Finite Group Databasebeta

← #34056058

Subgroups — #34056058

Order 19072.

348 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 121 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#23749932C212yesmaximal, complemented
3#23749917C211yesmaximal, characteristic, complemented
4#23749912C211yesmaximal, characteristic, complemented
5#23749881C212yesmaximal, complemented
6#23749873C212yesmaximal
7#23749847C212yesmaximal, complemented
8#23749832C211yesmaximal, characteristic, complemented
9#23749827C211yesmaximal, characteristic, complemented
10#23749649C211yesmaximal, characteristic, complemented
11#533×C149C211yesmaximal, characteristic, complemented
12C2×#14558726C2212yes—
13C2×#14558723C2212yes—
14C2×#14558720C2212yes—
15#18011905—21no—
16#18011903C2211yescharacteristic
17#18011899C2211yescharacteristic
18#18011894—21no—
19#18011890C2211yescharacteristic
20#18011885C2211yescharacteristic
21C4×Dic298C2211yescharacteristic
22C4×D596C2211yescharacteristic
23C4×C22⋊D149—21no—
24#18011868—21no—
25#18011844C2212yes—
26#18011842C2212yes—
27C4⋊#11924746C2211yescharacteristic
28C4⋊#11924746C2211yescharacteristic
29C4⋊#11924746C2212yes—
30#18011835C2212yes—
31#18011835C2212yes—
32#18011834C2212yes—
33#18011831C2212yes—
34C4⋊Q8×C149C2211yescharacteristic
35C4⋊Q8×C149C2211yescharacteristic
36#125×C149—21no—
37C22⋊Q8×C149—21no—
38C22⋊Q8×C149C2212yes—
39C4×Q8×C149—21no—
40C4×Q8×C149C2212yes—
41#117×C149—21no—
42C2×C42×C149C2211yescharacteristic
43C2×Dic298C2311yescharacteristic
44C2×D596C2311yescharacteristic
45C2×C22⋊D149—21no—
46C2×C4×D149—21no—
47#14558726—42no—
48#14558723—42no—
49#14558720—42no—
50C2×#11924746C2312yes—
51C2×#11924746C2312yes—
52C4⋊Dic149C2311yescharacteristic
53C4⋊Dic149C2311yescharacteristic
54#14558715—21no—
55#14558715—21no—
56#14558715—21no—
57#14558715—21no—
58C22⋊Dic149—21no—
59#14558713—21no—
60#14558713—21no—
61#14558713—21no—
62#14558713—21no—
63C4×Dic149—21no—
64C2×Q8×C149—21no—
65C2×Q8×C149C2312yes—
66C22×C4×C149D411yescharacteristic
67C22×C4×C149D411yescharacteristic
68C22×C4×C149C2311yescharacteristic
69C4⋊C4×C149—21no—
70C4⋊C4×C149—21no—
71C4⋊C4×C149—21no—
72C4⋊C4×C149—22no—
73C4⋊C4×C149—22no—
74C4⋊C4×C149C2312yes—
75C22⋊C4×C149—22no—
76C42×C149—22no—
77C42×C149D411yescharacteristic
78C42×C149D411yescharacteristic
79C42×C149C2311yescharacteristic
80C42×C149C2311yescharacteristic
81C22×D149—21no—
82Dic298—21no—
83Dic298—21no—
84D596—21no—
85D596—21no—
86C22⋊D149—42no—
87C2×Dic149—21no—
88C2×Dic149—21no—
89C2×Dic149—21no—
90C4×D149—42no—
91#11924746—22no—
92#11924746—22no—
93C23×C149C2×D411yescharacteristic
94Q8×C149—22no—
95Q8×C149—22no—
96Q8×C149—42no—
97C2×C4×C149—22no—
98C2×C4×C149—21no—
99C2×C4×C149—21no—
100C2×C4×C149—22no—
101C2×C4×C149—22no—
102C2×C4×C149—41no—
103C2×C4×C149C2×D411yescharacteristic
104C2×C4×C149C2×D411yescharacteristic
105C2×C4×C149C2×D411yescharacteristic
106C2×C4×C149C2×D411yescharacteristic
107C2×C4×C149C2×D411yescharacteristic
108C2×C4×C149C2411yescharacteristic
109C22×C149—21no—
110C22×C149—21no—
111C22×C149—21no—
112C22×C149C22×D411yescharacteristic
113C2×D149—41no—
114C2×D149—41no—
115C2×D149—41no—
116C4×C149—21no—
117C4×C149—21no—
118C4×C149—21no—
119C4×C149—21no—
120C4×C149—42no—
121C4×C149—42no—
122C4×C149#13712yes—
123C4×C149H(5,𝔽2)11yescharacteristic
124C4×C1492−1+411yescharacteristic
125Dic149—41no—
126Dic149—41no—
127Dic149—41no—
128C2×C149—41no—
129C2×C149#53711yescharacteristic
