Finite Group Databasebeta

← #30607563

Subgroups — #30607563

Order 15616.

496 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 92 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⋊#430C211yesmaximal, characteristic
2D61⋊#362C212yesmaximal, complemented
3D61⋊#349C211yesmaximal, characteristic
4#21460883C212yesmaximal, complemented
5#470×D61C211yesmaximal, characteristic
6C2×D61⋊M16—21no—
7D61⋊M32C2212yes—
8#16840777—24no—
9D61⋊#108—21no—
10D61⋊#108C2212yes—
11#16840681—24no—
12#16840659—21no—
13#16840658—21no—
14C2×Q16×D61C2211yescharacteristic
15C2×M16×D61C2211yescharacteristic
16C22⋊Q8×D61—21no—
17#16840021C411yescharacteristic
18#16840020C411yescharacteristic
19#16840019—21no—
20#16840018—21no—
21#16840017C411yescharacteristic
22#106×D61C2211yescharacteristic
23#103×D61—21no—
24C61×#470C411yescharacteristic
25C2×#11758213—22no—
26D61⋊M16—22no—
27D61⋊M16—22no—
28D61⋊M16—41no—
29D61⋊M16—41no—
30C2×#11758217—41no—
31C2×D61⋊C8—41no—
32#14519852—22no—
33#14519851—22no—
34D61⋊C16—22no—
35#14519848—22no—
36#14519848—22no—
37#14519847—22no—
38#14519847D414yes—
39C2×Q8×D61—21no—
40C22×C4×D61D411yescharacteristic
41C2×Dic244C2×C411yescharacteristic
42C2×#11758202—21no—
43Q16×D61—22no—
44Q16×D61—22no—
45C2×#11758194D411yescharacteristic
46C2×#11758189C2×C411yescharacteristic
47C2×#11758189D411yescharacteristic
48M16×D61—22no—
49M16×D61—22no—
50C2×C8×D61D411yescharacteristic
51C2×C8×D61C2311yescharacteristic
52#14519757—21no—
53#14519756—21no—
54#14519755—41no—
55#14519754—41no—
56#14519753—21no—
57C4⋊C4×D61—21no—
58C4⋊C4×D61—41no—
59C22⋊C4×D61—41no—
60#14519709C2×C411yescharacteristic
61#14519708—21no—
62#14519702—21no—
63#14519701—21no—
64#14519700—21no—
65C2×Q16×C61C2×C411yescharacteristic
66C2×M16×C61C2×C411yescharacteristic
67C22⋊Q8×C61—21no—
68#106×C61C2×C411yescharacteristic
69#103×C61—21no—
70C23×D61SD1611yescharacteristic
71C2×Q8×C61—21no—
72C22×C4×C61C22⋊C411yescharacteristic
73C22×Dic61D811yescharacteristic
74Q8×D61—41no—
75Q8×D61—41no—
76Q8×D61—41no—
77Q8×D61—41no—
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—41no—
83C2×C4×D61—41no—
84C2×C4×D61C22⋊C411yescharacteristic
85C2×C4×D61D811yescharacteristic
86C2×C4×D61SD1611yescharacteristic
87C2×C4×D61C2×D411yescharacteristic
88C2×Dic122—21no—
89C2×Dic122—41no—
90#11758217—42no—
91#11758217—42no—
92C2×#92420—42no—
93#11758213—24no—
94#11758213—42no—
95D61⋊C8—42no—
96D61⋊C8—42no—
97Q16×C61—22no—
98M16×C61—22no—
99C2×C8×C61C22⋊C411yescharacteristic
100C2×C8×C61C22×C411yescharacteristic
101C4⋊C4×C61—21no—
102C4⋊C4×C61—41no—
103C22⋊C4×C61—41no—
104C22⋊Dic61—41no—
105#11758202—42no—
106#11758198—41no—
107#11758198—41no—
108C4⋊Dic61—21no—
109C4⋊Dic61—41no—
110#11758196—41no—
111#11758196—41no—
112#11758196—41no—
113#11758194—22no—
