Finite Group Databasebeta

← C107×#1852 #28332535

Subgroups — C107×#1852 #28332535

Order 13696.

360 conjugacy classes of subgroups; only the 144 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 144 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
1C22×C4⋊C4×C107C211yesmaximal, characteristic
2C2×#107×C107C212yesmaximal, complemented
3C2×C22⋊C8×C107C211yesmaximal, characteristic
4#380×C107C211yesmaximal, characteristic
5#340×C107C212yesmaximal, complemented
6C23×C4×C107—21no—
7C23×C4×C107C2211yescharacteristic
8C22×C8×C107C2212yes—
9C2×C4⋊C4×C107—21no—
10C2×C4⋊C4×C107—24no—
11C2×C4⋊C4×C107C2211yescharacteristic
12C2×C4⋊C4×C107C2211yescharacteristic
13C2×C4⋊C4×C107C2212yes—
14C2×C22⋊C4×C107—21no—
15#107×C107—24no—
16C22⋊C8×C107C414yescomplemented
17#95×C107—21no—
18C24×C107D411yescharacteristic
19C22×C4×C107—22no—
20C22×C4×C107—22no—
21C22×C4×C107—24no—
22C22×C4×C107—22no—
23C22×C4×C107—21no—
24C22×C4×C107—21no—
25C22×C4×C107—42no—
26C22×C4×C107—42no—
27C22×C4×C107C2×C412yes—
28C22×C4×C107D411yescharacteristic
29C22×C4×C107Q812yes—
30C22×C4×C107C2311yescharacteristic
31C2×C8×C107—22no—
32C2×C8×C107—22no—
33C2×C8×C107C2×C414yescomplemented
34C4⋊C4×C107—24no—
35C4⋊C4×C107—22no—
36C4⋊C4×C107—22no—
37C4⋊C4×C107—22no—
38C4⋊C4×C107D414yes—
39C22⋊C4×C107—42no—
40C23×C107—21no—
41C23×C107—21no—
42C23×C107—21no—
43C23×C107—21no—
44C23×C107C4⋊C412yes—
45C23×C107D812yes—
46C23×C107Q1612yes—
47C23×C107C2×D411yescharacteristic
48C2×C4×C107—21no—
49C2×C4×C107—21no—
50C2×C4×C107—24no—
51C2×C4×C107—24no—
52C2×C4×C107—24no—
53C2×C4×C107—48no—
54C2×C4×C107—42no—
55C2×C4×C107—42no—
56C2×C4×C107—41no—
57C2×C4×C107—41no—
58C2×C4×C107—41no—
59C2×C4×C107—41no—
60C2×C4×C107—41no—
61C2×C4×C107—41no—
62C2×C4×C107C4⋊C412yes—
63C2×C4×C107C22×C411yescharacteristic
64C2×C4×C107C2×D412yes—
65C2×C4×C107C2×Q811yescharacteristic
66C2×C4×C107#4112yes—
67C8×C107—24no—
68C22×C107—22no—
69C22×C107—22no—
70C22×C107—22no—
71C22×C107—22no—
72C22×C107—22no—
73C22×C107—22no—
74C22×C107#10714yescomplemented
75C22×C107C2×C4⋊C411yescharacteristic
76C22×C107#12011yescharacteristic
77C22×C107#12311yescharacteristic
78C22×C107C2×D811yescharacteristic
79C22×C107C2×Q1611yescharacteristic
80C22×C107AGL(1,ℤ/8)11yescharacteristic
81C22×C107#13711yescharacteristic
82C4×C107—22no—
83C4×C107—44no—
84C4×C107—81no—
85C4×C107—81no—
86C4×C107C4×D412yes—
87C4×C107C22⋊Q812yes—
88C2×C107—24no—
89C2×C107#38511yescharacteristic
90C2×C107C2×#10711yescharacteristic
91C2×C107#42811yescharacteristic
92C2×C107#44711yescharacteristic
93C2×C107#45111yescharacteristic
94C2×C107#48011yescharacteristic
95C2×C107#48411yescharacteristic
96#1852C10711yesmaximal, characteristic, direct product factor, Sylow
97C107#185211yescharacteristic, direct product factor, Sylow
98C22×C4⋊C4C2×C10711yescharacteristic
