Finite Group Databasebeta

← #49171458

Subgroups — #49171458

Order 37504.

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

normal subgroups only

This group has 336 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
1Q8×Dic586C211yesmaximal, characteristic
2#34036854C211yesmaximal, characteristic
3#34036479C211yesmaximal, characteristic
4#34036478C212yesmaximal
5#34036425C211yesmaximal, characteristic
6#34036422C212yesmaximal
7#34036337C212yesmaximal
8#34036253C211yesmaximal, characteristic
9Q16×Dic293C212yesmaximal
10C4×#17989792C211yesmaximal, characteristic
11#462×C293C211yesmaximal, characteristic
12C2×#17989792C2211yescharacteristic
13#22627624—21no—
14#22627624C2211yescharacteristic
15#22627623—22no—
16#22627623C2212yes—
17#22627622C2212yes—
18#22627615—21no—
19#22627614—22no—
20Q8×Dic293C2212yes—
21Q8×Dic293C2212yes—
22C4×Dic586—21no—
23C4×Dic586C2211yescharacteristic
24C4×Dic586C2211yescharacteristic
25#22627589—21no—
26#22627558C2212yes—
27#22627557C2211yescharacteristic
28#22627553C2212yes—
29#22627549C2212yes—
30#22627548C2211yescharacteristic
31#22627548C2212yes—
32#22627548C2212yes—
33#22627547C2211yescharacteristic
34C4×#14556873C2211yescharacteristic
35C8×Dic293C2212yes—
36C2×Q16×C293C2212yes—
37C4⋊Q8×C293C2211yescharacteristic
38C4×Q8×C293C2211yescharacteristic
39C4⋊C8×C293C2211yescharacteristic
40#103×C293C2212yes—
41C2×Dic586—22no—
42C2×Dic586—21no—
43C2×Dic586D411yescharacteristic
44C2×Dic586C2311yescharacteristic
45#17989792—22no—
46C2×#14556873C2311yescharacteristic
47C2×#14556873C2311yescharacteristic
48C4⋊Dic293—22no—
49C4⋊Dic293—22no—
50C4⋊Dic293—21no—
51C4⋊Dic293D411yescharacteristic
52C4⋊Dic293C2311yescharacteristic
53C4⋊Dic293C2312yes—
54#17989781—22no—
55#17989781—22no—
56#17989781—22no—
57#17989781—21no—
58#17989781D412yes—
59C4×Dic293—22no—
60C4×Dic293—22no—
61C4×Dic293—21no—
62C4×Dic293C2312yes—
63C2×Q8×C293C2312yes—
64C2×Q8×C293C2311yescharacteristic
65Q16×C293—24no—
66C2×C8×C293C2312yes—
67C4⋊C4×C293—21no—
68C4⋊C4×C293—21no—
69C4⋊C4×C293—21no—
70C4⋊C4×C293C2311yescharacteristic
71C42×C293—21no—
72C42×C293C2311yescharacteristic
73Dic586—21no—
74Dic586—21no—
75Dic586—82no—
76Dic586—81no—
77Dic586Q1614yescomplemented
78C2×Dic293—21no—
79C2×Dic293—21no—
80C2×Dic293—22no—
81C2×Dic293C2×D412yes—
82C2×Dic293C2×D412yes—
83#14556873—21no—
84#14556873—21no—
85Q8×C293—21no—
86Q8×C293—22no—
87Q8×C293—22no—
88Q8×C293#4112yes—
89C2×C4×C293—21no—
90C2×C4×C293—21no—
91C2×C4×C293—22no—
92C2×C4×C293C2×D411yescharacteristic
93C2×C4×C293C2×D411yescharacteristic
94C2×C4×C293C2411yescharacteristic
95C8×C293—22no—
96C22×C293C22×D411yescharacteristic
97C4×C293—22no—
98C4×C293—21no—
99C4×C293—42no—
100C4×C293—41no—
101C4×C293C2×Q1612yes—
102C4×C293C2×#4111yescharacteristic
103C4×C2932−1+411yescharacteristic
