Finite Group Databasebeta

← #30603860

Subgroups — #30603860

Order 15616.

504 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 86 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⋊#349C212yesmaximal, complemented
2#21460754C212yesmaximal, complemented
3#21460753C212yesmaximal, complemented
4#21454261C211yesmaximal, characteristic
5D61⋊M32—22no—
6#16840659—22no—
7#16840658C2214yescomplemented
8C2×#41×D61C411yescharacteristic
9C22×#11758189C411yescharacteristic
10C2×M16×D61C2211yescharacteristic
11#16839730C411yescharacteristic
12#16839729C2211yescharacteristic
13#16839728C2211yescharacteristic
14#16839727—22no—
15#16839724—22no—
16C61×#408C411yescharacteristic
17#14519852—42no—
18#14519851—24no—
19D61⋊C16—42no—
20C2×#11758226C811yescharacteristic
21C2×#11758222—21no—
22C2×#11758222C2×C411yescharacteristic
23C2×#11758224—21no—
24C2×#11758224C811yescharacteristic
25#41×D61—42no—
26#41×D61—42no—
27C2×Q8×D61C811yescharacteristic
28C2×D4×D61—21no—
29C2×D4×D61C811yescharacteristic
30C22×C4×D61—21no—
31C22×C4×D61C2×C411yescharacteristic
32C2×#11758194C2311yescharacteristic
33C2×#11758189—21no—
34C2×#11758189—21no—
35C2×#11758189—42no—
36C2×#11758189D412yes—
37M16×D61—42no—
38C22×#92418C2×C411yescharacteristic
39C2×C8×D61D412yes—
40C22⋊#92418—22no—
41#14519689—22no—
42#14519689—22no—
43C2×#41×C61C2×C411yescharacteristic
44C2×M16×C61C2×C411yescharacteristic
45C22×C8×C61C2×C411yescharacteristic
46C22⋊C8×C61—22no—
47C23×D61—21no—
48C23×D61M1611yescharacteristic
49#41×C61—41no—
50#41×C61—41no—
51C2×Q8×C61C2×C811yescharacteristic
52C2×D4×C61—21no—
53C2×D4×C61C2×C811yescharacteristic
54C22×C4×C61—21no—
55C22×C4×C61C22×C411yescharacteristic
56C2×C22⋊D61—21no—
57C2×C22⋊D61—21no—
58C2×C22⋊D61—21no—
59C22×Dic61—21no—
60C22×Dic61M1611yescharacteristic
61#11758226—42no—
62Q8×D61—42no—
63#11758224—42no—
64#11758224—44no—
65D4×D61—42no—
66D4×D61—44no—
67#11758222—42no—
68#11758222—42no—
69#11758222—41no—
70#11758222—41no—
71C2×D244—21no—
72C2×D244C2×C811yescharacteristic
73C2×C4×D61—22no—
74C2×C4×D61—22no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—42no—
79C2×C4×D61—42no—
80C2×C4×D61C22⋊C411yescharacteristic
81C2×C4×D61C22⋊C411yescharacteristic
82C2×C4×D61C2×C811yescharacteristic
83C2×C4×D61C2×C811yescharacteristic
84C2×Dic122—21no—
85C2×Dic122C2×C811yescharacteristic
86M16×C61—41no—
87C2×C8×C61—21no—
88C2×C8×C61—41no—
89C2×C8×C61C22⋊C412yes—
90#11758194—41no—
91C2×#92418—21no—
92C2×#92418—41no—
93C2×#92418C2×D412yes—
94#11758189—42no—
95#11758189—42no—
96#11758189—42no—
97C8×D61—22no—
98C8×D61—22no—
99#11758187—44no—
100C23×C61—21no—
101C23×C61C2×M1611yescharacteristic
102C22×D61—22no—
103C22×D61—21no—
104C22×D61—42no—
105C22×D61—82no—
106C22×D61—81no—
107C22×D61C22⋊C811yescharacteristic
108C22×D61C22⋊C811yescharacteristic
109Q8×C61—41no—
110D4×C61—41no—
111D4×C61—42no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61C2×C22⋊C411yescharacteristic
118C2×C4×C61C22×C811yescharacteristic
119C22⋊D61—42no—
120C22⋊D61—42no—
121C22⋊D61—42no—
122C2×Dic61—22no—
123C2×Dic61—21no—
124C2×Dic61—42no—
125C2×Dic61C22⋊C811yescharacteristic
126C2×Dic61C22⋊C811yescharacteristic
127D244—41no—
128D244—42no—
129C4×D61—22no—
130C4×D61—21no—
131C4×D61—21no—
132C4×D61—22no—
133C4×D61—42no—
134C4×D61—42no—
135C4×D61—41no—
136C4×D61—41no—
137C4×D61#9912yes—
138C4×D61#10012yes—
139Dic122—42no—
140Dic122—41no—
141C8×C61—22no—
142C8×C61—41no—
143#92418—22no—
144#92418—41no—
145#11438—611nomaximal, Sylow
146C22×C61—21no—
147C22×C61—41no—
148C22×C61—42no—
149C22×C61—41no—
150C22×C61C2×C22⋊C811yescharacteristic
151C2×D61—21no—
152C2×D61—41no—
153C2×D61—41no—
154C2×D61—42no—
155C2×D61—41no—
156C2×D61—82no—
157C2×D61—84no—
158C2×D61#32312yes—
159C4×C61—21no—
160C4×C61—41no—
161C4×C61C2×#9911yescharacteristic
