Finite Group Databasebeta

← #34060562

Subgroups — #34060562

Order 19072.

292 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 84 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
1D149⋊(C4⋊C8)C211yesmaximal, characteristic
2C2×#18011974C212yesmaximal
3#23750569C211yesmaximal, characteristic
4#23750498C212yesmaximal
5C4×Q8×D149C211yesmaximal, characteristic
6C2×D149⋊C8C2212yes—
7C2×C4⋊#10597010C2212yes—
8#18011978—21no—
9C4⋊#11924753—21no—
10#18011974—24no—
11(C2×#10597010)⋊C4—21no—
12(C2×#10597010)⋊C4—21no—
13C2×Q8×D149C2211yescharacteristic
14Q8×Dic149C411yescharacteristic, complemented
15C4×Dic298—21no—
16C4×Dic298C411yescharacteristic, complemented
17#18011876—21no—
18#18011876C411yescharacteristic, complemented
19C4⋊C4×D149—21no—
20C4⋊C4×D149C2211yescharacteristic
21C42×D149—21no—
22C42×D149C2211yescharacteristic
23C4×Q8×C149C411yescharacteristic, complemented
24C22×#10597010—22no—
25D149⋊C8—22no—
26D149⋊C8—22no—
27C2×#11924753—22no—
28C4⋊#10597010—22no—
29C4⋊#10597010—22no—
30C2×Dic298—21no—
31C2×Dic298C2×C411yescharacteristic
32Q8×D149—21no—
33Q8×D149—21no—
34Q8×D149D412yes—
35Q8×D149Q812yes—
36C2×C4×D149—21no—
37C2×C4×D149—21no—
38C2×C4×D149D411yescharacteristic
39C2×C4×D149D411yescharacteristic
40C2×C4×D149C2311yescharacteristic
41C4⋊Dic149—21no—
42C4⋊Dic149C2×C411yescharacteristic
43#14558715—21no—
44#14558715—21no—
45#14558715—21no—
46C4×Dic149—21no—
47C4×Dic149—21no—
48C4×Dic149—21no—
49C4×Dic149C2×C411yescharacteristic
50C4×Dic149D411yescharacteristic
51C4×Dic149D411yescharacteristic
52C2×Q8×C149C2×C411yescharacteristic
53C4⋊C4×C149—21no—
54C4⋊C4×C149C2×C411yescharacteristic
55C42×C149—21no—
56C42×C149C2×C411yescharacteristic
57C2×#10597010—42no—
58C2×#10597010—42no—
59C2×#10597010—42no—
60#11924753—42no—
61C22×D149C2×D411yescharacteristic
62Dic298—21no—
63Dic298—22no—
64Dic298—22no—
65Dic298C4⋊C412yes—
66C2×Dic149—21no—
67C2×Dic149—21no—
68C2×Dic149C22⋊C411yescharacteristic
69C2×Dic149C22⋊C411yescharacteristic
70C2×Dic149C2×D411yescharacteristic
71C4×D149—22no—
72C4×D149—22no—
73C4×D149—22no—
74C4×D149—22no—
75C4×D149—42no—
76C4×D149C2×D411yescharacteristic
77C4×D149C2×Q811yescharacteristic
78C4×D149#4111yescharacteristic
79C4×D149#4111yescharacteristic
80Q8×C149—21no—
81Q8×C149C4⋊C412yes—
82C2×C4×C149—21no—
83C2×C4×C149—21no—
84C2×C4×C149C22⋊C411yescharacteristic
85C2×C4×C149C22⋊C411yescharacteristic
86C2×C4×C149C22×C411yescharacteristic
87C22×C149C2×C22⋊C411yescharacteristic
88C2×D149#12111yescharacteristic
89C2×D149C22⋊Q811yescharacteristic
90C2×D149#13512yes—
91C2×D149#13712yes—
92#10597010—82no—
93C4×C149—22no—
94C4×C149—21no—
95C4×C149—21no—
96C4×C149—41no—
97C4×C149C2×C4⋊C411yescharacteristic
98C4×C149#11711yescharacteristic
99Dic149—22no—
100Dic149—21no—
101Dic149—21no—
102Dic149—41no—
103Dic149#12111yescharacteristic
104Dic149C22⋊Q811yescharacteristic
