Finite Group Databasebeta

← C109×#11795 #42129789

Subgroups — C109×#11795 #42129789

Order 27904.

394 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2567C211yesmaximal, characteristic
2C4×#101×C109C211yesmaximal, characteristic
3C109×#1467C211yesmaximal, characteristic
4C109×#1354C214yesmaximal
5C2×C4⋊Q8×C109C411yescharacteristic
6C2×C4×Q8×C109C2211yescharacteristic
7#432×C109—21no—
8C2×#101×C109—21no—
9C4×M16×C109—21no—
10#395×C109C412yes—
11#395×C109C2212yes—
12#391×C109—21no—
13#389×C109—21no—
14#389×C109—21no—
15#384×C109—21no—
16C4×C4⋊C4×C109C411yescharacteristic
17#343×C109C2212yes—
18#324×C109—21no—
19#324×C109C2212yes—
20C22×Q8×C109C2×C412yes—
21C22×Q8×C109D411yescharacteristic
22C2×M16×C109—22no—
23C4⋊Q8×C109—41no—
24C4⋊Q8×C109—41no—
25C4×Q8×C109—41no—
26C4×Q8×C109—41no—
27C2×C4⋊C4×C109—21no—
28C2×C4⋊C4×C109—21no—
29C2×C4⋊C4×C109—21no—
30C2×C4⋊C4×C109—22no—
31C2×C4⋊C4×C109—22no—
32C2×C4⋊C4×C109C2×C411yescharacteristic
33C2×C4⋊C4×C109D411yescharacteristic
34C2×C4⋊C4×C109C2311yescharacteristic
35C2×C42×C109—21no—
36C2×C42×C109C2×C411yescharacteristic
37C2×C42×C109D411yescharacteristic
38C2×C42×C109D411yescharacteristic
39C4⋊C8×C109—41no—
40#101×C109—24no—
41C22⋊C8×C109—22no—
42#97×C109—41no—
43#97×C109—41no—
44C4×C8×C109—41no—
45#95×C109—22no—
46#95×C109—22no—
47#95×C109C2×C412yes—
48C2×Q8×C109—22no—
49C2×Q8×C109—22no—
50C2×Q8×C109—41no—
51C2×Q8×C109—42no—
52C2×Q8×C109—82no—
53C22×C4×C109—22no—
54C22×C4×C109—22no—
55C22×C4×C109C22⋊C411yescharacteristic
56C22×C4×C109C22⋊C411yescharacteristic
57C22×C4×C109C22⋊C411yescharacteristic
58C22×C4×C109C22⋊C411yescharacteristic
59C22×C4×C109C22×C411yescharacteristic
60C22×C4×C109C2×D411yescharacteristic
61C22×C4×C109C2×D411yescharacteristic
62M16×C109—24no—
63M16×C109—42no—
64C2×C8×C109—42no—
65C2×C8×C109—42no—
66C4⋊C4×C109—24no—
67C4⋊C4×C109—41no—
68C4⋊C4×C109—41no—
69C4⋊C4×C109—41no—
70C4⋊C4×C109—42no—
71C4⋊C4×C109—41no—
72C4⋊C4×C109—41no—
73C4⋊C4×C109—82no—
74C4⋊C4×C109—82no—
75C42×C109—21no—
76C42×C109—21no—
77C42×C109—21no—
78C42×C109—21no—
79C42×C109—21no—
80C42×C109—21no—
81C42×C109—42no—
82C23×C109C2×C22⋊C411yescharacteristic
83Q8×C109—44no—
84Q8×C109—84no—
85C2×C4×C109—21no—
86C2×C4×C109—21no—
87C2×C4×C109—21no—
88C2×C4×C109—21no—
89C2×C4×C109—22no—
90C2×C4×C109—24no—
91C2×C4×C109—21no—
92C2×C4×C109—21no—
93C2×C4×C109—21no—
94C2×C4×C109—21no—
95C2×C4×C109—21no—
96C2×C4×C109—21no—
97C2×C4×C109—42no—
98C2×C4×C109—42no—
99C2×C4×C109—41no—
100C2×C4×C109—41no—
101C2×C4×C109—41no—
102C2×C4×C109—42no—
103C2×C4×C109—42no—
104C2×C4×C109—42no—
105C2×C4×C109#9911yescharacteristic
106C2×C4×C109#9911yescharacteristic
107C2×C4×C109#10412yes—
108C2×C4×C109#13712yes—
109C8×C109—44no—
110C8×C109—82no—
111C22×C109—21no—
112C22×C109—21no—
113C22×C109C2×#9911yescharacteristic
114C22×C109#41911yescharacteristic
115C22×C109C2×#10411yescharacteristic
116C4×C109—21no—
117C4×C109—22no—
118C4×C109—22no—
119C4×C109—44no—
120C4×C109—41no—
121C4×C109—41no—
122C4×C109—41no—
123C4×C109—41no—
124C4×C109—82no—
125C4×C109#35612yes—
126#11795C10911yesmaximal, characteristic, direct product factor, Sylow
