Finite Group Databasebeta

← C109×#7484 #42125478

Subgroups — C109×#7484 #42125478

Order 27904.

266 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 66 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×#2132C211yesmaximal, characteristic
2C109×#1884C211yesmaximal, characteristic
3C109×#1536C211yesmaximal, characteristic
4#568×C109C411yescharacteristic
5#532×C109C2211yescharacteristic
6#432×C109—21no—
7#421×C109—21no—
8#413×C109—21no—
9#410×C109C411yescharacteristic
10#356×C109C412yescomplemented
11#355×C109—21no—
12#339×C109—21no—
13#329×C109—21no—
14#329×C109C412yescomplemented
15C2×#41×C109C2×C411yescharacteristic
16C2×#41×C109D411yescharacteristic
17#131×C109—42no—
18C2×M16×C109—21no—
19C2×M16×C109—41no—
20C2×M16×C109—41no—
21C4⋊Q8×C109C2×C411yescharacteristic
22#127×C109Q811yescharacteristic
23#124×C109C2×C411yescharacteristic
24#124×C109D411yescharacteristic
25#121×C109—41no—
26C4×D4×C109—41no—
27#117×C109—21no—
28C2×C42×C109D411yescharacteristic
29C4⋊C8×C109—41no—
30#104×C109—42no—
31#101×C109—22no—
32#100×C109—41no—
33#99×C109—41no—
34C22⋊C8×C109—41no—
35#97×C109—22no—
36#41×C109—41no—
37#41×C109—41no—
38#41×C109—41no—
39#41×C109—41no—
40C2×Q8×C109C4211yescharacteristic
41C2×Q8×C109C22⋊C411yescharacteristic
42C2×D4×C109—21no—
43C2×D4×C109—21no—
44C2×D4×C109—41no—
45C2×D4×C109C4⋊C411yescharacteristic
46C2×D4×C109C4⋊C411yescharacteristic
47C22×C4×C109—21no—
48C22×C4×C109—21no—
49C22×C4×C109—21no—
50C22×C4×C109C22⋊C411yescharacteristic
51M16×C109—22no—
52M16×C109—42no—
53M16×C109—41no—
54M16×C109—42no—
55M16×C109—81no—
56C2×C8×C109—41no—
57C2×C8×C109—42no—
58C2×C8×C109—42no—
59C2×C8×C109—81no—
60C4⋊C4×C109—41no—
61C4⋊C4×C109—41no—
62C22⋊C4×C109—41no—
63C22⋊C4×C109—41no—
64C22⋊C4×C109—41no—
65C42×C109—21no—
66C42×C109—41no—
67C42×C109C22⋊C411yescharacteristic
68C42×C109C4⋊C411yescharacteristic
69C23×C109—21no—
70C23×C109—21no—
71C23×C109#9911yescharacteristic
72Q8×C109—41no—
73Q8×C109—41no—
74D4×C109—41no—
75D4×C109—41no—
76D4×C109—42no—
77D4×C109—81no—
78D4×C109—82no—
79C2×C4×C109—21no—
80C2×C4×C109—21no—
81C2×C4×C109—21no—
82C2×C4×C109—21no—
83C2×C4×C109—21no—
84C2×C4×C109—21no—
85C2×C4×C109—41no—
86C2×C4×C109—41no—
87C2×C4×C109—41no—
88C2×C4×C109—41no—
89C2×C4×C109—81no—
90C2×C4×C109—81no—
91C2×C4×C109#9511yescharacteristic
92C2×C4×C109#9911yescharacteristic
93C8×C109—42no—
94C8×C109—82no—
95C8×C109—82no—
96C22×C109—21no—
97C22×C109—41no—
98C22×C109—41no—
99C22×C109—41no—
100C22×C109—81no—
101C22×C109—81no—
102C22×C109#34211yescharacteristic
103C4×C109—21no—
104C4×C109—41no—
105C4×C109—41no—
106C4×C109—41no—
107C4×C109—41no—
108C4×C109—161no—
109C4×C109AΣL(1,𝔽16)11yescharacteristic
110C4×C109#35211yescharacteristic
111#7484C10911yesmaximal, characteristic, direct product factor, Sylow
112C2×C109—21no—
113C2×C109—41no—
114C2×C109—81no—
115C2×C109—81no—
