Finite Group Databasebeta

← C107×#7491 #41033455

Subgroups — C107×#7491 #41033455

Order 27392.

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

normal subgroups only

This group has 276 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×#356×C107C211yesmaximal, characteristic
2C107×#1886C211yesmaximal, characteristic
3C2×#333×C107C211yesmaximal, characteristic
4C2×C4⋊Q8×C107C2211yescharacteristic
5#519×C107C411yescharacteristic
6C2×C4⋊C8×C107—21no—
7#419×C107—21no—
8C2×#101×C107—21no—
9C2×#101×C107C411yescharacteristic
10#356×C107—21no—
11#356×C107C412yescomplemented
12#339×C107—21no—
13#333×C107—21no—
14#333×C107C412yescomplemented
15C22×Q8×C107C2×C411yescharacteristic
16C22×Q8×C107D411yescharacteristic
17C2×M16×C107—21no—
18C2×M16×C107—41no—
19C22×C8×C107—41no—
20C4⋊Q8×C107—41no—
21C4⋊Q8×C107C2×C411yescharacteristic
22C4⋊Q8×C107C2×C411yescharacteristic
23C4⋊Q8×C107D411yescharacteristic
24C4⋊Q8×C107Q811yescharacteristic
25C4×Q8×C107—42no—
26#117×C107—21no—
27#117×C107—41no—
28C2×C4⋊C4×C107—41no—
29C2×C42×C107D411yescharacteristic
30C4⋊C8×C107—22no—
31C4⋊C8×C107—41no—
32#103×C107—42no—
33#101×C107—22no—
34#101×C107—41no—
35#101×C107—41no—
36C2×Q8×C107—21no—
37C2×Q8×C107—21no—
38C2×Q8×C107—41no—
39C2×Q8×C107—41no—
40C2×Q8×C107—41no—
41C2×Q8×C107—41no—
42C2×Q8×C107C4211yescharacteristic
43C2×Q8×C107C22⋊C411yescharacteristic
44C2×Q8×C107C4⋊C411yescharacteristic
45C2×Q8×C107C4⋊C411yescharacteristic
46C22×C4×C107—21no—
47C22×C4×C107—21no—
48C22×C4×C107—21no—
49C22×C4×C107C22⋊C411yescharacteristic
50M16×C107—42no—
51M16×C107—41no—
52M16×C107—41no—
53M16×C107—81no—
54C2×C8×C107—41no—
55C2×C8×C107—42no—
56C2×C8×C107—82no—
57C2×C8×C107—81no—
58C4⋊C4×C107—22no—
59C4⋊C4×C107—41no—
60C4⋊C4×C107—41no—
61C4⋊C4×C107—41no—
62C4⋊C4×C107—41no—
63C4⋊C4×C107—42no—
64C22⋊C4×C107—41no—
65C42×C107—21no—
66C42×C107—41no—
67C42×C107—42no—
68C42×C107C22⋊C411yescharacteristic
69C42×C107C4⋊C411yescharacteristic
70C23×C107#9911yescharacteristic
71Q8×C107—41no—
72Q8×C107—41no—
73Q8×C107—41no—
74Q8×C107—41no—
75Q8×C107—42no—
76Q8×C107—81no—
77C2×C4×C107—22no—
78C2×C4×C107—22no—
79C2×C4×C107—21no—
80C2×C4×C107—21no—
81C2×C4×C107—21no—
82C2×C4×C107—21no—
83C2×C4×C107—21no—
84C2×C4×C107—21no—
85C2×C4×C107—21no—
86C2×C4×C107—21no—
87C2×C4×C107—41no—
88C2×C4×C107—41no—
89C2×C4×C107—41no—
90C2×C4×C107—41no—
91C2×C4×C107—42no—
92C2×C4×C107#9511yescharacteristic
93C2×C4×C107#9911yescharacteristic
94C8×C107—82no—
95C8×C107—81no—
96C8×C107—82no—
97C22×C107—22no—
98C22×C107#34211yescharacteristic
99C22×C107AΣL(1,𝔽16)11yescharacteristic
100C22×C107#35211yescharacteristic
101C4×C107—21no—
102C4×C107—22no—
103C4×C107—21no—
104C4×C107—21no—
105C4×C107—21no—
106C4×C107—41no—
107C4×C107—41no—
108C4×C107—41no—
109C4×C107—41no—
110C4×C107—82no—
111#7491C10711yesmaximal, characteristic, direct product factor, Sylow
