Finite Group Databasebeta

← #29593858

Subgroups — #29593858

Order 15616.

344 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 65 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#21457477C211yesmaximal, characteristic
2#21448056C211yesmaximal, characteristic, complemented
3#21447962C211yesmaximal, characteristic, complemented
4#21445342C211yesmaximal, characteristic, complemented
5#21443863C211yesmaximal, characteristic, complemented
6#21443790C211yesmaximal, characteristic, complemented
7C61×#1330C211yesmaximal, characteristic, complemented
8C2×#14519810—21no—
9#16840421—21no—
10#16840167C2211yescharacteristic
11#16840146C2211yescharacteristic
12#16840052—21no—
13#16840008—21no—
14#16839985—21no—
15#16839920—21no—
16#16839909—21no—
17C4×Dic244C2211yescharacteristic
18#16839590—21no—
19#16839567—21no—
20#16839567—21no—
21#16839564—21no—
22#16839513C2211yescharacteristic
23#16839510—21no—
24C61×#436C2211yescharacteristic
25C61×C4⋊C16C2211yescharacteristic
26C61×#346C2211yescharacteristic
27C2×#11758222—21no—
28C22×Dic122—21no—
29#14519810—42no—
30#14519810—42no—
31C2×Dic244—21no—
32C2×Dic244D411yescharacteristic
33C2×Dic244D411yescharacteristic
34C2×#11758190—21no—
35C2×#11758190—21no—
36C2×D488D411yescharacteristic
37#14519777—21no—
38#14519765—21no—
39#14519763—41no—
40#14519756—21no—
41#14519755—41no—
42#14519751—21no—
43#14519749—41no—
44C4×Dic122—21no—
45#14519737—41no—
46#14519711—21no—
47#14519711—21no—
48#14519711D411yescharacteristic
49#14519708—41no—
50C4⋊#92418—21no—
51#14519702—21no—
52#14519702—21no—
53#14519699—21no—
54#14519698—41no—
55C2×M16×C61—21no—
56C4×D4×C61D411yescharacteristic
57C2×C16×C61—21no—
58C2×C16×C61—21no—
59C4⋊C8×C61D411yescharacteristic
60C22⋊C8×C61—21no—
61C4×C8×C61C2311yescharacteristic
62C2×D4×C61D811yescharacteristic
63C22×C4×C61—21no—
64C2×C22⋊D61—41no—
65C2×C22⋊D61—41no—
66C22×Dic61—41no—
67#11758222—42no—
68#11758222—81no—
69C2×D244—21no—
70C2×C4×D61—41no—
71C2×Dic122—21no—
72C2×Dic122—21no—
73C2×Dic122—42no—
74C2×Dic122—41no—
75C2×Dic122—41no—
76C2×Dic122—81no—
77M16×C61—41no—
78M16×C61—41no—
79C2×C8×C61—21no—
80C2×C8×C61C2×D411yescharacteristic
81C2×C8×C61C2×D411yescharacteristic
82C4⋊C4×C61D811yescharacteristic
83C22⋊C4×C61—21no—
84C42×C61C2×D411yescharacteristic
85C22⋊Dic61—41no—
86#11758198—41no—
87#11758198—41no—
88#11758198—41no—
89C4⋊Dic61—21no—
90C4⋊Dic61—41no—
91C4⋊Dic61—41no—
92#11758196—41no—
93#11758196—41no—
94C4×Dic61—41no—
95C2×#92418—41no—
96Dic244—21no—
97Dic244—41no—
98Dic244—42no—
99Dic244SD1612yes—
100D488—41no—
101#11758190—42no—
102#11758190—41no—
103#11758190—41no—
104C16×C61—41no—
105C16×C61—41no—
106C23×C61—21no—
107C22×D61—41no—
108D4×C61—41no—
109C2×C4×C61—21no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61#12011yescharacteristic
113C2×C4×C61C2×D811yescharacteristic
114C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
115C22⋊D61—82no—
116C22⋊D61—82no—
117C2×Dic61—41no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61—82no—
121C2×Dic61—81no—
122D244—41no—
123D244—41no—
124C4×D61—82no—
125Dic122—22no—
126Dic122—41no—
127Dic122—41no—
128Dic122—41no—
129Dic122—82no—
130Dic122—161no—
131C8×C61—21no—
132C8×C61—41no—
133C8×C61C2×SD1611yescharacteristic
134C8×C61AGL(1,ℤ/8)11yescharacteristic
135#92418—81no—
136#12377—611nomaximal, Sylow
137C22×C61—41no—
138C22×C61—41no—
139C22×C61—41no—
140C22×C61#44711yescharacteristic
141C2×D61—81no—
142C2×D61—81no—
143C2×D61—81no—
144C4×C61—21no—
145C4×C61—21no—
146C4×C61—41no—
147C4×C61#45011yescharacteristic
148C4×C61#45511yescharacteristic
149Dic61—42no—
150Dic61—81no—
151Dic61—81no—
152Dic61—161no—
