Finite Group Databasebeta

← #34057826

Subgroups — #34057826

Order 19072.

364 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 113 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
1C2×#18011934C211yesmaximal, characteristic, complemented
2#135×D149C211yesmaximal, characteristic, complemented
3#23750067C212yesmaximal, complemented
4#23750066C211yesmaximal, characteristic, complemented
5#23750063C211yesmaximal, characteristic, complemented
6#23750062C212yesmaximal, complemented
7#23750060C211yesmaximal, characteristic, complemented
8#23750058C212yesmaximal, complemented
9#23750056C212yesmaximal, complemented
10M32×D149C211yesmaximal, characteristic, complemented
11#510×C149C211yesmaximal, characteristic, complemented
12C2×#14558737—21no—
13#41×D149—21no—
14#18011934—21no—
15#18011934—21no—
16#18011934C2212yes—
17#18011934C2211yescharacteristic, complemented
18#18011934C2212yescomplemented
19#18011933C2211yescharacteristic
20#18011932—21no—
21#18011931—21no—
22#18011930C2211yescharacteristic, complemented
23Q16×D149C2211yescharacteristic, complemented
24C2×#14558723—21no—
25SD16×D149—21no—
26C2×D1192C2211yescharacteristic, complemented
27D8×D149C2211yescharacteristic, complemented
28C2×C8×D149C2211yescharacteristic
29#18011857C2212yescomplemented
30#18011856C2212yescomplemented
31#18011854C2212yescomplemented
32#18011854C2212yescomplemented
33D2384C2212yescomplemented
34#18011852C2212yescomplemented
35#18011851C2211yescharacteristic, complemented
36#18011850C2212yescomplemented
37C16×D149C2212yescomplemented
38#135×C149C2211yescharacteristic
39C2×Q16×C149C2211yescharacteristic, complemented
40Q32×C149C2212yescomplemented
41SD32×C149C2212yescomplemented
42M32×C149C2211yescharacteristic, complemented
43#14558737—21no—
44#14558737—22no—
45#14558737—22no—
46#14558737—41no—
47#14558737—41no—
48#14558736—21no—
49#14558736—41no—
50#14558735—21no—
51#14558735—41no—
52Q8×D149—21no—
53C2×D596—21no—
54C2×D596—41no—
55D4×D149—21no—
56D4×D149—41no—
57C2×C4×D149—41no—
58C2×C4×D149—41no—
59C2×C4×D149D411yescharacteristic
60Dic596C2311yescharacteristic
61#14558726—21no—
62#14558725—21no—
63#14558724—21no—
64#14558723—21no—
65#14558723—22no—
66#14558723—22no—
67D1192—21no—
68D1192C2311yescharacteristic
69D1192C2312yes—
70#14558721—21no—
71C2×#11924746D411yescharacteristic
72C8×D149D411yescharacteristic
73C8×D149D411yescharacteristic
74C8×D149C2311yescharacteristic
75C8×D149C2311yescharacteristic
76#14558711C2312yes—
77#41×C149—21no—
78C2×Q8×C149—21no—
79Q16×C149—21no—
80Q16×C149C2311yescharacteristic
81Q16×C149C2312yes—
82SD16×C149—21no—
83D8×C149C2311yescharacteristic
84C2×C8×C149C2311yescharacteristic
85C16×C149C2312yes—
86C22×D149—41no—
87C22×D149—41no—
88C22×D149D811yescharacteristic
89Dic298—21no—
90Dic298—41no—
91D596—21no—
92D596—22no—
93D596—41no—
94D596—42no—
95D596—42no—
96D596—41no—
97C22⋊D149—41no—
98C22⋊D149—41no—
99C22⋊D149—41no—
100C2×Dic149—41no—
101C2×Dic149D811yescharacteristic
102C4×D149—41no—
103C4×D149—41no—
104C4×D149—41no—
105C4×D149—42no—
106C4×D149—42no—
107C4×D149D811yescharacteristic
108C4×D149D811yescharacteristic
109C4×D149C2×D411yescharacteristic
110C4×D149C2×D411yescharacteristic
111#11924746C2×D411yescharacteristic
112#11924746C2×D411yescharacteristic
113Q8×C149—22no—
114Q8×C149—21no—
115Q8×C149—41no—
116D4×C149—21no—
117D4×C149—41no—
118C2×C4×C149—41no—
119C2×C4×C149—41no—
120C2×C4×C149C2×D411yescharacteristic
121C8×C149C2×D411yescharacteristic
122C8×C149C2411yescharacteristic
123C22×C149—41no—
124C22×C149C2×D811yescharacteristic
125C2×D149—41no—
126C2×D149—41no—
127C2×D149—42no—
128C2×D149—82no—
129C2×D149—82no—
130C2×D149C2×D811yescharacteristic
131C2×D149C2×D811yescharacteristic
132C4×C149—41no—
133C4×C149—42no—
134C4×C149C2×D811yescharacteristic
135C4×C149C22×D411yescharacteristic
136Dic149—41no—
137Dic149C2×D811yescharacteristic
138Dic149C2×D811yescharacteristic
139C2×C149—21no—
140C2×C149—81no—
141C2×C149C22×D811yescharacteristic
142D149—21no—
143D149—21no—
144D149—81no—
145D149—82no—
