Finite Group Databasebeta

← #34055912

Subgroups — #34055912

Order 19072.

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

normal subgroups only

This group has 362 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#23750159C211yesmaximal, characteristic
2#23750031C212yesmaximal, complemented
3#23749987C212yesmaximal, complemented
4#23749955C212yesmaximal, complemented
5#23749938C212yesmaximal
6#23749917C212yesmaximal, complemented
7#23749912C212yesmaximal, complemented
8#23749682C211yesmaximal, characteristic, complemented
9C2×C4⋊Q8×C149C211yesmaximal, characteristic, complemented
10#18011905—21no—
11#18011903C2211yescharacteristic
12#18011899C2211yescharacteristic
13#18011894—21no—
14#18011890C2211yescharacteristic
15#18011885C2211yescharacteristic
16C4×Dic298C2211yescharacteristic
17C4×D596C2211yescharacteristic
18C4×C22⋊D149—21no—
19#18011868—21no—
20#18011844C2214yes—
21#18011842C2214yes—
22C4⋊#11924746C2212yes—
23#18011834C2214yes—
24#18011831C2214yes—
25C22⋊#11924746C2212yes—
26#18011822C2212yes—
27C22×Q8×C149—21no—
28C4⋊Q8×C149—21no—
29C4⋊Q8×C149—21no—
30C4⋊Q8×C149C2212yes—
31C4⋊Q8×C149C2212yes—
32C2×C4⋊C4×C149—21no—
33C2×C4⋊C4×C149C2212yes—
34C2×C42×C149C2211yescharacteristic
35C2×Dic298C2311yescharacteristic
36C2×D596C2311yescharacteristic
37C2×C22⋊D149—21no—
38C2×C4×D149—21no—
39C2×#11924746C2314yes—
40C4⋊Dic149C2311yescharacteristic
41C4⋊Dic149C2311yescharacteristic
42#14558715—21no—
43#14558715—21no—
44#14558715—21no—
45#14558715—21no—
46C22⋊Dic149—21no—
47#14558713—21no—
48#14558713—21no—
49#14558713—21no—
50#14558713—21no—
51C4×Dic149—21no—
52C2×Q8×C149—22no—
53C2×Q8×C149—22no—
54C2×Q8×C149—44no—
55C22×C4×C149—22no—
56C22×C4×C149D411yescharacteristic
57C22×C4×C149D411yescharacteristic
58C22×C4×C149C2311yescharacteristic
59C4⋊C4×C149—22no—
60C4⋊C4×C149—22no—
61C4⋊C4×C149—22no—
62C4⋊C4×C149C2314yes—
63C42×C149D411yescharacteristic
64C42×C149D411yescharacteristic
65C42×C149C2311yescharacteristic
66C42×C149C2311yescharacteristic
67C22×D149—21no—
68Dic298—22no—
69D596—22no—
70C22⋊D149—42no—
71C2×Dic149—21no—
72C2×Dic149—21no—
73C2×Dic149—21no—
74C4×D149—42no—
75#11924746—24no—
76C23×C149C2×D411yescharacteristic
77Q8×C149—44no—
78Q8×C149—44no—
79C2×C4×C149—22no—
80C2×C4×C149—22no—
81C2×C4×C149—22no—
82C2×C4×C149—24no—
83C2×C4×C149—44no—
84C2×C4×C149C2×D411yescharacteristic
85C2×C4×C149C2×D411yescharacteristic
86C2×C4×C149C2×D411yescharacteristic
87C2×C4×C149C2×D411yescharacteristic
88C2×C4×C149C2×D411yescharacteristic
89C2×C4×C149C2411yescharacteristic
90C22×C149—21no—
91C22×C149—21no—
92C22×C149AGL(1,ℤ/8)12yes—
93C22×C149C22×D411yescharacteristic
94C2×D149—41no—
95C2×D149—41no—
96C2×D149—41no—
97C4×C149—21no—
98C4×C149—21no—
99C4×C149—21no—
100C4×C149—21no—
101C4×C149—44no—
102C4×C149#13712yes—
103C4×C1492−1+412yes—
104Dic149—41no—
105Dic149—41no—
106Dic149—41no—
107C2×C149—22no—
108C2×C149#53611yescharacteristic
109C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
110C2×C149C2×#13711yescharacteristic
