Finite Group Databasebeta

← C2×#34036376 #49168374

Subgroups — C2×#34036376 #49168374

Order 37504.

544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 157 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×#17989791C211yesmaximal, characteristic, complemented
2C22×#17989785C211yesmaximal, characteristic, complemented
3C2×#22627604C211yesmaximal, characteristic, complemented
4C2×#22627599C211yesmaximal, characteristic
5#34036376C218yesmaximal, direct product factor
6C2×#22627547C211yesmaximal, characteristic, complemented
7C2×#22627544C211yesmaximal, characteristic, complemented
8C2×#107×C293C211yesmaximal, characteristic, complemented
9C22×Dic586C2211yescharacteristic
10C22×D1172—21no—
11C22×D1172C2211yescharacteristic
12C22×C4×D293C2211yescharacteristic
13C2×#17989791—24no—
14C2×#17989791C2214yescomplemented
15C2×#17989785—24no—
16C2×#17989785C2214yescomplemented
17C22×#14556873C2211yescharacteristic
18#22627604—22no—
19#22627604C2214yescomplemented
20#22627599—22no—
21#22627599C2214yes—
22C2×C4⋊Dic293—21no—
23C2×#17989779—21no—
24C2×#17989779—21no—
25#22627547C2214yescomplemented
26#22627544C2214yescomplemented
27C22×C8×C293C2211yescharacteristic
28C2×C4⋊C4×C293C2211yescharacteristic
29C2×C4⋊C4×C293C2211yescharacteristic
30#107×C293C2214yescomplemented
31C23×D293—21no—
32C23×D293D411yescharacteristic
33C2×Dic586—21no—
34C2×Dic586—22no—
35C2×Dic586—22no—
36C2×Dic586C2312yes—
37C2×D1172—24no—
38C2×D1172—22no—
39C2×D1172—21no—
40C2×D1172—22no—
41C2×D1172—44no—
42C2×D1172C2312yes—
43C22×Dic293—21no—
44C22×Dic293D411yescharacteristic
45C2×C4×D293—22no—
46C2×C4×D293—22no—
47C2×C4×D293D412yes—
48C2×C4×D293C2312yes—
49#17989791—28no—
50#17989785—28no—
51C2×#14556873—22no—
52C2×#14556873C2312yes—
53C4⋊Dic293—24no—
54#17989779—24no—
55#17989779—24no—
56C22×C4×C293—21no—
57C22×C4×C293—21no—
58C22×C4×C293C2311yescharacteristic
59C2×C8×C293D414yescomplemented
60C2×C8×C293C2312yes—
61C4⋊C4×C293—21no—
62C4⋊C4×C293—21no—
63C4⋊C4×C293C2312yes—
64C4⋊C4×C293C2312yes—
65C22×D293—22no—
66C22×D293—22no—
67C22×D293—22no—
68C22×D293—22no—
69C22×D293—42no—
70C22×D293—42no—
71C22×D293—42no—
72C22×D293C2×D412yes—
73Dic586—22no—
74Dic586—22no—
75Dic586—42no—
76D1172—22no—
77D1172—22no—
78D1172—48no—
79D1172—42no—
80C2×Dic293—22no—
81C2×Dic293—22no—
82C2×Dic293—42no—
83C2×Dic293C2×D412yes—
84C4×D293—24no—
85C4×D293—22no—
86C4×D293—22no—
87#14556873—22no—
88C23×C293C2×D411yescharacteristic
89C2×C4×C293—22no—
90C2×C4×C293—22no—
91C2×C4×C293—42no—
92C2×C4×C293—42no—
93C2×C4×C293C2×D411yescharacteristic
94C2×C4×C293C2×D412yes—
95C2×C4×C293#4112yes—
96C2×C4×C293C2411yescharacteristic
97C8×C293C2×D414yescomplemented
98C22×C293#12112yes—
99C22×C293AGL(1,ℤ/8)12yes—
100C22×C293#13712yes—
101C22×C293C22×D411yescharacteristic
102C2×D293—22no—
103C2×D293—22no—
104C2×D293—22no—
105C2×D293—44no—
106C2×D293—42no—
107C2×D293—42no—
108C2×D293—42no—
109C2×D293—84no—
110C4×C293—42no—
111C4×C293—42no—
112C4×C293#12112yes—
113C4×C293C22×D411yescharacteristic
114C4×C293C2×#4111yescharacteristic
115Dic293—22no—
116Dic293—42no—
117C2×C293#46814yescomplemented
118C2×C293C2×#12111yescharacteristic
119C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
120C2×C293C2×#13711yescharacteristic
121D293—42no—
122D293—82no—
123C293C2×#46811yescharacteristic, complemented, Sylow
124C2×#468—2931nomaximal, Sylow
125C22×SD16—2931no—
126C22×M16—2931no—
127C2×C22⋊Q8—2931no—
