Finite Group Databasebeta

← C4×#329×C107 #41034186

Subgroups — C4×#329×C107 #41034186

Order 27392.

616 conjugacy classes of subgroups.

The subgroup lattice has 276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#124×C107C211yesmaximal, characteristic
2C4×#97×C107C212yesmaximal, complemented
3C2×#329×C107C212yesmaximal
4C107×#1295C212yesmaximal, complemented
5C2×#124×C107C2211yescharacteristic
6C2×C4×Q8×C107C411yescharacteristic
7C2×C4×D4×C107C411yescharacteristic
8C2×#97×C107—22no—
9C2×#97×C107C2214yes—
10C2×C4×C8×C107—22no—
11#391×C107C411yescharacteristic
12#390×C107C411yescharacteristic
13#388×C107—22no—
14#382×C107C2211yescharacteristic
15C4×C22⋊C4×C107—22no—
16C43×C107C2211yescharacteristic
17#329×C107C418yesdirect product factor
18C22×Q8×C107C2×C411yescharacteristic
19C22×D4×C107C2×C411yescharacteristic
20C23×C4×C107—21no—
21C22×C8×C107—24no—
22#124×C107—22no—
23#124×C107C2×C414yes—
24C4×Q8×C107—42no—
25C4×D4×C107—42no—
26C2×C4⋊C4×C107—21no—
27C2×C4⋊C4×C107C2×C411yescharacteristic
28C2×C4⋊C4×C107C2×C411yescharacteristic
29C2×C22⋊C4×C107—22no—
30C2×C22⋊C4×C107—22no—
31C2×C22⋊C4×C107—21no—
32C2×C42×C107—21no—
33C2×C42×C107C2×C411yescharacteristic
34C2×C42×C107C2×C411yescharacteristic
35C2×C42×C107D412yes—
36C2×C42×C107D412yes—
37C2×C42×C107C2311yescharacteristic
38#97×C107—28no—
39#97×C107—24no—
40#97×C107C2×C418yescomplemented
41C4×C8×C107—28no—
42#95×C107—22no—
43#95×C107—22no—
44C24×C107—21no—
45C2×Q8×C107—21no—
46C2×Q8×C107—41no—
47C2×Q8×C107—41no—
48C2×Q8×C107C4212yes—
49C2×D4×C107—21no—
50C2×D4×C107—41no—
51C2×D4×C107—41no—
52C2×D4×C107C4212yes—
53C22×C4×C107—21no—
54C22×C4×C107—21no—
55C22×C4×C107—21no—
56C22×C4×C107—42no—
57C22×C4×C107—44no—
58C22×C4×C107C22⋊C411yescharacteristic
59C22×C4×C107C22⋊C412yes—
60C22×C4×C107C22⋊C411yescharacteristic
61C22×C4×C107C22×C411yescharacteristic
62C22×C4×C107C2×D412yes—
63C2×C8×C107—28no—
64C2×C8×C107—28no—
65C2×C8×C107—28no—
66C4⋊C4×C107—41no—
67C4⋊C4×C107—41no—
68C4⋊C4×C107—42no—
69C22⋊C4×C107—28no—
70C22⋊C4×C107—42no—
71C22⋊C4×C107—44no—
72C42×C107—22no—
73C42×C107—24no—
74C42×C107—24no—
75C42×C107—41no—
76C42×C107—42no—
77C42×C107C22×C412yes—
78C42×C107#4112yes—
79C23×C107—22no—
80C23×C107—41no—
81C23×C107—41no—
82C23×C107—42no—
83C23×C107—42no—
84C23×C107C2×C22⋊C411yescharacteristic
85Q8×C107—42no—
86Q8×C107—42no—
87D4×C107—42no—
88D4×C107—42no—
89C2×C4×C107—21no—
90C2×C4×C107—22no—
91C2×C4×C107—21no—
92C2×C4×C107—22no—
93C2×C4×C107—22no—
94C2×C4×C107—22no—
95C2×C4×C107—22no—
96C2×C4×C107—21no—
97C2×C4×C107—22no—
98C2×C4×C107—41no—
99C2×C4×C107—41no—
100C2×C4×C107—41no—
101C2×C4×C107—41no—
102C2×C4×C107—42no—
103C2×C4×C107—42no—
104C2×C4×C107—84no—
105C2×C4×C107#10012yes—
106C2×C4×C107#10414yes—
107C2×C4×C107#10414yes—
108C2×C4×C107C2×C4211yescharacteristic
109C2×C4×C107#11711yescharacteristic
110C2×C4×C107C4×D414yes—
111C8×C107—216no—
112C22×C107—42no—
113C22×C107—44no—
114C22×C107—81no—
115C22×C107—82no—
116C22×C107—81no—
117C22×C107C4×C22⋊C411yescharacteristic
118C22×C107C2×#10011yescharacteristic
119C22×C107#41311yescharacteristic
120C22×C107C2×#10412yes—
121C22×C107C2×#10412yes—
122C4×C107—21no—
123C4×C107—21no—
124C4×C107—24no—
125C4×C107—24no—
126C4×C107—42no—
127C4×C107—41no—
128C4×C107—81no—
129C4×C107—81no—
130C4×C107#32914yesdirect product factor
131C4×#329C10711yesmaximal, characteristic, direct product factor, Sylow
132C2×C107—82no—
133C2×C107C2×#32911yescharacteristic
134C2×C107#152412yes—
135C2×C107#152511yescharacteristic
136C2×C107C4×#10011yescharacteristic
137C2×C107C4×#10412yes—
