Finite Group Databasebeta

← #34045750

Subgroups — #34045750

Order 19072.

348 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 69 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#23750423C211yesmaximal, characteristic
2C2×#18011941C211yesmaximal, characteristic, complemented
3#23750201C211yesmaximal, characteristic, complemented
4#23749643C211yesmaximal, characteristic, complemented
5#23749633C211yesmaximal, characteristic, complemented
6#23749395C211yesmaximal, characteristic, complemented
7#410×C149C211yesmaximal, characteristic, complemented
8C2×#14558736C2211yescharacteristic
9C22×Dic298C2211yescharacteristic
10#18011942—21no—
11#18011941—22no—
12#18011941—21no—
13#18011941—22no—
14#18011937—21no—
15#18011936—21no—
16#18011931—22no—
17C2×#14558726—21no—
18C2×#14558724—21no—
19C2×#14558720C2211yescharacteristic
20C2×#14558720C2211yescharacteristic
21#18011911—21no—
22#18011899—21no—
23#18011895—22no—
24#18011891—22no—
25#18011839—22no—
26#18011834—22no—
27C2×#41×C149C2211yescharacteristic
28#117×C149C2211yescharacteristic
29#117×C149C2211yescharacteristic
30#99×C149—22no—
31#14558736—21no—
32#14558736—21no—
33#14558736—21no—
34#14558736—21no—
35C2×Dic298—21no—
36C2×Dic298—21no—
37C2×Dic298—21no—
38C2×Dic298—21no—
39C2×Dic298—21no—
40C2×Dic298D411yescharacteristic
41C2×Dic298D412yes—
42C2×D596D411yescharacteristic
43C2×C22⋊D149—21no—
44C22×Dic149—21no—
45C2×C4×D149—21no—
46#14558726—24no—
47#14558726—22no—
48#14558724—24no—
49#14558724—22no—
50#14558723—22no—
51#14558721—22no—
52#14558720—21no—
53#14558720—21no—
54#14558720—21no—
55#14558720D412yes—
56C2×#11924746—21no—
57C2×#11924746D412yes—
58C4⋊Dic149—24no—
59#14558713—24no—
60#41×C149—21no—
61#41×C149—21no—
62#41×C149—21no—
63#41×C149—21no—
64C2×Q8×C149D411yescharacteristic
65C2×D4×C149—21no—
66C2×D4×C149D411yescharacteristic
67C22×C4×C149—21no—
68C22×C4×C149C2311yescharacteristic
69C4⋊C4×C149—21no—
70C4⋊C4×C149—21no—
71C22⋊C4×C149—21no—
72C22⋊C4×C149D412yes—
73C42×C149—21no—
74C42×C149—21no—
75C22×D149—21no—
76Dic298—22no—
77Dic298—21no—
78Dic298—22no—
79Dic298—21no—
80Dic298—41no—
81Dic298—41no—
82D596—21no—
83D596—21no—
84C22⋊D149—41no—
85C22⋊D149—41no—
86C2×Dic149—21no—
87C2×Dic149—22no—
88C2×Dic149—41no—
89C2×Dic149—41no—
90C4×D149—41no—
91C4×D149—41no—
92#11924746—22no—
93#11924746—22no—
94C23×C149—21no—
95C23×C149C2×D411yescharacteristic
96Q8×C149—21no—
97Q8×C149—21no—
98D4×C149—21no—
99D4×C149—21no—
100D4×C149—41no—
101D4×C149—41no—
102C2×C4×C149—22no—
103C2×C4×C149—21no—
104C2×C4×C149—41no—
105C2×C4×C149—41no—
106C2×C4×C149—41no—
107C2×C4×C149C2×D411yescharacteristic
108C2×C4×C149C2×D411yescharacteristic
109C2×C4×C149C2×D411yescharacteristic
110C2×C4×C149C2×D411yescharacteristic
111C2×C4×C149C2×D411yescharacteristic
112C2×C4×C149#4111yescharacteristic
113C22×C149—41no—
114C22×C149—41no—
115C22×C149—81no—
116C22×C149#12011yescharacteristic
117C22×C149#12111yescharacteristic
118C22×C149#12711yescharacteristic
119C2×D149—42no—
120C2×D149—41no—
121C4×C149—42no—
122C4×C149—41no—
123C4×C149—81no—
124C4×C149#12011yescharacteristic
125C4×C149#12011yescharacteristic
126C4×C149#12111yescharacteristic
127C4×C149#12111yescharacteristic
128Dic149—41no—
129Dic149—42no—
130C2×C149—21no—
131C2×C149—21no—
132C2×C149—21no—
