Finite Group Databasebeta

← C2×#20295186 #28372239

Subgroups — C2×#20295186 #28372239

Order 13952.

760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 760 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C22×#13182029C211yesmaximal, characteristic
2C22×#13182019C211yesmaximal, characteristic, complemented
3C22×#13182016C211yesmaximal, characteristic, complemented
4#20295186C218yesmaximal, direct product factor
5C2×#16812622C211yesmaximal, characteristic, complemented
6C2×#16812619C211yesmaximal, characteristic, complemented
7C2×C22⋊#11724784C211yesmaximal, characteristic, complemented
8C2×C22⋊Q8×C109C211yesmaximal, characteristic, complemented
9C2×#13182029—24no—
10C2×#13182029—24no—
11C2×#13182029—22no—
12C2×#13182029C2214yes—
13C22×Dic218C2211yescharacteristic
14C22×D436C2211yescharacteristic
15C22×C22⋊D109—21no—
16C22×C4×D109—21no—
17C2×#13182019—24no—
18C2×#13182019C2214yescomplemented
19C2×#13182016—24no—
20C2×#13182016C2214yescomplemented
21C22×#11724784C2211yescharacteristic
22C22×#11724784C2211yescharacteristic
23#16812622C2214yescomplemented
24#16812619C2214yescomplemented
25C22⋊#11724784C2214yescomplemented
26C22×Q8×C109C2211yescharacteristic
27C23×C4×C109C2211yescharacteristic
28C22⋊Q8×C109—22no—
29C22⋊Q8×C109C2214yescomplemented
30C2×C4⋊C4×C109—21no—
31C2×C4⋊C4×C109C2211yescharacteristic
32C2×C22⋊C4×C109—21no—
33C23×D109—21no—
34#13182029—216no—
35#13182029—28no—
36#13182029—28no—
37C2×Dic218—22no—
38C2×Dic218—21no—
39C2×Dic218D414yes—
40C2×Dic218C2312yes—
41C2×D436—22no—
42C2×D436—21no—
43C2×D436D414yes—
44C2×D436C2312yes—
45C2×C22⋊D109—28no—
46C2×C22⋊D109—24no—
47C22×Dic109—21no—
48C2×C4×D109—28no—
49C2×C4×D109—24no—
50#13182019—28no—
51#13182016—28no—
52C2×#11724784—22no—
53C2×#11724784—22no—
54C2×#11724784C2312yes—
55C2×#11724784C2312yes—
56C24×C109D411yescharacteristic
57C2×Q8×C109—21no—
58C2×Q8×C109—22no—
59C2×Q8×C109—22no—
60C2×Q8×C109C2312yes—
61C22×C4×C109—22no—
62C22×C4×C109—22no—
63C22×C4×C109—21no—
64C22×C4×C109—21no—
65C22×C4×C109D411yescharacteristic
66C22×C4×C109D412yes—
67C22×C4×C109C2312yes—
68C22×C4×C109C2311yescharacteristic
69C4⋊C4×C109—24no—
70C4⋊C4×C109—21no—
71C4⋊C4×C109C2312yes—
72C22⋊C4×C109—24no—
73C23×C109—22no—
74C23×C109—22no—
75C23×C109—22no—
76C23×C109C2×D412yes—
77C23×C109C2×D411yescharacteristic
78C22×D109—24no—
79C22×D109—22no—
80C22×D109—42no—
81C22×D109—42no—
82Q8×C109—22no—
83Q8×C109—22no—
84Q8×C109—42no—
85C2×C4×C109—22no—
86C2×C4×C109—24no—
87C2×C4×C109—22no—
88C2×C4×C109—22no—
89C2×C4×C109—22no—
90C2×C4×C109—22no—
91C2×C4×C109—42no—
92C2×C4×C109—42no—
93C2×C4×C109C2×D412yes—
94C2×C4×C109C2×D412yes—
95C2×C4×C109C2×D412yes—
96C2×C4×C109C2×D411yescharacteristic
97C2×C4×C109C2411yescharacteristic
98C22⋊D109—216no—
99C2×Dic109—24no—
100C2×Dic109—22no—
101D436—24no—
102D436—22no—
103D436C2×D414yes—
104C4×D109—216no—
105Dic218—24no—
106Dic218—22no—
107Dic218C2×D414yes—
108#11724784—22no—
109#11724784—22no—
110C22×C109—22no—
111C22×C109—22no—
112C22×C109—22no—
113C22×C109—44no—
114C22×C109#12012yes—
115C22×C109#13512yes—
116C22×C109#13712yes—
117C22×C109C22×D411yescharacteristic
118C2×D109—24no—
119C2×D109—42no—
120C2×D109—42no—
121C2×D109—48no—
122C4×C109—22no—
123C4×C109—42no—
124C4×C109—42no—
125C4×C109#12012yes—
126C4×C109C22×D411yescharacteristic
127C4×C109C22×D411yescharacteristic
128Dic109—24no—
129C2×C109—42no—
130C2×C109#45214yescomplemented
131C2×C109C2×#12011yescharacteristic
132C2×C109C2×#13511yescharacteristic
133C2×C109C2×#13711yescharacteristic
134D109—44no—
135C2×#452—1091nomaximal, Sylow
