Finite Group Databasebeta

← #49171434

Subgroups — #49171434

Order 37504.

350 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 125 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#34036852C211yesmaximal, characteristic, complemented
2#34036486C212yesmaximal, complemented
3#34036481C211yesmaximal, characteristic, complemented
4#34036433C212yesmaximal, complemented
5#34036416C211yesmaximal, characteristic, complemented
6#34036344C212yesmaximal
7#34036334C211yesmaximal, characteristic, complemented
8Q8×#14556873C211yesmaximal, characteristic, complemented
9C4×#17989790C212yesmaximal, complemented
10C4×#17989787C211yesmaximal, characteristic
11#554×C293C211yesmaximal, characteristic, complemented
12C2×#17989790C2212yes—
13C2×#17989787C2211yescharacteristic
14#22627624C2211yescharacteristic
15#22627619—22no—
16#22627612C2212yes—
17#22627600—21no—
18C4×Dic586C2212yes—
19C4×D1172C2211yescharacteristic
20#22627582—21no—
21#22627557C2211yescharacteristic
22#22627555C2212yes—
23C4⋊#14556873C2211yescharacteristic
24C4⋊#14556873C2212yes—
25#22627547C2212yes—
26#22627547C2212yes—
27#22627547C2212yes—
28#22627545C2211yescharacteristic
29#22627544C2211yescharacteristic
30#22627544C2212yes—
31C4×#14556873C2211yescharacteristic
32C4×#14556873C2212yes—
33C4⋊Q8×C293C2211yescharacteristic
34#125×C293C2212yes—
35C22⋊Q8×C293—21no—
36C22⋊Q8×C293—22no—
37C4×Q8×C293C2211yescharacteristic
38C4×D4×C293C2211yescharacteristic
39C4×D4×C293C2212yes—
40C2×C4⋊C4×C293—21no—
41C2×Dic586C2312yes—
42C2×D1172C2311yescharacteristic
43C2×C4×D293—21no—
44#17989790—24no—
45#17989787—22no—
46C2×#14556873C2311yescharacteristic
47C2×#14556873C2312yes—
48C2×#14556873C2311yescharacteristic
49C4⋊Dic293—21no—
50C4⋊Dic293—21no—
51C4⋊Dic293C2311yescharacteristic
52#17989781—22no—
53#17989779—21no—
54#17989779—22no—
55#17989779—22no—
56C4×Dic293—22no—
57C2×Q8×C293—21no—
58C2×Q8×C293D411yescharacteristic
59C2×D4×C293C2311yescharacteristic
60C22×C4×C293—21no—
61C22×C4×C293—22no—
62C4⋊C4×C293—22no—
63C4⋊C4×C293—21no—
64C4⋊C4×C293—22no—
65C4⋊C4×C293D412yes—
66C4⋊C4×C293D411yescharacteristic
67C4⋊C4×C293C2311yescharacteristic
68C4⋊C4×C293C2312yes—
69C22⋊C4×C293—21no—
70C22⋊C4×C293—22no—
71C42×C293C2311yescharacteristic
72C42×C293C2312yes—
73C22×D293—21no—
74Dic586—22no—
75Dic586—22no—
76D1172—21no—
77D1172—21no—
78C2×Dic293—21no—
79C2×Dic293—22no—
80C4×D293—42no—
81#14556873—21no—
82#14556873—22no—
83#14556873—21no—
84C23×C293—21no—
85Q8×C293—22no—
86Q8×C293—81no—
87D4×C293—21no—
88D4×C293#4112yes—
89C2×C4×C293—21no—
90C2×C4×C293—22no—
91C2×C4×C293—42no—
92C2×C4×C293—82no—
93C2×C4×C293C2×D412yes—
94C2×C4×C293C2×D411yescharacteristic
95C2×C4×C293C2×D412yes—
96C2×C4×C293C2×D411yescharacteristic
97C2×C4×C293C2411yescharacteristic
98C22×C293—22no—
99C22×C293—41no—
100C22×C293—41no—
101C22×C293C22×D411yescharacteristic
102C2×D293—41no—
103C2×D293—41no—
104C2×D293—41no—
105C4×C293—22no—
106C4×C293—22no—
107C4×C293—21no—
108C4×C293—41no—
109C4×C293—42no—
110C4×C293#13512yes—
111C4×C293C2×#4111yescharacteristic
112C4×C2932−1+411yescharacteristic
113Dic293—42no—
114Dic293—41no—
115C2×C293—42no—
116C2×C293#54811yescharacteristic
117C2×C293C2×#13511yescharacteristic
118C2×C293#57711yescharacteristic
