Finite Group Databasebeta

← D61⋊#1320 #30603851

Subgroups — D61⋊#1320 #30603851

Order 15616.

626 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 626 conjugacy classes of subgroups — too many to draw. Only its 88 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#21460752C212yesmaximal, complemented
3#21460751C212yesmaximal, complemented
4#407×D61C211yesmaximal, characteristic
5D61⋊M32—22no—
6#16840659—22no—
7#16840658C2214yescomplemented
8C23×C4×D61C411yescharacteristic
9C2×M16×D61C411yescharacteristic
10C2×M16×D61C2211yescharacteristic
11#16839726C2211yescharacteristic
12#16839725C411yescharacteristic
13#16839725C2211yescharacteristic
14#16839724—22no—
15C22⋊C8×D61—22no—
16C61×#407C411yescharacteristic
17#14519852—42no—
18#14519851—24no—
19D61⋊C16—42no—
20C24×D61C811yescharacteristic
21C23×Dic61C811yescharacteristic
22C22×C4×D61—21no—
23C22×C4×D61—21no—
24C22×C4×D61—21no—
25C22×C4×D61—21no—
26C22×C4×D61—41no—
27C22×C4×D61—41no—
28C22×C4×D61—41no—
29C22×C4×D61—41no—
30C22×C4×D61C811yescharacteristic
31C22×C4×D61C811yescharacteristic
32C22×C4×D61C2×C411yescharacteristic
33C22×C4×D61C2×C411yescharacteristic
34C2×#11758194C2×C411yescharacteristic
35C2×#11758194C2311yescharacteristic
36C2×#11758189—21no—
37C2×#11758189D412yes—
38M16×D61—41no—
39M16×D61—41no—
40M16×D61—41no—
41M16×D61—41no—
42C2×C8×D61—21no—
43C2×C8×D61D412yes—
44C22⋊#92418—22no—
45#14519689—22no—
46#14519689—22no—
47C23×C4×C61C2×C411yescharacteristic
48C2×M16×C61C2×C411yescharacteristic
49C2×M16×C61C2×C411yescharacteristic
50C22⋊C8×C61—22no—
51C24×C61C2×C811yescharacteristic
52C23×D61—21no—
53C23×D61—21no—
54C23×D61—41no—
55C23×D61—41no—
56C23×D61—44no—
57C23×D61C2×C811yescharacteristic
58C23×D61C2×C811yescharacteristic
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—41no—
62C22×C4×C61—41no—
63C22×C4×C61C2×C811yescharacteristic
64C22×C4×C61C22×C411yescharacteristic
65C22×Dic61—21no—
66C22×Dic61—21no—
67C22×Dic61—41no—
68C22×Dic61—41no—
69C22×Dic61C2×C811yescharacteristic
70C22×Dic61C2×C811yescharacteristic
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—42no—
82C2×C4×D61—42no—
83C2×C4×D61—42no—
84C2×C4×D61—42no—
85C2×C4×D61—42no—
86C2×C4×D61—42no—
87C2×C4×D61—41no—
88C2×C4×D61—41no—
89C2×C4×D61—41no—
90C2×C4×D61—41no—
91C2×C4×D61—41no—
92C2×C4×D61—41no—
93C2×C4×D61—41no—
94C2×C4×D61—41no—
95C2×C4×D61—41no—
96C2×C4×D61—41no—
97C2×C4×D61C22⋊C411yescharacteristic
98C2×C4×D61C22⋊C411yescharacteristic
99C2×C4×D61M1611yescharacteristic
100C2×C4×D61M1611yescharacteristic
101M16×C61—41no—
102M16×C61—41no—
103C2×C8×C61—21no—
104C2×C8×C61C22⋊C412yes—
105#11758194—41no—
106#11758194—41no—
107C2×#92418—21no—
108C2×#92418C2×D412yes—
109#11758189—42no—
110#11758189—42no—
111C8×D61—22no—
112C8×D61—22no—
113C8×D61—41no—
114C8×D61—41no—
115#11758187—44no—
116C23×C61—21no—
117C23×C61—41no—
118C23×C61—42no—
119C23×C61C22×C811yescharacteristic
120C22×D61—24no—
121C22×D61—21no—
122C22×D61—21no—
123C22×D61—21no—
124C22×D61—42no—
125C22×D61—42no—
126C22×D61—42no—
127C22×D61—42no—
128C22×D61—42no—
129C22×D61—42no—
130C22×D61—44no—
131C22×D61—44no—
