Finite Group Databasebeta

← #29593843

Subgroups — #29593843

Order 15616.

350 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 67 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#21457539C211yesmaximal, characteristic
2#21448046C211yesmaximal, characteristic, complemented
3#21447967C211yesmaximal, characteristic, complemented
4#21445219C211yesmaximal, characteristic, complemented
5#21443779C211yesmaximal, characteristic, complemented
6#21443773C211yesmaximal, characteristic, complemented
7C61×#1362C211yesmaximal, characteristic, complemented
8C2×#14519800—21no—
9#16840415—21no—
10#16840167C2211yescharacteristic
11#16840053—21no—
12#16840000—21no—
13#16839964—21no—
14#16839923—22no—
15C4×D488C2211yescharacteristic
16C8×D244C2211yescharacteristic
17#16839590—21no—
18#16839566—22no—
19#16839564—21no—
20C4×#11758185C2211yescharacteristic
21#16839510—21no—
22C61×#494C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C61×#335C2211yescharacteristic
25C2×#11758226—22no—
26#14519800—42no—
27#14519800—42no—
28C2×#11758201—22no—
29C2×D488D411yescharacteristic
30C2×C8×D61—21no—
31#14519777—21no—
32#14519762—42no—
33#14519753—22no—
34#14519752—41no—
35C4×D244—21no—
36C4×D244D411yescharacteristic
37C4⋊C4×D61—41no—
38C2×#11758185—21no—
39#14519711—21no—
40#14519711—21no—
41#14519711D411yescharacteristic
42#14519709—41no—
43C4⋊#92418D411yescharacteristic
44#14519701—22no—
45#14519699—21no—
46#14519699—41no—
47#14519689—21no—
48C2×Q16×C61—21no—
49C2×Q16×C61D412yes—
50C4⋊Q8×C61—21no—
51C2×C16×C61—21no—
52C4⋊C8×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C2×Q8×C61—22no—
55#11758226—44no—
56#11758226—82no—
57C2×D244—21no—
58C2×D244—42no—
59C2×D244D811yescharacteristic
60C2×C4×D61—21no—
61C2×C4×D61—42no—
62C2×C4×D61—41no—
63C2×Dic122—41no—
64Q16×C61—42no—
65Q16×C61—41no—
66Q16×C61—41no—
67C2×C8×C61—41no—
68C2×C8×C61C2×D411yescharacteristic
69C2×C8×C61C2×D411yescharacteristic
70C4⋊C4×C61—41no—
71C4⋊C4×C61—41no—
72C42×C61C2×D411yescharacteristic
73#11758201—44no—
74#11758198—21no—
75#11758198—42no—
76#11758198—41no—
77C4⋊Dic61—21no—
78C4⋊Dic61—41no—
79C4⋊Dic61—41no—
80C4⋊Dic61D811yescharacteristic
81#11758196—42no—
82C2×#92418—21no—
83D488—21no—
84D488SD1612yes—
85C8×D61—41no—
86C8×D61—41no—
87C16×C61—41no—
88#11758185—41no—
89C22×D61—21no—
90C22×D61—41no—
91Q8×C61—42no—
92Q8×C61—42no—
93C2×C4×C61—42no—
94C2×C4×C61#12011yescharacteristic
95C2×C4×C61C2×D811yescharacteristic
96C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
97C2×Dic61—21no—
98C2×Dic61—41no—
99C2×Dic61—81no—
100D244—22no—
101D244—21no—
102D244—21no—
103D244—41no—
104D244—84no—
105C4×D61—41no—
106C4×D61—41no—
107C4×D61—84no—
108C4×D61—81no—
109C4×D61—81no—
110Dic122—161no—
111C8×C61—21no—
112C8×C61—81no—
113C8×C61C2×SD1611yescharacteristic
114C8×C61AGL(1,ℤ/8)11yescharacteristic
115#92418—41no—
116#12375—611nomaximal, Sylow
117C22×C61#44711yescharacteristic
118C2×D61—41no—
119C2×D61—42no—
120C2×D61—41no—
121C2×D61—41no—
122C2×D61—81no—
123C2×D61—81no—
124C4×C61—21no—
125C4×C61—82no—
126C4×C61#45011yescharacteristic
127C4×C61#45511yescharacteristic
128C4×C61#50811yescharacteristic
129C4×C61#51011yescharacteristic
130Dic61—41no—
131Dic61—81no—
132Dic61—161no—
133#3283—611no—
134#2241—611no—
135#2226—611no—
