Finite Group Databasebeta

← C101×#12364 #38794515

Subgroups — C101×#12364 #38794515

Order 25856.

358 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 78 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
1C101×#3291C211yesmaximal, characteristic
2C101×#2230C212yesmaximal, complemented
3C101×#1705C211yesmaximal, characteristic, complemented
4C101×#1359C211yesmaximal, characteristic, complemented
5C101×#1335C212yesmaximal, complemented
6#577×C101—22no—
7#498×C101—21no—
8#498×C101C2211yescharacteristic, complemented
9#492×C101—21no—
10#492×C101C2211yescharacteristic
11#471×C101—22no—
12#456×C101—21no—
13#453×C101—21no—
14#443×C101C2212yes—
15#365×C101—22no—
16#364×C101C2212yescomplemented
17#360×C101—22no—
18C82×C101C2211yescharacteristic, complemented
192−1+4×C101—21no—
20H(5,𝔽2)×C101—21no—
21#137×C101—22no—
22#137×C101—42no—
23AGL(1,ℤ/8)×C101—22no—
24AGL(1,ℤ/8)×C101—42no—
25#135×C101—42no—
26#135×C101D412yes—
27C2×SD16×C101—22no—
28C2×SD16×C101—42no—
29C2×SD16×C101—42no—
30#131×C101—22no—
31C4⋊Q8×C101—21no—
32C4⋊Q8×C101D411yescharacteristic
33#127×C101D411yescharacteristic
34M32×C101—22no—
35#108×C101D412yes—
36#106×C101—22no—
37#106×C101—42no—
38#104×C101—22no—
39#101×C101—21no—
40#100×C101—21no—
41C4×C8×C101—21no—
42C4×C8×C101C2311yescharacteristic
43#41×C101—22no—
44#41×C101—42no—
45#41×C101—42no—
46#41×C101—81no—
47C2×Q8×C101—21no—
48C2×Q8×C101—41no—
49C2×Q8×C101—42no—
50C2×D4×C101—21no—
51C2×D4×C101—41no—
52C2×D4×C101—42no—
53C2×D4×C101—81no—
54Q16×C101—42no—
55Q16×C101SD1612yescomplemented
56SD16×C101—22no—
57SD16×C101—42no—
58SD16×C101—42no—
59SD16×C101—42no—
60SD16×C101—42no—
61SD16×C101—84no—
62D8×C101—42no—
63D8×C101SD1612yescomplemented
64M16×C101—22no—
65M16×C101—42no—
66C2×C8×C101—22no—
67C2×C8×C101—42no—
68C2×C8×C101C2×D412yes—
69C4⋊C4×C101—41no—
70C4⋊C4×C101—41no—
71C4⋊C4×C101—41no—
72C42×C101C2×D411yescharacteristic
73C16×C101—42no—
74C23×C101—41no—
75C23×C101—81no—
76Q8×C101—22no—
77Q8×C101—42no—
78Q8×C101—82no—
79Q8×C101—81no—
80D4×C101—22no—
81D4×C101—42no—
82D4×C101—42no—
83D4×C101—82no—
84D4×C101—82no—
85D4×C101—81no—
86C2×C4×C101—21no—
87C2×C4×C101—42no—
88C2×C4×C101—41no—
89C2×C4×C101—81no—
90C2×C4×C101—82no—
91C2×C4×C101—81no—
92C2×C4×C101#12011yescharacteristic
93C8×C101—24no—
94C8×C101—42no—
95C8×C101C2×SD1612yes—
96C8×C101AGL(1,ℤ/8)12yes—
97C22×C101—42no—
98C22×C101—81no—
99C22×C101—161no—
100C22×C101—321no—
101C22×C101#45311yescharacteristic
102C4×C101—22no—
103C4×C101—42no—
104C4×C101—81no—
105C4×C101—161no—
106C4×C101#45012yes—
107#12364C10111yesmaximal, characteristic, direct product factor, Sylow
108C2×C101—21no—
109C2×C101—82no—
110C2×C101—161no—
111C2×C101#162911yescharacteristic
112#3291C2×C10111yescharacteristic
113#2230C2×C10112yescomplemented
114#1705C2×C10111yescharacteristic, complemented
115#1359C2×C10111yescharacteristic, complemented
