Finite Group Databasebeta

← #34055763

Subgroups — #34055763

Order 19072.

396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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#23750237C211yesmaximal, characteristic, complemented
2#23750020C211yesmaximal, characteristic, complemented
3#23749997C211yesmaximal, characteristic, complemented
4#23749989C211yesmaximal, characteristic, complemented
5#23749979C211yesmaximal, characteristic, complemented
6#23749844C212yesmaximal, complemented
7#23749822C212yesmaximal, complemented
8#23749787C212yesmaximal, complemented
9#23749776C212yesmaximal, complemented
10#23749686C211yesmaximal, characteristic, complemented
11#535×C149C211yesmaximal, characteristic
12C2×#14558726C2212yescomplemented
13C2×#14558724C2212yes—
14C2×#14558724C2212yes—
15C2×#14558724C2212yescomplemented
16#18011911C2211yescharacteristic, complemented
17#18011904—22no—
18#18011903C2211yescharacteristic, complemented
19#18011901—22no—
20#18011890C2212yes—
21C4×Dic298C2212yescomplemented
22C4⋊#11924746C2212yescomplemented
23#18011835C2212yescomplemented
24#18011832C2212yes—
25#18011832C2212yes—
26#18011832C2212yescomplemented
27C22⋊#11924746C2212yes—
28#18011822C2211yescharacteristic, complemented
29C4×#11924746C2211yescharacteristic, complemented
30C2×#41×C149C2211yescharacteristic
31C22×D4×C149C2211yescharacteristic
32#127×C149C2211yescharacteristic
33#127×C149C2211yescharacteristic
34#124×C149C2211yescharacteristic
35#124×C149C2211yescharacteristic
36#121×C149—22no—
37#120×C149—22no—
38#117×C149C2211yescharacteristic
39C2×Dic298C2312yes—
40#14558726—42no—
41#14558724—42no—
42#14558724—42no—
43#14558724—42no—
44C2×#11924746C2312yes—
45C2×#11924746C2312yes—
46C4⋊Dic149—22no—
47C4⋊Dic149C2312yes—
48#14558715—22no—
49#14558715—22no—
50#14558715—22no—
51C22⋊Dic149—22no—
52C4×Dic149—22no—
53C24×C149—21no—
54#41×C149—42no—
55C2×Q8×C149C2311yescharacteristic
56C2×D4×C149—21no—
57C2×D4×C149—21no—
58C2×D4×C149—22no—
59C2×D4×C149—22no—
60C2×D4×C149—42no—
61C2×D4×C149C2311yescharacteristic
62C2×D4×C149C2311yescharacteristic
63C2×D4×C149C2311yescharacteristic
64C22×C4×C149—21no—
65C22×C4×C149C2311yescharacteristic
66C4⋊C4×C149D412yes—
67C22⋊C4×C149—22no—
68C22⋊C4×C149—22no—
69C22⋊C4×C149D412yes—
70C42×C149C2311yescharacteristic
71C42×C149C2311yescharacteristic
72Dic298—22no—
73Dic298—22no—
74C2×Dic149—22no—
75C2×Dic149—22no—
76#11924746—22no—
77#11924746—22no—
78C23×C149—21no—
79C23×C149—21no—
80C23×C149—21no—
81C23×C149—42no—
82C23×C149—82no—
83C23×C149C2×D411yescharacteristic
84Q8×C149—22no—
85D4×C149—22no—
86D4×C149—22no—
87D4×C149—22no—
88D4×C149—42no—
89D4×C149—42no—
90D4×C149—82no—
91D4×C149—82no—
92C2×C4×C149—22no—
93C2×C4×C149—21no—
94C2×C4×C149—42no—
95C2×C4×C149C2×D412yes—
96C2×C4×C149C2×D412yes—
97C2×C4×C149C2×D411yescharacteristic
98C2×C4×C149C2411yescharacteristic
99C22×C149—21no—
100C22×C149—22no—
101C22×C149—41no—
102C22×C149—41no—
103C22×C149—41no—
104C22×C149—42no—
105C22×C149—42no—
106C22×C149—42no—
107C22×C149—84no—
108C22×C149C22×D411yescharacteristic
109C4×C149—21no—
110C4×C149—22no—
111C4×C149—22no—
112C4×C149—41no—
113C4×C149H(5,𝔽2)12yes—
114Dic149—42no—
115Dic149—42no—
116C2×C149—41no—
117C2×C149—81no—
118C2×C149—81no—
119C2×C149—81no—
120C2×C149#53511yescharacteristic
121C2×C149#57712yes—