136#1675—611no—
137#1362D6111yescharacteristic, complemented
138#1331—611no—
139D4⋊C16—611no—
140C2×C61#163911yescharacteristic
141C2×C61#218911yescharacteristic
142C2×C61#219311yescharacteristic
143D61—81no—
144D61—82no—
145C2×#135—1221no—
146#547—1221no—
147#500—611no—
148#494C2×D6111yescharacteristic
149#476—1221no—
150#467—1221no—
151#461—1221no—
152#452—1222no—
153C4×D8—611no—
154C8×D4—611no—
155#367—1221no—
156C4⋊C16C2×D6111yescharacteristic
157#358—1222no—
158#357—1221no—
159C4×C16—611no—
160#335C2×D6111yescharacteristic
161#333—1221no—
162C61#1237511yescharacteristic, complemented, Sylow
163C2×#41—1222no—
164#135—2442no—
165#135—2442no—
166C2×Q16—21no—
167C2×Q16D24412yes—
168C2×SD16—1222no—
169C2×D8—611no—
170C22×C8—1221no—
171C4⋊Q8—21no—
172C4⋊Q8—1221no—
173#123—2442no—
174C22⋊Q8—1222no—
175#121—2441no—
176C4×D4—611no—
177C4×D4—1221no—
178C2×C4⋊C4—2441no—
179C2×C16—21no—
180C2×C16—1221no—
181#107—611no—
182#107—1221no—
183#107—1221no—
184#106—2441no—
185C4⋊C8—21no—
186C4⋊C8—611no—
187#103—1222no—
188#102—1221no—
189#102—2441no—
190C22⋊C8—1221no—
191C4×C8C22×D6111yescharacteristic
192#41—4882no—
193#41—2444no—
194C2×Q8—22no—
195C2×Q8—2441no—
196C2×D4—611no—
197C2×D4—1221no—
198C2×D4—2442no—
199C22×C4—1221no—
200C22×C4—2442no—
201C22×C4—2441no—
202Q16—42no—
203Q16—41no—
204Q16—41no—
205SD16—2444no—
206D8—612no—
207D8—1221no—
208C2×C8—41no—
209C2×C8—1221no—
210C2×C8—2441no—
211C2×C8—2441no—
212C2×C8C2×D24411yescharacteristic
213C2×C8D4×D6111yescharacteristic
214C4⋊C4—41no—
215C4⋊C4—41no—
216C4⋊C4—611no—
217C4⋊C4—1221no—
218C4⋊C4—2442no—
219C4⋊C4—2441no—
220C4⋊C4—2441no—
221C22⋊C4—1221no—
222C22⋊C4—2442no—
223C22⋊C4—2441no—
224C42D4×D6111yescharacteristic
225C16—41no—
226C16—2441no—
227C23—1221no—
228C23—2441no—
229Q8—42no—
230Q8—42no—
231Q8—9761no—
232D4—1221no—
233D4—1221no—
234D4—1222no—
235D4—4884no—
236D4—2441no—
237C2×C4—42no—
238C2×C4—1221no—
239C2×C4—4884no—
240C2×C4—4881no—
241C2×C4—4881no—
242C2×C4—4881no—
243C2×C4—2441no—
244C2×C4—2441no—
245C2×C4—2441no—
246C2×C4#1451974711yescharacteristic
247C2×C4D8×D6111yescharacteristic
248C2×C4#1451980411yescharacteristic
249C8—21no—
250C8—81no—
251C8—2441no—
252C8SD16×D6111yescharacteristic
253C8#1451980111yescharacteristic
254C22—4881no—
255C22—4881no—
256C22—2441no—
257C22—2441no—
258C22—2442no—
259C22—2441no—
260C22#1683989711yescharacteristic
261C4—21no—
262C4—82no—
263C4—9761no—
264C4—4881no—
265C4—2441no—
266C4#1683991411yescharacteristic
267C4#1683994211yescharacteristic
268C4#1684019311yescharacteristic
269C4#1684020411yescharacteristic
270C2—4882no—
271C2—4881no—
272C2#2144499911yescharacteristic
273C2#2144776211yescharacteristic
274C2#2144778611yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1362C2
socleC22×C61#447
prime radical#21457539C2
hypercenter#1362D61
hypocenterC61#12375
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
2. #21448046C2semidirect
3. #21447967C2semidirect
4. #21445219C2semidirect
5. #21443779C2semidirect
6. #21443773C2semidirect
7. C61×#1362C2semidirect
137. #1362D61semidirect
162. C61#12375semidirect

Maximal subgroups

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

subgroupindex
#214575392
#214480462
#214479672
#214452192
#214437792
#214437732
C61×#13622
#1237561