133C2×C149—81no—
134C2×C149#39211yescharacteristic
135D149—81no—
136C149#200911yescharacteristic, complemented, Sylow
137#2009—1491nomaximal, Sylow
138#575—1491no—
139C2×#137—1491no—
140#536—1491no—
141#421—1491no—
142#419—1491no—
143#410D14911yescharacteristic, complemented
144#344—1491no—
145C2×#41—1491no—
146C2×#41C2×D14911yescharacteristic
147C22×Q8—1491no—
148#137—2982no—
149#137—2981no—
150#137—2981no—
151#137—2982no—
152AGL(1,ℤ/8)—2981no—
153AGL(1,ℤ/8)—2981no—
154#135—2982no—
155C2×Q16—2981no—
156C2×SD16—2981no—
157C2×M16—1491no—
158C2×M16—1491no—
159C4⋊Q8—2981no—
160#124—2981no—
161#123—2982no—
162C22⋊Q8—2982no—
163#117C2×D14911yescharacteristic
164#117C2×D14911yescharacteristic
165#104—2982no—
166#103—2982no—
167#99—22no—
168#41—21no—
169#41—21no—
170#41—21no—
171#41—21no—
172#41—2981no—
173#41—2981no—
174#41—2981no—
175#41—2981no—
176C2×Q8—2981no—
177C2×Q8—2981no—
178C2×Q8—2981no—
179C2×Q8—2981no—
180C2×Q8—2981no—
181C2×Q8—1492no—
182C2×Q8—1491no—
183C2×Q8D59611yescharacteristic
184C2×D4—21no—
185C2×D4—2981no—
186C2×D4—1491no—
187C2×D4D59611yescharacteristic
188C22×C4—21no—
189C22×C4—2981no—
190C22×C4—2981no—
191C22×C4C22×D14911yescharacteristic
192Q16—2984no—
193Q16—2982no—
194SD16—2984no—
195SD16—2982no—
196SD16—2982no—
197D8—2982no—
198M16—2981no—
199M16—2981no—
200M16—2981no—
201M16—1492no—
202C2×C8—2981no—
203C2×C8—1492no—
204C4⋊C4—21no—
205C4⋊C4—21no—
206C4⋊C4—2984no—
207C22⋊C4—21no—
208C22⋊C4—2984no—
209C22⋊C4C22⋊D14912yes—
210C42—21no—
211C42—21no—
212C23—21no—
213C23—2981no—
214C23C2×C22⋊D14911yescharacteristic
215Q8—21no—
216Q8—21no—
217Q8—2982no—
218Q8—2981no—
219Q8—2982no—
220Q8—2981no—
221Q8—5961no—
222Q8—5961no—
223D4—21no—
224D4—21no—
225D4—41no—
226D4—41no—
227D4—2981no—
228D4—2981no—
229D4—5961no—
230D4—5961no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—2982no—
237C2×C4—2981no—
238C2×C4—5961no—
239C2×C4—5961no—
240C2×C4—5961no—
241C2×C4—5961no—
242C2×C4D4×D14911yescharacteristic
243C2×C4D4×D14911yescharacteristic
244C2×C4D4×D14911yescharacteristic
245C2×C4D4×D14911yescharacteristic
246C2×C4C2×D59611yescharacteristic
247C2×C4#1455873611yescharacteristic
248C8—2982no—
249C8—2982no—
250C22—41no—
251C22—41no—
252C22—81no—
253C22—5962no—
254C22—5961no—
255C22#1801187911yescharacteristic
256C22#1801188511yescharacteristic
257C22#1801190711yescharacteristic
258C4—42no—
259C4—41no—
260C4—81no—
261C4—5961no—
262C4—5962no—
263C4#1801188111yescharacteristic
264C4#1801188111yescharacteristic
265C4#1801188411yescharacteristic
266C4#1801188411yescharacteristic
267C2—21no—
268C2—21no—
269C2—21no—
270C2—81no—
271C2—11921no—
272C2#2374953411yescharacteristic
subgroupG/H
centerC2#23749534
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#410×C149C2
socleC2×C149#392
prime radical#23750423C2
hypercenter#410D149
hypocenterC149#2009
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
2. C2×#18011941C2semidirect
3. #23750201C2semidirect
4. #23749643C2semidirect
5. #23749633C2semidirect
6. #23749395C2semidirect
7. #410×C149C2semidirect
136. C149#2009semidirect
143. #410D149semidirect

Maximal subgroups

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

subgroupindex
#237504232
C2×#180119412
#237502012
#237496432
#237496332
#237493952
#410×C1492
#2009149