Finite Group Databasebeta

← #34081783

Subgroups — #34081783

Order 19328.

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×Dic302C211yesmaximal, characteristic
2#23752937C211yesmaximal, characteristic
3#23752562C211yesmaximal, characteristic
4#23752561C212yesmaximal
5#23752508C211yesmaximal, characteristic
6#23752505C212yesmaximal
7#23752420C212yesmaximal
8#23752336C211yesmaximal, characteristic
9Q16×Dic151C212yesmaximal
10C4×#14558994C211yesmaximal, characteristic
11#462×C151C211yesmaximal, characteristic
12C2×#14558994C2211yescharacteristic
13#18012739—21no—
14#18012739C2211yescharacteristic
15#18012738—22no—
16#18012738C2212yes—
17#18012737C2212yes—
18#18012730—21no—
19#18012729—22no—
20Q8×Dic151C2212yes—
21Q8×Dic151C2212yes—
22C4×Dic302—21no—
23C4×Dic302C2211yescharacteristic
24C4×Dic302C2211yescharacteristic
25#18012704—21no—
26#18012673C2212yes—
27#18012672C2211yescharacteristic
28Dic151⋊C8C2212yes—
29#18012664C2212yes—
30#18012663C2212yes—
31#18012663C2211yescharacteristic
32#18012663C2212yes—
33#18012662C2211yescharacteristic
34C4×C151⋊C8C2211yescharacteristic
35C8×Dic151C2212yes—
36C2×Q16×C151C2212yes—
37C4⋊Q8×C151C2211yescharacteristic
38C4×Q8×C151C2211yescharacteristic
39C4⋊C8×C151C2211yescharacteristic
40#103×C151C2212yes—
41C2×Dic302—22no—
42C2×Dic302—21no—
43C2×Dic302D411yescharacteristic
44C2×Dic302C2311yescharacteristic
45#14558994—22no—
46C2×C151⋊C8C2311yescharacteristic
47C2×C151⋊C8C2311yescharacteristic
48C4⋊Dic151—22no—
49C4⋊Dic151—22no—
50C4⋊Dic151—21no—
51C4⋊Dic151D411yescharacteristic
52C4⋊Dic151C2311yescharacteristic
53C4⋊Dic151C2312yes—
54Dic151⋊C4—22no—
55Dic151⋊C4—22no—
56Dic151⋊C4—22no—
57Dic151⋊C4—21no—
58Dic151⋊C4D412yes—
59C4×Dic151—22no—
60C4×Dic151—22no—
61C4×Dic151—21no—
62C4×Dic151C2312yes—
63C2×Q8×C151C2312yes—
64C2×Q8×C151C2311yescharacteristic
65Q16×C151—24no—
66C2×C8×C151C2312yes—
67C4⋊C4×C151—21no—
68C4⋊C4×C151—21no—
69C4⋊C4×C151—21no—
70C4⋊C4×C151C2311yescharacteristic
71C42×C151—21no—
72C42×C151C2311yescharacteristic
73Dic302—21no—
74Dic302—21no—
75Dic302—82no—
76Dic302—81no—
77Dic302Q1614yescomplemented
78C2×Dic151—21no—
79C2×Dic151—21no—
80C2×Dic151—22no—
81C2×Dic151C2×D412yes—
82C2×Dic151C2×D412yes—
83C151⋊C8—21no—
84C151⋊C8—21no—
85Q8×C151—21no—
86Q8×C151—22no—
87Q8×C151—22no—
88Q8×C151#4112yes—
89C2×C4×C151—21no—
90C2×C4×C151—22no—
91C2×C4×C151—21no—
92C2×C4×C151C2×D411yescharacteristic
93C2×C4×C151C2×D411yescharacteristic
94C2×C4×C151C2411yescharacteristic
95C8×C151—22no—
96C22×C151C22×D411yescharacteristic
97C4×C151—22no—
98C4×C151—21no—
99C4×C151—42no—
100C4×C151—41no—
101C4×C151C2×Q1612yes—
102C4×C151C2×#4111yescharacteristic
103C4×C1512−1+411yescharacteristic
104Dic151—22no—
105Dic151—41no—
106Dic151—41no—