136C109C2×#45211yescharacteristic, complemented, Sylow
137C22×#41—1091no—
138C22×Q16—1091no—
139C22×SD16—1091no—
140C2×C22⋊Q8D10911yescharacteristic, complemented
141#452—1098no—
142C2×#103—1091no—
143C2×#102—1091no—
144C2×C22⋊C8—1091no—
145C2×#41—1094no—
146C2×#41—2184no—
147C2×#41—2184no—
148C2×#41—2182no—
149C22×Q8—1091no—
150C22×Q8C2×D10911yescharacteristic
151C22×D4—1091no—
152C22×D4—2181no—
153C23×C4—2181no—
154C23×C4C2×D10911yescharacteristic
155C2×Q16—1094no—
156C2×Q16—2184no—
157C2×SD16—1094no—
158C2×SD16—2184no—
159C22×C8—1091no—
160C22×C8—1091no—
161C22⋊Q8—22no—
162C22⋊Q8C2×D10914yescomplemented
163C2×C4⋊C4—21no—
164C2×C4⋊C4C2×D10911yescharacteristic
165C2×C22⋊C4—21no—
166#103—1094no—
167#102—1094no—
168C22⋊C8—1094no—
169C24—2181no—
170C24C22⋊D10911yescharacteristic
171#41—2188no—
172#41—2188no—
173#41—21816no—
174C2×Q8—21no—
175C2×Q8—22no—
176C2×Q8—22no—
177C2×Q8—1094no—
178C2×Q8—1092no—
179C2×Q8—2182no—
180C2×Q8—2181no—
181C2×Q8C22×D10912yes—
182C2×D4—1094no—
183C2×D4—1092no—
184C2×D4—2188no—
185C2×D4—2184no—
186C2×D4—2182no—
187C2×D4—2181no—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—2188no—
193C22×C4—2181no—
194C22×C4—2184no—
195C22×C4C22⋊D10912yes—
196C22×C4C22⋊D10911yescharacteristic
197C22×C4C22×D10912yes—
198C22×C4C22×D10911yescharacteristic
199Q16—2188no—
200SD16—2188no—
201C2×C8—1092no—
202C2×C8—1092no—
203C2×C8—2182no—
204C2×C8—2182no—
205C4⋊C4—24no—
206C4⋊C4—21no—
207C4⋊C4C22×D10912yes—
208C22⋊C4—24no—
209C23—22no—
210C23—22no—
211C23—22no—
212C23—4362no—
213C23—4362no—
214C23—2184no—
215C23—2182no—
216C23C2×C22⋊D10912yes—
217C23C2×C22⋊D10911yescharacteristic
218Q8—22no—
219Q8—22no—
220Q8—42no—
221Q8—1094no—
222Q8—2184no—
223Q8—2182no—
224D4—1094no—
225D4—21816no—
226D4—2184no—
227D4—2182no—
228C2×C4—22no—
229C2×C4—24no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—21816no—
237C2×C4—2184no—
238C2×C4—2182no—
239C2×C4D4×D10912yes—
240C2×C4D4×D10912yes—
241C2×C4C2×C22⋊D10912yes—
242C2×C4C2×C22⋊D10911yescharacteristic
243C2×C4C23×D10911yescharacteristic
244C8—2182no—
245C8—2182no—
246C22—22no—
247C22—22no—
248C22—22no—
249C22—44no—
250C22—4368no—
251C22—4362no—
252C22—4362no—
253C22—2184no—
254C22#1681266712yes—
255C22#1681271912yes—
256C22#1681273012yes—
257C22C22×C22⋊D10911yescharacteristic
258C4—22no—
259C4—42no—
260C4—42no—
261C4—2184no—
262C4#1681266712yes—
263C4C2×D4×D10911yescharacteristic
264C4C2×D4×D10911yescharacteristic
265C2—42no—
266C2—4364no—
267C2#2029518614yesdirect product factor
268C2C2×#1681266711yescharacteristic
269C2C2×#1681271911yescharacteristic
270C2C2×#1681273011yescharacteristic
subgroupG/H
centerC23C2×C22⋊D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
FittingC2×C22⋊Q8×C109C2
socleC23×C109C2×D4
prime radicalC22×#13182029C2
hypercenterC2×C22⋊Q8D109
hypocenterC109C2×#452
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C22×#13182019C2semidirect
3. C22×#13182016C2semidirect
4. #20295186C2direct (N × H)
5. C2×#16812622C2semidirect
6. C2×#16812619C2semidirect
7. C2×C22⋊#11724784C2semidirect
8. C2×C22⋊Q8×C109C2semidirect
18. C2×#13182019C22semidirect
20. C2×#13182016C22semidirect
23. #16812622C22semidirect
24. #16812619C22semidirect
25. C22⋊#11724784C22semidirect
29. C22⋊Q8×C109C22semidirect
130. C2×C109#452semidirect
136. C109C2×#452semidirect
140. C2×C22⋊Q8D109semidirect
162. C22⋊Q8C2×D109semidirect
267. C2#20295186direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131820292
C22×#131820192
C22×#131820162
#202951862
C2×#168126222
C2×#168126192
C2×C22⋊#117247842
C2×C22⋊Q8×C1092
C2×#452109