Finite Group Databasebeta

← #49157752

Subgroups — #49157752

Order 37504.

282 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 51 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
1#34036706C211yesmaximal, characteristic
2#34036268C211yesmaximal, characteristic, complemented
3#34036048C211yesmaximal, characteristic, complemented
4#34035864C211yesmaximal, characteristic, complemented
5#34035863C211yesmaximal, characteristic, complemented
6#34035854C211yesmaximal, characteristic, complemented
7#448×C293C211yesmaximal, characteristic, complemented
8C2×#17989801—21no—
9C2×#17989789—21no—
10#22627602—21no—
11#22627601—21no—
12#22627598C2211yescharacteristic
13#22627597—21no—
14#22627596—21no—
15#22627596—21no—
16C2×#17989781—21no—
17C2×#17989781C2211yescharacteristic
18#22627548—21no—
19C22⋊#14556873C2211yescharacteristic
20#22627531—21no—
21#22627531C2211yescharacteristic
22C22×Q8×C293C2211yescharacteristic
23C2×SD16×C293—21no—
24#121×C293C2211yescharacteristic
25#103×C293—21no—
26C22⋊C8×C293C2211yescharacteristic
27#17989801—42no—
28#17989801—42no—
29C2×Dic586—21no—
30C2×D1172D411yescharacteristic
31C2×C22⋊D293—21no—
32C2×C22⋊D293—21no—
33C2×C22⋊D293—21no—
34C22×Dic293—21no—
35C22×Dic293—21no—
36C22×Dic293D411yescharacteristic
37C22×Dic293D411yescharacteristic
38C2×C4×D293—21no—
39#17989789—42no—
40C2×#14556873—21no—
41C4⋊Dic293D411yescharacteristic
42#17989781—21no—
43#17989781—21no—
44#17989781—21no—
45#17989781—42no—
46C22⋊Dic293—21no—
47#17989779—21no—
48#17989779—21no—
49C2×Q8×C293—21no—
50C2×Q8×C293—21no—
51C2×Q8×C293—42no—
52C2×D4×C293—21no—
53C2×D4×C293D411yescharacteristic
54C22×C4×C293—21no—
55C22×C4×C293C2311yescharacteristic
56SD16×C293—42no—
57C2×C8×C293—21no—
58C4⋊C4×C293D411yescharacteristic
59C22⋊C4×C293—21no—
60C22×D293—21no—
61Dic586—42no—
62D1172—41no—
63C22⋊D293—42no—
64C22⋊D293—41no—
65C22⋊D293—41no—
66C22⋊D293—81no—
67C2×Dic293—21no—
68C2×Dic293—21no—
69C2×Dic293—22no—
70C2×Dic293—21no—
71C2×Dic293—21no—
72C2×Dic293—42no—
73C2×Dic293—41no—
74C2×Dic293—41no—
75C2×Dic293—41no—
76C2×Dic293SD1612yescomplemented
77C4×D293—42no—
78#14556873—41no—
79C23×C293—21no—
80C23×C293C2×D411yescharacteristic
81Q8×C293—22no—
82Q8×C293—22no—
83Q8×C293—41no—
84Q8×C293—41no—
85D4×C293—41no—
86D4×C293—41no—
87D4×C293—41no—
88C2×C4×C293—22no—
89C2×C4×C293—21no—
90C2×C4×C293—41no—
91C2×C4×C293—41no—
92C2×C4×C293—41no—
93C2×C4×C293C2×D411yescharacteristic
94C2×C4×C293C2×D411yescharacteristic
95C8×C293—41no—
96C22×C293—21no—
97C22×C293—21no—
98C22×C293—41no—
99C22×C293—41no—
100C22×C293—41no—
101C22×C293#12011yescharacteristic
102C22×C293C2×SD1611yescharacteristic
103C22×C293AGL(1,ℤ/8)11yescharacteristic
104C2×D293—41no—
105C2×D293—41no—
106C2×D293—41no—
107C4×C293—21no—
108C4×C293—21no—
109C4×C293—41no—
110C4×C293—42no—
111Dic293—22no—
112Dic293—42no—
113Dic293—41no—
114Dic293—41no—
115C2×C293—21no—
116C2×C293—21no—
117C2×C293—81no—
118C2×C293#45011yescharacteristic
119C2×C293#45611yescharacteristic