107Dic151—42no—
108Dic151C2×Q1614yes—
109C2×C151#54811yescharacteristic
110C2×C151C22×Q1611yescharacteristic
111C2×C151#57711yescharacteristic
112C151#336311yescharacteristic, complemented, Sylow
113#3363—1511nomaximal, Sylow
114Q82—1511no—
115#557—1511no—
116#487—1511no—
117#487—1512no—
118#477—1511no—
119#477—1512no—
120#462—1512no—
121#462D15111yescharacteristic
122C8×Q8—1511no—
123C4×Q16—1512no—
124C4×Q16—1511no—
125C2×Q16—1511no—
126C2×Q16C2×D15112yes—
127C4⋊Q8—3021no—
128C4⋊Q8—3022no—
129C4⋊Q8—1512no—
130C4⋊Q8—1512no—
131C4⋊Q8—1511no—
132C4⋊Q8C2×D15111yescharacteristic
133#125—3022no—
134#125—3021no—
135C4×Q8—3021no—
136C4×Q8—3021no—
137C4×Q8—1512no—
138C4×Q8—1512no—
139C4×Q8—1511no—
140C4×Q8—1511no—
141C4×Q8C2×D15111yescharacteristic
142#107—1512no—
143#107—1511no—
144C4⋊C8—1512no—
145C4⋊C8C2×D15111yescharacteristic
146#103—1511no—
147#103—1512no—
148#103—1512no—
149#103—1512no—
150#103—1511no—
151#103C2×D15112yes—
152C4×C8—1512no—
153C4×C8—1511no—
154C2×Q8—3022no—
155C2×Q8—3021no—
156C2×Q8—1511no—
157C2×Q8—1511no—
158C2×Q8C22×D15112yes—
159C2×Q8C22×D15111yescharacteristic
160Q16—24no—
161Q16—3022no—
162C2×C8—1511no—
163C2×C8—1511no—
164C2×C8C22×D15112yes—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—3022no—
169C4⋊C4—3022no—
170C4⋊C4—3022no—
171C4⋊C4—3022no—
172C4⋊C4—3022no—
173C4⋊C4—3021no—
174C4⋊C4—3021no—
175C4⋊C4—1512no—
176C4⋊C4—1511no—
177C4⋊C4—1512no—
178C4⋊C4—1511no—
179C4⋊C4C22×D15111yescharacteristic
180C42—21no—
181C42—3022no—
182C42—3022no—
183C42—3021no—
184C42—1512no—
185C42C22×D15111yescharacteristic
186Q8—21no—
187Q8—22no—
188Q8—22no—
189Q8—3021no—
190Q8—3021no—
191Q8—1514no—
192Q8—12081no—
193Q8—12082no—
194Q8#1455900312yes—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—3021no—
199C2×C4—3021no—
200C2×C4—3022no—
201C2×C4—1512no—
202C2×C4—1512no—
203C2×C4D4×D15111yescharacteristic
204C2×C4D4×D15111yescharacteristic
205C2×C4C23×D15111yescharacteristic
206C8—22no—
207C8—3021no—
208C8—3021no—
209C22C2×D4×D15111yescharacteristic
210C4—21no—
211C4—22no—
212C4—41no—
213C4—42no—
214C4—3022no—
215C4—6042no—
216C4—6041no—
217C4—6041no—
218C4—1514no—
219C4Q16×D15112yes—
220C4C2×#1455900311yescharacteristic
221C4#1801278611yescharacteristic
222C2#2375286811yescharacteristic
223C2C2×Q16×D15111yescharacteristic
224C2#2375302111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#462×C151C2
socle, prime radicalC22×C151C22×D4
hypercenter#462D151
hypocenterC151#3363
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
77. Dic302Q16semidirect
112. C151#3363semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic3022
#237529372
#237525622
#237525612
#237525082
#237525052
#237524202
#237523362
Q16×Dic1512
C4×#145589942
#462×C1512
#3363151