Finite Group Databasebeta

← #29593853

Subgroups — #29593853

Order 15616.

344 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 63 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
1#21457474C211yesmaximal, characteristic
2#21447958C211yesmaximal, characteristic, complemented
3#21445339C211yesmaximal, characteristic, complemented
4#21443862C211yesmaximal, characteristic, complemented
5#21443790C211yesmaximal, characteristic, complemented
6#21443778C211yesmaximal, characteristic, complemented
7C61×#2243C211yesmaximal, characteristic, complemented
8C2×#14519806—21no—
9#16840420—21no—
10#16840049—21no—
11#16840005—21no—
12#16839981—21no—
13#16839916—21no—
14#16839904—21no—
15C4×Dic244C2211yescharacteristic
16#16839841C2211yescharacteristic
17#16839589—21no—
18C4⋊#11758185C2211yescharacteristic
19#16839565—21no—
20#16839513C2211yescharacteristic
21#16839511—21no—
22C61×#500C2211yescharacteristic
23C61×#495C2211yescharacteristic
24C61×#358—21no—
25C61×#357—21no—
26C61×#346C2211yescharacteristic
27C2×#11758224—21no—
28C2×Q8×D61—21no—
29#14519806—42no—
30#14519806—42no—
31C2×Dic244D411yescharacteristic
32C2×#11758202—21no—
33C2×#11758200—21no—
34C2×#11758189—21no—
35#14519763—41no—
36#14519754—41no—
37#14519753—21no—
38#14519750—41no—
39#14519748—21no—
40C4×Dic122—21no—
41C4×D244D411yescharacteristic
42#14519737—41no—
43C2×#11758185—21no—
44#14519711D411yescharacteristic
45#14519708—41no—
46C4⋊#92418—21no—
47C4⋊#92418D411yescharacteristic
48#14519702—21no—
49#14519701—21no—
50#14519698—21no—
51#14519697—41no—
52#14519689—21no—
53C2×Q16×C61D411yescharacteristic
54C2×SD16×C61—21no—
55C2×D8×C61D411yescharacteristic
56C4⋊Q8×C61—21no—
57#124×C61—21no—
58C2×C16×C61—21no—
59#107×C61—21no—
60#107×C61—21no—
61C4×C8×C61C2311yescharacteristic
62C2×Q8×C61—21no—
63C2×Q8×C61—41no—
64C2×D4×C61—21no—
65C2×C22⋊D61—41no—
66C2×C22⋊D61—41no—
67C22×Dic61—41no—
68Q8×D61—42no—
69Q8×D61—81no—
70#11758224—42no—
71#11758224—81no—
72C2×D244D811yescharacteristic
73C2×C4×D61—21no—
74C2×C4×D61—41no—
75C2×Dic122—21no—
76C2×Dic122—41no—
77Q16×C61—41no—
78SD16×C61—41no—
79SD16×C61—41no—
80D8×C61—41no—
81C2×C8×C61C2×D411yescharacteristic
82C2×C8×C61C2×D411yescharacteristic
83C4⋊C4×C61—41no—
84C4⋊C4×C61—41no—
85C22⋊C4×C61—41no—
86C22⋊C4×C61—41no—
87C42×C61C2×D411yescharacteristic
88C22⋊Dic61—41no—
89#11758202—42no—
90#11758200—42no—
91#11758198—21no—
92#11758198—41no—
93C4⋊Dic61—21no—
94C4⋊Dic61D811yescharacteristic
95#11758196—41no—
96#11758196—41no—
97C4×Dic61—41no—
98C2×#92418—21no—
99C2×#92418—41no—
100Dic244—21no—
101Dic244SD1612yes—
102#11758189—41no—
103#11758189—41no—
104C16×C61—41no—
105#11758185—41no—
106C23×C61—41no—
107C22×D61—21no—
108Q8×C61—41no—
109Q8×C61—41no—
110Q8×C61—161no—
111D4×C61—41no—
112D4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—81no—
115C2×C4×C61#12011yescharacteristic
116C2×C4×C61C2×D811yescharacteristic
117C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
118C22⋊D61—82no—
119C22⋊D61—82no—
120C2×Dic61—21no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—82no—
124D244—41no—
125C4×D61—41no—
126C4×D61—41no—
127C4×D61—82no—
128Dic122—22no—
129Dic122—41no—
130Dic122—82no—
131C8×C61—21no—
132C8×C61C2×SD1611yescharacteristic
133C8×C61AGL(1,ℤ/8)11yescharacteristic
134#92418—41no—
135#92418—81no—
136#12377—611nomaximal, Sylow
137C22×C61—81no—
138C22×C61—81no—
139C22×C61—81no—
140C22×C61#44711yescharacteristic
141C2×D61—41no—
142C2×D61—41no—
143C2×D61—41no—
144C4×C61—21no—
145C4×C61—21no—
146C4×C61—81no—
147C4×C61—161no—
148C4×C61#45011yescharacteristic
149C4×C61#45511yescharacteristic
150Dic61—42no—
151Dic61—41no—
152Dic61—81no—
153#3277—611no—
