Finite Group Databasebeta

← #29593946

Subgroups — #29593946

Order 15616.

302 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 61 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#21458905C211yesmaximal, characteristic
2#21448058C211yesmaximal, characteristic, complemented
3#21445334C211yesmaximal, characteristic, complemented
4#21443863C211yesmaximal, characteristic, complemented
5#21443800C211yesmaximal, characteristic, complemented
6#21443786C211yesmaximal, characteristic, complemented
7C61×#2226C211yesmaximal, characteristic, complemented
8#16840495—21no—
9#16840150—21no—
10#16840146C2211yescharacteristic
11#16839983—21no—
12#16839977—21no—
13#16839969—21no—
14#16839956—21no—
15#16839892C2211yescharacteristic
16#16839861—21no—
17#16839565—21no—
18#16839562—21no—
19#16839538C2211yescharacteristic
20#16839513C2211yescharacteristic
21#16839508—21no—
22C61×#500C2211yescharacteristic
23C4×D8×C61C2211yescharacteristic
24C61×#367—21no—
25C61×C4⋊C16C2211yescharacteristic
26C61×#357—21no—
27C2×Dic244D411yescharacteristic
28C2×#11758202—41no—
29C2×#11758190—21no—
30C2×#11758200—21no—
31C2×D488D411yescharacteristic
32C2×#11758199—21no—
33#14519773—21no—
34#14519765—21no—
35#14519764—21no—
36#14519763—41no—
37#14519760—41no—
38#14519759—41no—
39C4×Dic122D411yescharacteristic
40#14519742—21no—
41#14519739—21no—
42C4×C22⋊D61—41no—
43C2×#11758185—21no—
44C4⋊#92418—21no—
45C4⋊#92418D411yescharacteristic
46#14519706—21no—
47#14519701—41no—
48#14519700—21no—
49#14519697—21no—
50#14519687—21no—
51C2×D8×C61D411yescharacteristic
52C4⋊Q8×C61—21no—
53C4×D4×C61—21no—
54C2×C16×C61—21no—
55#107×C61—21no—
56#107×C61—21no—
57#107×C61D411yescharacteristic
58#102×C61—21no—
59C4×C8×C61C2311yescharacteristic
60C2×Q8×C61—41no—
61C2×D4×C61—21no—
62C22×C4×C61—41no—
63C2×C22⋊D61—41no—
64C2×C22⋊D61—41no—
65C2×D244—21no—
66C2×C4×D61—41no—
67C2×Dic122—21no—
68C2×Dic122D811yescharacteristic
69D8×C61—21no—
70D8×C61—21no—
71C2×C8×C61C2×D411yescharacteristic
72C2×C8×C61C2×D411yescharacteristic
73C4⋊C4×C61—21no—
74C4⋊C4×C61—41no—
75C4⋊C4×C61—41no—
76C22⋊C4×C61—41no—
77C42×C61C2×D411yescharacteristic
78C22⋊Dic61—41no—
79C22⋊Dic61—41no—
80#11758202—82no—
81#11758200—81no—
82#11758199—81no—
83#11758198—41no—
84#11758198—41no—
85#11758198—41no—
86C4⋊Dic61D811yescharacteristic
87#11758196—21no—
88#11758196—41no—
89C4×Dic61—21no—
90C4×Dic61—41no—
91C2×#92418—21no—
92C2×#92418—41no—
93Dic244—41no—
94D488—41no—
95#11758190—41no—
96#11758190—41no—
97C16×C61—41no—
98#11758185—41no—
99C23×C61—41no—
100C22×D61—41no—
101Q8×C61—81no—
102Q8×C61—81no—
103D4×C61—41no—
104D4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61—81no—
107C2×C4×C61—161no—
108C2×C4×C61#12011yescharacteristic
109C2×C4×C61C2×D811yescharacteristic
110C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
111C22⋊D61—82no—
112C22⋊D61—161no—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—41no—
116D244—41no—
117D244—41no—
118C4×D61—161no—
119Dic122—41no—
120Dic122—41no—
121Dic122—41no—
122C8×C61—21no—
123C8×C61#13511yescharacteristic
124C8×C61#13711yescharacteristic
125#92418—41no—
126#92418—81no—
127#12390—611nomaximal, Sylow
128C22×C61—81no—
129C22×C61—81no—
130C22×C61—81no—
131C22×C61#44711yescharacteristic
132C2×D61—81no—
133C2×D61—81no—
134C2×D61—81no—
135C4×C61—21no—
136C4×C61—21no—
137C4×C61—81no—
138C4×C61—161no—
139C4×C61#45211yescharacteristic
140C4×C61#45511yescharacteristic
141Dic61—41no—
142Dic61—41no—
143Dic61—81no—
144#3403—611no—
145#2243—611no—
