Finite Group Databasebeta

← #34057367

Subgroups — #34057367

Order 19072.

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×Dic298C211yesmaximal, characteristic
2#23750353C211yesmaximal, characteristic
3#23749976C211yesmaximal, characteristic
4#23749974C212yesmaximal
5#23749920C211yesmaximal, characteristic
6#23749919C212yesmaximal
7#23749835C211yesmaximal, characteristic
8#23749833C212yesmaximal
9C8×Dic298C211yesmaximal, characteristic
10#23749717C212yesmaximal
11C4×Q16×C149C211yesmaximal, characteristic
12C2×#14558726C2212yes—
13#18011911—21no—
14#18011911C2211yescharacteristic
15#18011911C2211yescharacteristic
16#18011910—22no—
17#18011910C2212yes—
18#18011909C2212yes—
19#18011903—21no—
20#18011901—22no—
21Q8×Dic149C2212yes—
22C4×Dic298—21no—
23C4×Dic298—21no—
24C4×Dic298C2211yescharacteristic
25#18011876C2212yes—
26#18011844C2212yes—
27C4⋊#11924746C2211yescharacteristic
28#18011840C2212yes—
29#18011836C2212yes—
30#18011836C2212yes—
31#18011835C2212yes—
32#18011834C2212yes—
33C8×Dic149C2212yes—
34C2×Q16×C149C2211yescharacteristic
35C4×Q8×C149C2211yescharacteristic
36C4×Q8×C149C2211yescharacteristic
37#107×C149C2211yescharacteristic
38#103×C149C2211yescharacteristic
39#103×C149C2211yescharacteristic
40C4×C8×C149C2211yescharacteristic
41C2×Dic298—22no—
42C2×Dic298—21no—
43C2×Dic298D411yescharacteristic
44C2×Dic298C2312yes—
45#14558726—24no—
46C2×#11924746C2312yes—
47C4⋊Dic149—22no—
48C4⋊Dic149—21no—
49C4⋊Dic149—21no—
50C4⋊Dic149—21no—
51C4⋊Dic149D411yescharacteristic
52C4⋊Dic149C2312yes—
53#14558715—22no—
54#14558715—22no—
55#14558715—22no—
56#14558715—22no—
57#14558715D412yes—
58C4×Dic149—22no—
59C4×Dic149—22no—
60C4×Dic149C2312yes—
61C2×Q8×C149C2311yescharacteristic
62C2×Q8×C149C2311yescharacteristic
63Q16×C149—22no—
64C2×C8×C149C2311yescharacteristic
65C2×C8×C149C2311yescharacteristic
66C4⋊C4×C149—21no—
67C4⋊C4×C149—21no—
68C4⋊C4×C149C2311yescharacteristic
69C4⋊C4×C149C2311yescharacteristic
70C42×C149—21no—
71C42×C149—21no—
72C42×C149C2311yescharacteristic
73Dic298—22no—
74Dic298—22no—
75Dic298—82no—
76Dic298—81no—
77Dic298Q1614yescomplemented
78C2×Dic149—22no—
79C2×Dic149—22no—
80C2×Dic149C2×D412yes—
81C2×Dic149C2×D412yes—
82#11924746—22no—
83Q8×C149—21no—
84Q8×C149—21no—
85Q8×C149—21no—
86Q8×C149#4112yes—
87C2×C4×C149—21no—
88C2×C4×C149—21no—
89C2×C4×C149—21no—
90C2×C4×C149—21no—
91C2×C4×C149C2×D411yescharacteristic
92C2×C4×C149C2×D411yescharacteristic
93C2×C4×C149C2411yescharacteristic
94C8×C149—21no—
95C8×C149—21no—
96C22×C149C22×D411yescharacteristic
97C4×C149—22no—
98C4×C149—21no—
99C4×C149—41no—
100C4×C149—41no—
101C4×C149—41no—
102C4×C149C2×Q1612yes—
103C4×C149C2×#4111yescharacteristic
104C4×C1492−1+411yescharacteristic
105Dic149—22no—
106Dic149—42no—
107Dic149—42no—
108Dic149C2×Q1614yes—
109C2×C149#54811yescharacteristic