128C2×#121—2931no—
129#468—2938no—
130C2×#107D29311yescharacteristic, complemented
131C2×#103—2931no—
132C2×#102—2931no—
133C22×Q8—2931no—
134C22×D4—2931no—
135C22×D4—5861no—
136C23×C4—2931no—
137C2×SD16—2934no—
138C2×SD16—5864no—
139C2×M16—2934no—
140C2×M16—5864no—
141C22×C8—2931no—
142C22×C8C2×D29311yescharacteristic
143C22⋊Q8—2934no—
144C22⋊Q8—5862no—
145#121—2934no—
146#121—5862no—
147C2×C4⋊C4—5861no—
148C2×C4⋊C4C2×D29311yescharacteristic
149C2×C4⋊C4C2×D29311yescharacteristic
150C2×C22⋊C4—5861no—
151C2×C22⋊C4—5861no—
152#107C2×D29314yescomplemented
153#103—2934no—
154#102—2934no—
155C24—2931no—
156C24—5861no—
157C2×Q8—2932no—
158C2×Q8—5861no—
159C2×Q8—5862no—
160C2×Q8—5862no—
161C2×D4—2932no—
162C2×D4—5864no—
163C2×D4—5861no—
164C2×D4—5862no—
165C2×D4—5862no—
166C2×D4—11724no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—2931no—
170C22×C4—2932no—
171C22×C4—2932no—
172C22×C4—5862no—
173C22×C4—5862no—
174C22×C4—5861no—
175C22×C4C22×D29311yescharacteristic
176SD16—5868no—
177M16—5868no—
178C2×C8—2932no—
179C2×C8—5862no—
180C2×C8D117214yescomplemented
181C2×C8C22×D29312yes—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—5864no—
185C4⋊C4C22×D29312yes—
186C4⋊C4C22×D29312yes—
187C22⋊C4—5864no—
188C22⋊C4—5864no—
189C23—2932no—
190C23—5862no—
191C23—5862no—
192C23—5862no—
193C23—5862no—
194C23—11722no—
195C23—11722no—
196C23—11722no—
197C23D4×D29311yescharacteristic
198Q8—5862no—
199Q8—5862no—
200Q8—11722no—
201D4—5862no—
202D4—5862no—
203D4—11728no—
204D4—11722no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—2932no—
210C2×C4—5862no—
211C2×C4—5864no—
212C2×C4—5862no—
213C2×C4—5862no—
214C2×C4—5862no—
215C2×C4—11722no—
216C2×C4D4×D29311yescharacteristic
217C2×C4C2×D117212yes—
218C2×C4#1798980312yes—
219C2×C4C23×D29311yescharacteristic
220C8—5862no—
221C8C2×D117214yescomplemented
222C22—23444no—
223C22—5862no—
224C22—5862no—
225C22—5862no—
226C22—11722no—
227C22—11722no—
228C22—11722no—
229C22—11724no—
230C22#2262759912yes—
231C22#2262764812yes—
232C22#2262765612yes—
233C22C2×D4×D29311yescharacteristic
234C4—42no—
235C4—42no—
236C4—5862no—
237C4—11722no—
238C4#2262759912yes—
239C4C22×D117211yescharacteristic
240C4C2×#1798980311yescharacteristic
241C2—23442no—
242C2—11722no—
243C2#3403637614yesdirect product factor
244C2C2×#2262759911yescharacteristic
245C2C2×#2262764811yescharacteristic
246C2C2×#2262765611yescharacteristic
subgroupG/H
centerC23D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
FittingC2×#107×C293C2
socleC23×C293C2×D4
prime radicalC2×#22627599C2
hypercenterC2×#107D293
hypocenterC293C2×#468
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
1. C22×#17989791C2semidirect
2. C22×#17989785C2semidirect
3. C2×#22627604C2semidirect
5. #34036376C2direct (N × H)
6. C2×#22627547C2semidirect
7. C2×#22627544C2semidirect
8. C2×#107×C293C2semidirect
14. C2×#17989791C22semidirect
16. C2×#17989785C22semidirect
19. #22627604C22semidirect
25. #22627547C22semidirect
26. #22627544C22semidirect
30. #107×C293C22semidirect
59. C2×C8×C293D4semidirect
97. C8×C293C2×D4semidirect
117. C2×C293#468semidirect
123. C293C2×#468semidirect
130. C2×#107D293semidirect
152. #107C2×D293semidirect
180. C2×C8D1172semidirect
221. C8C2×D1172semidirect
243. C2#34036376direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#179897912
C22×#179897852
C2×#226276042
C2×#226275992
#340363762
C2×#226275472
C2×#226275442
C2×#107×C2932
C2×#468293