Finite Group Databasebeta

← C107×#13468 #41039432

Subgroups — C107×#13468 #41039432

Order 27392.

304 conjugacy classes of subgroups.

The subgroup lattice has 274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#2155C211yesmaximal, characteristic, complemented
2C107×#2151C211yesmaximal, characteristic, complemented
3C107×#2143C211yesmaximal, characteristic
4C2×#359×C107C211yesmaximal, characteristic
5C107×#1976C211yesmaximal, characteristic
6C107×#1953C211yesmaximal, characteristic, complemented
7C107×#1382C211yesmaximal, characteristic, complemented
8C2×#135×C107C2211yescharacteristic
9C2×M32×C107C2211yescharacteristic
10C22×C16×C107C2211yescharacteristic
11#430×C107—21no—
12C2×#108×C107C2211yescharacteristic
13C2×#108×C107C2211yescharacteristic
14#427×C107C2211yescharacteristic
15#421×C107—21no—
16#410×C107—21no—
17#405×C107C2211yescharacteristic
18#365×C107—22no—
19C4⋊C16×C107—22no—
20#359×C107—22no—
21#359×C107—22no—
22#344×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—
33C2×M16×C107D411yescharacteristic
34C22×C8×C107C2311yescharacteristic
35#117×C107—21no—
36#117×C107D411yescharacteristic
37M32×C107—21no—
38M32×C107—21no—
39C2×C16×C107—21no—
40C2×C16×C107—21no—
41C2×C16×C107—21no—
42C2×C16×C107D412yes—
43#108×C107—21no—
44#108×C107—21no—
45#108×C107—21no—
46#108×C107—42no—
47#108×C107D412yes—
48#107×C107—21no—
49#106×C107—21no—
50#104×C107—42no—
51#99×C107—42no—
52#97×C107—21no—
53C4×C8×C107—21no—
54#41×C107—41no—
55#41×C107—41no—
56#41×C107—41no—
57#41×C107—41no—
58C2×Q8×C107—21no—
59C2×D4×C107—21no—
60C2×D4×C107—41no—
61C22×C4×C107—41no—
62C22×C4×C107C2×D411yescharacteristic
63Q16×C107—21no—
64Q16×C107—21no—
65SD16×C107—41no—
66SD16×C107—41no—
67D8×C107—21no—
68D8×C107—21no—
69M16×C107—22no—
70M16×C107—21no—
71M16×C107—21no—
72M16×C107—41no—
73M16×C107—41no—
74M16×C107—41no—
75C2×C8×C107—21no—
76C2×C8×C107—41no—
77C2×C8×C107—41no—
78C2×C8×C107C2×D411yescharacteristic
79C2×C8×C107C2×D411yescharacteristic
80C2×C8×C107C2×Q811yescharacteristic
81C2×C8×C107#4111yescharacteristic
82C2×C8×C107#4111yescharacteristic
83C2×C8×C107#4111yescharacteristic
84C4⋊C4×C107—21no—
85C4⋊C4×C107—41no—
86C22⋊C4×C107—41no—
87C22⋊C4×C107SD1612yes—
88C42×C107—21no—
89C42×C107—41no—
90C16×C107—22no—
91C16×C107—41no—
92C23×C107—41no—
93C23×C107C2×SD1611yescharacteristic
94Q8×C107—41no—
95Q8×C107—41no—
96D4×C107—41no—
97D4×C107—41no—
98D4×C107—81no—
99D4×C107—81no—
100C2×C4×C107—22no—
101C2×C4×C107—41no—
102C2×C4×C107—81no—
103C2×C4×C107—81no—
104C2×C4×C107—81no—
105C2×C4×C107#12111yescharacteristic
106C2×C4×C107#12111yescharacteristic
107C2×C4×C107C22⋊Q811yescharacteristic
108C2×C4×C107#13511yescharacteristic
109C2×C4×C107AGL(1,ℤ/8)11yescharacteristic
110C2×C4×C107AGL(1,ℤ/8)11yescharacteristic
111C8×C107—42no—
112C8×C107—41no—
113C8×C107—81no—
114C8×C107#12111yescharacteristic
115C8×C107C22⋊Q811yescharacteristic
116C8×C107C22⋊Q811yescharacteristic
117C8×C107#12611yescharacteristic
118C22×C107—41no—
119C22×C107—81no—
120C22×C107—161no—
121C22×C107#46011yescharacteristic
122C22×C107#46511yescharacteristic
123C22×C107#47611yescharacteristic
124C4×C107—42no—
125C4×C107—81no—
126C4×C107—161no—
127C4×C107#39611yescharacteristic
128C4×C107#46311yescharacteristic
129C4×C107#46911yescharacteristic
130C4×C107#47811yescharacteristic
131#13468C10711yesmaximal, characteristic, direct product factor, Sylow
132C2×C107—21no—
133C2×C107—21no—
134C2×C107—21no—
135C2×C107—161no—
136C2×C107#206511yescharacteristic
137#2155C2×C10711yescharacteristic, complemented
