Finite Group Databasebeta

← D61⋊#1315 #30603802

Subgroups — D61⋊#1315 #30603802

Order 15616.

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

normal subgroups only

This group has 534 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⋊(C22⋊C16)C212yesmaximal, complemented
2#21460742C212yesmaximal, complemented
3#21460741C212yesmaximal, complemented
4#408×D61C211yesmaximal, characteristic
5C2×D61⋊C16—22no—
6#16840657—22no—
7C22⋊#11758187C2214yescomplemented
8C2×#41×D61C411yescharacteristic
9C2×M16×D61C411yescharacteristic
10C22×C8×D61C2211yescharacteristic
11#16839730C2211yescharacteristic
12#16839729C2211yescharacteristic
13#16839728C411yescharacteristic
14#16839727—22no—
15C22⋊C8×D61—22no—
16C61×#408C411yescharacteristic
17D61⋊C16—44no—
18C2×#11758187—24no—
19C2×#11758226C811yescharacteristic
20C2×#11758222—21no—
21C2×#11758222C2×C411yescharacteristic
22C2×#11758224—21no—
23C2×#11758224C811yescharacteristic
24#41×D61—42no—
25#41×D61—42no—
26C2×Q8×D61C811yescharacteristic
27C2×D4×D61—21no—
28C2×D4×D61C811yescharacteristic
29C22×C4×D61—21no—
30C22×C4×D61C2×C411yescharacteristic
31C2×#11758194C2×C411yescharacteristic
32C2×#11758189—21no—
33M16×D61—42no—
34C22×#92418C2311yescharacteristic
35C2×C8×D61—21no—
36C2×C8×D61—42no—
37C2×C8×D61D412yes—
38C2×C8×D61D412yes—
39C22⋊#92418—22no—
40#14519689—22no—
41#14519689—22no—
42C2×#41×C61C2×C411yescharacteristic
43C2×M16×C61C2×C411yescharacteristic
44C22×C8×C61C2×C411yescharacteristic
45C22⋊C8×C61—22no—
46C23×D61—21no—
47C23×D61M1611yescharacteristic
48#41×C61—41no—
49#41×C61—41no—
50C2×Q8×C61C2×C811yescharacteristic
51C2×D4×C61—21no—
52C2×D4×C61C2×C811yescharacteristic
53C22×C4×C61—21no—
54C22×C4×C61C22×C411yescharacteristic
55C2×C22⋊D61—21no—
56C2×C22⋊D61—21no—
57C2×C22⋊D61—21no—
58C22×Dic61—21no—
59C22×Dic61M1611yescharacteristic
60#11758226—42no—
61Q8×D61—42no—
62#11758224—42no—
63#11758224—44no—
64D4×D61—42no—
65D4×D61—44no—
66#11758222—42no—
67#11758222—42no—
68#11758222—41no—
69#11758222—41no—
70C2×D244—21no—
71C2×D244C2×C811yescharacteristic
72C2×C4×D61—22no—
73C2×C4×D61—22no—
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—42no—
78C2×C4×D61—42no—
79C2×C4×D61C22⋊C411yescharacteristic
80C2×C4×D61C22⋊C411yescharacteristic
81C2×C4×D61C2×C811yescharacteristic
82C2×C4×D61C2×C811yescharacteristic
83C2×Dic122—21no—
84C2×Dic122C2×C811yescharacteristic
85M16×C61—41no—
86C2×C8×C61—21no—
87C2×C8×C61—41no—
88C2×C8×C61C22⋊C412yes—
89#11758194—41no—
90C2×#92418—21no—
91C2×#92418—41no—
92C2×#92418C2×D412yes—
93#11758189—42no—
94C8×D61—24no—
95C8×D61—42no—
96C8×D61—42no—
97#11758187—44no—
98C23×C61—21no—
99C23×C61C2×M1611yescharacteristic
100C22×D61—22no—
101C22×D61—24no—
102C22×D61—21no—
103C22×D61—42no—
104C22×D61—44no—
105C22×D61C22⋊C811yescharacteristic
106C22×D61C22⋊C811yescharacteristic
107Q8×C61—41no—
108D4×C61—41no—
109D4×C61—42no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61C2×C22⋊C411yescharacteristic
116C2×C4×C61C22×C811yescharacteristic
117C22⋊D61—42no—
118C22⋊D61—42no—
119C22⋊D61—42no—
120C2×Dic61—22no—
121C2×Dic61—21no—
122C2×Dic61—42no—
123C2×Dic61C22⋊C811yescharacteristic
124C2×Dic61C22⋊C811yescharacteristic
125D244—41no—
126D244—42no—
127C4×D61—22no—
128C4×D61—21no—
129C4×D61—21no—
130C4×D61—22no—
131C4×D61—42no—
132C4×D61—41no—
133C4×D61—41no—
134C4×D61—42no—
135C4×D61#9912yes—
136C4×D61#10012yes—
137Dic122—42no—
138Dic122—41no—
139C8×C61—22no—
140C8×C61—41no—
141#92418—22no—
142#92418—41no—
143C2×#1315—611nomaximal, Sylow
144C22×C61—22no—
145C22×C61—21no—
146C22×C61—42no—
147C22×C61—41no—
148C22×C61C2×C22⋊C811yescharacteristic
149C2×D61—22no—
150C2×D61—21no—
151C2×D61—44no—
152C2×D61—42no—
153C2×D61—41no—
154C2×D61—84no—
155C2×D61#32312yes—
156C2×D61#35014yes—
157C4×C61—21no—
158C4×C61—41no—
159C4×C61C2×#9911yescharacteristic
160C4×C61C2×#10011yescharacteristic
