Finite Group Databasebeta

← #34056494

Subgroups — #34056494

Order 19072.

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

normal subgroups only

This group has 444 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#23750442C211yesmaximal, characteristic, complemented
2#23750441C212yesmaximal, complemented
3#23750438C211yesmaximal, characteristic, complemented
4#23750003C211yesmaximal, characteristic, complemented
5#23749901C211yesmaximal, characteristic, complemented
6#23749899C212yesmaximal, complemented
7#23749810C212yesmaximal, complemented
8#23749806C212yesmaximal, complemented
9#23749741C211yesmaximal, characteristic, complemented
10#23749740C211yesmaximal, characteristic, complemented
11#473×C149C211yesmaximal, characteristic, complemented
12#18011959C2212yes—
13#18011958C2212yes—
14#18011944—22no—
15#18011944C2212yes—
16#18011944C2212yes—
17#18011943—22no—
18#18011943—22no—
19#18011942C2212yes—
20#18011940—22no—
21#18011934—21no—
22#18011933—21no—
23#18011933C2211yescharacteristic
24#18011932—22no—
25#18011931C2211yescharacteristic
26C2×Dic596—21no—
27C2×Dic596C2211yescharacteristic
28C2×#14558726C2212yes—
29Q16×D149—21no—
30Q16×D149—22no—
31#18011919C2212yes—
32#18011917C2211yescharacteristic
33#18011909C2212yes—
34#18011846C2211yescharacteristic
35#18011838C2211yescharacteristic
36#18011837C2211yescharacteristic
37#18011837C2212yes—
38#18011829C2212yes—
39C8×Dic149C2211yescharacteristic
40#137×C149C2212yes—
41C2×Q16×C149C2211yescharacteristic
42#131×C149C2211yescharacteristic
43#108×C149C2211yescharacteristic
44#101×C149C2212yes—
45#14558737—22no—
46#14558737—22no—
47#14558736—22no—
48#14558736—42no—
49#14558736C2311yescharacteristic
50#14558736C2312yes—
51#14558735—22no—
52#14558735—42no—
53C2×Dic298—22no—
54C2×Dic298C2312yes—
55Q8×D149—22no—
56Q8×D149—22no—
57Q8×D149—22no—
58Dic596—22no—
59Dic596—22no—
60Dic596—21no—
61Dic596—21no—
62Dic596D411yescharacteristic
63#14558726—22no—
64#14558726—22no—
65#14558726—22no—
66#14558726D411yescharacteristic
67#14558725—22no—
68#14558725—22no—
69#14558725D412yes—
70#14558724D411yescharacteristic
71#14558723—22no—
72#14558723D411yescharacteristic
73D1192D411yescharacteristic
74#14558721D411yescharacteristic
75#14558720C2311yescharacteristic
76#14558719—22no—
77#14558719—21no—
78C2×#11924746C2311yescharacteristic
79C8×D149—22no—
80C8×D149—21no—
81#14558715—42no—
82C4×Dic149C2311yescharacteristic
83#41×C149C2311yescharacteristic
84C2×Q8×C149C2312yes—
85Q16×C149—22no—
86Q16×C149—21no—
87Q16×C149—21no—
88SD16×C149—22no—
89M16×C149—21no—
90M16×C149C2312yes—
91M16×C149C2311yescharacteristic
92C2×C8×C149—21no—
93C2×C8×C149C2311yescharacteristic
94Dic298—22no—
95Dic298—22no—
96Dic298—42no—
97Dic298—42no—
98Dic298C2×D411yescharacteristic
99Dic298C2×D412yes—
100D596—42no—
101D596C2×D411yescharacteristic
102D596C2×D412yes—
103C22⋊D149—22no—
104C22⋊D149—21no—
105C22⋊D149—42no—
106C2×Dic149—21no—
107C2×Dic149—22no—
108C2×Dic149—42no—
109C4×D149—22no—
110C4×D149—21no—
111C4×D149—42no—
112C4×D149—42no—
113C4×D149—42no—
114#11924746—21no—
115#11924746C2×D411yescharacteristic
116#11924746C2×D411yescharacteristic
117Q8×C149—22no—
118Q8×C149—22no—
119Q8×C149C2×D411yescharacteristic
120D4×C149—21no—
121D4×C149C2×D411yescharacteristic
122C2×C4×C149—21no—
123C2×C4×C149—22no—
124C2×C4×C149C2411yescharacteristic
125C8×C149—21no—
126C8×C149—22no—
127C8×C149C2×D411yescharacteristic
128C8×C149C2×D411yescharacteristic
129C22×C149—21no—
130C22×C149H(5,𝔽2)11yescharacteristic
131C2×D149—22no—
132C2×D149—21no—
133C4×C149—21no—
134C4×C149—42no—
135C4×C149C22×D411yescharacteristic
136C4×C149C22×D411yescharacteristic
137Dic149—22no—