132C22×D61—44no—
133C22×D61—41no—
134C22×D61—41no—
135C22×D61—41no—
136C22×D61—44no—
137C22×D61C22⋊C811yescharacteristic
138C22×D61C22⋊C811yescharacteristic
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—42no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61C2×C22⋊C411yescharacteristic
147C2×C4×C61C2×M1611yescharacteristic
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—42no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61C22⋊C811yescharacteristic
156C2×Dic61C22⋊C811yescharacteristic
157C4×D61—21no—
158C4×D61—21no—
159C4×D61—21no—
160C4×D61—21no—
161C4×D61—21no—
162C4×D61—21no—
163C4×D61—42no—
164C4×D61—42no—
165C4×D61—42no—
166C4×D61—41no—
167C4×D61—41no—
168C4×D61—41no—
169C4×D61—41no—
170C4×D61—41no—
171C4×D61—41no—
172C4×D61#9911yescharacteristic
173C4×D61#9911yescharacteristic
174C4×D61#10011yescharacteristic
175C4×D61#10011yescharacteristic
176C8×C61—22no—
177C8×C61—41no—
178#92418—22no—
179#92418—41no—
180C2×#1320—611nomaximal, Sylow
181C22×C61—22no—
182C22×C61—21no—
183C22×C61—41no—
184C22×C61—41no—
185C22×C61—42no—
186C22×C61—42no—
187C22×C61—41no—
188C22×C61C2×C22⋊C811yescharacteristic
189C2×D61—22no—
190C2×D61—22no—
191C2×D61—21no—
192C2×D61—44no—
193C2×D61—42no—
194C2×D61—41no—
195C2×D61—48no—
196C2×D61—42no—
197C2×D61—41no—
198C2×D61—44no—
199C2×D61—42no—
200C2×D61—41no—
201C2×D61—42no—
202C2×D61#32311yescharacteristic
203C2×D61#32311yescharacteristic
204C4×C61—21no—
205C4×C61—41no—
206C4×C61C2×#9911yescharacteristic
207C4×C61C2×#10011yescharacteristic
208Dic61—21no—
209Dic61—41no—
210Dic61#32311yescharacteristic
211Dic61#32311yescharacteristic
212C2×#407—611no—
213C2×#349—612no—
214#1320—612no—
215#1320—612no—
216C2×C61—21no—
217C2×C61—42no—
218C2×C61—41no—
219C2×C61C2×#32311yescharacteristic
220D61—21no—
221D61—42no—
222D61—41no—
223D61#132012yescomplemented
224C24×C4—611no—
225C22×M16—611no—
226C22×M16—611no—
227C2×M32—1222no—
228#407—611no—
229#407—611no—
230#407—611no—
231#407—1222no—
232#407#692311yescharacteristic
233C2×C22⋊C8—1222no—
234#349—614no—
235#349—1222no—
236C61C2×#132011yescharacteristic, complemented, Sylow
237C25—611no—
238C23×C4—611no—
239C23×C4—611no—
240C23×C4—611no—
241C23×C4—611no—
242C23×C4—611no—
243C23×C4—1221no—
244C23×C4—1221no—
245C23×C4—1221no—
246C23×C4—1221no—
247C23×C4—2441no—
248C23×C4—2441no—
249C23×C4—2441no—
250C23×C4—2441no—
251C23×C4C2×#692311yescharacteristic
252C2×M16—611no—
253C2×M16—612no—
254C2×M16—611no—
255C2×M16—1221no—
256C2×M16—2441no—
257C2×M16—2441no—
258C2×M16—2441no—
259C2×M16—2441no—
260C2×M16C2×#692311yescharacteristic
261C2×M16C2×#692311yescharacteristic
262C22×C8—612no—
263C22×C8—1221no—
264M32—1224no—
265M32—2442no—
266C2×C16—2442no—
267C22⋊C8—22no—
268C22⋊C8—1222no—
269C22⋊C8—1222no—
270C22⋊C8—1222no—
271C24—611no—
272C24—611no—
273C24—1221no—
274C24—1221no—
275C24—2441no—
276C24—2441no—
277C24—2444no—
278C24D61⋊C811yescharacteristic
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—611no—
284C22×C4—611no—
285C22×C4—611no—
286C22×C4—611no—
287C22×C4—611no—
288C22×C4—611no—
289C22×C4—1221no—