154#2243D6111yescharacteristic, complemented
155#2225—611no—
156#1695—611no—
157#1360—611no—
158#1334—611no—
159#1330—611no—
160C2×C61—161no—
161C2×C61#163911yescharacteristic
162C2×C61#219111yescharacteristic
163C2×C61#219311yescharacteristic
164D61—81no—
165C2×#137—1221no—
166#548—1221no—
167#500C2×D6111yescharacteristic
168#495C2×D6111yescharacteristic
169#476—1221no—
170#468—1221no—
171#464—1221no—
172#451—1221no—
173#449—1221no—
174C4×Q16—611no—
175#436—611no—
176#367—1221no—
177C4⋊C16—611no—
178#358—21no—
179#358—1221no—
180#357—21no—
181#346C2×D6111yescharacteristic
182#334—611no—
183#333—1221no—
184C61#1237711yescharacteristic, complemented, Sylow
185C2×#41—1221no—
186C22×Q8—1221no—
187#137—2442no—
188#137—2442no—
189C2×Q16—611no—
190C2×Q16—1221no—
191C2×Q16C22⋊D6111yescharacteristic
192C2×SD16—21no—
193C2×SD16—1221no—
194C2×D8C22⋊D6111yescharacteristic
195C2×M16—1221no—
196C4⋊Q8—21no—
197#124—21no—
198#124—2441no—
199C22⋊Q8—1221no—
200C22⋊Q8—2441no—
201#121—1221no—
202#121—2441no—
203C4×Q8—1221no—
204C4×D4—611no—
205C4×D4—2441no—
206C2×C16—21no—
207C2×C16—1221no—
208#107—21no—
209#107—21no—
210#107—611no—
211#106—2441no—
212C4⋊C8—611no—
213C4⋊C8—1221no—
214#103—1221no—
215#103—1221no—
216#102—1221no—
217#102—2441no—
218C22⋊C8—1221no—
219C4×C8C22×D6111yescharacteristic
220#41—4881no—
221#41—2442no—
222C2×Q8—21no—
223C2×Q8—41no—
224C2×Q8—1221no—
225C2×Q8—4881no—
226C2×Q8—2441no—
227C2×Q8—2442no—
228C2×D4—21no—
229C2×D4—611no—
230C2×D4—2441no—
231C2×D4—2441no—
232C22×C4—1221no—
233C22×C4—2441no—
234C22×C4—2441no—
235Q16—41no—
236Q16—612no—
237Q16—1221no—
238Q16—2442no—
239SD16—41no—
240SD16—41no—
241SD16—2442no—
242D8—41no—
243M16—2441no—
244M16—2441no—
245C2×C8—1221no—
246C2×C8—2441no—
247C2×C8D4×D6111yescharacteristic
248C2×C8C2×C22⋊D6111yescharacteristic
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—611no—
252C4⋊C4—1221no—
253C4⋊C4—2441no—
254C4⋊C4—2441no—
255C22⋊C4—41no—
256C22⋊C4—41no—
257C22⋊C4—1221no—
258C22⋊C4—2441no—
259C22⋊C4—2441no—
260C42—2441no—
261C42D4×D6111yescharacteristic
262C16—41no—
263C16—2441no—
264C23—41no—
265C23—1221no—
266Q8—41no—
267Q8—41no—
268Q8—161no—
269Q8—1222no—
270Q8—4882no—
271Q8—2441no—
272D4—41no—
273D4—41no—
274D4—4882no—
275D4—4882no—
276D4—2441no—
277C2×C4—41no—
278C2×C4—81no—
279C2×C4—1221no—
280C2×C4—4882no—
281C2×C4—4882no—
282C2×C4—2441no—
283C2×C4—2441no—
284C2×C4—2441no—
285C2×C4—2441no—
286C2×C4#1451974511yescharacteristic
287C2×C4D8×D6111yescharacteristic
288C2×C4#1451980111yescharacteristic
289C8—21no—
290C8—4881no—
291C8—2441no—
292C8SD16×D6111yescharacteristic
293C8#1451980411yescharacteristic
294C22—81no—
295C22—81no—
296C22—81no—
297C22—2441no—
298C22—2441no—
299C22—2441no—
300C22#1683989411yescharacteristic
301C4—21no—
302C4—21no—
303C4—81no—
304C4—161no—
305C4—4881no—
306C4—2441no—
307C4—2442no—
308C4#1683991111yescharacteristic
309C4#1683993911yescharacteristic
310C2—161no—
311C2—4881no—
312C2#2144499511yescharacteristic
313C2#2144776811yescharacteristic
314C2#2144778011yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2243C2
socleC22×C61#447
prime radical#21457474C2
hypercenter#2243D61
hypocenterC61#12377
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2243

Complements

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

NH ≅ G/Ntype
2. #21447958C2semidirect
3. #21445339C2semidirect
4. #21443862C2semidirect
5. #21443790C2semidirect
6. #21443778C2semidirect
7. C61×#2243C2semidirect
154. #2243D61semidirect
184. C61#12377semidirect

Maximal subgroups

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

subgroupindex
#214574742
#214479582
#214453392
#214438622
#214437902
#214437782
C61×#22432
#1237761