114C2×#92418C22⋊C411yescharacteristic
115C2×#92418C2×D411yescharacteristic
116Dic244—22no—
117#11758189—22no—
118#11758189—22no—
119C8×D61—21no—
120C8×D61—21no—
121C8×D61C2×D412yes—
122C8×D61#4112yes—
123#11758187—42no—
124C23×C61#10211yescharacteristic
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—42no—
128C22×D61#10211yescharacteristic
129C22×D61C2×SD1611yescharacteristic
130Q8×C61—41no—
131Q8×C61—41no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61#10211yescharacteristic
137C2×C4×C61C2×C22⋊C411yescharacteristic
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61#10211yescharacteristic
143C2×Dic61C2×D811yescharacteristic
144C4×D61—21no—
145C4×D61—21no—
146C4×D61—21no—
147C4×D61—21no—
148C4×D61—21no—
149C4×D61—21no—
150C4×D61—82no—
151C4×D61—81no—
152C4×D61—81no—
153C4×D61#12011yescharacteristic
154C4×D61#12311yescharacteristic
155C4×D61AGL(1,ℤ/8)11yescharacteristic
156C4×D61#13711yescharacteristic
157Dic122—41no—
158Dic122—41no—
159Dic122—81no—
160Dic122—81no—
161#92420—44no—
162C8×C61—21no—
163C8×C61C4×D412yes—
164#92418—21no—
165#92418#12112yes—
166#13009—611nomaximal, Sylow
167C22×C61—21no—
168C22×C61—41no—
169C22×C61C2×#10211yescharacteristic
170C2×D61—22no—
171C2×D61—21no—
172C2×D61—42no—
173C2×D61—41no—
174C2×D61—81no—
175C2×D61#44811yescharacteristic
176C2×D61#48111yescharacteristic
177C4×C61—21no—
178C4×C61—81no—
179C4×C61—81no—
180C4×C61#38611yescharacteristic
181C4×C61#41711yescharacteristic
182Dic61—21no—
183Dic61—81no—
184Dic61—81no—
185Dic61#44711yescharacteristic
186Dic61#48011yescharacteristic
187C2×#470—611no—
188C2×#430—611no—
189C2×#362—612no—
190C2×#349—611no—
191#1383—612no—
192C2×C61—21no—
193C2×C61—41no—
194C2×C61#187411yescharacteristic
195D61—21no—
196D61—41no—
197D61#223912yes—
198C22×Q16—611no—
199C22×M16—611no—
200C22×M16—1221no—
201C2×C22⋊Q8—1221no—
202C2×M32—612no—
203#470—611no—
204#470—611no—
205#470—611no—
206#470—1221no—
207#470—1221no—
208#470#692311yescharacteristic
209#430—1224no—
210C2×#108—612no—
211C2×#108—1221no—
212C2×#106—611no—
213C2×#103—1221no—
214#362—1224no—
215#349—1221no—
216#349—1221no—
217C61#1300911yescharacteristic, complemented, Sylow
218C22×Q8—1221no—
219C23×C4—611no—
220C2×Q16—611no—
221C2×Q16—1222no—
222C2×Q16—1222no—
223C2×Q16—1221no—
224C2×Q16C2×#692311yescharacteristic
225C2×M16—611no—
226C2×M16—611no—
227C2×M16—611no—
228C2×M16—1222no—
229C2×M16—1222no—
230C2×M16—1222no—
231C2×M16—1222no—
232C2×M16—1222no—
233C2×M16—2441no—
234C2×M16—2441no—
235C2×M16—2441no—
236C2×M16C2×#692311yescharacteristic
237C22×C8—611no—
238C22×C8—611no—
239C22×C8—2441no—
240C22⋊Q8—21no—
241C22⋊Q8—1221no—
242C22⋊Q8—1221no—
243C22⋊Q8—1221no—
244C22⋊Q8—2441no—
245C22⋊Q8—2441no—
246C2×C4⋊C4—1221no—
247C2×C4⋊C4—2441no—
248C2×C22⋊C4—2441no—
