Finite Group Databasebeta

← #30605449

Subgroups — #30605449

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#21460811C212yesmaximal, complemented
4#21460809C212yesmaximal, complemented
5#21455396C211yesmaximal, characteristic
6C2×D61⋊C16—21no—
7C2×#14519847—21no—
8#16840733—21no—
9#16840657C2212yes—
10C22⋊#11758187—21no—
11#16840638C2212yes—
12C22×C8×D61C2211yescharacteristic
13#16840269—21no—
14#16840000C411yescharacteristic
15#16840000C2211yescharacteristic
16#16839995C411yescharacteristic
17#16839995C2211yescharacteristic
18#16839988—21no—
19#16839988—21no—
20#16839800C411yescharacteristic
21#16839758—21no—
22C2×#135×C61C411yescharacteristic
23C2×#11758213—22no—
24D61⋊C16—42no—
25C2×#11758187—22no—
26#14519847—42no—
27#14519834—41no—
28C22⋊#92420—41no—
29C22×C4×D61D411yescharacteristic
30C22×#92418D411yescharacteristic
31C2×C8×D61—42no—
32C2×C8×D61C2×C411yescharacteristic
33C2×C8×D61D411yescharacteristic
34C2×C8×D61D411yescharacteristic
35C2×C8×D61C2311yescharacteristic
36#14519758—41no—
37#14519753—21no—
38#14519753—21no—
39#14519748—21no—
40#14519748—21no—
41#14519745—41no—
42C4×C22⋊D61—41no—
43C4×C22⋊D61—41no—
44#14519736—21no—
45#14519711C2×C411yescharacteristic
46#14519711C2×C411yescharacteristic
47#14519709—21no—
48#14519701—21no—
49#14519701—21no—
50#14519698—21no—
51#14519698—21no—
52C2×#41×C61—21no—
53#135×C61—42no—
54C2×Q16×C61C2×C411yescharacteristic
55C2×SD16×C61—21no—
56C2×D8×C61C2×C411yescharacteristic
57C22×C8×C61C2×C411yescharacteristic
58C23×D61SD1611yescharacteristic
59#41×C61—42no—
60#41×C61—42no—
61C2×Q8×C61—21no—
62C2×D4×C61—21no—
63C2×D4×C61—41no—
64C22×C4×C61—41no—
65C22×C4×C61C22⋊C411yescharacteristic
66C2×C22⋊D61—41no—
67C2×C22⋊D61—41no—
68C22×Dic61D811yescharacteristic
69C2×C4×D61—41no—
70C2×C4×D61—41no—
71C2×C4×D61C22⋊C411yescharacteristic
72C2×C4×D61D811yescharacteristic
73C2×C4×D61SD1611yescharacteristic
74C2×C4×D61C2×D411yescharacteristic
75C2×#92420—42no—
76#11758213—42no—
77#11758213—42no—
78Q16×C61—41no—
79SD16×C61—42no—
80D8×C61—41no—
81C2×C8×C61—22no—
82C2×C8×C61C22⋊C411yescharacteristic
83C2×C8×C61C22×C411yescharacteristic
84C22⋊Dic61—41no—
85C22⋊Dic61—41no—
86C22⋊Dic61—41no—
87#11758198—41no—
88#11758198—41no—
89C4⋊Dic61—21no—
90C4⋊Dic61—21no—
91#11758196—41no—
92#11758196—41no—
93C4×Dic61—41no—
94C2×#92418—41no—
95C2×#92418C22⋊C411yescharacteristic
96C2×#92418C2×D411yescharacteristic
97C8×D61—22no—
98C8×D61—22no—
99C8×D61—41no—
100C8×D61—41no—
101#11758187—42no—
102C23×C61—41no—
103C23×C61#10211yescharacteristic
104C22×D61—22no—
105C22×D61—41no—
106C22×D61—41no—
107C22×D61#10211yescharacteristic
108C22×D61C2×SD1611yescharacteristic
109Q8×C61—41no—
110Q8×C61—41no—
111D4×C61—41no—
112D4×C61—41no—
113D4×C61—82no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—41no—
117C2×C4×C61—82no—
118C2×C4×C61#10211yescharacteristic
119C2×C4×C61C2×C22⋊C411yescharacteristic
120C22⋊D61—82no—
121C22⋊D61—82no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61#10211yescharacteristic
126C2×Dic61C2×D811yescharacteristic
127C4×D61—21no—
128C4×D61—21no—
129C4×D61—21no—
130C4×D61—21no—
131C4×D61—41no—
132C4×D61—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×C61—81no—
143C22×C61—81no—
