Finite Group Databasebeta

← #29593842

Subgroups — #29593842

Order 15616.

350 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 75 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#21448046C211yesmaximal, characteristic, complemented
2#21447966C211yesmaximal, characteristic, complemented
3#21445218C211yesmaximal, characteristic, complemented
4#21443868C211yesmaximal, characteristic, complemented
5#21443780C211yesmaximal, characteristic, complemented
6D4⋊#11758185C211yesmaximal, characteristic, complemented
7C61×#3283C211yesmaximal, characteristic
8#16840167C2211yescharacteristic
9#16840052—21no—
10#16839589—21no—
11C4⋊#11758185C2211yescharacteristic
12#16839566—22no—
13#16839563—21no—
14C4×#11758185C2211yescharacteristic
15#16839515C2211yescharacteristic
16#16839510—21no—
17C2×#135×C61—21no—
18C61×#547—21no—
19C61×#494C2211yescharacteristic
20C61×#467—21no—
21C61×#461—21no—
22C61×#452—22no—
23C4×D8×C61C2211yescharacteristic
24C8×D4×C61C2211yescharacteristic
25#14519777—21no—
26C2×#11758185—21no—
27C2×#11758185—21no—
28#14519711—21no—
29#14519711—21no—
30#14519708—41no—
31C4⋊#92418—21no—
32#14519698—41no—
33C2×#41×C61—22no—
34#135×C61—42no—
35#135×C61—42no—
36C2×Q16×C61—21no—
37C2×Q16×C61D412yes—
38C2×SD16×C61—22no—
39C2×D8×C61D411yescharacteristic
40C22×C8×C61—21no—
41C4⋊Q8×C61—21no—
42#123×C61—42no—
43C22⋊Q8×C61—22no—
44#121×C61—41no—
45C4×D4×C61—21no—
46C4×D4×C61D411yescharacteristic
47C2×C4⋊C4×C61—41no—
48#107×C61D411yescharacteristic
49C4⋊C8×C61D411yescharacteristic
50#103×C61—22no—
51#102×C61—21no—
52C22⋊C8×C61—21no—
53C4×C8×C61C2311yescharacteristic
54#41×C61—44no—
55#41×C61—82no—
56C2×Q8×C61—22no—
57C2×D4×C61—21no—
58C2×D4×C61—42no—
59C2×D4×C61D811yescharacteristic
60C22×C4×C61—21no—
61C22×C4×C61—42no—
62C22×C4×C61—41no—
63C2×Dic122—41no—
64Q16×C61—42no—
65Q16×C61—41no—
66Q16×C61—41no—
67SD16×C61—44no—
68D8×C61—21no—
69D8×C61SD1612yes—
70C2×C8×C61—21no—
71C2×C8×C61—41no—
72C2×C8×C61—41no—
73C2×C8×C61C2×D411yescharacteristic
74C2×C8×C61C2×D411yescharacteristic
75C4⋊C4×C61—21no—
76C4⋊C4×C61—42no—
77C4⋊C4×C61—41no—
78C4⋊C4×C61—41no—
79C4⋊C4×C61D811yescharacteristic
80C22⋊C4×C61—21no—
81C22⋊C4×C61—42no—
82C22⋊C4×C61—41no—
83C42×C61C2×D411yescharacteristic
84C4⋊Dic61—41no—
85C4⋊Dic61—41no—
86C2×#92418—41no—
87#11758185—41no—
88#11758185—41no—
89C23×C61—21no—
90C23×C61—41no—
91Q8×C61—42no—
92Q8×C61—42no—
93D4×C61—22no—
94D4×C61—21no—
95D4×C61—21no—
96D4×C61—41no—
97D4×C61—84no—
98C2×C4×C61—21no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61—41no—
102C2×C4×C61—42no—
103C2×C4×C61—84no—
104C2×C4×C61—81no—
105C2×C4×C61—81no—
106C2×C4×C61#12011yescharacteristic
107C2×C4×C61C2×D811yescharacteristic
108C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
109C2×Dic61—81no—
110Dic122—161no—
111C8×C61—21no—
112C8×C61—41no—
113C8×C61C2×SD1611yescharacteristic
114C8×C61AGL(1,ℤ/8)11yescharacteristic
115#92418—81no—
116#12375—611nomaximal, Sylow
117C22×C61—41no—
118C22×C61—42no—
119C22×C61—41no—
120C22×C61—41no—
121C22×C61—81no—
122C22×C61—81no—
123C22×C61#44711yescharacteristic
124C4×C61—21no—
125C4×C61—41no—
126C4×C61—82no—
127C4×C61—81no—
128C4×C61#45011yescharacteristic
129C4×C61#45511yescharacteristic
130C4×C61#50811yescharacteristic
131C4×C61#51011yescharacteristic
132Dic61—161no—
133#3283D6111yescharacteristic
134#2241—611no—
135#2226—611no—
136#1675—611no—
137#1362—611no—