116C2×C109#139011yescharacteristic
117#2132C2×C10911yescharacteristic
118#1884C2×C10911yescharacteristic
119#1536C2×C10911yescharacteristic
120C109#748411yescharacteristic, direct product factor, Sylow
121#568C4×C10911yescharacteristic
122#532C22×C10911yescharacteristic
123#432—21no—
124#421—21no—
125#413—21no—
126#410C4×C10911yescharacteristic
127#356C4×C10912yescomplemented
128#355—21no—
129#339—21no—
130#329—21no—
131#329C4×C10912yescomplemented
132C2×#41C2×C4×C10911yescharacteristic
133C2×#41D4×C10911yescharacteristic
134#131—42no—
135C2×M16—21no—
136C2×M16—41no—
137C2×M16—41no—
138C4⋊Q8C2×C4×C10911yescharacteristic
139#127Q8×C10911yescharacteristic
140#124C2×C4×C10911yescharacteristic
141#124D4×C10911yescharacteristic
142#121—41no—
143C4×D4—41no—
144#117—21no—
145C2×C42D4×C10911yescharacteristic
146C4⋊C8—41no—
147#104—42no—
148#101—22no—
149#100—41no—
150#99—41no—
151C22⋊C8—41no—
152#97—22no—
153#41—41no—
154#41—41no—
155#41—41no—
156#41—41no—
157C2×Q8C42×C10911yescharacteristic
158C2×Q8C22⋊C4×C10911yescharacteristic
159C2×D4—21no—
160C2×D4—21no—
161C2×D4—41no—
162C2×D4C4⋊C4×C10911yescharacteristic
163C2×D4C4⋊C4×C10911yescharacteristic
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4C22⋊C4×C10911yescharacteristic
168M16—22no—
169M16—42no—
170M16—41no—
171M16—42no—
172M16—81no—
173C2×C8—41no—
174C2×C8—42no—
175C2×C8—42no—
176C2×C8—81no—
177C4⋊C4—41no—
178C4⋊C4—41no—
179C22⋊C4—41no—
180C22⋊C4—41no—
181C22⋊C4—41no—
182C42—21no—
183C42—41no—
184C42C22⋊C4×C10911yescharacteristic
185C42C4⋊C4×C10911yescharacteristic
186C23—21no—
187C23—21no—
188C23#99×C10911yescharacteristic
189Q8—41no—
190Q8—41no—
191D4—41no—
192D4—41no—
193D4—42no—
194D4—81no—
195D4—82no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—81no—
207C2×C4—81no—
208C2×C4#95×C10911yescharacteristic
209C2×C4#99×C10911yescharacteristic
210C8—42no—
211C8—82no—
212C8—82no—
213C22—21no—
214C22—41no—
215C22—41no—
216C22—41no—
217C22—81no—
218C22—81no—
219C22#342×C10911yescharacteristic
220C4—21no—
221C4—41no—
222C4—41no—
223C4—41no—
224C4—41no—
225C4—161no—
226C4AΣL(1,𝔽16)×C10911yescharacteristic
227C4#352×C10911yescharacteristic
228C2—21no—
229C2—41no—
230C2—81no—
231C2—81no—
232C2C109×#139011yescharacteristic
subgroupG/H
center, socleC2×C109#1390
commutatorC2×Q8C42×C109
Frattini, cosocle#532C22×C109
prime radical#532×C109C22
LCSG ▷ C2×Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C109 ◁ C2×C4×C109 ◁ C22×C4×C109 ◁ #532×C109 ◁ G

Complements

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

NH ≅ G/Ntype
10. #356×C109C4semidirect
14. #329×C109C4semidirect
111. #7484C109direct (N × H)
120. C109#7484direct (N × H)
127. #356C4×C109semidirect
131. #329C4×C109semidirect

Maximal subgroups

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

subgroupindex
C109×#21322
C109×#18842
C109×#15362
#7484109