144C22×C61—81no—
145C22×C61C2×#10211yescharacteristic
146C2×D61—21no—
147C2×D61—21no—
148C2×D61—21no—
149C2×D61—21no—
150C2×D61—21no—
151C2×D61—44no—
152C2×D61#35912yes—
153C4×C61—21no—
154C4×C61—81no—
155C4×C61C2×#9911yescharacteristic
156C4×C61#42111yescharacteristic
157Dic61—21no—
158Dic61—21no—
159Dic61—81no—
160Dic61—81no—
161#3050—611no—
162C2×C22⋊C16—611no—
163#1810—611no—
164#1350—612no—
165#1349—612no—
166C2×C61—41no—
167C2×C61—161no—
168C2×C61#151911yescharacteristic
169C2×C61C2×#35911yescharacteristic
170C2×C61#214811yescharacteristic
171D61—22no—
172D61—41no—
173C2×#135#692311yescharacteristic
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—611no—
185#416—1221no—
186#407—1221no—
187C22⋊C16—612no—
188C22⋊C16—1221no—
189#341—612no—
190C61#1189311yescharacteristic, complemented, Sylow
191C2×#41—21no—
192C23×C4—611no—
193#135—42no—
194C2×Q16C2×#692311yescharacteristic
195C2×SD16—21no—
196C2×D8C2×#692311yescharacteristic
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—1221no—
214C2×C16—1222no—
215C2×C16—2442no—
216#108—2442no—
217#107—611no—
218#107—611no—
219#106—1221no—
220#103—1221no—
221#103—1221no—
222#102—1221no—
223#102—1221no—
224C22⋊C8—2441no—
225C22⋊C8—2441no—
226C24—611no—
227#41—42no—
228#41—42no—
229C2×Q8—21no—
230C2×D4—21no—
231C2×D4—41no—
232C2×D4—2441no—
233C2×D4—2441no—
234C22×C4—41no—
235C22×C4—611no—
236C22×C4—611no—
237C22×C4—611no—
238C22×C4—611no—
239C22×C4—611no—
240C22×C4—2441no—
241C22×C4—2441no—
242C22×C4C22⋊#692311yescharacteristic
243Q16—41no—
244SD16—42no—
245D8—41no—
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—1221no—
260C4⋊C4—1221no—
261C4⋊C4—2441no—
262C4⋊C4—2441no—
263C22⋊C4—2441no—
264C22⋊C4—2441no—
265C22⋊C4—2441no—
266C22⋊C4—2441no—
267C22⋊C4—2441no—
268C42—2441no—
269C16—2442no—
270C23—41no—
271C23—611no—
272C23—611no—
273C23—1222no—
274C23—2441no—
275C23—2441no—
276C23#1451983911yescharacteristic
277Q8—41no—
278Q8—41no—
279D4—41no—
280D4—41no—
281D4—82no—
282D4—4882no—
283D4—4882no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—41no—
287C2×C4—82no—
288C2×C4—611no—
289C2×C4—611no—
290C2×C4—1221no—
291C2×C4—1221no—
292C2×C4—1221no—
293C2×C4—1221no—
294C2×C4—2441no—
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#1451983512yes—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—81no—
310C22—81no—
311C22—81no—
312C22—612no—
313C22—1221no—
314C22—1221no—
315C22—1221no—
316C22—1221no—
317C22—1221no—
318C22—2444no—
319C22C2×#1451983911yescharacteristic
320C4—21no—
321C4—81no—
322C4—1221no—
323C4—1221no—
324C4—4881no—
325C4—4881no—
326C4C2×#1451983511yescharacteristic
327C4#1684076011yescharacteristic
328C2—41no—
329C2—161no—
330C2—1222no—
331C2—2441no—
332C2#2146125511yescharacteristic
333C2D61⋊#35911yescharacteristic
334C2#2146214711yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC2×#135×C61C4
socleC22×C61C2×#102
prime radical#21455396C2
cosocleC2×C8×D61C23
hypercenterC2×#135#6923
hypocenterC61#11893
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. D61⋊(C22⋊C16)C2semidirect
2. #21461698C2semidirect
3. #21460811C2semidirect
4. #21460809C2semidirect
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
#214608112
#214608092
#214553962
#1189361