290C22×C4—1221no—
291C22×C4—1221no—
292C22×C4—1221no—
293C22×C4—1221no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4—1221no—
299C22×C4—1221no—
300C22×C4—1221no—
301C22×C4—2441no—
302C22×C4—2441no—
303C22×C4—2441no—
304C22×C4—2441no—
305C22×C4—2441no—
306C22×C4—2441no—
307C22×C4—2442no—
308C22×C4—2442no—
309C22×C4—2442no—
310C22×C4—2442no—
311C22×C4—2442no—
312C22×C4—2442no—
313C22×C4—2441no—
314C22×C4—2441no—
315C22×C4—2441no—
316C22×C4—2441no—
317C22×C4—2441no—
318C22×C4—2441no—
319C22×C4D61⋊C811yescharacteristic
320C22×C4C22×#692311yescharacteristic
321M16—41no—
322M16—41no—
323M16—2442no—
324M16—2442no—
325M16—2441no—
326M16—2441no—
327C2×C8—21no—
328C2×C8—612no—
329C2×C8—1222no—
330C2×C8—1222no—
331C2×C8—1221no—
332C2×C8—2441no—
333C2×C8—2441no—
334C2×C8C22⋊#692312yes—
335C16—2444no—
336C23—21no—
337C23—41no—
338C23—42no—
339C23—611no—
340C23—611no—
341C23—1221no—
342C23—1221no—
343C23—1224no—
344C23—1221no—
345C23—2441no—
346C23—2442no—
347C23—2441no—
348C23—2441no—
349C23—2442no—
350C23—2442no—
351C23—2442no—
352C23—2442no—
353C23—2442no—
354C23—2444no—
355C23—2444no—
356C23—2444no—
357C23—2444no—
358C23C2×D61⋊C811yescharacteristic
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—611no—
367C2×C4—611no—
368C2×C4—611no—
369C2×C4—611no—
370C2×C4—611no—
371C2×C4—611no—
372C2×C4—1221no—
373C2×C4—1221no—
374C2×C4—1221no—
375C2×C4—1221no—
376C2×C4—1221no—
377C2×C4—1221no—
378C2×C4—1221no—
379C2×C4—1221no—
380C2×C4—1221no—
381C2×C4—2442no—
382C2×C4—2441no—
383C2×C4—2441no—
384C2×C4—2442no—
385C2×C4—2441no—
386C2×C4—2441no—
387C2×C4—2442no—
388C2×C4—2441no—
389C2×C4—2441no—
390C2×C4—2442no—
391C2×C4—2441no—
392C2×C4—2441no—
393C2×C4—2441no—
394C2×C4C2×C22⋊#692311yescharacteristic
395C2×C4D61⋊M1611yescharacteristic
396C8—22no—
397C8—41no—
398C8—1222no—
399C8—2441no—
400C22—22no—
401C22—21no—
402C22—41no—
403C22—41no—
404C22—42no—
405C22—42no—
406C22—41no—
407C22—611no—
408C22—611no—
409C22—1222no—
410C22—1222no—
411C22—1221no—
412C22—2441no—
413C22—2441no—
414C22—2442no—
415C22—2444no—
416C22—2442no—
417C22—2444no—
418C22—2442no—
419C22—2442no—
420C22—2448no—
421C22—2441no—
422C22D61⋊(C22⋊C8)11yescharacteristic
423C4—21no—
424C4—41no—
425C4—611no—
426C4—611no—
427C4—1221no—
428C4—2441no—
429C4D61⋊#9911yescharacteristic
430C4D61⋊#10011yescharacteristic
431C2—21no—
432C2—42no—
433C2—41no—
434C2—612no—
435C2—1221no—
436C2—2442no—
437C2—2441no—
438C2D61⋊#32311yescharacteristic
subgroupG/H
centerC4D61⋊#99
commutatorC23×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#407C4
socleC2×C61C2×#323
prime radicalC24×D61C8
cosocleC2×#11758194C23
hypercenter#407#6923
hypocenterC61C2×#1320
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #407

Complements

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

NH ≅ G/Ntype
1. D61⋊#349C2semidirect
2. #21460752C2semidirect
3. #21460751C2semidirect
7. #16840658C22semidirect
223. D61#1320semidirect
236. C61C2×#1320semidirect

Maximal subgroups

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

subgroupindex
D61⋊#3492
#214607522
#214607512
#407×D612
C2×#132061