Finite Group Databasebeta

← #34057570

Subgroups — #34057570

Order 19072.

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

normal subgroups only

This group has 338 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#23750350C211yesmaximal, characteristic, complemented
2#23750332C211yesmaximal, characteristic
3#23750026C212yesmaximal, complemented
4#23750021C211yesmaximal, characteristic, complemented
5#23749931C212yesmaximal, complemented
6#23749923C212yesmaximal
7#23749921C211yesmaximal, characteristic, complemented
8#23749749C211yesmaximal, characteristic, complemented
9#23749716C212yesmaximal
10C4×#14558724C211yesmaximal, characteristic
11#474×C149C211yesmaximal, characteristic
12C2×#14558724C2211yescharacteristic
13#18011911C2211yescharacteristic
14#18011909—21no—
15#18011902C2212yes—
16#18011902C2212yes—
17#18011901—22no—
18#18011890—21no—
19#18011888—22no—
20Q8×Dic149—21no—
21C4×Dic298C2211yescharacteristic
22C4×Dic298C2211yescharacteristic
23#18011876C2212yes—
24D4×Dic149C2212yes—
25C2×C4⋊Dic149—21no—
26#18011845C2212yes—
27#18011842C2212yes—
28#18011842C2211yescharacteristic
29#18011842C2212yes—
30#18011840C2212yes—
31#18011836C2212yes—
32#18011834C2211yescharacteristic
33#18011832C2211yescharacteristic
34C4×#11924746C2211yescharacteristic
35C8×Dic149C2212yes—
36C4⋊Q8×C149C2211yescharacteristic
37C4×D4×C149C2211yescharacteristic
38#107×C149C2212yes—
39C4⋊C8×C149C2211yescharacteristic
40#102×C149C2212yes—
41C2×Dic298—21no—
42C2×Dic298D411yescharacteristic
43C2×Dic298C2311yescharacteristic
44C22×Dic149—22no—
45#14558724Q814yescomplemented
46C2×#11924746C2311yescharacteristic
47C2×#11924746C2311yescharacteristic
48C4⋊Dic149—22no—
49C4⋊Dic149—22no—
50C4⋊Dic149—21no—
51C4⋊Dic149D411yescharacteristic
52C4⋊Dic149C2312yes—
53C4⋊Dic149C2311yescharacteristic
54#14558715—22no—
55#14558715—22no—
56#14558715—22no—
57#14558715—21no—
58#14558715D412yes—
59C22⋊Dic149—22no—
60C4×Dic149—22no—
61C4×Dic149—21no—
62C4×Dic149C2312yes—
63C2×Q8×C149—21no—
64C2×D4×C149C2311yescharacteristic
65C22×C4×C149—21no—
66C2×C8×C149C2312yes—
67C4⋊C4×C149—21no—
68C4⋊C4×C149C2312yes—
69C4⋊C4×C149C2311yescharacteristic
70C22⋊C4×C149—21no—
71C42×C149C2311yescharacteristic
72Dic298—22no—
73Dic298—21no—
74Dic298—81no—
75Dic298C2×Q812yes—
76C2×Dic149—21no—
77C2×Dic149—22no—
78C2×Dic149—21no—
79C2×Dic149—82no—
80C2×Dic149C2×D412yes—
81C2×Dic149C2×D412yes—
82#11924746—21no—
83#11924746C2×Q812yes—
84C23×C149—21no—
85Q8×C149—42no—
86D4×C149—21no—
87D4×C149C2×Q812yes—
88C2×C4×C149—21no—
89C2×C4×C149—22no—
90C2×C4×C149—42no—
91C2×C4×C149C2×D411yescharacteristic
92C2×C4×C149C2×D411yescharacteristic
93C2×C4×C149C2411yescharacteristic
94C8×C149—22no—
95C22×C149—22no—
96C22×C149—41no—
97C22×C149—41no—
98C22×C149C22×D411yescharacteristic
99C4×C149—21no—
100C4×C149—41no—
101C4×C149—42no—
102C4×C149#13512yes—
103C4×C149C22×Q811yescharacteristic
104C4×C1492−1+411yescharacteristic
105Dic149—22no—
106Dic149—22no—
107Dic149—22no—
108Dic149—41no—
