Finite Group Databasebeta

← #49159925

Subgroups — #49159925

Order 37504.

290 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 87 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×#22627623C211yesmaximal, characteristic
2C2×#22627549C211yesmaximal, characteristic
3C2×#22627547C211yesmaximal, characteristic
4#34036034C211yesmaximal, characteristic
5#34035891C211yesmaximal, characteristic
6#34035883C211yesmaximal, characteristic
7#340×C293C211yesmaximal, characteristic
8C22×Dic586—21no—
9C22×Dic586C2211yescharacteristic
10C22×#14556873C2211yescharacteristic
11#22627623—22no—
12#22627623—22no—
13C2×C4⋊Dic293C2211yescharacteristic
14C2×#17989781—21no—
15C2×C4×Dic293C2211yescharacteristic
16#22627549—22no—
17#22627547—22no—
18#22627531—21no—
19#22627531—21no—
20C22×C8×C293C2211yescharacteristic
21C2×C4⋊C4×C293C2211yescharacteristic
22C2×C4⋊C4×C293C2211yescharacteristic
23C2×Dic586—24no—
24C2×Dic586—21no—
25C2×Dic586—21no—
26C2×Dic586—21no—
27C2×Dic586—21no—
28C2×Dic586—21no—
29C2×Dic586—42no—
30C2×Dic586—42no—
31C2×Dic586Q812yescomplemented
32C22×Dic293—21no—
33C22×Dic293—21no—
34C22×Dic293D411yescharacteristic
35C22×Dic293D411yescharacteristic
36C2×#14556873—21no—
37C2×#14556873—21no—
38C2×#14556873—21no—
39C4⋊Dic293—21no—
40C4⋊Dic293D412yes—
41#17989781—24no—
42C4×Dic293—21no—
43C4×Dic293—21no—
44C22×C4×C293—21no—
45C22×C4×C293—21no—
46C22×C4×C293C2311yescharacteristic
47C2×C8×C293—21no—
48C2×C8×C293—21no—
49C2×C8×C293—21no—
50C4⋊C4×C293—21no—
51C4⋊C4×C293—21no—
52C4⋊C4×C293—21no—
53C4⋊C4×C293D412yes—
54Dic586—22no—
55Dic586—22no—
56Dic586—48no—
57Dic586—41no—
58Dic586—41no—
59C2×Dic293—21no—
60C2×Dic293—21no—
61C2×Dic293—21no—
62C2×Dic293—21no—
63C2×Dic293—22no—
64C2×Dic293—22no—
65C2×Dic293—41no—
66C2×Dic293—41no—
67C2×Dic293—41no—
68C2×Dic293—41no—
69C2×Dic293SD1612yes—
70C2×Dic293Q1612yes—
71#14556873—41no—
72C23×C293C2×D411yescharacteristic
73C2×C4×C293—22no—
74C2×C4×C293—41no—
75C2×C4×C293—41no—
76C2×C4×C293—41no—
77C2×C4×C293—41no—
78C2×C4×C293—41no—
79C2×C4×C293C2×D411yescharacteristic
80C2×C4×C293C2×D411yescharacteristic
81C2×C4×C293C2×Q811yescharacteristic
82C2×C4×C293#4111yescharacteristic
83C2×C4×C293#4111yescharacteristic
84C2×C4×C293#4111yescharacteristic
85C8×C293—41no—
86C22×C293#12011yescharacteristic
87C22×C293C22⋊Q811yescharacteristic
88C22×C293#12411yescharacteristic
89C22×C293C2×SD1611yescharacteristic
90C22×C293C2×Q1611yescharacteristic
91C22×C293AGL(1,ℤ/8)11yescharacteristic
92C22×C293#13711yescharacteristic
93C4×C293—42no—
94C4×C293—81no—
95C4×C293C22⋊Q811yescharacteristic
96C4×C293C22⋊Q811yescharacteristic
97C4×C293#12411yescharacteristic
98C4×C293#12411yescharacteristic
99Dic293—22no—
100Dic293—22no—
101Dic293—42no—
102Dic293—42no—
103C2×C293#39311yescharacteristic
104C2×C293#45011yescharacteristic
105C2×C293#45111yescharacteristic
106C2×C293#47511yescharacteristic
107C2×C293#47711yescharacteristic
108C2×C293#48711yescharacteristic