119D293—81no—
120C293#336011yescharacteristic, complemented, Sylow
121#3360—2931nomaximal, Sylow
122#556—2931no—
123#554D29311yescharacteristic, complemented
124#488—2932no—
125#487—2931no—
126#479—2932no—
127#476—2931no—
128#463—2932no—
129#461—2931no—
130C8×Q8—2931no—
131C4×SD16—2932no—
132C4×D8—2931no—
133C2×SD16—2932no—
134C2×D8—2931no—
135C4⋊Q8—2931no—
136C4⋊Q8C2×D29311yescharacteristic
137#126—5862no—
138#125C2×D29312yes—
139#124—2932no—
140C22⋊Q8—21no—
141C22⋊Q8—22no—
142C22⋊Q8—5861no—
143C4×Q8—2932no—
144C4×Q8C2×D29311yescharacteristic
145C4×D4—2931no—
146C4×D4C2×D29311yescharacteristic
147C4×D4C2×D29312yes—
148#117—5861no—
149C2×C4⋊C4—21no—
150#107—2931no—
151#106—2932no—
152C4⋊C8—2931no—
153C4⋊C8—2932no—
154#103—2932no—
155#103—2932no—
156#103—2932no—
157#102—2931no—
158#102—2931no—
159#102—2932no—
160C4×C8—2931no—
161C4×C8—2932no—
162C2×Q8—21no—
163C2×Q8—2932no—
164C2×Q8C22⋊D29311yescharacteristic
165C2×D4—2931no—
166C2×D4C22×D29311yescharacteristic
167C22×C4—21no—
168C22×C4—22no—
169C22×C4—5861no—
170SD16—5864no—
171D8—5862no—
172C2×C8—2931no—
173C2×C8—2932no—
174C2×C8—2931no—
175C4⋊C4—22no—
176C4⋊C4—21no—
177C4⋊C4—22no—
178C4⋊C4—2931no—
179C4⋊C4—5861no—
180C4⋊C4—5862no—
181C4⋊C4—5861no—
182C4⋊C4C22⋊D29311yescharacteristic
183C4⋊C4C22⋊D29312yes—
184C4⋊C4C22×D29312yes—
185C4⋊C4C22×D29311yescharacteristic
186C22⋊C4—21no—
187C22⋊C4—22no—
188C22⋊C4—5862no—
189C22⋊C4—5861no—
190C22⋊C4—5862no—
191C42—5862no—
192C42C22×D29311yescharacteristic
193C42C22×D29312yes—
194C23—21no—
195C23—5861no—
196Q8—22no—
197Q8—81no—
198Q8—5862no—
199Q8—5862no—
200D4—21no—
201D4—5861no—
202D4—5861no—
203D4#1798980312yes—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—42no—
207C2×C4—82no—
208C2×C4—5861no—
209C2×C4—5862no—
210C2×C4—11722no—
211C2×C4C2×C22⋊D29312yes—
212C2×C4C2×C22⋊D29312yes—
213C2×C4C2×C22⋊D29311yescharacteristic
214C2×C4C2×C22⋊D29311yescharacteristic
215C2×C4C23×D29311yescharacteristic
216C8—5861no—
217C8—5862no—
218C8—5861no—
219C22—22no—
220C22—41no—
221C22—41no—
222C22—11721no—
223C22—11721no—
224C22—11721no—
225C22C22×C22⋊D29311yescharacteristic
226C4—22no—
227C4—22no—
228C4—21no—
229C4—41no—
230C4—42no—
231C4—11722no—
232C4—11721no—
233C4#2262764412yes—
234C4C2×#1798980311yescharacteristic
235C4#2262767211yescharacteristic
236C2—42no—
237C2—23441no—
238C2#3403679011yescharacteristic
239C2C2×#2262764411yescharacteristic
240C2#3403694011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#554×C293C2
socleC22×C293C22×D4
prime radicalC2×#17989787C22
hypercenter#554D293
hypocenterC293#3360
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #554

Complements

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

NH ≅ G/Ntype
1. #34036852C2semidirect
2. #34036486C2semidirect
3. #34036481C2semidirect
4. #34036433C2semidirect
5. #34036416C2semidirect
7. #34036334C2semidirect
8. Q8×#14556873C2semidirect
9. C4×#17989790C2semidirect
11. #554×C293C2semidirect
120. C293#3360semidirect
123. #554D293semidirect

Maximal subgroups

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

subgroupindex
#340368522
#340364862
#340364812
#340364332
#340364162
#340363442
#340363342
Q8×#145568732
C4×#179897902
C4×#179897872
#554×C2932
#3360293