138#2151C2×C10711yescharacteristic, complemented
139#2143C2×C10711yescharacteristic
140C2×#359C2×C10711yescharacteristic
141#1976C2×C10711yescharacteristic
142#1953C2×C10711yescharacteristic, complemented
143#1382C2×C10711yescharacteristic, complemented
144C107#1346811yescharacteristic, direct product factor, Sylow
145C2×#135C22×C10711yescharacteristic
146C2×M32C22×C10711yescharacteristic
147C22×C16C22×C10711yescharacteristic
148#430—21no—
149C2×#108C22×C10711yescharacteristic
150C2×#108C22×C10711yescharacteristic
151#427C22×C10711yescharacteristic
152#421—21no—
153#410—21no—
154#405C22×C10711yescharacteristic
155#365—22no—
156C4⋊C16—22no—
157#359—22no—
158#359—22no—
159#344—21no—
160C2×#41—21no—
161#135—21no—
162#135—21no—
163#135—21no—
164#135—21no—
165C2×Q16Q8×C10711yescharacteristic
166C2×SD16—21no—
167C2×D8Q8×C10711yescharacteristic
168C2×M16—21no—
169C2×M16—21no—
170C2×M16D4×C10711yescharacteristic
171C22×C8C23×C10711yescharacteristic
172#117—21no—
173#117D4×C10711yescharacteristic
174M32—21no—
175M32—21no—
176C2×C16—21no—
177C2×C16—21no—
178C2×C16—21no—
179C2×C16D4×C10712yes—
180#108—21no—
181#108—21no—
182#108—21no—
183#108—42no—
184#108D4×C10712yes—
185#107—21no—
186#106—21no—
187#104—42no—
188#99—42no—
189#97—21no—
190C4×C8—21no—
191#41—41no—
192#41—41no—
193#41—41no—
194#41—41no—
195C2×Q8—21no—
196C2×D4—21no—
197C2×D4—41no—
198C22×C4—41no—
199C22×C4C2×D4×C10711yescharacteristic
200Q16—21no—
201Q16—21no—
202SD16—41no—
203SD16—41no—
204D8—21no—
205D8—21no—
206M16—22no—
207M16—21no—
208M16—21no—
209M16—41no—
210M16—41no—
211M16—41no—
212C2×C8—21no—
213C2×C8—41no—
214C2×C8—41no—
215C2×C8C2×D4×C10711yescharacteristic
216C2×C8C2×D4×C10711yescharacteristic
217C2×C8C2×Q8×C10711yescharacteristic
218C2×C8#41×C10711yescharacteristic
219C2×C8#41×C10711yescharacteristic
220C2×C8#41×C10711yescharacteristic
221C4⋊C4—21no—
222C4⋊C4—41no—
223C22⋊C4—41no—
224C22⋊C4SD16×C10712yes—
225C42—21no—
226C42—41no—
227C16—22no—
228C16—41no—
229C23—41no—
230C23C2×SD16×C10711yescharacteristic
231Q8—41no—
232Q8—41no—
233D4—41no—
234D4—41no—
235D4—81no—
236D4—81no—
237C2×C4—22no—
238C2×C4—41no—
239C2×C4—81no—
240C2×C4—81no—
241C2×C4—81no—
242C2×C4#121×C10711yescharacteristic
243C2×C4#121×C10711yescharacteristic
244C2×C4C22⋊Q8×C10711yescharacteristic
245C2×C4#135×C10711yescharacteristic
246C2×C4AGL(1,ℤ/8)×C10711yescharacteristic
247C2×C4AGL(1,ℤ/8)×C10711yescharacteristic
248C8—42no—
249C8—41no—
250C8—81no—
251C8#121×C10711yescharacteristic
252C8C22⋊Q8×C10711yescharacteristic
253C8C22⋊Q8×C10711yescharacteristic
254C8#126×C10711yescharacteristic
255C22—41no—
256C22—81no—
257C22—161no—
258C22#460×C10711yescharacteristic
259C22#465×C10711yescharacteristic
260C22#476×C10711yescharacteristic
261C4—42no—
262C4—81no—
263C4—161no—
264C4#396×C10711yescharacteristic
265C4#463×C10711yescharacteristic
266C4#469×C10711yescharacteristic
267C4#478×C10711yescharacteristic
268C2—21no—
269C2—21no—
270C2—21no—
271C2—161no—
272C2C107×#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 ◁ #405×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C107×#2155C2semidirect
2. C107×#2151C2semidirect
6. C107×#1953C2semidirect
7. C107×#1382C2semidirect
131. #13468C107direct (N × H)
137. #2155C2×C107semidirect
138. #2151C2×C107semidirect
142. #1953C2×C107semidirect
143. #1382C2×C107semidirect
144. C107#13468direct (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×#21512
C107×#21432
C2×#359×C1072
C107×#19762
C107×#19532
C107×#13822
#13468107