Finite Group Databasebeta

← C2×#34036389 #49168481

Subgroups — C2×#34036389 #49168481

Order 37504.

468 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C2×#22627655C211yesmaximal, characteristic, complemented
2C2×#22627650C211yesmaximal, characteristic
3C2×#22627630C211yesmaximal, characteristic, complemented
4#34036389C218yesmaximal, direct product factor
5C2×#22627560C211yesmaximal, characteristic, complemented
6C2×#22627543C211yesmaximal, characteristic, complemented
7C2×#22627541C211yesmaximal, characteristic, complemented
8C22×SD16×C293C211yesmaximal, characteristic, complemented
9C2×#17989802C2211yescharacteristic
10#22627655—22no—
11#22627655C2214yescomplemented
12#22627650—22no—
13#22627650C2214yes—
14C2×#17989792—21no—
15C2×#17989790—21no—
16C2×#17989789—21no—
17C2×#17989787—21no—
18#22627630—22no—
19#22627630C2214yescomplemented
20C2×#17989786C2211yescharacteristic
21C2×#17989786C2211yescharacteristic
22C2×#17989786C2211yescharacteristic
23C2×#17989785—21no—
24C2×C8×D293—21no—
25#22627560C2214yescomplemented
26#22627543C2214yescomplemented
27#22627541C2214yescomplemented
28C22×Q8×C293C2211yescharacteristic
29C22×D4×C293C2211yescharacteristic
30C2×SD16×C293—21no—
31C2×SD16×C293—21no—
32C2×SD16×C293—22no—
33C2×SD16×C293C2214yescomplemented
34C22×C8×C293C2211yescharacteristic
35#17989802—21no—
36#17989802—21no—
37#17989802D412yes—
38#17989802C2312yes—
39C2×Dic586D411yescharacteristic
40C2×D1172D411yescharacteristic
41C2×C22⋊D293—21no—
42C2×C4×D293—21no—
43#17989792—24no—
44#17989790—24no—
45#17989789—24no—
46#17989787—24no—
47#17989786—21no—
48#17989786—21no—
49#17989786—21no—
50#17989786C2312yes—
51#17989786C2312yes—
52#17989786C2312yes—
53#17989785—24no—
54C2×#14556873—21no—
55C2×#14556873—21no—
56C2×#14556873—21no—
57C8×D293—24no—
58C24×C293—21no—
59C2×Q8×C293—21no—
60C2×Q8×C293—21no—
61C2×Q8×C293—21no—
62C2×Q8×C293—21no—
63C2×Q8×C293—21no—
64C2×Q8×C293C2312yes—
65C2×D4×C293—21no—
66C2×D4×C293—21no—
67C2×D4×C293—21no—
68C2×D4×C293—21no—
69C2×D4×C293—21no—
70C2×D4×C293C2312yes—
71C22×C4×C293—21no—
72C22×C4×C293C2311yescharacteristic
73SD16×C293—24no—
74SD16×C293—24no—
75C2×C8×C293D411yescharacteristic
76C2×C8×C293D411yescharacteristic
77C2×C8×C293D412yes—
78C2×C8×C293C2312yes—
79C22×D293—21no—
80Dic586—21no—
81Dic586C2×D412yes—
82D1172—21no—
83D1172C2×D412yes—
84C22⋊D293—22no—
85C22⋊D293—22no—
86C2×Dic293—21no—
87C4×D293—22no—
88C4×D293—22no—
89#14556873—22no—
90#14556873—22no—
91#14556873—22no—
92C23×C293—22no—
93C23×C293—41no—
94C23×C293—41no—
95C23×C293—82no—
96C23×C293#4111yescharacteristic
97Q8×C293—22no—
98Q8×C293—22no—
99Q8×C293—41no—
100Q8×C293—41no—
101D4×C293—22no—
102D4×C293—22no—
103D4×C293—41no—
104D4×C293—41no—
105C2×C4×C293—22no—
106C2×C4×C293—41no—
107C2×C4×C293—41no—
108C2×C4×C293C2×D411yescharacteristic
109C2×C4×C293C2×D411yescharacteristic
110C2×C4×C293C2×D411yescharacteristic
111C2×C4×C293C2×D411yescharacteristic
112C2×C4×C293#4111yescharacteristic
113C2×C4×C293C2411yescharacteristic
114C8×C293C2×D412yes—
115C8×C293C2×D412yes—
116C22×C293—22no—
117C22×C293—42no—
118C22×C293—82no—
119C22×C293—82no—
120C22×C293—82no—
121C22×C293#12111yescharacteristic
122C22×C293#12111yescharacteristic
123C22×C293C2×#4111yescharacteristic
124C2×D293—22no—
125C2×D293—42no—
126C4×C293—42no—
127C4×C293#12111yescharacteristic
128C4×C293#12111yescharacteristic
129C4×C293C22×D411yescharacteristic
130C4×C293C22×D411yescharacteristic
131Dic293—22no—
132C2×C293—21no—
133C2×C293—21no—
134C2×C293—82no—
135C2×C293#47112yescomplemented
136C2×C293C2×#12111yescharacteristic
137D293—42no—
138C293C2×#47111yescharacteristic, complemented, Sylow
