Finite Group Databasebeta

← D61⋊#1318 #30603831

Subgroups — D61⋊#1318 #30603831

Order 15616.

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

normal subgroups only

This group has 834 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⋊#324C212yesmaximal, complemented
2#21460748C212yesmaximal, complemented
3#21460747C212yesmaximal, complemented
4#390×D61C211yesmaximal, characteristic
5D61⋊(C22⋊C8)—22no—
6#16840608—22no—
7#16840607C2214yescomplemented
8C22×D4×D61C411yescharacteristic
9C2×C4⋊C4×D61C2211yescharacteristic
10C2×C22⋊C4×D61—22no—
11C2×C42×D61C411yescharacteristic
12#16839665C2211yescharacteristic
13#16839664C2211yescharacteristic
14#16839663C411yescharacteristic
15#16839662—22no—
16C61×#390C411yescharacteristic
17C2×D61⋊C8—42no—
18#14519834—42no—
19C22⋊#92420—24no—
20C24×D61—21no—
21C22×D244C2×C411yescharacteristic
22C22×C22⋊D61—21no—
23C2×D4×D61—22no—
24C2×D4×D61—41no—
25C2×D4×D61—41no—
26C2×D4×D61—42no—
27C2×D4×D61C814yescomplemented
28C22×C4×D61—21no—
29C22×C4×D61C2×C411yescharacteristic
30C22×C4×D61D412yes—
31C2×C4⋊Dic61C2311yescharacteristic
32C2×#11758196D412yes—
33C4⋊C4×D61—41no—
34C4⋊C4×D61—41no—
35C2×C22⋊Dic61—22no—
36C2×#11758198—22no—
37C2×#11758198—22no—
38C22⋊C4×D61—48no—
39C2×C4×Dic61—21no—
40C2×C4×Dic61C2×C411yescharacteristic
41C42×D61—42no—
42C22×D4×C61C2×C411yescharacteristic
43C2×C4⋊C4×C61C2×C411yescharacteristic
44C2×C22⋊C4×C61—22no—
45C2×C42×C61C2×C411yescharacteristic
46C24×C61—21no—
47C23×D61—21no—
48C23×D61—24no—
49C23×D61—44no—
50C23×D61—44no—
51C23×D61—41no—
52C23×D61—41no—
53C23×D61—42no—
54C23×D61C22⋊C411yescharacteristic
55C2×D4×C61—21no—
56C2×D4×C61—41no—
57C2×D4×C61—41no—
58C2×D4×C61C2×C812yescomplemented
59C22×C4×C61—21no—
60C22×C4×C61C22⋊C412yes—
61C22×C4×C61C22×C411yescharacteristic
62C2×C22⋊D61—24no—
63C2×C22⋊D61—42no—
64C2×C22⋊D61—42no—
65C22×Dic61—21no—
66C22×Dic61C22⋊C411yescharacteristic
67C22×Dic61C2×D412yes—
68D4×D61—44no—
69D4×D61—44no—
70D4×D61—44no—
71D4×D61—44no—
72C2×D244—21no—
73C2×D244—41no—
74C2×D244—41no—
75C2×D244C2×C812yescomplemented
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—22no—
79C2×C4×D61—24no—
80C2×C4×D61—22no—
81C2×C4×D61—22no—
82C2×C4×D61—42no—
83C2×C4×D61—42no—
84C2×C4×D61—44no—
85C2×C4×D61C2×C812yes—
86C2×C4×D61M1612yes—
87C2×#92420—44no—
88D61⋊C8—84no—
89C4⋊C4×C61—41no—
90C22⋊C4×C61—44no—
91C42×C61—41no—
92C22⋊Dic61—44no—
93#11758198—44no—
94#11758198—44no—
95C4⋊Dic61—41no—
96#11758196—42no—
97C4×Dic61—42no—
98C4×Dic61—41no—
99C23×C61—22no—
100C23×C61—42no—
101C23×C61—42no—
102C23×C61—41no—
103C23×C61—41no—
104C23×C61C2×C22⋊C411yescharacteristic
105C22×D61—22no—
106C22×D61—22no—
107C22×D61—22no—
108C22×D61—416no—
109C22×D61—42no—
110C22×D61—42no—
111C22×D61—41no—
112C22×D61—41no—
113C22×D61—44no—
114C22×D61—44no—
115C22×D61—82no—
116C22×D61—82no—
117C22×D61—88no—
118C22×D61—82no—