146C149#341411yescharacteristic, complemented, Sylow
147#3414—1491nomaximal, Sylow
148C2×#135—1491no—
149C2×#135—1491no—
150#510—1491no—
151#510—1492no—
152#510D14911yescharacteristic, complemented
153#509—1491no—
154#509—1492no—
155#509—1491no—
156#508—1492no—
157#508—1492no—
158C2×M32—1491no—
159C2×#41—2981no—
160C2×#41—2981no—
161#135—2981no—
162#135—2981no—
163#135—2981no—
164#135—2981no—
165#135—1492no—
166#135—1491no—
167#135—1492no—
168#135—1491no—
169#135—1491no—
170#135C2×D14911yescharacteristic
171C2×Q16—1491no—
172C2×Q16C2×D14911yescharacteristic, complemented
173C2×SD16—2981no—
174C2×SD16—2981no—
175C2×D8—1491no—
176C2×D8—1491no—
177C22×C8—1491no—
178Q32—1492no—
179Q32C2×D14912yescomplemented
180SD32—1492no—
181SD32—1492no—
182SD32—1492no—
183SD32C2×D14912yescomplemented
184D16—1492no—
185D16—1492no—
186M32—1491no—
187M32—1492no—
188M32C2×D14911yescharacteristic, complemented
189C2×C16—1492no—
190#41—21no—
191#41—2981no—
192#41—2982no—
193#41—2981no—
194#41—2982no—
195#41—2981no—
196#41—5961no—
197#41—5961no—
198#41—5961no—
199#41—5961no—
200C2×Q8—21no—
201C2×Q8—2981no—
202C2×D4—2981no—
203C2×D4—2981no—
204C2×D4—5961no—
205C2×D4—5961no—
206C22×C4—5961no—
207C22×C4—5961no—
208C22×C4—1491no—
209Q16—21no—
210Q16—2981no—
211Q16—1491no—
212Q16C22×D14911yescharacteristic
213Q16C22×D14912yes—
214SD16—21no—
215SD16—2981no—
216SD16—2982no—
217SD16—2981no—
218SD16—2982no—
219SD16—2981no—
220D8—2981no—
221D8—2981no—
222D8—1491no—
223D8—1492no—
224D8C22×D14911yescharacteristic
225C2×C8—1491no—
226C2×C8—1491no—
227C2×C8—1491no—
228C2×C8—1491no—
229C2×C8—1491no—
230C2×C8C22×D14911yescharacteristic
231C16—1492no—
232C16C22×D14912yes—
233C23—5961no—
234C23—5961no—
235C23—1491no—
236Q8—21no—
237Q8—22no—
238Q8—41no—
239Q8—2981no—
240Q8—5961no—
241D4—21no—
242D4—41no—
243D4—2981no—
244D4—2982no—
245D4—5961no—
246D4—5962no—
247D4—5962no—
248D4—5961no—
249D4—5961no—
250D4—5961no—
251D4—5961no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—5961no—
255C2×C4—5961no—
256C2×C4—5962no—
257C2×C4—5962no—
258C2×C4—5961no—
259C2×C4—5961no—
260C2×C4—1491no—
261C2×C4—1491no—
262C2×C4—1491no—
263C2×C4—1491no—
264C2×C4—1491no—
265C2×C4D4×D14911yescharacteristic
266C8—1491no—
267C8—1491no—
268C8D4×D14911yescharacteristic
269C8C23×D14911yescharacteristic
270C22—41no—
271C22—5961no—
272C22—5962no—
273C22—5961no—
274C22—1491no—
275C22—1491no—
276C22—11922no—
277C22—11922no—
278C22D8×D14911yescharacteristic
279C4—41no—
280C4—42no—
281C4—5961no—
282C4—1491no—
283C4—1491no—
284C4D8×D14911yescharacteristic
285C4C2×D4×D14911yescharacteristic
286C2—21no—
287C2—81no—
288C2—2981no—
289C2—2981no—
290C2—11922no—
291C2—11921no—
292C2C2×D8×D14911yescharacteristic
subgroupG/H
centerC2C2×D8×D149
commutator, cosocleC8×C149C24
FrattiniC8C23×D149
Fitting#510×C149C2
socleC2×C149C22×D8
hypercenter#510D149
hypocenterC149#3414
LCSG ▷ C8×C149 ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
1. C2×#18011934C2semidirect
2. #135×D149C2semidirect
3. #23750067C2semidirect
4. #23750066C2semidirect
5. #23750063C2semidirect
6. #23750062C2semidirect
7. #23750060C2semidirect
8. #23750058C2semidirect
9. #23750056C2semidirect
10. M32×D149C2semidirect
11. #510×C149C2semidirect
17. #18011934C22semidirect
18. #18011934C22semidirect
22. #18011930C22semidirect
23. Q16×D149C22semidirect
26. C2×D1192C22semidirect
27. D8×D149C22semidirect
29. #18011857C22semidirect
30. #18011856C22semidirect
31. #18011854C22semidirect
32. #18011854C22semidirect
33. D2384C22semidirect
34. #18011852C22semidirect
35. #18011851C22semidirect
36. #18011850C22semidirect
37. C16×D149C22semidirect
39. C2×Q16×C149C22semidirect
40. Q32×C149C22semidirect
41. SD32×C149C22semidirect
42. M32×C149C22semidirect
146. C149#3414semidirect
152. #510D149semidirect
172. C2×Q16C2×D149semidirect
179. Q32C2×D149semidirect
183. SD32C2×D149semidirect
188. M32C2×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119342
#135×D1492
#237500672
#237500662
#237500632
#237500622
#237500602
#237500582
#237500562
M32×D1492
#510×C1492
#3414149