122C149#322211yescharacteristic, complemented, Sylow
123#3222—1491nomaximal, Sylow
124#541—1491no—
125#535D14911yescharacteristic
126#497—1491no—
127#492—1491no—
128#490—1491no—
129#488—1491no—
130#464—1492no—
131#460—1492no—
132#452—1492no—
133#450—1492no—
134#433—1491no—
135C2×#41C2×D14911yescharacteristic
136C22×D4C2×D14911yescharacteristic
137C2×Q16—1492no—
138C2×SD16—1492no—
139C2×SD16—1492no—
140C2×SD16—1492no—
141C4⋊Q8—1491no—
142#127C2×D14911yescharacteristic
143#127C2×D14911yescharacteristic
144#126—2982no—
145#125—2982no—
146#125—1491no—
147#124C2×D14911yescharacteristic
148#124C2×D14911yescharacteristic
149C22⋊Q8—1492no—
150#121—22no—
151#120—22no—
152C4×Q8—1492no—
153#117C2×D14911yescharacteristic
154C4⋊C8—1492no—
155#103—1492no—
156#102—1492no—
157#102—1492no—
158#102—1492no—
159C22⋊C8—1492no—
160#97—1491no—
161C4×C8—1491no—
162C24—21no—
163#41—42no—
164C2×Q8—1492no—
165C2×Q8C22×D14911yescharacteristic
166C2×D4—21no—
167C2×D4—21no—
168C2×D4—22no—
169C2×D4—22no—
170C2×D4—42no—
171C2×D4C22×D14911yescharacteristic
172C2×D4C22×D14911yescharacteristic
173C2×D4C22×D14911yescharacteristic
174C22×C4—21no—
175C22×C4C22×D14911yescharacteristic
176Q16—5962no—
177SD16—5962no—
178SD16—5962no—
179SD16—5962no—
180C2×C8—1492no—
181C2×C8—1492no—
182C4⋊C4—2982no—
183C4⋊C4—2982no—
184C4⋊C4—2982no—
185C4⋊C4—2982no—
186C4⋊C4—1492no—
187C4⋊C4C22⋊D14912yes—
188C22⋊C4—22no—
189C22⋊C4—22no—
190C22⋊C4—2982no—
191C22⋊C4C22⋊D14912yes—
192C42—2982no—
193C42C22×D14911yescharacteristic
194C42C22×D14911yescharacteristic
195C23—21no—
196C23—21no—
197C23—21no—
198C23—42no—
199C23—82no—
200C23C2×C22⋊D14911yescharacteristic
201Q8—22no—
202Q8—2982no—
203Q8—2982no—
204D4—22no—
205D4—22no—
206D4—22no—
207D4—42no—
208D4—42no—
209D4—82no—
210D4—82no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—42no—
214C2×C4—2982no—
215C2×C4—2982no—
216C2×C4C2×C22⋊D14912yes—
217C2×C4C2×C22⋊D14912yes—
218C2×C4C2×C22⋊D14911yescharacteristic
219C2×C4C23×D14911yescharacteristic
220C8—2982no—
221C8—2982no—
222C22—22no—
223C22—21no—
224C22—42no—
225C22—42no—
226C22—42no—
227C22—41no—
228C22—41no—
229C22—41no—
230C22—84no—
231C22C22×C22⋊D14911yescharacteristic
232C4—22no—
233C4—22no—
234C4—21no—
235C4—41no—
236C4—5962no—
237C4—5962no—
238C4#1801195612yes—
239C2—41no—
240C2—81no—
241C2—81no—
242C2—81no—
243C2#2375019211yescharacteristic
244C2#2375043612yes—
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting, prime radical#535×C149C2
socleC22×C149C22×D4
hypercenter#535D149
hypocenterC149#3222
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #23750237C2semidirect
2. #23750020C2semidirect
3. #23749997C2semidirect
4. #23749989C2semidirect
5. #23749979C2semidirect
6. #23749844C2semidirect
7. #23749822C2semidirect
8. #23749787C2semidirect
9. #23749776C2semidirect
10. #23749686C2semidirect
12. C2×#14558726C22semidirect
15. C2×#14558724C22semidirect
16. #18011911C22semidirect
18. #18011903C22semidirect
21. C4×Dic298C22semidirect
22. C4⋊#11924746C22semidirect
23. #18011835C22semidirect
26. #18011832C22semidirect
28. #18011822C22semidirect
29. C4×#11924746C22semidirect
122. C149#3222semidirect

Maximal subgroups

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

subgroupindex
#237502372
#237500202
#237499972
#237499892
#237499792
#237498442
#237498222
#237497872
#237497762
#237496862
#535×C1492
#3222149