138Dic149—21no—
139Dic149—22no—
140Dic149—42no—
141C2×C149—21no—
142C2×C149—41no—
143C2×C149D4211yescharacteristic
144D149—42no—
145D149—41no—
146C149#329311yescharacteristic, complemented, Sylow
147#3293—1491nomaximal, Sylow
148#578—1492no—
149#578—1491no—
150#578—1491no—
151#494—1491no—
152#473—1491no—
153#473—1492no—
154#473D14911yescharacteristic, complemented
155#456—1492no—
156#456—1492no—
157#443—1491no—
158#443—1491no—
1592−1+4—1492no—
1602−1+4—1492no—
161#137—2982no—
162#137—2982no—
163#137—2982no—
164#137—2982no—
165#137—1492no—
166#137—1492no—
167#137—1492no—
168#137C2×D14912yes—
169#135—2981no—
170#135—2982no—
171#135—2981no—
172#135—1491no—
173#135—1491no—
174C2×Q16—2981no—
175C2×Q16—2982no—
176C2×Q16—2981no—
177C2×Q16—1492no—
178C2×Q16—1491no—
179C2×Q16C2×D14911yescharacteristic
180#131—1492no—
181#131—1491no—
182#131C2×D14911yescharacteristic
183C4⋊Q8—1492no—
184#108—1491no—
185#108C2×D14911yescharacteristic
186#104—1491no—
187#104—1492no—
188#104—1491no—
189#101—1492no—
190#101C2×D14912yes—
191C4×C8—1491no—
192#41—2982no—
193#41—2982no—
194#41—2982no—
195#41—2982no—
196#41—5962no—
197#41—5962no—
198#41—1491no—
199#41—1492no—
200#41C22×D14911yescharacteristic
201C2×Q8—2982no—
202C2×Q8—2982no—
203C2×Q8—2982no—
204C2×Q8—2982no—
205C2×Q8—1492no—
206C2×Q8C22×D14912yes—
207Q16—22no—
208Q16—21no—
209Q16—21no—
210Q16—2982no—
211Q16—2982no—
212Q16—2982no—
213Q16—2982no—
214Q16—2982no—
215Q16—2981no—
216Q16—2981no—
217Q16—1491no—
218Q16—1491no—
219SD16—22no—
220SD16—2982no—
221SD16—2982no—
222SD16—2982no—
223SD16—1491no—
224SD16—1491no—
225SD16—1492no—
226D8—1491no—
227D8—1491no—
228M16—21no—
229M16—2982no—
230M16—2981no—
231M16—1491no—
232M16C22×D14912yes—
233M16C22×D14911yescharacteristic
234C2×C8—21no—
235C2×C8—2982no—
236C2×C8—2981no—
237C2×C8—1491no—
238C2×C8C22×D14911yescharacteristic
239C4⋊C4—5962no—
240C42—1491no—
241Q8—22no—
242Q8—22no—
243Q8—2982no—
244Q8—2982no—
245Q8—5962no—
246Q8—5962no—
247Q8—1491no—
248Q8—1492no—
249Q8D4×D14911yescharacteristic
250D4—21no—
251D4—2982no—
252D4—2981no—
253D4—5962no—
254D4—5962no—
255D4—1491no—
256D4—1492no—
257D4D4×D14911yescharacteristic
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—2981no—
261C2×C4—2982no—
262C2×C4—2981no—
263C2×C4—2982no—
264C2×C4—5962no—
265C2×C4—5962no—
266C2×C4—5962no—
267C2×C4—5962no—
268C2×C4C23×D14911yescharacteristic
269C8—21no—
270C8—22no—
271C8—2981no—
272C8—1491no—
273C8—1491no—
274C8D4×D14911yescharacteristic
275C8D4×D14911yescharacteristic
276C22—21no—
277C22—2982no—
278C22—2981no—
279C22#1801195711yescharacteristic
280C4—21no—
281C4—42no—
282C4—2982no—
283C4—2981no—
284C4—2982no—
285C4—5962no—
286C4C2×D4×D14911yescharacteristic
287C4C2×D4×D14911yescharacteristic
288C2—21no—
289C2—41no—
290C2—5962no—
291C2—5961no—
292C2#2375025911yescharacteristic
subgroupG/H
centerC2#23750259
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#473×C149C2
socleC2×C149D42
hypercenter#473D149
hypocenterC149#3293
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ #473

Complements

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

NH ≅ G/Ntype
1. #23750442C2semidirect
2. #23750441C2semidirect
3. #23750438C2semidirect
4. #23750003C2semidirect
5. #23749901C2semidirect
6. #23749899C2semidirect
7. #23749810C2semidirect
8. #23749806C2semidirect
9. #23749741C2semidirect
10. #23749740C2semidirect
11. #473×C149C2semidirect
146. C149#3293semidirect
154. #473D149semidirect

Maximal subgroups

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

subgroupindex
#237504422
#237504412
#237504382
#237500032
#237499012
#237498992
#237498102
#237498062
#237497412
#237497402
#473×C1492
#3293149