161Dic61—21no—
162Dic61—41no—
163Dic61#32312yes—
164C2×#408—611no—
165C2×C22⋊C16—612no—
166#1315—612no—
167#1315—612no—
168C2×C61—41no—
169C2×C61—81no—
170C2×C61C2×#32311yescharacteristic
171C2×C61C2×#35012yes—
172D61—41no—
173D61—81no—
174D61#131514yescomplemented
175C22×#41—611no—
176C22×M16—611no—
177C23×C8—611no—
178C22×C16—1222no—
179#408—611no—
180#408—611no—
181#408—611no—
182#408—1222no—
183#408#692311yescharacteristic
184C2×C22⋊C8—1222no—
185C22⋊C16—614no—
186C22⋊C16—1222no—
187C61C2×#131511yescharacteristic, complemented, Sylow
188C2×#41—611no—
189C2×#41—611no—
190C2×#41—611no—
191C2×#41—1221no—
192C2×#41—1221no—
193C2×#41—2442no—
194C2×#41—2442no—
195C2×#41C2×#692311yescharacteristic
196C22×Q8—611no—
197C22×D4—611no—
198C22×D4—1221no—
199C23×C4—611no—
200C23×C4—1221no—
201C2×M16—611no—
202C2×M16—1221no—
203C2×M16—2442no—
204C2×M16C2×#692311yescharacteristic
205C22×C8—611no—
206C22×C8—612no—
207C22×C8—612no—
208C22×C8—1221no—
209C22×C8—2442no—
210C22×C8C2×#692311yescharacteristic
211C2×C16—1224no—
212C2×C16—2444no—
213C22⋊C8—22no—
214C22⋊C8—1222no—
215C22⋊C8—1222no—
216C22⋊C8—1222no—
217C24—611no—
218C24—1221no—
219#41—41no—
220#41—41no—
221#41—2441no—
222#41—2441no—
223#41—2442no—
224#41—2442no—
225#41—2444no—
226#41—2442no—
227#41—2442no—
228C2×Q8—611no—
229C2×Q8—1221no—
230C2×Q8—2442no—
231C2×Q8D61⋊C811yescharacteristic
232C2×D4—21no—
233C2×D4—611no—
234C2×D4—1221no—
235C2×D4—1221no—
236C2×D4—1221no—
237C2×D4—1221no—
238C2×D4—2442no—
239C2×D4—2444no—
240C2×D4D61⋊C811yescharacteristic
241C22×C4—21no—
242C22×C4—611no—
243C22×C4—611no—
244C22×C4—611no—
245C22×C4—611no—
246C22×C4—611no—
247C22×C4—1222no—
248C22×C4—1222no—
249C22×C4—1221no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—2442no—
254C22×C4—2442no—
255C22×C4C22×#692311yescharacteristic
256M16—41no—
257M16—2442no—
258M16—2441no—
259C2×C8—21no—
260C2×C8—41no—
261C2×C8—612no—
262C2×C8—1224no—
263C2×C8—1221no—
264C2×C8—2442no—
265C2×C8—2442no—
266C2×C8—2441no—
267C2×C8C22⋊#692312yes—
268C16—2444no—
269C23—21no—
270C23—611no—
271C23—611no—
272C23—1222no—
273C23—1224no—
274C23—1221no—
275C23—2442no—
276C23—2444no—
277C23D61⋊M1611yescharacteristic
278Q8—41no—
279Q8—2441no—
280Q8—2442no—
281D4—41no—
282D4—42no—
283D4—2441no—
284D4—2442no—
285D4—2442no—
286D4—2442no—
287D4—2442no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—611no—
294C2×C4—612no—
295C2×C4—612no—
296C2×C4—611no—
297C2×C4—1222no—
298C2×C4—1222no—
299C2×C4—1222no—
300C2×C4—1221no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—2442no—
304C2×C4—2442no—
305C2×C4—2442no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4C2×C22⋊#692311yescharacteristic
309C2×C4C2×D61⋊C811yescharacteristic
310C8—22no—
311C8—41no—
312C8—1222no—
313C8—2441no—
314C22—22no—
315C22—21no—
316C22—42no—
317C22—41no—
318C22—614no—
319C22—612no—
320C22—1222no—
321C22—1221no—
322C22—4884no—
323C22—2444no—
324C22—2442no—
325C22—2441no—
326C22D61⋊(C22⋊C8)11yescharacteristic
327C4—21no—
328C4—41no—
329C4—612no—
330C4—1221no—
331C4—2441no—
332C4D61⋊#9911yescharacteristic
333C4D61⋊#10011yescharacteristic
334C2—41no—
335C2—81no—
336C2—614no—
337C2—4881no—
338C2—2441no—
339C2D61⋊#32311yescharacteristic
340C2D61⋊#35012yes—
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#408C4
socleC22×C61C2×C22⋊C8
prime radicalC2×#41×D61C4
cosocleC22×#92418C23
hypercenter#408#6923
hypocenterC61C2×#1315
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #408

Complements

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

NH ≅ G/Ntype
1. D61⋊(C22⋊C16)C2semidirect
2. #21460742C2semidirect
3. #21460741C2semidirect
7. C22⋊#11758187C22semidirect
174. D61#1315semidirect
187. C61C2×#1315semidirect

Maximal subgroups

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

subgroupindex
D61⋊(C22⋊C16)2
#214607422
#214607412
#408×D612
C2×#131561