no—
69C2×C4×D61—41no—
70C2×C4×D61C22⋊C411yescharacteristic
71C2×C4×D61D811yescharacteristic
72C2×C4×D61SD1611yescharacteristic
73C2×C4×D61C2×D411yescharacteristic
74C2×Dic122—21no—
75C2×#92420—42no—
76#11758213—42no—
77#11758213—42no—
78C2×C8×C61—22no—
79C2×C8×C61C22⋊C411yescharacteristic
80C2×C8×C61C22×C411yescharacteristic
81C4⋊C4×C61—21no—
82C4⋊C4×C61—21no—
83C22⋊C4×C61—41no—
84C42×C61—41no—
85#11758198—41no—
86#11758198—41no—
87#11758198—41no—
88#11758198—41no—
89C4⋊Dic61—41no—
90C4⋊Dic61—41no—
91C2×#92418—41no—
92C2×#92418C22⋊C411yescharacteristic
93C2×#92418C2×D411yescharacteristic
94Dic244—41no—
95D488—41no—
96#11758190—42no—
97C8×D61—22no—
98C8×D61—22no—
99C8×D61—41no—
100C8×D61—41no—
101#11758187—42no—
102C23×C61#10211yescharacteristic
103C22×D61—22no—
104C22×D61—41no—
105C22×D61—41no—
106C22×D61—41no—
107C22×D61#10211yescharacteristic
108C22×D61C2×SD1611yescharacteristic
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61#10211yescharacteristic
114C2×C4×C61C2×C22⋊C411yescharacteristic
115C22⋊D61—82no—
116C2×Dic61—41no—
117C2×Dic61—41no—
118C2×Dic61#10211yescharacteristic
119C2×Dic61C2×D811yescharacteristic
120D244—41no—
121D244—41no—
122D244—82no—
123D244—82no—
124C4×D61—21no—
125C4×D61—21no—
126C4×D61—21no—
127C4×D61—21no—
128C4×D61—41no—
129C4×D61—41no—
130C4×D61—82no—
131Dic122—41no—
132Dic122—41no—
133#92420—82no—
134C8×C61—21no—
135C8×C61#9912yes—
136#92418—21no—
137#92418—21no—
138#11893—611nomaximal, Sylow
139C22×C61—21no—
140C22×C61—21no—
141C22×C61—21no—
142C22×C61C2×#10211yescharacteristic
143C2×D61—21no—
144C2×D61—21no—
145C2×D61—21no—
146C2×D61—21no—
147C2×D61—21no—
148C2×D61—44no—
149C2×D61—81no—
150C2×D61—81no—
151C2×D61—81no—
152C2×D61#35912yes—
153C4×C61—21no—
154C4×C61—81no—
155C4×C61—81no—
156C4×C61C2×#9911yescharacteristic
157C4×C61#42111yescharacteristic
158Dic61—21no—
159Dic61—21no—
160Dic61—81no—
161#3050—611no—
162C2×C22⋊C16—611no—
163#1810—611no—
164#1350—612no—
165#1349—612no—
166C2×C61—41no—
167C2×C61#151911yescharacteristic
168C2×C61C2×#35911yescharacteristic
169C2×C61#214811yescharacteristic
170D61—22no—
171D61—41no—
172D61—161no—
173C2×#135—611no—
174C23×C8—611no—
175#525—1221no—
176C22×C16—1221no—
177#467—611no—
178#467—611no—
179#466—611no—
180#466—611no—
181#465—1221no—
182#465—1221no—
183C2×#108—1221no—
184#427#692311yescharacteristic
185#416—1221no—
186#407—1221no—
187C22⋊C16—612no—
188C22⋊C16—1221no—
189#341—612no—
190C61#1189311yescharacteristic, complemented, Sylow
191C2×#41—1221no—
192C23×C4—611no—
193#135—2442no—
194C2×Q16—611no—
195C2×SD16—1221no—
196C2×D8—611no—
197C2×M16—1222no—
198C22×C8—611no—
199C22×C8—611no—
200C22×C8—611no—
201C22×C8—611no—
202C22×C8—611no—
203C22×C8—2442no—
204C22×C8C2×#692311yescharacteristic
205#123—2441no—
206C22⋊Q8—1221no—
207C22⋊Q8—1221no—
208#121—1221no—
209#121—1221no—
