Finite Group Databasebeta

← #30607928

Subgroups — #30607928

Order 15616.

256 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 80 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
1C2×#16840686C211yesmaximal, characteristic
2#21462038C211yesmaximal, characteristic
3#21461938C211yesmaximal, characteristic
4#21461936C211yesmaximal, characteristic
5#21460888C211yesmaximal, characteristic
6#21460885C211yesmaximal, characteristic
7#21447612C211yesmaximal, characteristic
8D61⋊M32C2211yescharacteristic
9#16840777—21no—
10C2×#14519847C2211yescharacteristic
11#16840773—21no—
12C2×#14519845C2211yescharacteristic
13#16840725C2211yescharacteristic
14#16840686—21no—
15#16840686—21no—
16#16840653—21no—
17#16840652—21no—
18#16840645—21no—
19#16840641—21no—
20C2×#14519716C2211yescharacteristic
21#108×D61C2211yescharacteristic
22#108×D61C2211yescharacteristic
23#16839592C411yescharacteristic, complemented
24#16839591C411yescharacteristic, complemented
25#16839591C411yescharacteristic, complemented
26C61×#368C411yescharacteristic, complemented
27C2×#11758213—21no—
28D61⋊M16D411yescharacteristic
29#14519856D411yescharacteristic
30C2×C4⋊#6923—21no—
31#14519852—21no—
32#14519851—21no—
33D61⋊C16Q812yes—
34#14519848—41no—
35#14519847—21no—
36#14519847—21no—
37#14519847—41no—
38#14519846—41no—
39#14519845—21no—
40#14519845—21no—
41#14519845—41no—
42#14519831—21no—
43C8×#6923—21no—
44M16×D61—21no—
45M16×D61—21no—
46C2×C8×D61C2311yescharacteristic
47#14519716D411yescharacteristic
48#14519716D411yescharacteristic
49#14519716Q811yescharacteristic
50#14519716Q811yescharacteristic
51C2×#11758185C2×C411yescharacteristic
52#14519713C2×C411yescharacteristic
53#14519713C2×C411yescharacteristic
54#14519712—21no—
55#14519712—21no—
56C2×C16×C61C2×C411yescharacteristic
57#108×C61C2×C411yescharacteristic
58#108×C61C2×C411yescharacteristic
59C22×#6923—41no—
60C2×C4×D61C2×D411yescharacteristic
61C22⋊#6923—21no—
62#11758217—21no—
63C2×#92420—41no—
64C4⋊#6923—21no—
65C4⋊#6923—41no—
66C4⋊#6923—41no—
67C4×#6923—21no—
68#11758213—21no—
69#11758213—41no—
70#11758213—41no—
71D61⋊C8—21no—
72M16×C61—21no—
73M16×C61—21no—
74C2×C8×C61C22×C411yescharacteristic
75#11758194—21no—
76#11758194—21no—
77C2×#92418#4111yescharacteristic
78#11758189—41no—
79#11758189—41no—
80C8×D61—41no—
81C8×D61—41no—
82C8×D61C2×D411yescharacteristic
83C8×D61C2×Q811yescharacteristic
84C8×D61C2×Q811yescharacteristic
85C8×D61#4111yescharacteristic
86#11758187—22no—
87C16×C61C4⋊C411yescharacteristic
88C16×C61C4⋊C411yescharacteristic
89#11758185C4⋊C411yescharacteristic
90#11758185C4⋊C411yescharacteristic
91C22×D61#13711yescharacteristic
92C2×#6923—41no—
93C2×#6923—81no—
94C2×#6923—161no—
95C2×C4×C61C4×D411yescharacteristic
96C2×Dic61#13711yescharacteristic
97C4×D61#12111yescharacteristic
98C4×D61C4⋊Q811yescharacteristic
99C4×D61AGL(1,ℤ/8)11yescharacteristic
100C4×D61AGL(1,ℤ/8)11yescharacteristic
101#92420—41no—
102#92420—81no—
103C8×C61—41no—
104C8×C61—41no—
105C8×C61C2×C4⋊C411yescharacteristic
106C8×C61C4×Q811yescharacteristic
107#92418—41no—
108#92418—41no—
109#92418C22⋊Q811yescharacteristic
110#92418#12511yescharacteristic
111#13175—611nomaximal, Sylow
112C22×C61#44111yescharacteristic
113C2×D61—41no—
114C2×D61#46811yescharacteristic