153#3277—611no—
154#2243—611no—
155#2225—611no—
156#1695—611no—
157#1360—611no—
158#1334—611no—
159#1330D6111yescharacteristic, complemented
160C2×C61—81no—
161C2×C61#163911yescharacteristic
162C2×C61#219111yescharacteristic
163C2×C61#219311yescharacteristic
164D61—161no—
165C2×#137—1221no—
166#548—1221no—
167#500—611no—
168#495—611no—
169#476—1221no—
170#468—1221no—
171#464—1221no—
172#451—1221no—
173#449—1221no—
174C4×Q16—611no—
175#436C2×D6111yescharacteristic
176#367—1221no—
177C4⋊C16C2×D6111yescharacteristic
178#358—1221no—
179#358—1221no—
180#357—1221no—
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—611no—
191C2×Q16—1221no—
192C2×SD16—1221no—
193C2×SD16—1221no—
194C2×D8—611no—
195C2×M16—21no—
196C4⋊Q8—1221no—
197#124—1221no—
198#124—2441no—
199C22⋊Q8—1221no—
200C22⋊Q8—2441no—
201#121—1221no—
202#121—2441no—
203C4×Q8—1221no—
204C4×D4—2441no—
205C4×D4D24411yescharacteristic
206C2×C16—21no—
207C2×C16—21no—
208#107—611no—
209#107—1221no—
210#107—1221no—
211#106—2441no—
212C4⋊C8—1221no—
213C4⋊C8D24411yescharacteristic
214#103—1221no—
215#103—1221no—
216#102—1221no—
217#102—2441no—
218C22⋊C8—21no—
219C4×C8C22×D6111yescharacteristic
220#41—4881no—
221#41—2442no—
222C2×Q8—1221no—
223C2×Q8—1221no—
224C2×Q8—4881no—
225C2×Q8—2441no—
226C2×Q8—2442no—
227C2×Q8—2441no—
228C2×D4—1221no—
229C2×D4—2441no—
230C2×D4—2441no—
231C2×D4D48811yescharacteristic
232C22×C4—21no—
233C22×C4—2441no—
234C22×C4—2441no—
235Q16—612no—
236Q16—1221no—
237Q16—2441no—
238Q16—2442no—
239SD16—2442no—
240SD16—2441no—
241SD16—2441no—
242D8—2441no—
243M16—41no—
244M16—41no—
245C2×C8—21no—
246C2×C8—2441no—
247C2×C8D4×D6111yescharacteristic
248C2×C8D4×D6111yescharacteristic
249C4⋊C4—1221no—
250C4⋊C4—2441no—
251C4⋊C4—2441no—
252C4⋊C4—2441no—
253C4⋊C4—2441no—
254C4⋊C4D48811yescharacteristic
255C22⋊C4—21no—
256C22⋊C4—2441no—
257C22⋊C4—2441no—
258C22⋊C4—2441no—
259C22⋊C4—2441no—
260C42—2441no—
261C42C2×D24411yescharacteristic
262C16—41no—
263C16—41no—
264C23—21no—
265C23—2441no—
266Q8—1222no—
267Q8—9761no—
268Q8—4882no—
269Q8—2441no—
270Q8—2441no—
271Q8—2441no—
272D4—41no—
273D4—4882no—
274D4—4882no—
275D4—2441no—
276D4—2441no—
277C2×C4—21no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—4882no—
281C2×C4—4881no—
282C2×C4—4882no—
283C2×C4—2441no—
284C2×C4—2441no—
285C2×C4—2441no—
286C2×C4#1451974711yescharacteristic
287C2×C4C2×D48811yescharacteristic
288C2×C4#1451980511yescharacteristic
289C8—21no—
290C8—41no—
291C8—4881no—
292C8SD16×D6111yescharacteristic
293C8#1451980111yescharacteristic
294C22—41no—
295C22—41no—
296C22—41no—
297C22—4881no—
298C22—4881no—
299C22—4881no—
300C22#1683989811yescharacteristic
301C4—21no—
302C4—21no—
303C4—41no—
304C4—9761no—
305C4—4881no—
306C4—4881no—
307C4—2442no—
308C4#1683991411yescharacteristic
309C4#1683994111yescharacteristic
310C2—81no—
311C2—9761no—
312C2#2144500011yescharacteristic
313C2#2144777211yescharacteristic
314C2#2144778511yescharacteristic
subgroupG/H
centerC22#16839898
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1330C2
socleC22×C61#447
prime radical#21457477C2
hypercenter#1330D61
hypocenterC61#12377
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #436 ◁ #1330

Complements

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

NH ≅ G/Ntype
2. #21448056C2semidirect
3. #21447962C2semidirect
4. #21445342C2semidirect
5. #21443863C2semidirect
6. #21443790C2semidirect
7. C61×#1330C2semidirect
159. #1330D61semidirect
184. C61#12377semidirect

Maximal subgroups

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

subgroupindex
#214574772
#214480562
#214479622
#214453422
#214438632
#214437902
C61×#13302
#1237761