110C2×C149C22×Q1611yescharacteristic
111C2×C149#57711yescharacteristic
112C149#336311yescharacteristic, complemented, Sylow
113#3363—1491nomaximal, Sylow
114Q82—1491no—
115#557—1491no—
116#487—1492no—
117#487—1491no—
118#477—1491no—
119#477—1492no—
120#462—1492no—
121#462—1491no—
122C8×Q8—1491no—
123C4×Q16—1492no—
124C4×Q16D14911yescharacteristic
125C2×Q16—1492no—
126C2×Q16C2×D14911yescharacteristic
127C4⋊Q8—2981no—
128C4⋊Q8—2982no—
129C4⋊Q8—1492no—
130C4⋊Q8—1492no—
131C4⋊Q8—1491no—
132C4⋊Q8—1491no—
133#125—2981no—
134#125—2982no—
135C4×Q8—2981no—
136C4×Q8—2981no—
137C4×Q8—1492no—
138C4×Q8—1492no—
139C4×Q8—1491no—
140C4×Q8C2×D14911yescharacteristic
141C4×Q8C2×D14911yescharacteristic
142#107—1492no—
143#107C2×D14911yescharacteristic
144C4⋊C8—1492no—
145C4⋊C8—1491no—
146#103—1492no—
147#103—1492no—
148#103—1492no—
149#103—1492no—
150#103C2×D14911yescharacteristic
151#103C2×D14911yescharacteristic
152C4×C8—1492no—
153C4×C8C2×D14911yescharacteristic
154C2×Q8—2982no—
155C2×Q8—2981no—
156C2×Q8—1492no—
157C2×Q8—1491no—
158C2×Q8C22×D14911yescharacteristic
159C2×Q8C22×D14911yescharacteristic
160Q16—22no—
161Q16—2984no—
162C2×C8—1492no—
163C2×C8C22×D14911yescharacteristic
164C2×C8C22×D14911yescharacteristic
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—2982no—
168C4⋊C4—2982no—
169C4⋊C4—2982no—
170C4⋊C4—2982no—
171C4⋊C4—2982no—
172C4⋊C4—2981no—
173C4⋊C4—2981no—
174C4⋊C4—2981no—
175C4⋊C4—1492no—
176C4⋊C4—1492no—
177C4⋊C4—1491no—
178C4⋊C4C22×D14911yescharacteristic
179C4⋊C4C22×D14911yescharacteristic
180C42—21no—
181C42—21no—
182C42—2982no—
183C42—2982no—
184C42—1492no—
185C42C22×D14911yescharacteristic
186Q8—21no—
187Q8—21no—
188Q8—21no—
189Q8—2982no—
190Q8—2982no—
191Q8—1494no—
192Q8—11921no—
193Q8—11922no—
194Q8#1455873612yes—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—2982no—
200C2×C4—2982no—
201C2×C4—1492no—
202C2×C4—1492no—
203C2×C4D4×D14911yescharacteristic
204C2×C4D4×D14911yescharacteristic
205C2×C4C23×D14911yescharacteristic
206C8—21no—
207C8—21no—
208C8—2982no—
209C22C2×D4×D14911yescharacteristic
210C4—21no—
211C4—22no—
212C4—41no—
213C4—41no—
214C4—41no—
215C4—2982no—
216C4—5962no—
217C4—5962no—
218C4—1494no—
219C4Q16×D14912yes—
220C4C2×#1455873611yescharacteristic
221C4#1801195811yescharacteristic
222C2#2375028411yescharacteristic
223C2C2×Q16×D14911yescharacteristic
224C2#2375043211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC4×Q16×C149C2
socle, prime radicalC22×C149C22×D4
hypercenterC4×Q16D149
hypocenterC149#3363
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
77. Dic298Q16semidirect
112. C149#3363semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic2982
#237503532
#237499762
#237499742
#237499202
#237499192
#237498352
#237498332
C8×Dic2982
#237497172
C4×Q16×C1492
#3363149