Finite Group Databasebeta

← C107×#13466 #41039430

Subgroups — C107×#13466 #41039430

Order 27392.

314 conjugacy classes of subgroups.

The subgroup lattice has 284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#2155C211yesmaximal, characteristic, complemented
2C107×#2150C211yesmaximal, characteristic, complemented
3C107×#2145C211yesmaximal, characteristic
4C107×#2143C211yesmaximal, characteristic
5C107×#1974C211yesmaximal, characteristic
6C107×#1945C211yesmaximal, characteristic, complemented
7C107×#1388C211yesmaximal, characteristic, complemented
8C2×#135×C107C2211yescharacteristic
9C2×M32×C107C2211yescharacteristic
10C2×M32×C107C2211yescharacteristic
11C2×#108×C107C2211yescharacteristic
12C2×#108×C107C2211yescharacteristic
13#427×C107C2211yescharacteristic
14#424×C107—21no—
15C2×#104×C107—21no—
16#408×C107—21no—
17C2×C4×C8×C107C2211yescharacteristic
18#365×C107—22no—
19C4⋊C16×C107—22no—
20#360×C107—22no—
21#359×C107—22no—
22#339×C107—21no—
23C2×#41×C107—21no—
24#135×C107—21no—
25#135×C107—21no—
26#135×C107—21no—
27#135×C107—21no—
28C2×Q16×C107Q811yescharacteristic
29C2×SD16×C107—21no—
30C2×D8×C107Q811yescharacteristic
31C2×M16×C107—21no—
32C2×M16×C107—21no—
33C22×C8×C107D411yescharacteristic
34C22×C8×C107C2311yescharacteristic
35#117×C107—21no—
36C2×C42×C107D411yescharacteristic
37M32×C107—21no—
38M32×C107—21no—
39M32×C107—21no—
40M32×C107—21no—
41C2×C16×C107—21no—
42C2×C16×C107D412yes—
43#108×C107—21no—
44#108×C107—21no—
45#108×C107—21no—
46#108×C107—21no—
47#107×C107—21no—
48#106×C107D412yes—
49C4⋊C8×C107—42no—
50#104×C107—41no—
51#104×C107—41no—
52C22⋊C8×C107—42no—
53C4×C8×C107—21no—
54C4×C8×C107—21no—
55#41×C107—41no—
56#41×C107—41no—
57#41×C107—41no—
58#41×C107—41no—
59C2×Q8×C107—21no—
60C2×D4×C107—21no—
61C2×D4×C107—41no—
62C22×C4×C107—21no—
63C22×C4×C107—41no—
64C22×C4×C107C2×D411yescharacteristic
65Q16×C107—21no—
66Q16×C107—21no—
67SD16×C107—41no—
68SD16×C107—41no—
69D8×C107—21no—
70D8×C107—21no—
71M16×C107—41no—
72M16×C107—41no—
73M16×C107—41no—
74M16×C107—41no—
75C2×C8×C107—21no—
76C2×C8×C107—21no—
77C2×C8×C107—21no—
78C2×C8×C107—41no—
79C2×C8×C107—41no—
80C2×C8×C107C2×D411yescharacteristic
81C2×C8×C107C2×D411yescharacteristic
82C2×C8×C107C2×Q811yescharacteristic
83C2×C8×C107#4111yescharacteristic
84C2×C8×C107#4111yescharacteristic
85C2×C8×C107#4111yescharacteristic
86C4⋊C4×C107—22no—
87C22⋊C4×C107—41no—
88C42×C107—21no—
89C42×C107—41no—
90C42×C107SD1611yescharacteristic
91C42×C107SD1611yescharacteristic
92C16×C107—22no—
93C16×C107—41no—
94C23×C107—41no—
95C23×C107#13511yescharacteristic
96Q8×C107—41no—
97Q8×C107—41no—
98D4×C107—41no—
99D4×C107—41no—
100D4×C107—81no—
101D4×C107—81no—
102C2×C4×C107—21no—
103C2×C4×C107—21no—
104C2×C4×C107—42no—
105C2×C4×C107—42no—
106C2×C4×C107—41no—
107C2×C4×C107—81no—
108C2×C4×C107—81no—
109C2×C4×C107#12111yescharacteristic
110C2×C4×C107#12111yescharacteristic
111C2×C4×C107C22⋊Q811yescharacteristic
112C2×C4×C107C2×SD1611yescharacteristic
113C2×C4×C107AGL(1,ℤ/8)11yescharacteristic
114C2×C4×C107AGL(1,ℤ/8)11yescharacteristic
115C8×C107—41no—
116C8×C107—81no—
117C8×C107—81no—
118C8×C107#12111yescharacteristic
119C8×C107C22⋊Q811yescharacteristic
120C8×C107C22⋊Q811yescharacteristic
121C8×C107#12611yescharacteristic
122C22×C107—41no—
123C22×C107—82no—
124C22×C107—81no—
125C22×C107#46311yescharacteristic
126C22×C107#46511yescharacteristic
127C22×C107#47811yescharacteristic
128C4×C107—22no—
129C4×C107—41no—
130C4×C107—82no—
131C4×C107—81no—
132C4×C107#39611yescharacteristic
133C4×C107#46011yescharacteristic
134C4×C107#46911yescharacteristic
135C4×C107#47611yescharacteristic
136#13466C10711yesmaximal, characteristic, direct product factor, Sylow
137C2×C107—21no—
138C2×C107—21no—
139C2×C107—21no—
140C2×C107—161no—
141C2×C107#206511yescharacteristic