109C2×C293#48911yescharacteristic
110C293#202411yescharacteristic, complemented, Sylow
111#2024—2931nomaximal, Sylow
112C2×C4⋊Q8—2931no—
113C2×#103—2931no—
114C2×#103—2931no—
115#391—2931no—
116#340—2931no—
117#340D29311yescharacteristic
118#336—2931no—
119C22×Q8—2931no—
120C22×Q8—5861no—
121C22×C8—2931no—
122C22×C8C2×D29311yescharacteristic
123C4⋊Q8—5862no—
124C4⋊Q8—5862no—
125C2×C4⋊C4—2931no—
126C2×C4⋊C4—5861no—
127C2×C4⋊C4C2×D29311yescharacteristic
128C2×C4⋊C4C2×D29311yescharacteristic
129C2×C42—2931no—
130#103—5862no—
131#103—5862no—
132#95—5861no—
133#95—5861no—
134C2×Q8—2932no—
135C2×Q8—5864no—
136C2×Q8—5861no—
137C2×Q8—5861no—
138C2×Q8—5861no—
139C2×Q8—5861no—
140C2×Q8—5861no—
141C2×Q8—11722no—
142C2×Q8—11722no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—2931no—
146C22×C4—2931no—
147C22×C4—5861no—
148C22×C4—5861no—
149C22×C4C22×D29311yescharacteristic
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—5861no—
154C2×C8—5861no—
155C2×C8—5861no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—2932no—
160C4⋊C4—5864no—
161C4⋊C4—5861no—
162C4⋊C4D117212yes—
163C42—5861no—
164C42—5861no—
165C23D4×D29311yescharacteristic
166Q8—5862no—
167Q8—5862no—
168Q8—11728no—
169Q8—11721no—
170Q8—11721no—
171C2×C4—22no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—2932no—
178C2×C4—2932no—
179C2×C4—5861no—
180C2×C4—5861no—
181C2×C4—5861no—
182C2×C4—5861no—
183C2×C4—5862no—
184C2×C4—5862no—
185C2×C4—11721no—
186C2×C4—11721no—
187C2×C4—11721no—
188C2×C4—11721no—
189C2×C4D4×D29311yescharacteristic
190C2×C4C2×D117211yescharacteristic
191C2×C4Q8×D29311yescharacteristic
192C2×C4#1798980111yescharacteristic
193C2×C4#1798980211yescharacteristic
194C2×C4#1798980211yescharacteristic
195C8—41no—
196C8—11721no—
197C22#2262759411yescharacteristic
198C22#2262760211yescharacteristic
199C22#2262761011yescharacteristic
200C22SD16×D29311yescharacteristic
201C22Q16×D29311yescharacteristic
202C22#2262764811yescharacteristic
203C22#2262765311yescharacteristic
204C4—42no—
205C4—81no—
206C4—5862no—
207C4—5862no—
208C4—11722no—
209C4—11722no—
210C4#2262760211yescharacteristic
211C4#2262760411yescharacteristic
212C4#2262761011yescharacteristic
213C4#2262761211yescharacteristic
214C2#3403604211yescharacteristic
215C2#3403628111yescharacteristic
216C2#3403628611yescharacteristic
217C2#3403641311yescharacteristic
218C2#3403642311yescharacteristic
219C2#3403647811yescharacteristic
220C2#3403648711yescharacteristic
subgroupG/H
centerC23D4×D293
commutator, cosocleC22×C4×C293C23
FrattiniC22×C4C22×D293
Fitting#340×C293C2
socle, prime radicalC23×C293C2×D4
hypercenter#340D293
hypocenterC293#2024
LCSG ▷ C22×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
31. C2×Dic586Q8semidirect
110. C293#2024semidirect

Maximal subgroups

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

subgroupindex
C2×#226276232
C2×#226275492
C2×#226275472
#340360342
#340358912
#340358832
#340×C2932
#2024293