130C2×C149C2×#13711yescharacteristic
131C2×C149#57511yescharacteristic
132D149—81no—
133C149#325211yescharacteristic, complemented, Sylow
134#3252—1491nomaximal, Sylow
135#533D14911yescharacteristic, complemented
136#529—1491no—
137#479—1492no—
138#477—1491no—
139#476—1491no—
140#470—1492no—
141#468—1492no—
142#464—1492no—
143#462—1491no—
144#461—1491no—
145#423—1491no—
146C2×Q16—1492no—
147C2×SD16—1492no—
148C2×M16—1492no—
149C4⋊Q8C2×D14911yescharacteristic
150C4⋊Q8C2×D14911yescharacteristic
151#126—2981no—
152#125—21no—
153#125—1491no—
154#124—1491no—
155#123—2981no—
156C22⋊Q8—21no—
157C22⋊Q8—1491no—
158C22⋊Q8C2×D14912yes—
159#121—1491no—
160C4×Q8—21no—
161C4×Q8—1491no—
162C4×Q8C2×D14912yes—
163C4×D4—2981no—
164C4×D4—1491no—
165#117—21no—
166#117—2981no—
167C2×C42C2×D14911yescharacteristic
168#107—1492no—
169#106—1492no—
170C4⋊C8—1491no—
171C4⋊C8—1491no—
172C4⋊C8—1492no—
173#103—1492no—
174#103—1492no—
175#103—1492no—
176#102—1492no—
177C2×Q8—21no—
178C2×Q8—1491no—
179C2×Q8C22×D14912yes—
180C2×D4—2981no—
181C2×D4—1491no—
182C22×C4—2981no—
183C22×C4C22⋊D14911yescharacteristic
184C22×C4C22⋊D14911yescharacteristic
185C22×C4C22×D14911yescharacteristic
186Q16—5962no—
187SD16—5962no—
188M16—5962no—
189C2×C8—1492no—
190C2×C8—1492no—
191C4⋊C4—21no—
192C4⋊C4—21no—
193C4⋊C4—21no—
194C4⋊C4—22no—
195C4⋊C4—22no—
196C4⋊C4—2981no—
197C4⋊C4—2981no—
198C4⋊C4—2981no—
199C4⋊C4—2981no—
200C4⋊C4—1491no—
201C4⋊C4—1491no—
202C4⋊C4C22×D14912yes—
203C22⋊C4—22no—
204C22⋊C4—2981no—
205C22⋊C4—2981no—
206C22⋊C4—2981no—
207C22⋊C4—2981no—
208C22⋊C4—2981no—
209C42—22no—
210C42—2981no—
211C42C22⋊D14911yescharacteristic
212C42C22⋊D14911yescharacteristic
213C42C22×D14911yescharacteristic
214C42C22×D14911yescharacteristic
215C23—2981no—
216C23C2×C22⋊D14911yescharacteristic
217Q8—22no—
218Q8—22no—
219Q8—42no—
220Q8—2981no—
221Q8—2981no—
222D4—2981no—
223D4—2981no—
224D4—5962no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—41no—
231C2×C4—2981no—
232C2×C4—2981no—
233C2×C4—2981no—
234C2×C4—5962no—
235C2×C4C2×C22⋊D14911yescharacteristic
236C2×C4C2×C22⋊D14911yescharacteristic
237C2×C4C2×C22⋊D14911yescharacteristic
238C2×C4C2×C22⋊D14911yescharacteristic
239C2×C4C2×C22⋊D14911yescharacteristic
240C2×C4C23×D14911yescharacteristic
241C8—2982no—
242C8—2982no—
243C22—21no—
244C22—21no—
245C22—21no—
246C22—5961no—
247C22—5961no—
248C22—5961no—
249C22C22×C22⋊D14911yescharacteristic
250C4—21no—
251C4—21no—
252C4—21no—
253C4—21no—
254C4—42no—
255C4—42no—
256C4—5961no—
257C4—5961no—
258C4—5961no—
259C4#1801194212yes—
260C4#1801195711yescharacteristic
261C4#1801195811yescharacteristic
262C2—41no—
263C2—11921no—
264C2#2375020311yescharacteristic
265C2C2×#1801194211yescharacteristic
266C2#2375042311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#533×C149C2
socleC22×C149C22×D4
prime radical#18011885C22
hypercenter#533D149
hypocenterC149#3252
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #23749932C2semidirect
3. #23749917C2semidirect
4. #23749912C2semidirect
5. #23749881C2semidirect
7. #23749847C2semidirect
8. #23749832C2semidirect
9. #23749827C2semidirect
10. #23749649C2semidirect
11. #533×C149C2semidirect
133. C149#3252semidirect
135. #533D149semidirect

Maximal subgroups

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

subgroupindex
#237501592
#237499322
#237499172
#237499122
#237498812
#237498732
#237498472
#237498322
#237498272
#237496492
#533×C1492
#3252149