142#2155C2×C10711yescharacteristic, complemented
143#2150C2×C10711yescharacteristic, complemented
144#2145C2×C10711yescharacteristic
145#2143C2×C10711yescharacteristic
146#1974C2×C10711yescharacteristic
147#1945C2×C10711yescharacteristic, complemented
148#1388C2×C10711yescharacteristic, complemented
149C107#1346611yescharacteristic, direct product factor, Sylow
150C2×#135C22×C10711yescharacteristic
151C2×M32C22×C10711yescharacteristic
152C2×M32C22×C10711yescharacteristic
153C2×#108C22×C10711yescharacteristic
154C2×#108C22×C10711yescharacteristic
155#427C22×C10711yescharacteristic
156#424—21no—
157C2×#104—21no—
158#408—21no—
159C2×C4×C8C22×C10711yescharacteristic
160#365—22no—
161C4⋊C16—22no—
162#360—22no—
163#359—22no—
164#339—21no—
165C2×#41—21no—
166#135—21no—
167#135—21no—
168#135—21no—
169#135—21no—
170C2×Q16Q8×C10711yescharacteristic
171C2×SD16—21no—
172C2×D8Q8×C10711yescharacteristic
173C2×M16—21no—
174C2×M16—21no—
175C22×C8D4×C10711yescharacteristic
176C22×C8C23×C10711yescharacteristic
177#117—21no—
178C2×C42D4×C10711yescharacteristic
179M32—21no—
180M32—21no—
181M32—21no—
182M32—21no—
183C2×C16—21no—
184C2×C16D4×C10712yes—
185#108—21no—
186#108—21no—
187#108—21no—
188#108—21no—
189#107—21no—
190#106D4×C10712yes—
191C4⋊C8—42no—
192#104—41no—
193#104—41no—
194C22⋊C8—42no—
195C4×C8—21no—
196C4×C8—21no—
197#41—41no—
198#41—41no—
199#41—41no—
200#41—41no—
201C2×Q8—21no—
202C2×D4—21no—
203C2×D4—41no—
204C22×C4—21no—
205C22×C4—41no—
206C22×C4C2×D4×C10711yescharacteristic
207Q16—21no—
208Q16—21no—
209SD16—41no—
210SD16—41no—
211D8—21no—
212D8—21no—
213M16—41no—
214M16—41no—
215M16—41no—
216M16—41no—
217C2×C8—21no—
218C2×C8—21no—
219C2×C8—21no—
220C2×C8—41no—
221C2×C8—41no—
222C2×C8C2×D4×C10711yescharacteristic
223C2×C8C2×D4×C10711yescharacteristic
224C2×C8C2×Q8×C10711yescharacteristic
225C2×C8#41×C10711yescharacteristic
226C2×C8#41×C10711yescharacteristic
227C2×C8#41×C10711yescharacteristic
228C4⋊C4—22no—
229C22⋊C4—41no—
230C42—21no—
231C42—41no—
232C42SD16×C10711yescharacteristic
233C42SD16×C10711yescharacteristic
234C16—22no—
235C16—41no—
236C23—41no—
237C23#135×C10711yescharacteristic
238Q8—41no—
239Q8—41no—
240D4—41no—
241D4—41no—
242D4—81no—
243D4—81no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—81no—
250C2×C4—81no—
251C2×C4#121×C10711yescharacteristic
252C2×C4#121×C10711yescharacteristic
253C2×C4C22⋊Q8×C10711yescharacteristic
254C2×C4C2×SD16×C10711yescharacteristic
255C2×C4AGL(1,ℤ/8)×C10711yescharacteristic
256C2×C4AGL(1,ℤ/8)×C10711yescharacteristic
257C8—41no—
258C8—81no—
259C8—81no—
260C8#121×C10711yescharacteristic
261C8C22⋊Q8×C10711yescharacteristic
262C8C22⋊Q8×C10711yescharacteristic
263C8#126×C10711yescharacteristic
264C22—41no—
265C22—82no—
266C22—81no—
267C22#463×C10711yescharacteristic
268C22#465×C10711yescharacteristic
269C22#478×C10711yescharacteristic
270C4—22no—
271C4—41no—
272C4—82no—
273C4—81no—
274C4#396×C10711yescharacteristic
275C4#460×C10711yescharacteristic
276C4#469×C10711yescharacteristic
277C4#476×C10711yescharacteristic
278C2—21no—
279C2—21no—
280C2—21no—
281C2—161no—
282C2C107×#206511yescharacteristic
subgroupG/H
centerC4×C107#469
commutator, Frattini, cosocleC22×C8C23×C107
socleC2×C107#2065
prime radicalC2×#135×C107C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C107 ◁ C22×C4×C107 ◁ C2×C4×C8×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C107×#2155C2semidirect
2. C107×#2150C2semidirect
6. C107×#1945C2semidirect
7. C107×#1388C2semidirect
136. #13466C107direct (N × H)
142. #2155C2×C107semidirect
143. #2150C2×C107semidirect
147. #1945C2×C107semidirect
148. #1388C2×C107semidirect
149. C107#13466direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#21552
C107×#21502
C107×#21452
C107×#21432
C107×#19742
C107×#19452
C107×#13882
#13466107