119C22×D61—82no—
120C22×D61C22⋊C812yes—
121C22×D61#9911yescharacteristic
122C22×D61#9911yescharacteristic
123C22×D61#10012yes—
124D4×C61—42no—
125D4×C61—42no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—22no—
129C2×C4×C61—22no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—42no—
133C2×C4×C61C22×C811yescharacteristic
134C2×C4×C61C2×M1611yescharacteristic
135C22⋊D61—48no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—22no—
139C2×Dic61—22no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—42no—
143C2×Dic61C22⋊C812yes—
144D244—42no—
145D244—42no—
146C4×D61—22no—
147C4×D61—22no—
148C4×D61—22no—
149C4×D61—22no—
150C4×D61—48no—
151C4×D61—44no—
152C4×D61—82no—
153#92420—84no—
154C2×#1318—611nomaximal, Sylow
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—44no—
158C22×C61—42no—
159C22×C61—82no—
160C22×C61—81no—
161C22×C61—81no—
162C22×C61C2×C22⋊C811yescharacteristic
163C22×C61C2×#9911yescharacteristic
164C22×C61C2×#10011yescharacteristic
165C2×D61—21no—
166C2×D61—21no—
167C2×D61—24no—
168C2×D61—24no—
169C2×D61—44no—
170C2×D61—42no—
171C2×D61—88no—
172C2×D61—82no—
173C2×D61—81no—
174C2×D61—81no—
175C2×D61—88no—
176C2×D61#32312yes—
177C2×D61#32312yes—
178C2×D61#35312yes—
179C2×D61#35512yes—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—42no—
183C4×C61—42no—
184Dic61—22no—
185Dic61—42no—
186Dic61—42no—
187C2×#390—611no—
188C2×#324—612no—
189#1318—612no—
190#1318—612no—
191C2×C61—21no—
192C2×C61—21no—
193C2×C61—82no—
194C2×C61C2×#32311yescharacteristic
195C2×C61C2×#35311yescharacteristic
196C2×C61C2×#35511yescharacteristic
197D61—22no—
198D61—82no—
199D61#131814yescomplemented
200C23×D4—611no—
201C22×C4⋊C4—611no—
202C22×C22⋊C4—1222no—
203C22×C42—611no—
204C2×C22⋊C8—1222no—
205#390—611no—
206#390—611no—
207#390—611no—
208#390—1222no—
209#390#692311yescharacteristic
210#324—614no—
211#324—1222no—
212C61C2×#131811yescharacteristic, complemented, Sylow
213C25—1221no—
214C22×D4—614no—
215C22×D4—611no—
216C22×D4—1222no—
217C22×D4—1221no—
218C22×D4—2442no—
219C22×D4—2441no—
220C22×D4—2441no—
221C22×D4C2×#692311yescharacteristic
222C23×C4—611no—
223C23×C4—612no—
224C23×C4—1221no—
225C22×C8—2442no—
226C2×C4⋊C4—612no—
227C2×C4⋊C4—611no—
228C2×C4⋊C4—2441no—
229C2×C4⋊C4—2441no—
230C2×C4⋊C4C2×#692311yescharacteristic
231C2×C22⋊C4—22no—
232C2×C22⋊C4—1222no—
233C2×C22⋊C4—1222no—
234C2×C22⋊C4—1222no—
235C2×C22⋊C4—2448no—
236C2×C42—611no—
237C2×C42—1221no—
238C2×C42—2442no—
239C2×C42C2×#692311yescharacteristic
240C22⋊C8—1224no—
241C22⋊C8—2442no—
242C24—21no—
243C24—611no—
244C24—1224no—
245C24—1221no—
246C24—2441no—
247C24—2441no—
248C24—2442no—
249C24—2444no—
250C24—2444no—
251C2×D4—21no—
252C2×D4—41no—
253C2×D4—41no—
254C2×D4—612no—
255C2×D4—1224no—
256C2×D4—1221no—
257C2×D4—2441no—
258C2×D4—2441no—
259C2×D4—2444no—
260C2×D4—2444no—
261C2×D4—2444no—
262C2×D4—2444no—
