Finite Group Databasebeta

← C109×#7819 #42125813

Subgroups — C109×#7819 #42125813

Order 27904.

434 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 98 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
1C109×#2724C211yesmaximal, characteristic
2C109×#2093C211yesmaximal, characteristic
3C109×#2084C212yesmaximal, complemented
4C109×#1271C212yesmaximal, complemented
5C109×#1270C211yesmaximal, characteristic
6C2×#123×C109—21no—
7C2×#107×C109—21no—
8C2×#106×C109—22no—
9C2×#102×C109—21no—
10#398×C109—21no—
11#397×C109—22no—
12#390×C109C2211yescharacteristic
13#389×C109C2212yes—
14#385×C109—22no—
15#384×C109C2211yescharacteristic
16#340×C109—22no—
17#336×C109C2212yes—
18#336×C109C2211yescharacteristic
19C22×D4×C109D411yescharacteristic
20C23×C4×C109—21no—
21C22×C8×C109—22no—
22C22×C8×C109—21no—
23#123×C109—42no—
24#123×C109—42no—
25C2×C4⋊C4×C109—22no—
26C2×C4⋊C4×C109—22no—
27C2×C4⋊C4×C109—21no—
28C2×C4⋊C4×C109—21no—
29C2×C4⋊C4×C109D412yes—
30C2×C4⋊C4×C109D412yes—
31C2×C4⋊C4×C109D411yescharacteristic
32C2×C22⋊C4×C109—22no—
33C2×C22⋊C4×C109—21no—
34C2×C22⋊C4×C109—22no—
35C2×C42×C109C2311yescharacteristic
36#107×C109—42no—
37#106×C109—44no—
38#102×C109—42no—
39#95×C109—22no—
40#95×C109—21no—
41#95×C109—22no—
42C24×C109—21no—
43C2×D4×C109—21no—
44C2×D4×C109—41no—
45C2×D4×C109—41no—
46C2×D4×C109SD1612yes—
47C22×C4×C109—21no—
48C22×C4×C109—22no—
49C22×C4×C109—22no—
50C22×C4×C109—42no—
51C22×C4×C109—41no—
52C22×C4×C109—81no—
53C22×C4×C109—81no—
54C22×C4×C109C2×D411yescharacteristic
55C22×C4×C109C2×D412yes—
56C2×C8×C109—22no—
57C2×C8×C109—24no—
58C2×C8×C109—42no—
59C2×C8×C109—41no—
60C2×C8×C109—42no—
61C2×C8×C109—41no—
62C4⋊C4×C109—22no—
63C4⋊C4×C109—22no—
64C4⋊C4×C109—41no—
65C4⋊C4×C109—42no—
66C4⋊C4×C109—41no—
67C4⋊C4×C109—41no—
68C4⋊C4×C109—42no—
69C4⋊C4×C109—42no—
70C4⋊C4×C109—42no—
71C4⋊C4×C109—42no—
72C4⋊C4×C109—81no—
73C22⋊C4×C109—42no—
74C22⋊C4×C109—44no—
75C22⋊C4×C109—42no—
76C22⋊C4×C109—42no—
77C42×C109—41no—
78C23×C109—22no—
79C23×C109—42no—
80C23×C109—41no—
81C23×C109—42no—
82C23×C109—41no—
83C23×C109#12011yescharacteristic
84D4×C109—42no—
85D4×C109—81no—
86C2×C4×C109—21no—
87C2×C4×C109—22no—
88C2×C4×C109—22no—
89C2×C4×C109—21no—
90C2×C4×C109—42no—
91C2×C4×C109—42no—
92C2×C4×C109—42no—
93C2×C4×C109—42no—
94C2×C4×C109—41no—
95C2×C4×C109—42no—
96C2×C4×C109—42no—
97C2×C4×C109—42no—
98C2×C4×C109—84no—
99C2×C4×C109—82no—
100C2×C4×C109—81no—
101C2×C4×C109C2×SD1611yescharacteristic
102C2×C4×C109#13512yes—
103C2×C4×C109AGL(1,ℤ/8)12yes—
104C2×C4×C109AGL(1,ℤ/8)11yescharacteristic
105C8×C109—44no—
106C8×C109—42no—
107C22×C109—42no—
108C22×C109—44no—
109C22×C109—82no—
110C22×C109—81no—
111C22×C109—81no—
112C22×C109#44912yes—
113C22×C109#45011yescharacteristic
114C22×C109#45311yescharacteristic
115C22×C109#45612yes—
116C22×C109#45811yescharacteristic
117C4×C109—22no—
118C4×C109—22no—
119C4×C109—21no—
120C4×C109—21no—
121C4×C109—82no—
122C4×C109—81no—
123C4×C109—82no—
124C4×C109—161no—
125#7819C10911yesmaximal, characteristic, direct product factor, Sylow
126C2×C109—82no—
127C2×C109#160912yes—
128C2×C109#161311yescharacteristic