120C2×C293B(4,𝔽2)11yescharacteristic
121D293—81no—
122C293#160411yescharacteristic, complemented, Sylow
123#1604—2931nomaximal, Sylow
124#537—2931no—
125#448—2931no—
126#448D29311yescharacteristic, complemented
127#395—2931no—
128#327—2931no—
129#327—2931no—
130#324—2931no—
131C2×#41—5861no—
132C22×Q8C2×D29311yescharacteristic
133C2×SD16—21no—
134C2×SD16—5861no—
135C22⋊Q8—5861no—
136C22⋊Q8—5861no—
137#121—2931no—
138#121—5861no—
139#121—5861no—
140#121—5861no—
141#121C2×D29311yescharacteristic
142C2×C4⋊C4—2931no—
143C2×C4⋊C4—5861no—
144#103—21no—
145#103—5861no—
146C22⋊C8—2931no—
147C22⋊C8C2×D29311yescharacteristic
148#95—2931no—
149#95—5861no—
150#41—11722no—
151#41—11722no—
152C2×Q8—21no—
153C2×Q8—21no—
154C2×Q8—42no—
155C2×Q8—5861no—
156C2×D4—21no—
157C2×D4—2931no—
158C2×D4—5861no—
159C2×D4—5861no—
160C2×D4—5861no—
161C2×D4C22⋊D29311yescharacteristic
162C22×C4—21no—
163C22×C4—2931no—
164C22×C4—2931no—
165C22×C4—5861no—
166C22×C4—5861no—
167C22×C4—5861no—
168C22×C4C22×D29311yescharacteristic
169SD16—42no—
170SD16—11722no—
171C2×C8—21no—
172C2×C8—5861no—
173C4⋊C4—2931no—
174C4⋊C4—5861no—
175C4⋊C4—5861no—
176C4⋊C4—5861no—
177C4⋊C4—11722no—
178C4⋊C4C22⋊D29311yescharacteristic
179C22⋊C4—21no—
180C22⋊C4—5861no—
181C22⋊C4—5861no—
182C22⋊C4—5861no—
183C23—21no—
184C23—5861no—
185C23D4×D29311yescharacteristic
186Q8—22no—
187Q8—22no—
188Q8—41no—
189Q8—41no—
190Q8—11722no—
191D4—41no—
192D4—41no—
193D4—41no—
194D4—23441no—
195D4—11721no—
196D4—11722no—
197D4—11721no—
198D4—11721no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—2932no—
205C2×C4—5861no—
206C2×C4—5861no—
207C2×C4—5862no—
208C2×C4—5861no—
209C2×C4—5861no—
210C2×C4—11722no—
211C2×C4—11722no—
212C2×C4—11721no—
213C2×C4—11721no—
214C2×C4—11721no—
215C2×C4D4×D29311yescharacteristic
216C2×C4C2×C22⋊D29311yescharacteristic
217C8—41no—
218C8—11721no—
219C22—21no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—41no—
224C22—11721no—
225C22—11721no—
226C22—11721no—
227C22#2262759211yescharacteristic
228C22SD16×D29311yescharacteristic
229C22#2262765111yescharacteristic
230C4—21no—
231C4—21no—
232C4—41no—
233C4—42no—
234C4—5862no—
235C4—11722no—
236C4—11721no—
237C4—11721no—
238C2—21no—
239C2—21no—
240C2—81no—
241C2—23441no—
242C2#3403627811yescharacteristic
243C2#3403631011yescharacteristic
244C2#3403631511yescharacteristic
subgroupG/H
centerC22#22627592
commutator, cosocleC22×C4×C293C23
FrattiniC22×C4C22×D293
Fitting#448×C293C2
socleC22×C293#120
prime radical#34036706C2
hypercenter#448D293
hypocenterC293#1604
LCSG ▷ C22×C4×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
2. #34036268C2semidirect
3. #34036048C2semidirect
4. #34035864C2semidirect
5. #34035863C2semidirect
6. #34035854C2semidirect
7. #448×C293C2semidirect
76. C2×Dic293SD16semidirect
122. C293#1604semidirect
126. #448D293semidirect

Maximal subgroups

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

subgroupindex
#340367062
#340362682
#340360482
#340358642
#340358632
#340358542
#448×C2932
#1604293