263C2×D4—2442no—
264C2×D4—2442no—
265C2×D4D61⋊C812yescomplemented
266C22×C4—21no—
267C22×C4—611no—
268C22×C4—612no—
269C22×C4—612no—
270C22×C4—612no—
271C22×C4—1222no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—1222no—
275C22×C4—1222no—
276C22×C4—1224no—
277C22×C4—1221no—
278C22×C4—2444no—
279C22×C4—2442no—
280C22×C4—2442no—
281C22×C4C22⋊#692312yes—
282C22×C4C22×#692311yescharacteristic
283C2×C8—4884no—
284C2×C8—2444no—
285C4⋊C4—41no—
286C4⋊C4—2442no—
287C4⋊C4—2441no—
288C22⋊C4—44no—
289C22⋊C4—2444no—
290C22⋊C4—2444no—
291C22⋊C4—2444no—
292C42—41no—
293C42—2441no—
294C42—2442no—
295C23—22no—
296C23—42no—
297C23—42no—
298C23—41no—
299C23—41no—
300C23—611no—
301C23—612no—
302C23—611no—
303C23—612no—
304C23—1222no—
305C23—1222no—
306C23—1222no—
307C23—4882no—
308C23—4882no—
309C23—4888no—
310C23—4882no—
311C23—4882no—
312C23—2442no—
313C23—2442no—
314C23—2444no—
315C23—2444no—
316C23—24416no—
317C23—2441no—
318C23—2441no—
319C23C2×C22⋊#692311yescharacteristic
320D4—42no—
321D4—42no—
322D4—2442no—
323D4—2442no—
324D4—2448no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—612no—
333C2×C4—1222no—
334C2×C4—1222no—
335C2×C4—1222no—
336C2×C4—1222no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—1222no—
340C2×C4—1222no—
341C2×C4—4882no—
342C2×C4—2444no—
343C2×C4—2448no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4—2442no—
347C2×C4C2×D61⋊C811yescharacteristic
348C2×C4D61⋊M1611yescharacteristic
349C8—4884no—
350C22—21no—
351C22—21no—
352C22—44no—
353C22—42no—
354C22—82no—
355C22—81no—
356C22—81no—
357C22—612no—
358C22—612no—
359C22—612no—
360C22—612no—
361C22—1224no—
362C22—1224no—
363C22—1221no—
364C22—1221no—
365C22—4882no—
366C22—4888no—
367C22—4888no—
368C22—4881no—
369C22—4881no—
370C22—2444no—
371C22—2442no—
372C22D61⋊(C22⋊C8)11yescharacteristic
373C22D61⋊#9911yescharacteristic
374C22D61⋊#10011yescharacteristic
375C4—21no—
376C4—21no—
377C4—42no—
378C4—42no—
379C4—1222no—
380C4—2442no—
381C4—2442no—
382C2—21no—
383C2—21no—
384C2—82no—
385C2—614no—
386C2—1222no—
387C2—4882no—
388C2D61⋊#32311yescharacteristic
389C2D61⋊#35311yescharacteristic
390C2D61⋊#35511yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#390C4
socleC22×C61C2×#99
prime radicalC22×D4×D61C4
cosocleC2×C4⋊Dic61C23
hypercenter#390#6923
hypocenterC61C2×#1318
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #390

Complements

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

NH ≅ G/Ntype
1. D61⋊#324C2semidirect
2. #21460748C2semidirect
3. #21460747C2semidirect
7. #16840607C22semidirect
27. C2×D4×D61C8semidirect
58. C2×D4×C61C2×C8semidirect
75. C2×D244C2×C8semidirect
199. D61#1318semidirect
212. C61C2×#1318semidirect
265. C2×D4D61⋊C8semidirect

Maximal subgroups

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

subgroupindex
D61⋊#3242
#214607482
#214607472
#390×D612
C2×#131861