210#120—2441no—
211C4×D4—2441no—
212C4×D4—2441no—
213#117—21no—
214C2×C16—1222no—
215C2×C16—2442no—
216#108—2442no—
217#107C2×#692311yescharacteristic
218#107C2×#692311yescharacteristic
219#106—21no—
220#103—1221no—
221#103—1221no—
222#102—1221no—
223#102—1221no—
224C22⋊C8—2441no—
225C22⋊C8—2441no—
226C24—611no—
227#41—2442no—
228#41—2442no—
229C2×Q8—1221no—
230C2×D4—1221no—
231C2×D4—2441no—
232C2×D4—2441no—
233C2×D4—2441no—
234C22×C4—611no—
235C22×C4—611no—
236C22×C4—611no—
237C22×C4—611no—
238C22×C4—611no—
239C22×C4—2441no—
240C22×C4—2441no—
241C22×C4—2441no—
242C22×C4C22⋊#692311yescharacteristic
243Q16—2441no—
244SD16—2442no—
245D8—2441no—
246M16—2442no—
247M16—2442no—
248C2×C8—22no—
249C2×C8—611no—
250C2×C8—611no—
251C2×C8—1222no—
252C2×C8—1222no—
253C2×C8—2441no—
254C2×C8—2441no—
255C2×C8—2441no—
256C2×C8—2442no—
257C2×C8C22⋊#692311yescharacteristic
258C2×C8C22×#692311yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—2441no—
262C4⋊C4—2441no—
263C22⋊C4—41no—
264C22⋊C4—2441no—
265C22⋊C4—2441no—
266C22⋊C4—2441no—
267C22⋊C4—2441no—
268C42—41no—
269C16—2442no—
270C23—611no—
271C23—611no—
272C23—1222no—
273C23—2441no—
274C23—2441no—
275C23—2441no—
276C23#1451983911yescharacteristic
277Q8—2441no—
278Q8—2441no—
279D4—4882no—
280D4—4882no—
281D4—4882no—
282D4—2441no—
283D4—2441no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—611no—
289C2×C4—611no—
290C2×C4—1221no—
291C2×C4—1221no—
292C2×C4—1221no—
293C2×C4—1221no—
294C2×C4—4882no—
295C2×C4—2441no—
296C2×C4—2441no—
297C2×C4—2441no—
298C2×C4—2441no—
299C2×C4#1451983911yescharacteristic
300C2×C4C2×C22⋊#692311yescharacteristic
301C8—21no—
302C8—1221no—
303C8—1221no—
304C8—4882no—
305C8#1451983612yes—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—612no—
310C22—1221no—
311C22—1221no—
312C22—1221no—
313C22—1221no—
314C22—1221no—
315C22—4881no—
316C22—4881no—
317C22—4881no—
318C22—2444no—
319C22C2×#1451983911yescharacteristic
320C4—21no—
321C4—81no—
322C4—81no—
323C4—1221no—
324C4—1221no—
325C4—4881no—
326C4C2×#1451983611yescharacteristic
327C4#1684076111yescharacteristic
328C2—41no—
329C2—1222no—
330C2—9761no—
331C2—2441no—
332C2#2146125611yescharacteristic
333C2D61⋊#35911yescharacteristic
334C2#2146214711yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#427C4
socleC22×C61C2×#102
prime radical#21455401C2
cosocleC2×C8×D61C23
hypercenter#427#6923
hypocenterC61#11893
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #427

Complements

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

NH ≅ G/Ntype
1. D61⋊(C22⋊C16)C2semidirect
2. #21461698C2semidirect
3. #21460812C2semidirect
4. #21460810C2semidirect
190. C61#11893semidirect

Maximal subgroups

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

subgroupindex
D61⋊(C22⋊C16)2
#214616982
#214608122
#214608102
#214554012
#1189361