109Dic149—42no—
110C2×C149—42no—
111C2×C149D4×Q811yescharacteristic
112C2×C149C2×#13511yescharacteristic
113C2×C149#57711yescharacteristic
114C149#338111yescharacteristic, complemented, Sylow
115#3381—1491nomaximal, Sylow
116#557—1491no—
117#554—1491no—
118#499—1492no—
119#498—1491no—
120#479—1492no—
121#478—1492no—
122#477—1491no—
123#474D14911yescharacteristic
124C8×Q8—1491no—
125C4×SD16—1491no—
126C4×SD16—1492no—
127C2×SD16—1491no—
128C4⋊Q8—2981no—
129C4⋊Q8—1491no—
130C4⋊Q8C2×D14911yescharacteristic
131#125—2982no—
132#125—1492no—
133#125—1492no—
134C22⋊Q8—2982no—
135C22⋊Q8—2981no—
136C4×Q8—2981no—
137C4×Q8—1492no—
138C4×Q8—1491no—
139C4×Q8—1491no—
140C4×D4—1492no—
141C4×D4C2×D14911yescharacteristic
142C2×C4⋊C4—2981no—
143#107—1492no—
144#107C2×D14912yes—
145#106—1492no—
146#106—1491no—
147#106—1492no—
148C4⋊C8—1492no—
149C4⋊C8C2×D14911yescharacteristic
150#103—1492no—
151#103—1491no—
152#102—1491no—
153#102C2×D14912yes—
154C4×C8—1492no—
155C4×C8—1491no—
156C2×Q8—21no—
157C2×Q8—2981no—
158C2×Q8—1491no—
159C2×Q8—1491no—
160C2×D4C22×D14911yescharacteristic
161C22×C4—21no—
162C22×C4—2982no—
163SD16—1494no—
164C2×C8—1491no—
165C2×C8—1491no—
166C2×C8C22×D14912yes—
167C4⋊C4—21no—
168C4⋊C4—2982no—
169C4⋊C4—2982no—
170C4⋊C4—2982no—
171C4⋊C4—2982no—
172C4⋊C4—2982no—
173C4⋊C4—2981no—
174C4⋊C4—2981no—
175C4⋊C4—1491no—
176C4⋊C4—1492no—
177C4⋊C4—1491no—
178C4⋊C4—1492no—
179C4⋊C4C22×D14912yes—
180C4⋊C4C22×D14911yescharacteristic
181C22⋊C4—21no—
182C22⋊C4—2982no—
183C42—2982no—
184C42—2981no—
185C42—1492no—
186C42C22×D14911yescharacteristic
187C23—21no—
188Q8—42no—
189Q8—2982no—
190Q8—2981no—
191Q8—1492no—
192Q8—11921no—
193D4—21no—
194D4Q8×D14912yes—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—42no—
198C2×C4—2981no—
199C2×C4—2981no—
200C2×C4—2982no—
201C2×C4—1492no—
202C2×C4—1492no—
203C2×C4—11922no—
204C2×C4D4×D14911yescharacteristic
205C2×C4D4×D14911yescharacteristic
206C2×C4C23×D14911yescharacteristic
207C8—22no—
208C8—2981no—
209C8—1492no—
210C22—22no—
211C22—41no—
212C22—41no—
213C22C2×D4×D14911yescharacteristic
214C4—21no—
215C4—41no—
216C4—42no—
217C4—2982no—
218C4—2982no—
219C4—2982no—
220C4—5962no—
221C4—5961no—
222C4#1801193012yes—
223C4C2×Q8×D14911yescharacteristic
224C4#1801195811yescharacteristic
225C2—42no—
226C2#2375028811yescharacteristic
227C2C2×#1801193011yescharacteristic
228C2#2375043411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#474×C149C2
socleC22×C149C22×D4
prime radicalC2×D4×C149C23
hypercenter#474D149
hypocenterC149#3381
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #23750350C2semidirect
3. #23750026C2semidirect
4. #23750021C2semidirect
5. #23749931C2semidirect
7. #23749921C2semidirect
8. #23749749C2semidirect
45. #14558724Q8semidirect
114. C149#3381semidirect

Maximal subgroups

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

subgroupindex
#237503502
#237503322
#237500262
#237500212
#237499312
#237499232
#237499212
#237497492
#237497162
C4×#145587242
#474×C1492
#3381149