115C2×D61#50111yescharacteristic
116#6923—81no—
117#6923—161no—
118C4×C61#38911yescharacteristic
119C4×C61#44211yescharacteristic
120Dic61#46811yescharacteristic
121Dic61#50111yescharacteristic
122#2161—611no—
123C2×#365—611no—
124#2110—611no—
125#1953—611no—
126#1951—611no—
127#1385—611no—
128#1383—611no—
129C2×C61—21no—
130C2×C61#194311yescharacteristic
131D61—21no—
132D61—21no—
133C2×M32—611no—
134C2×M32—611no—
135#430—1221no—
136C2×#108—611no—
137C2×#108—611no—
138C2×#108—611no—
139#428—1221no—
140C2×#106—611no—
141#405—611no—
142#368—611no—
143#368—611no—
144#368—611no—
145#368#692311yescharacteristic, complemented
146#365—1221no—
147#365—1221no—
148#347—1221no—
149#347—1221no—
150#344—1221no—
151#343—1221no—
152C61#1317511yescharacteristic, complemented, Sylow
153C2×M16—611no—
154C2×M16—1221no—
155C2×M16—1221no—
156C2×M16—1221no—
157C22×C8—611no—
158#117—611no—
159C2×C4⋊C4—1221no—
160M32—611no—
161M32—611no—
162M32—611no—
163M32—611no—
164M32—1221no—
165M32—1221no—
166C2×C16—611no—
167C2×C16—612no—
168C2×C16C2×#692311yescharacteristic
169#108—611no—
170#108—611no—
171#108—1221no—
172#108—1221no—
173#108—1221no—
174#108—1221no—
175#108—2441no—
176#108—2441no—
177#108C2×#692311yescharacteristic
178#108C2×#692311yescharacteristic
179#107—2441no—
180#106—1221no—
181#106—1221no—
182#106—2441no—
183#97—1221no—
184C4×C8—1221no—
185C22×C4—611no—
186C22×C4—2441no—
187M16—21no—
188M16—21no—
189M16—1221no—
190M16—1221no—
191M16—1221no—
192M16—1221no—
193M16—2441no—
194M16—2441no—
195M16—2441no—
196M16—2441no—
197C2×C8—611no—
198C2×C8—611no—
199C2×C8—611no—
200C2×C8—611no—
201C2×C8—611no—
202C2×C8—1221no—
203C2×C8—2441no—
204C2×C8—2441no—
205C2×C8—2441no—
206C2×C8C22×#692311yescharacteristic
207C4⋊C4—1221no—
208C4⋊C4—2441no—
209C4⋊C4—2441no—
210C22⋊C4—1221no—
211C42—1221no—
212C16—611no—
213C16—611no—
214C16—1222no—
215C16C4⋊#692311yescharacteristic
216C16C4⋊#692311yescharacteristic
217C23—611no—
218C2×C4—611no—
219C2×C4—611no—
220C2×C4—611no—
221C2×C4—611no—
222C2×C4—611no—
223C2×C4—9761no—
224C2×C4—4881no—
225C2×C4—2441no—
226C2×C4D4×#692311yescharacteristic
227C8—41no—
228C8—41no—
229C8—611no—
230C8—611no—
231C8—4881no—
232C8—2441no—
233C8—2441no—
234C8—2441no—
235C8C2×C4⋊#692311yescharacteristic
236C8Q8×#692311yescharacteristic
237C22—611no—
238C22—611no—
239C22—2441no—
240C22#1684080211yescharacteristic
241C4—611no—
242C4—611no—
243C4—9761no—
244C4—4881no—
245C4#1684071311yescharacteristic
246C4#1684080311yescharacteristic
247C2—21no—
248C2—1221no—
249C2—1221no—
250C2#2146192411yescharacteristic
subgroupG/H
centerC2#21461924
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#368C4
socleC2×C61#1943
prime radicalC22×D61#137
cosocleC2×C8×D61C23
hypercenter#368#6923
hypocenterC61#13175
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #368

Complements

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

NH ≅ G/Ntype
23. #16839592C4semidirect
24. #16839591C4semidirect
25. #16839591C4semidirect
26. C61×#368C4semidirect
145. #368#6923semidirect
152. C61#13175semidirect

Maximal subgroups

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

subgroupindex
C2×#168406862
#214620382
#214619382
#214619362
#214608882
#214608852
#214476122
#1317561