112C2×C107—21no—
113C2×C107—21no—
114C2×C107#139011yescharacteristic
115C2×C107#140512yes—
116C2×#356C2×C10711yescharacteristic
117#1886C2×C10711yescharacteristic
118C2×#333C2×C10711yescharacteristic
119C107#749111yescharacteristic, direct product factor, Sylow
120C2×C4⋊Q8C22×C10711yescharacteristic
121#519C4×C10711yescharacteristic
122C2×C4⋊C8—21no—
123#419—21no—
124C2×#101—21no—
125C2×#101C4×C10711yescharacteristic
126#356—21no—
127#356C4×C10712yescomplemented
128#339—21no—
129#333—21no—
130#333C4×C10712yescomplemented
131C22×Q8C2×C4×C10711yescharacteristic
132C22×Q8D4×C10711yescharacteristic
133C2×M16—21no—
134C2×M16—41no—
135C22×C8—41no—
136C4⋊Q8—41no—
137C4⋊Q8C2×C4×C10711yescharacteristic
138C4⋊Q8C2×C4×C10711yescharacteristic
139C4⋊Q8D4×C10711yescharacteristic
140C4⋊Q8Q8×C10711yescharacteristic
141C4×Q8—42no—
142#117—21no—
143#117—41no—
144C2×C4⋊C4—41no—
145C2×C42D4×C10711yescharacteristic
146C4⋊C8—22no—
147C4⋊C8—41no—
148#103—42no—
149#101—22no—
150#101—41no—
151#101—41no—
152C2×Q8—21no—
153C2×Q8—21no—
154C2×Q8—41no—
155C2×Q8—41no—
156C2×Q8—41no—
157C2×Q8—41no—
158C2×Q8C42×C10711yescharacteristic
159C2×Q8C22⋊C4×C10711yescharacteristic
160C2×Q8C4⋊C4×C10711yescharacteristic
161C2×Q8C4⋊C4×C10711yescharacteristic
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4C22⋊C4×C10711yescharacteristic
166M16—42no—
167M16—41no—
168M16—41no—
169M16—81no—
170C2×C8—41no—
171C2×C8—42no—
172C2×C8—82no—
173C2×C8—81no—
174C4⋊C4—22no—
175C4⋊C4—41no—
176C4⋊C4—41no—
177C4⋊C4—41no—
178C4⋊C4—41no—
179C4⋊C4—42no—
180C22⋊C4—41no—
181C42—21no—
182C42—41no—
183C42—42no—
184C42C22⋊C4×C10711yescharacteristic
185C42C4⋊C4×C10711yescharacteristic
186C23#99×C10711yescharacteristic
187Q8—41no—
188Q8—41no—
189Q8—41no—
190Q8—41no—
191Q8—42no—
192Q8—81no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—42no—
208C2×C4#95×C10711yescharacteristic
209C2×C4#99×C10711yescharacteristic
210C8—82no—
211C8—81no—
212C8—82no—
213C22—22no—
214C22#342×C10711yescharacteristic
215C22AΣL(1,𝔽16)×C10711yescharacteristic
216C22#352×C10711yescharacteristic
217C4—21no—
218C4—22no—
219C4—21no—
220C4—21no—
221C4—21no—
222C4—41no—
223C4—41no—
224C4—41no—
225C4—41no—
226C4—82no—
227C2—21no—
228C2—21no—
229C2C107×#139011yescharacteristic
230C2C107×#140512yes—
subgroupG/H
center, socleC22×C107AΣL(1,𝔽16)
commutatorC2×Q8C42×C107
Frattini, cosocleC2×C4⋊Q8C22×C107
prime radicalC23×C107#99
LCSG ▷ C2×Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C107 ◁ C23×C107 ◁ C22×C4×C107 ◁ C2×C4⋊Q8×C107 ◁ G

Complements

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

NH ≅ G/Ntype
11. #356×C107C4semidirect
14. #333×C107C4semidirect
111. #7491C107direct (N × H)
119. C107#7491direct (N × H)
127. #356C4×C107semidirect
130. #333C4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#356×C1072
C107×#18862
C2×#333×C1072
#7491107