111D149—81no—
112C149#323811yescharacteristic, complemented, Sylow
113#3238—1491nomaximal, Sylow
114C2×C4⋊Q8D14911yescharacteristic, complemented
115#529—1491no—
116#501—1492no—
117#489—1492no—
118#483—1492no—
119#480—1492no—
120#477—1492no—
121#476—1492no—
122#432—1491no—
123C22×Q8—21no—
124C4⋊Q8—21no—
125C4⋊Q8—21no—
126C4⋊Q8C2×D14912yes—
127C4⋊Q8C2×D14912yes—
128#126—2981no—
129#125—1491no—
130#124—1491no—
131#123—2981no—
132C22⋊Q8—1491no—
133#121—1491no—
134C4×Q8—1491no—
135C4×D4—2981no—
136C4×D4—1491no—
137#117—2981no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4C2×D14912yes—
140C2×C42C2×D14911yescharacteristic
141#107—1494no—
142#106—1494no—
143C4⋊C8—1492no—
144#103—1494no—
145#102—1494no—
146C22⋊C8—1492no—
147#97—1492no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—44no—
151C2×Q8—1491no—
152C2×D4—2981no—
153C2×D4—1491no—
154C22×C4—22no—
155C22×C4—2981no—
156C22×C4C22⋊D14911yescharacteristic
157C22×C4C22⋊D14911yescharacteristic
158C22×C4C22×D14911yescharacteristic
159C2×C8—1494no—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C4⋊C4—22no—
163C4⋊C4—2981no—
164C4⋊C4—2981no—
165C4⋊C4—2981no—
166C4⋊C4—2981no—
167C4⋊C4—1491no—
168C4⋊C4—1491no—
169C4⋊C4C22×D14914yes—
170C22⋊C4—2981no—
171C22⋊C4—2981no—
172C22⋊C4—2981no—
173C22⋊C4—2981no—
174C22⋊C4—2981no—
175C42—2981no—
176C42C22⋊D14911yescharacteristic
177C42C22⋊D14911yescharacteristic
178C42C22×D14911yescharacteristic
179C42C22×D14911yescharacteristic
180C23—2981no—
181C23C2×C22⋊D14911yescharacteristic
182Q8—44no—
183Q8—44no—
184Q8—2982no—
185D4—2982no—
186D4—5962no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—24no—
191C2×C4—44no—
192C2×C4—2981no—
193C2×C4—2981no—
194C2×C4—2981no—
195C2×C4—5962no—
196C2×C4C2×C22⋊D14911yescharacteristic
197C2×C4C2×C22⋊D14911yescharacteristic
198C2×C4C2×C22⋊D14911yescharacteristic
199C2×C4C2×C22⋊D14911yescharacteristic
200C2×C4C2×C22⋊D14911yescharacteristic
201C2×C4C23×D14911yescharacteristic
202C8—2984no—
203C22—21no—
204C22—21no—
205C22—5961no—
206C22—5961no—
207C22—5961no—
208C22#1801193712yes—
209C22C22×C22⋊D14911yescharacteristic
210C4—21no—
211C4—21no—
212C4—21no—
213C4—21no—
214C4—44no—
215C4—5961no—
216C4—5961no—
217C4—5961no—
218C4#1801194212yes—
219C4#1801195912yes—
220C2—22no—
221C2—11921no—
222C2#2375019911yescharacteristic
223C2C2×#1801193711yescharacteristic
224C2C2×#1801194211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×C4⋊Q8×C149C2
socleC22×C149C22×D4
prime radical#18011885C22
hypercenterC2×C4⋊Q8D149
hypocenterC149#3238
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #23750031C2semidirect
3. #23749987C2semidirect
4. #23749955C2semidirect
6. #23749917C2semidirect
7. #23749912C2semidirect
8. #23749682C2semidirect
9. C2×C4⋊Q8×C149C2semidirect
112. C149#3238semidirect
114. C2×C4⋊Q8D149semidirect

Maximal subgroups

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

subgroupindex
#237501592
#237500312
#237499872
#237499552
#237499382
#237499172
#237499122
#237496822
C2×C4⋊Q8×C1492
#3238149