139C2×#471—2931nomaximal, Sylow
140C2×#137—2931no—
141C2×AGL(1,ℤ/8)—2931no—
142C22×SD16D29311yescharacteristic, complemented
143C2×#131—2931no—
144#471—2938no—
145C2×#108—2931no—
146C2×#101—2931no—
147C2×#100—2931no—
148C2×#41—2931no—
149C22×Q8C2×D29311yescharacteristic
150C22×D4C2×D29311yescharacteristic
151#137—2934no—
152#137—5862no—
153AGL(1,ℤ/8)—2934no—
154AGL(1,ℤ/8)—5862no—
155C2×Q16—5861no—
156C2×SD16—21no—
157C2×SD16—21no—
158C2×SD16—22no—
159C2×SD16—5861no—
160C2×SD16—5861no—
161C2×SD16C2×D29314yescomplemented
162C2×D8—5861no—
163#131—2934no—
164#131—5862no—
165C2×M16—2931no—
166C2×M16—2931no—
167C2×M16—2931no—
168C2×M16—5861no—
169C22×C8—5861no—
170C22×C8C2×D29311yescharacteristic
171#108—2934no—
172#101—2934no—
173#100—2934no—
174C24—21no—
175#41—2932no—
176#41—2932no—
177#41—5861no—
178#41—5861no—
179C2×Q8—21no—
180C2×Q8—21no—
181C2×Q8—21no—
182C2×Q8—21no—
183C2×Q8—21no—
184C2×Q8—2931no—
185C2×Q8C22×D29312yes—
186C2×D4—21no—
187C2×D4—21no—
188C2×D4—21no—
189C2×D4—21no—
190C2×D4—21no—
191C2×D4—2931no—
192C2×D4—5861no—
193C2×D4C22×D29312yes—
194C22×C4—21no—
195C22×C4—5861no—
196C22×C4C22×D29311yescharacteristic
197Q16—5864no—
198SD16—24no—
199SD16—24no—
200SD16—5864no—
201SD16—5864no—
202D8—5864no—
203M16—2932no—
204M16—2932no—
205M16—2932no—
206M16—5861no—
207M16—5861no—
208M16—5861no—
209M16—5864no—
210C2×C8—5861no—
211C2×C8—5861no—
212C2×C8—5861no—
213C2×C8—5864no—
214C2×C8C22⋊D29311yescharacteristic
215C2×C8C22⋊D29311yescharacteristic
216C2×C8C22⋊D29312yes—
217C2×C8C22×D29312yes—
218C23—22no—
219C23—41no—
220C23—41no—
221C23—82no—
222C23—5861no—
223C23#1798980111yescharacteristic
224Q8—22no—
225Q8—22no—
226Q8—41no—
227Q8—41no—
228Q8—2932no—
229Q8—5861no—
230D4—22no—
231D4—22no—
232D4—41no—
233D4—41no—
234D4—2932no—
235D4—5862no—
236D4—5862no—
237D4—5861no—
238C2×C4—22no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—5861no—
242C2×C4—5862no—
243C2×C4—5862no—
244C2×C4D4×D29311yescharacteristic
245C2×C4D4×D29311yescharacteristic
246C2×C4C2×C22⋊D29311yescharacteristic
247C2×C4C2×C22⋊D29311yescharacteristic
248C2×C4#1798980111yescharacteristic
249C2×C4C23×D29311yescharacteristic
250C8—5862no—
251C8—5862no—
252C8—5862no—
253C8C2×C22⋊D29312yes—
254C8C2×C22⋊D29312yes—
255C22—22no—
256C22—42no—
257C22—82no—
258C22—82no—
259C22—82no—
260C22—5862no—
261C22—11722no—
262C22#2262759511yescharacteristic
263C22#2262759511yescharacteristic
264C22C2×#1798980111yescharacteristic
265C4—42no—
266C4—5862no—
267C4#2262759511yescharacteristic
268C4#2262759511yescharacteristic
269C4C2×D4×D29311yescharacteristic
270C4C22×C22⋊D29311yescharacteristic
271C2—21no—
272C2—21no—
273C2—82no—
274C2—11722no—
275C2#3403638912yesdirect product factor
276C2C2×#2262759511yescharacteristic
subgroupG/H
centerC22#22627595
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
FittingC22×SD16×C293C2
socleC22×C293#121
prime radicalC2×#22627650C2
hypercenterC22×SD16D293
hypocenterC293C2×#471
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#22627655C2semidirect
3. C2×#22627630C2semidirect
4. #34036389C2direct (N × H)
5. C2×#22627560C2semidirect
6. C2×#22627543C2semidirect
7. C2×#22627541C2semidirect
8. C22×SD16×C293C2semidirect
11. #22627655C22semidirect
19. #22627630C22semidirect
25. #22627560C22semidirect
26. #22627543C22semidirect
27. #22627541C22semidirect
33. C2×SD16×C293C22semidirect
135. C2×C293#471semidirect
138. C293C2×#471semidirect
142. C22×SD16D293semidirect
161. C2×SD16C2×D293semidirect
275. C2#34036389direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#226276552
C2×#226276502
C2×#226276302
#340363892
C2×#226275602
C2×#226275432
C2×#226275412
C22×SD16×C2932
C2×#471293