104Dic293—22no—
105Dic293—41no—
106Dic293—41no—
107Dic293—42no—
108Dic293C2×Q1614yes—
109C2×C293#54811yescharacteristic
110C2×C293C22×Q1611yescharacteristic
111C2×C293#57711yescharacteristic
112C293#336311yescharacteristic, complemented, Sylow
113#3363—2931nomaximal, Sylow
114Q82—2931no—
115#557—2931no—
116#487—2931no—
117#487—2932no—
118#477—2931no—
119#477—2932no—
120#462—2932no—
121#462D29311yescharacteristic
122C8×Q8—2931no—
123C4×Q16—2932no—
124C4×Q16—2931no—
125C2×Q16—2931no—
126C2×Q16C2×D29312yes—
127C4⋊Q8—2932no—
128C4⋊Q8—2932no—
129C4⋊Q8—2931no—
130C4⋊Q8—5861no—
131C4⋊Q8—5862no—
132C4⋊Q8C2×D29311yescharacteristic
133#125—5862no—
134#125—5861no—
135C4×Q8—2931no—
136C4×Q8—2932no—
137C4×Q8—2932no—
138C4×Q8—2931no—
139C4×Q8—5861no—
140C4×Q8—5861no—
141C4×Q8C2×D29311yescharacteristic
142#107—2932no—
143#107—2931no—
144C4⋊C8—2932no—
145C4⋊C8C2×D29311yescharacteristic
146#103—2931no—
147#103—2932no—
148#103—2932no—
149#103—2932no—
150#103—2931no—
151#103C2×D29312yes—
152C4×C8—2932no—
153C4×C8—2931no—
154C2×Q8—2931no—
155C2×Q8—2931no—
156C2×Q8—5862no—
157C2×Q8—5861no—
158C2×Q8C22×D29312yes—
159C2×Q8C22×D29311yescharacteristic
160Q16—24no—
161Q16—5862no—
162C2×C8—2931no—
163C2×C8—2931no—
164C2×C8C22×D29312yes—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—2932no—
169C4⋊C4—2931no—
170C4⋊C4—2932no—
171C4⋊C4—2931no—
172C4⋊C4—5862no—
173C4⋊C4—5862no—
174C4⋊C4—5862no—
175C4⋊C4—5862no—
176C4⋊C4—5862no—
177C4⋊C4—5861no—
178C4⋊C4—5861no—
179C4⋊C4C22×D29311yescharacteristic
180C42—21no—
181C42—2932no—
182C42—5862no—
183C42—5862no—
184C42—5861no—
185C42C22×D29311yescharacteristic
186Q8—21no—
187Q8—22no—
188Q8—22no—
189Q8—2934no—
190Q8—23441no—
191Q8—23442no—
192Q8—5861no—
193Q8—5861no—
194Q8#1798980112yes—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—2932no—
199C2×C4—2932no—
200C2×C4—5861no—
201C2×C4—5862no—
202C2×C4—5861no—
203C2×C4D4×D29311yescharacteristic
204C2×C4D4×D29311yescharacteristic
205C2×C4C23×D29311yescharacteristic
206C8—22no—
207C8—5861no—
208C8—5861no—
209C22C2×D4×D29311yescharacteristic
210C4—22no—
211C4—21no—
212C4—42no—
213C4—41no—
214C4—2934no—
215C4—5862no—
216C4—11721no—
217C4—11722no—
218C4—11721no—
219C4Q16×D29312yes—
220C4C2×#1798980111yescharacteristic
221C4#2262767111yescharacteristic
222C2#3403678511yescharacteristic
223C2C2×Q16×D29311yescharacteristic
224C2#3403693811yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#462×C293C2
socle, prime radicalC22×C293C22×D4
hypercenter#462D293
hypocenterC293#3363
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
77. Dic586Q16semidirect
112. C293#3363semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic5862
#340368542
#340364792
#340364782
#340364252
#340364222
#340363372
#340362532
Q16×Dic2932
C4×#179897922
#462×C2932
#3363293