146#2226D6111yescharacteristic, complemented
147#1694—611no—
148#1360—611no—
149#1338—611no—
150#1333—611no—
151C2×C61—161no—
152C2×C61#164111yescharacteristic
153C2×C61#219011yescharacteristic
154C2×C61#219411yescharacteristic
155D61—161no—
156#559—1221no—
157#500C2×D6111yescharacteristic
158#496—1221no—
159#495—611no—
160#464—1221no—
161#463—1221no—
162#462—1221no—
163#459—1221no—
164#446—611no—
165#440—1221no—
166C4×D8C2×D6111yescharacteristic
167#367—21no—
168C4⋊C16C2×D6111yescharacteristic
169#358—1221no—
170#357—21no—
171#357—1221no—
172#346—611no—
173#334—611no—
174#332—1221no—
175C61#1239011yescharacteristic, complemented, Sylow
176C2×Q16—611no—
177C2×Q16—2441no—
178C2×SD16—1221no—
179C2×SD16—1221no—
180C2×D8—611no—
181C2×D8—1221no—
182C2×D8C22⋊D6111yescharacteristic
183C4⋊Q8—21no—
184#127—1221no—
185#124—1221no—
186#124—1221no—
187#124—2441no—
188#123—2441no—
189#123—2441no—
190C4×Q8—611no—
191C4×Q8—1221no—
192C4×D4—21no—
193C4×D4—1221no—
194C4×D4—2441no—
195C2×C16—21no—
196C2×C16—1221no—
197#107—21no—
198#107—21no—
199#107C22⋊D6111yescharacteristic
200C4⋊C8—611no—
201C4⋊C8—1221no—
202C4⋊C8—1221no—
203#103—1221no—
204#103—2441no—
205#102—21no—
206#102—1221no—
207#97—1221no—
208C4×C8C22×D6111yescharacteristic
209C2×Q8—41no—
210C2×Q8—611no—
211C2×Q8—1221no—
212C2×D4—21no—
213C2×D4—1221no—
214C2×D4—2441no—
215C2×D4—2441no—
216C22×C4—41no—
217C22×C4—2441no—
218Q16—4882no—
219Q16—2441no—
220SD16—4881no—
221SD16—2441no—
222SD16—2441no—
223D8—21no—
224D8—21no—
225D8—4881no—
226D8—2441no—
227C2×C8—1221no—
228C2×C8—2441no—
229C2×C8D4×D6111yescharacteristic
230C2×C8C2×C22⋊D6111yescharacteristic
231C4⋊C4—21no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—611no—
235C4⋊C4—1221no—
236C4⋊C4—2441no—
237C22⋊C4—41no—
238C22⋊C4—2441no—
239C22⋊C4—2441no—
240C22⋊C4—2441no—
241C22⋊C4—2441no—
242C22⋊C4—2441no—
243C42—1221no—
244C42—2441no—
245C42D4×D6111yescharacteristic
246C16—41no—
247C16—2441no—
248C23—41no—
249C23—2441no—
250Q8—81no—
251Q8—81no—
252Q8—2441no—
253Q8—2441no—
254Q8—2441no—
255D4—41no—
256D4—41no—
257D4—9761no—
258D4—4882no—
259D4—2441no—
260D4—2441no—
261C2×C4—41no—
262C2×C4—81no—
263C2×C4—161no—
264C2×C4—1221no—
265C2×C4—1221no—
266C2×C4—9761no—
267C2×C4—2441no—
268C2×C4#1451974511yescharacteristic
269C2×C4D8×D6111yescharacteristic
270C2×C4#1451980111yescharacteristic
271C8—21no—
272C8—4881no—
273C8—2441no—
274C8#1451979711yescharacteristic
275C8#1451980811yescharacteristic
276C22—81no—
277C22—81no—
278C22—81no—
279C22—4881no—
280C22—4881no—
281C22—4881no—
282C22#1683989411yescharacteristic
283C4—21no—
284C4—21no—
285C4—81no—
286C4—161no—
287C4—4881no—
288C4—2441no—
289C4—2441no—
290C4#1683992211yescharacteristic
291C4#1683993811yescharacteristic
292C2—161no—
293C2—9761no—
294C2#2144501111yescharacteristic
295C2#2144776311yescharacteristic
296C2#2144778911yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2226C2
socleC22×C61#447
prime radical#21458905C2
hypercenter#2226D61
hypocenterC61#12390
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2226

Complements

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

NH ≅ G/Ntype
2. #21448058C2semidirect
3. #21445334C2semidirect
4. #21443863C2semidirect
5. #21443800C2semidirect
6. #21443786C2semidirect
7. C61×#2226C2semidirect
146. #2226D61semidirect
175. C61#12390semidirect

Maximal subgroups

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

subgroupindex
#214589052
#214480582
#214453342
#214438632
#214438002
#214437862
C61×#22262
#1239061