Finite Group Databasebeta

← C107×#7504 #41033468

Subgroups — C107×#7504 #41033468

Order 27392.

336 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 70 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×#353×C107C212yesmaximal
2C107×#1961C211yesmaximal, characteristic
3C2×#127×C107C2211yescharacteristic
4C2×#102×C107—22no—
5C2×#99×C107—22no—
6C2×#97×C107C411yescharacteristic, complemented
7#382×C107C411yescharacteristic, complemented
8#353×C107—22no—
9#353×C107C414yescomplemented
10C22×D4×C107—41no—
11C22×D4×C107D412yes—
12C22×C8×C107—21no—
13#127×C107—41no—
14#127×C107C2×C412yes—
15#127×C107D411yescharacteristic
16#127×C107Q811yescharacteristic
17C2×C4⋊C4×C107—21no—
18C2×C22⋊C4×C107—42no—
19C2×C42×C107C2×C411yescharacteristic
20#102×C107—44no—
21#99×C107—24no—
22#99×C107—42no—
23#97×C107—41no—
24#95×C107—41no—
25C24×C107—22no—
26C2×D4×C107—22no—
27C2×D4×C107—42no—
28C2×D4×C107—42no—
29C2×D4×C107—42no—
30C2×D4×C107—41no—
31C2×D4×C107—41no—
32C2×D4×C107—84no—
33C2×D4×C107C22⋊C412yes—
34C2×D4×C107C4⋊C412yes—
35C22×C4×C107—21no—
36C22×C4×C107—41no—
37C22×C4×C107—82no—
38C22×C4×C107C22⋊C411yescharacteristic
39C2×C8×C107—22no—
40C2×C8×C107—41no—
41C2×C8×C107—41no—
42C4⋊C4×C107—42no—
43C22⋊C4×C107—44no—
44C22⋊C4×C107—82no—
45C42×C107—21no—
46C42×C107C4211yescharacteristic
47C42×C107C4⋊C411yescharacteristic
48C23×C107—22no—
49C23×C107—22no—
50C23×C107—42no—
51C23×C107—42no—
52C23×C107—84no—
53C23×C107#9911yescharacteristic
54D4×C107—42no—
55D4×C107—42no—
56D4×C107—82no—
57D4×C107—84no—
58D4×C107—82no—
59D4×C107—82no—
60C2×C4×C107—21no—
61C2×C4×C107—21no—
62C2×C4×C107—21no—
63C2×C4×C107—21no—
64C2×C4×C107—42no—
65C2×C4×C107—82no—
66C2×C4×C107—84no—
67C2×C4×C107—81no—
68C2×C4×C107—164no—
69C2×C4×C107#9511yescharacteristic
70C2×C4×C107#9911yescharacteristic
71C8×C107—42no—
72C22×C107—22no—
73C22×C107—42no—
74C22×C107—42no—
75C22×C107—82no—
76C22×C107—82no—
77C22×C107—84no—
78C22×C107—162no—
79C22×C107#34211yescharacteristic
80C22×C107#35311yescharacteristic
81C22×C107#35411yescharacteristic
82C4×C107—21no—
83C4×C107—21no—
84C4×C107—41no—
85C4×C107—41no—
86C4×C107—161no—
87C4×C107—164no—
88#7504C10711yesmaximal, characteristic, direct product factor, Sylow
89C2×C107—21no—
90C2×C107—21no—
91C2×C107—82no—
92C2×C107—82no—
93C2×C107#139311yescharacteristic
94C2×C107#141212yes—
95C2×#353C2×C10712yes—
96#1961C2×C10711yescharacteristic
97C107#750411yescharacteristic, direct product factor, Sylow
98C2×#127C22×C10711yescharacteristic
99C2×#102—22no—
100C2×#99—22no—
101C2×#97C4×C10711yescharacteristic, complemented
102#382C4×C10711yescharacteristic, complemented
103#353—22no—
104#353C4×C10714yescomplemented
105C22×D4—41no—
106C22×D4D4×C10712yes—
107C22×C8—21no—
108#127—41no—
109#127C2×C4×C10712yes—
110#127D4×C10711yescharacteristic
111#127Q8×C10711yescharacteristic
112C2×C4⋊C4—21no—
113C2×C22⋊C4—42no—
114C2×C42C2×C4×C10711yescharacteristic
115#102—44no—
116#99—24no—
117#99—42no—
118#97—41no—
119#95—41no—
120C24—22no—
121C2×D4—22no—
122C2×D4—42no—
123C2×D4—42no—
124C2×D4—42no—
125C2×D4—41no—
126C2×D4—41no—
127C2×D4—84no—
128C2×D4C22⋊C4×C10712yes—
129C2×D4C4⋊C4×C10712yes—
130C22×C4—21no—
131C22×C4—41no—
132C22×C4—82no—
133C22×C4C22⋊C4×C10711yescharacteristic
134C2×C8—22no—
135C2×C8—41no—
136C2×C8—41no—
137C4⋊C4—42no—
138C22⋊C4—44no—
139C22⋊C4—82no—
140C42—21no—
141C42C42×C10711yescharacteristic
142C42C4⋊C4×C10711yescharacteristic
143C23—22no—
144C23—22no—
145C23—42no—
146C23—42no—
147C23—84no—
148C23#99×C10711yescharacteristic
149D4—42no—
150D4—42no—
151D4—82no—
152D4—84no—
153D4—82no—
154D4—82no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—42no—
160C2×C4—82no—
161C2×C4—84no—
162C2×C4—81no—
163C2×C4—164no—
164C2×C4#95×C10711yescharacteristic
165C2×C4#99×C10711yescharacteristic
166C8—42no—
167C22—22no—
168C22—42no—
169C22—42no—
170C22—82no—
171C22—82no—
172C22—84no—
173C22—162no—
174C22#342×C10711yescharacteristic
175C22#353×C10711yescharacteristic
176C22#354×C10711yescharacteristic
177C4—21no—
178C4—21no—
179C4—41no—
180C4—41no—
181C4—161no—
182C4—164no—
183C2—21no—
184C2—21no—
185C2—82no—
186C2—82no—
187C2C107×#139311yescharacteristic
188C2C107×#141212yes—
subgroupG/H
center, socleC22×C107#354
commutatorC42C42×C107
Frattini, cosocleC2×#127C22×C107
prime radicalC2×#127×C107C22
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C107 ◁ C23×C107 ◁ C22×C4×C107 ◁ C2×#127×C107 ◁ G

Complements

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

NH ≅ G/Ntype
6. C2×#97×C107C4semidirect
7. #382×C107C4semidirect
9. #353×C107C4semidirect
88. #7504C107direct (N × H)
97. C107#7504direct (N × H)
101. C2×#97C4×C107semidirect
102. #382C4×C107semidirect
104. #353C4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#353×C1072
C107×#19612
#7504107