Finite Group Databasebeta

← C101×#7802 #38789953

Subgroups — C101×#7802 #38789953

Order 25856.

366 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2809C211yesmaximal, characteristic
2C101×#2096C211yesmaximal, characteristic
3C101×#2083C212yesmaximal
4C101×#1272C211yesmaximal, characteristic
5C101×#1271C212yesmaximal
6C2×#107×C101—22no—
7C2×#106×C101—21no—
8C2×#103×C101—21no—
9#400×C101—21no—
10#398×C101—22no—
11#391×C101—21no—
12#391×C101C2211yescharacteristic
13#389×C101C2212yes—
14#387×C101—22no—
15#384×C101C2211yescharacteristic
16#340×C101—22no—
17#336×C101C2211yescharacteristic
18#336×C101C2212yes—
19C22×Q8×C101D411yescharacteristic
20C22×C8×C101—21no—
21C22×C8×C101—22no—
22C2×C4⋊C4×C101—22no—
23C2×C4⋊C4×C101—21no—
24C2×C4⋊C4×C101—22no—
25C2×C4⋊C4×C101—21no—
26C2×C4⋊C4×C101—21no—
27C2×C4⋊C4×C101D412yes—
28C2×C4⋊C4×C101D411yescharacteristic
29C2×C4⋊C4×C101D412yes—
30C2×C42×C101—21no—
31C2×C42×C101C2311yescharacteristic
32#107×C101—44no—
33#106×C101—42no—
34#103×C101—42no—
35#95×C101—22no—
36#95×C101—22no—
37#95×C101—21no—
38#95×C101—22no—
39#95×C101—22no—
40C2×Q8×C101—21no—
41C2×Q8×C101—41no—
42C2×Q8×C101—41no—
43C2×Q8×C101Q1612yes—
44C22×C4×C101—21no—
45C22×C4×C101—21no—
46C22×C4×C101—22no—
47C22×C4×C101—22no—
48C22×C4×C101—41no—
49C22×C4×C101C2×D411yescharacteristic
50C22×C4×C101C2×D412yes—
51C2×C8×C101—22no—
52C2×C8×C101—24no—
53C2×C8×C101—42no—
54C2×C8×C101—41no—
55C2×C8×C101—42no—
56C2×C8×C101—41no—
57C4⋊C4×C101—22no—
58C4⋊C4×C101—22no—
59C4⋊C4×C101—41no—
60C4⋊C4×C101—42no—
61C4⋊C4×C101—41no—
62C4⋊C4×C101—41no—
63C4⋊C4×C101—42no—
64C4⋊C4×C101—42no—
65C4⋊C4×C101—42no—
66C4⋊C4×C101—42no—
67C4⋊C4×C101—81no—
68C4⋊C4×C101—81no—
69C42×C101—41no—
70C42×C101—81no—
71C23×C101#12011yescharacteristic
72Q8×C101—42no—
73Q8×C101—81no—
74C2×C4×C101—21no—
75C2×C4×C101—22no—
76C2×C4×C101—22no—
77C2×C4×C101—21no—
78C2×C4×C101—22no—
79C2×C4×C101—41no—
80C2×C4×C101—41no—
81C2×C4×C101—42no—
82C2×C4×C101—42no—
83C2×C4×C101—42no—
84C2×C4×C101—41no—
85C2×C4×C101—42no—
86C2×C4×C101—42no—
87C2×C4×C101—42no—
88C2×C4×C101—42no—
89C2×C4×C101—82no—
90C2×C4×C101—81no—
91C2×C4×C101C2×Q1611yescharacteristic
92C2×C4×C101#13512yes—
93C2×C4×C101AGL(1,ℤ/8)12yes—
94C2×C4×C101#13711yescharacteristic
95C8×C101—44no—
96C8×C101—42no—
97C22×C101#44912yes—
98C22×C101#45111yescharacteristic
99C22×C101#45311yescharacteristic
100C22×C101#45612yes—
101C22×C101#45811yescharacteristic
102C4×C101—22no—
103C4×C101—22no—
104C4×C101—21no—
105C4×C101—21no—
106C4×C101—42no—
107C4×C101—82no—
108C4×C101—82no—
109C4×C101—81no—
110C4×C101—161no—
111#7802C10111yesmaximal, characteristic, direct product factor, Sylow
112C2×C101#160912yes—
113C2×C101#161411yescharacteristic
114C2×C101#162411yescharacteristic
115C2×C101#164812yes—
116C2×C101#166011yescharacteristic
117#2809C2×C10111yescharacteristic
118#2096C2×C10111yescharacteristic
119#2083C2×C10112yes—
120#1272C2×C10111yescharacteristic
121#1271C2×C10112yes—
122C101#780211yescharacteristic, direct product factor, Sylow
123C2×#107—22no—
124C2×#106—21no—
125C2×#103—21no—
126#400—21no—
127#398—22no—
128#391—21no—
129#391C22×C10111yescharacteristic
130#389C22×C10112yes—
131#387—22no—
132#384C22×C10111yescharacteristic
133#340—22no—
134#336C22×C10112yes—
135#336C22×C10111yescharacteristic
136C22×Q8D4×C10111yescharacteristic
137C22×C8—22no—
138C22×C8—21no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4D4×C10112yes—
145C2×C4⋊C4D4×C10112yes—
146C2×C4⋊C4D4×C10111yescharacteristic
147C2×C42—21no—
148C2×C42C23×C10111yescharacteristic
149#107—44no—
150#106—42no—
151#103—42no—
152#95—21no—
153#95—22no—
154#95—22no—
155#95—22no—
156#95—22no—
157C2×Q8—21no—
158C2×Q8—41no—
159C2×Q8—41no—
160C2×Q8Q16×C10112yes—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—22no—
164C22×C4—22no—
165C22×C4—41no—
166C22×C4C2×D4×C10111yescharacteristic
167C22×C4C2×D4×C10112yes—
168C2×C8—22no—
169C2×C8—24no—
170C2×C8—42no—
171C2×C8—41no—
172C2×C8—42no—
173C2×C8—41no—
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—41no—
177C4⋊C4—42no—
178C4⋊C4—41no—
179C4⋊C4—41no—
180C4⋊C4—42no—
181C4⋊C4—42no—
182C4⋊C4—42no—
183C4⋊C4—42no—
184C4⋊C4—81no—
185C4⋊C4—81no—
186C42—41no—
187C42—81no—
188C23#120×C10111yescharacteristic
189Q8—42no—
190Q8—81no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—41no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—82no—
207C2×C4—81no—
208C2×C4C2×Q16×C10111yescharacteristic
209C2×C4#135×C10112yes—
210C2×C4AGL(1,ℤ/8)×C10112yes—
211C2×C4#137×C10111yescharacteristic
212C8—44no—
213C8—42no—
214C22#449×C10112yes—
215C22#451×C10111yescharacteristic
216C22#453×C10111yescharacteristic
217C22#456×C10112yes—
218C22#458×C10111yescharacteristic
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—42no—
224C4—82no—
225C4—81no—
226C4—82no—
227C4—161no—
228C2C101×#160912yes—
229C2C101×#161411yescharacteristic
230C2C101×#162411yescharacteristic
231C2C101×#164812yes—
232C2C101×#166011yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C101#120
commutator, Frattini, cosocleC2×C42C23×C101
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C101 ◁ C2×C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
111. #7802C101direct (N × H)
122. C101#7802direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#28092
C101×#20962
C101×#20832
C101×#12722
C101×#12712
#7802101