249M32—1222no—
250M32—1222no—
251C2×C16—1222no—
252#108—614no—
253#108—1222no—
254#108—1222no—
255#108—1222no—
256#106—611no—
257#106—1221no—
258#106C2×#692311yescharacteristic
259#103—21no—
260#103—1221no—
261#103—1221no—
262#103—1221no—
263C24—611no—
264C2×Q8—21no—
265C2×Q8—1221no—
266C2×Q8—2441no—
267C2×Q8—2441no—
268C2×Q8—2441no—
269C2×Q8—2441no—
270C2×Q8—2441no—
271C22×C4—611no—
272C22×C4—611no—
273C22×C4—611no—
274C22×C4—611no—
275C22×C4—611no—
276C22×C4—1221no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—2441no—
281C22×C4—2441no—
282C22×C4C22⋊#692311yescharacteristic
283Q16—22no—
284Q16—1222no—
285Q16—2442no—
286M16—22no—
287M16—1222no—
288M16—1222no—
289M16—1222no—
290M16—1224no—
291M16—2442no—
292M16—2442no—
293M16—2442no—
294C2×C8—611no—
295C2×C8—612no—
296C2×C8—612no—
297C2×C8—611no—
298C2×C8—1221no—
299C2×C8—1221no—
300C2×C8—2442no—
301C2×C8—2442no—
302C2×C8—2442no—
303C2×C8C22⋊#692311yescharacteristic
304C2×C8C22×#692311yescharacteristic
305C4⋊C4—21no—
306C4⋊C4—41no—
307C4⋊C4—1221no—
308C4⋊C4—2441no—
309C4⋊C4—2441no—
310C4⋊C4—2441no—
311C4⋊C4—2441no—
312C22⋊C4—41no—
313C22⋊C4—2441no—
314C22⋊C4—2441no—
315C22⋊C4—2441no—
316C16—2442no—
317C23—611no—
318C23—611no—
319C23—1221no—
320C23—1221no—
321C23—2442no—
322C23#1451983911yescharacteristic
323Q8—41no—
324Q8—41no—
325Q8—4881no—
326Q8—4881no—
327Q8—2441no—
328Q8—2441no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—611no—
334C2×C4—611no—
335C2×C4—611no—
336C2×C4—611no—
337C2×C4—611no—
338C2×C4—611no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—4881no—
348C2×C4—4881no—
349C2×C4—4882no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4#1451983911yescharacteristic
353C2×C4C2×C22⋊#692311yescharacteristic
354C8—21no—
355C8—612no—
356C8—1221no—
357C8—2444no—
358C8D4×#692312yes—
359C22—21no—
360C22—41no—
361C22—611no—
362C22—611no—
363C22—1222no—
364C22—1221no—
365C22—4881no—
366C22—2441no—
367C22—2442no—
368C22C2×#1451983911yescharacteristic
369C4—21no—
370C4—81no—
371C4—81no—
372C4—611no—
373C4—611no—
374C4—1221no—
375C4—4881no—
376C4—4881no—
377C4#1684071011yescharacteristic
378C4#1684075311yescharacteristic
379C2—21no—
380C2—41no—
381C2—612no—
382C2—1221no—
383C2—2441no—
384C2#2146180611yescharacteristic
subgroupG/H
centerC2#21461806
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#470C4
socleC2×C61#1874
prime radicalC23×D61SD16
cosocleC2×C8×D61C23
hypercenter#470#6923
hypocenterC61#13009
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #470

Complements

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

NH ≅ G/Ntype
2. D61⋊#362C2semidirect
4. #21460883C2semidirect
217. C61#13009semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4302
D61⋊#3622
D61⋊#3492
#214608832
#470×D612
#1300961