138C4×#124C2×C10711yescharacteristic
139C4×#97C2×C10712yescomplemented
140C2×#329C2×C10712yes—
141#1295C2×C10712yescomplemented
142C107C4×#32911yescharacteristic, direct product factor, Sylow
143C2×#124C22×C10711yescharacteristic
144C2×C4×Q8C4×C10711yescharacteristic
145C2×C4×D4C4×C10711yescharacteristic
146C2×#97—22no—
147C2×#97C22×C10714yes—
148C2×C4×C8—22no—
149#391C4×C10711yescharacteristic
150#390C4×C10711yescharacteristic
151#388—22no—
152#382C22×C10711yescharacteristic
153C4×C22⋊C4—22no—
154C43C22×C10711yescharacteristic
155#329C4×C10718yesdirect product factor
156C22×Q8C2×C4×C10711yescharacteristic
157C22×D4C2×C4×C10711yescharacteristic
158C23×C4—21no—
159C22×C8—24no—
160#124—22no—
161#124C2×C4×C10714yes—
162C4×Q8—42no—
163C4×D4—42no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4C2×C4×C10711yescharacteristic
166C2×C4⋊C4C2×C4×C10711yescharacteristic
167C2×C22⋊C4—22no—
168C2×C22⋊C4—21no—
169C2×C22⋊C4—22no—
170C2×C42—21no—
171C2×C42C2×C4×C10711yescharacteristic
172C2×C42C2×C4×C10711yescharacteristic
173C2×C42D4×C10712yes—
174C2×C42D4×C10712yes—
175C2×C42C23×C10711yescharacteristic
176#97—28no—
177#97—24no—
178#97C2×C4×C10718yescomplemented
179C4×C8—28no—
180#95—22no—
181#95—22no—
182C24—21no—
183C2×Q8—21no—
184C2×Q8—41no—
185C2×Q8—41no—
186C2×Q8C42×C10712yes—
187C2×D4—21no—
188C2×D4—41no—
189C2×D4—41no—
190C2×D4C42×C10712yes—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—42no—
195C22×C4—44no—
196C22×C4C22⋊C4×C10711yescharacteristic
197C22×C4C22⋊C4×C10712yes—
198C22×C4C22⋊C4×C10711yescharacteristic
199C22×C4C22×C4×C10711yescharacteristic
200C22×C4C2×D4×C10712yes—
201C2×C8—28no—
202C2×C8—28no—
203C2×C8—28no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—42no—
207C22⋊C4—28no—
208C22⋊C4—42no—
209C22⋊C4—44no—
210C42—22no—
211C42—24no—
212C42—24no—
213C42—41no—
214C42—42no—
215C42C22×C4×C10712yes—
216C42#41×C10712yes—
217C23—22no—
218C23—41no—
219C23—41no—
220C23—42no—
221C23—42no—
222C23C2×C22⋊C4×C10711yescharacteristic
223Q8—42no—
224Q8—42no—
225D4—42no—
226D4—42no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—84no—
243C2×C4#100×C10712yes—
244C2×C4#104×C10714yes—
245C2×C4#104×C10714yes—
246C2×C4C2×C42×C10711yescharacteristic
247C2×C4#117×C10711yescharacteristic
248C2×C4C4×D4×C10714yes—
249C8—216no—
250C22—42no—
251C22—44no—
252C22—81no—
253C22—82no—
254C22—81no—
255C22C4×C22⋊C4×C10711yescharacteristic
256C22C2×#100×C10711yescharacteristic
257C22#413×C10711yescharacteristic
258C22C2×#104×C10712yes—
259C22C2×#104×C10712yes—
260C4—21no—
261C4—21no—
262C4—24no—
263C4—24no—
264C4—42no—
265C4—41no—
266C4—81no—
267C4—81no—
268C4#329×C10714yesdirect product factor
269C2—82no—
270C2C2×#329×C10711yescharacteristic
271C2C107×#152412yes—
272C2C107×#152511yescharacteristic
273C2C4×#100×C10711yescharacteristic
274C2C4×#104×C10712yes—
subgroupG/H
centerC22×C4×C107C22⋊C4
commutatorC2×C4C2×C42×C107
Frattini, cosocleC2×C42C23×C107
socleC23×C107C2×C22⋊C4
prime radicalC22×D4×C107C2×C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C107 ◁ C43×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×#97×C107C2semidirect
4. C107×#1295C2semidirect
17. #329×C107C4direct (N × H)
40. #97×C107C2×C4semidirect
130. C4×C107#329direct (N × H)
131. C4×#329C107direct (N × H)
139. C4×#97C2×C107semidirect
141. #1295C2×C107semidirect
142. C107C4×#329direct (N × H)
155. #329C4×C107direct (N × H)
178. #97C2×C4×C107semidirect
268. C4#329×C107direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#124×C1072
C4×#97×C1072
C2×#329×C1072
C107×#12952
C4×#329107