127C2×C109—21no—
128C2×C109—21no—
129C2×C109#150811yescharacteristic
130C2×C109#212211yescharacteristic
131C2×C109C2×#35611yescharacteristic
132#2567C2×C10911yescharacteristic
133C4×#101C2×C10911yescharacteristic
134#1467C2×C10911yescharacteristic
135#1354C2×C10914yes—
136C109#1179511yescharacteristic, direct product factor, Sylow
137C2×C4⋊Q8C4×C10911yescharacteristic
138C2×C4×Q8C22×C10911yescharacteristic
139#432—21no—
140C2×#101—21no—
141C4×M16—21no—
142#395C4×C10912yes—
143#395C22×C10912yes—
144#391—21no—
145#389—21no—
146#389—21no—
147#384—21no—
148C4×C4⋊C4C4×C10911yescharacteristic
149#343C22×C10912yes—
150#324—21no—
151#324C22×C10912yes—
152C22×Q8C2×C4×C10912yes—
153C22×Q8D4×C10911yescharacteristic
154C2×M16—22no—
155C4⋊Q8—41no—
156C4⋊Q8—41no—
157C4×Q8—41no—
158C4×Q8—41no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4C2×C4×C10911yescharacteristic
165C2×C4⋊C4D4×C10911yescharacteristic
166C2×C4⋊C4C23×C10911yescharacteristic
167C2×C42—21no—
168C2×C42C2×C4×C10911yescharacteristic
169C2×C42D4×C10911yescharacteristic
170C2×C42D4×C10911yescharacteristic
171C4⋊C8—41no—
172#101—24no—
173C22⋊C8—22no—
174#97—41no—
175#97—41no—
176C4×C8—41no—
177#95—22no—
178#95—22no—
179#95C2×C4×C10912yes—
180C2×Q8—22no—
181C2×Q8—22no—
182C2×Q8—41no—
183C2×Q8—42no—
184C2×Q8—82no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4C22⋊C4×C10911yescharacteristic
188C22×C4C22⋊C4×C10911yescharacteristic
189C22×C4C22⋊C4×C10911yescharacteristic
190C22×C4C22⋊C4×C10911yescharacteristic
191C22×C4C22×C4×C10911yescharacteristic
192C22×C4C2×D4×C10911yescharacteristic
193C22×C4C2×D4×C10911yescharacteristic
194M16—24no—
195M16—42no—
196C2×C8—42no—
197C2×C8—42no—
198C4⋊C4—24no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—42no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—82no—
206C4⋊C4—82no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—21no—
212C42—21no—
213C42—42no—
214C23C2×C22⋊C4×C10911yescharacteristic
215Q8—44no—
216Q8—84no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—24no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4#99×C10911yescharacteristic
238C2×C4#99×C10911yescharacteristic
239C2×C4#104×C10912yes—
240C2×C4#137×C10912yes—
241C8—44no—
242C8—82no—
243C22—21no—
244C22—21no—
245C22C2×#99×C10911yescharacteristic
246C22#419×C10911yescharacteristic
247C22C2×#104×C10911yescharacteristic
248C4—22no—
249C4—22no—
250C4—21no—
251C4—44no—
252C4—41no—
253C4—41no—
254C4—41no—
255C4—41no—
256C4—82no—
257C4#356×C10912yes—
258C2—21no—
259C2—21no—
260C2C109×#150811yescharacteristic
261C2C109×#212211yescharacteristic
262C2C2×#356×C10911yescharacteristic
subgroupG/H
center, socleC22×C109C2×#99
commutatorC22×C4C22×C4×C109
Frattini, cosocleC2×C4⋊C4C23×C109
prime radicalC23×C109C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C109 ◁ C22×C4×C109 ◁ C2×C4×Q8×C109 ◁ G

Complements

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

NH ≅ G/Ntype
126. #11795C109direct (N × H)
136. C109#11795direct (N × H)

Maximal subgroups

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

subgroupindex
C109×#25672
C4×#101×C1092
C109×#14672
C109×#13542
#11795109