105C2×C149#38011yescharacteristic
106C2×C149#41611yescharacteristic
107C2×C149#41911yescharacteristic
108D149#46412yes—
109D149#47912yes—
110C149#180511yescharacteristic, complemented, Sylow
111#1805—1491nomaximal, Sylow
112C2×C4×Q8—1491no—
113C2×C4⋊C8—1491no—
114C2×#103—1492no—
115#382—1491no—
116#340—1492no—
117C22×Q8—1491no—
118C22×C8—1492no—
119C4×Q8—2981no—
120C4×Q8—2981no—
121C4×Q8—1491no—
122C4×Q8—1491no—
123C4×Q8—1491no—
124C4×Q8#1059701011yescharacteristic, complemented
125C2×C4⋊C4—2981no—
126C2×C4⋊C4—1492no—
127C2×C4⋊C4—1491no—
128C2×C42—2981no—
129C2×C42—1491no—
130C4⋊C8—2981no—
131C4⋊C8—2981no—
132#103—2984no—
133#95—2981no—
134#95—2981no—
135C2×Q8—2981no—
136C2×Q8—2981no—
137C2×Q8—2981no—
138C2×Q8—1492no—
139C2×Q8—1492no—
140C2×Q8—1491no—
141C2×Q8C2×#1059701011yescharacteristic
142C22×C4—2981no—
143C22×C4—2981no—
144C22×C4—2982no—
145C22×C4—1491no—
146C22×C4—1491no—
147C22×C4—1491no—
148C2×C8—2982no—
149C2×C8—2982no—
150C2×C8—2982no—
151C4⋊C4—21no—
152C4⋊C4—2981no—
153C4⋊C4—2981no—
154C4⋊C4—2981no—
155C4⋊C4—2981no—
156C4⋊C4—2982no—
157C4⋊C4—2982no—
158C4⋊C4—1491no—
159C4⋊C4C2×#1059701011yescharacteristic
160C42—21no—
161C42—2981no—
162C42—2981no—
163C42—2981no—
164C42—1491no—
165C42—1491no—
166C42—1491no—
167C42C2×#1059701011yescharacteristic
168C23—1491no—
169Q8—21no—
170Q8—2982no—
171Q8—2982no—
172Q8—2981no—
173Q8—1492no—
174Q8C4⋊#1059701012yes—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—2982no—
178C2×C4—2982no—
179C2×C4—2982no—
180C2×C4—2982no—
181C2×C4—2981no—
182C2×C4—2981no—
183C2×C4—5962no—
184C2×C4—5962no—
185C2×C4—5962no—
186C2×C4—5962no—
187C2×C4—1491no—
188C2×C4—1491no—
189C2×C4—1491no—
190C2×C4—1491no—
191C2×C4—1491no—
192C2×C4—1491no—
193C2×C4—1491no—
194C2×C4C22⋊#1059701011yescharacteristic
195C2×C4C22⋊#1059701011yescharacteristic
196C2×C4C22×#1059701011yescharacteristic
197C8—5962no—
198C22—1491no—
199C22—1491no—
200C22—1492no—
201C22—1492no—
202C22C2×C22⋊#1059701011yescharacteristic
203C4—22no—
204C4—21no—
205C4—21no—
206C4—41no—
207C4—2982no—
208C4—2981no—
209C4—2981no—
210C4—5961no—
211C4—1491no—
212C4—1491no—
213C4—11922no—
214C4C2×C4⋊#1059701011yescharacteristic
215C4#1801199011yescharacteristic
216C2—1492no—
217C2—1492no—
218C2#2375056711yescharacteristic
219C2#2375061511yescharacteristic
220C2#2375061811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC4×Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC22×D149C2×D4
cosocleC2×C4×D149C23
hypercenterC4×Q8#10597010
hypocenterC149#1805
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
14. Q8×Dic149C4semidirect
16. C4×Dic298C4semidirect
18. #18011876C4semidirect
23. C4×Q8×C149C4semidirect
110. C149#1805semidirect
124. C4×Q8#10597010semidirect

Maximal subgroups

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

subgroupindex
D149⋊(C4⋊C8)2
C2×#180119742
#237505692
#237504982
C4×Q8×D1492
#1805149