138#1331—611no—
139D4⋊C16—611no—
140C2×C61—81no—
141C2×C61—82no—
142C2×C61#163911yescharacteristic
143C2×C61#218911yescharacteristic
144C2×C61#219311yescharacteristic
145C2×#135—21no—
146#547—21no—
147#500—611no—
148#494C2×D6111yescharacteristic
149#476—1221no—
150#467—21no—
151#461—21no—
152#452—22no—
153C4×D8C2×D6111yescharacteristic
154C8×D4C2×D6111yescharacteristic
155#367—1221no—
156C4⋊C16—611no—
157#358—1222no—
158#357—1221no—
159C4×C16—611no—
160#335—611no—
161#333—1221no—
162C61#1237511yescharacteristic, complemented, Sylow
163C2×#41—22no—
164#135—42no—
165#135—42no—
166C2×Q16—21no—
167C2×Q16C22⋊D6112yes—
168C2×SD16—22no—
169C2×D8C22⋊D6111yescharacteristic
170C22×C8—21no—
171C4⋊Q8—21no—
172C4⋊Q8—1221no—
173#123—42no—
174C22⋊Q8—22no—
175#121—41no—
176C4×D4—21no—
177C4×D4C22⋊D6111yescharacteristic
178C2×C4⋊C4—41no—
179C2×C16—1221no—
180C2×C16—1221no—
181#107—1221no—
182#107—1221no—
183#107C22⋊D6111yescharacteristic
184#106—2441no—
185C4⋊C8—1221no—
186C4⋊C8C22⋊D6111yescharacteristic
187#103—22no—
188#102—21no—
189#102—2441no—
190C22⋊C8—21no—
191C4×C8C22×D6111yescharacteristic
192#41—44no—
193#41—82no—
194C2×Q8—22no—
195C2×Q8—2441no—
196C2×D4—21no—
197C2×D4—42no—
198C2×D4#1175819911yescharacteristic
199C22×C4—21no—
200C22×C4—42no—
201C22×C4—41no—
202Q16—42no—
203Q16—41no—
204Q16—41no—
205SD16—44no—
206D8—21no—
207D8#1175820012yes—
208C2×C8—21no—
209C2×C8—41no—
210C2×C8—41no—
211C2×C8—2441no—
212C2×C8C2×C22⋊D6111yescharacteristic
213C2×C8C2×C22⋊D6111yescharacteristic
214C4⋊C4—21no—
215C4⋊C4—42no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C4⋊C4—2441no—
219C4⋊C4—2441no—
220C4⋊C4#1175819911yescharacteristic
221C22⋊C4—21no—
222C22⋊C4—42no—
223C22⋊C4—41no—
224C42C2×C22⋊D6111yescharacteristic
225C16—2441no—
226C16—2441no—
227C23—21no—
228C23—41no—
229Q8—42no—
230Q8—42no—
231Q8—9761no—
232D4—21no—
233D4—21no—
234D4—22no—
235D4—41no—
236D4—84no—
237C2×C4—21no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—84no—
243C2×C4—81no—
244C2×C4—81no—
245C2×C4—4881no—
246C2×C4#1451974611yescharacteristic
247C2×C4C2×#1175819911yescharacteristic
248C2×C4#1451980311yescharacteristic
249C8—21no—
250C8—41no—
251C8—4881no—
252C8C2×#1175820011yescharacteristic
253C8#1451980311yescharacteristic
254C22—41no—
255C22—41no—
256C22—41no—
257C22—42no—
258C22—81no—
259C22—81no—
260C22#1683989611yescharacteristic
261C4—21no—
262C4—41no—
263C4—81no—
264C4—82no—
265C4—9761no—
266C4#1683991311yescharacteristic
267C4#1683994011yescharacteristic
268C4#1684019211yescharacteristic
269C4#1684020211yescharacteristic
270C2—81no—
271C2—82no—
272C2#2144499811yescharacteristic
273C2#2144775911yescharacteristic
274C2#2144778311yescharacteristic
subgroupG/H
centerC22#16839896
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
Fitting, prime radicalC61×#3283C2
socleC22×C61#447
hypercenter#3283D61
hypocenterC61#12375
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ #3283

Complements

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

NH ≅ G/Ntype
1. #21448046C2semidirect
2. #21447966C2semidirect
3. #21445218C2semidirect
4. #21443868C2semidirect
5. #21443780C2semidirect
6. D4⋊#11758185C2semidirect
162. C61#12375semidirect

Maximal subgroups

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

subgroupindex
#214480462
#214479662
#214452182
#214438682
#214437802
D4⋊#117581852
C61×#32832
#1237561