129C2×C109#162011yescharacteristic
130C2×C109#165412yes—
131C2×C109#166011yescharacteristic
132#2724C2×C10911yescharacteristic
133#2093C2×C10911yescharacteristic
134#2084C2×C10912yescomplemented
135#1271C2×C10912yescomplemented
136#1270C2×C10911yescharacteristic
137C109#781911yescharacteristic, direct product factor, Sylow
138C2×#123—21no—
139C2×#107—21no—
140C2×#106—22no—
141C2×#102—21no—
142#398—21no—
143#397—22no—
144#390C22×C10911yescharacteristic
145#389C22×C10912yes—
146#385—22no—
147#384C22×C10911yescharacteristic
148#340—22no—
149#336C22×C10912yes—
150#336C22×C10911yescharacteristic
151C22×D4D4×C10911yescharacteristic
152C23×C4—21no—
153C22×C8—22no—
154C22×C8—21no—
155#123—42no—
156#123—42no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4D4×C10912yes—
162C2×C4⋊C4D4×C10912yes—
163C2×C4⋊C4D4×C10911yescharacteristic
164C2×C22⋊C4—22no—
165C2×C22⋊C4—21no—
166C2×C22⋊C4—22no—
167C2×C42C23×C10911yescharacteristic
168#107—42no—
169#106—44no—
170#102—42no—
171#95—22no—
172#95—21no—
173#95—22no—
174C24—21no—
175C2×D4—21no—
176C2×D4—41no—
177C2×D4—41no—
178C2×D4SD16×C10912yes—
179C22×C4—21no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—42no—
183C22×C4—41no—
184C22×C4—81no—
185C22×C4—81no—
186C22×C4C2×D4×C10911yescharacteristic
187C22×C4C2×D4×C10912yes—
188C2×C8—22no—
189C2×C8—24no—
190C2×C8—42no—
191C2×C8—41no—
192C2×C8—42no—
193C2×C8—41no—
194C4⋊C4—22no—
195C4⋊C4—22no—
196C4⋊C4—41no—
197C4⋊C4—42no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—42no—
201C4⋊C4—42no—
202C4⋊C4—42no—
203C4⋊C4—42no—
204C4⋊C4—81no—
205C22⋊C4—42no—
206C22⋊C4—44no—
207C22⋊C4—42no—
208C22⋊C4—42no—
209C42—41no—
210C23—22no—
211C23—42no—
212C23—41no—
213C23—42no—
214C23—41no—
215C23#120×C10911yescharacteristic
216D4—42no—
217D4—81no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—84no—
231C2×C4—82no—
232C2×C4—81no—
233C2×C4C2×SD16×C10911yescharacteristic
234C2×C4#135×C10912yes—
235C2×C4AGL(1,ℤ/8)×C10912yes—
236C2×C4AGL(1,ℤ/8)×C10911yescharacteristic
237C8—44no—
238C8—42no—
239C22—42no—
240C22—44no—
241C22—81no—
242C22—82no—
243C22—81no—
244C22#449×C10912yes—
245C22#450×C10911yescharacteristic
246C22#453×C10911yescharacteristic
247C22#456×C10912yes—
248C22#458×C10911yescharacteristic
249C4—22no—
250C4—22no—
251C4—21no—
252C4—21no—
253C4—82no—
254C4—81no—
255C4—82no—
256C4—161no—
257C2—82no—
258C2C109×#160912yes—
259C2C109×#161311yescharacteristic
260C2C109×#162011yescharacteristic
261C2C109×#165412yes—
262C2C109×#166011yescharacteristic
subgroupG/H
center, socleC23×C109#120
commutator, Frattini, cosocleC2×C42C23×C109
prime radicalC22×D4×C109D4
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C109 ◁ C2×C42×C109 ◁ G

Complements

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

NH ≅ G/Ntype
3. C109×#2084C2semidirect
4. C109×#1271C2semidirect
125. #7819C109direct (N × H)
134. #2084C2×C109semidirect
135. #1271C2×C109semidirect
137. C109#7819direct (N × H)

Maximal subgroups

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

subgroupindex
C109×#27242
C109×#20932
C109×#20842
C109×#12712
C109×#12702
#7819109