162C4×C61C2×#10011yescharacteristic
163Dic61—21no—
164Dic61—41no—
165Dic61#32312yes—
166#2879—611no—
167C2×#349—612no—
168#1321—612no—
169#1321—612no—
170C2×C61—21no—
171C2×C61—41no—
172C2×C61—81no—
173C2×C61C2×#32311yescharacteristic
174D61—22no—
175D61—41no—
176D61—81no—
177C22×#41—611no—
178C22×M16—611no—
179C22×M16—611no—
180C2×M32—1222no—
181#408—611no—
182#408—611no—
183#408—611no—
184#408—1222no—
185#408#692311yescharacteristic
186#407—1222no—
187#349—614no—
188#349—1222no—
189C61#1143811yescharacteristic, complemented, Sylow
190C2×#41—611no—
191C2×#41—611no—
192C2×#41—611no—
193C2×#41—1221no—
194C2×#41—1221no—
195C2×#41—2442no—
196C2×#41—2442no—
197C2×#41C2×#692311yescharacteristic
198C22×Q8—611no—
199C22×D4—611no—
200C22×D4—1221no—
201C23×C4—611no—
202C23×C4—1221no—
203C2×M16—611no—
204C2×M16—612no—
205C2×M16—1221no—
206C2×M16—1221no—
207C2×M16—2442no—
208C2×M16—2442no—
209C2×M16C2×#692311yescharacteristic
210C22×C8—612no—
211C22×C8—611no—
212C22×C8C2×#692311yescharacteristic
213M32—1224no—
214M32—2442no—
215C2×C16—2442no—
216C22⋊C8—22no—
217C22⋊C8—1222no—
218C22⋊C8—1222no—
219C22⋊C8—1222no—
220C24—611no—
221C24—1221no—
222#41—41no—
223#41—41no—
224#41—2441no—
225#41—2441no—
226#41—2442no—
227#41—2442no—
228#41—2444no—
229#41—2442no—
230#41—2442no—
231C2×Q8—611no—
232C2×Q8—1221no—
233C2×Q8—2442no—
234C2×Q8D61⋊C811yescharacteristic
235C2×D4—21no—
236C2×D4—611no—
237C2×D4—1221no—
238C2×D4—1221no—
239C2×D4—1221no—
240C2×D4—1221no—
241C2×D4—2442no—
242C2×D4—2444no—
243C2×D4D61⋊C811yescharacteristic
244C22×C4—21no—
245C22×C4—611no—
246C22×C4—611no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—611no—
250C22×C4—1222no—
251C22×C4—1222no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—2442no—
257C22×C4—2442no—
258C22×C4C22×#692311yescharacteristic
259M16—41no—
260M16—2442no—
261M16—2442no—
262M16—2442no—
263M16—2441no—
264C2×C8—21no—
265C2×C8—41no—
266C2×C8—612no—
267C2×C8—1222no—
268C2×C8—1222no—
269C2×C8—1221no—
270C2×C8—2441no—
271C2×C8C22⋊#692312yes—
272C16—2444no—
273C23—21no—
274C23—611no—
275C23—611no—
276C23—1222no—
277C23—1221no—
278C23—4882no—
279C23—4881no—
280C23—2442no—
281C23D61⋊M1611yescharacteristic
282Q8—41no—
283Q8—2441no—
284Q8—2442no—
285D4—41no—
286D4—42no—
287D4—2441no—
288D4—2442no—
289D4—2442no—
290D4—2442no—
291D4—2442no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—611no—
298C2×C4—612no—
299C2×C4—612no—
300C2×C4—611no—
301C2×C4—1222no—
302C2×C4—1222no—
303C2×C4—1222no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—2442no—
308C2×C4—2442no—
309C2×C4—2442no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4C2×C22⋊#692311yescharacteristic
313C2×C4C2×D61⋊C811yescharacteristic
314C8—22no—
315C8—41no—
316C8—1222no—
317C8—2441no—
318C22—21no—
319C22—41no—
320C22—42no—
321C22—41no—
322C22—612no—
323C22—1221no—
324C22—4882no—
325C22—4884no—
326C22—2441no—
327C22—2442no—
328C22—2441no—
329C22—2441no—
330C22D61⋊(C22⋊C8)11yescharacteristic
331C4—21no—
332C4—41no—
333C4—612no—
334C4—1221no—
335C4—2441no—
336C4D61⋊#9911yescharacteristic
337C4D61⋊#10011yescharacteristic
338C2—21no—
339C2—41no—
340C2—81no—
341C2—1222no—
342C2—4881no—
343C2—2441no—
344C2D61⋊#32311yescharacteristic
subgroupG/H
centerC4D61⋊#99
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#408C4
socleC2×C61C2×#323
prime radicalC2×#41×D61C4
cosocleC2×#11758194C23
hypercenter#408#6923
hypocenterC61#11438
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #408

Complements

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

NH ≅ G/Ntype
1. D61⋊#349C2semidirect
2. #21460754C2semidirect
3. #21460753C2semidirect
7. #16840658C22semidirect
189. C61#11438semidirect

Maximal subgroups

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

subgroupindex
D61⋊#3492
#214607542
#214607532
#214542612
#1143861