99C2×#107C2×C10712yescomplemented
100C2×C22⋊C8C2×C10711yescharacteristic
101#380C2×C10711yescharacteristic
102#340C2×C10712yescomplemented
103C23×C4—21no—
104C23×C4C22×C10711yescharacteristic
105C22×C8C22×C10712yes—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—24no—
108C2×C4⋊C4C22×C10711yescharacteristic
109C2×C4⋊C4C22×C10711yescharacteristic
110C2×C4⋊C4C22×C10712yes—
111C2×C22⋊C4—21no—
112#107—24no—
113C22⋊C8C4×C10714yescomplemented
114#95—21no—
115C24D4×C10711yescharacteristic
116C22×C4—22no—
117C22×C4—22no—
118C22×C4—24no—
119C22×C4—22no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—42no—
123C22×C4—42no—
124C22×C4C2×C4×C10712yes—
125C22×C4D4×C10711yescharacteristic
126C22×C4Q8×C10712yes—
127C22×C4C23×C10711yescharacteristic
128C2×C8—22no—
129C2×C8—22no—
130C2×C8C2×C4×C10714yescomplemented
131C4⋊C4—24no—
132C4⋊C4—22no—
133C4⋊C4—22no—
134C4⋊C4—22no—
135C4⋊C4D4×C10714yes—
136C22⋊C4—42no—
137C23—21no—
138C23—21no—
139C23—21no—
140C23—21no—
141C23C4⋊C4×C10712yes—
142C23D8×C10712yes—
143C23Q16×C10712yes—
144C23C2×D4×C10711yescharacteristic
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—24no—
148C2×C4—24no—
149C2×C4—24no—
150C2×C4—48no—
151C2×C4—42no—
152C2×C4—42no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4C4⋊C4×C10712yes—
160C2×C4C22×C4×C10711yescharacteristic
161C2×C4C2×D4×C10712yes—
162C2×C4C2×Q8×C10711yescharacteristic
163C2×C4#41×C10712yes—
164C8—24no—
165C22—22no—
166C22—22no—
167C22—22no—
168C22—22no—
169C22—22no—
170C22—22no—
171C22#107×C10714yescomplemented
172C22C2×C4⋊C4×C10711yescharacteristic
173C22#120×C10711yescharacteristic
174C22#123×C10711yescharacteristic
175C22C2×D8×C10711yescharacteristic
176C22C2×Q16×C10711yescharacteristic
177C22AGL(1,ℤ/8)×C10711yescharacteristic
178C22#137×C10711yescharacteristic
179C4—22no—
180C4—44no—
181C4—81no—
182C4—81no—
183C4C4×D4×C10712yes—
184C4C22⋊Q8×C10712yes—
185C2—24no—
186C2#385×C10711yescharacteristic
187C2C2×#107×C10711yescharacteristic
188C2#428×C10711yescharacteristic
189C2#447×C10711yescharacteristic
190C2#451×C10711yescharacteristic
191C2#480×C10711yescharacteristic
192C2#484×C10711yescharacteristic
subgroupG/H
center, socleC23×C107C2×D4
commutatorC2×C4C22×C4×C107
Frattini, cosocleC22×C4C23×C107
prime radicalC24×C107D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C23×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#107×C107C2semidirect
5. #340×C107C2semidirect
16. C22⋊C8×C107C4semidirect
33. C2×C8×C107C2×C4semidirect
74. C22×C107#107semidirect
96. #1852C107direct (N × H)
97. C107#1852direct (N × H)
99. C2×#107C2×C107semidirect
102. #340C2×C107semidirect
113. C22⋊C8C4×C107semidirect
130. C2×C8C2×C4×C107semidirect
171. C22#107×C107semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×C1072
C2×#107×C1072
C2×C22⋊C8×C1072
#380×C1072
#340×C1072
#1852107