116#1335C2×C10112yescomplemented
117C101#1236411yescharacteristic, direct product factor, Sylow
118#577—22no—
119#498—21no—
120#498C22×C10111yescharacteristic, complemented
121#492—21no—
122#492C22×C10111yescharacteristic
123#471—22no—
124#456—21no—
125#453—21no—
126#443C22×C10112yes—
127#365—22no—
128#364C22×C10112yescomplemented
129#360—22no—
130C82C22×C10111yescharacteristic, complemented
1312−1+4—21no—
132H(5,𝔽2)—21no—
133#137—22no—
134#137—42no—
135AGL(1,ℤ/8)—22no—
136AGL(1,ℤ/8)—42no—
137#135—42no—
138#135D4×C10112yes—
139C2×SD16—22no—
140C2×SD16—42no—
141C2×SD16—42no—
142#131—22no—
143C4⋊Q8—21no—
144C4⋊Q8D4×C10111yescharacteristic
145#127D4×C10111yescharacteristic
146M32—22no—
147#108D4×C10112yes—
148#106—22no—
149#106—42no—
150#104—22no—
151#101—21no—
152#100—21no—
153C4×C8—21no—
154C4×C8C23×C10111yescharacteristic
155#41—22no—
156#41—42no—
157#41—42no—
158#41—81no—
159C2×Q8—21no—
160C2×Q8—41no—
161C2×Q8—42no—
162C2×D4—21no—
163C2×D4—41no—
164C2×D4—42no—
165C2×D4—81no—
166Q16—42no—
167Q16SD16×C10112yescomplemented
168SD16—22no—
169SD16—42no—
170SD16—42no—
171SD16—42no—
172SD16—42no—
173SD16—84no—
174D8—42no—
175D8SD16×C10112yescomplemented
176M16—22no—
177M16—42no—
178C2×C8—22no—
179C2×C8—42no—
180C2×C8C2×D4×C10112yes—
181C4⋊C4—41no—
182C4⋊C4—41no—
183C4⋊C4—41no—
184C42C2×D4×C10111yescharacteristic
185C16—42no—
186C23—41no—
187C23—81no—
188Q8—22no—
189Q8—42no—
190Q8—82no—
191Q8—81no—
192D4—22no—
193D4—42no—
194D4—42no—
195D4—82no—
196D4—82no—
197D4—81no—
198C2×C4—21no—
199C2×C4—42no—
200C2×C4—41no—
201C2×C4—81no—
202C2×C4—82no—
203C2×C4—81no—
204C2×C4#120×C10111yescharacteristic
205C8—24no—
206C8—42no—
207C8C2×SD16×C10112yes—
208C8AGL(1,ℤ/8)×C10112yes—
209C22—42no—
210C22—81no—
211C22—161no—
212C22—321no—
213C22#453×C10111yescharacteristic
214C4—22no—
215C4—42no—
216C4—81no—
217C4—161no—
218C4#450×C10112yes—
219C2—21no—
220C2—82no—
221C2—161no—
222C2C101×#162911yescharacteristic
subgroupG/H
center, socleC2×C101#1629
commutator, Frattini, cosocleC4×C8C23×C101
prime radicalC101×#3291C2
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C101 ◁ C2×C4×C101 ◁ C4×C8×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#2230C2semidirect
3. C101×#1705C2semidirect
4. C101×#1359C2semidirect
5. C101×#1335C2semidirect
8. #498×C101C22semidirect
16. #364×C101C22semidirect
18. C82×C101C22semidirect
55. Q16×C101SD16semidirect
63. D8×C101SD16semidirect
107. #12364C101direct (N × H)
113. #2230C2×C101semidirect
114. #1705C2×C101semidirect
115. #1359C2×C101semidirect
116. #1335C2×C101semidirect
117. C101#12364direct (N × H)
120. #498C22×C101semidirect
128. #364C22×C101semidirect
130. C82C22×C101semidirect
167. Q16SD16×C101semidirect
175. D8SD16×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#32912
C101×#22302
C101×#17052
C101×#13592
C101×#13352
#12364101